From 870075f34dd9fa5792bfbf413afd3b96f17e76a0 Mon Sep 17 00:00:00 2001
From: Stephane Glondu <steph@glondu.net>
Date: Fri, 8 Aug 2008 13:18:42 +0200
Subject: Imported Upstream version 8.2~beta4+dfsg

---
 CHANGES                                         |     29 +-
 COMPATIBILITY                                   |      4 +
 INSTALL.doc                                     |     81 +
 Makefile                                        |      3 +-
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 proofs/evar_refiner.ml                          |     23 +-
 proofs/logic.ml                                 |    200 +-
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 tactics/equality.ml                             |    143 +-
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 theories/Classes/EquivDec.v                     |      8 +-
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 theories/Numbers/Rational/BigQ/BigQ.v           |    188 +-
 theories/Numbers/Rational/BigQ/Q0Make.v         |   1412 -
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 theories/Program/Equality.v                     |     29 +-
 theories/Program/Tactics.v                      |     22 +-
 theories/Program/Utils.v                        |      6 +-
 theories/QArith/QArith_base.v                   |    145 +-
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 tools/coq_makefile.ml4                          |      8 +-
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 317 files changed, 17694 insertions(+), 106722 deletions(-)
 create mode 100644 INSTALL.doc
 create mode 100755 README.doc
 delete mode 100644 contrib/micromega/Micromegatac.v
 create mode 100644 contrib/micromega/Psatz.v
 delete mode 100644 doc/INSTALL
 delete mode 100644 doc/LICENCE
 create mode 100644 doc/LICENSE
 delete mode 100755 doc/README
 delete mode 100644 parsing/g_minicoq.ml4
 create mode 100644 test-suite/bugs/closed/shouldfail/1915.v
 create mode 100644 test-suite/bugs/closed/shouldsucceed/1905.v
 create mode 100644 test-suite/bugs/opened/shouldnotfail/1671.v
 create mode 100644 test-suite/failure/evarclear1.v
 create mode 100644 test-suite/failure/evarclear2.v
 create mode 100644 test-suite/output/ArgumentsScope.out
 create mode 100644 test-suite/output/ArgumentsScope.v
 create mode 100644 test-suite/output/Match_subterm.out
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 delete mode 100644 theories/Numbers/Rational/BigQ/Q0Make.v
 create mode 100644 theories/Numbers/Rational/BigQ/QMake.v
 delete mode 100644 theories/Numbers/Rational/BigQ/QMake_base.v
 delete mode 100644 theories/Numbers/Rational/BigQ/QbiMake.v
 delete mode 100644 theories/Numbers/Rational/BigQ/QifMake.v
 delete mode 100644 theories/Numbers/Rational/BigQ/QpMake.v
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 delete mode 100644 toplevel/fhimsg.ml
 delete mode 100644 toplevel/minicoq.ml

diff --git a/CHANGES b/CHANGES
index 675db3f1..01a81554 100644
--- a/CHANGES
+++ b/CHANGES
@@ -21,10 +21,16 @@ Language
 - Several evolutions of the module system (handling of module aliases, 
   functorial module types, an Include feature, etc). (TODO: Say more!)
 - Prop now a subtype of Set (predicative and impredicative forms).
+- Recursive inductive types in Prop with a single constructor of which
+  all arguments are in Prop is now considered to be a singleton
+  type. It consequently supports all eliminations to Prop, Set and Type.
+  As a consequence, Acc_rect has now a more direct proof [possible source
+  of easily fixed incompatibility in case of manual definition of a recursor
+  in a recursive singleton inductive type].
 
 Vernacular commands
 
-- Added option Global to "Arguments Scope" for section surviving. (DOC TODO)
+- Added option Global to "Arguments Scope" for section surviving.
 - Added option "Unset Elimination Schemes" to deactivate the automatic
   generation of elimination schemes.
 - Modification of the Scheme command so you can ask for the name to be
@@ -51,6 +57,8 @@ Vernacular commands
   that should be expanded first.
 - New command "Print Assumptions" to display all variables, parameters
   or axioms a theorem or definition relies on.
+- "Add Rec LoadPath" now provides references to libraries using partially
+  qualified names (this holds also for coqtop/coqc option -R).
 
 Libraries (DOC TO CHECK)
 
@@ -146,6 +154,8 @@ Libraries (DOC TO CHECK)
   descriptions: Epsilon.v, Description.v and IndefiniteDescription.v.
 - Definition of pred and minus made compatible with the structural
   decreasing criterion for use in fixpoints.
+- Files Relations/Rstar.v and Relations/Newman.v moved out to the user
+  contribution repository (contribution CoC_History).
 
 Notations, coercions, implicit arguments and type inference
 
@@ -174,6 +184,8 @@ Tactic Language
 
 - Second-order pattern-matching now working in Ltac "match" clauses
   (syntax for second-order unification variable is "@?X").
+- (?X ?Y) patterns now match any application instead of only unary 
+  applications (possible source of incompatibility).
 - Ltac accepts integer arguments (syntax is "ltac:nnn" for nnn an integer).
 - The general sequence tactical "expr_0 ; [ expr_1 | ... | expr_n ]"
   is extended so that at most one expr_i may have the form "expr .."
@@ -194,6 +206,7 @@ Tactic Language
   "let ... in ..." into a lazy one.
 - Patterns for hypotheses types in "match goal" are now interpreted in
   type_scope.
+- New printing of Ltac call trace for better debugging.
 
 Tactics
 
@@ -239,6 +252,9 @@ Tactics
   * "rewrite 3?A" means rewriting A at most three times.
   * "rewrite ?A" means rewriting A as long as possible (possibly never).
   * many of the above extensions can be combined with each other.  
+- Introduction patterns better respect the structure of context in presence of
+  missing or extra names in nested disjunction-conjunction patterns [possible 
+  source of rare incompatibilities].
 - New syntax "rename a into b, c into d" for "rename a into b; rename c into d"
 - New tactics "dependent induction/destruction H [ generalizing id_1 .. id_n ]"
   to do induction-inversion on instantiated inductive families à la BasicElim.
@@ -250,6 +266,7 @@ Tactics
 - Tactic "apply" now able to traverse conjunctions and to select the first 
   matching lemma among the components of the conjunction; tactic apply also
   able to apply lemmas of conclusion an empty type.
+- Tactic "apply" now supports application of several lemmas in a row.
 - Tactics "set" and "pose" can set functions using notation "(f x1..xn := c)".
 - New tactic "instantiate" (without argument).
 - Tactic firstorder "with" and "using" options have their meaning swapped for
@@ -268,6 +285,7 @@ Tactics
   now obsolete.
 - Tactics f_equal is now done in ML instead of Ltac: it now works on any 
   equality of functions, regardless of the arity of the function.
+- New options "before id", "at top", "at bottom" for tactics "move"/"intro".
 - Some more debug of reflexive omega (romega), and internal clarifications. 
   Moreover, romega now has a variant "romega with *" that can be also used
   on non-Z goals (nat, N, positive) via a call to a translation tactic named
@@ -275,6 +293,8 @@ Tactics
   independantly of romega. 
 - Tactic "remember" now supports an "in" clause to remember only selected 
   occurrences of a term.
+- Tactic "pose proof" supports name overwriting in case of specialization of an
+  hypothesis.
 
 Program
 
@@ -283,13 +303,11 @@ Program
   programming (id, apply, flip...)
 - More robust obligation handling, dependent pattern-matching and
   well-founded definitions.
-- New syntax " dest term as pat in term " for destructing objects using
-  an irrefutable pattern while keeping equalities (use this instead of 
-  "let" in Programs).
 - Program CoFixpoint is accepted, Program Fixpoint uses the new way to infer 
   which argument decreases structurally.
 - Program Lemma, Axiom etc... now permit to have obligations in the statement 
   iff they can be automatically solved by the default tactic.
+- Renamed "Obligations Tactic" command to "Obligation Tactic".
 - New command "Preterm [ of id ]" to see the actual term fed to Coq for
   debugging purposes.
 - New option "Transparent Obligations" to control the declaration of 
@@ -403,6 +421,8 @@ CoqIDE
 Tools
 
 - New stand-alone .vo files verifier "coqchk".
+- Extended -I coqtop/coqc option to specify a logical dir: "-I dir -as coqdir".
+- New coqtop/coqc option -exclude-dir to exclude subdirs for option -R.
 
 Miscellaneous
 
@@ -413,6 +433,7 @@ Miscellaneous
 - Syntax of "Test Printing Let ref" and "Test Printing If ref" changed into
   "Test Printing Let for ref" and "Test Printing If for ref".
 - An overhauled build system (new Makefiles); see dev/doc/build-system.txt
+- Add -browser option to configure script
 
 Changes from V8.1gamma to V8.1
 ==============================
diff --git a/COMPATIBILITY b/COMPATIBILITY
index b44f344d..d85a5f3f 100644
--- a/COMPATIBILITY
+++ b/COMPATIBILITY
@@ -39,6 +39,10 @@ Tactics
   the names in the brackets are synchronized so that H denotes the same
   hypothesis in every subgoal.
 
+- Application patterns with a meta variable in function position (?X ?Y) now
+  match arbitrary applications as expected. Use a nested 
+  [match X with (_ _) => fail 1 | _ => ..] to recover the old semantics.
+
 - Some bug fixes may lead to incompatibilities (see CHANGES for a detailed
   account).
 
diff --git a/INSTALL.doc b/INSTALL.doc
new file mode 100644
index 00000000..3eb72e08
--- /dev/null
+++ b/INSTALL.doc
@@ -0,0 +1,81 @@
+                           The Coq documentation
+                           =====================
+
+The Coq documentation includes 
+
+- A Reference Manual
+- A Tutorial
+- A document presenting the Coq standard library
+- A list of questions/answers in the FAQ style
+
+The sources of the documents are mainly made of LaTeX code from which
+user-readable PostScript or PDF files, or a user-browsable bunch of
+html files are generated.
+
+Prerequisite
+------------
+
+To produce the PostScript documents, the following tools
+are needed:
+
+  - latex (latex2e)
+  - dvips
+  - bibtex
+  - makeindex
+  - pngtopnm and pnmtops (for the Reference Manual and the FAQ)
+
+To produce the PDF documents, the following tools are needed:
+
+  - pdflatex
+  - bibtex
+
+To produce the html documents, the following tools are needed:
+
+  - hevea (e.g. 1.07 works)
+
+Compilation
+-----------
+
+To produce all documentation about Coq, just run:
+
+   make doc
+
+
+Alternatively, you can use some specific targets:
+
+   make doc-ps 
+   	to produce all PostScript documents
+
+   make doc-pdf
+        to produce all PDF documents
+
+   make doc-html
+        to produce all html documents
+
+   make refman
+        to produce all formats of the reference manual
+
+   make tutorial
+        to produce all formats of the tutorial
+
+   make rectutorial
+        to produce all formats of the tutorial on recursive types
+
+   make faq
+        to produce all formats of the FAQ
+
+   make stdlib
+   	to produce all formats of the Coq standard library 
+
+
+Installation
+------------
+
+To install all produced documents, do:
+
+  make DOCDIR=/some/directory/for/documentation install-doc
+
+DOCDIR defauts to /usr/share/doc/coq-x.y were x.y is the version number
+
+
+
diff --git a/Makefile b/Makefile
index 0cbc0f1c..1f770724 100644
--- a/Makefile
+++ b/Makefile
@@ -6,7 +6,7 @@
 #         #       GNU Lesser General Public License Version 2.1       #
 #######################################################################
 
-# $Id: Makefile 11029 2008-06-01 19:39:44Z herbelin $ 
+# $Id: Makefile 11309 2008-08-06 10:30:35Z herbelin $ 
 
 
 # Makefile for Coq
@@ -180,7 +180,6 @@ archclean: clean-ide cleantheories
 	rm -f bin/parser.opt$(EXE) bin/coq-interface.opt$(EXE)
 	find . -name '*.cmx' -or -name '*.cmxa' -or -name '*.[soa]' | xargs rm -f
 	rm -f $(TOOLS)
-	rm -f $(MINICOQ)
 
 clean-ide:
 	rm -f $(COQIDECMO) $(COQIDECMX) $(COQIDECMO:.cmo=.cmi) $(COQIDEBYTE) $(COQIDEOPT) $(COQIDE)
diff --git a/Makefile.build b/Makefile.build
index e759aafe..a5bae4ea 100644
--- a/Makefile.build
+++ b/Makefile.build
@@ -6,7 +6,7 @@
 #         #       GNU Lesser General Public License Version 2.1       #
 #######################################################################
 
-# $Id: Makefile.build 11174 2008-06-25 17:13:26Z notin $ 
+# $Id: Makefile.build 11309 2008-08-06 10:30:35Z herbelin $ 
 
 
 # Makefile for Coq
@@ -36,7 +36,12 @@ NOARG: world
 # build and install the three subsystems: coq, coqide, pcoq
 world: revision coq coqide pcoq
 
+ifeq ($(WITHDOC),all)
 install: install-coq install-coqide install-pcoq install-doc
+else
+install: install-coq install-coqide install-pcoq
+endif
+
 #install-manpages: install-coq-manpages install-pcoq-manpages
 
 ###########################################################################
@@ -491,7 +496,7 @@ install-pcoq-manpages:
 # tests
 ###########################################################################
 
-check:: world pcoq
+check:: world
 	cd test-suite; \
 	env COQBIN=../bin COQLIB=.. ./check -$(BEST) | tee check.log
 	if grep -F 'Error!' test-suite/check.log ; then false; fi
@@ -600,14 +605,6 @@ $(COQDOC): $(COQDOCCMO)
 	$(SHOW)'OCAMLC -o $@'
 	$(HIDE)$(OCAMLC) $(BYTEFLAGS) -custom -o $@ str.cma unix.cma $(COQDOCCMO)
 
-###########################################################################
-# minicoq
-###########################################################################
-
-$(MINICOQ): $(MINICOQCMO)
-	$(SHOW)'OCAMLC -o $@'
-	$(HIDE)$(OCAMLC) $(BYTEFLAGS) -custom -o $@ $(CMA) $(MINICOQCMO) $(OSDEPLIBS)
-
 ###########################################################################
 # Installation
 ###########################################################################
@@ -624,6 +621,7 @@ FULLCOQLIB=$(COQLIB:"$(OLDROOT)%="$(COQINSTALLPREFIX)%)
 FULLMANDIR=$(MANDIR:"$(OLDROOT)%="$(COQINSTALLPREFIX)%)
 FULLEMACSLIB=$(EMACSLIB:"$(OLDROOT)%="$(COQINSTALLPREFIX)%)
 FULLCOQDOCDIR=$(COQDOCDIR:"$(OLDROOT)%="$(COQINSTALLPREFIX)%)
+FULLDOCDIR=$(DOCDIR:"$(OLDROOT)%="$(COQINSTALLPREFIX)%)
 
 install-coq: install-binaries install-library install-coq-info
 install-coqlight: install-binaries install-library-light
@@ -632,12 +630,12 @@ install-binaries:: install-$(BEST) install-tools
 
 install-byte::
 	$(MKDIR) $(FULLBINDIR)
-	$(INSTALLBIN) $(COQMKTOP) $(COQC) $(COQTOPBYTE) $(FULLBINDIR)
+	$(INSTALLBIN) $(COQMKTOP) $(COQC) $(COQTOPBYTE) $(CSDPCERT) $(FULLBINDIR)
 	cd $(FULLBINDIR); ln -sf coqtop.byte$(EXE) coqtop$(EXE)
 
 install-opt::
 	$(MKDIR) $(FULLBINDIR)
-	$(INSTALLBIN) $(COQMKTOP) $(COQC) $(COQTOPBYTE) $(COQTOPOPT) $(FULLBINDIR)
+	$(INSTALLBIN) $(COQMKTOP) $(COQC) $(COQTOPBYTE) $(COQTOPOPT) $(CSDPCERT) $(FULLBINDIR)
 	cd $(FULLBINDIR); ln -sf coqtop.opt$(EXE) coqtop$(EXE)
 
 install-tools::
@@ -861,7 +859,7 @@ endif
 
 %.ml: %.mll
 	$(SHOW)'OCAMLLEX  $<'
-	$(HIDE)$(OCAMLLEX) "$*.mll" -o $@
+	$(HIDE)$(OCAMLLEX) -o $@ "$*.mll"
 
 %.ml %.mli: %.mly
 	$(SHOW)'OCAMLYACC $<'
diff --git a/Makefile.common b/Makefile.common
index 509ceedb..0a5d4260 100644
--- a/Makefile.common
+++ b/Makefile.common
@@ -46,8 +46,6 @@ COQBINARIES:= $(COQMKTOP) $(COQC) \
 endif
 OTHERBINARIES:=$(COQMKTOPBYTE) $(COQCBYTE)
 
-MINICOQ:=bin/minicoq$(EXE)
-
 CSDPCERT:=bin/csdpcert$(EXE)
 
 ###########################################################################
@@ -88,7 +86,7 @@ REFMANCOQTEXFILES:=\
   doc/refman/RefMan-oth.v.tex doc/refman/RefMan-ltac.v.tex \
   doc/refman/RefMan-decl.v.tex \
   doc/refman/Cases.v.tex doc/refman/Coercion.v.tex doc/refman/Extraction.v.tex \
-  doc/refman/Program.v.tex doc/refman/Omega.v.tex doc/refman/Polynom.v.tex \
+  doc/refman/Program.v.tex doc/refman/Omega.v.tex doc/refman/Micromega.v.tex doc/refman/Polynom.v.tex \
   doc/refman/Setoid.v.tex doc/refman/Helm.tex doc/refman/Classes.v.tex
 
 REFMANTEXFILES:=\
@@ -123,8 +121,8 @@ CONFIG:=\
   config/coq_config.cmo
 
 LIBREP:=\
-  lib/pp_control.cmo lib/pp.cmo lib/compat.cmo lib/util.cmo lib/bigint.cmo \
-  lib/hashcons.cmo lib/dyn.cmo lib/system.cmo lib/flags.cmo \
+  lib/pp_control.cmo lib/pp.cmo lib/compat.cmo lib/flags.cmo \
+  lib/util.cmo lib/bigint.cmo lib/hashcons.cmo lib/dyn.cmo lib/system.cmo \
   lib/bstack.cmo lib/edit.cmo lib/gset.cmo lib/gmap.cmo \
   lib/tlm.cmo lib/gmapl.cmo lib/profile.cmo lib/explore.cmo \
   lib/predicate.cmo lib/rtree.cmo lib/heap.cmo lib/option.cmo
@@ -411,8 +409,8 @@ COQDOCCMO:=$(CONFIG) tools/coqdoc/cdglobals.cmo tools/coqdoc/alpha.cmo \
 MCHECKER:=\
   config/coq_config.cmo \
   lib/pp_control.cmo lib/pp.cmo lib/compat.cmo \
-  lib/util.cmo lib/option.cmo lib/hashcons.cmo \
-  lib/system.cmo lib/flags.cmo \
+  lib/flags.cmo lib/util.cmo lib/option.cmo lib/hashcons.cmo \
+  lib/system.cmo \
   lib/predicate.cmo lib/rtree.cmo \
   kernel/names.cmo kernel/univ.cmo \
   kernel/esubst.cmo checker/term.cmo \
@@ -426,17 +424,11 @@ MCHECKER:=\
   checker/safe_typing.cmo checker/check.cmo \
   checker/check_stat.cmo checker/checker.cmo
 
-# minicoq
-
-MINICOQCMO:=$(CONFIG) $(LIBREP) $(KERNEL) \
-	   parsing/lexer.cmo parsing/g_minicoq.cmo \
-	   toplevel/fhimsg.cmo toplevel/minicoq.cmo
-
 # grammar modules with camlp4
 
 GRAMMARNEEDEDCMO:=\
-  lib/pp_control.cmo lib/pp.cmo lib/compat.cmo lib/util.cmo lib/bigint.cmo \
-  lib/dyn.cmo lib/flags.cmo lib/hashcons.cmo lib/predicate.cmo \
+  lib/pp_control.cmo lib/pp.cmo lib/compat.cmo lib/flags.cmo \
+  lib/util.cmo lib/bigint.cmo lib/dyn.cmo lib/hashcons.cmo lib/predicate.cmo \
   lib/rtree.cmo lib/option.cmo \
   kernel/names.cmo kernel/univ.cmo \
   kernel/esubst.cmo kernel/term.cmo kernel/mod_subst.cmo kernel/sign.cmo \
@@ -469,7 +461,7 @@ GRAMMARSCMO:=\
   parsing/g_prim.cmo parsing/g_tactic.cmo \
   parsing/g_ltac.cmo parsing/g_constr.cmo
 
-GRAMMARCMO:=$(GRAMMARNEEDEDCMO) $(CAMLP4EXTENSIONSCMO) $(GRAMMARSCMO)
+GRAMMARCMO:=$(CONFIG) $(GRAMMARNEEDEDCMO) $(CAMLP4EXTENSIONSCMO) $(GRAMMARSCMO)
 
 GRAMMARCMA:=parsing/grammar.cma
 
@@ -511,9 +503,9 @@ PRINTERSCMO:=\
   parsing/lexer.cmo interp/ppextend.cmo interp/genarg.cmo \
   interp/topconstr.cmo interp/notation.cmo interp/reserve.cmo		\
   library/impargs.cmo interp/constrextern.cmo \
-  interp/syntax_def.cmo interp/implicit_quantifiers.cmo  interp/constrintern.cmo \
-  proofs/proof_trees.cmo proofs/logic.cmo proofs/refiner.cmo \
-  proofs/tacexpr.cmo \
+  interp/syntax_def.cmo interp/implicit_quantifiers.cmo \
+  interp/constrintern.cmo proofs/proof_trees.cmo proofs/tacexpr.cmo \
+  proofs/proof_type.cmo proofs/logic.cmo proofs/refiner.cmo \
   proofs/evar_refiner.cmo proofs/pfedit.cmo proofs/tactic_debug.cmo \
   proofs/decl_mode.cmo \
   parsing/ppconstr.cmo parsing/extend.cmo parsing/pcoq.cmo \
@@ -622,8 +614,8 @@ FSETSVO:=$(FSETSBASEVO) $(FSETS_$(FSETS))
 ALLFSETS:=$(FSETSBASEVO) $(FSETS_all)
 
 RELATIONSVO:=$(addprefix theories/Relations/, \
- Newman.vo 		Operators_Properties.vo	Relation_Definitions.vo \
- Relation_Operators.vo 	Relations.vo 		Rstar.vo )
+ Operators_Properties.vo	Relation_Definitions.vo \
+ Relation_Operators.vo 		Relations.vo )
 
 WELLFOUNDEDVO:=$(addprefix theories/Wellfounded/, \
  Disjoint_Union.vo 	Inclusion.vo 	Inverse_Image.vo \
@@ -723,8 +715,7 @@ RATIONALSPECVIAQVO:=$(addprefix theories/Numbers/Rational/SpecViaQ/, \
  QSig.vo )
 
 RATIONALBIGQVO:=$(addprefix theories/Numbers/Rational/BigQ/, \
- QMake_base.vo	QpMake.vo	QvMake.vo	Q0Make.vo 	\
- QifMake.vo 	QbiMake.vo 	BigQ.vo )
+ QMake.vo	BigQ.vo )
 
 RATIONALVO:=$(RATIONALSPECVIAQVO) $(RATIONALBIGQVO)
 
@@ -767,7 +758,7 @@ MICROMEGAVO:=$(addprefix contrib/micromega/, \
   Env.vo                RingMicromega.vo \
   EnvRing.vo            VarMap.vo \
   OrderedRing.vo        ZCoeff.vo \
-  Micromegatac.vo       ZMicromega.vo \
+  Psatz.vo	       ZMicromega.vo \
   QMicromega.vo         RMicromega.vo \
   Tauto.vo )
 
@@ -872,13 +863,13 @@ STAGE2_TARGETS:=$(COQBINARIES) lib kernel byterun library proofs tactics \
   interp parsing pretyping highparsing toplevel hightactics \
   coqide-binaries coqide-byte coqide-opt $(COQIDEOPT) $(COQIDEBYTE) $(COQIDE) \
   pcoq-binaries $(COQINTERFACE) $(CSDPCERT) coqbinaries pcoq $(TOOLS) tools \
-  printers $(MINICOQ) debug
+  printers debug
 VO_TARGETS:=logic arith bool narith zarith qarith lists strings sets \
   fsets allfsets relations wellfounded ints reals allreals \
   setoids sorting natural integer rational numbers noreal \
   omega micromega ring setoid_ring dp xml extraction field fourier jprover \
   funind cc programs subtac rtauto
-DOC_TARGETS:=doc doc-html doc-ps doc-pdf stdlib refman tutorial faq rectutorial
+DOC_TARGETS:=doc doc-html doc-ps doc-pdf stdlib refman tutorial faq rectutorial refman-quick refman-nodep stdlib-nodep
 STAGE3_TARGETS:=world install coqide coqide-files coq coqlib \
   coqlight states pcoq-files check init theories theories-light contrib \
   $(DOC_TARGETS) $(VO_TARGETS)
diff --git a/Makefile.doc b/Makefile.doc
index 4046d5e7..54fa5f80 100644
--- a/Makefile.doc
+++ b/Makefile.doc
@@ -27,13 +27,19 @@ doc-ps:\
   doc/tutorial/Tutorial.v.ps doc/refman/Reference-Manual.ps \
   doc/faq/FAQ.v.ps doc/stdlib/Library.ps doc/RecTutorial/RecTutorial.v.ps
 
-refman:\
+refman: coq
+	$(MAKE) -f Makefile.stage3 refman-nodep
+
+refman-nodep:\
   doc/refman/html/index.html doc/refman/Reference-Manual.ps doc/refman/Reference-Manual.pdf
 
 tutorial:\
   doc/tutorial/Tutorial.v.html doc/tutorial/Tutorial.v.ps doc/tutorial/Tutorial.v.pdf
 
-stdlib:\
+stdlib: $(THEORIESVO) $(COQDOC)
+	$(MAKE) -f Makefile.stage3 stdlib-nodep
+
+stdlib-nodep:\
   doc/stdlib/html/index.html doc/stdlib/Library.ps doc/stdlib/Library.pdf
 
 faq:\
@@ -47,7 +53,7 @@ rectutorial:\
 ### Implicit rules
 ######################################################################
 
-%.v.tex: %.tex coq
+%.v.tex: %.tex
 	(cd `dirname $<`; $(COQSRC)/$(COQTEX) $(COQTEXOPTS) `basename $<`)
 
 %.ps: %.dvi
@@ -103,7 +109,7 @@ doc/refman/html/index.html: doc/refman/Reference-Manual.html $(REFMANPNGFILES) \
 	$(INSTALLLIB) doc/refman/cover.html doc/refman/menu.html doc/refman/html
 	$(INSTALLLIB) doc/refman/index.html doc/refman/html
 
-doc/refman-quick:
+refman-quick:
 	(cd doc/refman; \
 	 $(PDFLATEX) Reference-Manual.tex; \
 	 $(HEVEA) $(HEVEAOPTS) ./Reference-Manual.tex)
@@ -152,7 +158,7 @@ doc/faq/html/index.html: doc/faq/FAQ.v.html
 
 ### Standard library (browsable html format)
 
-doc/stdlib/index-body.html: $(THEORIESVO:.vo=.glob) $(COQDOC)
+doc/stdlib/index-body.html: 
 	- rm -rf doc/stdlib/html
 	$(MKDIR) doc/stdlib/html
 	$(COQDOC) -q -d doc/stdlib/html --multi-index --html \
@@ -169,7 +175,7 @@ doc/stdlib/html/index.html: doc/stdlib/index-list.html doc/stdlib/index-body.htm
 
 ### Standard library (light version, full version is definitely too big)
 
-doc/stdlib/Library.coqdoc.tex: $(THEORIESLIGHTVO:.vo=.glob) $(COQDOC)
+doc/stdlib/Library.coqdoc.tex: 
 	$(COQSRC)/$(COQDOC) -q --gallina --body-only --latex --stdout \
             -R theories Coq $(THEORIESLIGHTVO:.vo=.v) >> $@
 
@@ -215,26 +221,26 @@ ide/index_urls.txt: doc/refman/html/index.html
 install-doc: install-doc-meta install-doc-html install-doc-printable
 
 install-doc-meta:
-	$(MKDIR) $(DOCDIR)
-	$(INSTALLLIB) doc/LICENCE $(DOCDIR)/LICENCE.doc
+	$(MKDIR) $(FULLDOCDIR)
+	$(INSTALLLIB) doc/LICENSE $(FULLDOCDIR)/LICENSE.doc
 
 install-doc-html: doc-html
-	$(MKDIR) $(addprefix $(DOCDIR)/html/, refman stdlib faq)
-	$(INSTALLLIB) doc/refman/html/* $(DOCDIR)/html/refman 
-	$(INSTALLLIB) doc/stdlib/html/* $(DOCDIR)/html/stdlib 
-	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.html $(DOCDIR)/html/RecTutorial.html
-	$(INSTALLLIB) doc/faq/html/* $(DOCDIR)/html/faq
-	$(INSTALLLIB) doc/tutorial/Tutorial.v.html $(DOCDIR)/html/Tutorial.html
+	$(MKDIR) $(addprefix $(FULLDOCDIR)/html/, refman stdlib faq)
+	$(INSTALLLIB) doc/refman/html/* $(FULLDOCDIR)/html/refman 
+	$(INSTALLLIB) doc/stdlib/html/* $(FULLDOCDIR)/html/stdlib 
+	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.html $(FULLDOCDIR)/html/RecTutorial.html
+	$(INSTALLLIB) doc/faq/html/* $(FULLDOCDIR)/html/faq
+	$(INSTALLLIB) doc/tutorial/Tutorial.v.html $(FULLDOCDIR)/html/Tutorial.html
 
 install-doc-printable: doc-pdf doc-ps
-	$(MKDIR) $(DOCDIR)/ps $(DOCDIR)/pdf
+	$(MKDIR) $(FULLDOCDIR)/ps $(FULLDOCDIR)/pdf
 	$(INSTALLLIB) doc/refman/Reference-Manual.pdf \
-		doc/stdlib/Library.pdf $(DOCDIR)/pdf
+		doc/stdlib/Library.pdf $(FULLDOCDIR)/pdf
 	$(INSTALLLIB) doc/refman/Reference-Manual.ps \
-		doc/stdlib/Library.ps $(DOCDIR)/ps
-	$(INSTALLLIB) doc/tutorial/Tutorial.v.pdf $(DOCDIR)/pdf/Tutorial.pdf
-	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.pdf $(DOCDIR)/pdf/RecTutorial.pdf
-	$(INSTALLLIB) doc/faq/FAQ.v.pdf $(DOCDIR)/pdf/FAQ.pdf
-	$(INSTALLLIB) doc/tutorial/Tutorial.v.ps $(DOCDIR)/ps/Tutorial.ps
-	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.ps $(DOCDIR)/ps/RecTutorial.ps
-	$(INSTALLLIB) doc/faq/FAQ.v.ps $(DOCDIR)/ps/FAQ.ps
+		doc/stdlib/Library.ps $(FULLDOCDIR)/ps
+	$(INSTALLLIB) doc/tutorial/Tutorial.v.pdf $(FULLDOCDIR)/pdf/Tutorial.pdf
+	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.pdf $(FULLDOCDIR)/pdf/RecTutorial.pdf
+	$(INSTALLLIB) doc/faq/FAQ.v.pdf $(FULLDOCDIR)/pdf/FAQ.pdf
+	$(INSTALLLIB) doc/tutorial/Tutorial.v.ps $(FULLDOCDIR)/ps/Tutorial.ps
+	$(INSTALLLIB) doc/RecTutorial/RecTutorial.v.ps $(FULLDOCDIR)/ps/RecTutorial.ps
+	$(INSTALLLIB) doc/faq/FAQ.v.ps $(FULLDOCDIR)/ps/FAQ.ps
diff --git a/README.doc b/README.doc
new file mode 100755
index 00000000..4e72c894
--- /dev/null
+++ b/README.doc
@@ -0,0 +1,18 @@
+                           The Coq documentation
+                           =====================
+
+The Coq documentation includes:
+
+- a reference manual;
+- a generic tutorial on Coq;
+- a tutorial on recursive types;
+- a document presenting the Coq standard library;
+- a list of questions/answers in the FAQ style
+
+All these documents are available online from the Coq official site
+(http://coq.inria.fr), either as PS/PDF files or as HTML documents.
+
+The sources of the documentation are available along with the sources
+of the Coq proof assistant. It is released under the Open Publication
+License (see file doc/LICENSE in the sources of Coq)
+
diff --git a/checker/check.ml b/checker/check.ml
index f8844975..e91516c7 100644
--- a/checker/check.ml
+++ b/checker/check.ml
@@ -209,7 +209,7 @@ let locate_absolute_library dir =
   if loadpath = [] then raise LibUnmappedDir;
   try
     let name = string_of_id base^".vo" in
-    let _, file = System.where_in_path loadpath name in
+    let _, file = System.where_in_path false loadpath name in
     (dir, file)
   with Not_found ->
   (* Last chance, removed from the file system but still in memory *)
@@ -229,7 +229,7 @@ let locate_qualified_library qid =
     in
     if loadpath = [] then raise LibUnmappedDir;
     let name =  qid.basename^".vo" in
-    let path, file = System.where_in_path loadpath name in
+    let path, file = System.where_in_path true loadpath name in
     let dir =
       extend_dirpath (find_logical_path path) (id_of_string qid.basename) in
     (* Look if loaded *)
@@ -267,10 +267,8 @@ let try_locate_qualified_library qid =
 
 (*s Loading from disk to cache (preparation phase) *)
 
-let vo_magic_number = 08190 (* trunk *)
-
 let (raw_extern_library, raw_intern_library) =
-  System.raw_extern_intern vo_magic_number ".vo"
+  System.raw_extern_intern Coq_config.vo_magic_number ".vo"
 
 let with_magic_number_check f a =
   try f a
@@ -323,7 +321,8 @@ let get_deps (dir, f) =
 
 (* Read a compiled library and all dependencies, in reverse order.
    Do not include files that are already in the context. *)
-let rec intern_library (dir, f) needed =
+let rec intern_library seen (dir, f) needed =
+  if LibrarySet.mem dir seen then failwith "Recursive dependencies!";
   (* Look if in the current logical environment *)
   try let _ = find_library dir in needed
   with Not_found ->
@@ -332,28 +331,34 @@ let rec intern_library (dir, f) needed =
   else
     (* [dir] is an absolute name which matches [f] which must be in loadpath *)
     let m = intern_from_file (dir,f) in
-    (dir,m)::List.fold_right intern_mandatory_library m.library_deps needed
-
-(* digest error with checked modules could be a warning *)
-and intern_mandatory_library (dir,_) needed =
-  intern_library (try_locate_absolute_library dir) needed
+    let seen' = LibrarySet.add dir seen in
+    let deps =
+      List.map (fun (d,_) -> try_locate_absolute_library d) m.library_deps in
+    (dir,m) :: List.fold_right (intern_library seen') deps needed
 
 (* Compute the reflexive transitive dependency closure *)
-let rec fold_deps ff (dir,f) s =
-  if  LibrarySet.mem dir s then s
+let rec fold_deps seen ff (dir,f) (s,acc) =
+  if LibrarySet.mem dir seen then failwith "Recursive dependencies!";
+  if LibrarySet.mem dir s then (s,acc)
   else
     let deps = get_deps (dir,f) in
     let deps = List.map (fun (d,_) -> try_locate_absolute_library d) deps in
-    ff dir (List.fold_right (fold_deps ff) deps s)
+    let seen' = LibrarySet.add dir seen in
+    let (s',acc') = List.fold_right (fold_deps seen' ff) deps (s,acc) in
+    (LibrarySet.add dir s', ff dir acc')
+
+and fold_deps_list seen ff modl needed =
+  List.fold_right (fold_deps seen ff) modl needed
 
-and fold_deps_list  ff modl needed =
-  List.fold_right (fold_deps ff) modl needed
+let fold_deps_list ff modl acc =
+  snd (fold_deps_list LibrarySet.empty ff modl (LibrarySet.empty,acc))
 
 let recheck_library ~norec ~admit ~check =
   let ml = List.map try_locate_qualified_library check in
   let nrl = List.map try_locate_qualified_library norec in
   let al =  List.map try_locate_qualified_library admit in
-  let needed = List.rev (List.fold_right intern_library (ml@nrl) []) in
+  let needed = List.rev
+    (List.fold_right (intern_library LibrarySet.empty) (ml@nrl) []) in
   (* first compute the closure of norec, remove closure of check,
      add closure of admit, and finally remove norec and check *)
   let nochk = fold_deps_list LibrarySet.add nrl LibrarySet.empty in
diff --git a/checker/checker.ml b/checker/checker.ml
index 1c7ace12..7de25835 100644
--- a/checker/checker.ml
+++ b/checker/checker.ml
@@ -73,16 +73,14 @@ let convert_string d =
     failwith "caught"
 
 let add_rec_path ~unix_path:dir ~coq_root:coq_dirpath =
-  let dirs = all_subdirs dir in
-  let prefix = repr_dirpath coq_dirpath in
-  if dirs <> [] then
+  if exists_dir dir then
+    let dirs = all_subdirs dir in
+    let prefix = repr_dirpath coq_dirpath in
     let convert_dirs (lp,cp) =
-      (lp,Names.make_dirpath
-            ((List.map convert_string (List.rev cp))@prefix)) in
+      (lp,make_dirpath (List.map convert_string (List.rev cp)@prefix)) in
     let dirs = map_succeed convert_dirs dirs in
-    begin
-      List.iter Check.add_load_path dirs
-    end
+    List.iter Check.add_load_path dirs;
+    Check.add_load_path (dir,coq_dirpath)
   else
     msg_warning (str ("Cannot open " ^ dir))
 
@@ -101,6 +99,14 @@ let set_default_rec_include d =
   let p = Check.default_root_prefix in
   check_coq_overwriting p; 
   push_rec_include (d, p)
+let set_include d p =
+  let p = dirpath_of_string p in
+  check_coq_overwriting p;
+  push_include (d,p)
+let set_rec_include d p =
+  let p = dirpath_of_string p in
+  check_coq_overwriting p;
+  push_rec_include(d,p)
 
 (* Initializes the LoadPath according to COQLIB and Coq_config *)
 let init_load_path () =
@@ -174,9 +180,11 @@ let print_usage_channel co command =
   output_string co command;
   output_string co "Coq options are:\n";
   output_string co
-"  -I dir                 add directory dir in the include path
+"  -I dir -as coqdir      map physical dir to logical coqdir
+  -I dir                 map directory dir to the empty logical path
   -include dir           (idem)
-  -R dir coqdir          recursively map physical dir to logical coqdir 
+  -R dir -as coqdir      recursively map physical dir to logical coqdir 
+  -R dir coqdir          (idem)
 
   -admit module          load module and dependencies without checking
   -norec module          check module but admit dependencies without checking
@@ -297,11 +305,14 @@ let parse_args() =
    | "-impredicative-set" :: rem -> 
        set_engagement Declarations.ImpredicativeSet; parse rem
 
+    | ("-I"|"-include") :: d :: "-as" :: p :: rem -> set_include d p; parse rem
+    | ("-I"|"-include") :: d :: "-as" :: [] -> usage ()
     | ("-I"|"-include") :: d :: rem -> set_default_include d; parse rem
     | ("-I"|"-include") :: []       -> usage ()
 
-    | "-R" :: d :: p :: rem ->
-        push_rec_include (d, dirpath_of_string p);parse rem
+    | "-R" :: d :: "-as" :: p :: rem -> set_rec_include d p;parse rem
+    | "-R" :: d :: "-as" :: [] -> usage ()
+    | "-R" :: d :: p :: rem -> set_rec_include d p;parse rem
     | "-R" :: ([] | [_]) -> usage ()
 
     | "-debug" :: rem -> set_debug (); parse rem
diff --git a/config/Makefile.template b/config/Makefile.template
index e5061ebe..fc8af173 100644
--- a/config/Makefile.template
+++ b/config/Makefile.template
@@ -141,6 +141,9 @@ DOT=dot
 DOTOPTS=-Tps
 ODOCDOTOPTS=-dot -dot-reduce
 
+# Option to control compilation and installation of the documentation
+WITHDOC=WITHDOCOPT
+
 # make or sed are bogus and believe lines not terminating by a return
 # are inexistent
 
diff --git a/config/coq_config.mli b/config/coq_config.mli
index 23d3efbd..3898a0f3 100644
--- a/config/coq_config.mli
+++ b/config/coq_config.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: coq_config.mli 10122 2007-09-15 10:35:59Z letouzey $ i*)
+(*i $Id: coq_config.mli 11313 2008-08-07 11:15:03Z barras $ i*)
 
 val local : bool        (* local use (no installation) *)
 
@@ -28,12 +28,17 @@ val osdeplibs : string  (* OS dependant link options for ocamlc *)
 (* val defined : string list  (* options for lib/ocamlpp *) *)
 
 val version : string    (* version number of Coq *)
-val versionsi : string  (* version number of Coq\_SearchIsos *)
 val date : string       (* release date *)
 val compile_date : string (* compile date *)
+val vo_magic_number : int
+val state_magic_number : int
 
 val theories_dirs : string list
 val contrib_dirs : string list
 
 val exec_extension : string (* "" under Unix, ".exe" under MS-windows *)
 val with_geoproof : bool ref (* to (de)activate functions specific to Geoproof with Coqide *)
+
+val browser : string
+(** default web browser to use, may be overriden by environment
+    variable COQREMOTEBROWSER *)
diff --git a/configure b/configure
index 59cfcb9f..2747ee2f 100755
--- a/configure
+++ b/configure
@@ -6,8 +6,10 @@
 # 
 ##################################
 
-VERSION=8.2beta3
-DATE="Jun. 2008"
+VERSION=8.2beta4
+VOMAGIC=08193 
+STATEMAGIC=19764
+DATE="Aug. 2008"
 
 # a local which command for sh
 which () {
@@ -23,7 +25,7 @@ done
 }
 
 usage () {
-    echo "Available options for configure are:\n"
+    printf "Available options for configure are:\n"
     echo "-help"
     printf "\tDisplays this help page\n"
     echo "-prefix <dir>"
@@ -57,6 +59,10 @@ usage () {
     printf "\tSpecifies whether or not to compile full FSets/Reals library\n"
     echo "-coqide (opt|byte|no)"
     printf "\tSpecifies whether or not to compile Coqide\n"
+    echo "-browser <command>"
+    printf "\tUse <command> to open URL %%s\n"
+    echo "-with-doc (yes|no)"
+    printf "\tSpecifies whether or not to compile the documentation\n"
     echo "-with-geoproof (yes|no)"
     printf "\tSpecifies whether or not to use Geoproof binding\n"
     echo "-with-cc <file>"
@@ -113,7 +119,10 @@ fsets=all
 reals=all
 arch_spec=no
 coqide_spec=no
+browser_spec=no
 with_geoproof=false
+with_doc=all
+with_doc_spec=no
 
 COQSRC=`pwd`
 
@@ -183,6 +192,15 @@ while : ; do
 			  *) COQIDE=no
 		      esac
 		      shift;;
+    -browser|--browser) browser_spec=yes
+		      BROWSER=$2
+		      shift;;
+    -with-doc|--with-doc) with_doc_spec=yes
+		      case "$2" in
+			  yes|all) with_doc=all;;
+			  *) with_doc=no
+		      esac
+		      shift;;
     -with-geoproof|--with-geoproof) 
 	  case $2 in
 	      yes) with_geoproof=true;;
@@ -321,6 +339,15 @@ else
   echo "Cannot find GNU Make 3.81"
 fi
 
+# Browser command
+
+if [ "$browser_spec" = "no" ]; then
+    case $ARCH in
+        win32) BROWSER='C:\PROGRA~1\INTERN~1\IEXPLORE %s' ;;
+        *) BROWSER='firefox -remote "OpenURL(%s,new-tab)" || firefox %s &' ;;
+    esac
+fi
+
 #########################################
 # Objective Caml programs
 
@@ -594,6 +621,24 @@ esac
 #    "") MKTEXLSR=true;;
 #esac
 
+# "
+### Test if documentation can be compiled (latex, hevea)
+
+if test "$with_doc" = "all" 
+then
+    if test "`which latex`" = ""
+    then 
+	echo "latex was not found; documentation will not be available"
+	with_doc=no
+    else
+	if test "`which hevea`" = ""
+	then
+	    with_doc=no
+	    echo "hevea was not found: documentation will not be available"
+	fi
+    fi
+fi
+
 ###########################################
 # bindir, libdir, mandir, docdir, etc.
 
@@ -747,7 +792,13 @@ echo "  Reals theory                      : All"
 else
 echo "  Reals theory                      : Basic"
 fi
+if test "$with_doc" = "all"; then
+echo "  Documentation                     : All"
+else
+echo "  Documentation                     : None"
+fi
 echo "  CoqIde                            : $COQIDE"
+echo "  Web browser                       : $BROWSER"
 echo ""
 
 echo "  Paths for true installation:"
@@ -769,6 +820,10 @@ escape_var () {
 EOF
 }
 
+# Escaped version of browser command
+export BROWSER
+ESCBROWSER=`VAR=BROWSER escape_var`
+
 # damned backslashes under M$Windows
 case $ARCH in
     win32)
@@ -818,11 +873,13 @@ let best = "$best_compiler"
 let arch = "$ARCH"
 let osdeplibs = "$OSDEPLIBS"
 let version = "$VERSION"
-let versionsi = "$VERSIONSI"
 let date = "$DATE"
 let compile_date = "$COMPILEDATE"
+let vo_magic_number = $VOMAGIC
+let state_magic_number = $STATEMAGIC
 let exec_extension = "$EXE"
 let with_geoproof = ref $with_geoproof
+let browser = "$ESCBROWSER"
 
 END_OF_COQ_CONFIG
 
@@ -895,6 +952,7 @@ sed -e "s|LOCALINSTALLATION|$local|" \
     -e "s|REALSOPT|$reals|" \
     -e "s|COQIDEOPT|$COQIDE|" \
     -e "s|CHECKEDOUTSOURCETREE|$checkedout|" \
+    -e "s|WITHDOCOPT|$with_doc|" \
       "$COQSRC/config/Makefile.template" > "$COQSRC/config/Makefile"
 
 chmod a-w "$COQSRC/config/Makefile"
@@ -936,4 +994,4 @@ echo
 echo "*Warning* To compile the system for a new architecture"
 echo "          don't forget to do a 'make archclean' before './configure'."
 
-# $Id: configure 11181 2008-06-27 07:35:45Z notin $
+# $Id: configure 11320 2008-08-07 19:40:59Z notin $
diff --git a/contrib/extraction/modutil.ml b/contrib/extraction/modutil.ml
index 48444509..0c906712 100644
--- a/contrib/extraction/modutil.ml
+++ b/contrib/extraction/modutil.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: modutil.ml 10665 2008-03-14 12:10:09Z soubiran $ i*)
+(*i $Id: modutil.ml 11262 2008-07-24 20:59:29Z letouzey $ i*)
 
 open Names
 open Declarations
@@ -347,6 +347,73 @@ and optim_me to_appear s = function
       MEapply (optim_me to_appear s me, optim_me to_appear s me')
   | MEfunctor (mbid,mt,me) -> MEfunctor (mbid,mt, optim_me to_appear s me)
 
-let optimize_struct to_appear struc = 
-  let subst = ref (Refmap.empty : ml_ast Refmap.t) in 
-  List.map (fun (mp,lse) -> (mp, optim_se true to_appear subst lse)) struc
+(* After these optimisations, some dependencies may not be needed anymore. 
+   For monolithic extraction, we recompute a minimal set of dependencies. *)
+
+exception NoDepCheck
+
+let base_r = function
+  | ConstRef c as r -> r
+  | IndRef (kn,_) -> IndRef (kn,0)
+  | ConstructRef ((kn,_),_) -> IndRef (kn,0)
+  | _ -> assert false
+
+let reset_needed, add_needed, found_needed, is_needed =
+  let needed = ref Refset.empty in
+  ((fun l -> needed := Refset.empty),
+   (fun r -> needed := Refset.add (base_r r) !needed),
+   (fun r -> needed := Refset.remove (base_r r) !needed),
+   (fun r -> Refset.mem (base_r r) !needed))
+
+let declared_refs = function
+  | Dind (kn,_) -> [|IndRef (kn,0)|]
+  | Dtype (r,_,_) -> [|r|]
+  | Dterm (r,_,_) -> [|r|]
+  | Dfix (rv,_,_) -> rv
+
+(* Computes the dependencies of a declaration, except in case 
+   of custom extraction. *)
+
+let compute_deps_decl = function
+  | Dind (kn,ind) ->
+      (* Todo Later : avoid dependencies when Extract Inductive *)
+      ind_iter_references add_needed add_needed add_needed kn ind
+  | Dtype (r,ids,t) ->
+      if not (is_custom r) then type_iter_references add_needed t
+  | Dterm (r,u,t) ->
+      type_iter_references add_needed t;
+      if not (is_custom r) then
+	ast_iter_references add_needed add_needed add_needed u
+  | Dfix _ as d ->
+      (* Todo Later : avoid dependencies when Extract Constant *)
+      decl_iter_references add_needed add_needed add_needed d
+
+let rec depcheck_se = function
+  | [] -> []
+  | ((l,SEdecl d) as t)::se ->
+      let se' = depcheck_se se in
+      let rv = declared_refs d in
+      if not (array_exists is_needed rv) then
+	(Array.iter remove_info_axiom rv; se')
+      else
+	(Array.iter found_needed rv; compute_deps_decl d; t::se')
+  | _ -> raise NoDepCheck
+
+let rec depcheck_struct = function
+  | [] -> []
+  | (mp,lse)::struc ->
+      let struc' = depcheck_struct struc in
+      let lse' = depcheck_se lse in
+      (mp,lse')::struc'
+
+let optimize_struct to_appear struc =
+  let subst = ref (Refmap.empty : ml_ast Refmap.t) in
+  let opt_struc =
+    List.map (fun (mp,lse) -> (mp, optim_se true to_appear subst lse)) struc
+  in
+  try
+    if modular () then raise NoDepCheck;
+    reset_needed ();
+    List.iter add_needed to_appear;
+    depcheck_struct opt_struc
+  with NoDepCheck -> opt_struc
diff --git a/contrib/extraction/table.ml b/contrib/extraction/table.ml
index abf461c1..10f669e1 100644
--- a/contrib/extraction/table.ml
+++ b/contrib/extraction/table.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: table.ml 10348 2007-12-06 17:36:14Z aspiwack $ i*)
+(*i $Id: table.ml 11262 2008-07-24 20:59:29Z letouzey $ i*)
 
 open Names
 open Term
@@ -175,6 +175,7 @@ let info_axioms = ref Refset.empty
 let log_axioms = ref Refset.empty
 let init_axioms () = info_axioms := Refset.empty; log_axioms := Refset.empty
 let add_info_axiom r = info_axioms := Refset.add r !info_axioms
+let remove_info_axiom r = info_axioms := Refset.remove r !info_axioms
 let add_log_axiom r = log_axioms := Refset.add r !log_axioms
 
 (*s Extraction mode: modular or monolithic *)
diff --git a/contrib/extraction/table.mli b/contrib/extraction/table.mli
index ca02cb4d..4dbccd08 100644
--- a/contrib/extraction/table.mli
+++ b/contrib/extraction/table.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: table.mli 10245 2007-10-21 13:41:53Z letouzey $ i*)
+(*i $Id: table.mli 11262 2008-07-24 20:59:29Z letouzey $ i*)
 
 open Names
 open Libnames
@@ -77,6 +77,7 @@ val is_projection : global_reference -> bool
 val projection_arity : global_reference -> int
 
 val add_info_axiom : global_reference -> unit
+val remove_info_axiom : global_reference -> unit
 val add_log_axiom : global_reference -> unit
 
 val reset_tables : unit -> unit
diff --git a/contrib/firstorder/sequent.ml b/contrib/firstorder/sequent.ml
index c832d30f..e931f8fd 100644
--- a/contrib/firstorder/sequent.ml
+++ b/contrib/firstorder/sequent.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: sequent.ml 10824 2008-04-21 13:57:03Z msozeau $ *)
+(* $Id: sequent.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Term
 open Util
@@ -281,7 +281,7 @@ let create_with_auto_hints l depth gl=
 	searchtable_map dbname
       with Not_found-> 
 	error ("Firstorder: "^dbname^" : No such Hint database") in
-      Hint_db.iter g (snd hdb) in
+      Hint_db.iter g hdb in
     List.iter h l;
     !seqref
 
diff --git a/contrib/funind/functional_principles_proofs.ml b/contrib/funind/functional_principles_proofs.ml
index 3d80bd00..bd335d30 100644
--- a/contrib/funind/functional_principles_proofs.ml
+++ b/contrib/funind/functional_principles_proofs.ml
@@ -136,7 +136,7 @@ let change_hyp_with_using msg hyp_id t tac : tactic =
   fun g -> 
     let prov_id = pf_get_new_id hyp_id g in 
     tclTHENS
-      ((* observe_tac msg *) (forward (Some  (tclCOMPLETE tac)) (Genarg.IntroIdentifier prov_id) t))
+      ((* observe_tac msg *) (forward (Some  (tclCOMPLETE tac)) (dummy_loc,Genarg.IntroIdentifier prov_id) t))
       [tclTHENLIST 
       [	
 	(* observe_tac "change_hyp_with_using thin" *) (thin [hyp_id]);
@@ -388,7 +388,7 @@ let clean_hyp_with_heq ptes_infos eq_hyps hyp_id env sigma =
 		     in
 (* 		     observe_tac "rec hyp " *)
 		       (tclTHENS
-		       (assert_as true (Genarg.IntroIdentifier rec_pte_id) t_x)
+		       (assert_as true (dummy_loc, Genarg.IntroIdentifier rec_pte_id) t_x)
 		       [
 			 (* observe_tac "prove rec hyp" *) (prove_rec_hyp eq_hyps);
 (* 			observe_tac "prove rec hyp" *)
@@ -571,7 +571,7 @@ let instanciate_hyps_with_args (do_prove:identifier list -> tactic) hyps args_id
 	fun g -> 
 	  let prov_hid = pf_get_new_id hid g in
 	  tclTHENLIST[
-	    forward None (Genarg.IntroIdentifier prov_hid) (mkApp(mkVar hid,args));
+	    forward None (dummy_loc,Genarg.IntroIdentifier prov_hid) (mkApp(mkVar hid,args));
 	    thin [hid];
 	    h_rename [prov_hid,hid]
 	  ] g
@@ -1399,7 +1399,7 @@ let new_prove_with_tcc is_mes acc_inv hrec tcc_hyps eqs : tactic =
 				      false
 				      (true,5)
 				      [Lazy.force refl_equal]
-				      [empty_transparent_state, Auto.Hint_db.empty]
+				      [Auto.Hint_db.empty false]
 				  )
 			   )
 			)
@@ -1497,7 +1497,7 @@ let prove_principle_for_gen
 	    (tclTHEN
 	       (forward 
 		  (Some ((fun g -> (* observe_tac "prove wf" *) (tclCOMPLETE (wf_tac is_mes)) g)))
-		  (Genarg.IntroIdentifier wf_thm_id)
+		  (dummy_loc,Genarg.IntroIdentifier wf_thm_id)
 		  (mkApp (delayed_force well_founded,[|input_type;relation|])))
 	       (
 		 (* observe_tac  *)
@@ -1561,7 +1561,7 @@ let prove_principle_for_gen
 	);
       (* observe_tac "" *) (forward
 	 (Some (prove_rec_arg_acc))
-	 (Genarg.IntroIdentifier acc_rec_arg_id)
+	 (dummy_loc,Genarg.IntroIdentifier acc_rec_arg_id)
  	 (mkApp (delayed_force acc_rel,[|input_type;relation;mkVar rec_arg_id|]))
       );
 (*       observe_tac "reverting" *) (revert (List.rev (acc_rec_arg_id::args_ids)));
diff --git a/contrib/funind/g_indfun.ml4 b/contrib/funind/g_indfun.ml4
index dae76f2d..d435f513 100644
--- a/contrib/funind/g_indfun.ml4
+++ b/contrib/funind/g_indfun.ml4
@@ -90,11 +90,6 @@ END
 TACTIC EXTEND newfunind
    ["functional" "induction" ne_constr_list(cl) fun_ind_using(princl) with_names(pat)] -> 
      [ 
-       let pat = 
-	 match pat with 
-	   | None -> IntroAnonymous
-	   | Some pat -> pat
-       in
        let c = match cl with 
 	 | [] -> assert false
 	 | [c] -> c 
@@ -106,11 +101,6 @@ END
 TACTIC EXTEND snewfunind
    ["soft" "functional" "induction" ne_constr_list(cl) fun_ind_using(princl) with_names(pat)] -> 
      [ 
-       let pat = 
-	 match pat with 
-	   | None -> IntroAnonymous
-	   | Some pat -> pat
-       in
        let c = match cl with 
 	 | [] -> assert false
 	 | [c] -> c 
@@ -319,7 +309,7 @@ let poseq_unsafe idunsafe cstr gl =
   tclTHEN
     (Tactics.letin_tac None (Name idunsafe) cstr allClauses)
     (tclTHENFIRST 
-      (Tactics.assert_as true IntroAnonymous (mkEq typ (mkVar idunsafe) cstr)) 
+      (Tactics.assert_as true (Util.dummy_loc,IntroAnonymous) (mkEq typ (mkVar idunsafe) cstr)) 
       Tactics.reflexivity)
     gl
   
@@ -396,7 +386,7 @@ let finduction (oid:identifier option) (heuristic: fapp_info list -> fapp_info l
 	      fun gl -> 
 		  (functional_induction 
 		    true (applist (info.fname, List.rev !list_constr_largs)) 
-		    None IntroAnonymous) gl)) 
+		    None None) gl)) 
 	  nexttac)) ordered_info_list in
   (* we try each (f t u v) until one does not fail *)
   (* TODO: try also to mix functional schemes *)
diff --git a/contrib/funind/indfun.ml b/contrib/funind/indfun.ml
index a6cbb321..79ef0097 100644
--- a/contrib/funind/indfun.ml
+++ b/contrib/funind/indfun.ml
@@ -120,7 +120,7 @@ let functional_induction with_clean c princl pat =
 	 princ_infos
 	 args_as_induction_constr
 	 princ'
-	 pat
+	 (None,pat)
          None)
       subst_and_reduce
       g
diff --git a/contrib/funind/invfun.ml b/contrib/funind/invfun.ml
index 63d44916..f62d70ab 100644
--- a/contrib/funind/invfun.ml
+++ b/contrib/funind/invfun.ml
@@ -280,13 +280,13 @@ let prove_fun_correct functional_induction funs_constr graphs_constr schemes lem
       List.map
 	(fun (_,_,br_type) ->
 	   List.map
-	     (fun id -> Genarg.IntroIdentifier id)
+	     (fun id -> dummy_loc, Genarg.IntroIdentifier id)
 	     (generate_fresh_id (id_of_string "y") ids (List.length (fst (decompose_prod_assum br_type))))
 	)
 	branches
     in
     (* before building the full intro pattern for the principle *)
-    let pat = Genarg.IntroOrAndPattern intro_pats in
+    let pat = Some (dummy_loc,Genarg.IntroOrAndPattern intro_pats) in
     let eq_ind = Coqlib.build_coq_eq () in
     let eq_construct = mkConstruct((destInd eq_ind),1) in
     (* The next to referencies will be used to find out which constructor to apply in each branch *)
@@ -297,7 +297,7 @@ let prove_fun_correct functional_induction funs_constr graphs_constr schemes lem
       (* We get the identifiers of this branch *)
       let this_branche_ids =
 	List.fold_right
-	  (fun pat acc ->
+	  (fun (_,pat) acc ->
 	     match pat with
 	       | Genarg.IntroIdentifier id -> Idset.add id acc
 	       | _ -> anomaly "Not an identifier"
@@ -447,7 +447,7 @@ let prove_fun_correct functional_induction funs_constr graphs_constr schemes lem
       [ observe_tac "intro args_names" (tclMAP h_intro args_names);
 	observe_tac "principle" (forward
 	  (Some (h_exact f_principle))
-	  (Genarg.IntroIdentifier principle_id)
+	  (dummy_loc,Genarg.IntroIdentifier principle_id)
 	  princ_type);
 	tclTHEN_i
 	  (observe_tac "functional_induction" (
@@ -948,7 +948,7 @@ let functional_inversion kn hid fconst f_correct : tactic =
 	    h_generalize [applist(f_correct,(Array.to_list f_args)@[res;mkVar hid])];
 	    thin [hid];
 	    h_intro hid;
-	    Inv.inv FullInversion Genarg.IntroAnonymous (Rawterm.NamedHyp hid);
+	    Inv.inv FullInversion None (Rawterm.NamedHyp hid);
 	    (fun g ->
 	       let new_ids = List.filter (fun id -> not (Idset.mem id old_ids)) (pf_ids_of_hyps g) in 
 	       tclMAP (revert_graph kn pre_tac)  (hid::new_ids)  g
diff --git a/contrib/funind/recdef.ml b/contrib/funind/recdef.ml
index c9bf2f1f..5bd7a6b2 100644
--- a/contrib/funind/recdef.ml
+++ b/contrib/funind/recdef.ml
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: recdef.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: recdef.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Term
 open Termops
@@ -1157,7 +1157,7 @@ let rec introduce_all_values_eq cont_tac functional termine
       [] ->
        let heq2 = next_global_ident_away true heq_id ids in
 	tclTHENLIST
-	  [forward None (IntroIdentifier heq2)
+	  [forward None (dummy_loc,IntroIdentifier heq2)
              (mkApp(mkVar heq1, [|f_S(f_S(mkVar pmax))|]));
            simpl_iter (onHyp heq2);
            unfold_in_hyp [((true,[1]), evaluable_of_global_reference 
diff --git a/contrib/interface/blast.ml b/contrib/interface/blast.ml
index 6ec0fac4..767a7dd6 100644
--- a/contrib/interface/blast.ml
+++ b/contrib/interface/blast.ml
@@ -161,21 +161,22 @@ let rec e_trivial_fail_db db_list local_db goal =
 	  let d = pf_last_hyp g' in
 	  let hintl = make_resolve_hyp (pf_env g') (project g') d in
           (e_trivial_fail_db db_list
-	     (add_hint_list hintl local_db) g'))) ::
+	     (Hint_db.add_list hintl local_db) g'))) ::
     (List.map fst (e_trivial_resolve db_list local_db (pf_concl goal)) )
   in 
   tclFIRST (List.map tclCOMPLETE tacl) goal 
 
 and e_my_find_search db_list local_db hdc concl = 
   let hdc = head_of_constr_reference hdc in
-  let flags = Auto.auto_unif_flags in
   let hintl =
     if occur_existential concl then 
-      list_map_append (fun (st, db) -> List.map (fun x -> ({flags with Unification.modulo_delta = st}, x))
-	(Hint_db.map_all hdc db)) (local_db::db_list)
+      list_map_append (fun db -> 
+	let flags = {Auto.auto_unif_flags with Unification.modulo_delta = Hint_db.transparent_state db} in
+	  List.map (fun x -> flags, x) (Hint_db.map_all hdc db)) (local_db::db_list)
     else 
-      list_map_append (fun (st, db) -> List.map (fun x -> ({flags with Unification.modulo_delta = st}, x)) 
-	(Hint_db.map_auto (hdc,concl) db)) (local_db::db_list)
+      list_map_append (fun db -> 
+	let flags = {Auto.auto_unif_flags with Unification.modulo_delta = Hint_db.transparent_state db} in
+	  List.map (fun x -> flags, x) (Hint_db.map_auto (hdc,concl) db)) (local_db::db_list)
   in 
   let tac_of_hint = 
     fun (st, ({pri=b; pat = p; code=t} as _patac)) -> 
@@ -279,7 +280,7 @@ module MySearchProblem = struct
 	     let hintl = 
 	       make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
 	     in
-             let ldb = add_hint_list hintl (List.hd s.localdb) in
+             let ldb = Hint_db.add_list hintl (List.hd s.localdb) in
 	     { depth = s.depth; tacres = res; 
 	       last_tactic = pp; dblist = s.dblist;
 	       localdb = ldb :: List.tl s.localdb })
@@ -375,7 +376,7 @@ let rec trivial_fail_db db_list local_db gl =
     tclTHEN intro 
       (fun g'->
 	 let hintl = make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
-	 in trivial_fail_db db_list (add_hint_list hintl local_db) g')
+	 in trivial_fail_db db_list (Hint_db.add_list hintl local_db) g')
   in
   tclFIRST 
     (assumption::intro_tac::
@@ -383,14 +384,15 @@ let rec trivial_fail_db db_list local_db gl =
 	(trivial_resolve db_list local_db (pf_concl gl)))) gl
 
 and my_find_search db_list local_db hdc concl =
-  let flags = Auto.auto_unif_flags in
   let tacl = 
     if occur_existential concl then 
-      list_map_append (fun (st, db) -> List.map (fun x -> {flags with Unification.modulo_delta = st}, x) 
-	(Hint_db.map_all hdc db)) (local_db::db_list)
+      list_map_append (fun db -> 
+	let flags = {Auto.auto_unif_flags with Unification.modulo_delta = Hint_db.transparent_state db} in
+	  List.map (fun x -> flags, x) (Hint_db.map_all hdc db)) (local_db::db_list)
     else 
-      list_map_append (fun (st, db) -> List.map (fun x -> {flags with Unification.modulo_delta = st}, x)
-	(Hint_db.map_auto (hdc,concl) db)) (local_db::db_list)
+      list_map_append (fun db -> 
+	let flags = {Auto.auto_unif_flags with Unification.modulo_delta = Hint_db.transparent_state db} in
+	  List.map (fun x -> flags, x) (Hint_db.map_auto (hdc,concl) db)) (local_db::db_list)
   in
   List.map 
     (fun (st, {pri=b; pat=p; code=t} as _patac) -> 
@@ -477,7 +479,7 @@ let rec search_gen decomp n db_list local_db extra_sign goal =
 	   with Failure _ -> [] 
 	 in
          (free_try
-	  (search_gen decomp n db_list (add_hint_list hintl local_db) [d])
+	  (search_gen decomp n db_list (Hint_db.add_list hintl local_db) [d])
 	  g'))
   in
   let rec_tacs = 
diff --git a/contrib/interface/depends.ml b/contrib/interface/depends.ml
index dd40c5cc..203bc9e3 100644
--- a/contrib/interface/depends.ml
+++ b/contrib/interface/depends.ml
@@ -57,8 +57,7 @@ let explore_tree pfs =
   and explain_prim = function
     | Refine c -> "Refine " ^ (string_of_ppcmds (Printer.prterm c))
     | Intro identifier -> "Intro"
-    | Intro_replacing identifier -> "Intro_replacing"
-    | Cut (bool, identifier, types) -> "Cut"
+    | Cut (bool, _, identifier, types) -> "Cut"
     | FixRule (identifier, int, l) -> "FixRule"
     | Cofix (identifier, l) -> "Cofix"
     | Convert_concl (types, cast_kind) -> "Convert_concl"
@@ -269,7 +268,7 @@ let rec depends_of_gen_tactic_expr depends_of_'constr depends_of_'ind depends_of
 	     igtal
 	     acc)
     | TacMatch (_, tac, tacexpr_mrl) -> failwith "depends_of_tacexpr of a Match not implemented yet"
-    | TacMatchContext (_, _, tacexpr_mrl) -> failwith "depends_of_tacexpr of a Match Context not implemented yet"
+    | TacMatchGoal (_, _, tacexpr_mrl) -> failwith "depends_of_tacexpr of a Match Context not implemented yet"
     | TacFun tacfa -> depends_of_tac_fun_ast tacfa acc
     | TacArg tacarg -> depends_of_tac_arg tacarg acc
   and depends_of_atomic_tacexpr atexpr acc = let depends_of_'constr_with_bindings = depends_of_'a_with_bindings depends_of_'constr in match atexpr with
@@ -281,7 +280,8 @@ let rec depends_of_gen_tactic_expr depends_of_'constr depends_of_'ind depends_of
     | TacExact          c
     | TacExactNoCheck   c
     | TacVmCastNoCheck  c  -> depends_of_'constr c acc
-    | TacApply (_, _, cb) -> depends_of_'constr_with_bindings cb acc
+    | TacApply (_, _, [cb]) -> depends_of_'constr_with_bindings cb acc
+    | TacApply (_, _, _) -> failwith "TODO"
     | TacElim (_, cwb, cwbo) ->
 	depends_of_'constr_with_bindings cwb
 	  (Option.fold_right depends_of_'constr_with_bindings cwbo acc)
@@ -302,14 +302,13 @@ let rec depends_of_gen_tactic_expr depends_of_'constr depends_of_'ind depends_of
     | TacLetTac (_,c,_,_) -> depends_of_'constr c acc
 
     (* Derived basic tactics *)
-    | TacSimpleInduction _
-    | TacSimpleDestruct  _
+    | TacSimpleInductionDestruct _
     | TacDoubleInduction _ -> acc
-    | TacNewInduction (_, cwbial, cwbo, _, _)
-    | TacNewDestruct (_, cwbial, cwbo, _, _) ->
+    | TacInductionDestruct (_, _, [cwbial, cwbo, _, _]) ->
 	list_union_map (depends_of_'a_induction_arg depends_of_'constr_with_bindings)
 	  cwbial
 	  (Option.fold_right depends_of_'constr_with_bindings cwbo acc)
+    | TacInductionDestruct (_, _, _) -> failwith "TODO"
     | TacDecomposeAnd c
     | TacDecomposeOr  c -> depends_of_'constr c acc
     | TacDecompose (il, c) -> depends_of_'constr c (list_union_map depends_of_'ind il acc)
@@ -410,8 +409,7 @@ let depends_of_compound_rule cr acc = match cr with
 and depends_of_prim_rule pr acc = match pr with
   | Refine c                     -> depends_of_constr c acc
   | Intro id                     -> acc
-  | Intro_replacing id           -> acc
-  | Cut (_, _, t)                -> depends_of_constr t acc (* TODO: check what 2nd argument contains *)
+  | Cut (_, _, _, t)             -> depends_of_constr t acc (* TODO: check what 3nd argument contains *)
   | FixRule (_, _, l)            -> list_union_map (o depends_of_constr trd_of_3) l acc (* TODO: check what the arguments contain *)
   | Cofix (_, l)                 -> list_union_map (o depends_of_constr snd) l acc (* TODO: check what the arguments contain *)
   | Convert_concl (t, _)         -> depends_of_constr t acc
diff --git a/contrib/interface/pbp.ml b/contrib/interface/pbp.ml
index 06b957d9..65eadf13 100644
--- a/contrib/interface/pbp.ml
+++ b/contrib/interface/pbp.ml
@@ -48,7 +48,7 @@ type pbp_atom =
   | PbpTryClear of identifier list
   | PbpGeneralize of identifier * identifier list
   | PbpLApply of identifier (* = CutAndApply *)
-  | PbpIntros of intro_pattern_expr list
+  | PbpIntros of intro_pattern_expr located list
   | PbpSplit
   (* Existential *)
   | PbpExists of identifier
@@ -93,7 +93,7 @@ type pbp_rule = (identifier list *
                     pbp_sequence option;;
 
 
-let make_named_intro id = PbpIntros [IntroIdentifier id];;
+let make_named_intro id = PbpIntros [zz,IntroIdentifier id];;
 
 let make_clears str_list = PbpThen [PbpTryClear str_list]
 
@@ -171,7 +171,7 @@ let make_pbp_atomic_tactic = function
   | PbpRight -> TacAtom (zz, TacRight (false,NoBindings))
   | PbpIntros l -> TacAtom (zz, TacIntroPattern l)
   | PbpLApply h -> TacAtom (zz, TacLApply (make_var h))
-  | PbpApply h -> TacAtom (zz, TacApply (true,false,(make_var h,NoBindings)))
+  | PbpApply h -> TacAtom (zz, TacApply (true,false,[make_var h,NoBindings]))
   | PbpElim (hyp_name, names) ->
       let bind = List.map (fun s ->(zz,NamedHyp s,make_pbp_pattern s)) names in
       TacAtom
@@ -255,9 +255,9 @@ fun avoid c path -> match kind_of_term c, path with
 	or_and_tree_to_intro_pattern (id2::avoid) cont_expr path in
       let patt_list = 
 	if a = 1 then
-	  [cont_patt; IntroIdentifier id2]
+	  [zz,cont_patt; zz,IntroIdentifier id2]
 	else
-	  [IntroIdentifier id2; cont_patt] in
+	  [zz,IntroIdentifier id2; zz,cont_patt] in
       	(IntroOrAndPattern[patt_list], avoid_names, id, c, path, rank, 
 	 total_branches)
   | (App(oper, [|c1; c2|]), 2::3::path)
@@ -268,7 +268,7 @@ fun avoid c path -> match kind_of_term c, path with
 	     let id1 = next_global_ident x avoid in
 	     let cont_patt, avoid_names, id, c, path, rank, total_branches =
 	       or_and_tree_to_intro_pattern (id1::avoid) body path in
-	     (IntroOrAndPattern[[IntroIdentifier id1; cont_patt]],
+	     (IntroOrAndPattern[[zz,IntroIdentifier id1; zz,cont_patt]],
 	      avoid_names, id, c, path, rank, total_branches)
 	 | _ -> assert false)
   | (App(oper, [|c1; c2|]), 2::a::path)
@@ -282,9 +282,9 @@ fun avoid c path -> match kind_of_term c, path with
       let new_rank = if a = 1 then rank else rank+1 in
       let patt_list =
 	if a = 1 then
-	  [[cont_patt];[IntroIdentifier id2]]
+	  [[zz,cont_patt];[zz,IntroIdentifier id2]]
 	else
-	  [[IntroIdentifier id2];[cont_patt]] in
+	  [[zz,IntroIdentifier id2];[zz,cont_patt]] in
 	(IntroOrAndPattern patt_list, 
 	 avoid_names, id, c, path, new_rank, total_branches+1)
   | (_, path) -> let id = next_global_ident hyp_radix avoid in
@@ -305,13 +305,13 @@ let (imply_intro3: pbp_rule) = function
       let intro_patt, avoid_names, id, c, p, rank, total_branches =
 	or_and_tree_to_intro_pattern avoid prem path in
 	if total_branches = 1 then
-	  Some(chain_tactics [PbpIntros [intro_patt]]
+	  Some(chain_tactics [PbpIntros [zz,intro_patt]]
 		 (f avoid_names clear_names clear_flag (Some id)
 		    (kind_of_term c) path))
 	else
 	  Some
 	    (PbpThens
-	       ([PbpIntros [intro_patt]],
+	       ([PbpIntros [zz,intro_patt]],
 	    	auxiliary_goals clear_names clear_flag id
 		  (rank - 1)
 		  ((f avoid_names clear_names clear_flag (Some id)
@@ -667,7 +667,7 @@ let rec cleanup_clears str_list = function
 
 let rec optim3_aux str_list = function
     (PbpGeneralize (h,l1))::
-    (PbpIntros [IntroIdentifier s])::(PbpGeneralize (h',l2))::others
+    (PbpIntros [zz,IntroIdentifier s])::(PbpGeneralize (h',l2))::others
       when s=h' ->
       optim3_aux (s::str_list) (PbpGeneralize (h,l1@l2)::others)
   | (PbpTryClear names)::other ->
diff --git a/contrib/interface/showproof.ml b/contrib/interface/showproof.ml
index 953fb5e7..4b9c1332 100644
--- a/contrib/interface/showproof.ml
+++ b/contrib/interface/showproof.ml
@@ -1197,12 +1197,12 @@ let rec natural_ntree ig ntree =
 	  | TacAssumption -> natural_trivial ig lh g gs ltree
 	  | TacClear _ -> natural_clear ig lh g gs ltree
 (* Besoin de l'argument de la tactique *)
-	  | TacSimpleInduction (NamedHyp id) -> 
+	  | TacSimpleInductionDestruct (true,NamedHyp id) -> 
               natural_induction ig lh g gs ge id ltree false
 	  | TacExtend (_,"InductionIntro",[a]) -> 
               let id=(out_gen wit_ident a) in
               natural_induction ig lh g gs ge id ltree true
-	  | TacApply (_,false,(c,_)) -> natural_apply ig lh g gs (snd c) ltree
+	  | TacApply (_,false,[c,_]) -> natural_apply ig lh g gs (snd c) ltree
 	  | TacExact c -> natural_exact ig lh g gs (snd c) ltree
 	  | TacCut c -> natural_cut ig lh g gs (snd c) ltree
 	  | TacExtend (_,"CutIntro",[a]) ->
diff --git a/contrib/interface/xlate.ml b/contrib/interface/xlate.ml
index 7d1f57fe..da4908e5 100644
--- a/contrib/interface/xlate.ml
+++ b/contrib/interface/xlate.ml
@@ -615,8 +615,7 @@ let get_flag r =
   (* Rem: EVAR flag obsolète *)
   conv_flags, red_ids
 
-let rec xlate_intro_pattern =
- function
+let rec xlate_intro_pattern (loc,pat) = match pat with
   | IntroOrAndPattern [] -> assert false
   | IntroOrAndPattern (fp::ll) ->
       CT_disj_pattern
@@ -684,8 +683,8 @@ let xlate_one_unfold_block = function
 ;;
 
 let xlate_with_names = function
-    IntroAnonymous -> CT_coerce_ID_OPT_to_INTRO_PATT_OPT ctv_ID_OPT_NONE
-  | fp -> CT_coerce_INTRO_PATT_to_INTRO_PATT_OPT (xlate_intro_pattern fp)
+    None -> CT_coerce_ID_OPT_to_INTRO_PATT_OPT ctv_ID_OPT_NONE
+  | Some fp -> CT_coerce_INTRO_PATT_to_INTRO_PATT_OPT (xlate_intro_pattern fp)
 
 let rawwit_main_tactic = Pcoq.rawwit_tactic Pcoq.tactic_main_level
 
@@ -829,11 +828,11 @@ and xlate_tactic =
                          | [] -> assert false
                          | fst::others ->
                              CT_match_tac_rules(fst, others))
-   | TacMatchContext (_,_,[]) | TacMatchContext (true,_,_) -> failwith ""
-   | TacMatchContext (false,false,rule1::rules) ->
+   | TacMatchGoal (_,_,[]) | TacMatchGoal (true,_,_) -> failwith ""
+   | TacMatchGoal (false,false,rule1::rules) ->
          CT_match_context(xlate_context_rule rule1,
                           List.map xlate_context_rule rules)
-   | TacMatchContext (false,true,rule1::rules) ->
+   | TacMatchGoal (false,true,rule1::rules) ->
          CT_match_context_reverse(xlate_context_rule rule1,
                           List.map xlate_context_rule rules)
    | TacLetIn (false, l, t) ->
@@ -926,23 +925,26 @@ and xlate_tac =
     | TacExtend (_,"contradiction",[]) -> CT_contradiction
     | TacDoubleInduction (n1, n2) ->
 	CT_tac_double (xlate_quantified_hypothesis n1, xlate_quantified_hypothesis n2)
-    | TacExtend (_,"discriminate", [idopt]) ->
+    | TacExtend (_,"discriminate", []) ->
+     CT_discriminate_eq (CT_coerce_ID_OPT_to_ID_OR_INT_OPT ctv_ID_OPT_NONE)
+    | TacExtend (_,"discriminate", [id]) ->
      CT_discriminate_eq
          (xlate_quantified_hypothesis_opt
-	    (out_gen (wit_opt rawwit_quant_hyp) idopt))
-    | TacExtend (_,"simplify_eq", [idopt]) ->
-	let idopt1 = out_gen (wit_opt rawwit_quant_hyp) idopt in
-	let idopt2 = match idopt1 with
-	    None -> CT_coerce_ID_OPT_to_ID_OR_INT_OPT
-		(CT_coerce_NONE_to_ID_OPT CT_none)
-	  | Some v ->
-	      CT_coerce_ID_OR_INT_to_ID_OR_INT_OPT
-	      	(xlate_quantified_hypothesis v) in
-	  CT_simplify_eq idopt2
-    | TacExtend (_,"injection", [idopt]) ->
+	    (Some (out_gen rawwit_quant_hyp id)))
+    | TacExtend (_,"simplify_eq", []) ->
+	  CT_simplify_eq (CT_coerce_ID_OPT_to_ID_OR_INT_OPT
+		(CT_coerce_NONE_to_ID_OPT CT_none))
+    | TacExtend (_,"simplify_eq", [id]) ->
+	let id1 = out_gen rawwit_quant_hyp id in
+	let id2 = CT_coerce_ID_OR_INT_to_ID_OR_INT_OPT
+	      	(xlate_quantified_hypothesis id1) in
+	  CT_simplify_eq id2
+    | TacExtend (_,"injection", []) ->
+     CT_injection_eq (CT_coerce_ID_OPT_to_ID_OR_INT_OPT ctv_ID_OPT_NONE)
+    | TacExtend (_,"injection", [id]) ->
      CT_injection_eq
          (xlate_quantified_hypothesis_opt
-	    (out_gen (wit_opt rawwit_quant_hyp) idopt))
+	    (Some (out_gen rawwit_quant_hyp id)))
     | TacExtend (_,"injection_as", [idopt;ipat]) ->
 	xlate_error "TODO: injection as"
     | TacFix (idopt, n) ->
@@ -967,19 +969,22 @@ and xlate_tac =
 	CT_intros_until (CT_coerce_ID_to_ID_OR_INT (xlate_ident id))
     | TacIntrosUntil (AnonHyp n) -> 
 	CT_intros_until (CT_coerce_INT_to_ID_OR_INT (CT_int n))
-    | TacIntroMove (Some id1, Some (_,id2)) ->
-     CT_intro_after(CT_coerce_ID_to_ID_OPT (xlate_ident id1),xlate_ident id2)
-    | TacIntroMove (None, Some (_,id2)) ->
-	CT_intro_after(CT_coerce_NONE_to_ID_OPT CT_none, xlate_ident id2)
-    | TacMove (true, id1, id2) ->
+    | TacIntroMove (Some id1, MoveAfter id2) ->
+     CT_intro_after(CT_coerce_ID_to_ID_OPT (xlate_ident id1),xlate_hyp id2)
+    | TacIntroMove (None, MoveAfter id2) ->
+	CT_intro_after(CT_coerce_NONE_to_ID_OPT CT_none, xlate_hyp id2)
+    | TacMove (true, id1, MoveAfter id2) ->
 	CT_move_after(xlate_hyp id1, xlate_hyp id2)
     | TacMove (false, id1, id2) -> xlate_error "Non dep Move is only internal"
+    | TacMove _ -> xlate_error "TODO: move before, at top, at bottom"
     | TacIntroPattern patt_list ->
 	CT_intros
 	  (CT_intro_patt_list (List.map xlate_intro_pattern patt_list))
-    | TacIntroMove (Some id, None) ->
+    | TacIntroMove (Some id, MoveToEnd true) ->
      CT_intros (CT_intro_patt_list[CT_coerce_ID_to_INTRO_PATT(xlate_ident id)])
-    | TacIntroMove (None, None) ->  CT_intro (CT_coerce_NONE_to_ID_OPT CT_none)
+    | TacIntroMove (None, MoveToEnd true) ->
+	CT_intro (CT_coerce_NONE_to_ID_OPT CT_none)
+    | TacIntroMove _ -> xlate_error "TODO"
     | TacLeft (false,bindl) -> CT_left (xlate_bindings bindl)
     | TacRight (false,bindl) -> CT_right (xlate_bindings bindl)
     | TacSplit (false,false,bindl) -> CT_split (xlate_bindings bindl)
@@ -1150,11 +1155,12 @@ and xlate_tac =
 	xlate_error "TODO: trivial using"
     | TacReduce (red, l) ->
      CT_reduce (xlate_red_tactic red, xlate_clause l)
-    | TacApply (true,false,(c,bindl)) ->
+    | TacApply (true,false,[c,bindl]) ->
      CT_apply (xlate_formula c, xlate_bindings bindl)
-    | TacApply (true,true,(c,bindl)) ->
+    | TacApply (true,true,[c,bindl]) ->
      CT_eapply (xlate_formula c, xlate_bindings bindl)
-    | TacApply (false,_,_) -> xlate_error "TODO: simple (e)apply"
+    | TacApply (_,_,_) ->
+	xlate_error "TODO: simple (e)apply and iterated apply"
     | TacConstructor (false,n_or_meta, bindl) ->
 	let n = match n_or_meta with AI n -> n | MetaId _ -> xlate_error ""
 	in CT_constructor (CT_int n, xlate_bindings bindl)
@@ -1178,10 +1184,12 @@ and xlate_tac =
     | TacCase (false,(c1,sl)) ->
      CT_casetac (xlate_formula c1, xlate_bindings sl)
     | TacElim (true,_,_) | TacCase (true,_)
-    | TacNewDestruct (true,_,_,_,_) | TacNewInduction (true,_,_,_,_) ->
+    | TacInductionDestruct (_,true,_) ->
 	xlate_error "TODO: eelim, ecase, edestruct, einduction"
-    | TacSimpleInduction h -> CT_induction (xlate_quantified_hypothesis h)
-    | TacSimpleDestruct h -> CT_destruct (xlate_quantified_hypothesis h)
+    | TacSimpleInductionDestruct (true,h) ->
+	CT_induction (xlate_quantified_hypothesis h)
+    | TacSimpleInductionDestruct (false,h) ->
+	CT_destruct (xlate_quantified_hypothesis h)
     | TacCut c -> CT_cut (xlate_formula c)
     | TacLApply c -> CT_use (xlate_formula c)
     | TacDecompose ([],c) ->
@@ -1222,19 +1230,16 @@ and xlate_tac =
 	CT_dauto(xlate_int_or_var_opt_to_int_opt a, xlate_int_opt b)
     | TacDAuto (a, b, _) ->
 	xlate_error "TODO: dauto using"
-    | TacNewDestruct(false,a,b,c,None) ->
+    | TacInductionDestruct(true,false,[a,b,(None,c),None]) ->
 	CT_new_destruct
 	  (List.map  xlate_int_or_constr a, xlate_using b, 
 	   xlate_with_names c)
-    | TacNewInduction(false,a,b,c,None) ->
+    | TacInductionDestruct(false,false,[a,b,(None,c),None]) ->
 	CT_new_induction
 	  (List.map xlate_int_or_constr a, xlate_using b,
 	   xlate_with_names c)
-    | TacNewDestruct(false,a,b,c,_) -> xlate_error "TODO: destruct in"
-    | TacNewInduction(false,a,b,c,_) ->xlate_error "TODO: induction in"
-    (*| TacInstantiate (a, b, cl) -> 
-        CT_instantiate(CT_int a, xlate_formula b,
-		       assert false) *)
+    | TacInductionDestruct(_,false,_) -> 
+	xlate_error "TODO: clause 'in' and full 'as' of destruct/induction"
     | TacLetTac (na, c, cl, true) when cl = nowhere -> 
         CT_pose(xlate_id_opt_aux na, xlate_formula c)
     | TacLetTac (na, c, cl, true) ->
@@ -1243,13 +1248,13 @@ and xlate_tac =
 		     but the structures are different *)
 		  xlate_clause cl)
     | TacLetTac (na, c, cl, false) -> xlate_error "TODO: remember"
-    | TacAssert (None, IntroIdentifier id, c) -> 
+    | TacAssert (None, (_,IntroIdentifier id), c) -> 
         CT_assert(xlate_id_opt ((0,0),Name id), xlate_formula c)
-    | TacAssert (None, IntroAnonymous, c) -> 
+    | TacAssert (None, (_,IntroAnonymous), c) -> 
         CT_assert(xlate_id_opt ((0,0),Anonymous), xlate_formula c)
-    | TacAssert (Some (TacId []), IntroIdentifier id, c) -> 
+    | TacAssert (Some (TacId []), (_,IntroIdentifier id), c) -> 
         CT_truecut(xlate_id_opt ((0,0),Name id), xlate_formula c)
-    | TacAssert (Some (TacId []), IntroAnonymous, c) -> 
+    | TacAssert (Some (TacId []), (_,IntroAnonymous), c) -> 
         CT_truecut(xlate_id_opt ((0,0),Anonymous), xlate_formula c)
     | TacAssert _ ->
 	xlate_error "TODO: assert with 'as' and 'by' and pose proof with 'as'"
diff --git a/contrib/micromega/Micromegatac.v b/contrib/micromega/Micromegatac.v
deleted file mode 100644
index 13c7eace..00000000
--- a/contrib/micromega/Micromegatac.v
+++ /dev/null
@@ -1,79 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*                                                                      *)
-(* Micromega: A reflexive tactic using the Positivstellensatz           *)
-(*                                                                      *)
-(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
-(*                                                                      *)
-(************************************************************************)
-
-Require Import ZMicromega.
-Require Import QMicromega.
-Require Import RMicromega.
-Require Import QArith.
-Require Export Ring_normalize.
-Require Import ZArith.
-Require Import Raxioms.
-Require Export RingMicromega.
-Require Import VarMap.
-Require Tauto.
-
-Ltac micromegac dom d :=
-  let tac := lazymatch dom with
-  | Z => 
-    micromegap d ;
-    intros __wit __varmap __ff ; 
-    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
-    apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | R =>
-    rmicromegap d ;
-    intros __wit __varmap __ff ; 
-    change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ; 
-    apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | _ => fail "Unsupported domain"
-  end in tac.
-
-Tactic Notation "micromega" constr(dom) int_or_var(n) := micromegac dom n.
-Tactic Notation "micromega" constr(dom) := micromegac dom ltac:-1.
-
-Ltac zfarkas :=  omicronp ;
-  intros __wit __varmap __ff ; 
-  change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
-  apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
-
-Ltac omicron dom :=
-  let tac := lazymatch dom with
-  | Z =>
-    zomicronp ;
-    intros __wit __varmap __ff ;
-    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
-    apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | Q =>
-    qomicronp ; 
-    intros __wit __varmap __ff ; 
-    change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ; 
-    apply (QTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | R => 
-    romicronp ;
-    intros __wit __varmap __ff ;
-    change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ; 
-    apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | _ => fail "Unsupported domain"
-  end in tac.
-
-Ltac sos dom :=
-  let tac := lazymatch dom with
-  | Z =>
-    sosp ;
-    intros __wit __varmap __ff ;
-    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
-    apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
-  | _ => fail "Unsupported domain"
-  end in tac.
-
-
diff --git a/contrib/micromega/Psatz.v b/contrib/micromega/Psatz.v
new file mode 100644
index 00000000..b2dd9910
--- /dev/null
+++ b/contrib/micromega/Psatz.v
@@ -0,0 +1,75 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+(*                                                                      *)
+(* Micromega: A reflexive tactic using the Positivstellensatz           *)
+(*                                                                      *)
+(*  Frédéric Besson (Irisa/Inria) 2006-2008                             *)
+(*                                                                      *)
+(************************************************************************)
+
+Require Import ZMicromega.
+Require Import QMicromega.
+Require Import RMicromega.
+Require Import QArith.
+Require Export Ring_normalize.
+Require Import ZArith.
+Require Import Raxioms.
+Require Export RingMicromega.
+Require Import VarMap.
+Require Tauto.
+
+Ltac xpsatz dom d :=
+  let tac := lazymatch dom with
+  | Z => 
+    (sos_Z || psatz_Z d) ;
+    intros __wit __varmap __ff ; 
+    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
+    apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | R =>
+    (sos_R || psatz_R d) ;
+    intros __wit __varmap __ff ; 
+    change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ; 
+    apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | Q =>
+      (sos_Q || psatz_Q d) ;
+    intros __wit __varmap __ff ; 
+    change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ; 
+    apply (QTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | _ => fail "Unsupported domain"
+  end in tac.
+
+Tactic Notation "psatz" constr(dom) int_or_var(n) := xpsatz dom n.
+Tactic Notation "psatz" constr(dom) := xpsatz dom ltac:-1.
+
+Ltac psatzl dom :=
+  let tac := lazymatch dom with
+  | Z =>
+    psatzl_Z ;
+    intros __wit __varmap __ff ;
+    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
+    apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | Q =>
+    psatzl_Q ; 
+    intros __wit __varmap __ff ; 
+    change (Tauto.eval_f (Qeval_formula (@find Q 0%Q __varmap)) __ff) ; 
+    apply (QTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | R => 
+    psatzl_R ;
+    intros __wit __varmap __ff ;
+    change (Tauto.eval_f (Reval_formula (@find R 0%R __varmap)) __ff) ; 
+    apply (RTautoChecker_sound __ff __wit); vm_compute ; reflexivity
+  | _ => fail "Unsupported domain"
+  end in tac.
+
+
+
+Ltac lia := 
+  xlia ;
+  intros __wit __varmap __ff ;
+    change (Tauto.eval_f (Zeval_formula (@find Z Z0 __varmap)) __ff) ; 
+      apply (ZTautoChecker_sound __ff __wit); vm_compute ; reflexivity.
diff --git a/contrib/micromega/QMicromega.v b/contrib/micromega/QMicromega.v
index 9e95f6c4..c054f218 100644
--- a/contrib/micromega/QMicromega.v
+++ b/contrib/micromega/QMicromega.v
@@ -16,38 +16,11 @@ Require Import OrderedRing.
 Require Import RingMicromega.
 Require Import Refl.
 Require Import QArith.
-Require Import Qring.
-
-(* Qsrt has been removed from the library ? *)
-Definition Qsrt : ring_theory 0 1 Qplus Qmult Qminus Qopp Qeq.
-Proof.
-  constructor.
-  exact Qplus_0_l.
-  exact Qplus_comm.
-  exact Qplus_assoc.
-  exact Qmult_1_l.
-  exact Qmult_comm.
-  exact Qmult_assoc.
-  exact Qmult_plus_distr_l.
-  reflexivity.
-  exact Qplus_opp_r.
-Qed.
-
-
-Add Ring Qring : Qsrt.
-
-Lemma Qmult_neutral : forall x , 0 * x == 0.
-Proof.
-  intros.
-  compute.
-  reflexivity.
-Qed.
-
-(* Is there any qarith database ? *)
+Require Import Qfield.
 
 Lemma Qsor : SOR 0 1 Qplus Qmult Qminus Qopp Qeq  Qle Qlt.
 Proof.
-  constructor; intros ; subst ; try (intuition (subst; auto  with qarith)).
+  constructor; intros ; subst ; try (intuition (subst; auto with qarith)).
   apply Q_Setoid.
   rewrite H ; rewrite H0 ; reflexivity.
   rewrite H ; rewrite H0 ; reflexivity.
@@ -67,45 +40,12 @@ Proof.
   destruct(Q_dec n m) as [[H1 |H1] | H1 ] ; tauto.
   apply (Qplus_le_compat  p p n m  (Qle_refl p) H).
   generalize (Qmult_lt_compat_r 0 n m H0 H).
-  rewrite Qmult_neutral.
+  rewrite Qmult_0_l.
   auto.
   compute in H.
   discriminate.
 Qed.
 
-Definition Qeq_bool (p q : Q) : bool := Zeq_bool (Qnum p * ' Qden q)%Z  (Qnum q * ' Qden p)%Z.
-
-Definition Qle_bool (x y : Q) : bool := Zle_bool (Qnum x * ' Qden y)%Z (Qnum y * ' Qden x)%Z.
-
-Require ZMicromega.
-
-Lemma Qeq_bool_ok : forall x y, Qeq_bool x y = true -> x == y.
-Proof.
-  intros.
-  unfold Qeq_bool in H.
-  unfold Qeq.
-  apply (Zeqb_ok  _ _ H).
-Qed.
-
-
-Lemma Qeq_bool_neq : forall x y, Qeq_bool x y = false -> ~ x == y.
-Proof.
-  unfold Qeq_bool,Qeq.
-  red ; intros ; subst.
-  rewrite H0 in H.
-  apply  (ZMicromega.Zeq_bool_neq _ _ H).
-  reflexivity.
-Qed.
-
-Lemma Qle_bool_imp_le : forall x y : Q, Qle_bool x y = true -> x <= y.
-Proof.
-  unfold Qle_bool, Qle.
-  intros.
-  apply Zle_bool_imp_le ; auto.
-Qed.
-  
-
-
 
 Lemma QSORaddon :
   SORaddon 0 1 Qplus Qmult Qminus Qopp  Qeq  Qle (* ring elements *)
@@ -115,7 +55,7 @@ Lemma QSORaddon :
 Proof.
   constructor.
   constructor ; intros ; try reflexivity.
-  apply Qeq_bool_ok ; auto.
+  apply Qeq_bool_eq; auto.
   constructor.
   reflexivity.
   intros x y.
@@ -173,9 +113,9 @@ match o with
 | OpEq =>  Qeq
 | OpNEq => fun x y  => ~ x == y
 | OpLe => Qle
-| OpGe => Qge
+| OpGe => fun x y => Qle y x
 | OpLt => Qlt
-| OpGt => Qgt
+| OpGt => fun x y => Qlt y x
 end.
 
 Definition Qeval_formula (e:PolEnv Q) (ff : Formula Q) :=
diff --git a/contrib/micromega/RMicromega.v b/contrib/micromega/RMicromega.v
index ef28db32..7c6969c2 100644
--- a/contrib/micromega/RMicromega.v
+++ b/contrib/micromega/RMicromega.v
@@ -76,12 +76,12 @@ Proof.
   apply mult_IZR.
   apply Ropp_Ropp_IZR.
   apply IZR_eq.
-  apply Zeqb_ok ; auto.
+  apply Zeq_bool_eq ; auto.
   apply R_power_theory.
   intros x y.
   intro.
   apply IZR_neq.
-  apply ZMicromega.Zeq_bool_neq ; auto.
+  apply Zeq_bool_neq ; auto.
   intros. apply IZR_le.  apply Zle_bool_imp_le. auto.
 Qed.
 
@@ -97,9 +97,34 @@ Definition INZ (n:N) : R :=
 Definition Reval_expr := eval_pexpr  Rplus Rmult Rminus Ropp IZR Nnat.nat_of_N pow.
 
 
-Definition Reval_formula :=
+Definition Reval_op2 (o:Op2) : R -> R -> Prop :=
+    match o with
+      | OpEq =>  @eq R
+      | OpNEq => fun x y  => ~ x = y
+      | OpLe => Rle
+      | OpGe => Rge
+      | OpLt => Rlt
+      | OpGt => Rgt
+    end.
+
+
+Definition Reval_formula (e: PolEnv R) (ff : Formula Z) :=
+  let (lhs,o,rhs) := ff in Reval_op2 o (Reval_expr e lhs) (Reval_expr e rhs).
+
+Definition Reval_formula' :=
   eval_formula  Rplus Rmult Rminus Ropp (@eq R) Rle Rlt IZR Nnat.nat_of_N pow.
 
+Lemma Reval_formula_compat : forall env f, Reval_formula env f <-> Reval_formula' env f.
+Proof.
+  intros.
+  unfold Reval_formula.
+  destruct f.
+  unfold Reval_formula'.
+  unfold Reval_expr.
+  split ; destruct Fop ; simpl ; auto.
+  apply Rge_le.
+  apply Rle_ge.
+Qed.
 
 Definition Reval_nformula :=
   eval_nformula 0 Rplus Rmult Rminus Ropp (@eq R) Rle Rlt IZR Nnat.nat_of_N pow.
@@ -139,8 +164,9 @@ Proof.
   unfold RTautoChecker.
   apply (tauto_checker_sound  Reval_formula Reval_nformula).
   apply Reval_nformula_dec.
-  intros. unfold Reval_formula. now apply (cnf_normalise_correct Rsor).
-  intros. unfold Reval_formula. now apply (cnf_negate_correct Rsor).
+  intros. rewrite Reval_formula_compat.
+  unfold Reval_formula'. now apply (cnf_normalise_correct Rsor).
+  intros. rewrite Reval_formula_compat. unfold Reval_formula. now apply (cnf_negate_correct Rsor).
   intros t w0.
   apply RWeakChecker_sound.
 Qed.
diff --git a/contrib/micromega/ZMicromega.v b/contrib/micromega/ZMicromega.v
index 94c83f73..0855925a 100644
--- a/contrib/micromega/ZMicromega.v
+++ b/contrib/micromega/ZMicromega.v
@@ -39,15 +39,6 @@ Proof.
   apply Zmult_lt_0_compat ; auto.
 Qed.
 
-Lemma Zeq_bool_neq : forall x y, Zeq_bool x y = false -> x <> y.
-Proof.
-  red ; intros.
-  subst.
-  unfold Zeq_bool in H.
-  rewrite Zcompare_refl  in H.
-  discriminate.
-Qed.
-
 Lemma ZSORaddon :
   SORaddon 0 1 Zplus Zmult Zminus Zopp  (@eq Z) Zle (* ring elements *)
   0%Z 1%Z Zplus Zmult Zminus Zopp (* coefficients *)
@@ -56,7 +47,7 @@ Lemma ZSORaddon :
 Proof.
   constructor.
   constructor ; intros ; try reflexivity.
-  apply Zeqb_ok ; auto.
+  apply Zeq_bool_eq ; auto.
   constructor.
   reflexivity.
   intros x y.
diff --git a/contrib/micromega/certificate.ml b/contrib/micromega/certificate.ml
index 88e882e6..f4efcd08 100644
--- a/contrib/micromega/certificate.ml
+++ b/contrib/micromega/certificate.ml
@@ -108,7 +108,7 @@ struct
   if compare_num v (Int 0) <> 0
   then 
    if Monomial.compare Monomial.const k = 0
-   then 	Printf.fprintf o "%s " (string_of_num v)
+   then         Printf.fprintf o "%s " (string_of_num v)
    else Printf.fprintf o "%s*%a " (string_of_num v) Monomial.pp k) p  
 
  (* Get the coefficient of monomial mn *)
@@ -304,8 +304,8 @@ let factorise_linear_cone c =
       (match pending with
        | None -> rebuild_cone l (Some e) 
        | Some p -> (match factorise p e with
-	  | None -> Mc.S_Add(p, rebuild_cone l (Some e))
-	  | Some f -> rebuild_cone l (Some f) )
+          | None -> Mc.S_Add(p, rebuild_cone l (Some e))
+          | Some f -> rebuild_cone l (Some f) )
       ) in
 
   (rebuild_cone (List.sort Pervasives.compare (cone_list c [])) None)
@@ -387,10 +387,10 @@ let build_linear_system l =
   (* I need at least something strictly positive *)
  let strict = {
   coeffs = Vect.from_list ((Big_int unit_big_int)::
-			    (List.map (fun (x,y) -> 
-			     match y with Mc.Strict -> 
-			      Big_int unit_big_int 
-			      | _ -> Big_int zero_big_int) l));
+                            (List.map (fun (x,y) -> 
+                             match y with Mc.Strict -> 
+                              Big_int unit_big_int 
+                              | _ -> Big_int zero_big_int) l));
   op = Ge ; cst = Big_int unit_big_int } in
   (* Add the positivity constraint *)
   {coeffs = Vect.from_list ([Big_int unit_big_int]) ; 
@@ -414,22 +414,22 @@ let make_certificate n_spec cert li =
       in
       let rec scalar_product cert l =
        match cert with
-	| [] -> Mc.S_Z
-	| c::cert -> match l with
-	   | [] -> failwith "make_certificate(1)"
-	   | i::l ->  
-	      let r = scalar_product cert l in
-	       match compare_big_int c  zero_big_int with
-		| -1 -> Mc.S_Add (
-		   Mc.S_Ideal (Mc.PEc ( bint_to_cst c), Mc.S_In (Ml2C.nat i)), 
-		   r)
-		| 0  -> r
-		| _ ->  Mc.S_Add (
-		   Mc.S_Mult (Mc.S_Pos (bint_to_cst c), Mc.S_In (Ml2C.nat i)),
-		   r) in
+        | [] -> Mc.S_Z
+        | c::cert -> match l with
+           | [] -> failwith "make_certificate(1)"
+           | i::l ->  
+              let r = scalar_product cert l in
+               match compare_big_int c  zero_big_int with
+                | -1 -> Mc.S_Add (
+                   Mc.S_Ideal (Mc.PEc ( bint_to_cst c), Mc.S_In (Ml2C.nat i)), 
+                   r)
+                | 0  -> r
+                | _ ->  Mc.S_Add (
+                   Mc.S_Mult (Mc.S_Pos (bint_to_cst c), Mc.S_In (Ml2C.nat i)),
+                   r) in
        
       Some ((factorise_linear_cone 
-	      (simplify_cone n_spec (Mc.S_Add (cst, scalar_product cert' li)))))
+              (simplify_cone n_spec (Mc.S_Add (cst, scalar_product cert' li)))))
 
 
 exception Found of Monomial.t
@@ -444,7 +444,7 @@ let raw_certificate l =
   with x -> 
    if debug 
    then (Printf.printf "raw certificate %s" (Printexc.to_string x);   
-	 flush stdout) ;
+         flush stdout) ;
    None
 
 
@@ -462,9 +462,9 @@ let linear_prover n_spec l  =
   (fun (x,_) -> if snd' x = Mc.NonEqual then true else false) li in
  let l' = List.map 
   (fun (c,i) -> let (Mc.Pair(x,y)) = c in 
-		 match y with 
-		   Mc.NonEqual -> failwith "cannot happen" 
-		  |  y -> ((dev_form n_spec x, y),i)) l' in
+                 match y with 
+                   Mc.NonEqual -> failwith "cannot happen" 
+                  |  y -> ((dev_form n_spec x, y),i)) l' in
   
   simple_linear_prover n_spec l' 
 
@@ -513,106 +513,228 @@ let rec remove_assoc p x l =
 
 let eq x y = Vect.compare x y = 0
 
-(* Beurk... this code is a shame *)
+let  remove e  l  = List.fold_left (fun l x -> if eq x e then l else x::l) [] l
 
-let rec zlinear_prover sys = xzlinear_prover [] sys
 
-and xzlinear_prover enum l :  (Mc.proofTerm option) = 
- match linear_prover z_spec l with
-  | Some prf ->  Some (Mc.RatProof prf)
-  | None     ->  
+(* The prover is (probably) incomplete --
+   only searching for naive cutting planes *)
+
+let candidates sys = 
+ let ll = List.fold_right (
+  fun (Mc.Pair(e,k)) r -> 
+   match k with 
+    | Mc.NonStrict -> (dev_form z_spec e , Ge)::r
+    | Mc.Equal     ->  (dev_form z_spec e , Eq)::r 
+       (* we already know the bound -- don't compute it again *)
+    | _     -> failwith "Cannot happen candidates") sys [] in
+
+ let (sys,var_mn) = make_linear_system ll in
+ let vars = mapi (fun _ i -> Vect.set i (Int 1) Vect.null) var_mn in
+  (List.fold_left (fun l cstr ->   
+   let gcd = Big_int (Vect.gcd cstr.coeffs) in
+    if gcd =/ (Int 1) && cstr.op = Eq 
+    then l 
+    else  (Vect.mul (Int 1 // gcd) cstr.coeffs)::l) [] sys) @ vars
+
+
+let rec xzlinear_prover planes sys = 
+ match linear_prover z_spec sys with
+  | Some prf -> Some (Mc.RatProof prf)
+  | None     -> (* find the candidate with the smallest range *)
+     (* Grrr - linear_prover is also calling 'make_linear_system' *)
      let ll = List.fold_right (fun (Mc.Pair(e,k)) r -> match k with 
        Mc.NonEqual -> r  
       | k -> (dev_form z_spec e , 
-	     match k with
-	      | Mc.Strict | Mc.NonStrict -> Ge 
-		 (* Loss of precision -- weakness of fourier*)
-	      | Mc.Equal              -> Eq
-	      | Mc.NonEqual -> failwith "Cannot happen") :: r) l [] in
-
-     let (sys,var) = make_linear_system ll in
-     let res = 
-      match Fourier.find_Q_interval sys with
-       | Some(i,x,j) -> if i =/ j 
-	 then Some(i,Vect.set x (Int 1) Vect.null,i) else None 
-       | None -> None in
-     let res = match res with
-      | None ->
-	 begin
-	  let candidates = List.fold_right 
-	   (fun cstr acc -> 
-	    let gcd = Big_int (Vect.gcd cstr.coeffs) in
-	    let vect = Vect.mul (Int 1 // gcd) cstr.coeffs in
-	     if mem eq vect enum then acc
-	     else ((vect,Fourier.optimise vect sys)::acc)) sys [] in
-	  let candidates = List.fold_left (fun l (x,i) -> 
-	   match i with 
-	     None -> (x,Empty)::l 
-	    | Some i ->  (x,i)::l) [] (candidates) in
-	   match List.fold_left (fun (x1,i1) (x2,i2) -> 
-	    if smaller_itv i1 i2 
-	    then (x1,i1) else (x2,i2)) (Vect.null,Itv(None,None)) candidates 
-	   with
-	    | (i,Empty) -> None
-	    | (x,Itv(Some i, Some j))  -> Some(i,x,j)
-	    | (x,Point n) ->  Some(n,x,n)
-	    |   x        ->   match Fourier.find_Q_interval sys with
-		 | None -> None
-		 | Some(i,x,j) -> 
-		    if i =/ j 
-		    then Some(i,Vect.set x (Int 1) Vect.null,i) 
-		    else None 
-	 end
-      |   _ -> res in
-
-      match res with 
+             match k with
+               Mc.NonStrict -> Ge 
+              | Mc.Equal              -> Eq
+              | Mc.Strict | Mc.NonEqual -> failwith "Cannot happen") :: r) sys [] in
+     let (ll,var) = make_linear_system ll in
+     let candidates = List.fold_left (fun  acc vect -> 
+      match Fourier.optimise vect ll with
+       | None -> acc
+       | Some i -> 
+(*	  Printf.printf "%s in %s\n" (Vect.string vect) (string_of_intrvl i) ; *)
+	  flush stdout ; 
+	  (vect,i) ::acc)  [] planes in
+
+     let smallest_interval = 
+      match List.fold_left (fun (x1,i1) (x2,i2) -> 
+       if smaller_itv i1 i2 
+       then (x1,i1) else (x2,i2)) (Vect.null,Itv(None,None)) candidates 
+      with
+       | (x,Itv(Some i, Some j))  -> Some(i,x,j)
+       | (x,Point n) ->  Some(n,x,n)
+       |   x        ->   None (* This might be a cutting plane *)
+      in
+      match smallest_interval with
        | Some (lb,e,ub) -> 
-	  let (lbn,lbd) = 
-	   (Ml2C.bigint (sub_big_int (numerator lb)  unit_big_int),
-	   Ml2C.bigint (denominator lb)) in
-	  let (ubn,ubd) = 
-	   (Ml2C.bigint (add_big_int unit_big_int (numerator ub)) , 
-	   Ml2C.bigint (denominator ub)) in
-	  let expr = list_to_polynomial var (Vect.to_list e) in
-	   (match 
-	     (*x <= ub ->  x  > ub *)
-	     linear_prover  z_spec 
-	      (Mc.Pair(pplus (pmult (pconst ubd) expr) (popp (pconst  ubn)),
-		      Mc.NonStrict) :: l),
-	    (* lb <= x  -> lb > x *)
-	    linear_prover z_spec 
-	     (Mc.Pair( pplus  (popp (pmult  (pconst lbd) expr)) (pconst lbn) ,  
-		     Mc.NonStrict)::l) 
-	    with
-	     | Some cub , Some clb  ->   
-		(match zlinear_enum (e::enum)   expr 
-		  (ceiling_num lb)  (floor_num ub) l 
-		 with
-		 | None -> None
-		 | Some prf -> 
-		    Some (Mc.EnumProof(Ml2C.q lb,expr,Ml2C.q ub,clb,cub,prf)))
-	     | _ -> None
-	   )
+          let (lbn,lbd) = 
+           (Ml2C.bigint (sub_big_int (numerator lb)  unit_big_int),
+           Ml2C.bigint (denominator lb)) in
+          let (ubn,ubd) = 
+           (Ml2C.bigint (add_big_int unit_big_int (numerator ub)) , 
+           Ml2C.bigint (denominator ub)) in
+          let expr = list_to_polynomial var (Vect.to_list e) in
+           (match 
+             (*x <= ub ->  x  > ub *)
+             linear_prover  z_spec 
+              (Mc.Pair(pplus (pmult (pconst ubd) expr) (popp (pconst  ubn)),
+                      Mc.NonStrict) :: sys),
+            (* lb <= x  -> lb > x *)
+            linear_prover z_spec 
+             (Mc.Pair( pplus  (popp (pmult  (pconst lbd) expr)) (pconst lbn) ,  
+                     Mc.NonStrict)::sys) 
+            with
+             | Some cub , Some clb  ->   
+                (match zlinear_enum  (remove e planes)   expr 
+                  (ceiling_num lb)  (floor_num ub) sys 
+                 with
+                  | None -> None
+                  | Some prf -> 
+                     Some (Mc.EnumProof(Ml2C.q lb,expr,Ml2C.q ub,clb,cub,prf)))
+             | _ -> None
+           )
        |  _ -> None
-and xzlinear_enum enum expr clb cub l = 
+and zlinear_enum  planes expr clb cub l = 
  if clb >/  cub
  then Some Mc.Nil
  else 
   let pexpr = pplus (popp (pconst (Ml2C.bigint (numerator clb)))) expr in
   let sys' = (Mc.Pair(pexpr, Mc.Equal))::l in
-   match xzlinear_prover enum sys' with
+   (*let enum =  *)
+   match xzlinear_prover planes sys' with
     | None -> if debug then print_string "zlp?"; None
     | Some prf -> if debug then print_string "zlp!";
-    match zlinear_enum enum expr (clb +/ (Int 1)) cub l with
+    match zlinear_enum planes expr (clb +/ (Int 1)) cub l with
      | None -> None
      | Some prfl -> Some (Mc.Cons(prf,prfl))
 
-and zlinear_enum enum expr clb cub l = 
- let res = xzlinear_enum enum expr clb cub l in
-  if debug then Printf.printf "zlinear_enum %s %s -> %s\n" 
-   (string_of_num clb) 
-   (string_of_num cub) 
-   (match res with
-    | None -> "None"
-    | Some r -> "Some") ; res
+let zlinear_prover sys =  
+ let candidates = candidates sys in
+ (*  Printf.printf "candidates %d" (List.length candidates) ; *) 
+ xzlinear_prover candidates sys
+
+open Sos
+
+let rec scale_term t = 
+ match t with
+  | Zero    -> unit_big_int , Zero
+  | Const n ->  (denominator n) , Const (Big_int (numerator n))
+  | Var n   -> unit_big_int , Var n
+  | Inv _   -> failwith "scale_term : not implemented"
+  | Opp t   -> let s, t = scale_term t in s, Opp t
+  | Add(t1,t2) -> let s1,y1 = scale_term t1 and s2,y2 = scale_term t2 in
+    let g = gcd_big_int s1 s2 in
+    let s1' = div_big_int s1 g in
+    let s2' = div_big_int s2 g in
+    let e = mult_big_int g (mult_big_int s1' s2') in
+     if (compare_big_int e unit_big_int) = 0
+     then (unit_big_int, Add (y1,y2))
+     else 	e, Add (Mul(Const (Big_int s2'), y1),
+		       Mul (Const (Big_int s1'), y2))
+  | Sub _ -> failwith "scale term: not implemented"
+  | Mul(y,z) ->       let s1,y1 = scale_term y and s2,y2 = scale_term z in
+		       mult_big_int s1 s2 , Mul (y1, y2)
+  |  Pow(t,n) -> let s,t = scale_term t in
+		  power_big_int_positive_int s  n , Pow(t,n)
+  |   _ -> failwith "scale_term : not implemented"
+
+let scale_term t =
+ let (s,t') = scale_term t in
+  s,t'
+
+
+let get_index_of_ith_match f i l  =
+ let rec get j res l =
+  match l with
+   | [] -> failwith "bad index"
+   | e::l -> if f e
+     then 
+       (if j = i then res else get (j+1) (res+1) l )
+     else get j (res+1) l in
+  get 0 0 l
+
+
+let rec scale_certificate pos = match pos with
+ | Axiom_eq i ->  unit_big_int , Axiom_eq i
+ | Axiom_le i ->  unit_big_int , Axiom_le i
+ | Axiom_lt i ->   unit_big_int , Axiom_lt i
+ | Monoid l   -> unit_big_int , Monoid l
+ | Rational_eq n ->  (denominator n) , Rational_eq (Big_int (numerator n))
+ | Rational_le n ->  (denominator n) , Rational_le (Big_int (numerator n))
+ | Rational_lt n ->  (denominator n) , Rational_lt (Big_int (numerator n))
+ | Square t -> let s,t' =  scale_term t in 
+		mult_big_int s s , Square t'
+ | Eqmul (t, y) -> let s1,y1 = scale_term t and s2,y2 = scale_certificate y in
+		    mult_big_int s1 s2 , Eqmul (y1,y2)
+ | Sum (y, z) -> let s1,y1 = scale_certificate y 
+   and s2,y2 = scale_certificate z in
+   let g = gcd_big_int s1 s2 in
+   let s1' = div_big_int s1 g in
+   let s2' = div_big_int s2 g in
+    mult_big_int g (mult_big_int s1' s2'), 
+    Sum (Product(Rational_le (Big_int s2'), y1),
+	Product (Rational_le (Big_int s1'), y2))
+ | Product (y, z) -> 
+    let s1,y1 = scale_certificate y and s2,y2 = scale_certificate z in
+     mult_big_int s1 s2 , Product (y1,y2)
+
+
+open Micromega
+ let rec term_to_q_expr = function
+  | Const n ->  PEc (Ml2C.q n)
+  | Zero   ->  PEc ( Ml2C.q (Int 0))
+  | Var s   ->  PEX (Ml2C.index 
+		      (int_of_string (String.sub s 1 (String.length s - 1))))
+  | Mul(p1,p2) ->  PEmul(term_to_q_expr p1, term_to_q_expr p2)
+  | Add(p1,p2) ->   PEadd(term_to_q_expr p1, term_to_q_expr p2)
+  | Opp p ->   PEopp (term_to_q_expr p)
+  | Pow(t,n) ->  PEpow (term_to_q_expr t,Ml2C.n n)
+  | Sub(t1,t2) ->  PEsub (term_to_q_expr t1,  term_to_q_expr t2)
+  | _ -> failwith "term_to_q_expr: not implemented"
+
+let  q_cert_of_pos  pos = 
+ let rec _cert_of_pos = function
+   Axiom_eq i ->  Mc.S_In (Ml2C.nat i)
+  | Axiom_le i ->  Mc.S_In (Ml2C.nat i)
+  | Axiom_lt i ->  Mc.S_In (Ml2C.nat i)
+  | Monoid l  -> Mc.S_Monoid (Ml2C.list Ml2C.nat l)
+  | Rational_eq n | Rational_le n | Rational_lt n -> 
+     if compare_num n (Int 0) = 0 then Mc.S_Z else
+      Mc.S_Pos (Ml2C.q   n)
+  | Square t -> Mc.S_Square (term_to_q_expr  t)
+  | Eqmul (t, y) -> Mc.S_Ideal(term_to_q_expr t, _cert_of_pos y)
+  | Sum (y, z) -> Mc.S_Add  (_cert_of_pos y, _cert_of_pos z)
+  | Product (y, z) -> Mc.S_Mult (_cert_of_pos y, _cert_of_pos z) in
+  simplify_cone q_spec (_cert_of_pos pos)
+
+
+ let rec term_to_z_expr = function
+  | Const n ->  PEc (Ml2C.bigint (big_int_of_num n))
+  | Zero   ->  PEc ( Z0)
+  | Var s   ->  PEX (Ml2C.index 
+		      (int_of_string (String.sub s 1 (String.length s - 1))))
+  | Mul(p1,p2) ->  PEmul(term_to_z_expr p1, term_to_z_expr p2)
+  | Add(p1,p2) ->   PEadd(term_to_z_expr p1, term_to_z_expr p2)
+  | Opp p ->   PEopp (term_to_z_expr p)
+  | Pow(t,n) ->  PEpow (term_to_z_expr t,Ml2C.n n)
+  | Sub(t1,t2) ->  PEsub (term_to_z_expr t1,  term_to_z_expr t2)
+  | _ -> failwith "term_to_z_expr: not implemented"
+
+let  z_cert_of_pos  pos = 
+ let s,pos = (scale_certificate pos) in
+ let rec _cert_of_pos = function
+   Axiom_eq i ->  Mc.S_In (Ml2C.nat i)
+  | Axiom_le i ->  Mc.S_In (Ml2C.nat i)
+  | Axiom_lt i ->  Mc.S_In (Ml2C.nat i)
+  | Monoid l  -> Mc.S_Monoid (Ml2C.list Ml2C.nat l)
+  | Rational_eq n | Rational_le n | Rational_lt n -> 
+     if compare_num n (Int 0) = 0 then Mc.S_Z else
+      Mc.S_Pos (Ml2C.bigint (big_int_of_num  n))
+  | Square t -> Mc.S_Square (term_to_z_expr  t)
+  | Eqmul (t, y) -> Mc.S_Ideal(term_to_z_expr t, _cert_of_pos y)
+  | Sum (y, z) -> Mc.S_Add  (_cert_of_pos y, _cert_of_pos z)
+  | Product (y, z) -> Mc.S_Mult (_cert_of_pos y, _cert_of_pos z) in
+  simplify_cone z_spec (_cert_of_pos pos)
 
diff --git a/contrib/micromega/coq_micromega.ml b/contrib/micromega/coq_micromega.ml
index 29e2a183..02ff61a1 100644
--- a/contrib/micromega/coq_micromega.ml
+++ b/contrib/micromega/coq_micromega.ml
@@ -106,6 +106,7 @@ struct
      ["Coq" ; "micromega" ; "EnvRing"];
      ["Coq";"QArith"; "QArith_base"];
      ["Coq";"Reals" ; "Rdefinitions"];
+     ["Coq";"Reals" ; "Rpow_def"];
      ["LRing_normalise"]]
    
  let constant = gen_constant_in_modules "ZMicromega" coq_modules
@@ -163,6 +164,9 @@ struct
 
 
  let coq_Qmake = lazy (constant "Qmake")
+ let coq_R0    = lazy (constant "R0")
+ let coq_R1    = lazy (constant "R1")
+
 
  let coq_proofTerm = lazy (constant "ProofTerm")
  let coq_ratProof = lazy (constant "RatProof")
@@ -179,10 +183,36 @@ struct
  let coq_Zminus = lazy (constant "Zminus")
  let coq_Zopp = lazy (constant "Zopp")
  let coq_Zmult = lazy (constant "Zmult")
+ let coq_Zpower = lazy (constant "Zpower")
  let coq_N_of_Z = lazy 
   (gen_constant_in_modules "ZArithRing" 
     [["Coq";"setoid_ring";"ZArithRing"]] "N_of_Z")
 
+ let coq_Qgt = lazy (constant "Qgt")
+ let coq_Qge = lazy (constant "Qge")
+ let coq_Qle = lazy (constant "Qle")
+ let coq_Qlt = lazy (constant "Qlt")
+ let coq_Qeq = lazy (constant "Qeq")
+
+
+ let coq_Qplus = lazy (constant "Qplus")
+ let coq_Qminus = lazy (constant "Qminus")
+ let coq_Qopp = lazy (constant "Qopp")
+ let coq_Qmult = lazy (constant "Qmult")
+ let coq_Qpower = lazy (constant "Qpower")
+
+
+ let coq_Rgt = lazy (constant "Rgt")
+ let coq_Rge = lazy (constant "Rge")
+ let coq_Rle = lazy (constant "Rle")
+ let coq_Rlt = lazy (constant "Rlt")
+
+ let coq_Rplus = lazy (constant "Rplus")
+ let coq_Rminus = lazy (constant "Rminus")
+ let coq_Ropp = lazy (constant "Ropp")
+ let coq_Rmult = lazy (constant "Rmult")
+ let coq_Rpower = lazy (constant "pow")
+
 
  let coq_PEX = lazy (constant "PEX" )
  let coq_PEc = lazy (constant"PEc")
@@ -225,6 +255,7 @@ struct
   (gen_constant_in_modules "RingMicromega" 
     [["Coq" ; "micromega" ; "RingMicromega"] ; ["RingMicromega"] ] "Formula")
 
+
  type parse_error  = 
    | Ukn 
    | BadStr of string 
@@ -347,16 +378,11 @@ let dump_q q =
 
 let parse_q term =  
  match Term.kind_of_term term with
-  | Term.App(c, args) -> 
-     (
-      match Term.kind_of_term c with
-	Term.Construct((n,j),i) -> 
-      if Names.string_of_kn n  = "Coq.QArith.QArith_base#<>#Q"
-      then {Mc.qnum = parse_z args.(0) ; Mc.qden = parse_positive args.(1) }
+  | Term.App(c, args) -> if c = Lazy.force coq_Qmake then
+	{Mc.qnum = parse_z args.(0) ; Mc.qden = parse_positive args.(1) }
       else raise ParseError
-       |  _ -> raise ParseError
-     )
-  |   _ -> raise ParseError
+  |  _ -> raise ParseError
+
   
  let rec parse_list parse_elt term = 
   let (i,c) = get_left_construct term in
@@ -466,19 +492,6 @@ let parse_q term =
    pp_cone o e
 
 
-
-
- let rec parse_op term = 
-  let (i,c) = get_left_construct term in
-   match i with
-    | 1 -> Mc.OpEq
-    | 2 -> Mc.OpLe
-    | 3 -> Mc.OpGe
-    | 4 -> Mc.OpGt
-    | 5 -> Mc.OpLt
-    | i -> raise ParseError
-
-
  let rec dump_op = function
   | Mc.OpEq-> Lazy.force coq_OpEq
   | Mc.OpNEq-> Lazy.force coq_OpNEq
@@ -510,68 +523,52 @@ let parse_q term =
 		dump_op o ; 
 		dump_expr typ dump_constant e2|])
 
+ let assoc_const x l = 
+  try 
+  snd (List.find (fun (x',y) -> x = Lazy.force x') l)
+  with
+    Not_found -> raise ParseError
+
+ let zop_table = [ 
+  coq_Zgt, Mc.OpGt ; 
+  coq_Zge, Mc.OpGe ;
+  coq_Zlt, Mc.OpLt ;
+  coq_Zle, Mc.OpLe ]
+
+ let rop_table = [ 
+  coq_Rgt, Mc.OpGt ; 
+  coq_Rge, Mc.OpGe ;
+  coq_Rlt, Mc.OpLt ;
+  coq_Rle, Mc.OpLe ]
+
+ let qop_table = [ 
+  coq_Qlt, Mc.OpLt ;
+  coq_Qle, Mc.OpLe ;
+  coq_Qeq, Mc.OpEq
+ ]
 
 
  let parse_zop (op,args) =
   match kind_of_term op with
-   | Const x -> 
-      (match Names.string_of_con x with
-       | "Coq.ZArith.BinInt#<>#Zgt" -> (Mc.OpGt, args.(0), args.(1))
-       | "Coq.ZArith.BinInt#<>#Zge" -> (Mc.OpGe, args.(0), args.(1))
-       | "Coq.ZArith.BinInt#<>#Zlt" -> (Mc.OpLt, args.(0), args.(1))
-       | "Coq.ZArith.BinInt#<>#Zle" -> (Mc.OpLe, args.(0), args.(1))
-       (*| "Coq.Init.Logic#<>#not"    -> Mc.OpNEq  (* for backward compat *)*)
-       |   s -> raise ParseError
-      )
+   | Const x -> (assoc_const op zop_table, args.(0) , args.(1))
    |  Ind(n,0) -> 
-       (match Names.string_of_kn n with
-	| "Coq.Init.Logic#<>#eq" -> 
-	   if args.(0) <> Lazy.force coq_Z
-	   then raise ParseError
-	   else (Mc.OpEq, args.(1), args.(2))
-	|  _ -> raise ParseError)
+       if op = Lazy.force coq_Eq &&   args.(0) = Lazy.force coq_Z
+       then (Mc.OpEq, args.(1), args.(2))
+       else raise ParseError
    |   _ -> failwith "parse_zop"
 
 
  let parse_rop (op,args) =
-  try 
    match kind_of_term op with
-    | Const x -> 
-       (match Names.string_of_con x with
-	| "Coq.Reals.Rdefinitions#<>#Rgt" -> (Mc.OpGt, args.(0), args.(1))
-	| "Coq.Reals.Rdefinitions#<>#Rge" -> (Mc.OpGe, args.(0), args.(1))
-	| "Coq.Reals.Rdefinitions#<>#Rlt" -> (Mc.OpLt, args.(0), args.(1))
-	| "Coq.Reals.Rdefinitions#<>#Rle" -> (Mc.OpLe, args.(0), args.(1))
-	   (*| "Coq.Init.Logic#<>#not"-> Mc.OpNEq  (* for backward compat *)*)
-       |   s -> raise ParseError
-       )
+    | Const x -> (assoc_const op rop_table, args.(0) , args.(1))
     |  Ind(n,0) -> 
-	(match Names.string_of_kn n with
-	 | "Coq.Init.Logic#<>#eq" -> 
-	    (*   if args.(0) <> Lazy.force coq_R
-		 then raise ParseError
-		 else*) (Mc.OpEq, args.(1), args.(2))
-	 |  _ -> raise ParseError)
-    |   _ -> failwith "parse_rop"
-  with x -> 
-   (Pp.pp (Pp.str "parse_rop failure ") ; 
-    Pp.pp (Printer.prterm op) ; Pp.pp_flush ()) 
-   ; raise x
-
+       if op = Lazy.force coq_Eq &&   args.(0) = Lazy.force coq_R
+       then (Mc.OpEq, args.(1), args.(2))
+       else raise ParseError
+   |   _ -> failwith "parse_zop"
 
  let parse_qop (op,args) =
-  (
-   (match kind_of_term op with
-   | Const x -> 
-      (match Names.string_of_con x with
-       | "Coq.QArith.QArith_base#<>#Qgt" -> Mc.OpGt
-       | "Coq.QArith.QArith_base#<>#Qge" -> Mc.OpGe
-       | "Coq.QArith.QArith_base#<>#Qlt" -> Mc.OpLt
-       | "Coq.QArith.QArith_base#<>#Qle" -> Mc.OpLe
-       | "Coq.QArith.QArith_base#<>#Qeq" -> Mc.OpEq
-       |   s -> raise ParseError
-      )
-   |   _ -> failwith "parse_zop") , args.(0) , args.(1))
+   (assoc_const op qop_table, args.(0) , args.(1))
 
 
  module Env =
@@ -612,6 +609,14 @@ let parse_q term =
    | Ukn of string
 
 
+ let assoc_ops x l = 
+  try 
+    snd (List.find (fun (x',y) -> x = Lazy.force x') l)
+  with
+    Not_found -> Ukn "Oups"
+
+
+
  let parse_expr parse_constant parse_exp ops_spec env term = 
  if debug 
  then (Pp.pp (Pp.str "parse_expr: ");   
@@ -634,7 +639,7 @@ let parse_q term =
 	(
 	 match kind_of_term t with
 	  | Const c -> 
-	     ( match ops_spec (Names.string_of_con c) with
+	     ( match assoc_ops t ops_spec  with
 	      | Binop f -> combine env f (args.(0),args.(1))
 	      | Opp     -> let (expr,env) = parse_expr env args.(0) in
 			    (Mc.PEopp expr, env)
@@ -653,29 +658,29 @@ let parse_q term =
    parse_expr env term
     
 
-let zop_spec = function
- | "Coq.ZArith.BinInt#<>#Zplus"    -> Binop (fun x y -> Mc.PEadd(x,y))
- | "Coq.ZArith.BinInt#<>#Zminus"   -> Binop (fun x y -> Mc.PEsub(x,y)) 
- | "Coq.ZArith.BinInt#<>#Zmult"    -> Binop  (fun x y -> Mc.PEmul (x,y))
-  | "Coq.ZArith.BinInt#<>#Zopp"     ->  Opp
-  | "Coq.ZArith.Zpow_def#<>#Zpower" -> Power
-  |  s                                   -> Ukn s
+ let zop_spec = 
+   [ 
+     coq_Zplus , Binop (fun x y -> Mc.PEadd(x,y)) ;
+     coq_Zminus , Binop (fun x y -> Mc.PEsub(x,y)) ;
+     coq_Zmult  , Binop  (fun x y -> Mc.PEmul (x,y)) ; 
+     coq_Zopp   , Opp ; 
+     coq_Zpower , Power]
 
-let qop_spec = function
- | "Coq.QArith.QArith_base#<>#Qplus"    -> Binop (fun x y -> Mc.PEadd(x,y))
- | "Coq.QArith.QArith_base#<>#Qminus"   -> Binop (fun x y -> Mc.PEsub(x,y)) 
- | "Coq.QArith.QArith_base#<>#Qmult"    -> Binop  (fun x y -> Mc.PEmul (x,y)) 
-  | "Coq.QArith.QArith_base#<>#Qopp"     ->  Opp
-  | "Coq.QArith.QArith_base#<>#Qpower" -> Power
-  |  s                                   -> Ukn s
+let qop_spec = 
+  [
+     coq_Qplus , Binop (fun x y -> Mc.PEadd(x,y)) ;
+     coq_Qminus , Binop (fun x y -> Mc.PEsub(x,y)) ;
+     coq_Qmult  , Binop  (fun x y -> Mc.PEmul (x,y)) ; 
+     coq_Qopp   , Opp ; 
+     coq_Qpower , Power]
 
-let rop_spec = function
- | "Coq.Reals.Rdefinitions#<>#Rplus"    -> Binop (fun x y -> Mc.PEadd(x,y))
- | "Coq.Reals.Rdefinitions#<>#Rminus"   -> Binop (fun x y -> Mc.PEsub(x,y)) 
- | "Coq.Reals.Rdefinitions#<>#Rmult"    -> Binop  (fun x y -> Mc.PEmul (x,y))
- | "Coq.Reals.Rdefinitions#<>#Ropp"     -> Opp
- | "Coq.Reals.Rpow_def#<>#pow"          -> Power
- |  s                                        -> Ukn s
+let rop_spec = 
+  [
+     coq_Rplus , Binop (fun x y -> Mc.PEadd(x,y)) ;
+     coq_Rminus , Binop (fun x y -> Mc.PEsub(x,y)) ;
+     coq_Rmult  , Binop  (fun x y -> Mc.PEmul (x,y)) ; 
+     coq_Ropp   , Opp ; 
+     coq_Rpower , Power]
 
 
 
@@ -691,12 +696,12 @@ let rconstant term =
        Pp.pp (Pp.str "rconstant: ");
        Pp.pp (Printer.prterm  term); Pp.pp_flush ());
  match Term.kind_of_term term with
-  | Const x ->        
-     (match Names.string_of_con x with
-      | "Coq.Reals.Rdefinitions#<>#R0" -> Mc.Z0
-      | "Coq.Reals.Rdefinitions#<>#R1" -> Mc.Zpos Mc.XH
-      | _   -> raise ParseError
-     )
+  | Const x ->  
+      if term = Lazy.force coq_R0
+      then Mc.Z0
+      else if term = Lazy.force coq_R1
+      then Mc.Zpos Mc.XH
+      else raise ParseError
   |  _ -> raise ParseError
 
 
@@ -731,23 +736,6 @@ let parse_rexpr =
   
  (* generic parsing of arithmetic expressions *)
   
- let rec parse_conj parse_arith env term = 
-  match kind_of_term term with
-   | App(l,rst) -> 
-      (match kind_of_term l with
-       | Ind (n,_) -> 
-	  ( match Names.string_of_kn n with
-	   | "Coq.Init.Logic#<>#and" -> 
-	      let (e1,env) = parse_arith env rst.(0) in
-	      let (e2,env) = parse_conj parse_arith env rst.(1) in
-	       (Mc.Cons(e1,e2),env)
-	   |   _ -> (* This might be an equality *) 
-		let (e,env) = parse_arith env term in
-		 (Mc.Cons(e,Mc.Nil),env))
-       |  _ -> (* This is an arithmetic expression *)
-	   let (e,env) = parse_arith env term in
-	    (Mc.Cons(e,Mc.Nil),env))
-   |  _ -> failwith "parse_conj(2)"
 
 
 
@@ -850,46 +838,6 @@ let parse_rexpr =
    xdump f
     
 
- (* Backward compat *)
-
- let rec parse_concl parse_arith env term =
-  match kind_of_term term with
-   | Prod(_,expr,rst) -> (* a -> b *)
-      let (lhs,rhs,env) = parse_concl parse_arith env rst in
-      let (e,env) = parse_arith env expr in
-       (Mc.Cons(e,lhs),rhs,env)
-   | App(_,_) -> 
-      let (conj, env) = parse_conj parse_arith env term in
-       (Mc.Nil,conj,env)
-   |  Ind(n,_) -> 
-       (match (Names.string_of_kn n) with
-	| "Coq.Init.Logic#<>#False" -> (Mc.Nil,Mc.Nil,env)
-	|    s                           -> 
-	      print_string s ; flush stdout;
-	      failwith "parse_concl")
-   |  _ -> failwith "parse_concl"
-
-
- let rec parse_hyps parse_arith env goal_hyps hyps = 
-  match hyps with
-   | [] -> ([],goal_hyps,env)
-   | (i,t)::l -> 
-      let (li,lt,env) = parse_hyps parse_arith env goal_hyps l in
-       try 
-	let (c,env) = parse_arith env  t in
-	 (i::li, Mc.Cons(c,lt), env)
-       with  x -> 
-	(*(if debug then Printf.printf "parse_arith : %s\n" x);*)
-	(li,lt,env)
-
-
- let parse_goal parse_arith env hyps term = 
-  try
-   let (lhs,rhs,env) = parse_concl parse_arith env term in
-   let (li,lt,env) = parse_hyps parse_arith env lhs hyps in
-    (li,lt,rhs,env)
-  with Failure x -> raise ParseError
-   (* backward compat *)
 
 
  (* ! reverse the list of bindings *)
@@ -1235,8 +1183,8 @@ let lift_ratproof prover l =
   | Some c -> Some (Mc.RatProof c)
 
 
-type csdpcert = Certificate.Mc.z Certificate.Mc.coneMember option
-type micromega_polys = (Micromega.z Mc.pExpr, Mc.op1) Micromega.prod list
+type csdpcert = Sos.positivstellensatz option
+type micromega_polys = (Micromega.q Mc.pExpr, Mc.op1) Micromega.prod list
 type provername = string * int option
 
 let call_csdpcert provername poly =
@@ -1255,36 +1203,84 @@ let call_csdpcert provername poly =
   close_in ch_from; Sys.remove tmp_from;
   cert
 
-let omicron gl = 
+let rec z_to_q_expr e = 
+ match e with
+  | Mc.PEc z   -> Mc.PEc {Mc.qnum = z ; Mc.qden = Mc.XH}
+  | Mc.PEX x   -> Mc.PEX x
+  | Mc.PEadd(e1,e2) -> Mc.PEadd(z_to_q_expr e1, z_to_q_expr e2)
+  | Mc.PEsub(e1,e2) -> Mc.PEsub(z_to_q_expr e1, z_to_q_expr e2)
+  | Mc.PEmul(e1,e2) -> Mc.PEmul(z_to_q_expr e1, z_to_q_expr e2)
+  | Mc.PEopp(e) -> Mc.PEopp(z_to_q_expr e)
+  | Mc.PEpow(e,n) -> Mc.PEpow(z_to_q_expr e,n)
+
+
+let call_csdpcert_q provername poly = 
+ match call_csdpcert provername poly with
+  | None -> None
+  | Some cert -> 
+     let cert = Certificate.q_cert_of_pos cert in
+      match Mc.qWeakChecker (CamlToCoq.list (fun x -> x) poly)  cert with
+       | Mc.True -> Some cert
+       | Mc.False ->  (print_string "buggy certificate" ; flush stdout) ;None
+
+
+let call_csdpcert_z provername poly = 
+ let l = List.map (fun (Mc.Pair(e,o)) -> (Mc.Pair(z_to_q_expr e,o))) poly in
+  match call_csdpcert provername l with
+   | None -> None
+   | Some cert -> 
+      let cert = Certificate.z_cert_of_pos cert in
+       match Mc.zWeakChecker (CamlToCoq.list (fun x -> x) poly)  cert with
+	| Mc.True -> Some cert
+	| Mc.False ->  (print_string "buggy certificate" ; flush stdout) ;None
+
+
+
+
+let psatzl_Z gl = 
  micromega_gen parse_zarith  Mc.negate Mc.normalise zz_domain_spec
   [lift_ratproof 
     (Certificate.linear_prover Certificate.z_spec), "fourier refutation" ] gl
 
 
-let qomicron gl = 
+let psatzl_Q gl = 
  micromega_gen  parse_qarith Mc.cnf_negate Mc.cnf_normalise qq_domain_spec 
   [ Certificate.linear_prover Certificate.q_spec, "fourier refutation" ]   gl
 
-let romicron gl = 
+let psatz_Q i gl = 
+ micromega_gen parse_qarith Mc.cnf_negate Mc.cnf_normalise qq_domain_spec
+  [ call_csdpcert_q ("real_nonlinear_prover", Some i), "fourier refutation" ]  gl
+
+let psatzl_R gl = 
  micromega_gen  parse_rarith Mc.cnf_negate Mc.cnf_normalise rz_domain_spec 
   [ Certificate.linear_prover Certificate.z_spec, "fourier refutation" ]   gl
 
 
-let rmicromega i gl = 
- micromega_gen parse_rarith Mc.negate Mc.normalise rz_domain_spec
-  [ call_csdpcert ("real_nonlinear_prover", Some i), "fourier refutation" ]  gl
+let psatz_R i gl = 
+ micromega_gen parse_rarith Mc.cnf_negate Mc.cnf_normalise rz_domain_spec
+  [ call_csdpcert_z  ("real_nonlinear_prover", Some i), "fourier refutation" ]  gl
 
   
-let micromega i gl = 
+let psatz_Z i gl = 
  micromega_gen parse_zarith Mc.negate Mc.normalise zz_domain_spec 
- [lift_ratproof (call_csdpcert ("real_nonlinear_prover",Some i)), 
+ [lift_ratproof (call_csdpcert_z ("real_nonlinear_prover",Some i)), 
   "fourier refutation" ] gl
 
 
-let sos gl = 
+let sos_Z gl = 
  micromega_gen parse_zarith Mc.negate Mc.normalise  zz_domain_spec 
-  [lift_ratproof (call_csdpcert ("pure_sos", None)), "pure sos refutation"]  gl
+  [lift_ratproof (call_csdpcert_z ("pure_sos", None)), "pure sos refutation"]  gl
+
+let sos_Q gl = 
+ micromega_gen parse_qarith Mc.cnf_negate Mc.cnf_normalise  qq_domain_spec 
+  [call_csdpcert_q ("pure_sos", None), "pure sos refutation"]  gl
+
+let sos_R gl = 
+ micromega_gen parse_rarith Mc.cnf_negate Mc.cnf_normalise  rz_domain_spec 
+  [call_csdpcert_z ("pure_sos", None), "pure sos refutation"]  gl
+
+
 
-let zomicron gl = 
+let xlia gl = 
  micromega_gen parse_zarith Mc.negate Mc.normalise   zz_domain_spec 
   [Certificate.zlinear_prover, "zprover"] gl
diff --git a/contrib/micromega/csdpcert.ml b/contrib/micromega/csdpcert.ml
index cfaf6ae1..e451a38f 100644
--- a/contrib/micromega/csdpcert.ml
+++ b/contrib/micromega/csdpcert.ml
@@ -27,7 +27,7 @@ struct
  open Mc
 
  let rec expr_to_term = function
-  |  PEc z ->  Const  (Big_int (C2Ml.z_big_int z))
+  |  PEc z ->  Const  (C2Ml.q_to_num z)
   |  PEX v ->  Var ("x"^(string_of_int (C2Ml.index v)))
   |  PEmul(p1,p2) -> 
       let p1 = expr_to_term p1 in
@@ -40,25 +40,15 @@ struct
   |  PEopp p ->  Opp (expr_to_term p)
 
       
- let rec term_to_expr = function
-  | Const n ->  PEc (Ml2C.bigint (big_int_of_num n))
-  | Zero   ->  PEc ( Z0)
-  | Var s   ->  PEX (Ml2C.index 
-		      (int_of_string (String.sub s 1 (String.length s - 1))))
-  | Mul(p1,p2) ->  PEmul(term_to_expr p1, term_to_expr p2)
-  | Add(p1,p2) ->   PEadd(term_to_expr p1, term_to_expr p2)
-  | Opp p ->   PEopp (term_to_expr p)
-  | Pow(t,n) ->  PEpow (term_to_expr t,Ml2C.n n)
-  | Sub(t1,t2) ->  PEsub (term_to_expr t1,  term_to_expr t2)
-  | _ -> failwith "term_to_expr: not implemented"
-
- let term_to_expr e =
+
+
+(* let term_to_expr e =
   let e' = term_to_expr e in
    if debug 
    then Printf.printf "term_to_expr : %s - %s\n"  
     (string_of_poly (poly_of_term  e)) 
     (string_of_poly (poly_of_term (expr_to_term e')));
-   e'
+   e' *)
 
 end 
 open M      
@@ -66,110 +56,8 @@ open M
 open List
 open Mutils 
 
-let rec scale_term t = 
- match t with
-  | Zero    -> unit_big_int , Zero
-  | Const n ->  (denominator n) , Const (Big_int (numerator n))
-  | Var n   -> unit_big_int , Var n
-  | Inv _   -> failwith "scale_term : not implemented"
-  | Opp t   -> let s, t = scale_term t in s, Opp t
-  | Add(t1,t2) -> let s1,y1 = scale_term t1 and s2,y2 = scale_term t2 in
-    let g = gcd_big_int s1 s2 in
-    let s1' = div_big_int s1 g in
-    let s2' = div_big_int s2 g in
-    let e = mult_big_int g (mult_big_int s1' s2') in
-     if (compare_big_int e unit_big_int) = 0
-     then (unit_big_int, Add (y1,y2))
-     else 	e, Add (Mul(Const (Big_int s2'), y1),
-		       Mul (Const (Big_int s1'), y2))
-  | Sub _ -> failwith "scale term: not implemented"
-  | Mul(y,z) ->       let s1,y1 = scale_term y and s2,y2 = scale_term z in
-		       mult_big_int s1 s2 , Mul (y1, y2)
-  |  Pow(t,n) -> let s,t = scale_term t in
-		  power_big_int_positive_int s  n , Pow(t,n)
-  |   _ -> failwith "scale_term : not implemented"
-
-let scale_term t =
- let (s,t') = scale_term t in
-  s,t'
-   
-
 
 
-let rec scale_certificate pos = match pos with
- | Axiom_eq i ->  unit_big_int , Axiom_eq i
- | Axiom_le i ->  unit_big_int , Axiom_le i
- | Axiom_lt i ->   unit_big_int , Axiom_lt i
- | Monoid l   -> unit_big_int , Monoid l
- | Rational_eq n ->  (denominator n) , Rational_eq (Big_int (numerator n))
- | Rational_le n ->  (denominator n) , Rational_le (Big_int (numerator n))
- | Rational_lt n ->  (denominator n) , Rational_lt (Big_int (numerator n))
- | Square t -> let s,t' =  scale_term t in 
-		mult_big_int s s , Square t'
- | Eqmul (t, y) -> let s1,y1 = scale_term t and s2,y2 = scale_certificate y in
-		    mult_big_int s1 s2 , Eqmul (y1,y2)
- | Sum (y, z) -> let s1,y1 = scale_certificate y 
-   and s2,y2 = scale_certificate z in
-   let g = gcd_big_int s1 s2 in
-   let s1' = div_big_int s1 g in
-   let s2' = div_big_int s2 g in
-    mult_big_int g (mult_big_int s1' s2'), 
-    Sum (Product(Rational_le (Big_int s2'), y1),
-	Product (Rational_le (Big_int s1'), y2))
- | Product (y, z) -> 
-    let s1,y1 = scale_certificate y and s2,y2 = scale_certificate z in
-     mult_big_int s1 s2 , Product (y1,y2)
-
-
-let is_eq = function  Mc.Equal -> true | _ -> false
-let is_le = function  Mc.NonStrict -> true | _ -> false
-let is_lt = function  Mc.Strict -> true | _ -> false
-
-let get_index_of_ith_match f i l  =
- let rec get j res l =
-  match l with
-   | [] -> failwith "bad index"
-   | e::l -> if f e
-     then 
-       (if j = i then res else get (j+1) (res+1) l )
-     else get j (res+1) l in
-  get 0 0 l
-
-
-let  cert_of_pos eq le lt ll l pos = 
- let s,pos = (scale_certificate pos) in
- let rec _cert_of_pos = function
-   Axiom_eq i -> let idx = get_index_of_ith_match is_eq i l in
-		  Mc.S_In (Ml2C.nat idx)
-  | Axiom_le i -> let idx = get_index_of_ith_match is_le i l in
-		   Mc.S_In (Ml2C.nat idx)
-  | Axiom_lt i -> let idx = get_index_of_ith_match is_lt i l in
-		   Mc.S_In (Ml2C.nat idx)
-  | Monoid l  -> Mc.S_Monoid (Ml2C.list Ml2C.nat l)
-  | Rational_eq n | Rational_le n | Rational_lt n -> 
-     if compare_num n (Int 0) = 0 then Mc.S_Z else
-      Mc.S_Pos (Ml2C.bigint (big_int_of_num  n))
-  | Square t -> Mc.S_Square (term_to_expr  t)
-  | Eqmul (t, y) -> Mc.S_Ideal(term_to_expr t, _cert_of_pos y)
-  | Sum (y, z) -> Mc.S_Add  (_cert_of_pos y, _cert_of_pos z)
-  | Product (y, z) -> Mc.S_Mult (_cert_of_pos y, _cert_of_pos z) in
-  s, Certificate.simplify_cone Certificate.z_spec (_cert_of_pos pos)
-
-
-let  term_of_cert l pos = 
- let l = List.map fst' l in
- let rec _cert_of_pos = function
-  | Mc.S_In i -> expr_to_term (List.nth l (C2Ml.nat i))
-  | Mc.S_Pos p -> Const (C2Ml.num  p)
-  | Mc.S_Z     -> Const (Int 0)
-  | Mc.S_Square t -> Mul(expr_to_term t, expr_to_term t)
-  | Mc.S_Monoid m -> List.fold_right 
-     (fun x m -> Mul (expr_to_term (List.nth l (C2Ml.nat x)),m)) 
-     (C2Ml.list (fun x -> x) m)  (Const (Int 1))
-  | Mc.S_Ideal (t, y) -> Mul(expr_to_term t, _cert_of_pos y)
-  | Mc.S_Add (y, z) -> Add  (_cert_of_pos y, _cert_of_pos z)
-  | Mc.S_Mult (y, z) -> Mul (_cert_of_pos y, _cert_of_pos z) in
-  (_cert_of_pos pos)
 
 let rec canonical_sum_to_string = function s -> failwith "not implemented"
 
@@ -208,22 +96,6 @@ let rec sets_of_list l =
   | e::l -> let s = sets_of_list l in
 	     s@(List.map (fun s0 -> e::s0) s) 
 
-let  cert_of_pos  pos = 
- let s,pos = (scale_certificate pos) in
- let rec _cert_of_pos = function
-   Axiom_eq i ->  Mc.S_In (Ml2C.nat i)
-  | Axiom_le i ->  Mc.S_In (Ml2C.nat i)
-  | Axiom_lt i ->  Mc.S_In (Ml2C.nat i)
-  | Monoid l  -> Mc.S_Monoid (Ml2C.list Ml2C.nat l)
-  | Rational_eq n | Rational_le n | Rational_lt n -> 
-     if compare_num n (Int 0) = 0 then Mc.S_Z else
-      Mc.S_Pos (Ml2C.bigint (big_int_of_num  n))
-  | Square t -> Mc.S_Square (term_to_expr  t)
-  | Eqmul (t, y) -> Mc.S_Ideal(term_to_expr t, _cert_of_pos y)
-  | Sum (y, z) -> Mc.S_Add  (_cert_of_pos y, _cert_of_pos z)
-  | Product (y, z) -> Mc.S_Mult (_cert_of_pos y, _cert_of_pos z) in
-  s, Certificate.simplify_cone Certificate.z_spec (_cert_of_pos pos)
-
 (* The exploration is probably not complete - for simple cases, it works... *)
 let real_nonlinear_prover d l =
  try 
@@ -272,15 +144,7 @@ let real_nonlinear_prover d l =
 
   let proof = list_fold_right_elements 
    (fun s t -> Sum(s,t)) (proof_ne :: proofs_ideal @ proofs_cone) in
-   
-  let s,proof' = scale_certificate proof in
-  let cert  = snd (cert_of_pos proof') in
-   if debug 
-   then Printf.printf "cert poly : %s\n" 
-    (string_of_poly (poly_of_term (term_of_cert l cert)));
-   match Mc.zWeakChecker (Ml2C.list (fun x -> x) l)  cert with
-    | Mc.True -> Some cert
-    | Mc.False ->  (print_string "buggy certificate" ; flush stdout) ;None
+   Some proof
  with 
   | Sos.TooDeep -> None
 
@@ -300,16 +164,16 @@ let pure_sos  l =
 		     (term_of_poly p)), rst)) 
 		     polys (Rational_lt (Int 0))) in
   let proof = Sum(Axiom_lt i, pos) in
-  let s,proof' = scale_certificate proof in
-  let cert  = snd (cert_of_pos proof') in
-   Some cert
+(*  let s,proof' = scale_certificate proof in
+  let cert  = snd (cert_of_pos proof') in *)
+   Some proof
  with
   | Not_found -> (* This is no strict inequality *) None
   |  x        -> None
 
 
-type micromega_polys = (Micromega.z Mc.pExpr, Mc.op1) Micromega.prod list
-type csdp_certificate = Certificate.Mc.z Certificate.Mc.coneMember option
+type micromega_polys = (Micromega.q Mc.pExpr, Mc.op1) Micromega.prod list
+type csdp_certificate = Sos.positivstellensatz option
 type provername = string * int option
 
 let main () =
diff --git a/contrib/micromega/g_micromega.ml4 b/contrib/micromega/g_micromega.ml4
index 259b5d4b..50024e78 100644
--- a/contrib/micromega/g_micromega.ml4
+++ b/contrib/micromega/g_micromega.ml4
@@ -14,7 +14,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: g_micromega.ml4 10947 2008-05-19 19:10:40Z herbelin $ *)
+(* $Id: g_micromega.ml4 11306 2008-08-05 16:51:08Z notin $ *)
 
 open Quote
 open Ring
@@ -26,34 +26,49 @@ let out_arg = function
   | ArgVar _ -> anomaly "Unevaluated or_var variable"
   | ArgArg x -> x
 
-TACTIC EXTEND Micromega
-| [ "micromegap" int_or_var(i) ] -> [ Coq_micromega.micromega (out_arg i) ]
-| [ "micromegap" ] -> [ Coq_micromega.micromega (-1) ]
+TACTIC EXTEND PsatzZ
+| [ "psatz_Z" int_or_var(i) ] -> [ Coq_micromega.psatz_Z (out_arg i) ]
+| [ "psatz_Z" ] -> [ Coq_micromega.psatz_Z (-1) ]
 END
 
-TACTIC EXTEND Sos
-[ "sosp" ] -> [ Coq_micromega.sos]
+TACTIC EXTEND Sos_Z
+| [ "sos_Z" ] -> [ Coq_micromega.sos_Z]
+   END
+
+TACTIC EXTEND Sos_Q
+| [ "sos_Q" ] -> [ Coq_micromega.sos_Q]
+   END
+
+TACTIC EXTEND Sos_R
+| [ "sos_R" ] -> [ Coq_micromega.sos_R]
 END
 
 
 TACTIC EXTEND Omicron
-[ "omicronp"  ] -> [ Coq_micromega.omicron]
+[ "psatzl_Z"  ] -> [ Coq_micromega.psatzl_Z]
 END
 
 TACTIC EXTEND QOmicron
-[ "qomicronp"  ] -> [ Coq_micromega.qomicron]
+[ "psatzl_Q"  ] -> [ Coq_micromega.psatzl_Q]
 END
 
 
 TACTIC EXTEND ZOmicron
-[ "zomicronp"  ] -> [ Coq_micromega.zomicron]
+[ "xlia"  ] -> [ Coq_micromega.xlia]
 END
 
 TACTIC EXTEND ROmicron
-[ "romicronp"  ] -> [ Coq_micromega.romicron]
+[ "psatzl_R"  ] -> [ Coq_micromega.psatzl_R]
 END
 
 TACTIC EXTEND RMicromega
-| [ "rmicromegap" int_or_var(i) ] -> [ Coq_micromega.rmicromega (out_arg i) ]
-| [ "rmicromegap" ] -> [ Coq_micromega.rmicromega (-1) ]
+| [ "psatz_R" int_or_var(i) ] -> [ Coq_micromega.psatz_R (out_arg i) ]
+| [ "psatz_R" ] -> [ Coq_micromega.psatz_R (-1) ]
+END
+
+
+TACTIC EXTEND QMicromega
+| [ "psatz_Q" int_or_var(i) ] -> [ Coq_micromega.psatz_Q (out_arg i) ]
+| [ "psatz_Q" ] -> [ Coq_micromega.psatz_Q (-1) ]
 END
+
diff --git a/contrib/romega/ROmega.v b/contrib/romega/ROmega.v
index 68bc43bb..4281cc57 100644
--- a/contrib/romega/ROmega.v
+++ b/contrib/romega/ROmega.v
@@ -9,3 +9,4 @@
 Require Import ReflOmegaCore.
 Require Export Setoid.
 Require Export PreOmega.
+Require Export ZArith_base.
diff --git a/contrib/romega/ReflOmegaCore.v b/contrib/romega/ReflOmegaCore.v
index 9d379548..12176d66 100644
--- a/contrib/romega/ReflOmegaCore.v
+++ b/contrib/romega/ReflOmegaCore.v
@@ -7,7 +7,7 @@
 
  *************************************************************************)
 
-Require Import List Bool Sumbool EqNat Setoid Ring_theory Decidable.
+Require Import List Bool Sumbool EqNat Setoid Ring_theory Decidable ZArith_base.
 Delimit Scope Int_scope with I.
 
 (* Abstract Integers. *)
@@ -81,7 +81,6 @@ End Int.
 
 Module Z_as_Int <: Int.
 
-  Require Import ZArith_base.
   Open Scope Z_scope.
 
   Definition int := Z. 
diff --git a/contrib/setoid_ring/Field_theory.v b/contrib/setoid_ring/Field_theory.v
index 65a397ac..b2e5cc4b 100644
--- a/contrib/setoid_ring/Field_theory.v
+++ b/contrib/setoid_ring/Field_theory.v
@@ -1619,6 +1619,7 @@ split.
 generalize (PCond_cons_inv_l _ _ _ H1); simpl; auto.
 apply H0.
 generalize (PCond_cons_inv_r _ _ _ H1); simpl; auto.
+clear get_sign get_sign_spec. 
 generalize Hp; case l0; simpl; intuition.
 Qed.
 
diff --git a/contrib/setoid_ring/InitialRing.v b/contrib/setoid_ring/InitialRing.v
index c1fa963f..e664b3b7 100644
--- a/contrib/setoid_ring/InitialRing.v
+++ b/contrib/setoid_ring/InitialRing.v
@@ -38,14 +38,6 @@ Proof.
  exact Zmult_plus_distr_l. trivial. exact Zminus_diag.
 Qed.
 
- Lemma Zeqb_ok : forall x y, Zeq_bool x y = true -> x = y.
- Proof.
-  intros x y.
-  assert (H := Zcompare_Eq_eq x y);unfold Zeq_bool;
-  destruct (Zcompare x y);intros H1;auto;discriminate H1.
- Qed.
-
-
 (** Two generic morphisms from Z to (abrbitrary) rings, *)
 (**second one is more convenient for proofs but they are ext. equal*)
 Section ZMORPHISM.
@@ -174,7 +166,7 @@ Section ZMORPHISM.
    Zeq_bool x y = true -> [x] == [y].
  Proof.
   intros x y H.
-  assert (H1 := Zeqb_ok x y H);unfold IDphi in H1.
+  assert (H1 := Zeq_bool_eq x y H);unfold IDphi in H1.
   rewrite H1;rrefl.
  Qed.
   
diff --git a/contrib/setoid_ring/Ring_theory.v b/contrib/setoid_ring/Ring_theory.v
index 29feab5c..531ab3ca 100644
--- a/contrib/setoid_ring/Ring_theory.v
+++ b/contrib/setoid_ring/Ring_theory.v
@@ -494,7 +494,7 @@ Qed.
  Proof. intros;mrewrite. Qed.
 
  Lemma ARdistr_r : forall x y z, z * (x + y) == z*x + z*y.
- Proof. 
+ Proof.
   intros;mrewrite. 
   repeat rewrite (ARth.(ARmul_comm) z);sreflexivity.
  Qed.
diff --git a/contrib/setoid_ring/ZArithRing.v b/contrib/setoid_ring/ZArithRing.v
index 4a5b623b..942915ab 100644
--- a/contrib/setoid_ring/ZArithRing.v
+++ b/contrib/setoid_ring/ZArithRing.v
@@ -50,7 +50,7 @@ Ltac Zpower_neg :=
   end.   
 
 Add Ring Zr : Zth
-  (decidable Zeqb_ok, constants [Zcst], preprocess [Zpower_neg;unfold Zsucc],
+  (decidable Zeq_bool_eq, constants [Zcst], preprocess [Zpower_neg;unfold Zsucc],
    power_tac Zpower_theory [Zpow_tac],
     (* The two following option are not needed, it is the default chose when the set of 
         coefficiant is usual ring Z *)
diff --git a/contrib/setoid_ring/newring.ml4 b/contrib/setoid_ring/newring.ml4
index dd79801d..3d022add 100644
--- a/contrib/setoid_ring/newring.ml4
+++ b/contrib/setoid_ring/newring.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(*i $Id: newring.ml4 11094 2008-06-10 19:35:23Z herbelin $ i*)
+(*i $Id: newring.ml4 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 open Pp
 open Util
@@ -452,11 +452,14 @@ let (theory_to_obj, obj_to_theory) =
 
 
 let setoid_of_relation env a r =
-  lapp coq_mk_Setoid
-    [|a ; r ; 
-      Class_tactics.reflexive_proof env a r ; 
-      Class_tactics.symmetric_proof env a r ; 
-      Class_tactics.transitive_proof env a r |]
+  try 
+    lapp coq_mk_Setoid
+      [|a ; r ; 
+	Class_tactics.reflexive_proof env a r ; 
+	Class_tactics.symmetric_proof env a r ; 
+	Class_tactics.transitive_proof env a r |]
+  with Not_found ->
+    error "cannot find setoid relation"
 
 let op_morph r add mul opp req m1 m2 m3 =
   lapp coq_mk_reqe [| r; add; mul; opp; req; m1; m2; m3 |]
diff --git a/contrib/subtac/g_subtac.ml4 b/contrib/subtac/g_subtac.ml4
index 88243b60..4cf5336d 100644
--- a/contrib/subtac/g_subtac.ml4
+++ b/contrib/subtac/g_subtac.ml4
@@ -14,7 +14,7 @@
   Syntax for the subtac terms and types.
   Elaborated from correctness/psyntax.ml4 by Jean-Christophe Filliâtre *)
 
-(* $Id: g_subtac.ml4 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: g_subtac.ml4 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 
 open Flags
@@ -139,10 +139,10 @@ VERNAC COMMAND EXTEND Subtac_Admit_Obligations
     END
 
 VERNAC COMMAND EXTEND Subtac_Set_Solver
-| [ "Obligations" "Tactic" ":=" tactic(t) ] -> [ 
+| [ "Obligation" "Tactic" ":=" tactic(t) ] -> [ 
     Coqlib.check_required_library ["Coq";"Program";"Tactics"];
     Tacinterp.add_tacdef false 
-      [(Qualid (dummy_loc, qualid_of_string "Coq.Program.Tactics.obligations_tactic"), true, t)] ]
+      [(Qualid (dummy_loc, qualid_of_string "Coq.Program.Tactics.obligation_tactic"), true, t)] ]
 END
 
 VERNAC COMMAND EXTEND Subtac_Show_Obligations
diff --git a/contrib/subtac/subtac.ml b/contrib/subtac/subtac.ml
index a59ad6f5..7bfa107b 100644
--- a/contrib/subtac/subtac.ml
+++ b/contrib/subtac/subtac.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: subtac.ml 11150 2008-06-19 11:38:27Z msozeau $ *)
+(* $Id: subtac.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Global
 open Pp
@@ -229,7 +229,8 @@ let subtac (loc, command) =
       debug 2 (Himsg.explain_pretype_error env exn);
       raise e
 	
-  | (Stdpp.Exc_located (loc, e')) as e ->
+  | (Stdpp.Exc_located (loc, Proof_type.LtacLocated (_,e')) |
+     Stdpp.Exc_located (loc, e') as e) ->
       debug 2 (str "Parsing exception: ");
       (match e' with
       | Type_errors.TypeError (env, exn) ->
diff --git a/contrib/subtac/subtac_cases.ml b/contrib/subtac/subtac_cases.ml
index c7182bd2..04bf54d3 100644
--- a/contrib/subtac/subtac_cases.ml
+++ b/contrib/subtac/subtac_cases.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: subtac_cases.ml 11154 2008-06-19 18:42:19Z msozeau $ *)
+(* $Id: subtac_cases.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Cases
 open Util
@@ -2056,8 +2056,10 @@ let compile_cases loc style (typing_fun, isevars) (tycon : Evarutil.type_constra
 	    t, prepare_predicate_from_arsign_tycon loc env (Evd.evars_of !isevars)
 	      tomatchs sign (lift tomatchs_len t)
       in
-      let arity = 
-	it_mkProd_or_LetIn (lift neqs arity) (context_of_arsign eqs)
+      let neqs, arity = 
+	let ctx = context_of_arsign eqs in
+	let neqs = List.length ctx in
+	  neqs, it_mkProd_or_LetIn (lift neqs arity) ctx
       in
       let lets, matx = 
 	(* Type the rhs under the assumption of equations *)
diff --git a/contrib/subtac/subtac_classes.ml b/contrib/subtac/subtac_classes.ml
index 15addb44..9a5539e2 100644
--- a/contrib/subtac/subtac_classes.ml
+++ b/contrib/subtac/subtac_classes.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: subtac_classes.ml 11047 2008-06-03 23:08:00Z msozeau $ i*)
+(*i $Id: subtac_classes.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 open Pretyping
 open Evd
@@ -73,26 +73,18 @@ let interp_casted_constr_evars evdref env ?(impls=([],[])) c typ =
 let type_ctx_instance isevars env ctx inst subst =
   List.fold_left2
     (fun (subst, instctx) (na, _, t) ce ->
-      let t' = replace_vars subst t in
+      let t' = substl subst t in
       let c = interp_casted_constr_evars isevars env ce t' in
+      isevars := resolve_typeclasses ~onlyargs:true ~fail:true env !isevars;
       let d = na, Some c, t' in
-	(na, c) :: subst, d :: instctx)
+	c :: subst, d :: instctx)
     (subst, []) (List.rev ctx) inst
 
-(*let superclass_ce = CRef (Ident (dummy_loc, id_of_string ".superclass"))*)
-
 let type_class_instance_params isevars env id n ctx inst subst =
   List.fold_left2
     (fun (subst, instctx) (na, _, t) ce ->
       let t' = replace_vars subst t in
-      let c = 
-(* 	if ce = superclass_ce then *)
-	(* 	  (\* Control over the evars which are direct superclasses to avoid partial instanciations *)
-	(* 	     in instance search. *\) *)
-	(* 	  Evarutil.e_new_evar isevars env ~src:(dummy_loc, ImplicitArg (VarRef id, (n, Some na))) t' *)
-	(* 	else *)
-	interp_casted_constr_evars isevars env ce t' 
-      in
+      let c = interp_casted_constr_evars isevars env ce t' in
       let d = na, Some c, t' in
 	(na, c) :: subst, d :: instctx)
     (subst, []) (List.rev ctx) inst
@@ -140,9 +132,9 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=Class
   let k, ctx', imps, subst = 
     let c = Command.generalize_constr_expr tclass ctx in
     let c', imps = interp_type_evars_impls ~evdref:isevars env c in
-    let ctx, c = Classes.decompose_named_assum c' in
+    let ctx, c = Sign.decompose_prod_assum c' in
     let cl, args = Typeclasses.dest_class_app c in
-      cl, ctx, imps, substitution_of_constrs (List.map snd cl.cl_context) (List.rev (Array.to_list args))
+      cl, ctx, imps, (List.rev (Array.to_list args))
   in
   let id = 
     match snd instid with
@@ -155,11 +147,11 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=Class
 	  let i = Nameops.add_suffix (Classes.id_of_class k) "_instance_0" in
 	    Termops.next_global_ident_away false i (Termops.ids_of_context env)
   in
-  let env' = Classes.push_named_context ctx' env in
+  let env' = push_rel_context ctx' env in
   isevars := Evarutil.nf_evar_defs !isevars;
   isevars := resolve_typeclasses ~onlyargs:false ~fail:true env' !isevars;
   let sigma = Evd.evars_of !isevars in
-  let substctx = Typeclasses.nf_substitution sigma subst in
+  let substctx = List.map (Evarutil.nf_evar sigma) subst in
   let subst, _propsctx = 
     let props = 
       List.map (fun (x, l, d) -> 
@@ -172,8 +164,8 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=Class
 	List.fold_left
 	  (fun (props, rest) (id,_,_) -> 
 	    try 
-	      let ((loc, mid), c) = List.find (fun ((_,id'), c) -> id' = id) rest in
-	      let rest' = List.filter (fun ((_,id'), c) -> id' <> id) rest in
+	      let ((loc, mid), c) = List.find (fun ((_,id'), c) -> Name id' = id) rest in
+	      let rest' = List.filter (fun ((_,id'), c) -> Name id' <> id) rest in
 		Constrintern.add_glob loc (ConstRef (List.assoc mid k.cl_projs));
 		c :: props, rest'
 	    with Not_found -> (CHole (Util.dummy_loc, None) :: props), rest)
@@ -184,20 +176,13 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=Class
 	else
 	  type_ctx_instance isevars env' k.cl_props props substctx
   in
-  let inst_constr, ty_constr = instance_constructor k (List.rev_map snd subst) in
+  let inst_constr, ty_constr = instance_constructor k (List.rev subst) in
     isevars := Evarutil.nf_evar_defs !isevars;
-    let term = Evarutil.nf_isevar !isevars (it_mkNamedLambda_or_LetIn inst_constr ctx')
-    and termtype = Evarutil.nf_isevar !isevars (it_mkNamedProd_or_LetIn ty_constr ctx') 
+    let term = Evarutil.nf_isevar !isevars (it_mkLambda_or_LetIn inst_constr ctx')
+    and termtype = Evarutil.nf_isevar !isevars (it_mkProd_or_LetIn ty_constr ctx') 
     in
       isevars := undefined_evars !isevars;
       Evarutil.check_evars env Evd.empty !isevars termtype;
-(*   let imps =  *)
-(*     Util.list_map_i  *)
-(*       (fun i binder -> *)
-(* 	match binder with *)
-(* 	ExplByPos (i, Some na), (true, true)) *)
-(*       1 ctx *)
-(*   in *)
       let hook gr = 
 	let cst = match gr with ConstRef kn -> kn | _ -> assert false in
 	let inst = Typeclasses.new_instance k pri global cst in
diff --git a/contrib/subtac/subtac_classes.mli b/contrib/subtac/subtac_classes.mli
index 43f00107..afb0d38d 100644
--- a/contrib/subtac/subtac_classes.mli
+++ b/contrib/subtac/subtac_classes.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: subtac_classes.mli 10797 2008-04-15 13:19:33Z msozeau $ i*)
+(*i $Id: subtac_classes.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -26,11 +26,11 @@ open Classes
 
 val type_ctx_instance :     Evd.evar_defs ref ->
     Environ.env ->
-    (Names.identifier * 'a * Term.constr) list ->
+    ('a * Term.constr option * Term.constr) list ->
     Topconstr.constr_expr list ->
-    (Names.identifier * Term.constr) list ->
-    (Names.identifier * Term.constr) list *
-    (Names.identifier * Term.constr option * Term.constr) list
+    Term.constr list ->
+    Term.constr list *
+    ('a * Term.constr option * Term.constr) list
 
 val new_instance : 
   ?global:bool ->
diff --git a/contrib/subtac/subtac_coercion.ml b/contrib/subtac/subtac_coercion.ml
index b45e23d0..b046f0b3 100644
--- a/contrib/subtac/subtac_coercion.ml
+++ b/contrib/subtac/subtac_coercion.ml
@@ -6,7 +6,7 @@
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
-(* $Id: subtac_coercion.ml 11143 2008-06-18 15:52:42Z msozeau $ *)
+(* $Id: subtac_coercion.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -111,41 +111,31 @@ module Coercion = struct
       : (Term.constr -> Term.constr) option 
       =
     let x = nf_evar (evars_of !isevars) x and y = nf_evar (evars_of !isevars) y in
-(*       (try debug 1 (str "Coerce called for " ++ (my_print_constr env x) ++  *)
-(* 		  str " and "++ my_print_constr env y ++  *)
-(* 		  str " with evars: " ++ spc () ++ *)
-(* 		  my_print_evardefs !isevars); *)
-(*        with _ -> ()); *)
     let rec coerce_unify env x y =
-(*       (try debug 1 (str "coerce_unify from " ++ (my_print_constr env x) ++  *)
-(* 		  str " to "++ my_print_constr env y) *)
-(*        with _ -> ()); *)
       let x = hnf env isevars x and y = hnf env isevars y in
 	try 
 	  isevars := the_conv_x_leq env x y !isevars;
-	  (* 	(try debug 1 (str "Unified " ++ (my_print_constr env x) ++  *)
-	  (* 			str " and "++ my_print_constr env y); *)
-	  (* 	 with _ -> ()); *)
 	  None
 	with Reduction.NotConvertible -> coerce' env x y
     and coerce' env x y : (Term.constr -> Term.constr) option =
       let subco () = subset_coerce env isevars x y in
+      let dest_prod c =
+	match Reductionops.decomp_n_prod env (evars_of !isevars) 1 c with
+	| [(na,b,t)], c -> (na,t), c
+	| _ -> raise NoSubtacCoercion
+      in
       let rec coerce_application typ typ' c c' l l' =
 	let len = Array.length l in
 	let rec aux tele typ typ' i co = 
-(* 	  (try trace (str "coerce_application.aux from " ++ (my_print_constr env x) ++ *)
-(* 			 str " to "++ my_print_constr env y *)
-(* 		       ++ str "in env:" ++ my_print_env env); *)
-(* 	    with _ -> ()); *)
 	  if i < len then
 	    let hdx = l.(i) and hdy = l'.(i) in
 	      try isevars := the_conv_x_leq env hdx hdy !isevars;
-		let (n, eqT, restT) = destProd typ in
-		let (n', eqT', restT') = destProd typ' in
+		let (n, eqT), restT = dest_prod typ in
+		let (n', eqT'), restT' = dest_prod typ' in
 		aux (hdx :: tele) (subst1 hdx restT) (subst1 hdy restT') (succ i) co
 	      with Reduction.NotConvertible ->
-		let (n, eqT, restT) = destProd typ in
-		let (n', eqT', restT') = destProd typ' in
+		let (n, eqT), restT = dest_prod typ in
+		let (n', eqT'), restT' = dest_prod typ' in
 		let _ = 
 		  try isevars := the_conv_x_leq env eqT eqT' !isevars
 		  with Reduction.NotConvertible -> raise NoSubtacCoercion
@@ -163,12 +153,12 @@ module Coercion = struct
 				      [| eqT; hdx; pred; x; hdy; evar|]) in
 		  aux (hdy :: tele) (subst1 hdx restT) (subst1 hdy restT') (succ i)  (fun x -> eq_app (co x))
 	  else Some co
-	in aux [] typ typ' 0 (fun x -> x)
+	in 
+	  if isEvar c || isEvar c' then
+	    (* Second-order unification needed. *)
+	    raise NoSubtacCoercion;
+	  aux [] typ typ' 0 (fun x -> x)
       in
-(* 	(try trace (str "coerce' from " ++ (my_print_constr env x) ++ *)
-(* 		       str " to "++ my_print_constr env y *)
-(* 		       ++ str "in env:" ++ my_print_env env); *)
-(* 	  with _ -> ()); *)
 	match (kind_of_term x, kind_of_term y) with
 	  | Sort s, Sort s' -> 
 	      (match s, s' with
@@ -179,13 +169,6 @@ module Coercion = struct
 	  | Prod (name, a, b), Prod (name', a', b') ->
 	      let name' = Name (Nameops.next_ident_away (id_of_string "x") (Termops.ids_of_context env)) in
 	      let env' = push_rel (name', None, a') env in
-		
-(* 	      let c1 = coerce_unify env' (lift 1 a') (lift 1 a) in *)
-(* 	      let name'' = Name (Nameops.next_ident_away (id_of_string "x'") (Termops.ids_of_context env)) in *)
-(* 	      let env'' = push_rel (name'', Some (app_opt c1 (mkRel 1)), lift 1 a) env' in *)
-(* 	      let c2 = coerce_unify env'' (liftn 1 1 b) (lift 1 b') in *)
-(* 				     mkLetIn (name'', app_opt c1 (mkRel 1), (lift 1 a), *)
-
 	      let c1 = coerce_unify env' (lift 1 a') (lift 1 a) in
 		(* env, x : a' |- c1 : lift 1 a' > lift 1 a *)
 	      let coec1 = app_opt c1 (mkRel 1) in
@@ -295,7 +278,6 @@ module Coercion = struct
     and subset_coerce env isevars x y =
       match disc_subset x with
 	  Some (u, p) -> 
-	    (* trace (str "Inserting projection ");	     *)
 	    let c = coerce_unify env u y in
 	    let f x = 
 	      app_opt c (mkApp ((Lazy.force sig_).proj1, 
@@ -423,7 +405,11 @@ module Coercion = struct
       isevars, { uj_val = app_opt ct j.uj_val; 
 		 uj_type = typ' }
 
-
+  let inh_coerce_to_prod loc env isevars t =
+    let typ = whd_betadeltaiota env (evars_of isevars) (snd t) in
+    let _, typ' = mu env isevars typ in
+      isevars, (fst t, typ')
+	
   let inh_coerce_to_fail env evd rigidonly v t c1 =
     if rigidonly & not (Heads.is_rigid env c1 && Heads.is_rigid env t)
     then
@@ -504,14 +490,13 @@ module Coercion = struct
 	  None -> 0, 0
 	| Some (init, cur) -> init, cur
     in
-      (* a little more effort to get products is needed *)
-      try let rels, rng = decompose_prod_n nabs t in
+      try 
+	let rels, rng = Reductionops.decomp_n_prod env (evars_of isevars) nabs t in
 	(* The final range free variables must have been replaced by evars, we accept only that evars
 	   in rng are applied to free vars. *)
-	if noccur_with_meta 0 (succ nabsinit) rng then (
-(* 	  trace (str "No occur between 0 and " ++ int (succ nabsinit)); *)
+	if noccur_with_meta 1 (succ nabs) rng then (
 	  let env', t, t' =
-	    let env' = List.fold_right (fun (n, t) env -> push_rel (n, None, t) env) rels env in
+	    let env' = push_rel_context rels env in
 	      env', rng, lift nabs t'
 	  in
 	    try
@@ -523,6 +508,4 @@ module Coercion = struct
 		error_cannot_coerce env' sigma (t, t'))
 	else isevars
       with _ -> isevars
-(*  	trace (str "decompose_prod_n failed"); *)
-(*  	raise (Invalid_argument "Subtac_coercion.inh_conv_coerces_to") *)
 end
diff --git a/contrib/subtac/subtac_command.ml b/contrib/subtac/subtac_command.ml
index 5bff6ad1..a2f54b02 100644
--- a/contrib/subtac/subtac_command.ml
+++ b/contrib/subtac/subtac_command.ml
@@ -350,9 +350,27 @@ let compute_possible_guardness_evidences (n,_) (_, fixctx) fixtype =
 
 let push_named_context = List.fold_right push_named
 
+let check_evars env initial_sigma evd c =
+  let sigma = evars_of evd in
+  let c = nf_evar sigma c in
+  let rec proc_rec c =
+    match kind_of_term c with
+      | Evar (evk,args) ->
+          assert (Evd.mem sigma evk);
+	  if not (Evd.mem initial_sigma evk) then
+            let (loc,k) = evar_source evk evd in
+	      (match k with
+	      | QuestionMark _ -> ()
+	      | _ ->
+		  let evi = nf_evar_info sigma (Evd.find sigma evk) in
+		    Pretype_errors.error_unsolvable_implicit loc env sigma evi k None)
+      | _ -> iter_constr proc_rec c
+  in proc_rec c
+
 let interp_recursive fixkind l boxed =
   let env = Global.env() in
   let fixl, ntnl = List.split l in
+  let kind = if fixkind <> Command.IsCoFixpoint then Fixpoint else CoFixpoint in
   let fixnames = List.map (fun fix -> fix.Command.fix_name) fixl in
 
   (* Interp arities allowing for unresolved types *)
@@ -384,20 +402,17 @@ let interp_recursive fixkind l boxed =
   let rec_sign = nf_named_context_evar (evars_of evd) rec_sign in
     
   let recdefs = List.length rec_sign in
-(*   List.iter (check_evars env_rec Evd.empty evd) fixdefs; *)
-(*   List.iter (check_evars env Evd.empty evd) fixtypes; *)
-(*   check_mutuality env kind (List.combine fixnames fixdefs); *)
+  List.iter (check_evars env_rec Evd.empty evd) fixdefs;
+  List.iter (check_evars env Evd.empty evd) fixtypes;
+  Command.check_mutuality env kind (List.combine fixnames fixdefs);
 
   (* Russell-specific code *)
 
   (* Get the interesting evars, those that were not instanciated *)
   let isevars = Evd.undefined_evars evd in
-  trace (str "got undefined evars" ++ Evd.pr_evar_defs isevars);
   let evm = Evd.evars_of isevars in
-  trace (str "got the evm, recdefs is " ++ int recdefs);
   (* Solve remaining evars *)
   let rec collect_evars id def typ imps = 
-    let _ = try trace (str "In collect evars, isevars is: " ++ Evd.pr_evar_defs isevars) with _ -> () in
       (* Generalize by the recursive prototypes  *)
     let def = 
       Termops.it_mkNamedLambda_or_LetIn def rec_sign
diff --git a/contrib/subtac/subtac_command.mli b/contrib/subtac/subtac_command.mli
index 27520867..3a6a351b 100644
--- a/contrib/subtac/subtac_command.mli
+++ b/contrib/subtac/subtac_command.mli
@@ -42,6 +42,7 @@ val interp_binder :     Evd.evar_defs ref ->
     Environ.env -> Names.name -> Topconstr.constr_expr -> Term.constr
 
 
+
 val build_recursive :
   (fixpoint_expr * decl_notation) list -> bool -> unit
 
diff --git a/contrib/subtac/subtac_obligations.ml b/contrib/subtac/subtac_obligations.ml
index 55cdc7c4..a393e2c9 100644
--- a/contrib/subtac/subtac_obligations.ml
+++ b/contrib/subtac/subtac_obligations.ml
@@ -119,7 +119,7 @@ let from_prg : program_info ProgMap.t ref = ref ProgMap.empty
 let freeze () = !from_prg, !default_tactic_expr
 let unfreeze (v, t) = from_prg := v; set_default_tactic t
 let init () =
-  from_prg := ProgMap.empty; set_default_tactic (Subtac_utils.tactics_call "obligations_tactic" [])
+  from_prg := ProgMap.empty; set_default_tactic (Subtac_utils.tactics_call "obligation_tactic" [])
 
 let _ = 
   Summary.declare_summary "program-tcc-table"
@@ -442,6 +442,7 @@ and solve_obligation_by_tac prg obls i tac =
 	       true		 
 	    else false
 	  with
+	    | Stdpp.Exc_located(_, Proof_type.LtacLocated (_, Refiner.FailError (_, s)))
 	    | Stdpp.Exc_located(_, Refiner.FailError (_, s))
 	    | Refiner.FailError (_, s) ->
 		user_err_loc (obl.obl_location, "solve_obligation", s)
diff --git a/contrib/subtac/subtac_pretyping.ml b/contrib/subtac/subtac_pretyping.ml
index 0e987cf2..ad76bdeb 100644
--- a/contrib/subtac/subtac_pretyping.ml
+++ b/contrib/subtac/subtac_pretyping.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: subtac_pretyping.ml 11047 2008-06-03 23:08:00Z msozeau $ *)
+(* $Id: subtac_pretyping.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Global
 open Pp
@@ -117,7 +117,6 @@ let env_with_binders env isevars l =
   in aux (env, []) l
 
 let subtac_process env isevars id bl c tycon =
-(*   let bl = Implicit_quantifiers.ctx_of_class_binders (vars_of_env env) cbl @ l in *)
   let c = Command.abstract_constr_expr c bl in
   let tycon = 
     match tycon with
@@ -132,12 +131,14 @@ let subtac_process env isevars id bl c tycon =
   let imps = Implicit_quantifiers.implicits_of_rawterm c in
   let coqc, ctyp = interp env isevars c tycon in
   let evm = non_instanciated_map env isevars (evars_of !isevars) in
-    evm, coqc, (match tycon with Some (None, c) -> c | _ -> ctyp), imps
+  let ty = nf_isevar !isevars (match tycon with Some (None, c) -> c | _ -> ctyp) in
+    evm, coqc, ty, imps
 
 open Subtac_obligations
 
 let subtac_proof kind env isevars id bl c tycon =
   let evm, coqc, coqt, imps = subtac_process env isevars id bl c tycon in
-  let evm = Subtac_utils.evars_of_term evm Evd.empty coqc in
-  let evars, def, ty = Eterm.eterm_obligations env id !isevars evm 0 coqc coqt in
+  let evm' = Subtac_utils.evars_of_term evm Evd.empty coqc in
+  let evm' = Subtac_utils.evars_of_term evm evm' coqt in
+  let evars, def, ty = Eterm.eterm_obligations env id !isevars evm' 0 coqc coqt in
     add_definition id def ty ~implicits:imps ~kind:kind evars
diff --git a/contrib/subtac/subtac_pretyping_F.ml b/contrib/subtac/subtac_pretyping_F.ml
index afa5817f..559b6ac1 100644
--- a/contrib/subtac/subtac_pretyping_F.ml
+++ b/contrib/subtac/subtac_pretyping_F.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: subtac_pretyping_F.ml 11143 2008-06-18 15:52:42Z msozeau $ *)
+(* $Id: subtac_pretyping_F.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Pp
 open Util
@@ -246,6 +246,8 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
 		  uj_type = it_mkProd_or_LetIn j.uj_type ctxt })
             ctxtv vdef in
 	evar_type_fixpoint loc env isevars names ftys vdefj;
+	let ftys = Array.map (nf_evar (evars_of !isevars)) ftys in
+	let fdefs = Array.map (fun x -> nf_evar (evars_of !isevars) (j_val x)) vdefj in
 	let fixj = match fixkind with
 	  | RFix (vn,i) ->
 	      (* First, let's find the guard indexes. *)
@@ -260,11 +262,11 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
 		   | None -> list_map_i (fun i _ -> i) 0 ctxtv.(i))
 		vn)
 	      in 
-	      let fixdecls = (names,ftys,Array.map j_val vdefj) in 
+	      let fixdecls = (names,ftys,fdefs) in 
 	      let indexes = search_guard loc env possible_indexes fixdecls in 
 	      make_judge (mkFix ((indexes,i),fixdecls)) ftys.(i)
 	  | RCoFix i -> 
-	      let cofix = (i,(names,ftys,Array.map j_val vdefj)) in
+	      let cofix = (i,(names,ftys,fdefs)) in
 	      (try check_cofix env cofix with e -> Stdpp.raise_with_loc loc e);
 	      make_judge (mkCoFix cofix) ftys.(i) in
 	inh_conv_coerce_to_tycon loc env isevars fixj tycon
@@ -273,13 +275,15 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
 	inh_conv_coerce_to_tycon loc env isevars (pretype_sort s) tycon
 
     | RApp (loc,f,args) -> 
-	let length = List.length args in	 
+	let length = List.length args in 
 	let ftycon = 
-	  match tycon with
-	      None -> None
+	  if length > 0 then
+	    match tycon with
+	    | None -> None
 	    | Some (None, ty) -> mk_abstr_tycon length ty
 	    | Some (Some (init, cur), ty) ->
 		Some (Some (length + init, length + cur), ty)
+	  else tycon
 	in
 	let fj = pretype ftycon env isevars lvar f in
  	let floc = loc_of_rawconstr f in
@@ -291,23 +295,13 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
               let resty = whd_betadeltaiota env (evars_of !isevars) resj.uj_type in
       		match kind_of_term resty with
 		  | Prod (na,c1,c2) ->
-		      let hj = pretype (mk_tycon c1) env isevars lvar c in
+		      Option.iter (fun ty -> isevars :=
+			Coercion.inh_conv_coerces_to loc env !isevars resty ty) tycon;
+		      let evd, (_, _, tycon) = split_tycon loc env !isevars tycon in
+		      isevars := evd;
+		      let hj = pretype (mk_tycon (nf_isevar !isevars c1)) env isevars lvar c in
 		      let value, typ = applist (j_val resj, [j_val hj]), subst1 hj.uj_val c2 in
 		      let typ' = nf_isevar !isevars typ in
-		      let tycon = 
-			Option.map 
-			  (fun (abs, ty) ->
-			     match abs with
-				 None ->
-				   isevars := Coercion.inh_conv_coerces_to loc env !isevars typ'
-				     (abs, ty);
-				   (abs, ty)
-			       | Some (init, cur) ->
-				   isevars := Coercion.inh_conv_coerces_to loc env !isevars typ' 
-				     (abs, ty);
-				   (Some (init, pred cur), ty))
-			  tycon
-		      in 
 			apply_rec env (n+1) 
 			  { uj_val = nf_isevar !isevars value;
 			    uj_type = nf_isevar !isevars typ' }
@@ -319,7 +313,6 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
 			  (join_loc floc argloc) env (evars_of !isevars)
 	      		  resj [hj]
 	in
-	let ftycon = Option.map (lift_abstr_tycon_type (-1)) ftycon in
 	let resj = j_nf_evar (evars_of !isevars) (apply_rec env 1 fj ftycon args) in
 	let resj =
 	  match kind_of_term resj.uj_val with
@@ -332,12 +325,22 @@ module SubtacPretyping_F (Coercion : Coercion.S) = struct
 	  inh_conv_coerce_to_tycon loc env isevars resj tycon
 
     | RLambda(loc,name,k,c1,c2)      ->
-	let (name',dom,rng) = evd_comb1 (split_tycon loc env) isevars tycon in
+	let tycon' = evd_comb1 
+	  (fun evd tycon -> 
+	    match tycon with 
+	    | None -> evd, tycon 
+	    | Some ty -> 
+		let evd, ty' = Coercion.inh_coerce_to_prod loc env evd ty in
+		  evd, Some ty') 
+	  isevars tycon 
+	in
+	let (name',dom,rng) = evd_comb1 (split_tycon loc env) isevars tycon' in
 	let dom_valcon = valcon_of_tycon dom in
 	let j = pretype_type dom_valcon env isevars lvar c1 in
 	let var = (name,None,j.utj_val) in
 	let j' = pretype rng (push_rel var env) isevars lvar c2 in 
-	  judge_of_abstraction env name j j'
+	let resj = judge_of_abstraction env name j j' in
+	  inh_conv_coerce_to_tycon loc env isevars resj tycon
 
     | RProd(loc,name,k,c1,c2)        ->
 	let j = pretype_type empty_valcon env isevars lvar c1 in
diff --git a/contrib/subtac/test/ListsTest.v b/contrib/subtac/test/ListsTest.v
index 3ceea173..05fc0803 100644
--- a/contrib/subtac/test/ListsTest.v
+++ b/contrib/subtac/test/ListsTest.v
@@ -1,5 +1,5 @@
 (* -*- coq-prog-args: ("-emacs-U" "-debug") -*- *)
-Require Import Coq.subtac.Utils.
+Require Import Coq.Program.Program.
 Require Import List.
 
 Set Implicit Arguments.
@@ -7,7 +7,7 @@ Set Implicit Arguments.
 Section Accessors.
   Variable A : Set.
 
-  Program Definition myhd : forall { l : list A | length l <> 0 }, A :=  
+  Program Definition myhd : forall (l : list A | length l <> 0), A :=  
     fun l =>
       match l with
         | nil => !
@@ -39,7 +39,7 @@ Section app.
 
   Next Obligation.
     intros.
-    destruct_call app ; subtac_simpl.
+    destruct_call app ; program_simpl.
   Defined.
   
   Program Lemma app_id_l : forall l : list A, l = nil ++ l.
@@ -49,7 +49,7 @@ Section app.
   
   Program Lemma app_id_r : forall l : list A, l = l ++ nil.
   Proof.
-    induction l ; simpl ; auto.
+    induction l ; simpl in * ; auto. 
     rewrite <- IHl ; auto.
   Qed.
 
@@ -70,16 +70,24 @@ Section Nth.
 
   Next Obligation.
   Proof.
-    intros.
-    inversion H.
+    simpl in *. auto with arith. 
   Defined.
 
+  Next Obligation.
+  Proof.
+    inversion H.
+  Qed.
+
   Program Fixpoint nth' (l : list A) (n : nat | n < length l) { struct l } : A := 
     match l, n with
       | hd :: _, 0 => hd
       | _ :: tl, S n' => nth' tl n'
       | nil, _ => !
     end.
+  Next Obligation.
+  Proof.
+    simpl in *. auto with arith. 
+  Defined.
 
   Next Obligation.
   Proof.
diff --git a/contrib/subtac/test/take.v b/contrib/subtac/test/take.v
index 87ab47d6..2e17959c 100644
--- a/contrib/subtac/test/take.v
+++ b/contrib/subtac/test/take.v
@@ -1,9 +1,12 @@
 (* -*- coq-prog-args: ("-emacs-U" "-debug") -*- *)
 Require Import JMeq.
 Require Import List.
-Require Import Coq.subtac.Utils.
+Require Import Program.
 
 Set Implicit Arguments.
+Obligations Tactic := idtac.
+
+Print cons.
 
 Program Fixpoint take (A : Set) (l : list A) (n : nat | n <= length l) { struct l } : { l' : list A | length l' = n } :=
   match n with
@@ -16,21 +19,14 @@ Program Fixpoint take (A : Set) (l : list A) (n : nat | n <= length l) { struct
   end.
 
 Require Import Omega.
-
+Solve All Obligations.
 Next Obligation.
-  intros.
-  simpl in l0.
-  apply le_S_n ; exact l0.
-Defined.
-
-Next Obligation.
-  intros.
-  destruct_call take ; subtac_simpl.
+  destruct_call take ; program_simpl.
 Defined.
 
 Next Obligation.
   intros.
-  inversion l0.
+  inversion H.
 Defined.
 
 
diff --git a/contrib/xml/proofTree2Xml.ml4 b/contrib/xml/proofTree2Xml.ml4
index 9afd07a6..05be01bc 100644
--- a/contrib/xml/proofTree2Xml.ml4
+++ b/contrib/xml/proofTree2Xml.ml4
@@ -82,8 +82,7 @@ let first_word s =
 
 let string_of_prim_rule x = match x with
   | Proof_type.Intro _-> "Intro"
-  | Proof_type.Intro_replacing _-> "Intro_replacing"
-  | Proof_type.Cut (_,_,_) -> "Cut"
+  | Proof_type.Cut _ -> "Cut"
   | Proof_type.FixRule (_,_,_) -> "FixRule"
   | Proof_type.Cofix (_,_)-> "Cofix"
   | Proof_type.Refine _ -> "Refine"
diff --git a/dev/doc/style.txt b/dev/doc/style.txt
index 2e597dc4..a8924ba6 100644
--- a/dev/doc/style.txt
+++ b/dev/doc/style.txt
@@ -20,6 +20,32 @@ match expr with
   | A -> ...
   | B x -> ...
 
+Remarque : à partir de la 8.2 environ, la tendance est à utiliser le
+format suivant qui permet de limiter l'escalade d'indentation tout en
+produisant un aspect visuel intéressant de bloc :
+
+type t =
+| A 
+| B of machin
+
+match expr with
+| A -> ...
+| B x -> ...
+
+let f expr = match expr with
+| A -> ...
+| B x -> ...
+
+let f expr = function
+| A -> ...
+| B x -> ...
+
+Le deuxième cas est obtenu sous tuareg avec les réglages
+
+  (setq tuareg-with-indent 0)
+  (setq tuareg-function-indent 0)
+  (setq tuareg-let-always-indent nil) /// notons que cette dernière est bien 
+                                      /// pour les let mais pas pour les let-in
 
 Conditionnelles
 ===============
diff --git a/dev/top_printers.ml b/dev/top_printers.ml
index afae141b..a2285015 100644
--- a/dev/top_printers.ml
+++ b/dev/top_printers.ml
@@ -128,6 +128,8 @@ let ppenv e = pp
 
 let pptac = (fun x -> pp(Pptactic.pr_glob_tactic (Global.env()) x))
 
+let ppinsts c = pp (pr_instance_gmap c)
+
 let ppobj obj = Format.print_string (Libobject.object_tag obj)
 
 let cnt = ref 0
diff --git a/doc/INSTALL b/doc/INSTALL
deleted file mode 100644
index 9223a41b..00000000
--- a/doc/INSTALL
+++ /dev/null
@@ -1,65 +0,0 @@
-                           The Coq documentation
-                           =====================
-
-The Coq documentation includes 
-
-- A Reference Manual
-- A Tutorial
-- A document presenting the Coq standard library
-- A list of questions/answers in the FAQ style
-
-The sources of the documents are mainly made of LaTeX code from which
-user-readable PostScript or PDF files, or a user-browsable bunch of
-html files are generated.
-
-Prerequisite
-------------
-
-To produce the documents, you need the coqtop, coq-tex, coqdoc and
-gallina tools, with same version number as the current
-documentation. These four tools normally come with any basic Coq
-installation.
-
-In addition, to produce the PostScript documents, the following tools
-are needed:
-
-  - latex (latex2e)
-  - dvips
-  - bibtex
-  - makeindex
-  - pngtopnm and pnmtops (for the Reference Manual and the FAQ)
-
-To produce the PDF documents, the following tools are needed:
-
-  - pdflatex
-  - bibtex
-
-To produce the html documents, the following tools are needed:
-
-  - hevea (e.g. 1.07 works)
-
-To produce the documentation of the standard library, a source copy of
-the coq distribution is needed.
-
-Compilation
------------
-
-To produce all PostScript documents, do:                make all-ps
-To produce all PDF documents, do:                       make all-pdf
-To produce all html documents, do:                      make all-html
-To produce all formats of the Reference Manual, do:     make refman
-To produce all formats of the Tutorial, do:             make tutorial
-To produce all formats of the Coq Standard Library, do: make stdlib
-To produce all formats of the FAQ, do:                  make faq
-
-Installation
-------------
-
-To install all produced documents, do:
-
-  make DOCDIR=/some/directory/for/documentation install
-
-DOCDIR defauts to /usr/share/doc/coq-x.y were x.y is the version number
-
-
-
diff --git a/doc/LICENCE b/doc/LICENCE
deleted file mode 100644
index 99087480..00000000
--- a/doc/LICENCE
+++ /dev/null
@@ -1,630 +0,0 @@
-The Coq Reference Manual is a collective work from the Coq Development
-Team whose members are listed in the file CREDITS of the Coq source
-package. All related documents (the LaTeX and BibTeX sources, the
-embedded png files, and the PostScript, PDF and html outputs) are
-copyright (c) INRIA 1999-2006. The material connected to the Reference
-Manual may be distributed only subject to the terms and conditions set
-forth in the Open Publication License, v1.0 or later (the latest
-version is presently available at http://www.opencontent.org/openpub/).
-Options A and B are *not* elected.
-
-The Coq Tutorial is a work by Gérard Huet, Gilles Kahn and Christine
-Paulin-Mohring. All documents (the LaTeX source and the PostScript,
-PDF and html outputs) are copyright (c) INRIA 1999-2006. The material
-connected to the Coq Tutorial may be distributed only subject to the
-terms and conditions set forth in the Open Publication License, v1.0
-or later (the latest version is presently available at
-http://www.opencontent.org/openpub/). Options A and B are *not*
-elected.
-
-The Coq Standard Library is a collective work from the Coq Development
-Team whose members are listed in the file CREDITS of the Coq source
-package. All related documents (the Coq vernacular source files and
-the PostScript, PDF and html outputs) are copyright (c) INRIA
-1999-2006. The material connected to the Standard Library is
-distributed under the terms of the Lesser General Public License
-version 2.1 or later. 
-
-The FAQ (Coq for the Clueless) is a work by Pierre Castéran, Hugo
-Herbelin, Florent Kirchner, Benjamin Monate, and Julien Narboux. All
-documents (the LaTeX source and the PostScript, PDF and html outputs)
-are copyright (c) INRIA 2004-2006. The material connected to the FAQ
-(Coq for the Clueless) may be distributed only subject to the terms
-and conditions set forth in the Open Publication License, v1.0 or
-later (the latest version is presently available at
-http://www.opencontent.org/openpub/). Options A and B are *not*
-elected.
-
-The Tutorial on [Co-]Inductive Types in Coq is a work by Pierre
-Castéran and Eduardo Gimenez. All related documents (the LaTeX and
-BibTeX sources and the PostScript, PDF and html outputs) are copyright
-(c) INRIA 1997-2006. The material connected to the Tutorial on
-[Co-]Inductive Types in Coq may be distributed only subject to the
-terms and conditions set forth in the Open Publication License, v1.0
-or later (the latest version is presently available at
-http://www.opencontent.org/openpub/).  Options A and B are
-*not* elected.
-
-----------------------------------------------------------------------
-
-                      *Open Publication License*
-                           v1.0, 8 June 1999
-
-
-*I. REQUIREMENTS ON BOTH UNMODIFIED AND MODIFIED VERSIONS*
-
-The Open Publication works may be reproduced and distributed in whole or
-in part, in any medium physical or electronic, provided that the terms
-of this license are adhered to, and that this license or an
-incorporation of it by reference (with any options elected by the
-author(s) and/or publisher) is displayed in the reproduction.
-
-Proper form for an incorporation by reference is as follows:
-
-    Copyright (c) <year> by <author's name or designee>. This material
-    may be distributed only subject to the terms and conditions set
-    forth in the Open Publication License, vX.Y or later (the latest
-    version is presently available at http://www.opencontent.org/openpub/).
-
-The reference must be immediately followed with any options elected by
-the author(s) and/or publisher of the document (see section VI).
-
-Commercial redistribution of Open Publication-licensed material is
-permitted.
-
-Any publication in standard (paper) book form shall require the citation
-of the original publisher and author. The publisher and author's names
-shall appear on all outer surfaces of the book. On all outer surfaces of
-the book the original publisher's name shall be as large as the title of
-the work and cited as possessive with respect to the title.
-
-
-*II. COPYRIGHT*
-
-The copyright to each Open Publication is owned by its author(s) or
-designee.
-
-
-*III. SCOPE OF LICENSE*
-
-The following license terms apply to all Open Publication works, unless
-otherwise explicitly stated in the document.
-
-Mere aggregation of Open Publication works or a portion of an Open
-Publication work with other works or programs on the same media shall
-not cause this license to apply to those other works. The aggregate work
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-material and appropriate copyright notice.
-
-SEVERABILITY. If any part of this license is found to be unenforceable
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-
-NO WARRANTY. Open Publication works are licensed and provided "as is"
-without warranty of any kind, express or implied, including, but not
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-
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-*IV. REQUIREMENTS ON MODIFIED WORKS*
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diff --git a/doc/LICENSE b/doc/LICENSE
new file mode 100644
index 00000000..99087480
--- /dev/null
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@@ -0,0 +1,630 @@
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diff --git a/doc/README b/doc/README
deleted file mode 100755
index 14cb6e44..00000000
--- a/doc/README
+++ /dev/null
@@ -1,30 +0,0 @@
-You can get the whole documentation of Coq in the tar file all-ps-docs.tar.
-
-You can also get separately each document. The documentation of Coq
-V8.0 is divided into the following documents :
-
-     * Tutorial.ps: An introduction to the use of the Coq Proof Assistant;
-
-     * Reference-Manual.ps:
-
-       Base chapters:
-       - the description of Gallina, the language of Coq
-       - the description of the Vernacular, the commands of Coq
-       - the description of each tactic
-       - index on tactics, commands and error messages
-
-       Additional chapters:
-       - the extended Cases (C.Cornes)
-       - the coercions (A. Saïbi)
-       - the tactic Omega (P. Crégut)
-       - the extraction features (J.-C. Filliâtre and P. Letouzey) 
-       - the tactic Ring (S. Boutin and P. Loiseleur)
-       - the Setoid_replace tactic (C. Renard)
-       - etc.
-
-     * Library.ps: A description of the Coq standard library;
-
-     * rectypes.ps : A tutorial on recursive types by Eduardo Gimenez
-
-Documentation is also available in the PDF format and HTML format
-(online at http://coq.inria.fr or by ftp in the file doc-html.tar.gz).
diff --git a/ide/coq.ml b/ide/coq.ml
index 5166fb21..c560f0db 100644
--- a/ide/coq.ml
+++ b/ide/coq.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coq.ml 11126 2008-06-13 18:45:04Z herbelin $ *)
+(* $Id: coq.ml 11238 2008-07-19 09:34:03Z herbelin $ *)
 
 open Vernac
 open Vernacexpr
@@ -44,6 +44,8 @@ let init () =
      messages *)
 (**)
   Flags.make_silent true;
+  (* don't set a too large undo stack because Edit.create allocates an array *)
+  Pfedit.set_undo (Some 5000);
 (**)
   Coqtop.init_ide ()
 
@@ -98,7 +100,7 @@ let is_in_loadpath dir =
 let is_in_coq_path f = 
   try 
   let base = Filename.chop_extension (Filename.basename f) in
-  let _ = Library.locate_qualified_library 
+  let _ = Library.locate_qualified_library false
 	    (Libnames.make_qualid Names.empty_dirpath 
 	       (Names.id_of_string base)) in
   prerr_endline (f ^ " is in coq path");
@@ -246,9 +248,9 @@ let rec attribute_of_vernac_command = function
   | VernacSolveExistential _ -> [SolveCommand]
 
   (* MMode *)
-  | VernacDeclProof -> []
-  | VernacReturn -> []
-  | VernacProofInstr _ -> []
+  | VernacDeclProof -> [SolveCommand]
+  | VernacReturn -> [SolveCommand]
+  | VernacProofInstr _ -> [SolveCommand]
 
   (* Auxiliary file and library management *)
   | VernacRequireFrom _ -> []
diff --git a/ide/coq.png b/ide/coq.png
index 6ad66dbd..06aac459 100644
Binary files a/ide/coq.png and b/ide/coq.png differ
diff --git a/ide/coqide.ml b/ide/coqide.ml
index 12716197..07ee698f 100644
--- a/ide/coqide.ml
+++ b/ide/coqide.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coqide.ml 11126 2008-06-13 18:45:04Z herbelin $ *)
+(* $Id: coqide.ml 11221 2008-07-11 23:28:25Z herbelin $ *)
 
 open Preferences
 open Vernacexpr
@@ -543,8 +543,11 @@ type backtrack =
 | NoBacktrack
 
 let add_undo = function (n,a,b,p,l as x) -> if p = 0 then (n+1,a,b,p,l) else x
-let add_abort = function (n,a,b,0,l) -> (0,a+1,b,0,l) | (n,a,b,p,l) -> (n,a,b,p-1,l)
-let add_qed q (n,a,b,p,l) = (n,a,b,p+q,l)
+let add_abort = function
+  | (n,a,b,0,l) -> (0,a+1,b,0,l)
+  | (n,a,b,p,l) -> (n,a,b,p-1,l)
+let add_qed q (n,a,b,p,l as x) =
+  if q = 0 then x else (n,a,BacktrackToNextActiveMark,p+q,l)
 let add_backtrack (n,a,b,p,l) b' = (n,a,b',p,l)
 
 let update_proofs (n,a,b,p,cur_lems) prev_lems =
@@ -580,38 +583,46 @@ let pop_command undos t =
   ignore (pop ());
   undos
 
-let rec apply_backtrack l = function
-  | 0, BacktrackToMark mark -> reset_to mark
-  | 0, NoBacktrack -> ()
-  | 0, BacktrackToModSec id -> reset_to_mod id
-  | p, _ ->
-      (* re-synchronize Coq to the current state of the stack *)
-      if is_empty () then
-        Coq.reset_initial ()
-      else
-        begin
-          let t = top () in
-          let undos = (0,0,BacktrackToNextActiveMark,p,l) in
-          let (_,_,b,p,l) = pop_command undos t in
-          apply_backtrack l (p,b);
-          let reset_info = Coq.compute_reset_info (snd t.ast) in
-          interp_last t.ast;
-          repush_phrase reset_info t
-        end
-
-let rec apply_undos (n,a,b,p,l) =
-  (* Aborts *)
+let apply_aborts a =
   if a <> 0 then prerr_endline ("Applying "^string_of_int a^" aborts");
-  (try Util.repeat a Pfedit.delete_current_proof ()
-   with e -> prerr_endline "WARNING : found a closed environment"; raise e);
-  (* Undos *)
-  if n<>0 then 
+  try Util.repeat a Pfedit.delete_current_proof ()
+  with e -> prerr_endline "WARNING : found a closed environment"; raise e
+
+exception UndoStackExhausted
+
+let apply_tactic_undo n =
+  if n<>0 then
     (prerr_endline ("Applying "^string_of_int n^" undos");
-     try Pfedit.undo n
-     with _ -> (* Undo stack exhausted *)
-       apply_backtrack l (p,BacktrackToNextActiveMark));
-  (* Reset *)
-  apply_backtrack l (p,b)
+     try Pfedit.undo n with _ -> raise UndoStackExhausted)
+
+let apply_reset = function
+  | BacktrackToMark mark -> reset_to mark
+  | BacktrackToModSec id -> reset_to_mod id
+  | NoBacktrack -> ()
+  | BacktrackToNextActiveMark -> assert false
+
+let rec apply_undos (n,a,b,p,l as undos) =
+  if p = 0 & b <> BacktrackToNextActiveMark then
+    begin
+      apply_aborts a;
+      try
+	apply_tactic_undo n;
+	apply_reset b
+      with UndoStackExhausted ->
+	apply_undos (n,0,BacktrackToNextActiveMark,p,l)
+    end
+  else
+    (* re-synchronize Coq to the current state of the stack *)
+    if is_empty () then
+      Coq.reset_initial ()
+    else
+      begin
+        let t = top () in
+        apply_undos (pop_command undos t);
+        let reset_info = Coq.compute_reset_info (snd t.ast) in
+        interp_last t.ast;
+        repush_phrase reset_info t
+      end
 
 (* For electric handlers *)
 exception Found
@@ -3521,24 +3532,33 @@ with _ := Induction for _ Sort _.\n",61,10, Some GdkKeysyms._S);
        \n"
 							    in
 							    let initial_about (b:GText.buffer) =
-							      (try 
-								let image = lib_ide_file "coq.png" in
-								let startup_image = GdkPixbuf.from_file image in
-								b#insert_pixbuf ~iter:b#start_iter ~pixbuf:startup_image;
-								b#insert ~iter:b#start_iter "\t\t   "
-							       with _ -> ());
+							      let initial_string = "Welcome to CoqIDE, an Integrated Development Environment for Coq\n" in
 							      let coq_version = Coq.short_version () in
-							      b#insert ~iter:b#start_iter "\n\n";
-							      if Glib.Utf8.validate coq_version then b#insert ~iter:b#start_iter coq_version;
-							      b#insert ~iter:b#start_iter "\n   "
+								b#insert ~iter:b#start_iter "\n\n";
+								if Glib.Utf8.validate ("You are running " ^ coq_version) then b#insert ~iter:b#start_iter ("You are running " ^ coq_version);
+								if Glib.Utf8.validate initial_string then b#insert ~iter:b#start_iter initial_string;
+								(try 
+								    let image = lib_ide_file "coq.png" in
+								    let startup_image = GdkPixbuf.from_file image in
+								      b#insert ~iter:b#start_iter "\n\n";
+								      b#insert_pixbuf ~iter:b#start_iter ~pixbuf:startup_image;
+								      b#insert ~iter:b#start_iter "\n\n\t\t   "
+								  with _ -> ())
 							    in
 
 							    let about (b:GText.buffer) =
-							      if Glib.Utf8.validate about_full_string
-							      then b#insert about_full_string;
-							      let coq_version = Coq.version () in
-							      if Glib.Utf8.validate coq_version
-							      then b#insert coq_version
+							      (try 
+								  let image = lib_ide_file "coq.png" in
+								  let startup_image = GdkPixbuf.from_file image in
+								    b#insert ~iter:b#start_iter "\n\n";
+								    b#insert_pixbuf ~iter:b#start_iter ~pixbuf:startup_image;
+								    b#insert ~iter:b#start_iter "\n\n\t\t   "
+								with _ -> ());
+								if Glib.Utf8.validate about_full_string
+								then b#insert about_full_string;
+								let coq_version = Coq.version () in
+								  if Glib.Utf8.validate coq_version
+								  then b#insert coq_version
 
 							    in
 							      initial_about tv2#buffer;
diff --git a/ide/preferences.ml b/ide/preferences.ml
index 444b2c2b..dba56a77 100644
--- a/ide/preferences.ml
+++ b/ide/preferences.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: preferences.ml 11058 2008-06-06 08:21:03Z herbelin $ *)
+(* $Id: preferences.ml 11276 2008-07-28 00:28:34Z glondu $ *)
 
 open Configwin
 open Printf
@@ -507,12 +507,11 @@ let configure ?(apply=(fun () -> ())) () =
   in    
   let cmd_browse =
     let predefined = [
+      Coq_config.browser;
       "netscape -remote \"openURL(%s)\"";
       "mozilla -remote \"openURL(%s)\"";
-      "firefox -remote \"openURL(%s,new-tab)\" || firefox %s &";
       "firefox -remote \"openURL(%s,new-windows)\" || firefox %s &";
       "seamonkey -remote \"openURL(%s)\" || seamonkey %s &";
-      "C:\\PROGRA~1\\INTERN~1\\IEXPLORE %s";
       "open -a Safari %s &"
     ] in
     combo 
@@ -585,4 +584,3 @@ let configure ?(apply=(fun () -> ())) () =
   match x with 
     | Return_apply | Return_ok -> save_pref ()
     | Return_cancel -> ()
-
diff --git a/interp/constrextern.ml b/interp/constrextern.ml
index 141e8f8a..efb6c853 100644
--- a/interp/constrextern.ml
+++ b/interp/constrextern.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: constrextern.ml 11024 2008-05-30 12:41:39Z msozeau $ *)
+(* $Id: constrextern.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (*i*)
 open Pp
@@ -98,7 +98,7 @@ let ids_of_ctxt ctxt =
        (function c -> match kind_of_term c with
 	  | Var id -> id
 	  | _ ->
-       error "arbitrary substitution of references not implemented")
+       error "Arbitrary substitution of references not implemented.")
      ctxt)
 
 let idopt_of_name = function 
@@ -973,7 +973,7 @@ and raw_of_eqn env constr construct_nargs branch =
             buildrec new_ids (pat::patlist) new_env (n-1) b
 
 	| _ ->
-	    error "Unsupported branch in case-analysis while printing pattern"
+	    error "Unsupported branch in case-analysis while printing pattern."
   in 
   buildrec [] [] env construct_nargs branch
 
diff --git a/interp/constrintern.ml b/interp/constrintern.ml
index 9abee4d4..9af7e769 100644
--- a/interp/constrintern.ml
+++ b/interp/constrintern.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: constrintern.ml 11065 2008-06-06 22:39:43Z msozeau $ *)
+(* $Id: constrintern.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -50,7 +50,7 @@ let for_grammar f x =
 type internalisation_error =
   | VariableCapture of identifier
   | WrongExplicitImplicit
-  | NegativeMetavariable
+  | IllegalMetavariable
   | NotAConstructor of reference
   | UnboundFixName of bool * identifier
   | NonLinearPattern of identifier
@@ -66,8 +66,8 @@ let explain_wrong_explicit_implicit =
   str "Found an explicitly given implicit argument but was expecting" ++
   fnl () ++ str "a regular one"
 
-let explain_negative_metavariable =
-  str "Metavariable numbers must be positive"
+let explain_illegal_metavariable =
+  str "Metavariables allowed only in patterns"
 
 let explain_not_a_constructor ref =
   str "Unknown constructor: " ++ pr_reference ref
@@ -99,24 +99,26 @@ let explain_bad_explicitation_number n po =
       str "Bad explicitation name: found " ++ pr_id id ++ 
       str" but was expecting " ++ s
 
-let explain_internalisation_error = function
+let explain_internalisation_error e =
+  let pp = match e with
   | VariableCapture id -> explain_variable_capture id
   | WrongExplicitImplicit -> explain_wrong_explicit_implicit
-  | NegativeMetavariable -> explain_negative_metavariable
+  | IllegalMetavariable -> explain_illegal_metavariable
   | NotAConstructor ref -> explain_not_a_constructor ref
   | UnboundFixName (iscofix,id) -> explain_unbound_fix_name iscofix id
   | NonLinearPattern id -> explain_non_linear_pattern id
   | BadPatternsNumber (n1,n2) -> explain_bad_patterns_number n1 n2
-  | BadExplicitationNumber (n,po) -> explain_bad_explicitation_number n po
+  | BadExplicitationNumber (n,po) -> explain_bad_explicitation_number n po in
+  pp ++ str "."
 
 let error_unbound_patvar loc n =
   user_err_loc
     (loc,"glob_qualid_or_patvar", str "?" ++ pr_patvar n ++ 
-      str " is unbound")
+      str " is unbound.")
 
 let error_bad_inductive_type loc =
   user_err_loc (loc,"",str 
-    "This should be an inductive type applied to names or \"_\"")
+    "This should be an inductive type applied to names or \"_\".")
 
 let error_inductive_parameter_not_implicit loc =
   user_err_loc (loc,"", str
@@ -324,7 +326,7 @@ let set_var_scope loc id (_,scopt,scopes) varscopes =
     make_current_scope (Option.get !idscopes)
     <> make_current_scope (scopt,scopes) then
       user_err_loc (loc,"set_var_scope",
-      pr_id id ++ str " already occurs in a different scope")
+      pr_id id ++ str " already occurs in a different scope.")
   else
     idscopes := Some (scopt,scopes)
 
@@ -444,7 +446,7 @@ let intern_var (env,_,_ as genv) (ltacvars,vars2,vars3,(_,impls)) loc id =
   try
     match List.assoc id unbndltacvars with
       | None -> user_err_loc (loc,"intern_var",
-	  str "variable " ++ pr_id id ++ str " should be bound to a term")
+	  str "variable " ++ pr_id id ++ str " should be bound to a term.")
       | Some id0 -> Pretype_errors.error_var_not_found_loc loc id0
   with Not_found ->
   (* Is [id] a goal or section variable *)
@@ -463,14 +465,14 @@ let find_appl_head_data (_,_,_,(_,impls)) = function
   | x -> x,[],[],[]
 
 let error_not_enough_arguments loc =
-  user_err_loc (loc,"",str "Abbreviation is not applied enough")
+  user_err_loc (loc,"",str "Abbreviation is not applied enough.")
 
 let check_no_explicitation l =
   let l = List.filter (fun (a,b) -> b <> None) l in
   if l <> [] then
     let loc = fst (Option.get (snd (List.hd l))) in
     user_err_loc
-      (loc,"",str"Unexpected explicitation of the argument of an abbreviation")
+     (loc,"",str"Unexpected explicitation of the argument of an abbreviation.")
 
 (* Is it a global reference or a syntactic definition? *)
 let intern_qualid loc qid intern env args =
@@ -580,7 +582,7 @@ let check_number_of_pattern loc n l =
 let check_or_pat_variables loc ids idsl =
   if List.exists (fun ids' -> not (list_eq_set ids ids')) idsl then
     user_err_loc (loc, "", str 
-    "The components of this disjunctive pattern must bind the same variables")
+    "The components of this disjunctive pattern must bind the same variables.")
 
 let check_constructor_length env loc cstr pl pl0 =
   let n = List.length pl + List.length pl0 in
@@ -607,7 +609,7 @@ let message_redundant_alias (id1,id2) =
 (* Expanding notations *)
 
 let error_invalid_pattern_notation loc =
-  user_err_loc (loc,"",str "Invalid notation for pattern")
+  user_err_loc (loc,"",str "Invalid notation for pattern.")
 
 let chop_aconstr_constructor loc (ind,k) args =
   let nparams = (fst (Global.lookup_inductive ind)).Declarations.mind_nparams in
@@ -815,9 +817,9 @@ let locate_if_isevar loc na = function
 
 let check_hidden_implicit_parameters id (_,_,_,(indnames,_)) =
   if List.mem id indnames then
-    errorlabstrm "" (str "A parameter or name of an inductive type " ++
-    pr_id id ++ str " must not be used as a bound variable in the type \
-of its constructor")
+    errorlabstrm "" (strbrk "A parameter or name of an inductive type " ++
+    pr_id id ++ strbrk " must not be used as a bound variable in the type \
+of its constructor.")
 
 let push_name_env lvar (ids,tmpsc,scopes as env) = function
   | Anonymous -> env 
@@ -840,11 +842,9 @@ let intern_typeclass_binders intern_type lvar env bl =
 	(env, (na,bk,None,ty)::bl))
     env bl
 
-let intern_typeclass_binder intern_type lvar (env,bl) na b ty =
-  let ctx = (na, b, ty) in
-  let (fvs, bind) = Implicit_quantifiers.generalize_class_binders_raw (pi1 env) [ctx] in
-  let env, ifvs = intern_typeclass_binders intern_type lvar (env,bl) fvs in
-    intern_typeclass_binders intern_type lvar (env,ifvs) bind
+let intern_typeclass_binder intern_type lvar (env,bl) cb =
+  let (ids, fvs, bind) = Implicit_quantifiers.generalize_class_binder_raw (pi1 env) cb in
+    intern_typeclass_binders intern_type lvar (env,bl) (fvs@[bind])
     
 let intern_local_binder_aux intern intern_type lvar ((ids,ts,sc as env),bl) = function
   | LocalRawAssum(nal,bk,ty) ->
@@ -857,8 +857,8 @@ let intern_local_binder_aux intern intern_type lvar ((ids,ts,sc as env),bl) = fu
 		(fun ((ids,ts,sc),bl) (_,na) ->
 		  ((name_fold Idset.add na ids,ts,sc), (na,k,None,ty)::bl))
 		(env,bl) nal
-	| TypeClass b ->
-	    intern_typeclass_binder intern_type lvar (env,bl) (List.hd nal) b ty)
+	| TypeClass (b,b') ->
+	    intern_typeclass_binder intern_type lvar (env,bl) (List.hd nal, (b,b'), ty))
   | LocalRawDef((loc,na),def) ->
       ((name_fold Idset.add na ids,ts,sc),
       (na,Explicit,Some(intern env def),RHole(loc,Evd.BinderType na))::bl)
@@ -880,11 +880,11 @@ let check_projection isproj nargs r =
       (try
 	let n = Recordops.find_projection_nparams ref + 1 in
 	if nargs <> n then
-	  user_err_loc (loc,"",str "Projection has not the right number of explicit parameters");
+	  user_err_loc (loc,"",str "Projection has not the right number of explicit parameters.");
       with Not_found -> 
 	user_err_loc
-	(loc,"",pr_global_env Idset.empty ref ++ str " is not a registered projection"))
-  | _, Some _ -> user_err_loc (loc_of_rawconstr r, "", str "Not a projection")
+	(loc,"",pr_global_env Idset.empty ref ++ str " is not a registered projection."))
+  | _, Some _ -> user_err_loc (loc_of_rawconstr r, "", str "Not a projection.")
   | _, None -> ()
 
 let get_implicit_name n imps =
@@ -909,10 +909,11 @@ let extract_explicit_arg imps args =
 	  let id = match pos with
 	  | ExplByName id ->
 	      if not (exists_implicit_name id imps) then
-		user_err_loc (loc,"",str "Wrong argument name: " ++ pr_id id);
+		user_err_loc
+		  (loc,"",str "Wrong argument name: " ++ pr_id id ++ str ".");
 	      if List.mem_assoc id eargs then
 		user_err_loc (loc,"",str "Argument name " ++ pr_id id
-		++ str " occurs more than once");
+		++ str " occurs more than once.");
 	      id
 	  | ExplByPos (p,_id) ->
 	      let id =
@@ -921,11 +922,12 @@ let extract_explicit_arg imps args =
 		  if not (is_status_implicit imp) then failwith "imp";
 		  name_of_implicit imp
 		with Failure _ (* "nth" | "imp" *) ->
-		  user_err_loc (loc,"",str"Wrong argument position: " ++ int p)
+		  user_err_loc
+		    (loc,"",str"Wrong argument position: " ++ int p ++ str ".")
 	      in
 	      if List.mem_assoc id eargs then
 		user_err_loc (loc,"",str"Argument at position " ++ int p ++
-		  str " is mentioned more than once");
+		  str " is mentioned more than once.");
 	      id in
 	  ((id,(loc,a))::eargs,rargs)
   in aux args
@@ -1086,7 +1088,7 @@ let internalise sigma globalenv env allow_patvar lvar c =
     | CPatVar (loc, n) when allow_patvar ->
 	RPatVar (loc, n)
     | CPatVar (loc, _) ->
-	raise (InternalisationError (loc,NegativeMetavariable))
+	raise (InternalisationError (loc,IllegalMetavariable))
     | CEvar (loc, n, l) ->
 	REvar (loc, n, Option.map (List.map (intern env)) l)
     | CSort (loc, s) ->
@@ -1149,7 +1151,7 @@ let internalise sigma globalenv env allow_patvar lvar c =
 	let nal = List.map (function
 	  | RHole loc -> Anonymous
 	  | RVar (_,id) -> Name id
-	  | c -> user_err_loc (loc_of_rawconstr c,"",str "Not a name")) l in
+	  | c -> user_err_loc (loc_of_rawconstr c,"",str "Not a name.")) l in
 	let parnal,realnal = list_chop nparams nal in
 	if List.exists ((<>) Anonymous) parnal then
 	  error_inductive_parameter_not_implicit loc;
@@ -1173,9 +1175,9 @@ let internalise sigma globalenv env allow_patvar lvar c =
     in
       match bk with
 	| Default b -> default env b nal
-	| TypeClass b -> 
+	| TypeClass (b,b') -> 
 	    let env, ibind = intern_typeclass_binder intern_type lvar
-	      (env, []) (List.hd nal) b ty in
+	      (env, []) (List.hd nal,(b,b'),ty) in
 	    let body = intern_type env body in
 	      it_mkRProd ibind body
 					   
@@ -1189,9 +1191,9 @@ let internalise sigma globalenv env allow_patvar lvar c =
       | [] -> intern env body
     in match bk with
       | Default b -> default env b nal
-      | TypeClass b ->	  
+      | TypeClass (b, b') ->	  
 	  let env, ibind = intern_typeclass_binder intern_type lvar
-	    (env, []) (List.hd nal) b ty in
+	    (env, []) (List.hd nal,(b,b'),ty) in
 	  let body = intern env body in
 	    it_mkRLambda ibind body
 	      
@@ -1221,7 +1223,8 @@ let internalise sigma globalenv env allow_patvar lvar c =
 	  if eargs <> [] then 
 	    (let (id,(loc,_)) = List.hd eargs in
 	       user_err_loc (loc,"",str "Not enough non implicit
-	    arguments to accept the argument bound to " ++ pr_id id));
+	    arguments to accept the argument bound to " ++ 
+		 pr_id id ++ str"."));
 	  []
       | ([], rargs) ->
 	  assert (eargs = []);
@@ -1275,23 +1278,6 @@ let intern_ltac isarity ltacvars sigma env c =
 
 type manual_implicits = (explicitation * (bool * bool)) list
 
-let implicits_of_rawterm l = 
-  let rec aux i c = 
-    match c with
-	RProd (loc, na, bk, t, b) | RLambda (loc, na, bk, t, b) -> 
-	  let rest = aux (succ i) b in
-	    if bk = Implicit then
-	      let name =
-		match na with
-		    Name id -> Some id
-		  | Anonymous -> None
-	      in
-		(ExplByPos (i, name), (true, true)) :: rest
-	    else rest
-      | RLetIn (loc, na, t, b) -> aux i b
-      | _ -> []
-  in aux 1 l
-
 (*********************************************************************)
 (* Functions to parse and interpret constructions *)
 
@@ -1321,11 +1307,11 @@ let interp_constr_evars_gen_impls ?evdref
   match evdref with 
     | None -> 
 	let c = intern_gen (kind=IsType) ~impls Evd.empty env c in
-	let imps = implicits_of_rawterm c in
+	let imps = Implicit_quantifiers.implicits_of_rawterm c in
 	  Default.understand_gen kind Evd.empty env c, imps
     | Some evdref ->
 	let c = intern_gen (kind=IsType) ~impls (Evd.evars_of !evdref) env c in
-	let imps = implicits_of_rawterm c in
+	let imps = Implicit_quantifiers.implicits_of_rawterm c in
 	  Default.understand_tcc_evars evdref env kind c, imps
 
 let interp_constr_evars_gen evdref env ?(impls=([],[])) kind c =
diff --git a/interp/coqlib.ml b/interp/coqlib.ml
index 65e4dcd5..ca758458 100644
--- a/interp/coqlib.ml
+++ b/interp/coqlib.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coqlib.ml 11072 2008-06-08 16:13:37Z herbelin $ *)
+(* $Id: coqlib.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -70,7 +70,7 @@ let check_required_library d =
      (dummy_loc,make_qualid (make_dirpath (List.rev prefix)) m)
 *)
 (* or failing ...*)
-    error ("Library "^(string_of_dirpath dir)^" has to be required first")
+    error ("Library "^(string_of_dirpath dir)^" has to be required first.")
 
 (************************************************************************)
 (* Specific Coq objects *)
diff --git a/interp/genarg.ml b/interp/genarg.ml
index 49c157f2..c54dfe23 100644
--- a/interp/genarg.ml
+++ b/interp/genarg.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: genarg.ml 10753 2008-04-04 14:55:47Z herbelin $ *)
+(* $Id: genarg.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -75,24 +75,24 @@ let create_arg s =
 let exists_argtype s = List.mem s !dyntab
 
 type intro_pattern_expr =
-  | IntroOrAndPattern of case_intro_pattern_expr
+  | IntroOrAndPattern of or_and_intro_pattern_expr
   | IntroWildcard
-  | IntroIdentifier of identifier
-  | IntroAnonymous
   | IntroRewrite of bool
+  | IntroIdentifier of identifier
   | IntroFresh of identifier
-and case_intro_pattern_expr = intro_pattern_expr list list
+  | IntroAnonymous
+and or_and_intro_pattern_expr = (loc * intro_pattern_expr) list list
 
-let rec pr_intro_pattern = function
-  | IntroOrAndPattern pll -> pr_case_intro_pattern pll
+let rec pr_intro_pattern (_,pat) = match pat with
+  | IntroOrAndPattern pll -> pr_or_and_intro_pattern pll
   | IntroWildcard -> str "_"
-  | IntroIdentifier id -> pr_id id
-  | IntroAnonymous -> str "?"
   | IntroRewrite true -> str "->"
   | IntroRewrite false -> str "<-"
+  | IntroIdentifier id -> pr_id id
   | IntroFresh id -> str "?" ++ pr_id id
+  | IntroAnonymous -> str "?"
 
-and pr_case_intro_pattern = function
+and pr_or_and_intro_pattern = function
   | [pl] ->
       str "(" ++ hv 0 (prlist_with_sep pr_coma pr_intro_pattern pl) ++ str ")"
   | pll ->
diff --git a/interp/genarg.mli b/interp/genarg.mli
index 3548585b..da175078 100644
--- a/interp/genarg.mli
+++ b/interp/genarg.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: genarg.mli 10753 2008-04-04 14:55:47Z herbelin $ i*)
+(*i $Id: genarg.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Util
 open Names
@@ -32,16 +32,16 @@ type open_rawconstr = unit * rawconstr_and_expr
 type 'a with_ebindings = 'a * open_constr bindings
 
 type intro_pattern_expr =
-  | IntroOrAndPattern of case_intro_pattern_expr
+  | IntroOrAndPattern of or_and_intro_pattern_expr
   | IntroWildcard
-  | IntroIdentifier of identifier
-  | IntroAnonymous
   | IntroRewrite of bool
+  | IntroIdentifier of identifier
   | IntroFresh of identifier
-and case_intro_pattern_expr = intro_pattern_expr list list
+  | IntroAnonymous
+and or_and_intro_pattern_expr = (loc * intro_pattern_expr) list list
 
-val pr_intro_pattern : intro_pattern_expr -> Pp.std_ppcmds
-val pr_case_intro_pattern : case_intro_pattern_expr -> Pp.std_ppcmds
+val pr_intro_pattern : intro_pattern_expr located -> Pp.std_ppcmds
+val pr_or_and_intro_pattern : or_and_intro_pattern_expr -> Pp.std_ppcmds
 
 (* The route of a generic argument, from parsing to evaluation
 
@@ -128,15 +128,16 @@ val wit_int_or_var : (int or_var,tlevel) abstract_argument_type
 
 val rawwit_string : (string,rlevel) abstract_argument_type
 val globwit_string : (string,glevel) abstract_argument_type
+
 val wit_string : (string,tlevel) abstract_argument_type
 
 val rawwit_pre_ident : (string,rlevel) abstract_argument_type
 val globwit_pre_ident : (string,glevel) abstract_argument_type
 val wit_pre_ident : (string,tlevel) abstract_argument_type
 
-val rawwit_intro_pattern : (intro_pattern_expr,rlevel) abstract_argument_type
-val globwit_intro_pattern : (intro_pattern_expr,glevel) abstract_argument_type
-val wit_intro_pattern : (intro_pattern_expr,tlevel) abstract_argument_type
+val rawwit_intro_pattern : (intro_pattern_expr located,rlevel) abstract_argument_type
+val globwit_intro_pattern : (intro_pattern_expr located,glevel) abstract_argument_type
+val wit_intro_pattern : (intro_pattern_expr located,tlevel) abstract_argument_type
 
 val rawwit_ident : (identifier,rlevel) abstract_argument_type
 val globwit_ident : (identifier,glevel) abstract_argument_type
diff --git a/interp/implicit_quantifiers.ml b/interp/implicit_quantifiers.ml
index d480ad39..a83071d1 100644
--- a/interp/implicit_quantifiers.ml
+++ b/interp/implicit_quantifiers.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: implicit_quantifiers.ml 10922 2008-05-12 12:47:17Z msozeau $ i*)
+(*i $Id: implicit_quantifiers.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -29,7 +29,6 @@ open Pp
 let ids_of_list l = 
   List.fold_right Idset.add l Idset.empty
 
-
 let locate_reference qid =
   match Nametab.extended_locate qid with
     | TrueGlobal ref -> true
@@ -88,44 +87,17 @@ let rec make_fresh ids env x =
 let freevars_of_ids env ids = 
   List.filter (is_freevar env (Global.env())) ids
 
-let compute_constrs_freevars env constrs =
-  let ids = 
-    List.rev (List.fold_left 
-		 (fun acc x -> free_vars_of_constr_expr x acc) 
-		 [] constrs)
-  in freevars_of_ids env ids
-
-(* let compute_context_freevars env ctx = *)
-(*   let ids = *)
-(*     List.rev *)
-(*       (List.fold_left *)
-(* 	  (fun acc (_,i,x) -> free_vars_of_constr_expr x acc) *)
-(* 	  [] constrs) *)
-(*   in freevars_of_ids ids *)
-
-let compute_constrs_freevars_binders env constrs =
-  let elts = compute_constrs_freevars env constrs in
-    List.map (fun id -> (dummy_loc, id), CHole (dummy_loc, None)) elts
-
 let binder_list_of_ids ids =
   List.map (fun id -> LocalRawAssum ([dummy_loc, Name id], Default Implicit, CHole (dummy_loc, None))) ids
       
 let next_ident_away_from id avoid = make_fresh avoid (Global.env ()) id
-(*   let rec name_rec id = *)
-(*     if Idset.mem id avoid then name_rec (Nameops.lift_ident id) else id in  *)
-(*   name_rec id  *)
-
-let ids_of_named_context_avoiding avoid l =
-  List.fold_left (fun (ids, avoid) id -> 
-    let id' = next_ident_away_from id avoid in id' :: ids, Idset.add id' avoid) 
-    ([], avoid) (Termops.ids_of_named_context l)
     
 let combine_params avoid fn applied needed =
   let named, applied = 
     List.partition 
       (function
 	  (t, Some (loc, ExplByName id)) -> 
-	    if not (List.exists (fun (_, (id', _, _)) -> id = id') needed) then
+	    if not (List.exists (fun (_, (id', _, _)) -> Name id = id') needed) then
 	      user_err_loc (loc,"",str "Wrong argument name: " ++ Nameops.pr_id id);
 	    true
 	| _ -> false) applied
@@ -138,13 +110,13 @@ let combine_params avoid fn applied needed =
     match app, need with
 	[], [] -> List.rev ids, avoid
 
-      | app, (_, (id, _, _)) :: need when List.mem_assoc id named ->
+      | app, (_, (Name id, _, _)) :: need when List.mem_assoc id named ->
 	  aux (List.assoc id named :: ids) avoid app need
 	    
-      | (x, None) :: app, (None, (id, _, _)) :: need ->
+      | (x, None) :: app, (None, (Name id, _, _)) :: need ->
 	  aux (x :: ids) avoid app need
 	    
-      | _, (Some cl, (id, _, _) as d) :: need -> 
+      | _, (Some cl, (Name id, _, _) as d) :: need -> 
 	  let t', avoid' = fn avoid d in
 	    aux (t' :: ids) avoid' app need
 
@@ -155,12 +127,14 @@ let combine_params avoid fn applied needed =
 	    aux (t' :: ids) avoid' app need
 
       | _ :: _, [] -> failwith "combine_params: overly applied typeclass"
+
+      | _, _ -> raise (Invalid_argument "combine_params")
   in aux [] avoid applied needed
 
 let combine_params_freevar avoid applied needed =
   combine_params avoid
     (fun avoid (_, (id, _, _)) -> 
-      let id' = next_ident_away_from id avoid in
+      let id' = next_ident_away_from (Nameops.out_name id) avoid in
 	(CRef (Ident (dummy_loc, id')), Idset.add id' avoid))
     applied needed
 
@@ -201,19 +175,6 @@ let full_class_binders env l =
 	| Explicit -> (x :: l', avoid))
       ([], avoid) l
   in List.rev l'
-      
-let constr_expr_of_constraint (kind, id) l =
-  match kind with
-    | Implicit -> CAppExpl (fst id, (None, Ident id), l)
-    | Explicit -> CApp (fst id, (None, CRef (Ident id)),
-		       List.map (fun x -> x, None) l)
-
-(*    | CApp of loc * (proj_flag * constr_expr) *  *)
-(*         (constr_expr * explicitation located option) list *)
-
-
-let constrs_of_context l =
-  List.map (fun (_, id, l) -> constr_expr_of_constraint id l) l
 
 let compute_context_freevars env ctx =
   let bound, ids = 
@@ -232,41 +193,50 @@ let resolve_class_binders env l =
   in
     fv_ctx, ctx
 
-let generalize_class_binders env l = 
-  let fv_ctx, cstrs = resolve_class_binders env l in
-    List.map (fun ((loc, id), t) -> LocalRawAssum ([loc, Name id], Default Implicit, t)) fv_ctx,
-  List.map (fun (iid, bk, c) -> LocalRawAssum ([iid], Default Implicit, c)) 
-    cstrs
+let full_class_binder env (iid, (bk, bk'), cl as c) = 
+  let avoid = Idset.union env (ids_of_list (compute_context_vars env [c])) in
+  let c, avoid =
+    match bk' with
+    | Implicit -> 
+	let (loc, id, l) = 
+	  try destClassAppExpl cl 
+	  with Not_found -> 
+	    user_err_loc (constr_loc cl, "class_binders", str"Not an applied type class")
+	in
+	let gr = Nametab.global id in
+	  (try
+	      let c = class_info gr in
+	      let args, avoid = combine_params_freevar avoid l (List.rev c.cl_context) in
+		(iid, bk, CAppExpl (loc, (None, id), args)), avoid
+	    with Not_found -> not_a_class (Global.env ()) (constr_of_global gr))
+    | Explicit -> ((iid,bk,cl), avoid)
+  in c
+
+let compute_constraint_freevars env (oid, _, x) =
+  let bound = match snd oid with Name n -> Idset.add n env | Anonymous -> env in
+  let ids = free_vars_of_constr_expr x ~bound [] in
+    freevars_of_ids env (List.rev ids)
+
+let resolve_class_binder env c = 
+  let cstr = full_class_binder env c in
+  let fv_ctx = 
+    let elts = compute_constraint_freevars env cstr in
+      List.map (fun id -> (dummy_loc, id), CHole (dummy_loc, None)) elts
+  in fv_ctx, cstr
+    
+let generalize_class_binder_raw env c = 
+  let env = Idset.union env (Termops.vars_of_env (Global.env())) in
+  let fv_ctx, cstr = resolve_class_binder env c in
+  let ids' = List.fold_left (fun acc ((loc, id), t) -> Idset.add id acc) env fv_ctx in
+  let ctx' = List.map (fun ((loc, id), t) -> ((loc, Name id), Implicit, t)) fv_ctx in
+    ids', ctx', cstr
 
 let generalize_class_binders_raw env l = 
   let env = Idset.union env (Termops.vars_of_env (Global.env())) in
   let fv_ctx, cstrs = resolve_class_binders env l in
     List.map (fun ((loc, id), t) -> ((loc, Name id), Implicit, t)) fv_ctx,
   List.map (fun (iid, bk, c) -> (iid, Implicit, c)) cstrs
-
-let ctx_of_class_binders env l = 
-  let (x, y) = generalize_class_binders env l in x @ y
 	
-let implicits_of_binders l = 
-  let rec aux i l = 
-    match l with 
-	[] -> []
-      | hd :: tl -> 
-	  let res, reslen = 
-	    match hd with
-		LocalRawAssum (nal, Default Implicit, t) -> 
-		  list_map_i (fun i (_,id) ->
-		    let name =
-		      match id with
-			  Name id -> Some id
-			| Anonymous -> None
-		    in ExplByPos (i, name), (true, true))
-		    i nal, List.length nal
-	      | LocalRawAssum (nal, _, _) -> [], List.length nal
-	      | LocalRawDef _ -> [], 1
-	  in res @ (aux (i + reslen) tl)
-  in aux 1 l
-  
 let implicits_of_rawterm l = 
   let rec aux i c = 
     match c with
diff --git a/interp/implicit_quantifiers.mli b/interp/implicit_quantifiers.mli
index ff81dc10..1ee81ce9 100644
--- a/interp/implicit_quantifiers.mli
+++ b/interp/implicit_quantifiers.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: implicit_quantifiers.mli 10739 2008-04-01 14:45:20Z herbelin $ i*)
+(*i $Id: implicit_quantifiers.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -39,30 +39,23 @@ val make_fresh : Names.Idset.t -> Environ.env -> identifier -> identifier
 val free_vars_of_binders :
   ?bound:Idset.t -> Names.identifier list -> local_binder list -> Idset.t * Names.identifier list
 
-val compute_constrs_freevars : Idset.t -> constr_expr list -> identifier list
-val compute_constrs_freevars_binders : Idset.t -> constr_expr list -> (identifier located * constr_expr) list
 val resolve_class_binders : Idset.t -> typeclass_context -> 
   (identifier located * constr_expr) list * typeclass_context
 
 val full_class_binders : Idset.t -> typeclass_context -> typeclass_context
+
+val generalize_class_binder_raw : Idset.t -> name located * (binding_kind * binding_kind) * constr_expr -> 
+  Idset.t * typeclass_context * typeclass_constraint
   
 val generalize_class_binders_raw : Idset.t -> typeclass_context -> 
   (name located * binding_kind * constr_expr) list * (name located * binding_kind * constr_expr) list
 
-val ctx_of_class_binders : Idset.t -> typeclass_context -> local_binder list
-
-val implicits_of_binders : local_binder list -> (Topconstr.explicitation * (bool * bool)) list
-
 val implicits_of_rawterm : Rawterm.rawconstr -> (Topconstr.explicitation * (bool * bool)) list
 
 val combine_params : Names.Idset.t ->
-  (Names.Idset.t -> (global_reference * bool) option * (Names.identifier * Term.constr option * Term.types) ->
+  (Names.Idset.t -> (global_reference * bool) option * (Names.name * Term.constr option * Term.types) ->
     Topconstr.constr_expr * Names.Idset.t) ->
   (Topconstr.constr_expr * Topconstr.explicitation located option) list ->
-  ((global_reference * bool) option * Term.named_declaration) list ->
+  ((global_reference * bool) option * Term.rel_declaration) list ->
   Topconstr.constr_expr list * Names.Idset.t
 
-
-val ids_of_named_context_avoiding :     Names.Idset.t ->
-    Sign.named_context -> Names.Idset.elt list * Names.Idset.t
-
diff --git a/interp/notation.ml b/interp/notation.ml
index 98a199ad..9e83b860 100644
--- a/interp/notation.ml
+++ b/interp/notation.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: notation.ml 10893 2008-05-07 09:20:43Z herbelin $ *)
+(* $Id: notation.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (*i*)
 open Util
@@ -78,7 +78,7 @@ let declare_scope scope =
 
 let find_scope scope =
   try Gmap.find scope !scope_map
-  with Not_found -> error ("Scope "^scope^" is not declared")
+  with Not_found -> error ("Scope "^scope^" is not declared.")
 
 let check_scope sc = let _ = find_scope sc in ()
 
@@ -159,7 +159,7 @@ let find_delimiters_scope loc key =
   try Gmap.find key !delimiters_map
   with Not_found -> 
     user_err_loc 
-    (loc, "find_delimiters", str ("Unknown scope delimiting key "^key))
+    (loc, "find_delimiters", str ("Unknown scope delimiting key "^key^"."))
 
 (* Uninterpretation tables *)
 
@@ -251,7 +251,7 @@ let check_required_module loc sc (sp,d) =
   with Not_found ->
     user_err_loc (loc,"prim_token_interpreter",
     str ("Cannot interpret in "^sc^" without requiring first module "
-    ^(list_last d)))
+    ^(list_last d)^"."))
 
 (* Look if some notation or numeral printer in [scope] can be used in
    the scope stack [scopes], and if yes, using delimiters or not *)
@@ -348,7 +348,7 @@ let interp_prim_token_gen g loc p local_scopes =
     user_err_loc (loc,"interp_prim_token",
     (match p with
       | Numeral n -> str "No interpretation for numeral " ++ pr_bigint n
-      | String s -> str "No interpretation for string " ++ qs s))
+      | String s -> str "No interpretation for string " ++ qs s) ++ str ".")
 
 let interp_prim_token =
   interp_prim_token_gen (fun x -> x)
@@ -361,7 +361,7 @@ let rec interp_notation loc ntn local_scopes =
   try find_interpretation (find_notation ntn) scopes
   with Not_found ->
     user_err_loc
-    (loc,"",str ("Unknown interpretation for notation \""^ntn^"\""))
+    (loc,"",str ("Unknown interpretation for notation \""^ntn^"\"."))
 
 let uninterp_notations c =
   Gmapl.find (rawconstr_key c) !notations_key_table
@@ -464,10 +464,10 @@ let subst_arguments_scope (_,subst,(req,r,scl)) =
   (ArgsScopeNoDischarge,fst (subst_global subst r),scl)
 
 let discharge_arguments_scope (_,(req,r,l)) =
-  if req = ArgsScopeNoDischarge then None
-  else Some (req,pop_global_reference r,l)
+  if req = ArgsScopeNoDischarge or (isVarRef r & Lib.is_in_section r) then None
+  else Some (req,Lib.discharge_global r,l)
 
-let rebuild_arguments_scope (_,(req,r,l)) =
+let rebuild_arguments_scope (req,r,l) =
   match req with
     | ArgsScopeNoDischarge -> assert false
     | ArgsScopeAuto ->
@@ -493,8 +493,7 @@ let declare_arguments_scope_gen req r scl =
   Lib.add_anonymous_leaf (inArgumentsScope (req,r,scl))
 
 let declare_arguments_scope local ref scl =
-  let req =
-    if local or isVarRef ref then ArgsScopeNoDischarge else ArgsScopeManual in
+  let req = if local then ArgsScopeNoDischarge else ArgsScopeManual in
   declare_arguments_scope_gen req ref scl
 
 let find_arguments_scope r =
@@ -503,8 +502,7 @@ let find_arguments_scope r =
 
 let declare_ref_arguments_scope ref =
   let t = Global.type_of_global ref in
-  let req = if isVarRef ref then ArgsScopeNoDischarge else ArgsScopeAuto in
-  declare_arguments_scope_gen req ref (compute_arguments_scope t)
+  declare_arguments_scope_gen ArgsScopeAuto ref (compute_arguments_scope t)
 
 (********************************)
 (* Encoding notations as string *)
@@ -627,12 +625,12 @@ let global_reference_of_notation test (ntn,(sc,c,_)) =
   | _ -> None
 
 let error_ambiguous_notation loc _ntn =
-  user_err_loc (loc,"",str "Ambiguous notation")
+  user_err_loc (loc,"",str "Ambiguous notation.")
 
 let error_notation_not_reference loc ntn =
   user_err_loc (loc,"",
     str "Unable to interpret " ++ quote (str ntn) ++
-    str " as a reference")
+    str " as a reference.")
 
 let interp_notation_as_global_reference loc test ntn =
   let ntns = browse_notation true ntn !scope_map in
diff --git a/interp/topconstr.ml b/interp/topconstr.ml
index b858eecb..a51b6bb0 100644
--- a/interp/topconstr.ml
+++ b/interp/topconstr.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: topconstr.ml 11024 2008-05-30 12:41:39Z msozeau $ *)
+(* $Id: topconstr.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (*i*)
 open Pp
@@ -150,7 +150,7 @@ let compare_rawconstr f t1 t2 = match t1,t2 with
     | RPatVar _ | REvar _ | RLetTuple _ | RIf _ | RCast _),_
   | _,(RLetIn _ | RCases _ | RRec _ | RDynamic _
       | RPatVar _ | REvar _ | RLetTuple _ | RIf _ | RCast _)
-      -> error "Unsupported construction in recursive notations"
+      -> error "Unsupported construction in recursive notations."
   | (RRef _ | RVar _ | RApp _ | RLambda _ | RProd _ | RHole _ | RSort _), _
       -> false
 
@@ -168,13 +168,13 @@ let discriminate_patterns foundvars nl l1 l2 =
   | _ -> compare_rawconstr (aux (n+1)) c1 c2 in
   let l = list_map2_i aux 0 l1 l2 in
   if not (List.for_all ((=) true) l) then
-    error "Both ends of the recursive pattern differ";
+    error "Both ends of the recursive pattern differ.";
   match !diff with
-    | None ->  error "Both ends of the recursive pattern are the same"
+    | None ->  error "Both ends of the recursive pattern are the same."
     | Some (x,y,_ as discr) ->
 	List.iter (fun id ->
           if List.mem id !foundvars
-          then error "Variables used in the recursive part of a pattern are not allowed to occur outside of the recursive part";
+          then errorlabstrm "" (strbrk "Variables used in the recursive part of a pattern are not allowed to occur outside of the recursive part.");
           foundvars := id::!foundvars) [x;y];
 	discr
 
@@ -212,7 +212,7 @@ let aconstr_and_vars_of_rawconstr a =
       Array.iter (fun id -> found := id::!found) idl;
       let dll = Array.map (List.map (fun (na,bk,oc,b) -> 
 	 if bk <> Explicit then 
-	   error "Binders marked as implicit not allowed in notations";
+	   error "Binders marked as implicit not allowed in notations.";
 	 add_name found na; (na,Option.map aux oc,aux b))) dll in
       ARec (fk,idl,dll,Array.map aux tl,Array.map aux bl)
   | RCast (_,c,k) -> ACast (aux c, 
@@ -223,17 +223,17 @@ let aconstr_and_vars_of_rawconstr a =
   | RRef (_,r) -> ARef r
   | RPatVar (_,(_,n)) -> APatVar n
   | RDynamic _ | REvar _ ->
-      error "Existential variables not allowed in notations"
+      error "Existential variables not allowed in notations."
 
   (* Recognizing recursive notations *)
   and terminator_of_pat f1 ll1 lr1 = function
   | RApp (loc,f2,l2) ->
-      if not (eq_rawconstr f1 f2) then error
-	"Cannot recognize the same head to both ends of the recursive pattern";
+      if not (eq_rawconstr f1 f2) then errorlabstrm ""
+	(strbrk "Cannot recognize the same head to both ends of the recursive pattern.");
       let nl = List.length ll1 in
       let nr = List.length lr1 in
       if List.length l2 <> nl + nr + 1 then
-	error "Both ends of the recursive pattern have different lengths";
+	error "Both ends of the recursive pattern have different lengths.";
       let ll2,l2' = list_chop nl l2 in
       let t = List.hd l2' and lr2 = List.tl l2' in
       let x,y,order = discriminate_patterns found nl (ll1@lr1) (ll2@lr2) in
@@ -241,8 +241,8 @@ let aconstr_and_vars_of_rawconstr a =
         if order then RApp (loc,f2,ll2@RVar (loc,ldots_var)::lr2)
         else RApp (loc,f1,ll1@RVar (loc,ldots_var)::lr1) in
       (if order then y else x),(if order then x else y), aux iter, aux t, order
-  | _ -> error "One end of the recursive pattern is not an application"
-    
+  | _ -> error "One end of the recursive pattern is not an application."
+
   and make_aconstr_list f args =
     let rec find_patterns acc = function
       | RApp(_,RVar (_,a),[c]) :: l when a = ldots_var ->
@@ -250,7 +250,7 @@ let aconstr_and_vars_of_rawconstr a =
 	  let x,y,iter,term,lassoc = terminator_of_pat f (List.rev acc) l c in
 	  AList (x,y,iter,term,lassoc)
       | a::l -> find_patterns (a::acc) l
-      | [] -> error "Ill-formed recursive notation"
+      | [] -> error "Ill-formed recursive notation."
     in find_patterns [] args
 
   in
@@ -262,7 +262,7 @@ let aconstr_of_rawconstr vars a =
   let a,foundvars = aconstr_and_vars_of_rawconstr a in
   let check_type x =
     if not (List.mem x foundvars) then
-      error ((string_of_id x)^" is unbound in the right-hand-side") in
+      error ((string_of_id x)^" is unbound in the right-hand-side.") in
   List.iter check_type vars;
   a
 
@@ -590,7 +590,7 @@ type notation = string
 
 type explicitation = ExplByPos of int * identifier option | ExplByName of identifier
 
-type binder_kind = Default of binding_kind | TypeClass of binding_kind
+type binder_kind = Default of binding_kind | TypeClass of binding_kind * binding_kind
 
 type proj_flag = int option (* [Some n] = proj of the n-th visible argument *)
 
@@ -853,7 +853,7 @@ let coerce_to_id = function
   | CRef (Ident (loc,id)) -> (loc,id)
   | a -> user_err_loc
         (constr_loc a,"coerce_to_id",
-         str "This expression should be a simple identifier")
+         str "This expression should be a simple identifier.")
 
 (* Used in correctness and interface *)
 
diff --git a/interp/topconstr.mli b/interp/topconstr.mli
index d4fef0dc..2ac9da11 100644
--- a/interp/topconstr.mli
+++ b/interp/topconstr.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: topconstr.mli 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: topconstr.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Pp
@@ -95,7 +95,7 @@ type notation = string
 
 type explicitation = ExplByPos of int * identifier option | ExplByName of identifier
   
-type binder_kind = Default of binding_kind | TypeClass of binding_kind
+type binder_kind = Default of binding_kind | TypeClass of binding_kind * binding_kind
 
 type proj_flag = int option (* [Some n] = proj of the n-th visible argument *)
 
diff --git a/kernel/environ.ml b/kernel/environ.ml
index ad435eb5..86e02623 100644
--- a/kernel/environ.ml
+++ b/kernel/environ.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: environ.ml 11001 2008-05-27 16:56:07Z aspiwack $ *)
+(* $Id: environ.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -379,17 +379,14 @@ let insert_after_hyp (ctxt,vals) id d check =
 
 (* To be used in Logic.clear_hyps *)
 let remove_hyps ids check_context check_value (ctxt, vals) =
-  let ctxt,vals,rmv = 
-    List.fold_right2 (fun (id,_,_ as d) (id',v) (ctxt,vals,rmv) ->
+  List.fold_right2 (fun (id,_,_ as d) (id',v) (ctxt,vals) ->
       if List.mem id ids then 
-	(ctxt,vals,id::rmv)
+	(ctxt,vals)
       else 	  
 	let nd = check_context d in
 	let nv = check_value v in
-	  (nd::ctxt,(id',nv)::vals,rmv))
-		     ctxt vals ([],[],[])
-  in ((ctxt,vals),rmv)
-
+	  (nd::ctxt,(id',nv)::vals))
+		     ctxt vals ([],[])
 
 
 
diff --git a/kernel/environ.mli b/kernel/environ.mli
index 30f555a4..97e19782 100644
--- a/kernel/environ.mli
+++ b/kernel/environ.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: environ.mli 11001 2008-05-27 16:56:07Z aspiwack $ i*)
+(*i $Id: environ.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -222,7 +222,7 @@ val insert_after_hyp : named_context_val -> variable ->
   named_declaration -> 
     (named_context -> unit) -> named_context_val
 
-val remove_hyps : identifier list -> (named_declaration -> named_declaration) -> (Pre_env.lazy_val -> Pre_env.lazy_val) -> named_context_val -> named_context_val * identifier list
+val remove_hyps : identifier list -> (named_declaration -> named_declaration) -> (Pre_env.lazy_val -> Pre_env.lazy_val) -> named_context_val -> named_context_val
 
 
 (* spiwack: functions manipulating the retroknowledge *)
diff --git a/kernel/indtypes.ml b/kernel/indtypes.ml
index 7cedebbd..01b8aca1 100644
--- a/kernel/indtypes.ml
+++ b/kernel/indtypes.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: indtypes.ml 10920 2008-05-12 10:19:32Z herbelin $ *)
+(* $Id: indtypes.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -254,16 +254,19 @@ let typecheck_inductive env mie =
     array_fold_map2' (fun ((id,full_arity,ar_level),cn,info,lc,_) lev cst ->
       let sign, s = dest_arity env full_arity in
       let status,cst = match s with
-      | Type _ when ar_level <> None (* Explicitly polymorphic *) ->
+      | Type u when ar_level <> None (* Explicitly polymorphic *) 
+            && no_upper_constraints u cst ->
 	  (* The polymorphic level is a function of the level of the *)
 	  (* conclusions of the parameters *)
-	  Inr (param_ccls, lev), cst
+          (* We enforce [u >= lev] in case [lev] has a strict upper *)
+          (* constraints over [u] *)
+	  Inr (param_ccls, lev), enforce_geq u lev cst
       | Type u (* Not an explicit occurrence of Type *) ->
 	  Inl (info,full_arity,s), enforce_geq u lev cst
       | Prop Pos when engagement env <> Some ImpredicativeSet ->
 	  (* Predicative set: check that the content is indeed predicative *)
 	  if not (is_type0m_univ lev) & not (is_type0_univ lev) then
-	    error "Large non-propositional inductive types must be in Type";
+	    error "Large non-propositional inductive types must be in Type.";
 	  Inl (info,full_arity,s), cst
       | Prop _ ->
 	  Inl (info,full_arity,s), cst in
@@ -598,7 +601,6 @@ let build_inductive env env_ar params isrecord isfinite inds nmr recargs cst =
 	      poly_level = lev; 
 	    }, all_sorts
       | Inl ((issmall,isunit),ar,s) ->
-	  let isunit = isunit && ntypes = 1 && not (is_recursive recargs.(0)) in
 	  let kelim = allowed_sorts issmall isunit s in
 	    Monomorphic {
 		mind_user_arity = ar;
diff --git a/kernel/inductive.ml b/kernel/inductive.ml
index 9415941d..4bb8e9d6 100644
--- a/kernel/inductive.ml
+++ b/kernel/inductive.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: inductive.ml 10920 2008-05-12 10:19:32Z herbelin $ *)
+(* $Id: inductive.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -218,7 +218,7 @@ let type_of_constructor cstr (mib,mip) =
   let specif = mip.mind_user_lc in
   let i = index_of_constructor cstr in
   let nconstr = Array.length mip.mind_consnames in
-  if i > nconstr then error "Not enough constructors in the type";
+  if i > nconstr then error "Not enough constructors in the type.";
   constructor_instantiate (fst ind) mib specif.(i-1)
 
 let arities_of_specif kn (mib,mip) = 
@@ -228,7 +228,9 @@ let arities_of_specif kn (mib,mip) =
 let arities_of_constructors ind specif = 
   arities_of_specif (fst ind) specif
 
-
+let type_of_constructors ind (mib,mip) =
+  let specif = mip.mind_user_lc in
+  Array.map (constructor_instantiate (fst ind) mib) specif
 
 (************************************************************************)
 
diff --git a/kernel/inductive.mli b/kernel/inductive.mli
index c2c38d8d..8059051b 100644
--- a/kernel/inductive.mli
+++ b/kernel/inductive.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: inductive.mli 9420 2006-12-08 15:34:09Z barras $ i*)
+(*i $Id: inductive.mli 11301 2008-08-04 19:41:18Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -47,6 +47,9 @@ val type_of_constructor : constructor -> mind_specif -> types
 (* Return constructor types in normal form *)
 val arities_of_constructors : inductive -> mind_specif -> types array
 
+(* Return constructor types in user form *)
+val type_of_constructors : inductive -> mind_specif -> types array
+
 (* Transforms inductive specification into types (in nf) *)
 val arities_of_specif : mutual_inductive -> mind_specif -> types array 
 
diff --git a/kernel/modops.ml b/kernel/modops.ml
index 9242a757..7bed3254 100644
--- a/kernel/modops.ml
+++ b/kernel/modops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: modops.ml 11142 2008-06-18 15:37:31Z soubiran $ i*)
+(*i $Id: modops.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Util
@@ -22,51 +22,51 @@ open Mod_subst
 
 
 let error_existing_label l = 
-  error ("The label "^string_of_label l^" is already declared")
+  error ("The label "^string_of_label l^" is already declared.")
 
-let error_declaration_not_path _ = error "Declaration is not a path"
+let error_declaration_not_path _ = error "Declaration is not a path."
 
-let error_application_to_not_path _ = error "Application to not path"
+let error_application_to_not_path _ = error "Application to not path."
 
-let error_not_a_functor _ = error "Application of not a functor"
+let error_not_a_functor _ = error "Application of not a functor."
 
-let error_incompatible_modtypes _ _ = error "Incompatible module types"
+let error_incompatible_modtypes _ _ = error "Incompatible module types."
 
-let error_not_equal _ _ = error "Not equal modules"
+let error_not_equal _ _ = error "Non equal modules."
 
-let error_not_match l _ = error ("Signature components for label "^string_of_label l^" do not match")
+let error_not_match l _ = error ("Signature components for label "^string_of_label l^" do not match.")
 
-let error_no_such_label l = error ("No such label "^string_of_label l)
+let error_no_such_label l = error ("No such label "^string_of_label l^".")
 
 let error_incompatible_labels l l' = 
   error ("Opening and closing labels are not the same: "
 	 ^string_of_label l^" <> "^string_of_label l'^" !")
 
 let error_result_must_be_signature () = 
-  error "The result module type must be a signature"
+  error "The result module type must be a signature."
 
 let error_signature_expected mtb =
-  error "Signature expected"
+  error "Signature expected."
 
 let error_no_module_to_end _ = 
-  error "No open module to end"
+  error "No open module to end."
 
 let error_no_modtype_to_end _ =
-  error "No open module type to end"
+  error "No open module type to end."
 
 let error_not_a_modtype_loc loc s = 
-  user_err_loc (loc,"",str ("\""^s^"\" is not a module type"))
+  user_err_loc (loc,"",str ("\""^s^"\" is not a module type."))
 
 let error_not_a_module_loc loc s = 
-  user_err_loc (loc,"",str ("\""^s^"\" is not a module"))
+  user_err_loc (loc,"",str ("\""^s^"\" is not a module."))
 
 let error_not_a_module s = error_not_a_module_loc dummy_loc s
 
 let error_not_a_constant l = 
-  error ("\""^(string_of_label l)^"\" is not a constant")
+  error ("\""^(string_of_label l)^"\" is not a constant.")
 
 let error_with_incorrect l =
-  error ("Incorrect constraint for label \""^(string_of_label l)^"\"")
+  error ("Incorrect constraint for label \""^(string_of_label l)^"\".")
 
 let error_a_generative_module_expected l =
   error ("The module " ^ string_of_label l ^ " is not generative. Only " ^
@@ -79,7 +79,7 @@ let error_local_context lo =
 	error ("The local context is not empty.")
     | (Some l) ->
 	error ("The local context of the component "^
-	       (string_of_label l)^" is not empty")
+	       (string_of_label l)^" is not empty.")
 
 
 let error_no_such_label_sub l l1 l2 =
diff --git a/kernel/names.ml b/kernel/names.ml
index 26bcc2eb..25f03495 100644
--- a/kernel/names.ml
+++ b/kernel/names.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: names.ml 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: names.ml 11238 2008-07-19 09:34:03Z herbelin $ *)
 
 open Pp
 open Util
@@ -101,7 +101,7 @@ let label_of_mbid (_,s,_) = s
 
 
 let mk_label l = l
-let string_of_label l = l
+let string_of_label = string_of_id
 
 let id_of_label l = l
 let label_of_id id = id
diff --git a/kernel/safe_typing.ml b/kernel/safe_typing.ml
index 6906fb29..3c7461b2 100644
--- a/kernel/safe_typing.ml
+++ b/kernel/safe_typing.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: safe_typing.ml 11170 2008-06-25 08:31:04Z soubiran $ *)
+(* $Id: safe_typing.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -163,7 +163,7 @@ let safe_push_named (id,_,_ as d) env =
   let _ =
     try
       let _ = lookup_named id env in 
-      error ("identifier "^string_of_id id^" already defined")
+      error ("Identifier "^string_of_id id^" already defined.")
     with Not_found -> () in
   Environ.push_named d env
 
@@ -446,7 +446,7 @@ let end_module l restype senv =
    let senv = add_constraints (struct_expr_constraints struct_expr) senv in
    let msid,str = match (eval_struct senv.env struct_expr) with
      | SEBstruct(msid,str_l) -> msid,str_l
-     | _ -> error ("You cannot Include a higher-order Module or Module Type" )
+     | _ -> error ("You cannot Include a higher-order Module or Module Type.")
    in
    let mp_sup = senv.modinfo.modpath in
    let str1 = subst_signature_msid msid mp_sup str in
@@ -660,7 +660,7 @@ let check_engagement env c =
     | Some ImpredicativeSet, Some ImpredicativeSet -> ()
     | _, None -> ()
     | _, Some ImpredicativeSet ->
-        error "Needs option -impredicative-set"
+        error "Needs option -impredicative-set."
 
 let set_engagement c senv =
   {senv with
@@ -739,9 +739,10 @@ let check_imports senv needed =
     try
       let actual_stamp = List.assoc id imports in
       if stamp <> actual_stamp then
-	error ("Inconsistent assumptions over module " ^(string_of_dirpath id))
+	error
+	  ("Inconsistent assumptions over module "^(string_of_dirpath id)^".")
     with Not_found -> 
-      error ("Reference to unknown module " ^ (string_of_dirpath id))
+      error ("Reference to unknown module "^(string_of_dirpath id)^".")
   in
   List.iter check needed
 
diff --git a/kernel/term.ml b/kernel/term.ml
index c920c80b..1f3d2635 100644
--- a/kernel/term.ml
+++ b/kernel/term.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: term.ml 10859 2008-04-27 16:46:15Z herbelin $ *)
+(* $Id: term.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (* This module instantiates the structure of generic deBruijn terms to Coq *)
 
@@ -370,16 +370,22 @@ let destProd c = match kind_of_term c with
   | Prod (x,t1,t2) -> (x,t1,t2) 
   | _ -> invalid_arg "destProd"
 
+let isProd c = match kind_of_term c with | Prod _ -> true | _ -> false
+
 (* Destructs the abstraction [x:t1]t2 *)
 let destLambda c = match kind_of_term c with 
   | Lambda (x,t1,t2) -> (x,t1,t2) 
   | _ -> invalid_arg "destLambda"
 
+let isLambda c = match kind_of_term c with | Lambda _ -> true | _ -> false
+
 (* Destructs the let [x:=b:t1]t2 *)
 let destLetIn c = match kind_of_term c with 
   | LetIn (x,b,t1,t2) -> (x,b,t1,t2) 
   | _ -> invalid_arg "destProd"
 
+let isLetIn c =  match kind_of_term c with LetIn _ -> true | _ -> false
+
 (* Destructs an application *)
 let destApp c = match kind_of_term c with
   | App (f,a) -> (f, a)
@@ -389,10 +395,6 @@ let destApplication = destApp
 
 let isApp c = match kind_of_term c with App _ -> true | _ -> false
 
-let isProd c = match kind_of_term c with | Prod _ -> true | _ -> false
-
-let isLambda c = match kind_of_term c with | Lambda _ -> true | _ -> false
-
 (* Destructs a constant *)
 let destConst c = match kind_of_term c with
   | Const kn -> kn
@@ -419,22 +421,27 @@ let destConstruct c = match kind_of_term c with
   | Construct (kn, a as r) -> r
   | _ -> invalid_arg "dest"
 
-let isConstruct c = match kind_of_term c with
-    Construct _ -> true | _ -> false
+let isConstruct c = match kind_of_term c with Construct _ -> true | _ -> false
 
 (* Destructs a term <p>Case c of lc1 | lc2 .. | lcn end *)
 let destCase c = match kind_of_term c with
   | Case (ci,p,c,v) -> (ci,p,c,v)
   | _ -> anomaly "destCase"
 
+let isCase c =  match kind_of_term c with Case _ -> true | _ -> false
+
 let destFix c = match kind_of_term c with 
   | Fix fix -> fix
   | _ -> invalid_arg "destFix"
-	
+
+let isFix c =  match kind_of_term c with Fix _ -> true | _ -> false
+
 let destCoFix c = match kind_of_term c with 
   | CoFix cofix -> cofix
   | _ -> invalid_arg "destCoFix"
 
+let isCoFix c =  match kind_of_term c with CoFix _ -> true | _ -> false
+
 (******************************************************************)
 (* Cast management                                                *)
 (******************************************************************)
diff --git a/kernel/term.mli b/kernel/term.mli
index 6236dc39..3b5a2bc1 100644
--- a/kernel/term.mli
+++ b/kernel/term.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: term.mli 10859 2008-04-27 16:46:15Z herbelin $ i*)
+(*i $Id: term.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -230,9 +230,13 @@ val isSort : constr -> bool
 val isCast : constr -> bool
 val isApp : constr -> bool
 val isLambda : constr -> bool
+val isLetIn : constr -> bool
 val isProd : constr -> bool
 val isConst : constr -> bool
 val isConstruct : constr -> bool
+val isFix : constr -> bool
+val isCoFix : constr -> bool
+val isCase : constr -> bool
 
 val is_Prop : constr -> bool
 val is_Set  : constr -> bool
diff --git a/kernel/term_typing.ml b/kernel/term_typing.ml
index 0f649057..f50a0b83 100644
--- a/kernel/term_typing.ml
+++ b/kernel/term_typing.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: term_typing.ml 10877 2008-04-30 21:58:41Z herbelin $ *)
+(* $Id: term_typing.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -60,7 +60,7 @@ let safe_push_named (id,_,_ as d) env =
   let _ =
     try
       let _ = lookup_named id env in 
-      error ("identifier "^string_of_id id^" already defined")
+      error ("Identifier "^string_of_id id^" already defined.")
     with Not_found -> () in
   push_named d env
 
diff --git a/kernel/univ.ml b/kernel/univ.ml
index 3791c3e1..11a5452c 100644
--- a/kernel/univ.ml
+++ b/kernel/univ.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: univ.ml 11063 2008-06-06 16:03:45Z soubiran $ *)
+(* $Id: univ.ml 11301 2008-08-04 19:41:18Z herbelin $ *)
 
 (* Initial Caml version originates from CoC 4.8 [Dec 1988] *)
 (* Extension with algebraic universes by HH [Sep 2001] *)
@@ -550,6 +550,11 @@ let subst_large_constraint u u' v =
 let subst_large_constraints =
   List.fold_right (fun (u,u') -> subst_large_constraint u u')
 
+let no_upper_constraints u cst =
+  match u with
+  | Atom u -> Constraint.for_all (fun (u1,_,_) -> u1 <> u) cst
+  | Max _ -> anomaly "no_upper_constraints"
+
 (* Pretty-printing *)
 
 let num_universes g =
diff --git a/kernel/univ.mli b/kernel/univ.mli
index 0a1a8328..668e99a0 100644
--- a/kernel/univ.mli
+++ b/kernel/univ.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: univ.mli 11063 2008-06-06 16:03:45Z soubiran $ i*)
+(*i $Id: univ.mli 11301 2008-08-04 19:41:18Z herbelin $ i*)
 
 (* Universes. *)
 
@@ -76,6 +76,8 @@ val subst_large_constraint : universe -> universe -> universe -> universe
 val subst_large_constraints : 
   (universe * universe) list -> universe -> universe
 
+val no_upper_constraints : universe -> constraints -> bool
+
 (*s Pretty-printing of universes. *)
 
 val pr_uni : universe -> Pp.std_ppcmds
diff --git a/lib/flags.ml b/lib/flags.ml
index de971c7c..16ae0c64 100644
--- a/lib/flags.ml
+++ b/lib/flags.ml
@@ -6,9 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: flags.ml 11077 2008-06-09 11:26:32Z herbelin $ i*)
-
-open Util
+(*i $Id: flags.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 let with_option o f x =
   let old = !o in o:=true;
@@ -78,6 +76,8 @@ let print_hyps_limit () = !print_hyps_limit
 (* A list of the areas of the system where "unsafe" operation
  * has been requested *)
 
+module Stringset = Set.Make(struct type t = string let compare = compare end)
+
 let unsafe_set = ref Stringset.empty
 let add_unsafe s = unsafe_set := Stringset.add s !unsafe_set
 let is_unsafe s = Stringset.mem s !unsafe_set
@@ -126,7 +126,4 @@ let browser_cmd_fmt =
   let coq_netscape_remote_var = "COQREMOTEBROWSER" in
   Sys.getenv coq_netscape_remote_var
  with
-  Not_found ->
-   if Sys.os_type = "Win32"
-   then "C:\\PROGRA~1\\INTERN~1\\IEXPLORE %s"
-   else "firefox -remote \"OpenURL(%s,new-tab)\" || firefox %s &"
+  Not_found -> Coq_config.browser
diff --git a/lib/system.ml b/lib/system.ml
index aa71ddfa..22eb52ee 100644
--- a/lib/system.ml
+++ b/lib/system.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: system.ml 10437 2008-01-11 14:50:44Z bertot $ *)
+(* $Id: system.ml 11209 2008-07-05 10:17:49Z herbelin $ *)
 
 open Pp
 open Util
@@ -68,6 +68,14 @@ let string_of_physical_path p = p
 let exists_dir dir =
   try let _ = opendir dir in true with Unix_error _ -> false
 
+let skipped_dirnames = ref ["CVS"; "_darcs"]
+
+let exclude_search_in_dirname f = skipped_dirnames := f :: !skipped_dirnames
+
+let ok_dirname f = 
+  f <> "" && f.[0] <> '.' && not (List.mem f !skipped_dirnames) &&
+  try ignore (check_ident f); true with _ -> false
+
 let all_subdirs ~unix_path:root =
   let l = ref [] in
   let add f rel = l := (f, rel) :: !l in
@@ -76,8 +84,7 @@ let all_subdirs ~unix_path:root =
     try
       while true do
 	let f = readdir dirh in
-	if f <> "" && f.[0] <> '.' && (not Coq_config.local or (f <> "CVS"))
-        then
+	if ok_dirname f then
 	  let file = Filename.concat dir f in
 	  try 
 	    if (stat file).st_kind = S_DIR then begin
@@ -90,52 +97,44 @@ let all_subdirs ~unix_path:root =
     with End_of_file ->
       closedir dirh
   in
-  if exists_dir root then
-   begin
-     add root [];
-     traverse root []
-   end ;
+  if exists_dir root then traverse root [];
   List.rev !l
 
-let where_in_path path filename =
-  let rec search acc = function
+let where_in_path warn path filename =
+  let rec search = function
     | lpe :: rem ->
 	let f = Filename.concat lpe filename in
 	  if Sys.file_exists f 
-	  then (search ((lpe,f)::acc) rem) 
-	  else search acc rem
-    | [] -> acc in
-  let rec check_and_warn cont acc l = 
+	  then (lpe,f) :: search rem
+	  else search rem
+    | [] -> [] in
+  let rec check_and_warn l =
     match l with
-      | [] -> if cont then assert false else raise Not_found
-      | [ (lpe, f) ] -> 
-	  if cont then begin
-	      warning (acc ^ (string_of_physical_path lpe) ^ " ]");
-	      warning ("Loading " ^ f)
-	    end;
-	  (lpe, f)
+      | [] -> raise Not_found
       | (lpe, f) :: l' -> 
-	  if cont then
-	    check_and_warn true (acc ^ (string_of_physical_path lpe) ^ "; ") l'
-	  else
-	    check_and_warn true 
-	      (filename ^ " has been found in [ " ^ (string_of_physical_path lpe) ^ "; ") l' 
-  in
-    check_and_warn false "" (search [] path)
-  
+	  if warn & l' <> [] then
+	    msg_warning
+	      (str filename ++ str " has been found in" ++ spc () ++
+	       hov 0 (str "[ " ++
+	         hv 0 (prlist_with_sep pr_semicolon (fun (lpe,_) -> str lpe) l)
+	         ++ str " ];") ++ fnl () ++
+	       str "loading " ++ str f);
+	  (lpe, f) in
+  check_and_warn (search path)
+
 let find_file_in_path paths filename =
   if not (Filename.is_implicit filename) then
     let root = Filename.dirname filename in
     root, filename
   else 
-    try where_in_path paths filename
+    try where_in_path true paths filename
     with Not_found ->
       errorlabstrm "System.find_file_in_path"
 	(hov 0 (str "Can't find file" ++ spc () ++ str filename ++ spc () ++ 
 		str "on loadpath"))
 
 let is_in_path lpath filename =
-  try ignore (where_in_path lpath filename); true
+  try ignore (where_in_path false lpath filename); true
   with Not_found -> false
 
 let make_suffix name suffix =
diff --git a/lib/system.mli b/lib/system.mli
index 6d535464..eb83cbf8 100644
--- a/lib/system.mli
+++ b/lib/system.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: system.mli 9398 2006-11-21 21:51:18Z herbelin $ i*)
+(*i $Id: system.mli 11209 2008-07-05 10:17:49Z herbelin $ i*)
 
 (*s Files and load paths. Load path entries remember the original root
     given by the user. For efficiency, we keep the full path (field
@@ -16,9 +16,11 @@
 type physical_path = string
 type load_path = physical_path list
 
+val exclude_search_in_dirname : string -> unit
+
 val all_subdirs : unix_path:string -> (physical_path * string list) list
 val is_in_path : load_path -> string -> bool
-val where_in_path : load_path -> string -> physical_path * string
+val where_in_path : bool -> load_path -> string -> physical_path * string
 
 val physical_path_of_string : string -> physical_path
 val string_of_physical_path : physical_path -> string
diff --git a/lib/util.ml b/lib/util.ml
index 9fa92f94..75ee4246 100644
--- a/lib/util.ml
+++ b/lib/util.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1       *)
 (***********************************************************************)
 
-(* $Id: util.ml 11083 2008-06-09 22:08:14Z herbelin $ *)
+(* $Id: util.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 
@@ -576,6 +576,12 @@ let list_fold_left_i f =
   in 
   it_list_f 
 
+let rec list_fold_left3 f accu l1 l2 l3 =
+  match (l1, l2, l3) with
+    ([], [], []) -> accu
+  | (a1::l1, a2::l2, a3::l3) -> list_fold_left3 f (f accu a1 a2 a3) l1 l2 l3
+  | (_, _, _) -> invalid_arg "list_fold_left3"
+
 (* [list_fold_right_and_left f [a1;...;an] hd =
    f (f (... (f (f hd
                    an
@@ -1196,6 +1202,8 @@ let pr_opt_no_spc pr = function None -> mt () | Some x -> pr x
 
 let nth n = str (ordinal n)
 
+(* [prlist pr [a ; ... ; c]] outputs [pr a ++ ... ++ pr c] *)
+
 let rec prlist elem l = match l with 
   | []   -> mt ()
   | h::t -> Stream.lapp (fun () -> elem h) (prlist elem t)
@@ -1207,6 +1215,9 @@ let rec prlist_strict elem l = match l with
   | []   -> mt ()
   | h::t -> (elem h)++(prlist_strict elem t)
 
+(* [prlist_with_sep sep pr [a ; ... ; c]] outputs
+   [pr a ++ sep() ++ ... ++ sep() ++ pr c] *)
+
 let rec prlist_with_sep sep elem l = match l with
   | []   -> mt ()
   | [h]  -> elem h
@@ -1214,6 +1225,23 @@ let rec prlist_with_sep sep elem l = match l with
       let e = elem h and s = sep() and r = prlist_with_sep sep elem t in
       e ++ s ++ r
 
+(* Print sequence of objects separated by space (unless an element is empty) *)
+
+let rec pr_sequence elem = function
+  | []   -> mt ()
+  | [h]  -> elem h
+  | h::t ->
+      let e = elem h and r = pr_sequence elem t in
+      if e = mt () then r else e ++ spc () ++ r
+
+(* [pr_enum pr [a ; b ; ... ; c]] outputs 
+   [pr a ++ str "," ++ pr b ++ str "," ++ ... ++ str "and" ++ pr c] *)
+
+let pr_enum pr l =
+  let c,l' = list_sep_last l in
+  prlist_with_sep pr_coma pr l' ++
+  (if l'<>[] then str " and" ++ spc () else mt()) ++ pr c
+
 let pr_vertical_list pr = function
   | [] -> str "none" ++ fnl ()
   | l -> fnl () ++ str "  " ++ hov 0 (prlist_with_sep pr_fnl pr l) ++ fnl ()
@@ -1228,6 +1256,9 @@ let prvecti elem v =
   in
   if n = 0 then mt () else pr (n - 1)
 
+(* [prvect_with_sep sep pr [|a ; ... ; c|]] outputs
+   [pr a ++ sep() ++ ... ++ sep() ++ pr c] *)
+
 let prvect_with_sep sep elem v =
   let rec pr n =
     if n = 0 then 
@@ -1239,8 +1270,16 @@ let prvect_with_sep sep elem v =
   let n = Array.length v in
   if n = 0 then mt () else pr (n - 1)
 
+(* [prvect pr [|a ; ... ; c|]] outputs [pr a ++ ... ++ pr c] *)
+
 let prvect elem v = prvect_with_sep mt elem v
 
+let pr_located pr (loc,x) =
+  if Flags.do_translate() && loc<>dummy_loc then
+    let (b,e) = unloc loc in
+    comment b ++ pr x ++ comment e
+  else pr x
+
 let surround p = hov 1 (str"(" ++ p ++ str")")
 
 (*s Size of ocaml values. *)
diff --git a/lib/util.mli b/lib/util.mli
index 7807bbbd..99ad3c03 100644
--- a/lib/util.mli
+++ b/lib/util.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1       *)
 (***********************************************************************)
 
-(*i $Id: util.mli 11083 2008-06-09 22:08:14Z herbelin $ i*)
+(*i $Id: util.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Pp
@@ -132,6 +132,7 @@ val list_fold_right_i :  (int -> 'a -> 'b -> 'b) -> int -> 'a list -> 'b -> 'b
 val list_fold_left_i :  (int -> 'a -> 'b -> 'a) -> int -> 'a -> 'b list -> 'a
 val list_fold_right_and_left :
     ('a -> 'b -> 'b list -> 'a) -> 'b list -> 'a -> 'a
+val list_fold_left3 : ('a -> 'b -> 'c -> 'd -> 'a) -> 'a -> 'b list -> 'c list -> 'd list -> 'a
 val list_for_all_i : (int -> 'a -> bool) -> int -> 'a list -> bool
 val list_except : 'a -> 'a list -> 'a list
 val list_remove : 'a -> 'a list -> 'a list
@@ -279,6 +280,9 @@ val prvecti : (int -> 'a -> std_ppcmds) -> 'a array -> std_ppcmds
 val prvect_with_sep :
    (unit -> std_ppcmds) -> ('b -> std_ppcmds) -> 'b array -> std_ppcmds
 val pr_vertical_list : ('b -> std_ppcmds) -> 'b list -> std_ppcmds
+val pr_enum : ('a -> std_ppcmds) -> 'a list -> std_ppcmds
+val pr_located : ('a -> std_ppcmds) -> 'a located -> std_ppcmds
+val pr_sequence : ('a -> std_ppcmds) -> 'a list -> std_ppcmds
 val surround : std_ppcmds -> std_ppcmds
 
 
diff --git a/library/declare.ml b/library/declare.ml
index 07810e3c..4bdc11c3 100644
--- a/library/declare.ml
+++ b/library/declare.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: declare.ml 10840 2008-04-23 21:29:34Z herbelin $ *)
+(* $Id: declare.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (** This module is about the low-level declaration of logical objects *)
 
@@ -57,10 +57,12 @@ let cache_variable ((sp,_),o) =
   let impl,opaq,cst,keep = match d with (* Fails if not well-typed *)
     | SectionLocalAssum (ty, impl, keep) ->
         let cst = Global.push_named_assum (id,ty) in
-        impl, true, cst, (if keep then Some ty else None)
+	let impl = if impl then Lib.Implicit else Lib.Explicit in
+	let keep = if keep then Some ty else None in
+	impl, true, cst, keep
     | SectionLocalDef (c,t,opaq) -> 
         let cst = Global.push_named_def (id,c,t) in
-        false, opaq, cst, None in
+        Lib.Explicit, opaq, cst, None in
   Nametab.push (Nametab.Until 1) (restrict_path 0 sp) (VarRef id);
   add_section_variable id impl keep;
   Dischargedhypsmap.set_discharged_hyps sp [];
@@ -116,7 +118,7 @@ let cache_constant ((sp,kn),(cdt,dhyps,kind)) =
 
 let discharged_hyps kn sechyps =
   let (_,dir,_) = repr_kn kn in
-  let args = array_map_to_list destVar (instance_from_named_context sechyps) in
+  let args = Array.to_list (instance_from_variable_context sechyps) in
   List.rev (List.map (Libnames.make_path dir) args)
 
 let discharge_constant ((sp,kn),(cdt,dhyps,kind)) =
@@ -124,7 +126,7 @@ let discharge_constant ((sp,kn),(cdt,dhyps,kind)) =
   let cb = Global.lookup_constant con in
   let repl = replacement_context () in
   let sechyps = section_segment_of_constant con in
-  let recipe = { d_from=cb; d_modlist=repl; d_abstract=sechyps } in
+  let recipe = { d_from=cb; d_modlist=repl; d_abstract=named_of_variable_context sechyps } in
   Some (GlobalRecipe recipe,(discharged_hyps kn sechyps)@dhyps,kind)
 
 (* Hack to reduce the size of .vo: we keep only what load/open needs *)
@@ -235,7 +237,7 @@ let discharge_inductive ((sp,kn),(dhyps,mie)) =
   let repl = replacement_context () in
   let sechyps = section_segment_of_mutual_inductive kn in
   Some (discharged_hyps kn sechyps,
-        Discharge.process_inductive sechyps repl mie)
+        Discharge.process_inductive (named_of_variable_context sechyps) repl mie)
 
 let dummy_one_inductive_entry mie = {
   mind_entry_typename = mie.mind_entry_typename;
diff --git a/library/declaremods.ml b/library/declaremods.ml
index 123417a6..b630b5dc 100644
--- a/library/declaremods.ml
+++ b/library/declaremods.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: declaremods.ml 11142 2008-06-18 15:37:31Z soubiran $ i*)
+(*i $Id: declaremods.ml 11246 2008-07-22 15:10:05Z soubiran $ i*)
 open Pp
 open Util
 open Names
@@ -433,10 +433,12 @@ and subst_module_alias ((sp,kn),subst,(entry,substobjs,_)) =
 			 mod_entry_expr = 
 			      Some (MSEident mp')},sub),
 		    substobjs, match mbids with
-		      | [] -> 
+		      | [] -> let subst = update_subst subst' (map_mp mp' mp) in
 			  Some (subst_objects (dir,(mp',empty_dirpath)) 
-				  (join subst' (join (map_msid msid mp')
-						  (map_mp mp mp'))) objs)
+				  (join (join subst' subst) (join (map_msid msid mp')
+						  (map_mp mp mp')))
+				   objs)
+			    
 		      | _ -> None)
 		     
 	      | _ -> anomaly "Modops: Not an alias"
diff --git a/library/heads.ml b/library/heads.ml
index 626f1795..970ae87b 100644
--- a/library/heads.ml
+++ b/library/heads.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: heads.ml 10841 2008-04-24 07:19:57Z herbelin $ *)
+(* $Id: heads.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Pp
 open Util
@@ -158,7 +158,7 @@ let discharge_head (_,(ref,k)) =
   | EvalConstRef cst -> Some (EvalConstRef (pop_con cst), k)
   | EvalVarRef id -> None
 
-let rebuild_head (info,(ref,k)) =
+let rebuild_head (ref,k) =
   (ref, compute_head ref)
 
 let export_head o = Some o
diff --git a/library/impargs.ml b/library/impargs.ml
index cae1986e..3a505ddb 100644
--- a/library/impargs.ml
+++ b/library/impargs.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: impargs.ml 10796 2008-04-15 12:00:50Z herbelin $ *)
+(* $Id: impargs.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -20,13 +20,14 @@ open Libobject
 open Lib
 open Nametab
 open Pp
-open Termops
 open Topconstr
+open Termops
 
 (*s Flags governing the computation of implicit arguments *)
 
 type implicits_flags = {
   main : bool;
+  manual : bool;                     (* automatic or manual only *)
   strict : bool;                   (* true = strict *)
   strongly_strict : bool;            (* true = strongly strict *)
   reversible_pattern : bool;
@@ -38,6 +39,7 @@ type implicits_flags = {
 
 let implicit_args = ref { 
   main = false;
+  manual = false;
   strict = true;
   strongly_strict = false;
   reversible_pattern = false;
@@ -48,6 +50,10 @@ let implicit_args = ref {
 let make_implicit_args flag =
   implicit_args := { !implicit_args with main = flag }
 
+let make_manual_implicit_args flag =
+  implicit_args := { !implicit_args with main = if flag then true else !implicit_args.main;
+    manual = flag }
+
 let make_strict_implicit_args flag =
   implicit_args := { !implicit_args with strict = flag }
 
@@ -64,6 +70,7 @@ let make_maximal_implicit_args flag =
   implicit_args := { !implicit_args with maximal = flag }
 
 let is_implicit_args () = !implicit_args.main
+let is_manual_implicit_args () = !implicit_args.manual
 let is_strict_implicit_args () = !implicit_args.strict
 let is_strongly_strict_implicit_args () = !implicit_args.strongly_strict
 let is_reversible_pattern_implicit_args () = !implicit_args.reversible_pattern
@@ -88,7 +95,7 @@ let set_maximality imps b =
 
 (*s Computation of implicit arguments *)
 
-(* We remember various information about why an argument is (automatically)
+(* We remember various information about why an argument is
    inferable as implicit
 
 - [DepRigid] means that the implicit argument can be found by
@@ -105,6 +112,8 @@ let set_maximality imps b =
   inferable following a rigid path (useful to know how to print a
   partial application)
 
+- [Manual] means the argument has been explicitely set as implicit.
+
   We also consider arguments inferable from the conclusion but it is
   operational only if [conclusion_matters] is true.
 *)
@@ -117,7 +126,7 @@ type implicit_explanation =
   | DepRigid of argument_position
   | DepFlex of argument_position
   | DepFlexAndRigid of (*flex*) argument_position * (*rig*) argument_position
-  | Manual of bool
+  | Manual
 
 let argument_less = function
   | Hyp n, Hyp n' -> n<n'
@@ -137,7 +146,7 @@ let update pos rig (na,st) =
       | Some (DepFlex fpos) ->
           if argument_less (pos,fpos) or pos=fpos then DepRigid pos
           else DepFlexAndRigid (fpos,pos)
-      | Some (Manual _) -> assert false
+      | Some Manual -> assert false
   else
     match st with
       | None -> DepFlex pos
@@ -147,7 +156,7 @@ let update pos rig (na,st) =
           if argument_less (pos,fpos) then DepFlexAndRigid (pos,rpos) else x
       | Some (DepFlex fpos as x) ->
           if argument_less (pos,fpos) then DepFlex pos else x
-      | Some (Manual _) -> assert false
+      | Some Manual -> assert false
   in na, Some e
 
 (* modified is_rigid_reference with a truncated env *)
@@ -241,11 +250,7 @@ let compute_implicits_flags env f all t =
     f.reversible_pattern f.contextual all env t
     
 let set_implicit id imp insmax =
-  (id,(match imp with None -> Manual false | Some imp -> imp),insmax)
-
-let merge_imps f = function 
-    None -> Some (Manual f)
-  | x -> x
+  (id,(match imp with None -> Manual | Some imp -> imp),insmax)
 
 let rec assoc_by_pos k = function
     (ExplByPos (k', x), b) :: tl when k = k' -> (x,b), tl
@@ -262,7 +267,7 @@ let compute_manual_implicits env flags t enriching l =
       let (id, (b, f)), l' = assoc_by_pos k l in
 	if f then
 	  let id = match id with Some id -> id | None -> id_of_string ("arg_" ^ string_of_int k) in
-	    l', Some (id,Manual f,b)
+	    l', Some (id,Manual,b)
 	else l, None
     with Not_found -> l, None
   in
@@ -274,11 +279,11 @@ let compute_manual_implicits env flags t enriching l =
       let l',imp,m =
 	try 
 	  let (b, f) = List.assoc (ExplByName id) l in
-	  List.remove_assoc (ExplByName id) l, merge_imps f imp,Some b
+	  List.remove_assoc (ExplByName id) l, (Some Manual), (Some b)
 	with Not_found ->
 	try 
 	  let (id, (b, f)), l' = assoc_by_pos k l in
-	    l', merge_imps f imp,Some b
+	    l', (Some Manual), (Some b)
 	with Not_found ->
 	  l,imp, if enriching && imp <> None then Some flags.maximal else None
       in
@@ -305,11 +310,15 @@ let compute_manual_implicits env flags t enriching l =
   in
   merge 1 l autoimps
 
+let const v _ = v
+
 let compute_implicits_auto env f manual t =
   match manual with
-      [] -> let l = compute_implicits_flags env f false t in
-	      prepare_implicits f l
-    | _ -> compute_manual_implicits env f t true manual
+  | [] -> 
+      let l = compute_implicits_flags env f false t in
+	if f.manual then List.map (const None) l
+	else prepare_implicits f l
+  | _ -> compute_manual_implicits env f t (not f.manual) manual
 	
 let compute_implicits env t = compute_implicits_auto env !implicit_args [] t
 
@@ -333,10 +342,6 @@ let maximal_insertion_of = function
   | Some (_,_,b) -> b
   | None -> anomaly "Not an implicit argument"
 
-let forced_implicit = function
-  | Some (_,Manual b,_) -> b
-  | _ -> false
-
 (* [in_ctx] means we know the expected type, [n] is the index of the argument *)
 let is_inferable_implicit in_ctx n = function
   | None -> false
@@ -346,7 +351,7 @@ let is_inferable_implicit in_ctx n = function
   | Some (_,DepRigid Conclusion,_) -> in_ctx
   | Some (_,DepFlex Conclusion,_) -> false
   | Some (_,DepFlexAndRigid (_,Conclusion),_) -> in_ctx
-  | Some (_,Manual _,_) -> true
+  | Some (_,Manual,_) -> true
 
 let positions_of_implicits =
   let rec aux n = function
@@ -417,9 +422,18 @@ let list_split_at index l =
     | [] -> failwith "list_split_at: Invalid argument"
   in aux 0 [] l
     
-let merge_impls oimpls impls =
-  let oimpls, _ = list_split_at (List.length oimpls - List.length impls) oimpls in
-    oimpls @ impls
+let merge_impls oldimpls newimpls =
+  let (before, news), olds = 
+    let len = List.length newimpls - List.length oldimpls in
+      if len >= 0 then list_split_at len newimpls, oldimpls
+      else 
+	let before, after = list_split_at (-len) oldimpls in
+	  (before, newimpls), after
+  in
+    before @ (List.map2 (fun orig ni ->
+      match orig with
+      | Some (_, Manual, _) -> orig
+      | _ -> ni) olds news)
 
 (* Caching implicits *)
 
@@ -453,34 +467,67 @@ let subst_implicits_decl subst (r,imps as o) =
 let subst_implicits (_,subst,(req,l)) =
   (ImplLocal,list_smartmap (subst_implicits_decl subst) l)
 
+let impls_of_context ctx =
+  List.rev_map (fun (id,impl,_,_) -> if impl = Lib.Implicit then Some (id, Manual, true) else None)
+    (List.filter (fun (_,_,b,_) -> b = None) ctx)
+
+let section_segment_of_reference = function
+  | ConstRef con -> section_segment_of_constant con
+  | IndRef (kn,_) | ConstructRef ((kn,_),_) ->
+      section_segment_of_mutual_inductive kn
+  | _ -> []
+
 let discharge_implicits (_,(req,l)) =
   match req with
   | ImplLocal -> None
   | ImplInteractive (ref,flags,exp) -> 
-      Some (ImplInteractive (pop_global_reference ref,flags,exp),l)
+      let vars = section_segment_of_reference ref in
+      let ref' = pop_global_reference ref in
+      let l' = [ref', impls_of_context vars @ snd (List.hd l)] in
+      Some (ImplInteractive (ref',flags,exp),l')
   | ImplConstant (con,flags) ->
-      Some (ImplConstant (pop_con con,flags),l)
+      let con' = pop_con con in
+      let l' = [ConstRef con',impls_of_context (section_segment_of_constant con) @ snd (List.hd l)] in
+	Some (ImplConstant (con',flags),l')
   | ImplMutualInductive (kn,flags) ->
-      Some (ImplMutualInductive (pop_kn kn,flags),l)
+      let l' = List.map (fun (gr, l) -> 
+	let vars = section_segment_of_reference gr in
+	  (pop_global_reference gr, impls_of_context vars @ l)) l 
+      in
+	Some (ImplMutualInductive (pop_kn kn,flags),l')
 
-let rebuild_implicits (info,(req,l)) =
-  let manual = List.fold_left (fun acc (id, impl, keep) -> 
-    if impl then (ExplByName id, (true, true)) :: acc else acc)
-    [] info
-  in
+let rebuild_implicits (req,l) =
   let l' = match req with
   | ImplLocal -> assert false
   | ImplConstant (con,flags) -> 
-      [ConstRef con, compute_constant_implicits flags manual con]
+      let oldimpls = snd (List.hd l) in
+      let newimpls = compute_constant_implicits flags [] con in
+      [ConstRef con, merge_impls oldimpls newimpls]
   | ImplMutualInductive (kn,flags) ->
-      compute_all_mib_implicits flags manual kn
+      let newimpls = compute_all_mib_implicits flags [] kn in
+      let rec aux olds news = 
+	match olds, news with
+	| (_, oldimpls) :: old, (gr, newimpls) :: tl ->
+	    (gr, merge_impls oldimpls newimpls) :: aux old tl
+	| [], [] -> []
+	| _, _ -> assert false
+      in aux l newimpls
+
   | ImplInteractive (ref,flags,o) ->
       match o with
-      | ImplAuto -> [ref,compute_global_implicits flags manual ref]
-      | ImplManual l -> 
-	  let auto = compute_global_implicits flags manual ref in
-(* 	  let auto = if flags.main then auto else List.map (fun _ -> None) auto in *)
-	  let l' = merge_impls auto l in [ref,l']
+      | ImplAuto -> 
+	  let oldimpls = snd (List.hd l) in
+	  let newimpls = compute_global_implicits flags [] ref in
+	    [ref,merge_impls oldimpls newimpls]
+      | ImplManual m -> 
+	  let oldimpls = snd (List.hd l) in
+	  let auto = 
+	    if flags.main then
+	      let newimpls = compute_global_implicits flags [] ref in
+		merge_impls oldimpls newimpls
+	    else oldimpls
+	  in
+	  let l' = merge_impls auto m in [ref,l']
   in (req,l')
 
 let export_implicits (req,_ as x) = 
@@ -545,6 +592,12 @@ let maybe_declare_manual_implicits local ref enriching l =
   if l = [] then ()
   else declare_manual_implicits local ref enriching l
 
+let lift_implicits n = 
+  List.map (fun x -> 
+    match fst x with 
+	ExplByPos (k, id) -> ExplByPos (k + n, id), snd x
+      | _ -> x)
+
 (*s Registration as global tables *)
 
 let init () = implicits_table := Refmap.empty
diff --git a/library/impargs.mli b/library/impargs.mli
index 5b55af82..705efd31 100644
--- a/library/impargs.mli
+++ b/library/impargs.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: impargs.mli 10741 2008-04-02 15:47:07Z msozeau $ i*)
+(*i $Id: impargs.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -20,6 +20,7 @@ open Nametab
     are outside the kernel, which knows nothing about implicit arguments. *)
 
 val make_implicit_args : bool -> unit
+val make_manual_implicit_args : bool -> unit
 val make_strict_implicit_args : bool -> unit
 val make_strongly_strict_implicit_args : bool -> unit
 val make_reversible_pattern_implicit_args : bool -> unit
@@ -27,6 +28,7 @@ val make_contextual_implicit_args : bool -> unit
 val make_maximal_implicit_args : bool -> unit
 
 val is_implicit_args : unit -> bool
+val is_manual_implicit_args : unit -> bool
 val is_strict_implicit_args : unit -> bool
 val is_strongly_strict_implicit_args : unit -> bool
 val is_reversible_pattern_implicit_args : unit -> bool
@@ -38,16 +40,25 @@ val with_implicits : implicits_flags -> ('a -> 'b) -> 'a -> 'b
 
 (*s An [implicits_list] is a list of positions telling which arguments
     of a reference can be automatically infered *)
-type implicit_status
-type implicits_list = implicit_status list
 
-type implicit_explanation
+
+type argument_position =
+  | Conclusion
+  | Hyp of int
+
+type implicit_explanation =
+  | DepRigid of argument_position
+  | DepFlex of argument_position
+  | DepFlexAndRigid of (*flex*) argument_position * (*rig*) argument_position
+  | Manual
+
+type implicit_status = (identifier * implicit_explanation * bool) option
+type implicits_list = implicit_status list
 
 val is_status_implicit : implicit_status -> bool
 val is_inferable_implicit : bool -> int -> implicit_status -> bool
 val name_of_implicit : implicit_status -> identifier
 val maximal_insertion_of : implicit_status -> bool
-val forced_implicit : implicit_status -> bool
 
 val positions_of_implicits : implicits_list -> int list
 
@@ -83,3 +94,30 @@ val maybe_declare_manual_implicits : bool -> global_reference -> bool ->
   manual_explicitation list -> unit
 
 val implicits_of_global : global_reference -> implicits_list
+
+val lift_implicits : int -> manual_explicitation list -> manual_explicitation list
+
+val merge_impls : implicits_list -> implicits_list -> implicits_list
+
+type implicit_interactive_request =
+  | ImplAuto
+  | ImplManual of implicit_status list
+
+type implicit_discharge_request =
+  | ImplLocal
+  | ImplConstant of constant * implicits_flags
+  | ImplMutualInductive of kernel_name * implicits_flags
+  | ImplInteractive of global_reference * implicits_flags * 
+      implicit_interactive_request
+
+val discharge_implicits :     'a *
+    (implicit_discharge_request *
+     (Libnames.global_reference *
+      (Names.identifier * implicit_explanation * bool) option list)
+     list) ->
+    (implicit_discharge_request *
+     (Libnames.global_reference *
+      (Names.identifier * implicit_explanation * bool) option list)
+     list)
+    option
+
diff --git a/library/lib.ml b/library/lib.ml
index ce3d2520..fa71bb2f 100644
--- a/library/lib.ml
+++ b/library/lib.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: lib.ml 10982 2008-05-24 14:32:25Z herbelin $ *)
+(* $Id: lib.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Pp
 open Util
@@ -214,9 +214,9 @@ let add_leaf id obj =
   add_entry oname (Leaf obj);
   oname
 
-let add_discharged_leaf id varinfo obj =
+let add_discharged_leaf id obj =
   let oname = make_oname id in
-  let newobj = rebuild_object (varinfo, obj) in
+  let newobj = rebuild_object obj in
   cache_object (oname,newobj);
   add_entry oname (Leaf newobj)
 
@@ -436,11 +436,14 @@ let what_is_opened () = find_entry_p is_something_opened
    - the list of variables on which each inductive depends in this section
    - the list of substitution to do at section closing 
 *)
+type binding_kind = Explicit | Implicit
 
-type abstr_list = Sign.named_context Cmap.t * Sign.named_context KNmap.t
+type variable_info = Names.identifier * binding_kind * Term.constr option * Term.types
+type variable_context = variable_info list
+type abstr_list = variable_context Names.Cmap.t * variable_context Names.KNmap.t
 
 let sectab =
-  ref ([] : ((identifier * bool * Term.types option) list * Cooking.work_list * abstr_list) list)
+  ref ([] : ((Names.identifier * binding_kind * Term.types option) list * Cooking.work_list * abstr_list) list)
 
 let add_section () =
   sectab := ([],(Cmap.empty,KNmap.empty),(Cmap.empty,KNmap.empty)) :: !sectab
@@ -451,25 +454,34 @@ let add_section_variable id impl keep =
     | (vars,repl,abs)::sl -> sectab := ((id,impl,keep)::vars,repl,abs)::sl
 
 let rec extract_hyps = function
-  | ((id,impl,keep)::idl,(id',_,_ as d)::hyps) when id=id' -> d :: extract_hyps (idl,hyps)
-  | ((id,impl,Some ty)::idl,hyps) -> (id,None,ty) :: extract_hyps (idl,hyps)
+  | ((id,impl,keep)::idl,(id',b,t)::hyps) when id=id' -> (id',impl,b,t) :: extract_hyps (idl,hyps)
+  | ((id,impl,Some ty)::idl,hyps) -> (id,impl,None,ty) :: extract_hyps (idl,hyps)
   | (id::idl,hyps) -> extract_hyps (idl,hyps)
   | [], _ -> []
 
+let instance_from_variable_context sign =
+  let rec inst_rec = function
+    | (id,b,None,_) :: sign -> id :: inst_rec sign
+    | _ :: sign -> inst_rec sign
+    | [] -> [] in
+  Array.of_list (inst_rec sign)
+
+let named_of_variable_context = List.map (fun (id,_,b,t) -> (id,b,t))
+
 let add_section_replacement f g hyps =
   match !sectab with
   | [] -> ()
   | (vars,exps,abs)::sl ->
     let sechyps = extract_hyps (vars,hyps) in
-    let args = Sign.instance_from_named_context (List.rev sechyps) in
-    sectab := (vars,f (Array.map Term.destVar args) exps,g sechyps abs)::sl
+    let args = instance_from_variable_context (List.rev sechyps) in
+    sectab := (vars,f args exps,g sechyps abs)::sl
 	
 let add_section_kn kn =
-  let f = (fun x (l1,l2) -> (l1,KNmap.add kn x l2)) in
+  let f x (l1,l2) = (l1,Names.KNmap.add kn x l2) in
   add_section_replacement f f
 
 let add_section_constant kn =
-  let f = (fun x (l1,l2) -> (Cmap.add kn x l1,l2)) in
+  let f x (l1,l2) = (Names.Cmap.add kn x l1,l2) in
   add_section_replacement f f
 
 let replacement_context () = pi2 (List.hd !sectab)
@@ -482,13 +494,22 @@ let section_segment_of_constant con =
 let section_segment_of_mutual_inductive kn =
   KNmap.find kn (snd (pi3 (List.hd !sectab)))
 
+let rec list_mem_assoc_in_triple x = function
+    [] -> raise Not_found
+  | (a,_,_)::l -> compare a x = 0 or list_mem_assoc_in_triple x l
+
 let section_instance = function
-  | VarRef id -> [||]
+  | VarRef id ->
+      if list_mem_assoc_in_triple id (pi1 (List.hd !sectab)) then [||]
+      else raise Not_found
   | ConstRef con ->
       Cmap.find con (fst (pi2 (List.hd !sectab)))
   | IndRef (kn,_) | ConstructRef ((kn,_),_) ->
       KNmap.find kn (snd (pi2 (List.hd !sectab)))
 
+let is_in_section ref =
+  try ignore (section_instance ref); true with Not_found -> false
+
 let init_sectab () = sectab := []
 let freeze_sectab () = !sectab
 let unfreeze_sectab s = sectab := s
@@ -551,10 +572,6 @@ let close_section id =
     with Not_found ->
       error "no opened section"
   in
-  let var_info = List.map
-    (fun (x, y, z) -> (x, y, match z with Some _ -> true | None -> false))
-    (variables_context ())
-  in
   let (secdecls,secopening,before) = split_lib oname in
   lib_stk := before;
   let full_olddir = fst !path_prefix in
@@ -563,7 +580,7 @@ let close_section id =
   if !Flags.xml_export then !xml_close_section id;
   let newdecls = List.map discharge_item secdecls in
   Summary.section_unfreeze_summaries fs;
-  List.iter (Option.iter (fun (id,o) -> add_discharged_leaf id var_info o)) newdecls;
+  List.iter (Option.iter (fun (id,o) -> add_discharged_leaf id o)) newdecls;
   Cooking.clear_cooking_sharing ();
   Nametab.push_dir (Nametab.Until 1) full_olddir (DirClosedSection full_olddir)
 
diff --git a/library/lib.mli b/library/lib.mli
index 64074cfd..d35fcc09 100644
--- a/library/lib.mli
+++ b/library/lib.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: lib.mli 11046 2008-06-03 22:48:06Z msozeau $ i*)
+(*i $Id: lib.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Util
@@ -171,17 +171,24 @@ val reset_initial : unit -> unit
 val set_xml_open_section : (identifier -> unit) -> unit
 val set_xml_close_section : (identifier -> unit) -> unit
 
+type binding_kind = Explicit | Implicit
 
 (*s Section management for discharge *)
+type variable_info = Names.identifier * binding_kind * Term.constr option * Term.types
+type variable_context = variable_info list
 
-val section_segment_of_constant : constant -> Sign.named_context
-val section_segment_of_mutual_inductive: mutual_inductive -> Sign.named_context
+val instance_from_variable_context : variable_context -> Names.identifier array
+val named_of_variable_context : variable_context -> Sign.named_context
 
-val section_instance : global_reference -> identifier array
+val section_segment_of_constant : Names.constant -> variable_context
+val section_segment_of_mutual_inductive: Names.mutual_inductive -> variable_context
 
-val add_section_variable : identifier -> bool -> Term.types option -> unit
-val add_section_constant : constant -> Sign.named_context -> unit
-val add_section_kn : kernel_name -> Sign.named_context -> unit
+val section_instance : Libnames.global_reference -> Names.identifier array
+val is_in_section : Libnames.global_reference -> bool
+
+val add_section_variable : Names.identifier -> binding_kind -> Term.types option -> unit
+val add_section_constant : Names.constant -> Sign.named_context -> unit
+val add_section_kn : Names.kernel_name -> Sign.named_context -> unit
 val replacement_context : unit ->
   (identifier array Cmap.t * identifier array KNmap.t)
 
diff --git a/library/libnames.ml b/library/libnames.ml
index 31822da4..d0c6e8b9 100644
--- a/library/libnames.ml
+++ b/library/libnames.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: libnames.ml 10580 2008-02-22 13:39:13Z lmamane $ i*)
+(*i $Id: libnames.ml 11209 2008-07-05 10:17:49Z herbelin $ i*)
 
 open Pp
 open Util
@@ -89,6 +89,8 @@ let drop_dirpath_prefix d1 d2 =
   let d = Util.list_drop_prefix (List.rev (repr_dirpath d1)) (List.rev (repr_dirpath d2)) in
     make_dirpath (List.rev d)
 
+let append_dirpath d1 d2 = make_dirpath (repr_dirpath d2 @ repr_dirpath d1)
+
 (* To know how qualified a name should be to be understood in the current env*)
 let add_dirpath_prefix id d = make_dirpath (repr_dirpath d @ [id])
 
diff --git a/library/libnames.mli b/library/libnames.mli
index d4942061..76c406db 100644
--- a/library/libnames.mli
+++ b/library/libnames.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: libnames.mli 10308 2007-11-09 09:40:21Z herbelin $ i*)
+(*i $Id: libnames.mli 11209 2008-07-05 10:17:49Z herbelin $ i*)
 
 (*i*)
 open Pp
@@ -59,6 +59,7 @@ val chop_dirpath : int -> dir_path -> dir_path * dir_path
 val drop_dirpath_prefix : dir_path -> dir_path -> dir_path
 val extract_dirpath_prefix : int -> dir_path -> dir_path
 val is_dirpath_prefix_of : dir_path -> dir_path -> bool
+val append_dirpath : dir_path -> dir_path -> dir_path
 
 module Dirset : Set.S with type elt = dir_path
 module Dirmap : Map.S with type key = dir_path
diff --git a/library/libobject.ml b/library/libobject.ml
index ff78f527..6b302447 100644
--- a/library/libobject.ml
+++ b/library/libobject.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: libobject.ml 10741 2008-04-02 15:47:07Z msozeau $ *)
+(* $Id: libobject.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -28,8 +28,6 @@ let relax b = relax_flag := b;;
 type 'a substitutivity = 
     Dispose | Substitute of 'a | Keep of 'a | Anticipate of 'a
 
-type discharge_info = (identifier * bool * bool) list
-
 type 'a object_declaration = {
   object_name : string;
   cache_function : object_name * 'a -> unit;
@@ -38,7 +36,7 @@ type 'a object_declaration = {
   classify_function : object_name * 'a -> 'a substitutivity;
   subst_function : object_name * substitution * 'a -> 'a;
   discharge_function : object_name * 'a -> 'a option;
-  rebuild_function : discharge_info * 'a -> 'a;
+  rebuild_function : 'a -> 'a;
   export_function : 'a -> 'a option }
 
 let yell s = anomaly s
@@ -52,7 +50,7 @@ let default_object s = {
     yell ("The object "^s^" does not know how to substitute!"));
   classify_function = (fun (_,obj) -> Keep obj);
   discharge_function = (fun _ -> None);
-  rebuild_function = (fun (_,x) -> x);
+  rebuild_function = (fun x -> x);
   export_function = (fun _ -> None)} 
 
 
@@ -78,7 +76,7 @@ type dynamic_object_declaration = {
   dyn_subst_function : object_name * substitution * obj -> obj;
   dyn_classify_function : object_name * obj -> obj substitutivity;
   dyn_discharge_function : object_name * obj -> obj option;
-  dyn_rebuild_function : discharge_info * obj -> obj;
+  dyn_rebuild_function : obj -> obj;
   dyn_export_function : obj -> obj option }
 
 let object_tag lobj = Dyn.tag lobj
@@ -116,8 +114,8 @@ let declare_object odecl =
       Option.map infun (odecl.discharge_function (oname,outfun lobj))
     else 
       anomaly "somehow we got the wrong dynamic object in the dischargefun"
-  and rebuild (varinfo,lobj) = 
-    if Dyn.tag lobj = na then infun (odecl.rebuild_function (varinfo,outfun lobj))
+  and rebuild lobj = 
+    if Dyn.tag lobj = na then infun (odecl.rebuild_function (outfun lobj))
     else anomaly "somehow we got the wrong dynamic object in the rebuildfun"
   and exporter lobj = 
     if Dyn.tag lobj = na then 
@@ -174,7 +172,7 @@ let classify_object ((_,lobj) as node) =
 let discharge_object ((_,lobj) as node) = 
   apply_dyn_fun None (fun d -> d.dyn_discharge_function node) lobj
 
-let rebuild_object ((_,lobj) as node) =
+let rebuild_object (lobj as node) =
   apply_dyn_fun lobj (fun d -> d.dyn_rebuild_function node) lobj
 
 let export_object lobj =
diff --git a/library/libobject.mli b/library/libobject.mli
index 5f6cf13b..4ec5746b 100644
--- a/library/libobject.mli
+++ b/library/libobject.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: libobject.mli 10840 2008-04-23 21:29:34Z herbelin $ i*)
+(*i $Id: libobject.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -71,8 +71,6 @@ open Mod_subst
 type 'a substitutivity = 
     Dispose | Substitute of 'a | Keep of 'a | Anticipate of 'a
 
-type discharge_info = (identifier * bool * bool) list
-
 type 'a object_declaration = {
   object_name : string;
   cache_function : object_name * 'a -> unit;
@@ -81,7 +79,7 @@ type 'a object_declaration = {
   classify_function : object_name * 'a -> 'a substitutivity;
   subst_function : object_name * substitution * 'a -> 'a;
   discharge_function : object_name * 'a -> 'a option;
-  rebuild_function : discharge_info * 'a -> 'a;
+  rebuild_function : 'a -> 'a;
   export_function : 'a -> 'a option }
 
 (* The default object is a "Keep" object with empty methods. 
@@ -116,5 +114,5 @@ val subst_object : object_name * substitution * obj -> obj
 val classify_object : object_name * obj -> obj substitutivity
 val export_object : obj -> obj option
 val discharge_object : object_name * obj -> obj option
-val rebuild_object : discharge_info * obj -> obj
+val rebuild_object : obj -> obj
 val relax : bool -> unit
diff --git a/library/library.ml b/library/library.ml
index 2904edc2..73928a9b 100644
--- a/library/library.ml
+++ b/library/library.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: library.ml 11181 2008-06-27 07:35:45Z notin $ *)
+(* $Id: library.ml 11313 2008-08-07 11:15:03Z barras $ *)
 
 open Pp
 open Util
@@ -25,9 +25,9 @@ open Declaremods
 
 type logical_path = dir_path
 
-let load_paths = ref ([],[] : System.physical_path list * logical_path list)
+let load_paths = ref ([] : (System.physical_path * logical_path * bool) list)
 
-let get_load_paths () = fst !load_paths
+let get_load_paths () = List.map pi1 !load_paths
 
 (* Hints to partially detects if two paths refer to the same repertory *)
 let rec remove_path_dot p = 
@@ -57,12 +57,12 @@ let canonical_path_name p =
     (* We give up to find a canonical name and just simplify it... *)
     strip_path p
 
-let find_logical_path phys_dir = 
+let find_logical_path phys_dir =
   let phys_dir = canonical_path_name phys_dir in
-  match list_filter2 (fun p d -> p = phys_dir) !load_paths with
-  | _,[dir] -> dir
-  | _,[] -> Nameops.default_root_prefix
-  | _,l -> anomaly ("Two logical paths are associated to "^phys_dir)
+  match List.filter (fun (p,d,_) -> p = phys_dir) !load_paths with
+  | [_,dir,_] -> dir
+  | [] -> Nameops.default_root_prefix
+  | l -> anomaly ("Two logical paths are associated to "^phys_dir)
 
 let is_in_load_paths phys_dir =
   let dir = canonical_path_name phys_dir in
@@ -71,12 +71,12 @@ let is_in_load_paths phys_dir =
     List.exists check_p lp 
 
 let remove_load_path dir =
-  load_paths := list_filter2 (fun p d -> p <> dir) !load_paths
+  load_paths := List.filter (fun (p,d,_) -> p <> dir) !load_paths
 
-let add_load_path (phys_path,coq_path) =
+let add_load_path isroot (phys_path,coq_path) =
   let phys_path = canonical_path_name phys_path in
-    match list_filter2 (fun p d -> p = phys_path) !load_paths with
-      | _,[dir] ->
+    match List.filter (fun (p,d,_) -> p = phys_path) !load_paths with
+      | [_,dir,_] ->
 	  if coq_path <> dir 
             (* If this is not the default -I . to coqtop *)
             && not
@@ -91,18 +91,54 @@ let add_load_path (phys_path,coq_path) =
 		   pr_dirpath dir ++ strbrk "; it is remapped to " ++
 		   pr_dirpath coq_path);
 	      remove_load_path phys_path;
-	      load_paths := (phys_path::fst !load_paths, coq_path::snd !load_paths)
+	      load_paths := (phys_path,coq_path,isroot) :: !load_paths;
 	    end
-      | _,[] ->
-	  load_paths := (phys_path :: fst !load_paths, coq_path :: snd !load_paths)
+      | [] ->
+	  load_paths := (phys_path,coq_path,isroot) :: !load_paths;
       | _ -> anomaly ("Two logical paths are associated to "^phys_path)
 
 let physical_paths (dp,lp) = dp
 
-let load_paths_of_dir_path dir =
-  fst (list_filter2 (fun p d -> d = dir) !load_paths)
-    
-let get_full_load_paths () = List.combine (fst !load_paths) (snd !load_paths)
+let extend_path_with_dirpath p dir =
+  List.fold_left Filename.concat p 
+    (List.map string_of_id (List.rev (repr_dirpath dir)))
+
+let root_paths_matching_dir_path dir =
+  let rec aux = function
+  | [] -> []
+  | (p,d,true) :: l when is_dirpath_prefix_of d dir ->
+      let suffix = drop_dirpath_prefix d dir in
+      extend_path_with_dirpath p suffix :: aux l
+  | _ :: l -> aux l in
+  aux !load_paths
+
+(* Root p is bound to A.B.C.D and we require file C.D.E.F *)
+(* We may mean A.B.C.D.E.F, or A.B.C.D.C.D.E.F *)
+
+(* Root p is bound to A.B.C.C and we require file C.C.E.F *)
+(* We may mean A.B.C.C.E.F, or A.B.C.C.C.E.F, or A.B.C.C.C.C.E.F *)
+
+let intersections d1 d2 =
+  let rec aux d1 =
+    if d1 = empty_dirpath then [d2] else
+      let rest = aux (snd (chop_dirpath 1 d1)) in
+      if is_dirpath_prefix_of d1 d2 then drop_dirpath_prefix d1 d2 :: rest
+      else rest in
+  aux d1
+
+let loadpaths_matching_dir_path dir =
+  let rec aux = function
+  | [] -> []
+  | (p,d,true) :: l ->
+      let inters = intersections d dir in
+      List.map (fun tl -> (extend_path_with_dirpath p tl,append_dirpath d tl))
+	inters @
+	aux l
+  | (p,d,_) :: l ->
+      (extend_path_with_dirpath p dir,append_dirpath d dir) :: aux l in
+  aux !load_paths
+
+let get_full_load_paths () = List.map (fun (a,b,c) -> (a,b)) !load_paths
 
 (************************************************************************)
 (*s Modules on disk contain the following informations (after the magic 
@@ -197,6 +233,12 @@ let library_full_filename dir =
   try LibraryFilenameMap.find dir !libraries_filename_table
   with Not_found -> "<unavailable filename>"
 
+let overwrite_library_filenames f =
+  let f =
+    if Filename.is_relative f then Filename.concat (Sys.getcwd ()) f else f in
+  LibraryMap.iter (fun dir _ -> register_library_filename dir f)
+    !libraries_table
+
 let library_is_loaded dir =
   try let _ = find_library dir in true
   with Not_found -> false
@@ -312,10 +354,8 @@ let (in_import, out_import) =
 
 (*s Loading from disk to cache (preparation phase) *)
 
-let vo_magic_number = 08193 (* v8.2beta3 *)
-
 let (raw_extern_library, raw_intern_library) =
-  System.raw_extern_intern vo_magic_number ".vo"
+  System.raw_extern_intern Coq_config.vo_magic_number ".vo"
 
 let with_magic_number_check f a =
   try f a
@@ -335,11 +375,11 @@ type library_location = LibLoaded | LibInPath
 let locate_absolute_library dir =
   (* Search in loadpath *)
   let pref, base = split_dirpath dir in
-  let loadpath = load_paths_of_dir_path pref in
+  let loadpath = root_paths_matching_dir_path pref in
   if loadpath = [] then raise LibUnmappedDir;
   try
     let name = (string_of_id base)^".vo" in
-    let _, file = System.where_in_path loadpath name in
+    let _, file = System.where_in_path false loadpath name in
     (dir, file)
   with Not_found ->
   (* Last chance, removed from the file system but still in memory *)
@@ -348,20 +388,15 @@ let locate_absolute_library dir =
   else
     raise LibNotFound
 
-let locate_qualified_library qid =
+let locate_qualified_library warn qid =
   try
     (* Search library in loadpath *)
-    let dir, base = repr_qualid qid in 
-    let loadpath =
-      if repr_dirpath dir = [] then get_load_paths ()
-      else 
-        (* we assume dir is an absolute dirpath *)
-	load_paths_of_dir_path dir
-    in
+    let dir, base = repr_qualid qid in
+    let loadpath = loadpaths_matching_dir_path dir in
     if loadpath = [] then raise LibUnmappedDir;
-    let name =  (string_of_id base)^".vo" in
-    let path, file = System.where_in_path loadpath name in
-    let dir = extend_dirpath (find_logical_path path) base in
+    let name = string_of_id base ^ ".vo" in
+    let lpath, file = System.where_in_path warn (List.map fst loadpath) name in
+    let dir = extend_dirpath (List.assoc lpath loadpath) base in
     (* Look if loaded *)
     if library_is_loaded dir then (LibLoaded, dir, library_full_filename dir)
     (* Otherwise, look for it in the file system *)
@@ -387,7 +422,7 @@ let try_locate_absolute_library dir =
 
 let try_locate_qualified_library (loc,qid) =
   try
-    let (_,dir,f) = locate_qualified_library qid in
+    let (_,dir,f) = locate_qualified_library (Flags.is_verbose()) qid in
     dir,f
   with e -> 
     explain_locate_library_error qid e
@@ -590,8 +625,7 @@ let import_module export (loc,qid) =
 (*s Initializing the compilation of a library. *)
 
 let start_library f = 
-  let _,longf = 
-    System.find_file_in_path (get_load_paths ()) (f^".v") in
+  let _,longf = System.find_file_in_path (get_load_paths ()) (f^".v") in
   let ldir0 = find_logical_path (Filename.dirname longf) in
   let id = id_of_string (Filename.basename f) in
   let ldir = extend_dirpath ldir0 id in
@@ -609,9 +643,9 @@ let current_reexports () =
 
 let error_recursively_dependent_library dir =
   errorlabstrm ""
-    (str "Unable to use logical name" ++ spc() ++ pr_dirpath dir ++ spc() ++ 
-     str "to save current library" ++ spc() ++ str"because" ++ spc() ++ 
-     str "it already depends on a library of this name.")
+    (strbrk "Unable to use logical name " ++ pr_dirpath dir ++ 
+     strbrk " to save current library because" ++
+     strbrk " it already depends on a library of this name.")
 
 let save_library_to dir f =
   let cenv, seg = Declaremods.end_library dir in
diff --git a/library/library.mli b/library/library.mli
index 27ace544..a66a77bc 100644
--- a/library/library.mli
+++ b/library/library.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: library.mli 8877 2006-05-30 16:37:04Z notin $ i*)
+(*i $Id: library.mli 11209 2008-07-05 10:17:49Z herbelin $ i*)
 
 (*i*)
 open Util
@@ -52,6 +52,9 @@ val opened_libraries : unit -> dir_path list
   (* - Return the full filename of a loaded library. *)
 val library_full_filename : dir_path -> string
 
+  (* - Overwrite the filename of all libraries (used when restoring a state) *)
+val overwrite_library_filenames : string -> unit
+
 (*s Hook for the xml exportation of libraries *)
 val set_xml_require : (dir_path -> unit) -> unit
 
@@ -61,11 +64,10 @@ val set_xml_require : (dir_path -> unit) -> unit
 
 val get_load_paths : unit -> System.physical_path list
 val get_full_load_paths : unit -> (System.physical_path * dir_path) list
-val add_load_path : System.physical_path * dir_path -> unit
+val add_load_path : bool -> System.physical_path * dir_path -> unit
 val remove_load_path : System.physical_path -> unit
 val find_logical_path : System.physical_path -> dir_path
 val is_in_load_paths : System.physical_path -> bool
-val load_paths_of_dir_path : dir_path -> System.physical_path list
 
 (*s Locate a library in the load paths *)
 exception LibUnmappedDir
@@ -73,7 +75,7 @@ exception LibNotFound
 type library_location = LibLoaded | LibInPath
 
 val locate_qualified_library :
-  qualid -> library_location * dir_path * System.physical_path
+  bool -> qualid -> library_location * dir_path * System.physical_path
 
 (*s Statistics: display the memory use of a library. *)
 val mem : dir_path -> Pp.std_ppcmds
diff --git a/library/states.ml b/library/states.ml
index 169a3857..7f7fef47 100644
--- a/library/states.ml
+++ b/library/states.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: states.ml 9100 2006-08-31 18:04:26Z herbelin $ *)
+(* $Id: states.ml 11313 2008-08-07 11:15:03Z barras $ *)
 
 open System
 
@@ -19,12 +19,13 @@ let unfreeze (fl,fs) =
   Lib.unfreeze fl;
   Summary.unfreeze_summaries fs
 
-let state_magic_number = 19764
-
 let (extern_state,intern_state) =
-  let (raw_extern, raw_intern) = extern_intern state_magic_number ".coq" in
+  let (raw_extern, raw_intern) =
+    extern_intern Coq_config.state_magic_number ".coq" in
   (fun s -> raw_extern s (freeze())),
-  (fun s -> unfreeze (raw_intern (Library.get_load_paths ()) s))
+  (fun s ->
+    unfreeze (raw_intern (Library.get_load_paths ()) s);
+    Library.overwrite_library_filenames s)
 
 (* Rollback. *)
 
diff --git a/parsing/egrammar.ml b/parsing/egrammar.ml
index 9416bff2..825d1af0 100644
--- a/parsing/egrammar.ml
+++ b/parsing/egrammar.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: egrammar.ml 10987 2008-05-26 12:28:36Z herbelin $ *)
+(* $Id: egrammar.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -114,27 +114,33 @@ let make_constr_prod_item univ assoc from forpat = function
 let prepare_empty_levels entry (pos,p4assoc,name,reinit) =
   grammar_extend entry pos reinit [(name, p4assoc, [])]
 
-let extend_constr entry (n,assoc,pos,p4assoc,name,reinit) mkact (forpat,pt) =
+let pure_sublevels level symbs =
+  map_succeed (function
+  | Gramext.Snterml (_,n) when Some (int_of_string n) <> level ->
+      int_of_string n
+  | _ ->
+      failwith "") symbs
+
+let extend_constr (entry,level) (n,assoc) mkact forpat pt =
   let univ = get_univ "constr" in
   let pil = List.map (make_constr_prod_item univ assoc n forpat) pt in
   let (symbs,ntl) = List.split pil in
-  let needed_levels = register_empty_levels forpat symbs in
+  let pure_sublevels = pure_sublevels level symbs in
+  let needed_levels = register_empty_levels forpat pure_sublevels in
+  let pos,p4assoc,name,reinit = find_position forpat assoc level in
   List.iter (prepare_empty_levels entry) needed_levels;
   grammar_extend entry pos reinit [(name, p4assoc, [symbs, mkact ntl])]
 
 let extend_constr_notation (n,assoc,ntn,rule) =
   (* Add the notation in constr *)
   let mkact loc env = CNotation (loc,ntn,List.map snd env) in
-  let (e,level) = get_constr_entry false (ETConstr (n,())) in
-  let pos,p4assoc,name,reinit = find_position false assoc level in
-  extend_constr e (ETConstr(n,()),assoc,pos,p4assoc,name,reinit)
-    (make_constr_action mkact) (false,rule);
+  let e = get_constr_entry false (ETConstr (n,())) in
+  extend_constr e (ETConstr(n,()),assoc) (make_constr_action mkact) false rule;
   (* Add the notation in cases_pattern *)
   let mkact loc env = CPatNotation (loc,ntn,List.map snd env) in
-  let (e,level) = get_constr_entry true (ETConstr (n,())) in
-  let pos,p4assoc,name,reinit = find_position true assoc level in
-  extend_constr e (ETConstr (n,()),assoc,pos,p4assoc,name,reinit)
-    (make_cases_pattern_action mkact) (true,rule)
+  let e = get_constr_entry true (ETConstr (n,())) in
+  extend_constr e (ETConstr (n,()),assoc) (make_cases_pattern_action mkact)
+    true rule
 
 (**********************************************************************)
 (** Making generic actions in type generic_argument                   *)
@@ -228,7 +234,7 @@ let rec interp_entry_name up_level s =
       try get_entry (get_univ "prim") s
       with _ ->
       try get_entry (get_univ "constr") s
-      with _ -> error ("Unknown entry "^s)
+      with _ -> error ("Unknown entry "^s^".")
     in
     let o = object_of_typed_entry e in
     let t = type_of_typed_entry e in
@@ -248,7 +254,7 @@ let get_tactic_entry n =
   else if 1<=n && n<5 then
     weaken_entry Tactic.tactic_expr, Some (Gramext.Level (string_of_int n))
   else 
-    error ("Invalid Tactic Notation level: "^(string_of_int n))
+    error ("Invalid Tactic Notation level: "^(string_of_int n)^".")
 
 (* Declaration of the tactic grammar rule *)
 
@@ -261,7 +267,7 @@ let add_tactic_entry (key,lev,prods,tac) =
   let rules = 
     if lev = 0 then begin
       if not (head_is_ident prods) then
-	error "Notation for simple tactic must start with an identifier";
+	error "Notation for simple tactic must start with an identifier.";
       let mkact s tac loc l =
 	(TacAlias(loc,s,l,tac):raw_atomic_tactic_expr) in
       make_rule univ (mkact key tac) mkprod prods
diff --git a/parsing/g_ascii_syntax.ml b/parsing/g_ascii_syntax.ml
index b262b978..944e2338 100644
--- a/parsing/g_ascii_syntax.ml
+++ b/parsing/g_ascii_syntax.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1       *)
 (***********************************************************************)
 
-(*i $Id: g_ascii_syntax.ml 10744 2008-04-03 14:09:56Z herbelin $ i*)
+(*i $Id: g_ascii_syntax.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Pp
 open Util
@@ -53,7 +53,7 @@ let interp_ascii_string dloc s =
       then int_of_string s
       else
 	user_err_loc (dloc,"interp_ascii_string",
-	  str "Expects a single character or a three-digits ascii code") in
+	  str "Expects a single character or a three-digits ascii code.") in
   interp_ascii dloc p
 
 let uninterp_ascii r =
diff --git a/parsing/g_constr.ml4 b/parsing/g_constr.ml4
index ba61eb61..b93fdadd 100644
--- a/parsing/g_constr.ml4
+++ b/parsing/g_constr.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(* $Id: g_constr.ml4 11024 2008-05-30 12:41:39Z msozeau $ *)
+(* $Id: g_constr.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pcoq
 open Constr
@@ -47,7 +47,7 @@ let rec index_and_rec_order_of_annot loc bl ann =
     | lids, (Some (loc, n), ro) ->
         if List.exists (fun (_, x) -> x = Name n) lids then
 	  Some (loc, n), ro
-        else user_err_loc(loc,"index_of_annot", Pp.str"no such fix variable")
+        else user_err_loc(loc,"index_of_annot", Pp.str"No such fix variable.")
     | _, (None, r) -> None, r
 
 let mk_fixb (id,bl,ann,body,(loc,tyc)) =
@@ -61,7 +61,7 @@ let mk_cofixb (id,bl,ann,body,(loc,tyc)) =
   let _ = Option.map (fun (aloc,_) ->
     Util.user_err_loc
       (aloc,"Constr:mk_cofixb",
-       Pp.str"Annotation forbidden in cofix expression")) (fst ann) in
+       Pp.str"Annotation forbidden in cofix expression.")) (fst ann) in
   let ty = match tyc with
       Some ty -> ty
     | None -> CHole (loc, None) in
@@ -326,7 +326,7 @@ GEXTEND Gram
           | CPatAtom (_, Some r) -> CPatCstr (loc, r, lp)
           | _ -> Util.user_err_loc 
               (cases_pattern_expr_loc p, "compound_pattern",
-               Pp.str "Constructor expected"))
+               Pp.str "Constructor expected."))
       | p = pattern; "as"; id = ident ->
 	  CPatAlias (loc, p, id) ]
     | "1" LEFTA
@@ -398,7 +398,12 @@ GEXTEND Gram
         [LocalRawAssum ([id],Default Implicit,c)]
     | "{"; id=name; idl=LIST1 name; "}" -> 
         List.map (fun id -> LocalRawAssum ([id],Default Implicit,CHole (loc, None))) (id::idl)
-    | "["; tc = LIST1 typeclass_constraint_binder SEP ","; "]" -> tc
+    | "("; "("; tc = LIST1 typeclass_constraint SEP "," ; ")"; ")" ->
+	List.map (fun (n, b, t) -> LocalRawAssum ([n], TypeClass (Explicit, b), t)) tc
+    | "{"; "{"; tc = LIST1 typeclass_constraint SEP "," ; "}"; "}" ->
+	List.map (fun (n, b, t) -> LocalRawAssum ([n], TypeClass (Implicit, b), t)) tc
+    | "["; tc = LIST1 typeclass_constraint SEP ","; "]" -> 
+	List.map (fun (n, b, t) -> LocalRawAssum ([n], TypeClass (Implicit, b), t)) tc
     ] ]
   ;
   binder:
@@ -407,19 +412,14 @@ GEXTEND Gram
       | "{"; idl=LIST1 name; ":"; c=lconstr; "}" -> (idl,Default Implicit,c) 
     ] ]
   ;
-  typeclass_constraint_binder:
-    [ [ tc = typeclass_constraint ->
-      let (n,bk,t) = tc in
-	LocalRawAssum ([n], TypeClass bk, t)
-    ] ]
-  ;
-
   typeclass_constraint:
     [ [ "!" ; c = operconstr LEVEL "200" -> (loc, Anonymous), Explicit, c
-    | iid=ident_colon ; expl = [ "!" -> Explicit | -> Implicit ] ; c = operconstr LEVEL "200" ->
-	(loc, Name iid), expl, c
-    | c = operconstr LEVEL "200" ->
-	(loc, Anonymous), Implicit, c
+      | "{"; id = name; "}"; ":" ; expl = [ "!" -> Explicit | -> Implicit ] ; c = operconstr LEVEL "200" ->
+	  id, expl, c
+      | iid=ident_colon ; expl = [ "!" -> Explicit | -> Implicit ] ; c = operconstr LEVEL "200" ->
+	  (loc, Name iid), expl, c
+      | c = operconstr LEVEL "200" ->
+	  (loc, Anonymous), Implicit, c
     ] ]
   ;
   
diff --git a/parsing/g_intsyntax.ml b/parsing/g_intsyntax.ml
index 6ab8f99c..a589ccf1 100644
--- a/parsing/g_intsyntax.ml
+++ b/parsing/g_intsyntax.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: g_intsyntax.ml 11087 2008-06-10 13:29:52Z letouzey $ i*)
+(*i $Id: g_intsyntax.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (* digit-based syntax for int31, bigN bigZ and bigQ *)
 
@@ -122,7 +122,7 @@ let int31_of_pos_bigint dloc n =
   RApp (dloc, ref_construct, List.rev (args 31 n))
 
 let error_negative dloc =
-  Util.user_err_loc (dloc, "interp_int31", Pp.str "int31 are only non-negative numbers")
+  Util.user_err_loc (dloc, "interp_int31", Pp.str "int31 are only non-negative numbers.")
 
 let interp_int31 dloc n = 
   if is_pos_or_zero n then
@@ -212,7 +212,7 @@ let bigN_of_pos_bigint dloc n =
   result hght (word_of_pos_bigint dloc hght n)
   
 let bigN_error_negative dloc =
-  Util.user_err_loc (dloc, "interp_bigN", Pp.str "bigN are only non-negative numbers")
+  Util.user_err_loc (dloc, "interp_bigN", Pp.str "bigN are only non-negative numbers.")
 
 let interp_bigN dloc n = 
   if is_pos_or_zero n then
diff --git a/parsing/g_ltac.ml4 b/parsing/g_ltac.ml4
index 78a9fbc7..dbd81e7f 100644
--- a/parsing/g_ltac.ml4
+++ b/parsing/g_ltac.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(* $Id: g_ltac.ml4 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: g_ltac.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -72,10 +72,10 @@ GEXTEND Gram
       | ta0 = tactic_expr; "||"; ta1 = tactic_expr -> TacOrelse (ta0,ta1) ]
     | "1" RIGHTA
       [ b = match_key; IDENT "goal"; "with"; mrl = match_context_list; "end" ->
-          TacMatchContext (b,false,mrl)
+          TacMatchGoal (b,false,mrl)
       | b = match_key; IDENT "reverse"; IDENT "goal"; "with";
         mrl = match_context_list; "end" ->
-          TacMatchContext (b,true,mrl)
+          TacMatchGoal (b,true,mrl)
       |	b = match_key; c = tactic_expr; "with"; mrl = match_list; "end" ->
           TacMatch (b,c,mrl)
       | IDENT "first" ; "["; l = LIST0 tactic_expr SEP "|"; "]" ->
diff --git a/parsing/g_minicoq.ml4 b/parsing/g_minicoq.ml4
deleted file mode 100644
index a9275cf9..00000000
--- a/parsing/g_minicoq.ml4
+++ /dev/null
@@ -1,177 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(*i camlp4use: "pa_extend.cmo" i*)
-
-(* $Id: g_minicoq.ml4 10007 2007-07-16 09:18:44Z corbinea $ *)
-
-open Pp
-open Util
-open Names
-open Univ
-open Term
-open Environ
-
-let lexer =
-  {Token.func = Lexer.func; Token.using = Lexer.add_token;
-   Token.removing = (fun _ -> ()); Token.tparse = Lexer.tparse;
-   Token.text = Lexer.token_text}
-;;
-
-type command =
-  | Definition of identifier * constr option * constr
-  | Parameter of identifier * constr
-  | Variable of identifier * constr
-  | Inductive of 
-      (identifier * constr) list *
-      (identifier * constr * (identifier * constr) list) list
-  | Check of constr
-
-let gram = Grammar.create lexer
-
-let term = Grammar.Entry.create gram "term"
-let name = Grammar.Entry.create gram "name"
-let nametype = Grammar.Entry.create gram "nametype"
-let inductive = Grammar.Entry.create gram "inductive"
-let constructor = Grammar.Entry.create gram "constructor"
-let command = Grammar.Entry.create gram "command"
-
-let path_of_string s = make_path [] (id_of_string s)
-
-EXTEND
-  name: 
-  [ [ id = IDENT -> Name (id_of_string id)
-    | "_" -> Anonymous
-  ] ];
-  nametype: 
-  [ [ id = IDENT; ":"; t = term -> (id_of_string id, t) 
-  ] ];
-  term: 
-  [ [ id = IDENT -> 
-	mkVar (id_of_string id) 
-    | IDENT "Rel"; n = INT ->
-	mkRel (int_of_string n)
-    | "Set" ->
-	mkSet
-    | "Prop" ->
-	mkProp
-    | "Type" ->
-	mkType (new_univ())
-    | "Const"; id = IDENT ->
-	mkConst (path_of_string id, [||])
-    | "Ind"; id = IDENT; n = INT ->
-	let n = int_of_string n in
-	mkMutInd ((path_of_string id, n), [||])
-    | "Construct"; id = IDENT; n = INT; i = INT ->
-	let n = int_of_string n and i = int_of_string i in
-	mkMutConstruct (((path_of_string id, n), i), [||])
-    | "["; na = name; ":"; t = term; "]"; c = term ->
-	mkLambda (na,t,c)
-    | "("; na = name; ":"; t = term; ")"; c = term ->
-	mkProd (na,t,c)
-    | c1 = term; "->"; c2 = term ->
-	mkArrow c1 c2
-    | "("; id = IDENT; cl = LIST1 term; ")" ->
-	let c = mkVar (id_of_string id) in
-	mkApp (c, Array.of_list cl)
-    | "("; cl = LIST1 term; ")" ->
-	begin match cl with
-	  | [c] -> c
-	  | c::cl -> mkApp (c, Array.of_list cl)
-	end
-    | "("; c = term; "::"; t = term; ")" ->
-	mkCast (c, t)
-    | "<"; p = term; ">"; 
-	IDENT "Case"; c = term; ":"; "Ind"; id = IDENT; i = INT;
-	"of"; bl = LIST0 term; "end" ->
-	  let ind = (path_of_string id,int_of_string i) in
-	  let nc = List.length bl in
-	  let dummy_pats = Array.create nc RegularPat in
-	  let dummy_ci = [||],(ind,[||],nc,None,dummy_pats) in
-	  mkMutCase (dummy_ci, p, c, Array.of_list bl)
-  ] ];
-  command: 
-  [ [ "Definition"; id = IDENT; ":="; c = term; "." ->
-	Definition (id_of_string id, None, c)
-    | "Definition"; id = IDENT; ":"; t = term; ":="; c = term; "." ->
-	Definition (id_of_string id, Some t, c)
-    | "Parameter"; id = IDENT; ":"; t = term; "." ->
-	Parameter (id_of_string id, t)
-    | "Variable"; id = IDENT; ":"; t = term; "." ->
-	Variable (id_of_string id, t)
-    | "Inductive"; "["; params = LIST0 nametype SEP ";"; "]"; 
-      inds = LIST1 inductive SEP "with" ->
-	Inductive (params, inds)
-    | IDENT "Check"; c = term; "." ->
-	Check c
-    | EOI -> raise End_of_file
-  ] ];
-  inductive: 
-  [ [ id = IDENT; ":"; ar = term; ":="; constrs = LIST0 constructor SEP "|" ->
-        (id_of_string id,ar,constrs)
-  ] ];
-  constructor:
-  [ [ id = IDENT; ":"; c = term -> (id_of_string id,c) ] ];
-END
-
-(* Pretty-print. *)
-
-let print_univers = ref false
-let print_casts = ref false
-
-let print_type u =
-  if !print_univers then (str "Type" ++ pr_uni u)
-  else (str "Type")
-
-let print_name = function
-  | Anonymous -> (str "_")
-  | Name id -> pr_id id
-
-let print_rel bv n = print_name (List.nth bv (pred n))
-
-let rename bv = function
-  | Anonymous -> Anonymous
-  | Name id as na -> 
-      let idl = 
-	List.fold_left 
-	  (fun l n -> match n with Name x -> x::l | _ -> l) [] bv 
-      in
-      if List.mem na bv then Name (next_ident_away id idl) else na
-
-let rec pp bv t =
-  match kind_of_term t with
-  | Sort (Prop Pos) -> (str "Set")
-  | Sort (Prop Null) -> (str "Prop")
-  | Sort (Type u) -> print_type u
-  | Lambda (na, t, c) ->
-      (str"[" ++ print_name na ++ str":" ++ pp bv t ++ str"]" ++ pp (na::bv) c)
-  | Prod (Anonymous, t, c) ->
-      (pp bv t ++ str"->" ++ pp (Anonymous::bv) c)
-  | Prod (na, t, c) ->
-      (str"(" ++ print_name na ++ str":" ++ pp bv t ++ str")" ++ pp (na::bv) c)
-  | Cast (c, t) ->
-      if !print_casts then 
-	(str"(" ++ pp bv c ++ str"::" ++ pp bv t ++ str")")
-      else 
-	pp bv c
-  | App(h, v) ->
-      (str"(" ++ pp bv h ++ spc () ++
-         prvect_with_sep (fun () -> (spc ())) (pp bv) v ++ str")")
-  | Const (sp, _) ->
-      (str"Const " ++ pr_id (basename sp))
-  | Ind ((sp,i), _) ->
-      (str"Ind " ++ pr_id (basename sp) ++ str" " ++ int i)
-  | Construct (((sp,i),j), _) ->
-      (str"Construct " ++ pr_id (basename sp) ++ str" " ++ int i ++ 
-	 str" " ++ int j)
-  | Var id -> pr_id id
-  | Rel n -> print_rel bv n
-  | _ -> (str"<???>")
-
-let pr_term _ ctx = pp (fold_rel_context (fun _ (n,_,_) l -> n::l) ctx [])
-
diff --git a/parsing/g_prim.ml4 b/parsing/g_prim.ml4
index c3792d65..1e738384 100644
--- a/parsing/g_prim.ml4
+++ b/parsing/g_prim.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(*i $Id: g_prim.ml4 10155 2007-09-28 22:36:35Z glondu $ i*)
+(*i $Id: g_prim.ml4 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Pcoq
 open Names
@@ -23,6 +23,16 @@ open Nametab
 
 let local_make_qualid l id = make_qualid (make_dirpath l) id
 
+let my_int_of_string loc s =
+  try
+    let n = int_of_string s in
+    (* To avoid Array.make errors (that e.g. Undo uses), we set a *)
+    (* more restricted limit than int_of_string does *)
+    if n > 1024 * 2048 then raise Exit;
+    n
+  with Failure _ | Exit ->
+    Util.user_err_loc (loc,"",Pp.str "Cannot support a so large number.")
+
 GEXTEND Gram
   GLOBAL: 
     bigint natural integer identref name ident var preident
@@ -79,7 +89,7 @@ GEXTEND Gram
   ;
   ne_string:
     [ [ s = STRING -> 
-        if s="" then Util.user_err_loc(loc,"",Pp.str"Empty string"); s
+        if s="" then Util.user_err_loc(loc,"",Pp.str"Empty string."); s
     ] ]
   ;
   dirpath:
@@ -90,11 +100,11 @@ GEXTEND Gram
     [ [ s = STRING -> s ] ]
   ;
   integer:
-    [ [ i = INT      -> int_of_string i
-      | "-"; i = INT -> - int_of_string i ] ]
+    [ [ i = INT      -> my_int_of_string loc i
+      | "-"; i = INT -> - my_int_of_string loc i ] ]
   ;
   natural:
-    [ [ i = INT -> int_of_string i ] ]
+    [ [ i = INT -> my_int_of_string loc i ] ]
   ;
   bigint: (* Negative numbers are dealt with specially *)
     [ [ i = INT -> (Bigint.of_string i) ] ]
diff --git a/parsing/g_tactic.ml4 b/parsing/g_tactic.ml4
index c0a4ba5b..49f00d40 100644
--- a/parsing/g_tactic.ml4
+++ b/parsing/g_tactic.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(* $Id: g_tactic.ml4 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: g_tactic.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Pcoq
@@ -26,7 +26,7 @@ let _ = List.iter (fun s -> Lexer.add_token("",s)) tactic_kw
 
 (* Hack to parse "(x:=t)" as an explicit argument without conflicts with the *)
 (* admissible notation "(x t)" *)
-let lpar_id_coloneq =
+let test_lpar_id_coloneq =
   Gram.Entry.of_parser "lpar_id_coloneq"
     (fun strm ->
       match Stream.npeek 1 strm with
@@ -34,9 +34,7 @@ let lpar_id_coloneq =
             (match Stream.npeek 2 strm with
               | [_; ("IDENT",s)] ->
                   (match Stream.npeek 3 strm with
-	            | [_; _; ("", ":=")] ->
-                        Stream.junk strm; Stream.junk strm; Stream.junk strm;
-                        Names.id_of_string s
+	            | [_; _; ("", ":=")] -> ()
 	            | _ -> raise Stream.Failure)
 	      | _ -> raise Stream.Failure)
 	| _ -> raise Stream.Failure)
@@ -56,7 +54,7 @@ let test_lpar_idnum_coloneq =
         | _ -> raise Stream.Failure)
 
 (* idem for (x:t) *)
-let lpar_id_colon =
+let test_lpar_id_colon =
   Gram.Entry.of_parser "lpar_id_colon"
     (fun strm ->
       match Stream.npeek 1 strm with
@@ -64,9 +62,7 @@ let lpar_id_colon =
             (match Stream.npeek 2 strm with
               | [_; ("IDENT",id)] ->
                   (match Stream.npeek 3 strm with
-                    | [_; _; ("", ":")] ->
-                        Stream.junk strm; Stream.junk strm; Stream.junk strm;
-                        Names.id_of_string id
+                    | [_; _; ("", ":")] -> ()
                     | _ -> raise Stream.Failure)
               | _ -> raise Stream.Failure)
         | _ -> raise Stream.Failure)
@@ -131,15 +127,15 @@ let mk_fix_tac (loc,id,bl,ann,ty) =
       | _, Some x ->
           let ids = List.map snd (List.flatten (List.map pi1 bl)) in
           (try list_index (snd x) ids
-          with Not_found -> error "no such fix variable")
-      | _ -> error "cannot guess decreasing argument of fix" in
+          with Not_found -> error "No such fix variable.")
+      | _ -> error "Cannot guess decreasing argument of fix." in
   (id,n,CProdN(loc,bl,ty))
 
 let mk_cofix_tac (loc,id,bl,ann,ty) =
   let _ = Option.map (fun (aloc,_) ->
     Util.user_err_loc
       (aloc,"Constr:mk_cofix_tac",
-       Pp.str"Annotation forbidden in cofix expression")) ann in
+       Pp.str"Annotation forbidden in cofix expression.")) ann in
   (id,CProdN(loc,bl,ty))
 
 (* Functions overloaded by quotifier *)
@@ -162,6 +158,8 @@ let mkCLambdaN_simple bl c =
     let loc = join_loc (fst (List.hd (pi1 (List.hd bl)))) (constr_loc c) in
     mkCLambdaN_simple_loc loc bl c
 
+let loc_of_ne_list l = join_loc (fst (List.hd l)) (fst (list_last l))
+
 let map_int_or_var f = function
   | Rawterm.ArgArg x -> Rawterm.ArgArg (f x)
   | Rawterm.ArgVar _ as y -> y
@@ -237,27 +235,32 @@ GEXTEND Gram
   intropatterns:
     [ [ l = LIST0 simple_intropattern -> l ]]
   ;
-  simple_intropattern:
-    [ [ "["; tc = LIST1 intropatterns SEP "|" ; "]" -> IntroOrAndPattern tc
-      | "()" -> IntroOrAndPattern [[]]
-      | "("; si = simple_intropattern; ")" -> IntroOrAndPattern [[si]]
+  disjunctive_intropattern:
+    [ [ "["; tc = LIST1 intropatterns SEP "|"; "]" -> loc,IntroOrAndPattern tc
+      | "()" -> loc,IntroOrAndPattern [[]]
+      | "("; si = simple_intropattern; ")" -> loc,IntroOrAndPattern [[si]]
       | "("; si = simple_intropattern; ","; 
              tc = LIST1 simple_intropattern SEP "," ; ")" -> 
-	       IntroOrAndPattern [si::tc]
+	       loc,IntroOrAndPattern [si::tc]
       | "("; si = simple_intropattern; "&"; 
 	     tc = LIST1 simple_intropattern SEP "&" ; ")" -> 
 	  (* (A & B & C) is translated into (A,(B,C)) *)
 	  let rec pairify = function 
 	    | ([]|[_]|[_;_]) as l -> IntroOrAndPattern [l]
-	    | t::q -> IntroOrAndPattern [[t;pairify q]]
-	  in pairify (si::tc)
-      | "_" -> IntroWildcard
-      | prefix = pattern_ident -> IntroFresh prefix
-      | "?" -> IntroAnonymous
-      | id = ident -> IntroIdentifier id
-      | "->" -> IntroRewrite true
-      | "<-" -> IntroRewrite false
-      ] ]
+	    | t::q -> IntroOrAndPattern [[t;(loc_of_ne_list q,pairify q)]]
+	  in loc,pairify (si::tc) ] ]
+  ;
+  naming_intropattern:
+    [ [ prefix = pattern_ident -> loc, IntroFresh prefix
+      | "?" -> loc, IntroAnonymous
+      | id = ident -> loc, IntroIdentifier id ] ]
+  ;
+  simple_intropattern:
+    [ [ pat = disjunctive_intropattern -> pat
+      | pat = naming_intropattern -> pat
+      | "_" -> loc, IntroWildcard
+      | "->" -> loc, IntroRewrite true
+      | "<-" -> loc, IntroRewrite false ] ]
   ;
   simple_binding:
     [ [ "("; id = ident; ":="; c = lconstr; ")" -> (loc, NamedHyp id, c)
@@ -402,7 +405,18 @@ GEXTEND Gram
     [ [ "using"; el = constr_with_bindings -> el ] ]
   ;
   with_names:
-    [ [ "as"; ipat = simple_intropattern -> ipat | -> IntroAnonymous ] ]
+    [ [ "as"; ipat = simple_intropattern -> ipat
+      | -> dummy_loc,IntroAnonymous ] ]
+  ;
+  with_inversion_names:
+    [ [ "as"; ipat = disjunctive_intropattern -> Some ipat
+      | -> None ] ]
+  ;
+  with_induction_names:
+    [ [ "as"; eq = OPT naming_intropattern; ipat = disjunctive_intropattern
+        -> (eq,Some ipat)
+      | "as"; eq = naming_intropattern -> (Some eq,None)
+      | -> (None,None) ] ]
   ;
   as_name:
     [ [ "as"; id = ident -> Names.Name id | -> Names.Anonymous ] ]
@@ -439,30 +453,40 @@ GEXTEND Gram
   oriented_rewriter : 
     [ [ b = orient; p = rewriter -> let (m,c) = p in (b,m,c) ] ]
   ; 
+  induction_clause:
+    [ [ lc = LIST1 induction_arg; ipats = with_induction_names; 
+        el = OPT eliminator; cl = opt_clause -> (lc,el,ipats,cl) ] ]
+  ;
+  move_location:
+    [ [ IDENT "after"; id = id_or_meta -> MoveAfter id
+      | IDENT "before"; id = id_or_meta -> MoveBefore id
+      | "at"; IDENT "bottom" -> MoveToEnd true
+      | "at"; IDENT "top" -> MoveToEnd false ] ]
+  ;
   simple_tactic:
     [ [ 
       (* Basic tactics *)
         IDENT "intros"; IDENT "until"; id = quantified_hypothesis -> 
 	  TacIntrosUntil id
       | IDENT "intros"; pl = intropatterns -> TacIntroPattern pl
-      | IDENT "intro"; id = ident; IDENT "after"; id2 = identref ->
-	  TacIntroMove (Some id, Some id2)
-      | IDENT "intro"; IDENT "after"; id2 = identref ->
-	  TacIntroMove (None, Some id2)
-      | IDENT "intro"; id = ident -> TacIntroMove (Some id, None)
-      | IDENT "intro" -> TacIntroMove (None, None)
+      | IDENT "intro"; id = ident; hto = move_location ->
+	  TacIntroMove (Some id, hto)
+      | IDENT "intro"; hto = move_location -> TacIntroMove (None, hto)
+      | IDENT "intro"; id = ident -> TacIntroMove (Some id, no_move)
+      | IDENT "intro" -> TacIntroMove (None, no_move)
 
       | IDENT "assumption" -> TacAssumption
       | IDENT "exact"; c = constr -> TacExact c
       | IDENT "exact_no_check"; c = constr -> TacExactNoCheck c
       | IDENT "vm_cast_no_check"; c = constr -> TacVmCastNoCheck c
 
-      | IDENT "apply"; cl = constr_with_bindings -> TacApply (true,false,cl)
-      | IDENT "eapply"; cl = constr_with_bindings -> TacApply (true,true,cl)
-      | IDENT "simple"; IDENT "apply"; cl = constr_with_bindings -> 
-          TacApply (false,false,cl)
-      | IDENT "simple"; IDENT "eapply"; cl = constr_with_bindings -> 
-          TacApply (false, true,cl)
+      | IDENT "apply"; cl = LIST1 constr_with_bindings SEP "," ->
+	  TacApply (true,false,cl)
+      | IDENT "eapply"; cl = LIST1 constr_with_bindings SEP "," ->
+          TacApply (true,true,cl)
+      | IDENT "simple"; IDENT "apply"; cl = LIST1 constr_with_bindings SEP "," 
+          -> TacApply (false,false,cl)
+      | IDENT "simple"; IDENT "eapply"; cl = LIST1 constr_with_bindings SEP ","           -> TacApply (false,true,cl)
       | IDENT "elim"; cl = constr_with_bindings; el = OPT eliminator ->
           TacElim (false,cl,el)
       | IDENT "eelim"; cl = constr_with_bindings; el = OPT eliminator ->
@@ -492,10 +516,12 @@ GEXTEND Gram
           TacLetTac (na,c,p,false)
 
       (* Begin compatibility *)
-      | IDENT "assert"; id = lpar_id_coloneq; c = lconstr; ")" -> 
-	  TacAssert (None,IntroIdentifier id,c)
-      | IDENT "assert"; id = lpar_id_colon; c = lconstr; ")"; tac=by_tactic -> 
-	  TacAssert (Some tac,IntroIdentifier id,c)
+      | IDENT "assert"; test_lpar_id_coloneq; "("; (loc,id) = identref; ":="; 
+	  c = lconstr; ")" -> 
+	  TacAssert (None,(loc,IntroIdentifier id),c)
+      | IDENT "assert"; test_lpar_id_colon; "("; (loc,id) = identref; ":"; 
+	  c = lconstr; ")"; tac=by_tactic -> 
+	  TacAssert (Some tac,(loc,IntroIdentifier id),c)
       (* End compatibility *)
 
       | IDENT "assert"; c = constr; ipat = with_names; tac = by_tactic ->
@@ -521,23 +547,19 @@ GEXTEND Gram
 
       (* Derived basic tactics *)
       | IDENT "simple"; IDENT"induction"; h = quantified_hypothesis ->
-          TacSimpleInduction h
-      | IDENT "induction"; lc = LIST1 induction_arg; ids = with_names; 
-	  el = OPT eliminator; cl = opt_clause -> 
-	    TacNewInduction (false,lc,el,ids,cl)
-      | IDENT "einduction"; lc = LIST1 induction_arg; ids = with_names; 
-	  el = OPT eliminator; cl = opt_clause ->
-	    TacNewInduction (true,lc,el,ids,cl)
+          TacSimpleInductionDestruct (true,h)
+      | IDENT "induction"; ic = induction_clause ->
+	  TacInductionDestruct (true,false,[ic])
+      | IDENT "einduction"; ic = induction_clause ->
+	  TacInductionDestruct(true,true,[ic])
       | IDENT "double"; IDENT "induction"; h1 = quantified_hypothesis;
 	  h2 = quantified_hypothesis -> TacDoubleInduction (h1,h2)
       | IDENT "simple"; IDENT "destruct"; h = quantified_hypothesis ->
-          TacSimpleDestruct h
-      | IDENT "destruct"; lc = LIST1 induction_arg; ids = with_names; 
-	  el = OPT eliminator; cl = opt_clause ->
-	    TacNewDestruct (false,lc,el,ids,cl)
-      | IDENT "edestruct"; lc = LIST1 induction_arg; ids = with_names; 
-	  el = OPT eliminator; cl = opt_clause ->
-	    TacNewDestruct (true,lc,el,ids,cl)
+          TacSimpleInductionDestruct (false,h)
+      | IDENT "destruct"; ic = induction_clause ->
+	  TacInductionDestruct(false,false,[ic])
+      | IDENT "edestruct";  ic = induction_clause ->
+	  TacInductionDestruct(false,true,[ic])
       | IDENT "decompose"; IDENT "record" ; c = constr -> TacDecomposeAnd c
       | IDENT "decompose"; IDENT "sum"; c = constr -> TacDecomposeOr c
       | IDENT "decompose"; "["; l = LIST1 smart_global; "]"; c = constr
@@ -565,8 +587,8 @@ GEXTEND Gram
       | IDENT "clear"; "-"; l = LIST1 id_or_meta -> TacClear (true, l)
       | IDENT "clear"; l = LIST0 id_or_meta -> TacClear (l=[], l)
       | IDENT "clearbody"; l = LIST1 id_or_meta -> TacClearBody l
-      | IDENT "move"; id1 = id_or_meta; IDENT "after"; id2 = id_or_meta -> 
-	  TacMove (true,id1,id2)
+      | IDENT "move"; dep = [IDENT "dependent" -> true | -> false]; 
+	  hfrom = id_or_meta; hto = move_location -> TacMove (dep,hfrom,hto)
       | IDENT "rename"; l = LIST1 rename SEP "," -> TacRename l
       | IDENT "revert"; l = LIST1 id_or_meta -> TacRevert l
 
@@ -601,16 +623,19 @@ GEXTEND Gram
 	  | IDENT "inversion" -> FullInversion
 	  | IDENT "inversion_clear" -> FullInversionClear ];
 	  hyp = quantified_hypothesis; 
-	  ids = with_names; co = OPT ["with"; c = constr -> c] ->
+	  ids = with_inversion_names; co = OPT ["with"; c = constr -> c] ->
 	    TacInversion (DepInversion (k,co,ids),hyp)
       | IDENT "simple"; IDENT "inversion";
-	  hyp = quantified_hypothesis; ids = with_names; cl = simple_clause ->
+	  hyp = quantified_hypothesis; ids = with_inversion_names;
+	  cl = simple_clause ->
 	    TacInversion (NonDepInversion (SimpleInversion, cl, ids), hyp)
       | IDENT "inversion"; 
-	  hyp = quantified_hypothesis; ids = with_names; cl = simple_clause ->
+	  hyp = quantified_hypothesis; ids = with_inversion_names;
+	  cl = simple_clause ->
 	    TacInversion (NonDepInversion (FullInversion, cl, ids), hyp)
       | IDENT "inversion_clear"; 
-	  hyp = quantified_hypothesis; ids = with_names; cl = simple_clause ->
+	  hyp = quantified_hypothesis; ids = with_inversion_names; 
+	  cl = simple_clause ->
 	    TacInversion (NonDepInversion (FullInversionClear, cl, ids), hyp)
       | IDENT "inversion"; hyp = quantified_hypothesis; 
 	  "using"; c = constr; cl = simple_clause ->
diff --git a/parsing/g_vernac.ml4 b/parsing/g_vernac.ml4
index 00469ad5..87c11164 100644
--- a/parsing/g_vernac.ml4
+++ b/parsing/g_vernac.ml4
@@ -9,7 +9,7 @@
 (*i camlp4deps: "parsing/grammar.cma" i*)
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(* $Id: g_vernac.ml4 11083 2008-06-09 22:08:14Z herbelin $ *)
+(* $Id: g_vernac.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 
 open Pp
@@ -113,7 +113,7 @@ let test_plurial_form = function
 
 let no_coercion loc (c,x) =
   if c then Util.user_err_loc
-    (loc,"no_coercion",Pp.str"no coercion allowed here");
+    (loc,"no_coercion",str"No coercion allowed here.");
   x
 
 (* Gallina declarations *)
@@ -271,7 +271,7 @@ GEXTEND Gram
 		    Some (loc, id)
 		    else Util.user_err_loc
                       (loc,"Fixpoint",
-                      Pp.str "No argument named " ++ Nameops.pr_id id))
+                       str "No argument named " ++ Nameops.pr_id id ++ str"."))
               | None -> 
 		  (* If there is only one argument, it is the recursive one, 
 		     otherwise, we search the recursive index later *)
@@ -311,7 +311,7 @@ GEXTEND Gram
           LocalRawAssum(l,ty) -> (l,ty)
         | LocalRawDef _ ->
             Util.user_err_loc
-              (loc,"fix_param",Pp.str"defined binder not allowed here")) ] ]
+              (loc,"fix_param",Pp.str"defined binder not allowed here.")) ] ]
   ;
 *)
   (* ... with coercions *)
@@ -491,7 +491,7 @@ GEXTEND Gram
 	 props = typeclass_field_types ->
 	   VernacClass (qid, pars, s, (match sup with None -> [] | Some l -> l), props)
 	     
-      | IDENT "Context"; c = typeclass_context -> 
+      | IDENT "Context"; c = binders_let -> 
 	  VernacContext c
 	    
       | global = [ IDENT "Global" -> true | -> false ];
diff --git a/parsing/g_xml.ml4 b/parsing/g_xml.ml4
index 5b2d8668..72d5d275 100644
--- a/parsing/g_xml.ml4
+++ b/parsing/g_xml.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo" i*)
 
-(* $Id: g_xml.ml4 10727 2008-03-28 20:22:43Z msozeau $ *)
+(* $Id: g_xml.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -31,7 +31,7 @@ type xml = XmlTag of loc * string * attribute list * xml list
 let check_tags loc otag ctag =
   if otag <> ctag then
     user_err_loc (loc,"",str "closing xml tag " ++ str ctag ++ 
-      str "does not match open xml tag " ++ str otag)
+      str "does not match open xml tag " ++ str otag ++ str ".")
 
 let xml_eoi = (Gram.Entry.create "xml_eoi" : xml Gram.Entry.e)
 
@@ -55,11 +55,19 @@ GEXTEND Gram
   ;
 END
 
+(* Errors *)
+
+let error_expect_one_argument loc =
+  user_err_loc (loc,"",str "wrong number of arguments (expect one).")
+
+let error_expect_no_argument loc =
+  user_err_loc (loc,"",str "wrong number of arguments (expect none).")
+
 (* Interpreting attributes *)
 
 let nmtoken (loc,a) =
   try int_of_string a
-  with Failure _ -> user_err_loc (loc,"",str "nmtoken expected")
+  with Failure _ -> user_err_loc (loc,"",str "nmtoken expected.")
   
 let interp_xml_attr_qualid = function
   | "uri", s -> qualid_of_string s
@@ -94,7 +102,7 @@ let sort_of_cdata (loc,a) = match a with
   | "Prop" -> RProp Null
   | "Set" -> RProp Pos
   | "Type" -> RType None
-  | _ -> user_err_loc (loc,"",str "sort expected")
+  | _ -> user_err_loc (loc,"",str "sort expected.")
 
 let get_xml_sort al = sort_of_cdata (get_xml_attr "value" al)
 
@@ -188,18 +196,18 @@ let rec interp_xml_constr = function
       RCast (loc, interp_xml_term x1, CastConv (DEFAULTcast, interp_xml_type x2))
   | XmlTag (loc,"SORT",al,[]) ->
       RSort (loc, get_xml_sort al)
-  | XmlTag (loc,s,_,_) -> user_err_loc (loc,"", str "Unexpected tag " ++ str s)
+  | XmlTag (loc,s,_,_) ->
+      user_err_loc (loc,"", str "Unexpected tag " ++ str s ++ str ".")
 
 and interp_xml_tag s = function
   | XmlTag (loc,tag,al,xl) when tag=s -> (loc,al,xl)
   | XmlTag (loc,tag,_,_) -> user_err_loc (loc, "", 
-    str "Expect tag " ++ str s ++ str " but find " ++ str s)
+    str "Expect tag " ++ str s ++ str " but find " ++ str s ++ str ".")
 
 and interp_xml_constr_alias s x =
   match interp_xml_tag s x with
     | (_,_,[x]) -> interp_xml_constr x
-    | (loc,_,_) -> 
-        user_err_loc (loc,"",str "wrong number of arguments (expect one)")
+    | (loc,_,_) -> error_expect_one_argument loc
 
 and interp_xml_term x = interp_xml_constr_alias "term" x
 and interp_xml_type x = interp_xml_constr_alias "type" x
@@ -215,8 +223,7 @@ and interp_xml_substitution x = interp_xml_constr_alias "substitution" x
 and interp_xml_decl_alias s x =
   match interp_xml_tag s x with
     | (_,al,[x]) -> (get_xml_binder al, interp_xml_constr x)
-    | (loc,_,_) -> 
-        user_err_loc (loc,"",str "wrong number of arguments (expect one)")
+    | (loc,_,_) -> error_expect_one_argument loc
 
 and interp_xml_def x = interp_xml_decl_alias "def" x
 and interp_xml_decl x = interp_xml_decl_alias "decl" x
@@ -227,17 +234,17 @@ and interp_xml_recursionOrder x =
     match s with
 	"Structural" -> 
 	  (match l with [] -> RStructRec
-	     | _ -> user_err_loc (loc, "", str "wrong number of arguments (expected none)"))
+	     | _ -> error_expect_no_argument loc)
       | "WellFounded" -> 
 	  (match l with
 	       [c] -> RWfRec (interp_xml_type c)
-	     | _ -> user_err_loc (loc, "", str "wrong number of arguments (expected one)"))
+	     | _ -> error_expect_one_argument loc)
       | "Measure" -> 
 	  (match l with
 	       [c] -> RMeasureRec (interp_xml_type c)
-	     | _ -> user_err_loc (loc, "", str "wrong number of arguments (expected one)"))
+	     | _ -> error_expect_one_argument loc)
       | _ ->
-          user_err_loc (locs,"",str "invalid recursion order")
+          user_err_loc (locs,"",str "Invalid recursion order.")
 
 and interp_xml_FixFunction x =
   match interp_xml_tag "FixFunction" x with
@@ -248,15 +255,15 @@ and interp_xml_FixFunction x =
   | (loc,al,[x1;x2]) ->
       ((Some (nmtoken (get_xml_attr "recIndex" al)), RStructRec),
        (get_xml_name al, interp_xml_type x1, interp_xml_body x2))
-  | (loc,_,_) -> 
-        user_err_loc (loc,"",str "wrong number of arguments (expect one)")
+  | (loc,_,_) ->
+      error_expect_one_argument loc
 
 and interp_xml_CoFixFunction x =
   match interp_xml_tag "CoFixFunction" x with
   | (loc,al,[x1;x2]) ->
       (get_xml_name al, interp_xml_type x1, interp_xml_body x2)
     | (loc,_,_) -> 
-        user_err_loc (loc,"",str "wrong number of arguments (expect one)")
+	error_expect_one_argument loc
 
 (* Interpreting tactic argument *)
 
@@ -266,7 +273,8 @@ let rec interp_xml_tactic_arg = function
   | XmlTag (loc,"CALL",al,xl) ->
       let ltacref = ltacref_of_cdata (get_xml_attr "uri" al) in
       TacCall(loc,ArgArg ltacref,List.map interp_xml_tactic_arg xl)
-  | XmlTag (loc,s,_,_) -> user_err_loc (loc,"", str "Unexpected tag " ++ str s)
+  | XmlTag (loc,s,_,_) ->
+      user_err_loc (loc,"", str "Unexpected tag " ++ str s ++ str ".")
 
 let parse_tactic_arg ch =
   interp_xml_tactic_arg
diff --git a/parsing/g_zsyntax.ml b/parsing/g_zsyntax.ml
index aab266c0..8b9c0d22 100644
--- a/parsing/g_zsyntax.ml
+++ b/parsing/g_zsyntax.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: g_zsyntax.ml 10806 2008-04-16 23:51:06Z letouzey $ *)
+(* $Id: g_zsyntax.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pcoq
 open Pp
@@ -57,7 +57,7 @@ let pos_of_bignat dloc x =
 
 let error_non_positive dloc = 
   user_err_loc (dloc, "interp_positive",
-    str "Only strictly positive numbers in type \"positive\"")
+    str "Only strictly positive numbers in type \"positive\".")
 
 let interp_positive dloc n =
   if is_strictly_pos n then pos_of_bignat dloc n
@@ -113,7 +113,7 @@ let n_of_binnat dloc pos_or_neg n =
     RRef (dloc, glob_N0)
 
 let error_negative dloc =
-  user_err_loc (dloc, "interp_N", str "No negative numbers in type \"N\"")
+  user_err_loc (dloc, "interp_N", str "No negative numbers in type \"N\".")
 
 let n_of_int dloc n =
   if is_pos_or_zero n then n_of_binnat dloc true n
diff --git a/parsing/lexer.ml4 b/parsing/lexer.ml4
index c1e4cfc6..1b0c24da 100644
--- a/parsing/lexer.ml4
+++ b/parsing/lexer.ml4
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: lexer.ml4 11059 2008-06-06 09:29:20Z herbelin $ i*)
+(*i $Id: lexer.ml4 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 
 (*i camlp4use: "pr_o.cmo" i*) 
@@ -324,43 +324,49 @@ let rec comment bp = parser bp2
 (* Parse a special token, using the [token_tree] *)
 
 (* Peek as much utf-8 lexemes as possible *)
-(* then look if a special token is obtained *)
-let rec special tt cs =
-  match Stream.peek cs with
-    | Some c -> progress_from_byte 0 tt cs c
-    | None -> tt.node
-
-  (* nr is the number of char peeked; n the number of char in utf8 block *)
-and progress_utf8 nr n c tt cs =
+(* and retain the longest valid special token obtained *)
+let rec progress_further last nj tt cs =
+  try progress_from_byte last nj tt cs (List.nth (Stream.npeek (nj+1) cs) nj)
+  with Failure _ -> last
+
+and update_longest_valid_token last nj tt cs =
+  match tt.node with
+  | Some _ as last' ->
+      for i=1 to nj do Stream.junk cs done; 
+      progress_further last' 0 tt cs
+  | None ->
+      progress_further last nj tt cs
+
+(* nr is the number of char peeked since last valid token *)
+(* n the number of char in utf8 block *)
+and progress_utf8 last nj n c tt cs =
   try
     let tt = CharMap.find c tt.branch in
-    let tt =
-      if n=1 then tt else
-	match Stream.npeek (n-nr) cs with
-	| l when List.length l = n-nr ->
-	    let l = Util.list_skipn (1-nr) l in
-	    List.iter (check_utf8_trailing_byte cs) l;
-	    List.fold_left (fun tt c -> CharMap.find c tt.branch) tt l
-	| _ -> 
-	    error_utf8 cs
-    in
-    for i=1 to n-nr do Stream.junk cs done;
-    special tt cs
+    if n=1 then
+      update_longest_valid_token last (nj+n) tt cs
+    else
+      match Util.list_skipn (nj+1) (Stream.npeek (nj+n) cs) with
+      | l when List.length l = n-1 ->
+	 List.iter (check_utf8_trailing_byte cs) l;
+	 let tt = List.fold_left (fun tt c -> CharMap.find c tt.branch) tt l in
+	 update_longest_valid_token last (nj+n) tt cs
+      | _ -> 
+	  error_utf8 cs
   with Not_found ->
-    tt.node
+    last
 
-and progress_from_byte nr tt cs = function
+and progress_from_byte last nj tt cs = function
   (* Utf8 leading byte *)
-  | '\x00'..'\x7F' as c -> progress_utf8 nr 1 c tt cs
-  | '\xC0'..'\xDF' as c -> progress_utf8 nr 2 c tt cs
-  | '\xE0'..'\xEF' as c -> progress_utf8 nr 3 c tt cs
-  | '\xF0'..'\xF7' as c -> progress_utf8 nr 4 c tt cs
+  | '\x00'..'\x7F' as c -> progress_utf8 last nj 1 c tt cs
+  | '\xC0'..'\xDF' as c -> progress_utf8 last nj 2 c tt cs
+  | '\xE0'..'\xEF' as c -> progress_utf8 last nj 3 c tt cs
+  | '\xF0'..'\xF7' as c -> progress_utf8 last nj 4 c tt cs
   | _ (* '\x80'..\xBF'|'\xF8'..'\xFF' *) ->
       error_utf8 cs
 
 (* Must be a special token *)
 let process_chars bp c cs =
-  let t = progress_from_byte 1 !token_tree cs c in
+  let t = progress_from_byte None (-1) !token_tree cs c in
   let ep = Stream.count cs in
   match t with
     | Some t -> (("", t), (bp, ep))
diff --git a/parsing/pcoq.ml4 b/parsing/pcoq.ml4
index 70a41ddc..2e55b656 100644
--- a/parsing/pcoq.ml4
+++ b/parsing/pcoq.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo pa_macro.cmo" i*)
 
-(*i $Id: pcoq.ml4 10987 2008-05-26 12:28:36Z herbelin $ i*)
+(*i $Id: pcoq.ml4 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Pp
 open Util
@@ -247,7 +247,7 @@ let get_entry (u, utab) s =
     Hashtbl.find utab s 
   with Not_found -> 
     errorlabstrm "Pcoq.get_entry"
-      (str "unknown grammar entry " ++ str u ++ str ":" ++ str s)
+      (str "Unknown grammar entry " ++ str u ++ str ":" ++ str s ++ str ".")
 
 let new_entry etyp (u, utab) s =
   let ename = u ^ ":" ^ s in
@@ -307,12 +307,12 @@ let get_generic_entry s =
   try
     object_of_typed_entry (Hashtbl.find utab s)
   with Not_found -> 
-    error ("unknown grammar entry "^u^":"^s)
+    error ("Unknown grammar entry "^u^":"^s^".")
 
 let get_generic_entry_type (u,utab) s =
   try type_of_typed_entry (Hashtbl.find utab s)
   with Not_found -> 
-    error ("unknown grammar entry "^u^":"^s)
+    error ("Unknown grammar entry "^u^":"^s^".")
 
 let force_entry_type (u, utab) s etyp =
   try
@@ -578,7 +578,7 @@ let error_level_assoc p current expected =
   errorlabstrm ""
     (str "Level " ++ int p ++ str " is already declared " ++
      pr_assoc current ++ str " associative while it is now expected to be " ++
-     pr_assoc expected ++ str " associative")
+     pr_assoc expected ++ str " associative.")
 
 let find_position_gen forpat ensure assoc lev =
   let ccurrent,pcurrent as current = List.hd !level_stack in
@@ -628,13 +628,13 @@ let rec list_mem_assoc_triple x = function
   | [] -> false
   | (a,b,c) :: l -> a = x or list_mem_assoc_triple x l
 
-let register_empty_levels forpat symbs =
-  map_succeed (function
-    | Gramext.Snterml (_,n) when
-	let levels = (if forpat then snd else fst) (List.hd !level_stack) in
-	not (list_mem_assoc_triple (int_of_string n) levels) ->
-	find_position_gen forpat true None (Some (int_of_string n))
-    | _ -> failwith "") symbs
+let register_empty_levels forpat levels =
+  map_succeed (fun n ->
+    let levels = (if forpat then snd else fst) (List.hd !level_stack) in
+    if not (list_mem_assoc_triple n levels) then
+      find_position_gen forpat true None (Some n)
+    else
+      failwith "") levels
 
 let find_position forpat assoc level =
   find_position_gen forpat false assoc level
@@ -695,7 +695,7 @@ let compute_entry allow_create adjust forpat = function
   | ETPattern -> weaken_entry Constr.pattern, None, false
   | ETOther ("constr","annot") -> 
       weaken_entry Constr.annot, None, false
-  | ETConstrList _ -> error "List of entries cannot be registered"
+  | ETConstrList _ -> error "List of entries cannot be registered."
   | ETOther (u,n) ->
       let u = get_univ u in
       let e =
@@ -762,6 +762,6 @@ let coerce_reference_to_id = function
   | Ident (_,id) -> id
   | Qualid (loc,_) ->
       user_err_loc (loc, "coerce_reference_to_id",
-        str "This expression should be a simple identifier")
+        str "This expression should be a simple identifier.")
 
 let coerce_global_to_id = coerce_reference_to_id
diff --git a/parsing/pcoq.mli b/parsing/pcoq.mli
index 44a3686e..525727ce 100644
--- a/parsing/pcoq.mli
+++ b/parsing/pcoq.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: pcoq.mli 10987 2008-05-26 12:28:36Z herbelin $ i*)
+(*i $Id: pcoq.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Util
 open Names
@@ -188,7 +188,7 @@ module Tactic :
     val int_or_var : int or_var Gram.Entry.e
     val red_expr : raw_red_expr Gram.Entry.e
     val simple_tactic : raw_atomic_tactic_expr Gram.Entry.e
-    val simple_intropattern : Genarg.intro_pattern_expr Gram.Entry.e
+    val simple_intropattern : Genarg.intro_pattern_expr located Gram.Entry.e
     val tactic_arg : raw_tactic_arg Gram.Entry.e
     val tactic_expr : raw_tactic_expr Gram.Entry.e
     val binder_tactic : raw_tactic_expr Gram.Entry.e
@@ -229,7 +229,7 @@ val find_position :
 
 val synchronize_level_positions : unit -> unit
 
-val register_empty_levels : bool -> Compat.token Gramext.g_symbol list ->
+val register_empty_levels : bool -> int list ->
     (Gramext.position option * Gramext.g_assoc option *
      string option * Gramext.g_assoc option) list
 
diff --git a/parsing/ppconstr.ml b/parsing/ppconstr.ml
index 985396f5..5f6ffe87 100644
--- a/parsing/ppconstr.ml
+++ b/parsing/ppconstr.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: ppconstr.ml 11094 2008-06-10 19:35:23Z herbelin $ *)      
+(* $Id: ppconstr.ml 11309 2008-08-06 10:30:35Z herbelin $ *)      
 
 (*i*)
 open Util
@@ -96,12 +96,6 @@ let pr_patnotation = pr_notation_gen decode_patlist_value
 let pr_delimiters key strm =
   strm ++ str ("%"^key)
 
-let pr_located pr (loc,x) =
-  if Flags.do_translate() && loc<>dummy_loc then
-    let (b,e) = unloc loc in
-    comment b ++ pr x ++ comment e
-  else pr x
-
 let pr_com_at n =
   if Flags.do_translate() && n <> 0 then comment n 
   else mt()
@@ -219,13 +213,13 @@ let surround_binder k p =
   match k with
       Default Explicit -> hov 1 (str"(" ++ p ++ str")")
     | Default Implicit -> hov 1 (str"{" ++ p ++ str"}")
-    | TypeClass b -> hov 1 (str"[" ++ p ++ str"]")
+    | TypeClass _ -> hov 1 (str"[" ++ p ++ str"]")
 
 let surround_implicit k p =
   match k with
       Default Explicit -> p
     | Default Implicit -> (str"{" ++ p ++ str"}")
-    | TypeClass b -> (str"[" ++ p ++ str"]")
+    | TypeClass _ -> (str"[" ++ p ++ str"]")
 
 let pr_binder many pr (nal,k,t) =
   match t with
@@ -719,7 +713,7 @@ let pr_red_expr (pr_constr,pr_lconstr,pr_ref) = function
       hov 1 (str "pattern" ++
         pr_arg (prlist_with_sep pr_coma (pr_with_occurrences pr_constr)) l)
         
-  | Red true -> error "Shouldn't be accessible from user"
+  | Red true -> error "Shouldn't be accessible from user."
   | ExtraRedExpr s -> str s
   | CbvVm -> str "vm_compute"
 
diff --git a/parsing/ppconstr.mli b/parsing/ppconstr.mli
index a0eb4ad9..8047e968 100644
--- a/parsing/ppconstr.mli
+++ b/parsing/ppconstr.mli
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
  
-(*i $Id: ppconstr.mli 11094 2008-06-10 19:35:23Z herbelin $ i*)
+(*i $Id: ppconstr.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Pp
 open Environ
@@ -35,7 +35,6 @@ val prec_less : int -> int * Ppextend.parenRelation -> bool
  
 val pr_tight_coma : unit -> std_ppcmds
 
-val pr_located : ('a -> std_ppcmds) -> 'a located -> std_ppcmds
 val pr_or_var : ('a -> std_ppcmds) -> 'a or_var -> std_ppcmds
 val pr_metaid : identifier -> std_ppcmds
 
diff --git a/parsing/pptactic.ml b/parsing/pptactic.ml
index f955d83b..6a7ae9bc 100644
--- a/parsing/pptactic.ml
+++ b/parsing/pptactic.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: pptactic.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: pptactic.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Names
@@ -58,7 +58,7 @@ let declare_extra_genarg_pprule (rawwit, f) (globwit, g) (wit, h) =
   let s = match unquote wit with
     | ExtraArgType s -> s 
     | _ -> error
-	"Can declare a pretty-printing rule only for extra argument types"
+	"Can declare a pretty-printing rule only for extra argument types."
   in
   let f prc prlc prtac x = f prc prlc prtac (out_gen rawwit x) in
   let g prc prlc prtac x = g prc prlc prtac (out_gen globwit x) in
@@ -142,41 +142,40 @@ let out_bindings = function
 
 let rec pr_raw_generic prc prlc prtac prref (x:Genarg.rlevel Genarg.generic_argument) =
   match Genarg.genarg_tag x with
-  | BoolArgType -> pr_arg str (if out_gen rawwit_bool x then "true" else "false")
-  | IntArgType -> pr_arg int (out_gen rawwit_int x)
-  | IntOrVarArgType -> pr_arg (pr_or_var pr_int) (out_gen rawwit_int_or_var x)
-  | StringArgType -> spc () ++ str "\"" ++ str (out_gen rawwit_string x) ++ str "\""
-  | PreIdentArgType -> pr_arg str (out_gen rawwit_pre_ident x)
-  | IntroPatternArgType -> pr_arg pr_intro_pattern 
-      (out_gen rawwit_intro_pattern x)
-  | IdentArgType -> pr_arg pr_id (out_gen rawwit_ident x)
-  | VarArgType -> pr_arg (pr_located pr_id) (out_gen rawwit_var x)
-  | RefArgType -> pr_arg prref (out_gen rawwit_ref x)
-  | SortArgType -> pr_arg pr_rawsort (out_gen rawwit_sort x)
-  | ConstrArgType -> pr_arg prc (out_gen rawwit_constr x)
+  | BoolArgType -> str (if out_gen rawwit_bool x then "true" else "false")
+  | IntArgType -> int (out_gen rawwit_int x)
+  | IntOrVarArgType -> pr_or_var pr_int (out_gen rawwit_int_or_var x)
+  | StringArgType -> str "\"" ++ str (out_gen rawwit_string x) ++ str "\""
+  | PreIdentArgType -> str (out_gen rawwit_pre_ident x)
+  | IntroPatternArgType -> pr_intro_pattern (out_gen rawwit_intro_pattern x)
+  | IdentArgType -> pr_id (out_gen rawwit_ident x)
+  | VarArgType -> pr_located pr_id (out_gen rawwit_var x)
+  | RefArgType -> prref (out_gen rawwit_ref x)
+  | SortArgType -> pr_rawsort (out_gen rawwit_sort x)
+  | ConstrArgType -> prc (out_gen rawwit_constr x)
   | ConstrMayEvalArgType ->
-      pr_arg (pr_may_eval prc prlc (pr_or_by_notation prref))
+      pr_may_eval prc prlc (pr_or_by_notation prref)
         (out_gen rawwit_constr_may_eval x)
-  | QuantHypArgType ->
-      pr_arg pr_quantified_hypothesis (out_gen rawwit_quant_hyp x)
+  | QuantHypArgType -> pr_quantified_hypothesis (out_gen rawwit_quant_hyp x)
   | RedExprArgType ->
-      pr_arg (pr_red_expr (prc,prlc,pr_or_by_notation prref))
+      pr_red_expr (prc,prlc,pr_or_by_notation prref)
         (out_gen rawwit_red_expr x)
-  | OpenConstrArgType b -> pr_arg prc (snd (out_gen (rawwit_open_constr_gen b) x))
+  | OpenConstrArgType b -> prc (snd (out_gen (rawwit_open_constr_gen b) x))
   | ConstrWithBindingsArgType -> 
-      pr_arg (pr_with_bindings prc prlc) (out_gen rawwit_constr_with_bindings x)
+      pr_with_bindings prc prlc (out_gen rawwit_constr_with_bindings x)
   | BindingsArgType -> 
-      pr_arg (pr_bindings_no_with prc prlc) (out_gen rawwit_bindings x)
+      pr_bindings_no_with prc prlc (out_gen rawwit_bindings x)
   | List0ArgType _ -> 
-      hov 0 (fold_list0 (fun x a -> pr_raw_generic prc prlc prtac prref x ++ a) x (mt()))
+      hov 0 (pr_sequence (pr_raw_generic prc prlc prtac prref)
+	(fold_list0 (fun a l -> a::l) x []))
   | List1ArgType _ ->
-      hov 0 (fold_list1 (fun x a -> pr_raw_generic prc prlc prtac prref x ++ a) x (mt()))
+      hov 0 (pr_sequence (pr_raw_generic prc prlc prtac prref)
+	(fold_list1 (fun a l -> a::l) x []))
   | OptArgType _ -> hov 0 (fold_opt (pr_raw_generic prc prlc prtac prref) (mt()) x)
   | PairArgType _ ->
       hov 0
         (fold_pair
-	  (fun a b -> pr_raw_generic prc prlc prtac prref a ++ spc () ++ 
-            pr_raw_generic prc prlc prtac prref b)
+	  (fun a b -> pr_sequence (pr_raw_generic prc prlc prtac prref) [a;b])
 	  x)
   | ExtraArgType s -> 
       try pi1 (Stringmap.find s !genarg_pprule) prc prlc prtac x
@@ -185,107 +184,105 @@ let rec pr_raw_generic prc prlc prtac prref (x:Genarg.rlevel Genarg.generic_argu
 
 let rec pr_glob_generic prc prlc prtac x =
   match Genarg.genarg_tag x with
-  | BoolArgType -> pr_arg str (if out_gen globwit_bool x then "true" else "false")
-  | IntArgType -> pr_arg int (out_gen globwit_int x)
-  | IntOrVarArgType -> pr_arg (pr_or_var pr_int) (out_gen globwit_int_or_var x)
-  | StringArgType -> spc () ++ str "\"" ++ str (out_gen globwit_string x) ++ str "\""
-  | PreIdentArgType -> pr_arg str (out_gen globwit_pre_ident x)
-  | IntroPatternArgType ->
-      pr_arg pr_intro_pattern (out_gen globwit_intro_pattern x)
-  | IdentArgType -> pr_arg pr_id (out_gen globwit_ident x)
-  | VarArgType -> pr_arg (pr_located pr_id) (out_gen globwit_var x)
-  | RefArgType -> pr_arg (pr_or_var (pr_located pr_global)) (out_gen globwit_ref x)
-  | SortArgType -> pr_arg pr_rawsort (out_gen globwit_sort x)
-  | ConstrArgType -> pr_arg prc (out_gen globwit_constr x)
+  | BoolArgType -> str (if out_gen globwit_bool x then "true" else "false")
+  | IntArgType -> int (out_gen globwit_int x)
+  | IntOrVarArgType -> pr_or_var pr_int (out_gen globwit_int_or_var x)
+  | StringArgType -> str "\"" ++ str (out_gen globwit_string x) ++ str "\""
+  | PreIdentArgType -> str (out_gen globwit_pre_ident x)
+  | IntroPatternArgType -> pr_intro_pattern (out_gen globwit_intro_pattern x)
+  | IdentArgType -> pr_id (out_gen globwit_ident x)
+  | VarArgType -> pr_located pr_id (out_gen globwit_var x)
+  | RefArgType -> pr_or_var (pr_located pr_global) (out_gen globwit_ref x)
+  | SortArgType -> pr_rawsort (out_gen globwit_sort x)
+  | ConstrArgType -> prc (out_gen globwit_constr x)
   | ConstrMayEvalArgType ->
-      pr_arg (pr_may_eval prc prlc
-        (pr_or_var (pr_and_short_name pr_evaluable_reference)))
+      pr_may_eval prc prlc
+        (pr_or_var (pr_and_short_name pr_evaluable_reference))
         (out_gen globwit_constr_may_eval x)
   | QuantHypArgType ->
-      pr_arg pr_quantified_hypothesis (out_gen globwit_quant_hyp x)
+      pr_quantified_hypothesis (out_gen globwit_quant_hyp x)
   | RedExprArgType ->
-      pr_arg (pr_red_expr 
-        (prc,prlc,pr_or_var (pr_and_short_name pr_evaluable_reference)))
+      pr_red_expr 
+        (prc,prlc,pr_or_var (pr_and_short_name pr_evaluable_reference))
         (out_gen globwit_red_expr x)
-  | OpenConstrArgType b -> pr_arg prc (snd (out_gen (globwit_open_constr_gen b) x))
+  | OpenConstrArgType b -> prc (snd (out_gen (globwit_open_constr_gen b) x))
   | ConstrWithBindingsArgType -> 
-      pr_arg (pr_with_bindings prc prlc) (out_gen globwit_constr_with_bindings x)
+      pr_with_bindings prc prlc (out_gen globwit_constr_with_bindings x)
   | BindingsArgType -> 
-      pr_arg (pr_bindings_no_with prc prlc) (out_gen globwit_bindings x)
+      pr_bindings_no_with prc prlc (out_gen globwit_bindings x)
   | List0ArgType _ -> 
-      hov 0 (fold_list0 (fun x a -> pr_glob_generic prc prlc prtac x ++ a) x (mt()))
+      hov 0 (pr_sequence (pr_glob_generic prc prlc prtac)
+	(fold_list0 (fun a l -> a::l) x []))
   | List1ArgType _ ->
-      hov 0 (fold_list1 (fun x a -> pr_glob_generic prc prlc prtac x ++ a) x (mt()))
+      hov 0 (pr_sequence (pr_glob_generic prc prlc prtac)
+	(fold_list1 (fun a l -> a::l) x []))
   | OptArgType _ -> hov 0 (fold_opt (pr_glob_generic prc prlc prtac) (mt()) x)
   | PairArgType _ ->
       hov 0
         (fold_pair
-	  (fun a b -> pr_glob_generic prc prlc prtac a ++ spc () ++ 
-            pr_glob_generic prc prlc prtac b)
+	  (fun a b -> pr_sequence (pr_glob_generic prc prlc prtac) [a;b])
 	  x)
   | ExtraArgType s -> 
       try pi2 (Stringmap.find s !genarg_pprule) prc prlc prtac x
-      with Not_found -> str " [no printer for " ++ str s ++ str "] "
+      with Not_found -> str "[no printer for " ++ str s ++ str "] "
 
 open Closure
 
 let rec pr_generic prc prlc prtac x =
   match Genarg.genarg_tag x with
-  | BoolArgType -> pr_arg str (if out_gen wit_bool x then "true" else "false")
-  | IntArgType -> pr_arg int (out_gen wit_int x)
-  | IntOrVarArgType -> pr_arg (pr_or_var pr_int) (out_gen wit_int_or_var x)
-  | StringArgType -> spc () ++ str "\"" ++ str (out_gen wit_string x) ++ str "\""
-  | PreIdentArgType -> pr_arg str (out_gen wit_pre_ident x)
-  | IntroPatternArgType -> 
-      pr_arg pr_intro_pattern (out_gen wit_intro_pattern x)
-  | IdentArgType -> pr_arg pr_id (out_gen wit_ident x)
-  | VarArgType -> pr_arg pr_id (out_gen wit_var x)
-  | RefArgType -> pr_arg pr_global (out_gen wit_ref x)
-  | SortArgType -> pr_arg pr_sort (out_gen wit_sort x)
-  | ConstrArgType -> pr_arg prc (out_gen wit_constr x)
-  | ConstrMayEvalArgType ->
-      pr_arg prc (out_gen wit_constr_may_eval x)
-  | QuantHypArgType ->
-      pr_arg pr_quantified_hypothesis (out_gen wit_quant_hyp x)
+  | BoolArgType -> str (if out_gen wit_bool x then "true" else "false")
+  | IntArgType -> int (out_gen wit_int x)
+  | IntOrVarArgType -> pr_or_var pr_int (out_gen wit_int_or_var x)
+  | StringArgType -> str "\"" ++ str (out_gen wit_string x) ++ str "\""
+  | PreIdentArgType -> str (out_gen wit_pre_ident x)
+  | IntroPatternArgType -> pr_intro_pattern (out_gen wit_intro_pattern x)
+  | IdentArgType -> pr_id (out_gen wit_ident x)
+  | VarArgType -> pr_id (out_gen wit_var x)
+  | RefArgType -> pr_global (out_gen wit_ref x)
+  | SortArgType -> pr_sort (out_gen wit_sort x)
+  | ConstrArgType -> prc (out_gen wit_constr x)
+  | ConstrMayEvalArgType -> prc (out_gen wit_constr_may_eval x)
+  | QuantHypArgType -> pr_quantified_hypothesis (out_gen wit_quant_hyp x)
   | RedExprArgType ->
-      pr_arg (pr_red_expr (prc,prlc,pr_evaluable_reference)) 
-        (out_gen wit_red_expr x)
-  | OpenConstrArgType b -> pr_arg prc (snd (out_gen (wit_open_constr_gen b) x))
+      pr_red_expr (prc,prlc,pr_evaluable_reference) (out_gen wit_red_expr x)
+  | OpenConstrArgType b -> prc (snd (out_gen (wit_open_constr_gen b) x))
   | ConstrWithBindingsArgType ->
       let (c,b) = out_gen wit_constr_with_bindings x in
-      pr_arg (pr_with_bindings prc prlc) (c,out_bindings b)
+      pr_with_bindings prc prlc (c,out_bindings b)
   | BindingsArgType -> 
-      pr_arg (pr_bindings_no_with prc prlc)
-        (out_bindings (out_gen wit_bindings x))
-  | List0ArgType _ -> 
-      hov 0 (fold_list0 (fun x a -> pr_generic prc prlc prtac x ++ a) x (mt()))
+      pr_bindings_no_with prc prlc (out_bindings (out_gen wit_bindings x))
+  | List0ArgType _ ->
+      hov 0 (pr_sequence (pr_generic prc prlc prtac)
+	(fold_list0 (fun a l -> a::l) x []))
   | List1ArgType _ ->
-      hov 0 (fold_list1 (fun x a -> pr_generic prc prlc prtac x ++ a) x (mt()))
+      hov 0 (pr_sequence (pr_generic prc prlc prtac)
+	(fold_list1 (fun a l -> a::l) x []))
   | OptArgType _ -> hov 0 (fold_opt (pr_generic prc prlc prtac) (mt()) x)
   | PairArgType _ ->
       hov 0
-        (fold_pair
-	  (fun a b -> pr_generic prc prlc prtac a ++ spc () ++ 
-            pr_generic prc prlc prtac b)
+        (fold_pair (fun a b -> pr_sequence (pr_generic prc prlc prtac) [a;b])
 	  x)
   | ExtraArgType s -> 
       try pi3 (Stringmap.find s !genarg_pprule) prc prlc prtac x
-      with Not_found -> str " [no printer for " ++ str s ++ str "]"
+      with Not_found -> str "[no printer for " ++ str s ++ str "]"
 
-let rec pr_tacarg_using_rule pr_gen = function
-  | Some s :: l, al -> spc () ++ str s ++ pr_tacarg_using_rule pr_gen (l,al)
-  | None :: l, a :: al -> pr_gen a ++ pr_tacarg_using_rule  pr_gen (l,al)
-  | [], [] -> mt ()
+let rec tacarg_using_rule_token pr_gen = function
+  | Some s :: l, al -> str s :: tacarg_using_rule_token pr_gen (l,al)
+  | None :: l, a :: al -> pr_gen a :: tacarg_using_rule_token pr_gen (l,al)
+  | [], [] -> []
   | _ -> failwith "Inconsistent arguments of extended tactic"
 
-let pr_extend_gen prgen lev s l =
+let pr_tacarg_using_rule pr_gen l=
+  pr_sequence (fun x -> x) (tacarg_using_rule_token pr_gen l)
+
+let pr_extend_gen pr_gen lev s l =
   try 
     let tags = List.map genarg_tag l in
     let (lev',pl) = Hashtbl.find prtac_tab (s,tags) in
-    let p = pr_tacarg_using_rule prgen (pl,l) in
+    let p = pr_tacarg_using_rule pr_gen (pl,l) in
     if lev' > lev then surround p else p
   with Not_found ->
-    str s ++ prlist prgen l ++ str " (* Generic printer *)"
+    str s ++ spc() ++ pr_sequence pr_gen l ++ str" (* Generic printer *)"
 
 let pr_raw_extend prc prlc prtac = 
   pr_extend_gen (pr_raw_generic prc prlc prtac pr_reference)
@@ -366,9 +363,22 @@ let pr_with_constr prc = function
   | None -> mt ()
   | Some c -> spc () ++ hov 1 (str "with" ++ spc () ++ prc c)
 
+let pr_with_induction_names = function
+  | None, None -> mt ()
+  | eqpat, ipat ->
+      spc () ++ hov 1 (str "as" ++ pr_opt pr_intro_pattern eqpat ++ 
+                       pr_opt pr_intro_pattern ipat)
+
+let pr_as_intro_pattern ipat =
+  spc () ++ hov 1 (str "as" ++ spc () ++ pr_intro_pattern ipat)
+
+let pr_with_inversion_names = function
+  | None -> mt ()
+  | Some ipat -> pr_as_intro_pattern ipat
+
 let pr_with_names = function
-  | IntroAnonymous -> mt ()
-  | ipat -> spc () ++ hov 1 (str "as" ++ spc () ++ pr_intro_pattern ipat)
+  | _,IntroAnonymous -> mt ()
+  | ipat -> pr_as_intro_pattern ipat
 
 let pr_as_name = function
   | Anonymous -> mt ()
@@ -454,7 +464,7 @@ let pr_induction_kind = function
   | FullInversion -> str "inversion"
   | FullInversionClear -> str "inversion_clear"
 
-let pr_lazy lz = if lz then str "lazy " else mt ()
+let pr_lazy lz = if lz then str "lazy" else mt ()
 
 let pr_match_pattern pr_pat = function
   | Term a -> pr_pat a
@@ -489,8 +499,9 @@ let pr_funvar = function
   | None -> spc () ++ str "_"
   | Some id -> spc () ++ pr_id id
 
-let pr_let_clause k pr (id,t) =
-  hov 0 (str k ++ pr_lident id ++ str " :=" ++ brk (1,1) ++ pr (TacArg t))
+let pr_let_clause k pr (id,(bl,t)) =
+  hov 0 (str k ++ pr_lident id ++ prlist pr_funvar bl ++ 
+         str " :=" ++ brk (1,1) ++ pr (TacArg t))
 
 let pr_let_clauses recflag pr = function
   | hd::tl ->
@@ -599,6 +610,10 @@ let pr_intarg n = spc () ++ int n in
 (* Some printing combinators *)
 let pr_eliminator cb = str "using" ++ pr_arg pr_with_bindings cb in
 
+let extract_binders = function
+  | Tacexp (TacFun (lvar,body)) -> (lvar,Tacexp body)
+  | body -> ([],body) in
+
 let pr_binder_fix (nal,t) =
 (*  match t with
   | CHole _ -> spc() ++ prlist_with_sep spc (pr_lname) nal
@@ -644,7 +659,7 @@ let pr_cofix_tac (id,c) =
   (* Printing tactics as arguments *)
 let rec pr_atom0 = function
   | TacIntroPattern [] -> str "intros"
-  | TacIntroMove (None,None) -> str "intro"
+  | TacIntroMove (None,hto) when hto = no_move -> str "intro"
   | TacAssumption -> str "assumption"
   | TacAnyConstructor (false,None) -> str "constructor"
   | TacAnyConstructor (true,None) -> str "econstructor"
@@ -672,12 +687,10 @@ and pr_atom1 = function
       hov 1 (str "intros" ++ spc () ++ prlist_with_sep spc pr_intro_pattern p)
   | TacIntrosUntil h ->
       hv 1 (str "intros until" ++ pr_arg pr_quantified_hypothesis h)
-  | TacIntroMove (None,None) as t -> pr_atom0 t
-  | TacIntroMove (Some id1,None) -> str "intro " ++ pr_id id1
-  | TacIntroMove (ido1,Some id2) ->
-      hov 1
-      (str "intro" ++ pr_opt pr_id ido1 ++ spc () ++ str "after " ++
-       pr_lident id2)
+  | TacIntroMove (None,hto) as t when hto = no_move -> pr_atom0 t
+  | TacIntroMove (Some id,hto) when hto = no_move -> str "intro " ++ pr_id id
+  | TacIntroMove (ido,hto) ->
+      hov 1 (str"intro" ++ pr_opt pr_id ido ++ pr_move_location pr_ident hto)
   | TacAssumption as t -> pr_atom0 t
   | TacExact c -> hov 1 (str "exact" ++ pr_constrarg c)
   | TacExactNoCheck c -> hov 1 (str "exact_no_check" ++ pr_constrarg c)
@@ -685,7 +698,7 @@ and pr_atom1 = function
   | TacApply (a,ev,cb) ->
       hov 1 ((if a then mt() else str "simple ") ++
              str (with_evars ev "apply") ++ spc () ++ 
-             pr_with_bindings cb)
+             prlist_with_sep pr_coma pr_with_bindings cb)
   | TacElim (ev,cb,cbo) ->
       hov 1 (str (with_evars ev "elim") ++ pr_arg pr_with_bindings cb ++ 
         pr_opt pr_eliminator cbo)
@@ -737,22 +750,17 @@ and pr_atom1 = function
 	     ++ str "in" ++ pr_hyp_location pr_ident (id,[],(hloc,ref None)))
 *)
   (* Derived basic tactics *)
-  | TacSimpleInduction h ->
-      hov 1 (str "simple induction" ++ pr_arg pr_quantified_hypothesis h)
-  | TacNewInduction (ev,h,e,ids,cl) ->
-      hov 1 (str (with_evars ev "induction") ++ spc () ++
-	     prlist_with_sep spc (pr_induction_arg pr_lconstr pr_constr) h ++
-	     pr_with_names ids ++
-             pr_opt pr_eliminator e ++
-             pr_opt_no_spc (pr_clauses pr_ident) cl)
-  | TacSimpleDestruct h ->
-      hov 1 (str "simple destruct" ++ pr_arg pr_quantified_hypothesis h)
-  | TacNewDestruct (ev,h,e,ids,cl) ->
-      hov 1 (str (with_evars ev "destruct") ++ spc () ++
-             prlist_with_sep spc (pr_induction_arg pr_lconstr pr_constr) h ++ 
-	     pr_with_names ids ++
-             pr_opt pr_eliminator e ++
-             pr_opt_no_spc (pr_clauses pr_ident) cl)
+  | TacSimpleInductionDestruct (isrec,h) ->
+      hov 1 (str "simple " ++ str (if isrec then "induction" else "destruct")
+             ++ pr_arg pr_quantified_hypothesis h)
+  | TacInductionDestruct (isrec,ev,l) ->
+      hov 1 (str (with_evars ev (if isrec then "induction" else "destruct")) ++
+             spc () ++
+             prlist_with_sep pr_coma (fun (h,e,ids,cl) ->
+	       prlist_with_sep spc (pr_induction_arg pr_lconstr pr_constr) h ++
+	       pr_with_induction_names ids ++
+               pr_opt pr_eliminator e ++
+               pr_opt_no_spc (pr_clauses pr_ident) cl) l)
   | TacDoubleInduction (h1,h2) ->
       hov 1
         (str "double induction" ++  
@@ -796,8 +804,8 @@ and pr_atom1 = function
       (* Rem: only b = true is available for users *)
       assert b;
       hov 1
-        (str "move" ++ brk (1,1) ++ pr_ident id1 ++ spc () ++ 
-	 str "after" ++ brk (1,1) ++ pr_ident id2)
+        (str "move" ++ brk (1,1) ++ pr_ident id1 ++ 
+	 pr_move_location pr_ident id2)
   | TacRename l ->
       hov 1
         (str "rename" ++ brk (1,1) ++
@@ -852,11 +860,11 @@ and pr_atom1 = function
   | TacInversion (DepInversion (k,c,ids),hyp) ->
       hov 1 (str "dependent " ++ pr_induction_kind k ++ spc () ++
       pr_quantified_hypothesis hyp ++
-      pr_with_names ids ++ pr_with_constr pr_constr c)
+      pr_with_inversion_names ids ++ pr_with_constr pr_constr c)
   | TacInversion (NonDepInversion (k,cl,ids),hyp) ->
       hov 1 (pr_induction_kind k ++ spc () ++
       pr_quantified_hypothesis hyp ++
-      pr_with_names ids ++ pr_simple_clause pr_ident cl)
+      pr_with_inversion_names ids ++ pr_simple_clause pr_ident cl)
   | TacInversion (InversionUsing (c,cl),hyp) ->
       hov 1 (str "inversion" ++ spc() ++ pr_quantified_hypothesis hyp ++ 
       spc () ++ str "using" ++ spc () ++ pr_constr c ++ 
@@ -874,6 +882,7 @@ let rec pr_tac inherited tac =
         str "using " ++ pr_id s),
       labstract
   | TacLetIn (recflag,llc,u) ->
+      let llc = List.map (fun (id,t) -> (id,extract_binders t)) llc in
       v 0
        (hv 0 (pr_let_clauses recflag (pr_tac ltop) llc ++ str " in") ++
        fnl () ++ pr_tac (llet,E) u),
@@ -886,7 +895,7 @@ let rec pr_tac inherited tac =
 	lrul
         ++ fnl() ++ str "end"),
       lmatch
-  | TacMatchContext (lz,lr,lrul) ->
+  | TacMatchGoal (lz,lr,lrul) ->
       hov 0 (pr_lazy lz ++ 
 	str (if lr then "match reverse goal with" else "match goal with")
 	++ prlist
diff --git a/parsing/pptactic.mli b/parsing/pptactic.mli
index e5162dae..e24f666f 100644
--- a/parsing/pptactic.mli
+++ b/parsing/pptactic.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: pptactic.mli 9842 2007-05-20 17:44:23Z herbelin $ i*)
+(*i $Id: pptactic.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Pp
 open Genarg
@@ -78,6 +78,8 @@ val pr_extend :
   (tolerability -> glob_tactic_expr -> std_ppcmds) -> int ->
     string -> typed_generic_argument list -> std_ppcmds
 
+val pr_ltac_constant : Nametab.ltac_constant -> std_ppcmds
+
 val pr_raw_tactic : env -> raw_tactic_expr -> std_ppcmds
 
 val pr_raw_tactic_level : env -> tolerability -> raw_tactic_expr -> std_ppcmds
diff --git a/parsing/ppvernac.ml b/parsing/ppvernac.ml
index ac2adde2..67cd6f72 100644
--- a/parsing/ppvernac.ml
+++ b/parsing/ppvernac.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: ppvernac.ml 11059 2008-06-06 09:29:20Z herbelin $ *)  
+(* $Id: ppvernac.ml 11309 2008-08-06 10:30:35Z herbelin $ *)  
 
 open Pp
 open Names
@@ -403,9 +403,6 @@ let pr_constrarg c = spc () ++ pr_constr c in
 let pr_lconstrarg c = spc () ++ pr_lconstr c in
 let pr_intarg n = spc () ++ int n in
 let pr_lident_constr sep (i,c) = pr_lident i ++ sep ++ pr_constrarg c in
-let pr_lname_lident_constr (oi,bk,a) = 
-  (match snd oi with Anonymous -> mt () | Name id -> pr_lident (fst oi, id) ++ spc () ++ str":" ++ spc ()) 
-  ++ pr_lconstr a in
 let pr_instance_def sep (i,l,c) = pr_lident i ++ prlist_with_sep spc pr_lident l 
   ++ sep ++ pr_constrarg c in
 
@@ -717,8 +714,7 @@ let rec pr_vernac = function
  | VernacContext l ->
      hov 1 (
        str"Context" ++ spc () ++ str"[" ++ spc () ++
-	 prlist_with_sep (fun () -> str"," ++ spc()) pr_lname_lident_constr l ++
-	 spc () ++ str "]")
+	 pr_and_type_binders_arg l ++ spc () ++ str "]")
 	      
 
  | VernacDeclareInstance id ->
@@ -808,10 +804,7 @@ let rec pr_vernac = function
 	  (Global.env())
 	  body in
       hov 1
-        (((*if !Flags.p1 then
-	  (if rc then str "Recursive " else mt()) ++
-	  str "Tactic Definition " else*)
-	    (* Rec by default *) str "Ltac ") ++
+        ((str "Ltac ") ++
         prlist_with_sep (fun () -> fnl() ++ str"with ") pr_tac_body l)
   | VernacHints (local,dbnames,h) ->
       pr_hints local dbnames h pr_constr pr_pattern_expr
diff --git a/parsing/prettyp.ml b/parsing/prettyp.ml
index 401ef7fe..3aa51c53 100644
--- a/parsing/prettyp.ml
+++ b/parsing/prettyp.ml
@@ -10,7 +10,7 @@
  * on May-June 2006 for implementation of abstraction of pretty-printing of objects.
  *)
 
-(* $Id: prettyp.ml 10971 2008-05-22 17:12:11Z barras $ *)
+(* $Id: prettyp.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -219,7 +219,7 @@ let pr_located_qualid = function
   | ModuleType (qid,_) ->
       str "Module Type" ++ spc () ++ pr_sp (Nametab.full_name_modtype qid)
   | Undefined qid ->    
-      pr_qualid qid ++ str " is not a defined object"
+      pr_qualid qid ++ spc () ++ str "not a defined object."
 
 let print_located_qualid ref =
   let (loc,qid) = qualid_of_reference ref in
@@ -303,7 +303,7 @@ let build_inductive sp tyi =
     | Polymorphic ar ->
 	it_mkProd_or_LetIn (mkSort (Type ar.poly_level)) mip.mind_arity_ctxt in
   let arity = hnf_prod_applist env fullarity args in
-  let cstrtypes = arities_of_constructors env (sp,tyi) in
+  let cstrtypes = type_of_constructors env (sp,tyi) in
   let cstrtypes =
     Array.map (fun c -> hnf_prod_applist env c args) cstrtypes in
   let cstrnames = mip.mind_consnames in
@@ -599,12 +599,12 @@ let read_sec_context r =
   let dir =
     try Nametab.locate_section qid
     with Not_found ->
-      user_err_loc (loc,"read_sec_context", str "Unknown section") in
+      user_err_loc (loc,"read_sec_context", str "Unknown section.") in
   let rec get_cxt in_cxt = function
     | (_,Lib.OpenedSection ((dir',_),_) as hd)::rest ->
         if dir = dir' then (hd::in_cxt) else get_cxt (hd::in_cxt) rest
     | (_,Lib.ClosedSection _)::rest ->
-        error "Cannot print the contents of a closed section"
+        error "Cannot print the contents of a closed section."
 	(* LEM: Actually, we could if we wanted to. *)
     | [] -> []
     | hd::rest -> get_cxt (hd::in_cxt) rest 
@@ -648,7 +648,7 @@ let print_name ref =
     print_leaf_entry true (oname,lobj)
   with Not_found ->
     errorlabstrm
-      "print_name" (pr_qualid qid ++ spc () ++ str "not a defined object")
+      "print_name" (pr_qualid qid ++ spc () ++ str "not a defined object.")
 
 let print_opaque_name qid = 
   let env = Global.env () in
@@ -658,7 +658,7 @@ let print_opaque_name qid =
         if cb.const_body <> None then
 	  print_constant_with_infos cst
         else 
-	  error "not a defined constant"
+	  error "Not a defined constant."
     | IndRef (sp,_) ->
         print_inductive sp
     | ConstructRef cstr -> 
@@ -736,7 +736,8 @@ let index_of_class cl =
   try 
     fst (class_info cl)
   with _ -> 
-    errorlabstrm "index_of_class" (pr_class cl ++ str" is not a defined class")
+    errorlabstrm "index_of_class"
+      (pr_class cl ++ spc() ++ str "not a defined class.")
 
 let print_path_between cls clt = 
   let i = index_of_class cls in
@@ -746,7 +747,8 @@ let print_path_between cls clt =
       lookup_path_between (i,j) 
     with _ -> 
       errorlabstrm "index_cl_of_id"
-        (str"No path between " ++ pr_class cls ++ str" and " ++ pr_class clt)
+        (str"No path between " ++ pr_class cls ++ str" and " ++ pr_class clt
+	 ++ str ".")
   in
   print_path ((i,j),p)
 
diff --git a/parsing/printer.ml b/parsing/printer.ml
index 6a19cb0a..b126cc9c 100644
--- a/parsing/printer.ml
+++ b/parsing/printer.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: printer.ml 11001 2008-05-27 16:56:07Z aspiwack $ *)
+(* $Id: printer.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -28,6 +28,7 @@ open Refiner
 open Pfedit
 open Ppconstr
 open Constrextern
+open Tacexpr
 
 let emacs_str s alts = 
   match !Flags.print_emacs, !Flags.print_emacs_safechar with
@@ -318,7 +319,7 @@ let rec pr_evars_int i = function
 
 let default_pr_subgoal n =
   let rec prrec p = function
-    | [] -> error "No such goal"
+    | [] -> error "No such goal."
     | g::rest ->
        	if p = 1 then
           let pg = default_pr_goal g in
@@ -421,14 +422,14 @@ let pr_prim_rule = function
   | Intro id -> 
       str"intro " ++ pr_id id
 	
-  | Intro_replacing id -> 
-      (str"intro replacing "  ++ pr_id id)
-	
-  | Cut (b,id,t) ->
-      if b then
-        (str"assert " ++ pr_constr t)
-      else
-        (str"cut " ++ pr_constr t ++ str ";[intro " ++ pr_id id ++ str "|idtac]")
+  | Cut (b,replace,id,t) ->
+     if b then
+       (* TODO: express "replace" *)
+       (str"assert " ++ str"(" ++ pr_id id ++ str":" ++ pr_lconstr t ++ str")")
+     else
+       let cl = if replace then str"clear " ++ pr_id id ++ str"; " else mt() in
+       (str"cut " ++ pr_constr t ++ 
+        str ";[" ++ cl ++ str"intro " ++ pr_id id ++ str"|idtac]")
 	
   | FixRule (f,n,[]) ->
       (str"fix " ++ pr_id f ++ str"/" ++ int n)
@@ -472,7 +473,7 @@ let pr_prim_rule = function
       
   | Move (withdep,id1,id2) ->
       (str (if withdep then "dependent " else "") ++
-	 str"move "  ++ pr_id id1 ++ str " after " ++ pr_id id2)
+	 str"move "  ++ pr_id id1 ++ pr_move_location pr_id id2)
 
   | Rename (id1,id2) ->
       (str "rename " ++ pr_id id1 ++ str " into " ++ pr_id id2)
@@ -527,3 +528,14 @@ let pr_assumptionset env s =
     in
     (Option.default (mt ()) vars) ++ (Option.default (mt ()) axioms)
 
+let cmap_to_list m = Cmap.fold (fun k v acc -> v :: acc) m []
+
+open Typeclasses
+
+let pr_instance i = 
+  pr_global (ConstRef (instance_impl i))
+    
+let pr_instance_gmap insts =
+  prlist_with_sep fnl (fun (gr, insts) ->
+    prlist_with_sep fnl pr_instance (cmap_to_list insts))
+    (Gmap.to_list insts)
diff --git a/parsing/printer.mli b/parsing/printer.mli
index 935fca12..40bb9122 100644
--- a/parsing/printer.mli
+++ b/parsing/printer.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: printer.mli 11001 2008-05-27 16:56:07Z aspiwack $ i*)
+(*i $Id: printer.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Pp
@@ -22,6 +22,7 @@ open Termops
 open Evd
 open Proof_type
 open Rawterm
+open Tacexpr
 (*i*)
 
 (* These are the entry points for printing terms, context, tac, ... *)
@@ -137,3 +138,5 @@ val set_printer_pr : printer_pr -> unit
 
 val default_printer_pr : printer_pr
 
+val pr_instance_gmap : (global_reference, Typeclasses.instance Names.Cmap.t) Gmap.t ->
+  Pp.std_ppcmds
diff --git a/parsing/q_coqast.ml4 b/parsing/q_coqast.ml4
index 24562459..a4cfe27a 100644
--- a/parsing/q_coqast.ml4
+++ b/parsing/q_coqast.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "q_MLast.cmo pa_macro.cmo" i*)
 
-(* $Id: q_coqast.ml4 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: q_coqast.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -62,6 +62,10 @@ let mlexpr_of_reference = function
   | Libnames.Qualid (loc,qid) -> <:expr< Libnames.Qualid $dloc$ $mlexpr_of_qualid qid$ >>
   | Libnames.Ident (loc,id) -> <:expr< Libnames.Ident $dloc$ $mlexpr_of_ident id$ >>
 
+let mlexpr_of_located f (loc,x) = <:expr< ($dloc$, $f x$) >>
+
+let mlexpr_of_loc loc = <:expr< $dloc$ >>
+
 let mlexpr_of_by_notation f = function
   | Genarg.AN x -> <:expr< Genarg.AN $f x$ >>
   | Genarg.ByNotation (loc,s) -> <:expr< Genarg.ByNotation $dloc$ $str:s$ >>
@@ -85,10 +89,6 @@ let mlexpr_of_quantified_hypothesis = function
   | Rawterm.AnonHyp n -> <:expr< Rawterm.AnonHyp $mlexpr_of_int n$ >>
   | Rawterm.NamedHyp id ->  <:expr< Rawterm.NamedHyp $mlexpr_of_ident id$ >>
 
-let mlexpr_of_located f (loc,x) = <:expr< ($dloc$, $f x$) >>
-
-let mlexpr_of_loc loc = <:expr< $dloc$ >>
-
 let mlexpr_of_or_var f = function
   | Rawterm.ArgArg x -> <:expr< Rawterm.ArgArg $f x$ >>
   | Rawterm.ArgVar id -> <:expr< Rawterm.ArgVar $mlexpr_of_located mlexpr_of_ident id$ >>
@@ -139,7 +139,7 @@ let mlexpr_of_binding_kind = function
 
 let mlexpr_of_binder_kind = function
   | Topconstr.Default b -> <:expr< Topconstr.Default $mlexpr_of_binding_kind b$ >>
-  | Topconstr.TypeClass b -> <:expr< Topconstr.TypeClass $mlexpr_of_binding_kind b$ >>
+  | Topconstr.TypeClass (b,b') -> <:expr< Topconstr.TypeClass $mlexpr_of_pair mlexpr_of_binding_kind mlexpr_of_binding_kind (b,b')$ >>
 
 let rec mlexpr_of_constr = function
   | Topconstr.CRef (Libnames.Ident (loc,id)) when is_meta (string_of_id id) ->
@@ -242,6 +242,11 @@ let mlexpr_of_binding = mlexpr_of_pair mlexpr_of_binding_kind mlexpr_of_constr
 let mlexpr_of_constr_with_binding =
   mlexpr_of_pair mlexpr_of_constr mlexpr_of_binding_kind
 
+let mlexpr_of_move_location f = function
+  | Tacexpr.MoveAfter id -> <:expr< Tacexpr.MoveAfter $f id$ >>
+  | Tacexpr.MoveBefore id -> <:expr< Tacexpr.MoveBefore $f id$ >>
+  | Tacexpr.MoveToEnd b -> <:expr< Tacexpr.MoveToEnd $mlexpr_of_bool b$ >>
+
 let mlexpr_of_induction_arg = function
   | Tacexpr.ElimOnConstr c ->
       <:expr< Tacexpr.ElimOnConstr $mlexpr_of_constr_with_binding c$ >>
@@ -279,13 +284,13 @@ let mlexpr_of_message_token = function
 let rec mlexpr_of_atomic_tactic = function
   (* Basic tactics *)
   | Tacexpr.TacIntroPattern pl ->
-      let pl = mlexpr_of_list mlexpr_of_intro_pattern pl in
+      let pl = mlexpr_of_list (mlexpr_of_located mlexpr_of_intro_pattern) pl in
       <:expr< Tacexpr.TacIntroPattern $pl$ >>
   | Tacexpr.TacIntrosUntil h ->
       <:expr< Tacexpr.TacIntrosUntil $mlexpr_of_quantified_hypothesis h$ >>
   | Tacexpr.TacIntroMove (idopt,idopt') ->
       let idopt = mlexpr_of_ident_option idopt in
-      let idopt'=mlexpr_of_option (mlexpr_of_located mlexpr_of_ident) idopt' in
+      let idopt'= mlexpr_of_move_location mlexpr_of_hyp idopt' in
       <:expr< Tacexpr.TacIntroMove $idopt$ $idopt'$ >>
   | Tacexpr.TacAssumption ->
       <:expr< Tacexpr.TacAssumption >>
@@ -296,7 +301,7 @@ let rec mlexpr_of_atomic_tactic = function
   | Tacexpr.TacVmCastNoCheck c ->
       <:expr< Tacexpr.TacVmCastNoCheck $mlexpr_of_constr c$ >>
   | Tacexpr.TacApply (b,false,cb) ->
-      <:expr< Tacexpr.TacApply $mlexpr_of_bool b$ False $mlexpr_of_constr_with_binding cb$ >>
+      <:expr< Tacexpr.TacApply $mlexpr_of_bool b$ False $mlexpr_of_list mlexpr_of_constr_with_binding cb$ >>
   | Tacexpr.TacElim (false,cb,cbo) ->
       let cb = mlexpr_of_constr_with_binding cb in
       let cbo = mlexpr_of_option mlexpr_of_constr_with_binding cbo in
@@ -332,7 +337,7 @@ let rec mlexpr_of_atomic_tactic = function
   | Tacexpr.TacCut c ->
       <:expr< Tacexpr.TacCut $mlexpr_of_constr c$ >>
   | Tacexpr.TacAssert (t,ipat,c) ->
-      let ipat = mlexpr_of_intro_pattern ipat in
+      let ipat = mlexpr_of_located mlexpr_of_intro_pattern ipat in
       <:expr< Tacexpr.TacAssert $mlexpr_of_option mlexpr_of_tactic t$ $ipat$ 
 	      $mlexpr_of_constr c$ >>
   | Tacexpr.TacGeneralize cl ->
@@ -348,18 +353,18 @@ let rec mlexpr_of_atomic_tactic = function
 	      $mlexpr_of_bool b$ >>
 
   (* Derived basic tactics *)
-  | Tacexpr.TacSimpleInduction h ->
-      <:expr< Tacexpr.TacSimpleInduction ($mlexpr_of_quantified_hypothesis h$) >>
-  | Tacexpr.TacNewInduction (false,cl,cbo,ids,cls) ->
-      let cbo = mlexpr_of_option mlexpr_of_constr_with_binding cbo in
-      let ids = mlexpr_of_intro_pattern ids in
-      <:expr< Tacexpr.TacNewInduction False $mlexpr_of_list mlexpr_of_induction_arg cl$ $cbo$ $ids$ $mlexpr_of_option mlexpr_of_clause cls$ >>
-  | Tacexpr.TacSimpleDestruct h ->
-      <:expr< Tacexpr.TacSimpleDestruct $mlexpr_of_quantified_hypothesis h$ >>
-  | Tacexpr.TacNewDestruct (false,c,cbo,ids,cls) ->
-      let cbo = mlexpr_of_option mlexpr_of_constr_with_binding cbo in
-      let ids = mlexpr_of_intro_pattern ids in
-      <:expr< Tacexpr.TacNewDestruct False $mlexpr_of_list mlexpr_of_induction_arg c$ $cbo$ $ids$ $mlexpr_of_option mlexpr_of_clause cls$ >>
+  | Tacexpr.TacSimpleInductionDestruct (isrec,h) ->
+      <:expr< Tacexpr.TacSimpleInductionDestruct $mlexpr_of_bool isrec$
+                  $mlexpr_of_quantified_hypothesis h$ >>
+  | Tacexpr.TacInductionDestruct (isrec,ev,l) ->
+      <:expr< Tacexpr.TacInductionDestruct $mlexpr_of_bool isrec$ $mlexpr_of_bool ev$ 
+	$mlexpr_of_list (mlexpr_of_quadruple 
+	  (mlexpr_of_list mlexpr_of_induction_arg)
+	  (mlexpr_of_option mlexpr_of_constr_with_binding)
+	  (mlexpr_of_pair
+	    (mlexpr_of_option (mlexpr_of_located mlexpr_of_intro_pattern))
+	    (mlexpr_of_option (mlexpr_of_located mlexpr_of_intro_pattern)))
+	  (mlexpr_of_option mlexpr_of_clause)) l$ >>
 
   (* Context management *)
   | Tacexpr.TacClear (b,l) ->
@@ -371,7 +376,7 @@ let rec mlexpr_of_atomic_tactic = function
   | Tacexpr.TacMove (dep,id1,id2) ->
       <:expr< Tacexpr.TacMove $mlexpr_of_bool dep$
               $mlexpr_of_hyp id1$
-              $mlexpr_of_hyp id2$ >>
+              $mlexpr_of_move_location mlexpr_of_hyp id2$ >>
 
   (* Constructors *)
   | Tacexpr.TacLeft (ev,l) ->
@@ -462,8 +467,8 @@ and mlexpr_of_tactic : (Tacexpr.raw_tactic_expr -> MLast.expr) = function
         $mlexpr_of_bool lz$
         $mlexpr_of_tactic t$
         $mlexpr_of_list (mlexpr_of_match_rule mlexpr_of_tactic) l$>>
-  | Tacexpr.TacMatchContext (lz,lr,l) ->
-      <:expr< Tacexpr.TacMatchContext 
+  | Tacexpr.TacMatchGoal (lz,lr,l) ->
+      <:expr< Tacexpr.TacMatchGoal 
         $mlexpr_of_bool lz$
         $mlexpr_of_bool lr$
         $mlexpr_of_list (mlexpr_of_match_rule mlexpr_of_tactic) l$>>
diff --git a/parsing/q_util.ml4 b/parsing/q_util.ml4
index da78e287..da4329bb 100644
--- a/parsing/q_util.ml4
+++ b/parsing/q_util.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "q_MLast.cmo" i*)
 
-(* $Id: q_util.ml4 10091 2007-08-24 10:57:37Z herbelin $ *)
+(* $Id: q_util.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (* This file defines standard combinators to build ml expressions *)
 
@@ -53,6 +53,11 @@ let mlexpr_of_triple m1 m2 m3 (a1,a2,a3)=
   let loc = join_loc (MLast.loc_of_expr e1) (MLast.loc_of_expr e3) in
   <:expr< ($e1$, $e2$, $e3$) >>
 
+let mlexpr_of_quadruple m1 m2 m3 m4 (a1,a2,a3,a4)=
+  let e1 = m1 a1 and e2 = m2 a2 and e3 = m3 a3 and e4 = m4 a4 in
+  let loc = join_loc (MLast.loc_of_expr e1) (MLast.loc_of_expr e4) in
+  <:expr< ($e1$, $e2$, $e3$, $e4$) >>
+
 (* We don't give location for tactic quotation! *)
 let loc = dummy_loc
 
diff --git a/parsing/q_util.mli b/parsing/q_util.mli
index 901f9198..b950e68f 100644
--- a/parsing/q_util.mli
+++ b/parsing/q_util.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: q_util.mli 9265 2006-10-24 08:35:38Z herbelin $ i*)
+(*i $Id: q_util.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 val patt_of_expr : MLast.expr -> MLast.patt
 
@@ -20,6 +20,10 @@ val mlexpr_of_triple :
   ('a -> MLast.expr) -> ('b -> MLast.expr) -> ('c -> MLast.expr)
     -> 'a * 'b * 'c -> MLast.expr
 
+val mlexpr_of_quadruple :
+  ('a -> MLast.expr) -> ('b -> MLast.expr) ->
+    ('c -> MLast.expr) -> ('d -> MLast.expr) -> 'a * 'b * 'c * 'd -> MLast.expr
+
 val mlexpr_of_bool : bool -> MLast.expr
 
 val mlexpr_of_int : int -> MLast.expr
diff --git a/parsing/search.ml b/parsing/search.ml
index c375826c..c6ff4c04 100644
--- a/parsing/search.ml
+++ b/parsing/search.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: search.ml 10840 2008-04-23 21:29:34Z herbelin $ *)
+(* $Id: search.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -150,7 +150,7 @@ let rec id_from_pattern = function
   | PVar id -> Nametab.locate (make_qualid [] (string_of_id id))
  *)
   | PApp (p,_) -> id_from_pattern p
-  | _ -> error "the pattern is not simple enough"
+  | _ -> error "The pattern is not simple enough."
 	
 let raw_pattern_search extra_filter display_function pat =
   let name = id_from_pattern pat in
diff --git a/parsing/tacextend.ml4 b/parsing/tacextend.ml4
index 3d71af84..695677a3 100644
--- a/parsing/tacextend.ml4
+++ b/parsing/tacextend.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo q_MLast.cmo" i*)
 
-(* $Id: tacextend.ml4 10091 2007-08-24 10:57:37Z herbelin $ *)
+(* $Id: tacextend.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Genarg
@@ -206,7 +206,7 @@ EXTEND
         let t, g = Q_util.interp_entry_name loc e sep in
         TacNonTerm (loc, t, g, Some s)
       | s = STRING ->
-	if s = "" then Util.user_err_loc (loc,"",Pp.str "Empty terminal");
+	if s = "" then Util.user_err_loc (loc,"",Pp.str "Empty terminal.");
         TacTerm s
     ] ]
   ;
diff --git a/parsing/tactic_printer.ml b/parsing/tactic_printer.ml
index c5b77774..e0836984 100644
--- a/parsing/tactic_printer.ml
+++ b/parsing/tactic_printer.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tactic_printer.ml 11146 2008-06-19 08:26:38Z corbinea $ *)
+(* $Id: tactic_printer.ml 11313 2008-08-07 11:15:03Z barras $ *)
 
 open Pp
 open Util
@@ -90,7 +90,8 @@ let pr_change gl =
   str"change " ++
   pr_lconstr_env (Global.env_of_context gl.evar_hyps) gl.evar_concl ++ str"."
 
-let rec print_decl_script tac_printer nochange sigma pf =
+let print_decl_script tac_printer ?(nochange=true) sigma pf =
+  let rec print_prf pf =
   match pf.ref with
     | None ->
 	(if nochange then 
@@ -99,46 +100,38 @@ let rec print_decl_script tac_printer nochange sigma pf =
 	   pr_change pf.goal)
 	++ fnl ()
     | Some (Daimon,[]) -> str "(* Some proof has been skipped here *)"
-    | Some (Prim Change_evars,[subpf]) ->   
-	print_decl_script tac_printer nochange sigma subpf
+    | Some (Prim Change_evars,[subpf]) -> print_prf subpf
     | Some (Nested(Proof_instr (opened,instr),_) as rule,subprfs) ->
 	begin
 	  match instr.instr,subprfs with
 	    Pescape,[{ref=Some(_,subsubprfs)}] ->
 	      hov 7
 		(pr_rule_dot_fnl rule ++
-		   prlist_with_sep pr_fnl tac_printer subsubprfs) ++ fnl () ++
-		if opened then mt () else str "return."
+		  prlist_with_sep pr_fnl tac_printer subsubprfs) ++ fnl () ++
+	      if opened then mt () else str "return."
 	  | Pclaim _,[body;cont] ->
-	      hov 2
-		(pr_rule_dot_fnl rule ++
-		   print_decl_script tac_printer nochange sigma body) ++ 
-		fnl () ++
-		if opened then mt () else str "end claim." ++ fnl () ++
-		  print_decl_script tac_printer nochange sigma cont
+	      hov 2 (pr_rule_dot_fnl rule ++ print_prf body) ++ fnl () ++
+	      (if opened then mt () else str "end claim." ++ fnl ()) ++
+	      print_prf cont
 	  | Pfocus _,[body;cont] ->
-	      hov 2 
-		(pr_rule_dot_fnl rule ++
-		   print_decl_script tac_printer nochange sigma body) ++ 
-		fnl () ++
-		if opened then mt () else str "end focus." ++ fnl () ++
-		  print_decl_script tac_printer nochange sigma cont
+	      hov 2 (pr_rule_dot_fnl rule ++ print_prf body) ++ 
+	      fnl () ++
+	      (if opened then mt () else str "end focus." ++ fnl ()) ++
+	      print_prf cont
 	  | (Psuppose _ |Pcase (_,_,_)),[body;cont] ->
-	      hov 2 
-		(pr_rule_dot_fnl rule ++
-		   print_decl_script tac_printer nochange sigma body) ++ 
-		fnl () ++
-		print_decl_script tac_printer nochange sigma cont 
+	      hov 2 (pr_rule_dot_fnl rule ++ print_prf body) ++ fnl () ++
+	      print_prf cont 
 	  | _,[next] ->
-	      pr_rule_dot_fnl rule ++
-		print_decl_script tac_printer nochange sigma next
+	      pr_rule_dot_fnl rule ++ print_prf next
 	  | _,[] ->
 	      pr_rule_dot rule		
 	  | _,_ -> anomaly "unknown branching instruction"
 	end
-    | _ -> anomaly "Not Applicable"
+    | _ -> anomaly "Not Applicable" in
+  print_prf pf
 
-let rec print_script nochange sigma pf =
+let print_script ?(nochange=true) sigma pf =
+  let rec print_prf pf =
   match pf.ref with
     | None ->
         (if nochange then 
@@ -153,26 +146,25 @@ let rec print_script nochange sigma pf =
 	end ++
 	  begin
 	    hov 0 (str "proof." ++ fnl () ++ 
-		     print_decl_script (print_script nochange sigma) 
-		     nochange sigma (List.hd script))
+		     print_decl_script print_prf 
+		     ~nochange sigma (List.hd script))
 	  end ++ fnl () ++
 	  begin
 	    if opened then mt () else (str "end proof." ++ fnl ())
 	  end
     | Some(Daimon,spfl) ->
 	((if nochange then (mt ()) else (pr_change pf.goal ++ fnl ())) ++
-	   prlist_with_sep pr_fnl
-           (print_script nochange sigma) spfl )
+	   prlist_with_sep pr_fnl print_prf spfl )
     | Some(rule,spfl) ->
 	((if nochange then (mt ()) else (pr_change pf.goal ++ fnl ())) ++
 	   pr_rule_dot_fnl rule ++
-	   prlist_with_sep pr_fnl
-           (print_script nochange sigma) spfl )	
+	   prlist_with_sep pr_fnl print_prf spfl ) in
+  print_prf pf
 
 (* printed by Show Script command *)
 
-let print_treescript nochange sigma pf =
-  let rec aux pf =
+let print_treescript ?(nochange=true) sigma pf =
+  let rec print_prf pf =
     match pf.ref with
     | None ->
         if nochange then 
@@ -184,23 +176,21 @@ let print_treescript nochange sigma pf =
 	begin
 	  if nochange then mt () else pr_change pf.goal ++ fnl ()
 	end ++
-	  hov 0 
+	hov 0 
 	  begin str "proof." ++ fnl () ++
-	    print_decl_script aux
-	    nochange sigma (List.hd script) 
+	    print_decl_script print_prf ~nochange sigma (List.hd script) 
 	  end ++ fnl () ++ 
-	  begin
-	    if opened then mt () else (str "end proof." ++ fnl ())
-	  end
+	begin
+	  if opened then mt () else (str "end proof." ++ fnl ())
+	end
     | Some(Daimon,spfl) ->
-	((if nochange then (mt ()) else (pr_change pf.goal ++ fnl ())) ++
-	   prlist_with_sep pr_fnl
-           (print_script nochange sigma) spfl )
+	(if nochange then mt () else pr_change pf.goal ++ fnl ()) ++
+	prlist_with_sep pr_fnl (print_script ~nochange sigma) spfl
     | Some(r,spfl) ->
         let indent = if List.length spfl >= 2 then 1 else 0 in
-        (if nochange then mt () else (pr_change pf.goal ++ fnl ())) ++
-        hv indent (pr_rule_dot_fnl r ++ prlist_with_sep mt aux spfl)
-  in hov 0 (aux pf)
+        (if nochange then mt () else pr_change pf.goal ++ fnl ()) ++
+        hv indent (pr_rule_dot_fnl r ++ prlist_with_sep fnl print_prf spfl)
+  in hov 0 (print_prf pf)
 
 let rec print_info_script sigma osign pf =
   let {evar_hyps=sign; evar_concl=cl} = pf.goal in
diff --git a/parsing/tactic_printer.mli b/parsing/tactic_printer.mli
index 676dbdf2..affc5ec2 100644
--- a/parsing/tactic_printer.mli
+++ b/parsing/tactic_printer.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tactic_printer.mli 10580 2008-02-22 13:39:13Z lmamane $ i*)
+(*i $Id: tactic_printer.mli 11313 2008-08-07 11:15:03Z barras $ i*)
 
 (*i*)
 open Pp
@@ -23,6 +23,6 @@ val pr_rule     : rule -> std_ppcmds
 val pr_tactic   : tactic_expr -> std_ppcmds
 val pr_proof_instr : Decl_expr.proof_instr -> Pp.std_ppcmds
 val print_script :
-  bool -> evar_map -> proof_tree -> std_ppcmds
+  ?nochange:bool -> evar_map -> proof_tree -> std_ppcmds
 val print_treescript :
-  bool -> evar_map -> proof_tree -> std_ppcmds
+  ?nochange:bool -> evar_map -> proof_tree -> std_ppcmds
diff --git a/parsing/vernacextend.ml4 b/parsing/vernacextend.ml4
index d12ca098..08feb17a 100644
--- a/parsing/vernacextend.ml4
+++ b/parsing/vernacextend.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4use: "pa_extend.cmo q_MLast.cmo" i*)
 
-(* $Id: vernacextend.ml4 10091 2007-08-24 10:57:37Z herbelin $ *)
+(* $Id: vernacextend.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Genarg
@@ -110,7 +110,7 @@ EXTEND
   rule:
     [ [ "["; s = STRING; l = LIST0 args; "]"; "->"; "["; e = Pcaml.expr; "]"
         -> 
-      if s = "" then Util.user_err_loc (loc,"",Pp.str "Command name is empty");
+      if s = "" then Util.user_err_loc (loc,"",Pp.str"Command name is empty.");
       (s,l,<:expr< fun () -> $e$ >>)
     ] ]
   ;
diff --git a/pretyping/cases.ml b/pretyping/cases.ml
index 1d7da3f3..9482bf92 100644
--- a/pretyping/cases.ml
+++ b/pretyping/cases.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: cases.ml 11085 2008-06-10 08:54:43Z herbelin $ *)
+(* $Id: cases.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -114,8 +114,8 @@ let force_name =
 
 open Pp
 
-let mssg_may_need_inversion () =
-  str "Found a matching with no clauses on a term unknown to have an empty inductive type"
+let msg_may_need_inversion () =
+  strbrk "Found a matching with no clauses on a term unknown to have an empty inductive type."
 
 (* Utils *)
 let make_anonymous_patvars n =
@@ -535,7 +535,7 @@ let set_used_pattern eqn = eqn.used := true
 
 let extract_rhs pb =
   match pb.mat with 
-    | [] -> errorlabstrm "build_leaf" (mssg_may_need_inversion())
+    | [] -> errorlabstrm "build_leaf" (msg_may_need_inversion())
     | eqn::_ ->
 	set_used_pattern eqn;
         eqn.rhs
@@ -1654,7 +1654,7 @@ let extract_arity_signature env0 tomatchl tmsign =
 	    | None -> [na,Option.map (lift n) bo,lift n typ]
 	    | Some (loc,_,_,_) -> 
  	    user_err_loc (loc,"",
-	    str "Unexpected type annotation for a term of non inductive type"))
+	    str"Unexpected type annotation for a term of non inductive type."))
       | IsInd (term,IndType(indf,realargs),_) ->
           let indf' = lift_inductive_family n indf in
 	  let (ind,params) = dest_ind_family indf' in
@@ -1663,7 +1663,7 @@ let extract_arity_signature env0 tomatchl tmsign =
 	    match t with
 	      | Some (loc,ind',nparams,realnal) ->
 		  if ind <> ind' then
-		    user_err_loc (loc,"",str "Wrong inductive type");
+		    user_err_loc (loc,"",str "Wrong inductive type.");
 		  if List.length params <> nparams
 		    or nrealargs <> List.length realnal then
 		      anomaly "Ill-formed 'in' clause in cases";
diff --git a/pretyping/classops.ml b/pretyping/classops.ml
index 83ba05bb..b5a5709e 100644
--- a/pretyping/classops.ml
+++ b/pretyping/classops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: classops.ml 10840 2008-04-23 21:29:34Z herbelin $ *)
+(* $Id: classops.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -376,7 +376,7 @@ let coercion_of_reference r =
   let ref = Nametab.global r in
   if not (coercion_exists ref) then
     errorlabstrm "try_add_coercion" 
-      (Nametab.pr_global_env Idset.empty ref ++ str" is not a coercion");
+      (Nametab.pr_global_env Idset.empty ref ++ str" is not a coercion.");
   ref
 
 module CoercionPrinting =
diff --git a/pretyping/clenv.ml b/pretyping/clenv.ml
index 03f84809..8dfec2be 100644
--- a/pretyping/clenv.ml
+++ b/pretyping/clenv.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: clenv.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: clenv.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -377,11 +377,11 @@ let check_bindings bl =
     | NamedHyp s :: _ -> 
 	errorlabstrm ""
 	  (str "The variable " ++ pr_id s ++ 
-	   str " occurs more than once in binding list");
+	   str " occurs more than once in binding list.");
     | AnonHyp n :: _ ->
 	errorlabstrm ""
 	  (str "The position " ++ int n ++
-	   str " occurs more than once in binding list")
+	   str " occurs more than once in binding list.")
     | [] -> ()
 
 let meta_of_binder clause loc mvs = function
@@ -389,17 +389,17 @@ let meta_of_binder clause loc mvs = function
   | AnonHyp n ->
       try List.nth mvs (n-1)
       with (Failure _|Invalid_argument _) ->
-        errorlabstrm "" (str "No such binder")
+        errorlabstrm "" (str "No such binder.")
 
 let error_already_defined b =
   match b with
     | NamedHyp id ->
         errorlabstrm ""
           (str "Binder name \"" ++ pr_id id ++
-           str"\" already defined with incompatible value")
+           str"\" already defined with incompatible value.")
     | AnonHyp n ->
         anomalylabstrm ""
-          (str "Position " ++ int n ++ str" already defined")
+          (str "Position " ++ int n ++ str" already defined.")
 
 let clenv_unify_binding_type clenv c t u =
   if isMeta (fst (whd_stack u)) then
@@ -440,7 +440,7 @@ let clenv_constrain_last_binding c clenv =
   let all_mvs = collect_metas clenv.templval.rebus in
   let k =
     try list_last all_mvs 
-    with Failure _ -> error "clenv_constrain_with_bindings" in
+    with Failure _ -> anomaly "clenv_constrain_with_bindings" in
   clenv_assign_binding clenv k (Evd.empty,c)
 
 let clenv_constrain_dep_args hyps_only bl clenv =
@@ -451,8 +451,9 @@ let clenv_constrain_dep_args hyps_only bl clenv =
     if List.length occlist = List.length bl then
       List.fold_left2 clenv_assign_binding clenv occlist bl
     else 
-      error ("Not the right number of missing arguments (expected "
-	     ^(string_of_int (List.length occlist))^")")
+      errorlabstrm "" 
+	(strbrk "Not the right number of missing arguments (expected " ++
+	 int (List.length occlist) ++ str ").")
 
 (****************************************************************)
 (* Clausal environment for an application *)
diff --git a/pretyping/coercion.ml b/pretyping/coercion.ml
index 3c37a49f..3074c4c4 100644
--- a/pretyping/coercion.ml
+++ b/pretyping/coercion.ml
@@ -5,7 +5,7 @@
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
-(* $Id: coercion.ml 10883 2008-05-05 13:55:24Z herbelin $ *)
+(* $Id: coercion.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -43,6 +43,10 @@ module type S = sig
   val inh_coerce_to_base : loc ->
     env -> evar_defs -> unsafe_judgment -> evar_defs * unsafe_judgment
     
+  (* [inh_coerce_to_prod env isevars t] coerces [t] to a product type *)
+  val inh_coerce_to_prod : loc ->
+    env -> evar_defs -> type_constraint_type -> evar_defs * type_constraint_type
+
   (* [inh_conv_coerce_to loc env evd j t] coerces [j] to an object of type 
      [t]; i.e. it inserts a coercion into [j], if needed, in such a way [t] and
      [j.uj_type] are convertible; it fails if no coercion is applicable *)
@@ -160,6 +164,8 @@ module Default = struct
 
   let inh_coerce_to_base loc env evd j = (evd, j)
 
+  let inh_coerce_to_prod loc env evd t = (evd, t)
+
   let inh_coerce_to_fail env evd rigidonly v t c1 =
     if rigidonly & not (Heads.is_rigid env c1 && Heads.is_rigid env t)
     then
diff --git a/pretyping/coercion.mli b/pretyping/coercion.mli
index b1c8e893..8705080f 100644
--- a/pretyping/coercion.mli
+++ b/pretyping/coercion.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: coercion.mli 10840 2008-04-23 21:29:34Z herbelin $ i*)
+(*i $Id: coercion.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Util
@@ -39,6 +39,10 @@ module type S = sig
      type its base type (the notion depends on the coercion system) *)
   val inh_coerce_to_base : loc ->
     env -> evar_defs -> unsafe_judgment -> evar_defs * unsafe_judgment
+
+  (* [inh_coerce_to_prod env isevars t] coerces [t] to a product type *)
+  val inh_coerce_to_prod : loc ->
+    env -> evar_defs -> type_constraint_type -> evar_defs * type_constraint_type
     
   (* [inh_conv_coerce_to loc env isevars j t] coerces [j] to an object of type 
      [t]; i.e. it inserts a coercion into [j], if needed, in such a way [t] and
diff --git a/pretyping/detyping.ml b/pretyping/detyping.ml
index 81bb41ef..73dc5d46 100644
--- a/pretyping/detyping.ml
+++ b/pretyping/detyping.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: detyping.ml 11073 2008-06-08 20:24:51Z herbelin $ *)
+(* $Id: detyping.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -49,14 +49,14 @@ let encode_bool r =
   let (_,lc as x) = encode_inductive r in
   if not (has_two_constructors lc) then
     user_err_loc (loc_of_reference r,"encode_if",
-      str "This type has not exactly two constructors");
+      str "This type has not exactly two constructors.");
   x
 
 let encode_tuple r =
   let (_,lc as x) = encode_inductive r in
   if not (isomorphic_to_tuple lc) then
     user_err_loc (loc_of_reference r,"encode_tuple",
-      str "This type cannot be seen as a tuple type");
+      str "This type cannot be seen as a tuple type.");
   x
 
 module PrintingCasesMake =
diff --git a/pretyping/evarconv.ml b/pretyping/evarconv.ml
index 58951302..323cd06f 100644
--- a/pretyping/evarconv.ml
+++ b/pretyping/evarconv.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: evarconv.ml 11157 2008-06-21 10:45:51Z herbelin $ *)
+(* $Id: evarconv.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -99,21 +99,21 @@ let check_conv_record (t1,l1) (t2,l2) =
 	      lookup_canonical_conversion 
 		(proji, Sort_cs (family_of_sort s)),[]
 	  | _ -> 
-	      let c2 = try global_of_constr t2 with _ -> raise Not_found in
+	      let c2 = global_of_constr t2 in
 		lookup_canonical_conversion (proji, Const_cs c2),l2
       with Not_found -> 
 	lookup_canonical_conversion (proji,Default_cs),[]
     in
-    let { o_DEF = c; o_INJ=n; o_TABS = bs; o_TPARAMS = params; o_TCOMPS = us } 
-	= canon_s in
+    let { o_DEF = c; o_INJ=n; o_TABS = bs; 
+          o_TPARAMS = params; o_NPARAMS = nparams; o_TCOMPS = us } = canon_s in
     let params1, c1, extra_args1 =
-      match list_chop (List.length params) l1 with 
+      match list_chop nparams l1 with 
 	| params1, c1::extra_args1 -> params1, c1, extra_args1
-	| _ -> assert false in
+	| _ -> raise Not_found in
     let us2,extra_args2 = list_chop (List.length us) l2_effective in
     c,bs,(params,params1),(us,us2),(extra_args1,extra_args2),c1,
     (n,applist(t2,l2))
-  with _ -> 
+  with Failure _ | Not_found -> 
     raise Not_found
 
 (* Precondition: one of the terms of the pb is an uninstantiated evar,
@@ -272,33 +272,42 @@ and evar_eqappr_x env evd pbty (term1,l1 as appr1) (term2,l2 as appr2) =
 	ise_try evd [f1; f4]
 
     | MaybeFlexible flex1, MaybeFlexible flex2 ->
-	let f2 i =
-          if flex1 = flex2 then
-            ise_list2 i (fun i -> evar_conv_x env i CONV) l1 l2
-          else (i,false)
-	and f3 i =
+	let f1 i =
+	  if flex1 = flex2 then
+	    ise_list2 i (fun i -> evar_conv_x env i CONV) l1 l2
+	  else
+	     (i,false)
+	and f2 i =
 	  (try conv_record env i
              (try check_conv_record appr1 appr2
 	      with Not_found -> check_conv_record appr2 appr1)
            with Not_found -> (i,false))
-	and f4 i =
+	and f3 i =
           (* heuristic: unfold second argument first, exception made
              if the first argument is a beta-redex (expand a constant
-             only if necessary) *)
-          let val2 =
-            match kind_of_term flex1 with
-                Lambda _ -> None
-              | _ -> eval_flexible_term env flex2 in
-	  match val2 with
+             only if necessary) or the second argument is potentially
+             usable as a canonical projection *)
+	  if isLambda flex1 or is_open_canonical_projection (evars_of i) appr2
+	  then
+	    match eval_flexible_term env flex1 with
+	    | Some v1 ->
+		evar_eqappr_x env i pbty (evar_apprec env i l1 v1) appr2
+	    | None ->
+		match eval_flexible_term env flex2 with
+		| Some v2 ->
+		    evar_eqappr_x env i pbty appr1 (evar_apprec env i l2 v2)
+		| None -> (i,false)
+	  else
+	    match eval_flexible_term env flex2 with
 	    | Some v2 ->
 		evar_eqappr_x env i pbty appr1 (evar_apprec env i l2 v2)
 	    | None ->
 		match eval_flexible_term env flex1 with
-		  | Some v1 ->
-		      evar_eqappr_x env i pbty (evar_apprec env i l1 v1) appr2
-		  | None -> (i,false)
+		| Some v1 ->
+		    evar_eqappr_x env i pbty (evar_apprec env i l1 v1) appr2
+		| None -> (i,false)
 	in 
-	ise_try evd [f2; f3; f4]
+	ise_try evd [f1; f2; f3]
 
     | Flexible ev1, Rigid _ ->
 	if 
@@ -496,7 +505,7 @@ let choose_less_dependent_instance evk evd term args =
   let evi = Evd.find (evars_of evd) evk in
   let subst = make_pure_subst evi args in
   let subst' = List.filter (fun (id,c) -> c = term) subst in
-  if subst' = [] then error "Too complex unification problem" else
+  if subst' = [] then error "Too complex unification problem." else
   Evd.evar_define evk (mkVar (fst (List.hd subst'))) evd
 
 let apply_conversion_problem_heuristic env evd pbty t1 t2 =
@@ -506,12 +515,12 @@ let apply_conversion_problem_heuristic env evd pbty t1 t2 =
   let (term2,l2 as appr2) = decompose_app t2 in
   match kind_of_term term1, kind_of_term term2 with
   | Evar (evk1,args1), (Rel _|Var _) when l1 = [] & l2 = [] ->
-      (* The typical kind of constraint coming from patter-matching return
+      (* The typical kind of constraint coming from pattern-matching return
          type inference *)
       assert (array_for_all (fun a -> a = term2 or isEvar a) args1);
       choose_less_dependent_instance evk1 evd term2 args1, true
   | (Rel _|Var _), Evar (evk2,args2) when l1 = [] & l2 = [] ->
-      (* The typical kind of constraint coming from patter-matching return
+      (* The typical kind of constraint coming from pattern-matching return
          type inference *)
       assert (array_for_all ((=) term1) args2);
       choose_less_dependent_instance evk2 evd term1 args2, true
diff --git a/pretyping/evarutil.ml b/pretyping/evarutil.ml
index fafce268..130e23b8 100644
--- a/pretyping/evarutil.ml
+++ b/pretyping/evarutil.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: evarutil.ml 11127 2008-06-14 15:39:46Z herbelin $ *)
+(* $Id: evarutil.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -374,42 +374,41 @@ let restrict_upon_filter evd evi evk p args =
   else
     evd,evk,args
 
-exception Dependency_error of identifier
+let collect_vars c =
+  let rec collrec acc c =
+    match kind_of_term c with
+    | Var id -> list_add_set id acc
+    | _      -> fold_constr collrec acc c
+  in
+  collrec [] c
 
-module EvkOrd = 
-struct
-  type t = Term.existential_key
-  let compare = Pervasives.compare
-end
+type clear_dependency_error =
+| OccurHypInSimpleClause of identifier option
+| EvarTypingBreak of existential
 
-module EvkSet = Set.Make(EvkOrd)
+exception ClearDependencyError of identifier * clear_dependency_error
 
-let rec check_and_clear_in_constr evdref c ids hist =
+let rec check_and_clear_in_constr evdref err ids c =
   (* returns a new constr where all the evars have been 'cleaned'
      (ie the hypotheses ids have been removed from the contexts of
-     evars *)
+     evars) *)
   let check id' = 
     if List.mem id' ids then
-      raise (Dependency_error id')
+      raise (ClearDependencyError (id',err))
   in 
     match kind_of_term c with
-      | ( Rel _ | Meta _ | Sort _ ) -> c
-
-      | ( Const _ | Ind _ | Construct _ ) -> 
-	  let vars = Environ.vars_of_global (Global.env()) c in
-	    List.iter check vars; c
+      | Var id' ->
+	  check id'; c
 
-      | Var id' ->  
-	  check id'; mkVar id'
+      | ( Const _ | Ind _ | Construct _ ) ->
+          let vars = Environ.vars_of_global (Global.env()) c in
+            List.iter check vars; c
 
       | Evar (evk,l as ev) -> 
 	  if Evd.is_defined_evar !evdref ev then
 	    (* If evk is already defined we replace it by its definition *)
-	    let nc = nf_evar (evars_of !evdref) c in 
-	      (check_and_clear_in_constr evdref nc ids hist)
-	  else if EvkSet.mem evk hist then
-	    (* Loop detection => do nothing *)
-	    c
+	    let nc = whd_evar (evars_of !evdref) c in 
+	      (check_and_clear_in_constr evdref err ids nc)
 	  else 
 	    (* We check for dependencies to elements of ids in the
 	       evar_info corresponding to e and in the instance of
@@ -418,16 +417,32 @@ let rec check_and_clear_in_constr evdref c ids hist =
 	       removed *)
 	    let evi = Evd.find (evars_of !evdref) evk in
 	    let ctxt = Evd.evar_filtered_context evi in
-	    let (nhyps,nargs,rids) = 
+	    let (nhyps,nargs,rids) =
 	      List.fold_right2 
 		(fun (rid,ob,c as h) a (hy,ar,ri) ->
-		  match kind_of_term a with
-		    | Var id -> if List.mem id ids then (hy,ar,id::ri) else (h::hy,a::ar,ri)
-		    | _ -> (h::hy,a::ar,ri)
-		) 	      
+		  (* Check if some id to clear occurs in the instance
+		     a of rid in ev and remember the dependency *)
+		  match 
+		    List.filter (fun id -> List.mem id ids) (collect_vars a)
+		  with
+		  | id :: _ -> (hy,ar,(rid,id)::ri)
+		  | _ ->
+		  (* Check if some rid to clear in the context of ev
+		     has dependencies in another hyp of the context of ev
+		     and transitively remember the dependency *)
+		  match List.filter (fun (id,_) -> occur_var_in_decl (Global.env()) id h) ri with
+		  | rid' :: _ -> (hy,ar,(rid,List.assoc rid ri)::ri)
+		  | _ ->
+		  (* No dependency at all, we can keep this ev's context hyp *)
+		      (h::hy,a::ar,ri))
 		ctxt (Array.to_list l) ([],[],[]) in
-	    (* nconcl must be computed ids (non instanciated hyps) *)
-	    let nconcl = check_and_clear_in_constr evdref (evar_concl evi) rids (EvkSet.add evk hist) in
+	    (* Check if some rid to clear in the context of ev has dependencies
+	       in the type of ev and adjust the source of the dependency *)
+	    let nconcl =
+	      try check_and_clear_in_constr evdref (EvarTypingBreak ev)
+		    (List.map fst rids) (evar_concl evi) 
+	      with ClearDependencyError (rid,err) -> 
+		raise (ClearDependencyError (List.assoc rid rids,err)) in
 
 	    let env = Sign.fold_named_context push_named nhyps ~init:(empty_env) in
 	    let ev'= e_new_evar evdref env ~src:(evar_source evk !evdref) nconcl in
@@ -435,24 +450,19 @@ let rec check_and_clear_in_constr evdref c ids hist =
 	      let (evk',_) = destEvar ev' in
 		mkEvar(evk', Array.of_list nargs)
 
-      | _ -> map_constr (fun c -> check_and_clear_in_constr evdref c ids hist) c
+      | _ -> map_constr (check_and_clear_in_constr evdref err ids) c
 
 let clear_hyps_in_evi evdref hyps concl ids =
-  (* clear_evar_hyps erases hypotheses ids in hyps, checking if some
+  (* clear_hyps_in_evi erases hypotheses ids in hyps, checking if some
      hypothesis does not depend on a element of ids, and erases ids in
      the contexts of the evars occuring in evi *)
-  let nconcl = try check_and_clear_in_constr evdref concl ids EvkSet.empty
-    with Dependency_error id' -> error (string_of_id id' ^ " is used in conclusion") in
-  let (nhyps,_) = 
-    let check_context (id,ob,c) = 
-      try
-	(id,
-	(match ob with 
-	    None -> None
-	  | Some b -> Some (check_and_clear_in_constr evdref b ids EvkSet.empty)),
-	check_and_clear_in_constr evdref c ids EvkSet.empty)
-      with Dependency_error id' -> error (string_of_id id' ^ " is used in hypothesis "
-					   ^ string_of_id id) 
+  let nconcl =
+    check_and_clear_in_constr evdref (OccurHypInSimpleClause None) ids concl in
+  let nhyps = 
+    let check_context (id,ob,c) =
+      let err = OccurHypInSimpleClause (Some id) in
+      (id, Option.map (check_and_clear_in_constr evdref err ids) ob,
+	check_and_clear_in_constr evdref err ids c)
     in
     let check_value vk =
       match !vk with
@@ -469,6 +479,7 @@ let clear_hyps_in_evi evdref hyps concl ids =
   in
   (nhyps,nconcl)
 
+
 (* Expand rels and vars that are bound to other rels or vars so that 
    dependencies in variables are canonically associated to the most ancient
    variable in its family of aliased variables *)
@@ -883,7 +894,7 @@ let rec invert_definition env evd (evk,argsv as ev) rhs =
 and evar_define env (evk,_ as ev) rhs evd =
   try
     let (evd',body) = invert_definition env evd ev rhs in
-    if occur_meta body then error "Meta cannot occur in evar body";
+    if occur_meta body then error "Meta cannot occur in evar body.";
     (* invert_definition may have instantiate some evars of rhs with evk *)
     (* so we recheck acyclicity *)
     if occur_evar evk body then error_occur_check env (evars_of evd) evk body;
@@ -1057,22 +1068,7 @@ let check_evars env initial_sigma evd c =
 	  if not (Evd.mem initial_sigma evk) then
             let (loc,k) = evar_source evk evd in
 	    let evi = nf_evar_info sigma (Evd.find sigma evk) in
-	    let explain =
-	      let f (_,_,t1,t2) =
-		(try head_evar t1 = evk with Failure _ -> false)
-		or (try head_evar t2 = evk with Failure _ -> false) in
-	      let check_several c inst =
-		let _,argsv = destEvar c in
-		let l = List.filter (eq_constr inst) (Array.to_list argsv) in
-		let n = List.length l in
-		(* Maybe should we select one instead of failing ... *)
-		if n >= 2 then Some (SeveralInstancesFound n) else None in
-	      match List.filter f (snd (extract_all_conv_pbs evd)) with
-	      | (_,_,t1,t2)::_ ->
-		  if isEvar t2 then check_several t2 t1 
-		  else check_several t1 t2
-	      | [] -> None
-	    in  error_unsolvable_implicit loc env sigma evi k explain
+	    error_unsolvable_implicit loc env sigma evi k None
       | _ -> iter_constr proc_rec c
   in proc_rec c
 
@@ -1183,11 +1179,12 @@ let split_tycon loc env evd tycon =
 		 if cur = 0 then 
 		   let evd', (x, dom, rng) = real_split c in
 		     evd, (Anonymous, 
-			       Some (Some (init, 0), dom), 
-			       Some (Some (init, 0), rng))
+			  Some (None, dom), 
+			  Some (None, rng))
 		 else
-		   evd, (Anonymous, None, Some (Some (init, pred cur), c)))
-
+		   evd, (Anonymous, None, 
+			Some (if cur = 1 then None,c else Some (init, pred cur), c)))
+	    
 let valcon_of_tycon x = 
   match x with
     | Some (None, t) -> Some t
diff --git a/pretyping/evarutil.mli b/pretyping/evarutil.mli
index c915d4b0..ca446c01 100644
--- a/pretyping/evarutil.mli
+++ b/pretyping/evarutil.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: evarutil.mli 11136 2008-06-18 10:41:34Z herbelin $ i*)
+(*i $Id: evarutil.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Util
@@ -172,7 +172,15 @@ val pr_tycon_type : env -> type_constraint_type -> Pp.std_ppcmds
 val pr_tycon : env -> type_constraint -> Pp.std_ppcmds
 
 
-(**********************************)
-(* Removing hyps in evars'context *)
+(*********************************************************************)
+(* Removing hyps in evars'context;                                   *)
+(* raise OccurHypInSimpleClause if the removal breaks dependencies   *)
+
+type clear_dependency_error =
+| OccurHypInSimpleClause of identifier option
+| EvarTypingBreak of existential
+
+exception ClearDependencyError of identifier * clear_dependency_error
+
 val clear_hyps_in_evi : evar_defs ref -> named_context_val -> types ->
   identifier list -> named_context_val * types
diff --git a/pretyping/evd.ml b/pretyping/evd.ml
index 76a5ff26..bf3cd623 100644
--- a/pretyping/evd.ml
+++ b/pretyping/evd.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: evd.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: evd.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -523,6 +523,8 @@ let pr_sort_constraints (_,sm) = pr_sort_cstrs sm
 
 let meta_list evd = metamap_to_list evd.metas
 
+let find_meta evd mv = Metamap.find mv evd.metas
+
 let undefined_metas evd =
   List.sort Pervasives.compare (map_succeed (function
     | (n,Clval(_,_,typ)) -> failwith ""
@@ -598,13 +600,13 @@ let meta_with_name evd id =
   match mvnodef, mvl with
     | _,[]  -> 
 	errorlabstrm "Evd.meta_with_name"
-          (str"No such bound variable " ++ pr_id id)
+          (str"No such bound variable " ++ pr_id id ++ str".")
     | ([n],_|_,[n]) -> 
 	n
     | _  -> 
 	errorlabstrm "Evd.meta_with_name"
           (str "Binder name \"" ++ pr_id id ++
-           str"\" occurs more than once in clause")
+           strbrk "\" occurs more than once in clause.")
 
 
 let meta_merge evd1 evd2 =
diff --git a/pretyping/evd.mli b/pretyping/evd.mli
index 1acc811b..5810f93d 100644
--- a/pretyping/evd.mli
+++ b/pretyping/evd.mli
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: evd.mli 10883 2008-05-05 13:55:24Z herbelin $ i*)
+(*i $Id: evd.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Util
@@ -100,6 +100,8 @@ val sig_sig : 'a sigma -> evar_map
 (*********************************************************************)
 (* Meta map *)
 
+module Metamap : Map.S with type key = metavariable
+
 module Metaset : Set.S with type elt = metavariable
 
 val meta_exists : (metavariable -> bool) -> Metaset.t -> bool
@@ -197,6 +199,7 @@ val extract_all_conv_pbs : evar_defs -> evar_defs * evar_constraint list
 
 
 (* Metas *)
+val find_meta : evar_defs -> metavariable -> clbinding
 val meta_list : evar_defs -> (metavariable * clbinding) list
 val meta_defined : evar_defs -> metavariable -> bool
 (* [meta_fvalue] raises [Not_found] if meta not in map or [Anomaly] if
diff --git a/pretyping/indrec.ml b/pretyping/indrec.ml
index 2325baec..b4b8f0b8 100644
--- a/pretyping/indrec.ml
+++ b/pretyping/indrec.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: indrec.ml 10410 2007-12-31 13:11:55Z msozeau $ *)
+(* $Id: indrec.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -591,12 +591,10 @@ let lookup_eliminator ind_sp s =
   try constr_of_global (Nametab.locate (make_short_qualid id))
   with Not_found ->
     errorlabstrm "default_elim"
-      (str "Cannot find the elimination combinator " ++
-       pr_id id ++ spc () ++
-       str "The elimination of the inductive definition " ++
-       pr_id id ++ spc () ++ str "on sort " ++ 
-       spc () ++ pr_sort_family s ++
-       str " is probably not allowed")
+      (strbrk "Cannot find the elimination combinator " ++
+       pr_id id ++ strbrk ", the elimination of the inductive definition " ++
+       pr_id id ++ strbrk " on sort " ++ pr_sort_family s ++
+       strbrk " is probably not allowed.")
 
 
 (*  let env = Global.env() in
diff --git a/pretyping/inductiveops.ml b/pretyping/inductiveops.ml
index 0daff713..127cd0f2 100644
--- a/pretyping/inductiveops.ml
+++ b/pretyping/inductiveops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: inductiveops.ml 10114 2007-09-06 07:36:14Z herbelin $ *)
+(* $Id: inductiveops.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -31,6 +31,11 @@ let type_of_constructor env cstr =
   Inductive.lookup_mind_specif env (inductive_of_constructor cstr) in
  Inductive.type_of_constructor cstr specif
 
+(* Return constructor types in user form *)
+let type_of_constructors env ind =
+ let specif = Inductive.lookup_mind_specif env ind in
+  Inductive.type_of_constructors ind specif
+
 (* Return constructor types in normal form *)
 let arities_of_constructors env ind =
  let specif = Inductive.lookup_mind_specif env ind in
@@ -87,7 +92,7 @@ let mis_nf_constructor_type (ind,mib,mip) j =
   and ntypes = mib.mind_ntypes
   and nconstr = Array.length mip.mind_consnames in
   let make_Ik k = mkInd ((fst ind),ntypes-k-1) in 
-  if j > nconstr then error "Not enough constructors in the type";
+  if j > nconstr then error "Not enough constructors in the type.";
   substl (list_tabulate make_Ik ntypes) specif.(j-1)
 
 (* Arity of constructors excluding parameters and local defs *)
diff --git a/pretyping/inductiveops.mli b/pretyping/inductiveops.mli
index 9e370fec..1d24659c 100644
--- a/pretyping/inductiveops.mli
+++ b/pretyping/inductiveops.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: inductiveops.mli 9707 2007-03-15 16:36:15Z herbelin $ i*)
+(*i $Id: inductiveops.mli 11301 2008-08-04 19:41:18Z herbelin $ i*)
 
 open Names
 open Term
@@ -22,6 +22,7 @@ val type_of_inductive    : env -> inductive -> types
 
 (* Return type as quoted by the user *)
 val type_of_constructor  : env -> constructor -> types
+val type_of_constructors : env -> inductive -> types array
 
 (* Return constructor types in normal form *)
 val arities_of_constructors : env -> inductive -> types array
diff --git a/pretyping/matching.ml b/pretyping/matching.ml
index aaa4c3f0..d066a58d 100644
--- a/pretyping/matching.ml
+++ b/pretyping/matching.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: matching.ml 10451 2008-01-18 17:20:28Z barras $ *)
+(* $Id: matching.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (*i*)
 open Util
@@ -85,7 +85,7 @@ let matches_core convert allow_partial_app pat c =
 	    List.map
 	      (function
 		 | PRel n -> n
-		 | _ -> error "Only bound indices allowed in second order pattern matching")
+		 | _ -> error "Only bound indices allowed in second order pattern matching.")
 	      args in
 	  let frels = Intset.elements (free_rels cT) in
 	  if list_subset frels relargs then
@@ -185,7 +185,7 @@ let matches_core convert allow_partial_app pat c =
   in 
   Sort.list (fun (a,_) (b,_) -> a<b) (sorec [] [] pat c)
 
-let matches = matches_core None false
+let matches = matches_core None true
 
 let pmatches = matches_core None true
 
diff --git a/pretyping/pattern.ml b/pretyping/pattern.ml
index 5df5c9fb..057f9d1c 100644
--- a/pretyping/pattern.ml
+++ b/pretyping/pattern.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: pattern.ml 10785 2008-04-13 21:41:54Z herbelin $ *)
+(* $Id: pattern.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -133,7 +133,7 @@ let map_pattern f = map_pattern_with_binders (fun () -> ()) (fun () -> f) ()
 
 let rec instantiate_pattern lvar = function
   | PVar id as x -> (try Lazy.force(List.assoc id lvar) with Not_found -> x)
-  | (PFix _ | PCoFix _) -> error ("Not instantiable pattern")
+  | (PFix _ | PCoFix _) -> error ("Non instantiable pattern.")
   | c -> map_pattern (instantiate_pattern lvar) c
 
 let rec liftn_pattern k n = function
@@ -264,7 +264,7 @@ let rec pat_of_raw metas vars = function
              
   | r ->
       let loc = loc_of_rawconstr r in
-      user_err_loc (loc,"pattern_of_rawconstr", Pp.str "Pattern not supported")
+      user_err_loc (loc,"pattern_of_rawconstr", Pp.str"Non supported pattern.")
 
 and pat_of_raw_branch loc metas vars ind brs i =
   let bri = List.filter
@@ -272,23 +272,23 @@ and pat_of_raw_branch loc metas vars ind brs i =
         (_,_,[PatCstr(_,c,lv,Anonymous)],_) -> snd c = i+1
       | (loc,_,_,_) ->
           user_err_loc (loc,"pattern_of_rawconstr",
-                        Pp.str "Not supported pattern")) brs in
+                        Pp.str "Non supported pattern.")) brs in
   match bri with
     | [(_,_,[PatCstr(_,(indsp,_),lv,_)],br)] ->
 	if ind <> None & ind <> Some indsp then
           user_err_loc (loc,"pattern_of_rawconstr",
-            Pp.str "All constructors must be in the same inductive type");
+            Pp.str "All constructors must be in the same inductive type.");
         let lna =
           List.map
             (function PatVar(_,na) -> na
               | PatCstr(loc,_,_,_) ->
                   user_err_loc (loc,"pattern_of_rawconstr",
-                                Pp.str "Not supported pattern")) lv in
+                                Pp.str "Non supported pattern.")) lv in
         let vars' = List.rev lna @ vars in 
 	List.length lv, rev_it_mkPLambda lna (pat_of_raw metas vars' br)
     | _ -> user_err_loc (loc,"pattern_of_rawconstr",
                          str "No unique branch for " ++ int (i+1) ++
-                         str"-th constructor")
+                         str"-th constructor.")
 
 let pattern_of_rawconstr c =
   let metas = ref [] in
diff --git a/pretyping/pretyping.ml b/pretyping/pretyping.ml
index 5f0999cb..a3246bc8 100644
--- a/pretyping/pretyping.ml
+++ b/pretyping/pretyping.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: pretyping.ml 11047 2008-06-03 23:08:00Z msozeau $ *)
+(* $Id: pretyping.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -66,7 +66,7 @@ let search_guard loc env possible_indexes fixdefs =
 	    try check_fix env fix; raise (Found indexes) 
 	    with TypeError _ -> ())
 	 (list_combinations possible_indexes); 
-       let errmsg = "cannot guess decreasing argument of fix" in 
+       let errmsg = "Cannot guess decreasing argument of fix." in 
        if loc = dummy_loc then error errmsg else 
 	 user_err_loc (loc,"search_guard", Pp.str errmsg)
      with Found indexes -> indexes)
@@ -244,7 +244,7 @@ module Pretyping_F (Coercion : Coercion.S) = struct
     try (* To build a nicer ltac error message *)
       match List.assoc id unbndltacvars with
       | None -> user_err_loc (loc,"",
-	  str "variable " ++ pr_id id ++ str " should be bound to a term")
+	  str "Variable " ++ pr_id id ++ str " should be bound to a term.")
       | Some id0 -> Pretype_errors.error_var_not_found_loc loc id0
     with Not_found ->
       error_var_not_found_loc loc id
@@ -356,7 +356,9 @@ module Pretyping_F (Coercion : Coercion.S) = struct
 		   uj_type = it_mkProd_or_LetIn j.uj_type ctxt })
             ctxtv vdef in
 	evar_type_fixpoint loc env evdref names ftys vdefj;
-	let fixj = match fixkind with
+	let ftys = Array.map (nf_evar (evars_of !evdref)) ftys in
+	let fdefs = Array.map (fun x -> nf_evar (evars_of !evdref) (j_val x)) vdefj in
+ 	let fixj = match fixkind with
 	  | RFix (vn,i) ->
 	      (* First, let's find the guard indexes. *)
 	      (* If recursive argument was not given by user, we try all args.
@@ -370,11 +372,11 @@ module Pretyping_F (Coercion : Coercion.S) = struct
 		   | None -> list_map_i (fun i _ -> i) 0 ctxtv.(i))
 		vn)
 	      in 
-	      let fixdecls = (names,ftys,Array.map j_val vdefj) in 
+	      let fixdecls = (names,ftys,fdefs) in 
 	      let indexes = search_guard loc env possible_indexes fixdecls in 
 	      make_judge (mkFix ((indexes,i),fixdecls)) ftys.(i)
 	  | RCoFix i ->
-	      let cofix = (i,(names,ftys,Array.map j_val vdefj)) in
+	      let cofix = (i,(names,ftys,fdefs)) in
 	      (try check_cofix env cofix with e -> Stdpp.raise_with_loc loc e);
 	      make_judge (mkCoFix cofix) ftys.(i) in
 	inh_conv_coerce_to_tycon loc env evdref fixj tycon
@@ -459,10 +461,10 @@ module Pretyping_F (Coercion : Coercion.S) = struct
 	in
 	let cstrs = get_constructors env indf in
 	  if Array.length cstrs <> 1 then
-            user_err_loc (loc,"",str "Destructing let is only for inductive types with one constructor");
+            user_err_loc (loc,"",str "Destructing let is only for inductive types with one constructor.");
 	  let cs = cstrs.(0) in
 	    if List.length nal <> cs.cs_nargs then
-              user_err_loc (loc,"", str "Destructing let on this type expects " ++ int cs.cs_nargs ++ str " variables");
+              user_err_loc (loc,"", str "Destructing let on this type expects " ++ int cs.cs_nargs ++ str " variables.");
 	    let fsign = List.map2 (fun na (_,c,t) -> (na,c,t))
               (List.rev nal) cs.cs_args in
 	    let env_f = push_rels fsign env in
@@ -525,7 +527,7 @@ module Pretyping_F (Coercion : Coercion.S) = struct
 	let cstrs = get_constructors env indf in 
 	  if Array.length cstrs <> 2 then
             user_err_loc (loc,"",
-			  str "If is only for inductive types with two constructors");
+			  str "If is only for inductive types with two constructors.");
 
 	  let arsgn = 
 	    let arsgn,_ = get_arity env indf in
@@ -613,7 +615,7 @@ module Pretyping_F (Coercion : Coercion.S) = struct
 	    j
 	      (*inh_conv_coerce_to_tycon loc env evdref j tycon*)
 	else
-	  user_err_loc (loc,"pretype",(str "Not a constr tagged Dynamic"))
+	  user_err_loc (loc,"pretype",(str "Not a constr tagged Dynamic."))
 
   (* [pretype_type valcon env evdref lvar c] coerces [c] into a type *)
   and pretype_type valcon env evdref lvar = function
diff --git a/pretyping/rawterm.ml b/pretyping/rawterm.ml
index 62798a45..3726b8df 100644
--- a/pretyping/rawterm.ml
+++ b/pretyping/rawterm.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: rawterm.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: rawterm.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (*i*)
 open Util
@@ -36,7 +36,7 @@ type rawsort = RProp of Term.contents | RType of Univ.universe option
 
 type binder_kind = BProd | BLambda | BLetIn
 
-type binding_kind = Explicit | Implicit
+type binding_kind = Lib.binding_kind = Explicit | Implicit
 
 type quantified_hypothesis = AnonHyp of int | NamedHyp of identifier
 
diff --git a/pretyping/rawterm.mli b/pretyping/rawterm.mli
index 2ba8022f..eecee8b0 100644
--- a/pretyping/rawterm.mli
+++ b/pretyping/rawterm.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: rawterm.mli 11094 2008-06-10 19:35:23Z herbelin $ i*)
+(*i $Id: rawterm.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Util
@@ -40,7 +40,7 @@ type rawsort = RProp of Term.contents | RType of Univ.universe option
 
 type binder_kind = BProd | BLambda | BLetIn
 
-type binding_kind = Explicit | Implicit
+type binding_kind = Lib.binding_kind = Explicit | Implicit
 
 type quantified_hypothesis = AnonHyp of int | NamedHyp of identifier
 
diff --git a/pretyping/recordops.ml b/pretyping/recordops.ml
index bd73740f..06289434 100644
--- a/pretyping/recordops.ml
+++ b/pretyping/recordops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: recordops.ml 10577 2008-02-19 10:18:19Z corbinea $ *)
+(* $Id: recordops.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -109,6 +109,7 @@ that maps the pair (Li,ci) to the following data
     o_DEF = c
     o_TABS = B1...Bk
     o_PARAMS = a1...am
+    o_NARAMS = m
     o_TCOMP = ui1...uir
 
 *)
@@ -118,6 +119,7 @@ type obj_typ = {
   o_INJ : int;      (* position of trivial argument (negative= none) *)
   o_TABS : constr list;    (* ordered *)
   o_TPARAMS : constr list; (* ordered *)
+  o_NPARAMS : int;
   o_TCOMPS : constr list } (* ordered *)
 
 type cs_pattern =
@@ -126,10 +128,11 @@ type cs_pattern =
   | Sort_cs of sorts_family
   | Default_cs
 
-let object_table =
-  (ref [] : ((global_reference * cs_pattern) * obj_typ) list ref)
+let object_table = ref (Refmap.empty : (cs_pattern * obj_typ) list Refmap.t)
 
-let canonical_projections () = !object_table
+let canonical_projections () = 
+  Refmap.fold (fun x -> List.fold_right (fun (y,c) acc -> ((x,y),c)::acc))
+    !object_table []
 
 let keep_true_projections projs kinds =
   map_succeed (function (p,true) -> p | _ -> failwith "")
@@ -177,15 +180,18 @@ let compute_canonical_projections (con,ind) =
 	   | _ -> l)
       [] lps in
   List.map (fun (refi,c,inj,argj) ->
-    (refi,c),{o_DEF=v; o_INJ=inj; o_TABS=lt; o_TPARAMS=params; o_TCOMPS=argj})
+    (refi,c),
+    {o_DEF=v; o_INJ=inj; o_TABS=lt; 
+     o_TPARAMS=params; o_NPARAMS=List.length params; o_TCOMPS=argj})
     comp
 
 let open_canonical_structure i (_,o) =
   if i=1 then
     let lo = compute_canonical_projections o in
-    List.iter (fun (o,_ as x) ->
-      if not (List.mem_assoc o !object_table) then
-	object_table := x :: (!object_table)) lo
+    List.iter (fun ((proj,cs_pat),s) ->
+      let l = try Refmap.find proj !object_table with Not_found -> [] in
+      if not (List.mem_assoc cs_pat l) then
+        object_table := Refmap.add proj ((cs_pat,s)::l) !object_table) lo
 
 let cache_canonical_structure o =
   open_canonical_structure 1 o
@@ -215,7 +221,7 @@ let add_canonical_structure x = Lib.add_anonymous_leaf (inCanonStruc x)
 
 let error_not_structure ref =
   errorlabstrm "object_declare"
-    (Nameops.pr_id (id_of_global ref) ++ str" is not a structure object")
+    (Nameops.pr_id (id_of_global ref) ++ str" is not a structure object.")
 
 let check_and_decompose_canonical_structure ref =
   let sp = match ref with ConstRef sp -> sp | _ -> error_not_structure ref in
@@ -241,7 +247,15 @@ let declare_canonical_structure ref =
 
 let outCanonicalStructure x = fst (outCanonStruct x)
 
-let lookup_canonical_conversion o = List.assoc o !object_table
+let lookup_canonical_conversion (proj,pat) =
+  List.assoc pat (Refmap.find proj !object_table)
+
+let is_open_canonical_projection sigma (c,args) =
+  try 
+    let l = Refmap.find (global_of_constr c) !object_table in
+    let n = (snd (List.hd l)).o_NPARAMS in
+    try isEvar (whd_evar sigma (List.nth args n)) with Failure _ -> false
+  with Not_found -> false
 
 let freeze () =
   !structure_table, !projection_table, !object_table
@@ -251,7 +265,7 @@ let unfreeze (s,p,o) =
 
 let init () =
   structure_table := Indmap.empty; projection_table := Cmap.empty;
-  object_table:=[]
+  object_table := Refmap.empty
 
 let _ = init()
 
diff --git a/pretyping/recordops.mli b/pretyping/recordops.mli
index 7a7d941d..74f6a9ce 100755
--- a/pretyping/recordops.mli
+++ b/pretyping/recordops.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: recordops.mli 10577 2008-02-19 10:18:19Z corbinea $ i*)
+(*i $Id: recordops.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -47,11 +47,14 @@ type obj_typ = {
   o_INJ : int;      (* position of trivial argument *)
   o_TABS : constr list;    (* ordered *)
   o_TPARAMS : constr list; (* ordered *)
+  o_NPARAMS : int;
   o_TCOMPS : constr list } (* ordered *)
 
 val cs_pattern_of_constr : constr -> cs_pattern * int * constr list
  
 val lookup_canonical_conversion : (global_reference * cs_pattern) -> obj_typ
 val declare_canonical_structure : global_reference -> unit
+val is_open_canonical_projection :
+  Evd.evar_map -> (constr * constr list) -> bool
 val canonical_projections : unit -> 
   ((global_reference * cs_pattern) * obj_typ) list
diff --git a/pretyping/reductionops.ml b/pretyping/reductionops.ml
index 6fc30aae..2f507318 100644
--- a/pretyping/reductionops.ml
+++ b/pretyping/reductionops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: reductionops.ml 11010 2008-05-28 15:25:19Z barras $ *)
+(* $Id: reductionops.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -518,9 +518,11 @@ let whd_eta c = app_stack (local_whd_state_gen eta (c,empty_stack))
 (* Replacing defined evars for error messages *)
 let rec whd_evar sigma c =
   match kind_of_term c with
-    | Evar (ev,args)
-        when Evd.mem sigma ev & Evd.is_defined sigma ev ->
-	whd_evar sigma (Evd.existential_value sigma (ev,args))
+    | Evar ev ->
+	let d = 
+	  try Some (Evd.existential_value sigma ev)
+	  with NotInstantiatedEvar | Not_found -> None in
+	(match d with Some c -> whd_evar sigma c | None -> c)
     | Sort s when is_sort_variable sigma s -> whd_sort_variable sigma c
     | _ -> collapse_appl c
 
@@ -773,7 +775,7 @@ let splay_arity env sigma c =
   let l, c = splay_prod env sigma c in
   match kind_of_term c with
     | Sort s -> l,s
-    | _ -> error "not an arity"
+    | _ -> invalid_arg "splay_arity"
 
 let sort_of_arity env c = snd (splay_arity env Evd.empty c)
 
@@ -783,7 +785,7 @@ let decomp_n_prod env sigma n =
       | Prod (n,a,c0) ->
 	  decrec (push_rel (n,None,a) env)
 	    (m-1) (Sign.add_rel_decl (n,None,a) ln) c0
-      | _                      -> error "decomp_n_prod: Not enough products"
+      | _                      -> invalid_arg "decomp_n_prod"
   in 
   decrec env n Sign.empty_rel_context
 
diff --git a/pretyping/reductionops.mli b/pretyping/reductionops.mli
index d48055cf..1ac36b2a 100644
--- a/pretyping/reductionops.mli
+++ b/pretyping/reductionops.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: reductionops.mli 11010 2008-05-28 15:25:19Z barras $ i*)
+(*i $Id: reductionops.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -111,7 +111,6 @@ val whd_betadeltaiota_nolet_stack :  contextual_stack_reduction_function
 val whd_betaetalet_stack : local_stack_reduction_function
 val whd_betalet_stack : local_stack_reduction_function
 
-val whd_state : local_state_reduction_function
 val whd_beta_state : local_state_reduction_function
 val whd_betaiota_state : local_state_reduction_function
 val whd_betaiotazeta_state : local_state_reduction_function
diff --git a/pretyping/tacred.ml b/pretyping/tacred.ml
index 50401502..57fdbb09 100644
--- a/pretyping/tacred.ml
+++ b/pretyping/tacred.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tacred.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: tacred.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -543,7 +543,7 @@ let try_red_product env sigma c =
 
 let red_product env sigma c = 
   try try_red_product env sigma c
-  with Redelimination -> error "Not reducible"
+  with Redelimination -> error "Not reducible."
 
 (*
 (* This old version of hnf uses betadeltaiota instead of itself (resp 
@@ -698,7 +698,7 @@ let unfold env sigma name =
   if is_evaluable env name then
     clos_norm_flags (unfold_red name) env sigma
   else
-    error (string_of_evaluable_ref env name^" is opaque")
+    error (string_of_evaluable_ref env name^" is opaque.")
 
 (* [unfoldoccs : (readable_constraints -> (int list * section_path) -> constr -> constr)]
  * Unfolds the constant name in a term c following a list of occurrences occl.
@@ -709,7 +709,7 @@ let unfoldoccs env sigma ((nowhere_except_in,locs as plocs),name) c =
   else
     let (nbocc,uc) = substlin env name 1 plocs c in
     if nbocc = 1 then 
-      error ((string_of_evaluable_ref env name)^" does not occur");
+      error ((string_of_evaluable_ref env name)^" does not occur.");
     let rest = List.filter (fun o -> o >= nbocc) locs in
     if rest <> [] then error_invalid_occurrence rest;
     nf_betaiota uc
@@ -722,7 +722,7 @@ let unfoldn loccname env sigma c =
 let fold_one_com com env sigma c =
   let rcom =
     try red_product env sigma com
-    with Redelimination -> error "Not reducible" in
+    with Redelimination -> error "Not reducible." in
   (* Reason first on the beta-iota-zeta normal form of the constant as
      unfold produces it, so that the "unfold f; fold f" configuration works
      to refold fix expressions *)
@@ -757,7 +757,7 @@ let compute = cbv_betadeltaiota
 let abstract_scheme env sigma (locc,a) c =
   let ta = Retyping.get_type_of env sigma a in
   let na = named_hd env ta Anonymous in
-  if occur_meta ta then error "cannot find a type for the generalisation";
+  if occur_meta ta then error "Cannot find a type for the generalisation.";
   if occur_meta a then 
     mkLambda (na,ta,c)
   else 
@@ -785,14 +785,14 @@ let reduce_to_ind_gen allow_product env sigma t =
 	  if allow_product then
 	    elimrec (push_rel (n,None,ty) env) t' ((n,None,ty)::l)
 	  else
-	    errorlabstrm "" (str"Not an inductive definition")
+	    errorlabstrm "" (str"Not an inductive definition.")
       | _ ->
 	  (* Last chance: we allow to bypass the Opaque flag (as it
 	     was partially the case between V5.10 and V8.1 *)
 	  let t' = whd_betadeltaiota env sigma t in
 	  match kind_of_term (fst (decompose_app t')) with
 	    | Ind ind-> (ind, it_mkProd_or_LetIn t' l)
-	    | _ -> errorlabstrm "" (str"Not an inductive product")
+	    | _ -> errorlabstrm "" (str"Not an inductive product.")
   in
   elimrec env t []
 
@@ -843,7 +843,7 @@ let reduce_to_ref_gen allow_product env sigma ref t =
     let (mind,t) = reduce_to_ind_gen allow_product env sigma t in
     if IndRef mind <> ref then
       errorlabstrm "" (str "Cannot recognize a statement based on " ++ 
-        Nametab.pr_global_env Idset.empty ref)
+        Nametab.pr_global_env Idset.empty ref ++ str".")
     else
       t
   else
@@ -857,7 +857,7 @@ let reduce_to_ref_gen allow_product env sigma ref t =
 	  else 
 	     errorlabstrm "" 
 	       (str "Cannot recognize an atomic statement based on " ++ 
-	        Nametab.pr_global_env Idset.empty ref)
+	        Nametab.pr_global_env Idset.empty ref ++ str".")
       | _ ->
 	  try 
 	    if global_of_constr c = ref 
@@ -870,7 +870,7 @@ let reduce_to_ref_gen allow_product env sigma ref t =
           with NotStepReducible ->
 	    errorlabstrm ""
 	      (str "Cannot recognize a statement based on " ++ 
-	       Nametab.pr_global_env Idset.empty ref)
+	       Nametab.pr_global_env Idset.empty ref ++ str".")
   in
   elimrec env t []
 
diff --git a/pretyping/termops.ml b/pretyping/termops.ml
index e31024bb..1ce53e88 100644
--- a/pretyping/termops.ml
+++ b/pretyping/termops.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: termops.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: termops.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -639,7 +639,7 @@ let error_invalid_occurrence l =
   let l = list_uniquize (List.sort Pervasives.compare l) in
   errorlabstrm ""
     (str ("Invalid occurrence " ^ plural (List.length l) "number" ^": ") ++ 
-     prlist_with_sep spc int l)
+     prlist_with_sep spc int l ++ str ".")
 
 let subst_term_occ_gen (nowhere_except_in,locs) occ c t =
   let maxocc = List.fold_right max locs 0 in
@@ -817,21 +817,15 @@ let names_of_rel_context env =
 
 (**** Globality of identifiers *)
 
-(* TODO temporary hack!!! *)
 let rec is_imported_modpath = function
-  | MPfile dp -> dp <> (Lib.library_dp ())
-(*  | MPdot (mp,_) -> is_imported_modpath mp *)
-  | _ -> false
+  | MPfile dp -> true
+  | p -> false
 
 let is_imported_ref = function
   | VarRef _ -> false
   | IndRef (kn,_)
-  | ConstructRef ((kn,_),_) 
-(*  | ModTypeRef ln  *) -> 
+  | ConstructRef ((kn,_),_) ->
       let (mp,_,_) = repr_kn kn in is_imported_modpath mp
-(*  | ModRef mp ->
-      is_imported_modpath mp
-*)
   | ConstRef kn ->
       let (mp,_,_) = repr_con kn in is_imported_modpath mp
 
diff --git a/pretyping/termops.mli b/pretyping/termops.mli
index 94aff66f..645b7d72 100644
--- a/pretyping/termops.mli
+++ b/pretyping/termops.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: termops.mli 11166 2008-06-22 13:23:35Z herbelin $ i*)
+(*i $Id: termops.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 open Util
 open Pp
@@ -185,7 +185,7 @@ val mkLambda_or_LetIn_name : env -> constr -> rel_declaration -> constr
 val it_mkProd_or_LetIn_name   : env -> types -> rel_context -> types
 val it_mkLambda_or_LetIn_name : env -> constr -> rel_context -> constr
 
-(* Get the last arg of a constr intended to be nn application *)
+(* Get the last arg of a constr intended to be an application *)
 val last_arg : constr -> constr
 
 (* name contexts *)
diff --git a/pretyping/typeclasses.ml b/pretyping/typeclasses.ml
index a2392033..86168a1f 100644
--- a/pretyping/typeclasses.ml
+++ b/pretyping/typeclasses.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: typeclasses.ml 11143 2008-06-18 15:52:42Z msozeau $ i*)
+(*i $Id: typeclasses.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -35,12 +35,10 @@ type typeclass = {
   cl_impl : global_reference; 
 
   (* Context in which the definitions are typed. Includes both typeclass parameters and superclasses. *)
-  cl_context : ((global_reference * bool) option * named_declaration) list; 
-
-  cl_params: int;
+  cl_context : ((global_reference * bool) option * rel_declaration) list; 
 
   (* Context of definitions and properties on defs, will not be shared *)
-  cl_props : named_context;
+  cl_props : rel_context;
   
   (* The method implementaions as projections. *)
   cl_projs : (identifier * constant) list;
@@ -111,13 +109,13 @@ let gmap_cmap_merge old ne =
     Gmap.fold (fun cl insts acc -> 
       let oldinsts = try Gmap.find cl old with Not_found -> Cmap.empty in
 	Gmap.add cl (cmap_union oldinsts insts) acc)
-      Gmap.empty ne
+      ne Gmap.empty
   in
     Gmap.fold (fun cl insts acc -> 
       if Gmap.mem cl ne' then acc
       else Gmap.add cl insts acc)
-      ne' old
-      
+      old ne'
+
 let add_instance_hint_ref = ref (fun id pri -> assert false)
 let register_add_instance_hint =
   (:=) add_instance_hint_ref
@@ -154,7 +152,7 @@ let subst (_,subst,(cl,m,inst)) =
   let do_subst_projs projs = list_smartmap (fun (x, y) -> (x, do_subst_con y)) projs in
   let subst_class k cl classes = 
     let k = do_subst_gr k in
-    let cl' = { cl with cl_impl = k;
+    let cl' = { cl_impl = k;
 		cl_context = do_subst_ctx cl.cl_context;
 		cl_props = do_subst_named cl.cl_props;
 		cl_projs = do_subst_projs cl.cl_projs; }
@@ -176,8 +174,14 @@ let subst (_,subst,(cl,m,inst)) =
     (classes, m, instances)
 
 let discharge (_,(cl,m,inst)) =
-  let discharge_named (cl, r) =
-    Option.smartmap (fun (gr, b) -> Lib.discharge_global gr, b) cl, r
+  let discharge_context subst rel =
+    let ctx, _ =
+      List.fold_right
+	(fun (gr, (id, b, t)) (ctx, k) -> 
+	  let gr' = Option.map (fun (gr, b) -> Lib.discharge_global gr, b) gr in
+	    ((gr', (id, Option.map (substn_vars k subst) b, substn_vars k subst t)) :: ctx), succ k)
+	rel ([], 0)
+    in ctx
   in
   let abs_context cl =
     match cl.cl_impl with
@@ -190,10 +194,11 @@ let discharge (_,(cl,m,inst)) =
     let cl' =
       if cl_impl' == cl.cl_impl then cl
       else
+	let ctx = abs_context cl in
 	{ cl with cl_impl = cl_impl';
 	  cl_context = 
-	    List.map (fun x -> None, x) (abs_context cl) @	
-	      (list_smartmap discharge_named cl.cl_context);
+	    List.map (fun (na,impl,b,t) -> None, (Name na,b,t)) ctx @
+	      (discharge_context (List.map (fun (na, _, _, _) -> na) ctx) cl.cl_context);
 	  cl_projs = list_smartmap (fun (x, y) -> x, Lib.discharge_con y) cl.cl_projs }
     in Gmap.add cl_impl' cl' acc
   in
@@ -211,7 +216,7 @@ let discharge (_,(cl,m,inst)) =
   let instances = Gmap.fold subst_inst inst Gmap.empty in
     Some (classes, m, instances)
       
-let rebuild (_,(cl,m,inst)) =
+let rebuild (cl,m,inst) =
   let inst = 
     Gmap.map (fun insts -> 
       Cmap.fold (fun k is insts -> 
@@ -277,49 +282,14 @@ let add_instance i =
   add_instance_hint i.is_impl i.is_pri;
   update ()
 
+let all_instances () = 
+  Gmap.fold (fun k v acc -> 
+    Cmap.fold (fun k v acc -> v :: acc) v acc)
+    !instances []
+
 let instances r = 
   let cl = class_info r in instances_of cl
-
-let solve_instanciation_problem = ref (fun _ _ _ _ -> assert false)
-let solve_instanciations_problem = ref (fun _ _ _ _ _ -> assert false)
-
-let resolve_typeclass env ev evi (evd, defined as acc) =
-  try
-    assert(evi.evar_body = Evar_empty);
-    !solve_instanciation_problem env evd ev evi
-  with Exit -> acc
-
-let resolve_one_typeclass env types =
-  try
-    let evi = Evd.make_evar (Environ.named_context_val env) types in
-    let ev = 1 in
-    let evm = Evd.add Evd.empty ev evi in
-    let evd = Evd.create_evar_defs evm in
-    let evd', b = !solve_instanciation_problem env evd ev evi in
-      if b then 
-	let evm' = Evd.evars_of evd' in
-	  match Evd.evar_body (Evd.find evm' ev) with
-	      Evar_empty -> raise Not_found
-	    | Evar_defined c -> c
-      else raise Not_found
-  with Exit -> raise Not_found
-
-let resolve_one_typeclass_evd env evd types =
-  try
-    let ev = Evarutil.e_new_evar evd env types in
-    let (ev,_) = destEvar ev in
-    let evd', b =
-	!solve_instanciation_problem env !evd ev (Evd.find (Evd.evars_of !evd) ev)
-    in
-      evd := evd';
-      if b then 
-	let evm' = Evd.evars_of evd' in
-	  match Evd.evar_body (Evd.find evm' ev) with
-	      Evar_empty -> raise Not_found
-	    | Evar_defined c -> Evarutil.nf_evar evm' c
-      else raise Not_found
-  with Exit -> raise Not_found
-
+    
 let method_typeclass ref = 
   match ref with 
     | ConstRef c -> 
@@ -349,51 +319,6 @@ let is_implicit_arg k =
     | InternalHole -> true
     | _ -> false
 
-let destClassApp c = 
-  match kind_of_term c with
-    | App (ki, args) when isInd ki -> 
-	Some (destInd ki, args)
-    | _ when isInd c -> Some (destInd c, [||])
-    | _ -> None
-
-let is_independent evm ev = 
-  Evd.fold (fun ev' evi indep -> indep && 
-    (ev = ev' || 
-	evi.evar_body <> Evar_empty ||
-	not (Termops.occur_evar ev evi.evar_concl)))
-    evm true
-    
-
-(*   try !solve_instanciations_problem env (Evarutil.nf_evar_defs evd) *)
-(*   with _ -> *)
-(*   let evm = Evd.evars_of evd in *)
-(*   let tc_evars =  *)
-(*     let f ev evi acc = *)
-(*       let (l, k) = Evd.evar_source ev evd in *)
-(* 	if not check || is_implicit_arg k then *)
-(* 	  match destClassApp evi.evar_concl with *)
-(* 	    | Some (i, args) when is_class i ->  *)
-(* 		Evd.add acc ev evi *)
-(* 	    | _ -> acc *)
-(* 	else acc *)
-(*     in Evd.fold f evm Evd.empty *)
-(*   in *)
-(*   let rec sat evars = *)
-(*     let evm = Evd.evars_of evars in *)
-(*     let (evars', progress) =  *)
-(*       Evd.fold  *)
-(* 	(fun ev evi acc ->  *)
-(* 	  if (Evd.mem tc_evars ev || not (Evd.mem evm ev))  *)
-(* 	    && evi.evar_body = Evar_empty then *)
-(* 	    resolve_typeclass env ev evi acc  *)
-(* 	  else acc) *)
-(* 	evm (evars, false)  *)
-(*     in *)
-(*       if not progress then evars' *)
-(*       else *)
-(* 	sat (Evarutil.nf_evar_defs evars') *)
-(*   in sat (Evarutil.nf_evar_defs evd) *)
-  
 let class_of_constr c = 
   let extract_cl c =
     try Some (class_info (global_of_constr c)) with _ -> None
@@ -432,26 +357,26 @@ let mark_unresolvables sigma =
     Evd.add evs ev (mark_unresolvable evi))
     sigma Evd.empty
     
+let rec is_class_type c =
+  match kind_of_term c with
+  | Prod (_, _, t) -> is_class_type t
+  | _ -> class_of_constr c <> None
+
+let is_class_evar evi = 
+  is_class_type evi.Evd.evar_concl
+    
 let has_typeclasses evd =
   Evd.fold (fun ev evi has -> has || 
-    (evi.evar_body = Evar_empty && class_of_constr evi.evar_concl <> None 
-	&& is_resolvable evi))
+    (evi.evar_body = Evar_empty && is_class_evar evi && is_resolvable evi))
     evd false
 
+let solve_instanciations_problem = ref (fun _ _ _ _ _ -> assert false)
+let solve_instanciation_problem = ref (fun _ _ _ -> assert false)
+
 let resolve_typeclasses ?(onlyargs=false) ?(split=true) ?(fail=true) env evd =
   if not (has_typeclasses (Evd.evars_of evd)) then evd
   else
     !solve_instanciations_problem env (Evarutil.nf_evar_defs evd) onlyargs split fail
 
-type substitution = (identifier * constr) list
-
-let substitution_of_named_context isevars env id n subst l = 
-  List.fold_right
-    (fun (na, _, t) subst -> 
-      let t' = replace_vars subst t in
-      let b = Evarutil.e_new_evar isevars env ~src:(dummy_loc, ImplicitArg (VarRef id, (n, Some na))) t' in
-	(na, b) :: subst)
-    l subst
-
-let nf_substitution sigma subst = 
-  List.map (function (na, c) -> na, Reductionops.nf_evar sigma c) subst
+let resolve_one_typeclass env evm t =
+  !solve_instanciation_problem env evm t
diff --git a/pretyping/typeclasses.mli b/pretyping/typeclasses.mli
index a3118053..fdbb78a9 100644
--- a/pretyping/typeclasses.mli
+++ b/pretyping/typeclasses.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: typeclasses.mli 11161 2008-06-21 14:32:47Z msozeau $ i*)
+(*i $Id: typeclasses.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -30,12 +30,10 @@ type typeclass = {
 
   (* Context in which the definitions are typed. Includes both typeclass parameters and superclasses. 
      The boolean indicates if the typeclass argument is a direct superclass. *)
-  cl_context : ((global_reference * bool) option * named_declaration) list; 
-
-  cl_params : int; (* This is the length of the suffix of the context which should be considered explicit parameters. *)
+  cl_context : ((global_reference * bool) option * rel_declaration) list; 
 
   (* Context of definitions and properties on defs, will not be shared *)
-  cl_props : named_context;
+  cl_props : rel_context;
 
   (* The methods implementations of the typeclass as projections. *)
   cl_projs : (identifier * constant) list;
@@ -43,33 +41,32 @@ type typeclass = {
 
 type instance
 
-val instance_impl : instance -> constant
-
-val new_instance : typeclass -> int option -> bool -> constant -> instance
-  
 val instances : global_reference -> instance list
 val typeclasses : unit -> typeclass list
+val all_instances : unit -> instance list
+
 val add_class : typeclass -> unit
-val add_instance : instance -> unit
 
-val register_add_instance_hint : (constant -> int option -> unit) -> unit
-val add_instance_hint : constant -> int option -> unit
+val new_instance : typeclass -> int option -> bool -> constant -> instance
+val add_instance : instance -> unit
 
 val class_info : global_reference -> typeclass (* raises a UserError if not a class *)
-val is_class : global_reference -> bool
+
 val class_of_constr : constr -> typeclass option
 val dest_class_app : constr -> typeclass * constr array (* raises a UserError if not a class *)
 
+val instance_impl : instance -> constant
+
+val is_class : global_reference -> bool
 val is_instance : global_reference -> bool
 val is_method : constant -> bool
 
+val is_implicit_arg : hole_kind -> bool
+
 (* Returns the term and type for the given instance of the parameters and fields
    of the type class. *)
-val instance_constructor : typeclass -> constr list -> constr * types
 
-val resolve_one_typeclass : env -> types -> types (* Raises Not_found *)
-val resolve_one_typeclass_evd : env -> evar_defs ref -> types -> types (* Raises Not_found *)
-val resolve_typeclass : env -> evar -> evar_info -> evar_defs * bool -> evar_defs * bool
+val instance_constructor : typeclass -> constr list -> constr * types
 
 (* Use evar_extra for marking resolvable evars. *)
 val bool_in : bool -> Dyn.t
@@ -78,28 +75,15 @@ val bool_out : Dyn.t -> bool
 val is_resolvable : evar_info -> bool
 val mark_unresolvable : evar_info -> evar_info
 val mark_unresolvables : evar_map -> evar_map
+val is_class_evar : evar_info -> bool
 
-val resolve_typeclasses : ?onlyargs:bool -> ?split:bool -> ?fail:bool -> env -> evar_defs -> evar_defs
-
-val solve_instanciation_problem : (env -> evar_defs -> existential_key -> evar_info -> evar_defs * bool) ref
-val solve_instanciations_problem : (env -> evar_defs -> bool -> bool -> bool -> evar_defs) ref
-
-type substitution = (identifier * constr) list
+val resolve_typeclasses : ?onlyargs:bool -> ?split:bool -> ?fail:bool -> 
+  env -> evar_defs -> evar_defs
+val resolve_one_typeclass : env -> evar_map -> types -> constr
 
-val substitution_of_named_context : 
-  evar_defs ref -> env -> identifier -> int ->
-  substitution -> named_context -> substitution
-
-val nf_substitution : evar_map -> substitution -> substitution
-
-val is_implicit_arg : hole_kind -> bool
-
-(* debug *)
+val register_add_instance_hint : (constant -> int option -> unit) -> unit
+val add_instance_hint : constant -> int option -> unit
 
-(* val subst :  *)
-(*     'a * Mod_subst.substitution * *)
-(*     ((Libnames.global_reference, typeclass) Gmap.t * 'b * *)
-(*      ('c, instance list) Gmap.t) -> *)
-(*     (Libnames.global_reference, typeclass) Gmap.t * 'b * *)
-(*     ('c, instance list) Gmap.t *)
+val solve_instanciations_problem : (env -> evar_defs -> bool -> bool -> bool -> evar_defs) ref
+val solve_instanciation_problem : (env -> evar_map -> types -> constr) ref
 
diff --git a/pretyping/typeclasses_errors.ml b/pretyping/typeclasses_errors.ml
index 9faac94d..8844baab 100644
--- a/pretyping/typeclasses_errors.ml
+++ b/pretyping/typeclasses_errors.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: typeclasses_errors.ml 11150 2008-06-19 11:38:27Z msozeau $ i*)
+(*i $Id: typeclasses_errors.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -29,7 +29,7 @@ type typeclass_error =
     | UnboundMethod of global_reference * identifier located (* Class name, method *)
     | NoInstance of identifier located * constr list
     | UnsatisfiableConstraints of evar_defs * (evar_info * hole_kind) option
-    | MismatchedContextInstance of contexts * constr_expr list * named_context (* found, expected *)
+    | MismatchedContextInstance of contexts * constr_expr list * rel_context (* found, expected *)
 
 exception TypeClassError of env * typeclass_error
 
diff --git a/pretyping/typeclasses_errors.mli b/pretyping/typeclasses_errors.mli
index 6491372f..a79307d0 100644
--- a/pretyping/typeclasses_errors.mli
+++ b/pretyping/typeclasses_errors.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: typeclasses_errors.mli 11105 2008-06-11 13:47:21Z msozeau $ i*)
+(*i $Id: typeclasses_errors.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -29,7 +29,7 @@ type typeclass_error =
     | UnboundMethod of global_reference * identifier located (* Class name, method *)
     | NoInstance of identifier located * constr list
     | UnsatisfiableConstraints of evar_defs * (evar_info * hole_kind) option
-    | MismatchedContextInstance of contexts * constr_expr list * named_context (* found, expected *)
+    | MismatchedContextInstance of contexts * constr_expr list * rel_context (* found, expected *)
 
 exception TypeClassError of env * typeclass_error
 
@@ -41,4 +41,4 @@ val no_instance : env -> identifier located -> constr list -> 'a
 
 val unsatisfiable_constraints : env -> evar_defs -> evar option -> 'a
 
-val mismatched_ctx_inst : env -> contexts -> constr_expr list -> named_context -> 'a
+val mismatched_ctx_inst : env -> contexts -> constr_expr list -> rel_context -> 'a
diff --git a/pretyping/unification.ml b/pretyping/unification.ml
index fc812594..b3c920a2 100644
--- a/pretyping/unification.ml
+++ b/pretyping/unification.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: unification.ml 11157 2008-06-21 10:45:51Z herbelin $ *)
+(* $Id: unification.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -239,9 +239,9 @@ let unify_0_with_initial_metas subst conv_at_top env sigma cv_pb flags m n =
       | Some c ->
 	  unirec_rec curenv pb b substn cM (whd_betaiotazeta (mkApp(c,l2)))
       | None ->
-      error_cannot_unify env sigma (cM,cN)
+      error_cannot_unify curenv sigma (cM,cN)
     else
-      error_cannot_unify env sigma (cM,cN)
+      error_cannot_unify curenv sigma (cM,cN)
 
   in
     if (not(occur_meta m)) &&
diff --git a/proofs/evar_refiner.ml b/proofs/evar_refiner.ml
index 99ab7ef1..d19d81e0 100644
--- a/proofs/evar_refiner.ml
+++ b/proofs/evar_refiner.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: evar_refiner.ml 11047 2008-06-03 23:08:00Z msozeau $ *)
+(* $Id: evar_refiner.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -22,25 +22,28 @@ open Refiner
 
 (* w_tactic pour instantiate *) 
 
-let w_refine ev rawc evd =
-  if Evd.is_defined (evars_of evd) ev then 
+let w_refine evk rawc evd =
+  if Evd.is_defined (evars_of evd) evk then 
     error "Instantiate called on already-defined evar";
-  let e_info = Evd.find (evars_of evd) ev in
+  let e_info = Evd.find (evars_of evd) evk in
   let env = Evd.evar_env e_info in
-  let sigma,typed_c = 
+  let sigma,typed_c =
     try Pretyping.Default.understand_tcc ~resolve_classes:false
       (evars_of evd) env ~expected_type:e_info.evar_concl rawc
-    with _ -> error ("The term is not well-typed in the environment of " ^
-			string_of_existential ev)
+    with _ ->
+      let loc = Rawterm.loc_of_rawconstr rawc in
+      user_err_loc 
+        (loc,"",Pp.str ("Instance is not well-typed in the environment of " ^
+			string_of_existential evk))
   in
-    evar_define ev typed_c (evars_reset_evd sigma evd)
+    evar_define evk typed_c (evars_reset_evd sigma evd)
 
 (* vernac command Existential *)
 
 let instantiate_pf_com n com pfts = 
   let gls = top_goal_of_pftreestate pfts in
   let sigma = gls.sigma in 
-  let (sp,evi) (* as evc *) = 
+  let (evk,evi) = 
     let evl = Evarutil.non_instantiated sigma in
       if (n <= 0) then
 	error "incorrect existential variable index"
@@ -52,5 +55,5 @@ let instantiate_pf_com n com pfts =
   let env = Evd.evar_env evi in
   let rawc = Constrintern.intern_constr sigma env com in 
   let evd = create_goal_evar_defs sigma in
-  let evd' = w_refine sp rawc evd in
+  let evd' = w_refine evk rawc evd in
     change_constraints_pftreestate (evars_of evd') pfts
diff --git a/proofs/logic.ml b/proofs/logic.ml
index 6e78f134..21ee9a9f 100644
--- a/proofs/logic.ml
+++ b/proofs/logic.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: logic.ml 10877 2008-04-30 21:58:41Z herbelin $ *)
+(* $Id: logic.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -27,6 +27,7 @@ open Typeops
 open Type_errors
 open Retyping
 open Evarutil
+open Tacexpr
  
 type refiner_error =
 
@@ -47,13 +48,15 @@ open Pretype_errors
 
 let rec catchable_exception = function
   | Stdpp.Exc_located(_,e) -> catchable_exception e
+  | LtacLocated(_,e) -> catchable_exception e
   | Util.UserError _ | TypeError _ 
   | RefinerError _ | Indrec.RecursionSchemeError _
   | Nametab.GlobalizationError _ | PretypeError (_,VarNotFound _)
   (* unification errors *)
   | PretypeError(_,(CannotUnify _|CannotUnifyLocal _|CannotGeneralize _
 		   |NoOccurrenceFound _|CannotUnifyBindingType _|NotClean _
-		   |CannotFindWellTypedAbstraction _)) -> true
+		   |CannotFindWellTypedAbstraction _
+		   |UnsolvableImplicit _)) -> true
   | _ -> false
 
 (* Tells if the refiner should check that the submitted rules do not
@@ -70,11 +73,10 @@ let with_check = Flags.with_option check
    (instead of iterating on the list of identifier to be removed, which
    forces the user to give them in order). *)
 
-let clear_hyps sigma ids gl =
+let clear_hyps sigma ids sign cl =
   let evdref = ref (Evd.create_goal_evar_defs sigma) in
-  let (hyps,concl) =
-    Evarutil.clear_hyps_in_evi evdref gl.evar_hyps gl.evar_concl ids in
-    (mk_goal hyps concl gl.evar_extra, evars_of !evdref)
+  let (hyps,concl) = Evarutil.clear_hyps_in_evi evdref sign cl ids in
+  (hyps,concl,evars_of !evdref)
 
 (* The ClearBody tactic *)
 
@@ -83,13 +85,13 @@ let clear_hyps sigma ids gl =
 let apply_to_hyp sign id f =
   try apply_to_hyp sign id f 
   with Hyp_not_found -> 
-    if !check then error "No such assumption"
+    if !check then error "No such assumption."
     else sign
 
 let apply_to_hyp_and_dependent_on sign id f g =
   try apply_to_hyp_and_dependent_on sign id f g 
   with Hyp_not_found -> 
-    if !check then error "No such assumption"
+    if !check then error "No such assumption."
     else sign
 
 let check_typability env sigma c =
@@ -109,7 +111,7 @@ let remove_hyp_body env sigma id =
     apply_to_hyp_and_dependent_on (named_context_val env) id
       (fun (_,c,t) _ ->
 	match c with
-	| None -> error ((string_of_id id)^" is not a local definition")
+	| None -> error ((string_of_id id)^" is not a local definition.")
 	| Some c ->(id,None,t))
       (fun (id',c,t as d) sign ->
 	(if !check then
@@ -126,24 +128,42 @@ let remove_hyp_body env sigma id =
 
 (* Auxiliary functions for primitive MOVE tactic
  *
- * [move_after with_dep toleft (left,(hfrom,typfrom),right) hto] moves
- * hyp [hfrom] just after the hyp [hto] which belongs to the hyps on the 
+ * [move_hyp with_dep toleft (left,(hfrom,typfrom),right) hto] moves
+ * hyp [hfrom] at location [hto] which belongs to the hyps on the 
  * left side [left] of the full signature if [toleft=true] or to the hyps 
  * on the right side [right] if [toleft=false].
  * If [with_dep] then dependent hypotheses are moved accordingly. *)
 
+let error_no_such_hypothesis id =
+  error ("No such hypothesis: " ^ string_of_id id ^ ".")
+
+let rec get_hyp_after h = function
+  | [] -> error_no_such_hypothesis h
+  | (hyp,_,_) :: right ->
+      if hyp = h then
+	match right with (id,_,_)::_ -> MoveBefore id | [] -> MoveToEnd false
+      else
+       get_hyp_after h right
+
 let split_sign hfrom hto l =
   let rec splitrec left toleft = function
-    | [] -> error ("No such hypothesis : " ^ (string_of_id hfrom))
+    | [] -> error_no_such_hypothesis hfrom
     | (hyp,c,typ) as d :: right ->
       	if hyp = hfrom then 
-	  (left,right,d,toleft) 
-      	else 
-	  splitrec (d::left) (toleft or (hyp = hto)) right
+	  (left,right,d, toleft or hto = MoveToEnd true)
+      	else
+	  splitrec (d::left) 
+	    (toleft or hto = MoveAfter hyp or hto = MoveBefore hyp)
+	    right
   in 
     splitrec [] false l
 
-let move_after with_dep toleft (left,(idfrom,_,_ as declfrom),right) hto =
+let hyp_of_move_location = function
+  | MoveAfter id -> id 
+  | MoveBefore id -> id
+  | _ -> assert false
+
+let move_hyp with_dep toleft (left,(idfrom,_,_ as declfrom),right) hto =
   let env = Global.env() in
   let test_dep (hyp,c,typ as d) (hyp2,c,typ2 as d2) =
     if toleft
@@ -151,23 +171,27 @@ let move_after with_dep toleft (left,(idfrom,_,_ as declfrom),right) hto =
     else occur_var_in_decl env hyp d2
   in
   let rec moverec first middle = function
-    | [] -> error ("No such hypothesis : " ^ (string_of_id hto))
+    | [] ->
+	if match hto with MoveToEnd _ -> false | _ -> true then
+	  error_no_such_hypothesis (hyp_of_move_location hto);
+	List.rev first @ List.rev middle
+    | (hyp,_,_) :: _ as right when hto = MoveBefore hyp ->
+	List.rev first @ List.rev middle @ right
     | (hyp,_,_) as d :: right ->
 	let (first',middle') =
       	  if List.exists (test_dep d) middle then 
-	    if with_dep & (hyp <> hto) then 
+	    if with_dep & hto <> MoveAfter hyp then 
 	      (first, d::middle)
             else 
-	      error 
-		("Cannot move "^(string_of_id idfrom)^" after "
-		 ^(string_of_id hto)
-		 ^(if toleft then ": it occurs in " else ": it depends on ")
-		 ^(string_of_id hyp))
-          else 
+	      errorlabstrm "" (str "Cannot move " ++ pr_id idfrom ++
+	        pr_move_location pr_id hto ++ 
+	        str (if toleft then ": it occurs in " else ": it depends on ")
+	        ++ pr_id hyp ++ str ".")
+          else
 	    (d::first, middle)
 	in
-      	if hyp = hto then 
-	  (List.rev first')@(List.rev middle')@right
+      	if hto = MoveAfter hyp then
+	  List.rev first' @ List.rev middle' @ right
       	else 
 	  moverec first' middle' right
   in
@@ -183,53 +207,11 @@ let move_after with_dep toleft (left,(idfrom,_,_ as declfrom),right) hto =
     List.fold_left (fun sign d -> push_named_context_val d sign)
       right left
 
-let check_backward_dependencies sign d =
-  if not (Idset.for_all
-	    (fun id -> mem_named_context id sign)
-	    (global_vars_set_of_decl (Global.env()) d))
-  then
-    error "Can't introduce at that location: free variable conflict"
-
-
-let check_forward_dependencies id tail =
-  let env = Global.env() in
-  List.iter
-    (function (id',_,_ as decl) ->
-       if occur_var_in_decl env id decl then
-	 error ((string_of_id id) ^ " is used in hypothesis " 
-		^ (string_of_id id')))
-    tail
-
-let check_goal_dependency id cl =
-  let env = Global.env() in
-    if Idset.mem id (global_vars_set env cl) then
-      error (string_of_id id^" is used in conclusion")
-
 let rename_hyp id1 id2 sign =
   apply_to_hyp_and_dependent_on sign id1
     (fun (_,b,t) _ -> (id2,b,t))
     (fun d _ -> map_named_declaration (replace_vars [id1,mkVar id2]) d)
 
-let replace_hyp sign id d cl =
-  if !check then
-    check_goal_dependency id cl;
-  apply_to_hyp sign id
-    (fun sign _ tail ->
-      if !check then
-	(check_backward_dependencies sign d;
-	 check_forward_dependencies id tail); 
-      d)
-
-(* why we dont check that id does not appear in tail ??? *)
-let insert_after_hyp sign id d =
-  try 
-    insert_after_hyp sign id d 
-      (fun sign ->
-	if !check then check_backward_dependencies sign d)
-  with Hyp_not_found ->
-    if !check then error "No such assumption"
-    else sign
-
 (************************************************************************)
 (************************************************************************)
 (* Implementation of the logical rules *)
@@ -375,19 +357,14 @@ and mk_casegoals sigma goal goalacc p c =
   (acc'',lbrty,conclty)
 
 
-let error_use_instantiate () =
-  errorlabstrm "Logic.prim_refiner"
-    (str"cannot intro when there are open metavars in the domain type" ++
-       spc () ++ str"- use Instantiate")
-
 let convert_hyp sign sigma (id,b,bt as d) =
   apply_to_hyp sign id
     (fun _ (_,c,ct) _ ->
        let env = Global.env_of_context sign in
        if !check && not (is_conv env sigma bt ct) then
-	 error ("Incorrect change of the type of "^(string_of_id id));
+	 error ("Incorrect change of the type of "^(string_of_id id)^".");
        if !check && not (Option.Misc.compare (is_conv env sigma) b c) then
-	 error ("Incorrect change of the body of "^(string_of_id id));
+	 error ("Incorrect change of the body of "^(string_of_id id)^".");
        d)
 
 (* Normalizing evars in a goal. Called by tactic Local_constraints
@@ -420,12 +397,10 @@ let prim_refiner r sigma goal =
 	  error "New variable is already declared";
         (match kind_of_term (strip_outer_cast cl) with
 	   | Prod (_,c1,b) ->
-	       if occur_meta c1 then error_use_instantiate();
 	       let sg = mk_goal (push_named_context_val (id,None,c1) sign)
 			  (subst1 (mkVar id) b) in
 	       ([sg], sigma)
 	   | LetIn (_,c1,t1,b) ->
-	       if occur_meta c1 or occur_meta t1 then error_use_instantiate();
 	       let sg =
 		 mk_goal (push_named_context_val (id,Some c1,t1) sign)
 		   (subst1 (mkVar id) b) in
@@ -433,28 +408,19 @@ let prim_refiner r sigma goal =
 	   | _ ->
 	       raise (RefinerError IntroNeedsProduct))
 	
-    | Intro_replacing id ->
-	(match kind_of_term (strip_outer_cast cl) with
-           | Prod (_,c1,b) ->
-	       if occur_meta c1 then error_use_instantiate();
-	       let sign' = replace_hyp sign id (id,None,c1) cl in
-	       let sg = mk_goal sign' (subst1 (mkVar id) b) in
-	       ([sg], sigma)
-           | LetIn (_,c1,t1,b) ->
-	       if occur_meta c1 then error_use_instantiate();
-	       let sign' = replace_hyp sign id (id,Some c1,t1) cl in
-	       let sg = mk_goal sign' (subst1 (mkVar id) b) in
-	       ([sg], sigma)
-	   | _ ->
-	       raise (RefinerError IntroNeedsProduct))
-	
-    | Cut (b,id,t) ->
-    	if !check && mem_named_context id (named_context_of_val sign) then
-	  error "New variable is already declared";
-        if occur_meta t then error_use_instantiate();
+    | Cut (b,replace,id,t) ->
         let sg1 = mk_goal sign (nf_betaiota t) in
-        let sg2 = mk_goal (push_named_context_val (id,None,t) sign) cl in
-        if b then ([sg1;sg2],sigma) else ([sg2;sg1], sigma)
+	let sign,cl,sigma =
+	  if replace then
+	    let nexthyp = get_hyp_after id (named_context_of_val sign) in
+	    let sign,cl,sigma = clear_hyps sigma [id] sign cl in
+	    move_hyp true false ([],(id,None,t),named_context_of_val sign)
+	      nexthyp,
+	      cl,sigma
+	  else
+	    (push_named_context_val (id,None,t) sign),cl,sigma in
+        let sg2 = mk_goal sign cl in
+        if b then ([sg1;sg2],sigma) else ([sg2;sg1],sigma)
 
     | FixRule (f,n,rest) ->
      	let rec check_ind env k cl = 
@@ -464,10 +430,10 @@ let prim_refiner r sigma goal =
 		  try 
 		    fst (find_inductive env sigma c1)
 		  with Not_found -> 
-		    error "cannot do a fixpoint on a non inductive type"
+		    error "Cannot do a fixpoint on a non inductive type."
             	else 
 		  check_ind (push_rel (na,None,c1) env) (k-1) b
-            | _ -> error "not enough products"
+            | _ -> error "Not enough products."
 	in
 	let (sp,_) = check_ind env n cl in
 	let all = (f,n,cl)::rest in
@@ -475,10 +441,10 @@ let prim_refiner r sigma goal =
 	  | (f,n,ar)::oth ->
 	      let (sp',_)  = check_ind env n ar in 
 	      if not (sp=sp') then 
-		error ("fixpoints should be on the same " ^ 
-		       "mutual inductive declaration");
+		error ("Fixpoints should be on the same " ^ 
+		       "mutual inductive declaration.");
 	      if !check && mem_named_context f (named_context_of_val sign) then
-		error "name already used in the environment";
+		error "Name already used in the environment";
 	      mk_sign (push_named_context_val (f,None,ar) sign) oth
 	  | [] -> 
 	      List.map (fun (_,_,c) -> mk_goal sign c) all
@@ -495,8 +461,7 @@ let prim_refiner r sigma goal =
 		  let _ = find_coinductive env sigma b in ()
                 with Not_found -> 
 		  error ("All methods must construct elements " ^
-			  "in coinductiv-> goal
-e types")
+			  "in coinductive types.")
 	in
 	let all = (f,cl)::others in
      	List.iter (fun (_,c) -> check_is_coind env c) all;
@@ -504,7 +469,7 @@ e types")
           | (f,ar)::oth ->
 	      (try
                 (let _ = lookup_named_val f sign in
-                error "name already used in the environment")
+                error "Name already used in the environment.")
               with
               |	Not_found ->
                   mk_sign (push_named_context_val (f,None,ar) sign) oth)
@@ -533,8 +498,8 @@ e types")
 
     (* And now the structural rules *)
     | Thin ids -> 
-	let (ngl, nsigma) = clear_hyps sigma ids goal in
-	  ([ngl], nsigma)
+	let (hyps,concl,nsigma) = clear_hyps sigma ids sign cl in
+	  ([mk_goal hyps concl], nsigma)
 	
     | ThinBody ids ->
 	let clear_aux env id =
@@ -550,13 +515,13 @@ e types")
   	let (left,right,declfrom,toleft) = 
 	  split_sign hfrom hto (named_context_of_val sign) in
   	let hyps' = 
-	  move_after withdep toleft (left,declfrom,right) hto in
+	  move_hyp withdep toleft (left,declfrom,right) hto in
   	  ([mk_goal hyps' cl], sigma)
 
     | Rename (id1,id2) ->
         if !check & id1 <> id2 &&
 	  List.mem id2 (ids_of_named_context (named_context_of_val sign)) then
-          error ((string_of_id id2)^" is already used");
+          error ((string_of_id id2)^" is already used.");
         let sign' = rename_hyp id1 id2 sign in
         let cl' = replace_vars [id1,mkVar id2] cl in
           ([mk_goal sign' cl'], sigma)
@@ -617,20 +582,9 @@ let prim_extractor subfun vl pft =
 		let cb = subst_proof_vars vl b in
 		let cty = subst_proof_vars vl ty in
 		  mkLetIn (Name id, cb, cty, subfun (add_proof_var id vl) spf)
-	    | _ -> error "incomplete proof!")
+	    | _ -> error "Incomplete proof!")
 	    
-      | Some (Prim (Intro_replacing id),[spf]) ->
-	  (match kind_of_term (strip_outer_cast cl) with
-	    | Prod (_,ty,_) ->
-		let cty = subst_proof_vars vl ty in
-		  mkLambda (Name id, cty, subfun (add_proof_var id vl) spf)
-	    | LetIn (_,b,ty,_) ->
-		let cb = subst_proof_vars vl b in
-		let cty = subst_proof_vars vl ty in
-		  mkLetIn (Name id, cb, cty, subfun (add_proof_var id vl) spf)
-	    | _ -> error "incomplete proof!")
-
-      | Some (Prim (Cut (b,id,t)),[spf1;spf2]) ->
+      | Some (Prim (Cut (b,_,id,t)),[spf1;spf2]) ->
           let spf1, spf2 = if b then spf1, spf2 else spf2, spf1 in
 	    mkLetIn (Name id,subfun vl spf1,subst_proof_vars vl t,
                     subfun (add_proof_var id vl) spf2)
diff --git a/proofs/proof_type.ml b/proofs/proof_type.ml
index dbe40780..41935c9c 100644
--- a/proofs/proof_type.ml
+++ b/proofs/proof_type.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: proof_type.ml 9842 2007-05-20 17:44:23Z herbelin $ *)
+(*i $Id: proof_type.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (*i*)
 open Environ
@@ -28,8 +28,7 @@ open Pattern
 
 type prim_rule =
   | Intro of identifier
-  | Intro_replacing of identifier
-  | Cut of bool * identifier * types
+  | Cut of bool * bool * identifier * types
   | FixRule of identifier * int * (identifier * int * constr) list
   | Cofix of identifier * (identifier * constr) list
   | Refine of constr
@@ -37,7 +36,7 @@ type prim_rule =
   | Convert_hyp of named_declaration
   | Thin of identifier list
   | ThinBody of identifier list
-  | Move of bool * identifier * identifier
+  | Move of bool * identifier * identifier move_location
   | Rename of identifier * identifier
   | Change_evars
 
@@ -94,3 +93,16 @@ and tactic_arg =
 
 type hyp_location = identifier Tacexpr.raw_hyp_location
 
+type ltac_call_kind = 
+  | LtacNotationCall of string
+  | LtacNameCall of ltac_constant
+  | LtacAtomCall of glob_atomic_tactic_expr * atomic_tactic_expr option ref
+  | LtacVarCall of identifier * glob_tactic_expr
+  | LtacConstrInterp of rawconstr *
+      ((identifier * constr) list * (identifier * identifier option) list)
+
+type ltac_trace = (loc * ltac_call_kind) list
+
+exception LtacLocated of (ltac_call_kind * ltac_trace * loc) * exn
+
+let abstract_tactic_box = ref (ref None)
diff --git a/proofs/proof_type.mli b/proofs/proof_type.mli
index 4fbcda4c..a7057a7d 100644
--- a/proofs/proof_type.mli
+++ b/proofs/proof_type.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: proof_type.mli 9842 2007-05-20 17:44:23Z herbelin $ i*)
+(*i $Id: proof_type.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Environ
@@ -28,8 +28,7 @@ open Pattern
 
 type prim_rule =
   | Intro of identifier
-  | Intro_replacing of identifier
-  | Cut of bool * identifier * types
+  | Cut of bool * bool * identifier * types
   | FixRule of identifier * int * (identifier * int * constr) list
   | Cofix of identifier * (identifier * constr) list
   | Refine of constr
@@ -37,7 +36,7 @@ type prim_rule =
   | Convert_hyp of named_declaration
   | Thin of identifier list
   | ThinBody of identifier list
-  | Move of bool * identifier * identifier
+  | Move of bool * identifier * identifier move_location
   | Rename of identifier * identifier
   | Change_evars
 
@@ -128,3 +127,17 @@ and tactic_arg =
      Tacexpr.gen_tactic_arg
 
 type hyp_location = identifier Tacexpr.raw_hyp_location
+
+type ltac_call_kind = 
+  | LtacNotationCall of string
+  | LtacNameCall of ltac_constant
+  | LtacAtomCall of glob_atomic_tactic_expr * atomic_tactic_expr option ref
+  | LtacVarCall of identifier * glob_tactic_expr
+  | LtacConstrInterp of rawconstr *
+      ((identifier * constr) list * (identifier * identifier option) list)
+
+type ltac_trace = (loc * ltac_call_kind) list
+
+exception LtacLocated of (ltac_call_kind * ltac_trace * loc) * exn
+
+val abstract_tactic_box : atomic_tactic_expr option ref ref
diff --git a/proofs/refiner.ml b/proofs/refiner.ml
index 172a7d70..6e08e741 100644
--- a/proofs/refiner.ml
+++ b/proofs/refiner.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: refiner.ml 11021 2008-05-29 16:48:18Z barras $ *)
+(* $Id: refiner.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -189,7 +189,6 @@ let leaf g =
 let check_subproof_connection gl spfl =
   list_for_all2eq (fun g pf -> Evd.eq_evar_info g pf.goal) gl spfl
 
-
 let abstract_operation syntax semantics gls =
   let (sgl_sigma,validation) = semantics gls in
   let hidden_proof = validation (List.map leaf sgl_sigma.it) in
@@ -204,6 +203,7 @@ let abstract_tactic_expr ?(dflt=false) te tacfun gls =
   abstract_operation (Tactic(te,dflt)) tacfun gls	
 
 let abstract_tactic ?(dflt=false) te =
+  !abstract_tactic_box := Some te;
   abstract_tactic_expr ~dflt (Tacexpr.TacAtom (dummy_loc,te))
 
 let abstract_extended_tactic ?(dflt=false) s args = 
@@ -491,13 +491,18 @@ let tclNOTSAMEGOAL (tac : tactic) goal =
       (str"Tactic generated a subgoal identical to the original goal.")
   else rslt
 
-let catch_failerror = function
-  | e when catchable_exception e -> check_for_interrupt ()
-  | FailError (0,_) | Stdpp.Exc_located(_, FailError (0,_)) ->
+let catch_failerror e =
+  if catchable_exception e then check_for_interrupt ()
+  else match e with
+  | FailError (0,_) | Stdpp.Exc_located(_, FailError (0,_)) 
+  | Stdpp.Exc_located(_, LtacLocated (_,FailError (0,_)))  ->
       check_for_interrupt ()
   | FailError (lvl,s) -> raise (FailError (lvl - 1, s))
-  | Stdpp.Exc_located (s,FailError (lvl,s')) ->
-      raise (Stdpp.Exc_located (s,FailError (lvl - 1, s')))
+  | Stdpp.Exc_located(s,FailError (lvl,s')) ->
+      raise (Stdpp.Exc_located(s,FailError (lvl - 1, s')))
+  | Stdpp.Exc_located(s,LtacLocated (s'',FailError (lvl,s')))  ->
+      raise
+       (Stdpp.Exc_located(s,LtacLocated (s'',FailError (lvl - 1,s'))))
   | e -> raise e
 
 (* ORELSE0 t1 t2 tries to apply t1 and if it fails, applies t2 *)
@@ -548,14 +553,8 @@ let ite_gen tcal tac_if continue tac_else gl=
     try 
       tcal tac_if0 continue gl
     with (* Breakpoint *)
-      | e when catchable_exception e ->
-	  check_for_interrupt (); tac_else0 e gl
-      | (FailError (0,_) | Stdpp.Exc_located(_, FailError (0,_))) as e ->
-	  check_for_interrupt (); tac_else0 e gl
-      | FailError (lvl,s) -> raise (FailError (lvl - 1, s))
-      | Stdpp.Exc_located (s,FailError (lvl,s')) ->
-	  raise (Stdpp.Exc_located (s,FailError (lvl - 1, s')))
-	
+      | e -> catch_failerror e; tac_else0 e gl
+
 (* Try the first tactic and, if it succeeds, continue with 
    the second one, and if it fails, use the third one *)
 
@@ -754,9 +753,7 @@ let extract_open_pftreestate pts =
 
 let extract_pftreestate pts =
   if pts.tstack <> [] then
-    errorlabstrm "extract_pftreestate"
-      (str"Cannot extract from a proof-tree in which we have descended;" ++
-         spc () ++ str"Please ascend to the root");
+    errorlabstrm "extract_pftreestate" (str"Proof blocks need to be closed");
   let pfterm,subgoals = extract_open_pftreestate pts in
   let exl = Evarutil.non_instantiated pts.tpfsigma in
   if subgoals <> [] or exl <> [] then
diff --git a/proofs/tacexpr.ml b/proofs/tacexpr.ml
index d0789980..8e51171f 100644
--- a/proofs/tacexpr.ml
+++ b/proofs/tacexpr.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tacexpr.ml 11100 2008-06-11 11:10:31Z herbelin $ i*)
+(*i $Id: tacexpr.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Names
 open Topconstr
@@ -65,6 +65,20 @@ type hyp_location_flag = (* To distinguish body and type of local defs *)
 
 type 'a raw_hyp_location = 'a with_occurrences * hyp_location_flag
 
+type 'id move_location =
+  | MoveAfter of 'id
+  | MoveBefore of 'id
+  | MoveToEnd of bool
+
+let no_move = MoveToEnd true
+
+open Pp
+
+let pr_move_location pr_id = function
+  | MoveAfter id -> brk(1,1) ++ str "after " ++ pr_id id
+  | MoveBefore id -> brk(1,1) ++ str "before " ++ pr_id id
+  | MoveToEnd toleft -> str (if toleft then " at bottom" else " at top")
+
 type 'a induction_arg =
   | ElimOnConstr of 'a
   | ElimOnIdent of identifier located
@@ -76,8 +90,10 @@ type inversion_kind =
   | FullInversionClear
 
 type ('c,'id) inversion_strength =
-  | NonDepInversion of inversion_kind * 'id list * intro_pattern_expr
-  | DepInversion of inversion_kind * 'c option * intro_pattern_expr
+  | NonDepInversion of 
+      inversion_kind * 'id list * intro_pattern_expr located option
+  | DepInversion of
+      inversion_kind * 'c option * intro_pattern_expr located option
   | InversionUsing of 'c * 'id list
 
 type ('a,'b) location = HypLocation of 'a | ConclLocation of 'b
@@ -106,6 +122,11 @@ let simple_clause_of = function
 | _ ->
     error "not a simple clause (one hypothesis or conclusion)"
 
+type ('constr,'id) induction_clause = 
+    ('constr with_bindings induction_arg list * 'constr with_bindings option * 
+     (intro_pattern_expr located option * intro_pattern_expr located option) *
+     'id gclause option)
+
 type multi = 
   | Precisely of int
   | UpTo of int
@@ -130,14 +151,14 @@ type ('a,'t) match_rule =
 
 type ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_atomic_tactic_expr =
   (* Basic tactics *)
-  | TacIntroPattern of intro_pattern_expr list
+  | TacIntroPattern of intro_pattern_expr located list
   | TacIntrosUntil of quantified_hypothesis
-  | TacIntroMove of identifier option * identifier located option
+  | TacIntroMove of identifier option * 'id move_location
   | TacAssumption
   | TacExact of 'constr
   | TacExactNoCheck of 'constr
   | TacVmCastNoCheck of 'constr
-  | TacApply of advanced_flag * evars_flag * 'constr with_bindings
+  | TacApply of advanced_flag * evars_flag * 'constr with_bindings list
   | TacElim of evars_flag * 'constr with_bindings * 
       'constr with_bindings option
   | TacElimType of 'constr
@@ -149,19 +170,14 @@ type ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_atomic_tactic_expr =
   | TacCofix of identifier option
   | TacMutualCofix of hidden_flag * identifier * (identifier * 'constr) list
   | TacCut of 'constr
-  | TacAssert of 'tac option * intro_pattern_expr * 'constr
+  | TacAssert of 'tac option * intro_pattern_expr located * 'constr
   | TacGeneralize of ('constr with_occurrences * name) list
   | TacGeneralizeDep of 'constr
   | TacLetTac of name * 'constr * 'id gclause * letin_flag
 
   (* Derived basic tactics *)
-  | TacSimpleInduction of quantified_hypothesis
-  | TacNewInduction of evars_flag * 'constr with_bindings induction_arg list * 
-      'constr with_bindings option * intro_pattern_expr * 'id gclause option
-  | TacSimpleDestruct of quantified_hypothesis
-  | TacNewDestruct of evars_flag * 'constr with_bindings induction_arg list *
-      'constr with_bindings option * intro_pattern_expr * 'id gclause option
-
+  | TacSimpleInductionDestruct of rec_flag * quantified_hypothesis
+  | TacInductionDestruct of rec_flag * evars_flag * ('constr,'id) induction_clause list
   | TacDoubleInduction of quantified_hypothesis * quantified_hypothesis
   | TacDecomposeAnd of 'constr
   | TacDecomposeOr of 'constr
@@ -181,7 +197,7 @@ type ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_atomic_tactic_expr =
   (* Context management *)
   | TacClear of bool * 'id list
   | TacClearBody of 'id list
-  | TacMove of bool * 'id * 'id
+  | TacMove of bool * 'id * 'id move_location
   | TacRename of ('id *'id) list
   | TacRevert of 'id list
 
@@ -236,7 +252,7 @@ and ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr =
   | TacInfo of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
   | TacLetIn of rec_flag * (identifier located * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg) list * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr
   | TacMatch of lazy_flag * ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr * ('pat,('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr) match_rule list
-  | TacMatchContext of lazy_flag * direction_flag * ('pat,('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr) match_rule list
+  | TacMatchGoal of lazy_flag * direction_flag * ('pat,('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_expr) match_rule list
   | TacFun of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_fun_ast
   | TacArg of ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg
 
@@ -249,7 +265,7 @@ and ('constr,'pat,'cst,'ind,'ref,'id,'tac) gen_tactic_arg =
   | TacVoid
   | MetaIdArg      of loc * bool * string
   | ConstrMayEval  of ('constr,'cst) may_eval
-  | IntroPattern   of intro_pattern_expr
+  | IntroPattern   of intro_pattern_expr located
   | Reference      of 'ref
   | Integer        of int
   | TacCall        of loc *
diff --git a/proofs/tacmach.ml b/proofs/tacmach.ml
index 213cc13f..6bbaff08 100644
--- a/proofs/tacmach.ml
+++ b/proofs/tacmach.ml
@@ -6,8 +6,9 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tacmach.ml 10544 2008-02-09 11:31:35Z herbelin $ *)
+(* $Id: tacmach.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
+open Pp
 open Util
 open Names
 open Nameops
@@ -58,7 +59,7 @@ let pf_get_hyp gls id =
   try 
     Sign.lookup_named id (pf_hyps gls)
   with Not_found -> 
-    error ("No such hypothesis : " ^ (string_of_id id))
+    error ("No such hypothesis: " ^ (string_of_id id))
 
 let pf_get_hyp_typ gls id =
   let (_,_,ty)= (pf_get_hyp gls id) in
@@ -175,15 +176,11 @@ let refiner = refiner
 let introduction_no_check id =
   refiner (Prim (Intro id))
 
-(* This does not check that the dependencies are correct *)
-let intro_replacing_no_check whereid gl = 
-  refiner (Prim (Intro_replacing whereid)) gl
-
-let internal_cut_no_check id t gl = 
-  refiner (Prim (Cut (true,id,t))) gl
+let internal_cut_no_check replace id t gl = 
+  refiner (Prim (Cut (true,replace,id,t))) gl
 
-let internal_cut_rev_no_check id t gl = 
-  refiner (Prim (Cut (false,id,t))) gl
+let internal_cut_rev_no_check replace id t gl = 
+  refiner (Prim (Cut (false,replace,id,t))) gl
 
 let refine_no_check c gl = 
   refiner (Prim (Refine c)) gl
@@ -220,13 +217,12 @@ let mutual_cofix f others gl =
 (* Versions with consistency checks *)
 
 let introduction id    = with_check (introduction_no_check id) 
-let intro_replacing id = with_check (intro_replacing_no_check id)
-let internal_cut d t     = with_check (internal_cut_no_check d t)
-let internal_cut_rev d t = with_check (internal_cut_rev_no_check d t)
+let internal_cut b d t = with_check (internal_cut_no_check b d t)
+let internal_cut_rev b d t = with_check (internal_cut_rev_no_check b d t)
 let refine c           = with_check (refine_no_check c)
 let convert_concl d sty = with_check (convert_concl_no_check d sty)
 let convert_hyp d      = with_check (convert_hyp_no_check d)
-let thin l             = with_check (thin_no_check l)
+let thin c             = with_check (thin_no_check c)
 let thin_body c        = with_check (thin_body_no_check c)
 let move_hyp b id id'  = with_check (move_hyp_no_check b id id') 
 let rename_hyp l       = with_check (rename_hyp_no_check l)
diff --git a/proofs/tacmach.mli b/proofs/tacmach.mli
index 8b0053a4..2fc66e71 100644
--- a/proofs/tacmach.mli
+++ b/proofs/tacmach.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tacmach.mli 11094 2008-06-10 19:35:23Z herbelin $ i*)
+(*i $Id: tacmach.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -123,15 +123,15 @@ val change_constraints_pftreestate :
 
 val refiner                   : rule -> tactic
 val introduction_no_check     : identifier -> tactic
-val intro_replacing_no_check  : identifier -> tactic
-val internal_cut_no_check     : identifier -> types -> tactic
-val internal_cut_rev_no_check : identifier -> types -> tactic
+val internal_cut_no_check     : bool -> identifier -> types -> tactic
+val internal_cut_rev_no_check : bool -> identifier -> types -> tactic
 val refine_no_check           : constr -> tactic
 val convert_concl_no_check    : types -> cast_kind -> tactic
 val convert_hyp_no_check      : named_declaration -> tactic
 val thin_no_check             : identifier list -> tactic
 val thin_body_no_check        : identifier list -> tactic
-val move_hyp_no_check         : bool -> identifier -> identifier -> tactic
+val move_hyp_no_check         :
+  bool -> identifier -> identifier move_location -> tactic
 val rename_hyp_no_check       : (identifier*identifier) list -> tactic
 val mutual_fix      :
   identifier -> int -> (identifier * int * constr) list -> tactic
@@ -140,15 +140,14 @@ val mutual_cofix    : identifier -> (identifier * constr) list -> tactic
 (*s The most primitive tactics with consistency and type checking *)
 
 val introduction     : identifier -> tactic
-val intro_replacing  : identifier -> tactic
-val internal_cut     : identifier -> types -> tactic
-val internal_cut_rev : identifier -> types -> tactic
+val internal_cut     : bool -> identifier -> types -> tactic
+val internal_cut_rev : bool -> identifier -> types -> tactic
 val refine           : constr -> tactic
 val convert_concl    : types -> cast_kind -> tactic
 val convert_hyp      : named_declaration -> tactic
 val thin             : identifier list -> tactic
 val thin_body        : identifier list -> tactic
-val move_hyp         : bool -> identifier -> identifier -> tactic
+val move_hyp         : bool -> identifier -> identifier move_location -> tactic
 val rename_hyp       : (identifier*identifier) list -> tactic
 
 (*s Tactics handling a list of goals. *)
diff --git a/scripts/coqmktop.ml b/scripts/coqmktop.ml
index 850cc961..e87a195f 100644
--- a/scripts/coqmktop.ml
+++ b/scripts/coqmktop.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coqmktop.ml 10947 2008-05-19 19:10:40Z herbelin $ *)
+(* $Id: coqmktop.ml 11260 2008-07-24 20:53:12Z letouzey $ *)
 
 (* coqmktop is a script to link Coq, analogous to ocamlmktop.
    The command line contains options specific to coqmktop, options for the
@@ -318,7 +318,6 @@ let main () =
 	   (string_of_int (String.length command)) ^ " characters)");
 	flush Pervasives.stdout 
       end;
-    print_string command;
     let retcode = Sys.command command in
     clean main_file;
     (* command gives the exit code in HSB, and signal in LSB !!! *)
diff --git a/tactics/auto.ml b/tactics/auto.ml
index 2a5bb95c..066ed786 100644
--- a/tactics/auto.ml
+++ b/tactics/auto.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: auto.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: auto.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -91,18 +91,20 @@ type search_entry = stored_data list * stored_data list * stored_data Btermdn.t
 
 let empty_se = ([],[],Btermdn.create ())
 
-let add_tac t (l,l',dn) =
-  match t.pat with
-      None -> if not (List.mem t l) then (insert t l, l', dn) else (l, l', dn)
-    | Some pat -> if not (List.mem t l') then (l, insert t l', Btermdn.add dn (pat,t)) else (l, l', dn)
+let add_tac pat t st (l,l',dn) =
+  match pat with
+  | None -> if not (List.mem t l) then (insert t l, l', dn) else (l, l', dn)
+  | Some pat -> if not (List.mem t l') then (l, insert t l', Btermdn.add st dn (pat,t)) else (l, l', dn)
 
-
-let lookup_tacs (hdc,c) (l,l',dn) =
-  let l'  = List.map snd (Btermdn.lookup dn c) in
+let rebuild_dn st (l,l',dn) =
+  (l, l', List.fold_left (fun dn t -> Btermdn.add (Some st) dn (Option.get t.pat, t))
+    (Btermdn.create ()) l')
+    
+let lookup_tacs (hdc,c) st (l,l',dn) =
+  let l'  = List.map snd (Btermdn.lookup st dn c) in
   let sl' = Sort.list pri_order l' in
     Sort.merge pri_order l sl'
 
-
 module Constr_map = Map.Make(struct 
 			       type t = global_reference
 			       let compare = Pervasives.compare 
@@ -110,12 +112,18 @@ module Constr_map = Map.Make(struct
 
 module Hint_db = struct
 
-  type t = search_entry Constr_map.t
-
-  let empty = Constr_map.empty
+  type t = { 
+    hintdb_state : Names.transparent_state;
+    use_dn : bool;
+    hintdb_map : search_entry Constr_map.t
+  }
 
+  let empty use_dn = { hintdb_state = empty_transparent_state;
+		       use_dn = use_dn;
+		       hintdb_map = Constr_map.empty }
+    
   let find key db =
-    try Constr_map.find key db
+    try Constr_map.find key db.hintdb_map
     with Not_found -> empty_se
 
   let map_all k db =
@@ -123,21 +131,49 @@ module Hint_db = struct
       Sort.merge pri_order l l'
    
   let map_auto (k,c) db =
-    lookup_tacs (k,c) (find k db)
+    let st = if db.use_dn then Some db.hintdb_state else None in
+      lookup_tacs (k,c) st (find k db)
 
-  let add_one (k,v) db =
-    let oval = find k db in 
-      Constr_map.add k (add_tac v oval) db
+  let is_exact = function 
+    | Give_exact _ -> true
+    | _ -> false
 
+  let add_one (k,v) db =
+    let st',rebuild =
+      match v.code with
+      | Unfold_nth egr ->
+	  let (ids,csts) = db.hintdb_state in
+	    (match egr with
+	    | EvalVarRef id -> (Idpred.add id ids, csts)
+	    | EvalConstRef cst -> (ids, Cpred.add cst csts)), true
+      | _ -> db.hintdb_state, false
+    in
+    let dnst, db = 
+      if db.use_dn then 
+	Some st', { db with hintdb_map = Constr_map.map (rebuild_dn st') db.hintdb_map }
+      else None, db
+    in
+    let oval = find k db in
+    let pat = if not db.use_dn && is_exact v.code then None else v.pat in
+      { db with hintdb_map = Constr_map.add k (add_tac pat v dnst oval) db.hintdb_map;
+	hintdb_state = st' }
+	
   let add_list l db = List.fold_right add_one l db
+    
+  let iter f db = Constr_map.iter (fun k (l,l',_) -> f k (l@l')) db.hintdb_map
+    
+  let transparent_state db = db.hintdb_state
 
-  let iter f db = Constr_map.iter (fun k (l,l',_) -> f k (l@l')) db
+  let set_transparent_state db st = { db with hintdb_state = st }
 
+  let set_rigid db cst = 
+    let (ids,csts) = db.hintdb_state in
+      { db with hintdb_state = (ids, Cpred.remove cst csts) }
 end
 
 module Hintdbmap = Gmap
 
-type hint_db = Names.transparent_state * Hint_db.t
+type hint_db = Hint_db.t
 
 type frozen_hint_db_table = (string,hint_db) Hintdbmap.t 
 
@@ -158,7 +194,9 @@ let current_db_names () =
 (*                       Definition of the summary                        *)
 (**************************************************************************)
 
-let init     () = searchtable := Hintdbmap.empty
+let auto_init : (unit -> unit) ref = ref (fun () -> ())
+  
+let init     () = searchtable := Hintdbmap.empty; !auto_init ()
 let freeze   () = !searchtable
 let unfreeze fs = searchtable := fs
 
@@ -182,7 +220,11 @@ let rec nb_hyp c = match kind_of_term c with
 
 let try_head_pattern c = 
   try head_pattern_bound c
-  with BoundPattern -> error "Bound head variable"
+  with BoundPattern -> error "Bound head variable."
+
+let dummy_goal = 
+  {it = make_evar empty_named_context_val mkProp;
+   sigma = empty}
 
 let make_exact_entry pri (c,cty) =
   let cty = strip_outer_cast cty in
@@ -190,12 +232,11 @@ let make_exact_entry pri (c,cty) =
     | Prod (_,_,_) -> 
 	failwith "make_exact_entry"
     | _ ->
+        let ce = mk_clenv_from dummy_goal (c,cty) in
+	let c' = clenv_type ce in
+	let pat = Pattern.pattern_of_constr c' in
 	(head_of_constr_reference (List.hd (head_constr cty)),
-	   { pri=(match pri with Some pri -> pri | None -> 0); pat=None; code=Give_exact c })
-
-let dummy_goal = 
-  {it = make_evar empty_named_context_val mkProp;
-   sigma = empty}
+	   { pri=(match pri with Some pri -> pri | None -> 0); pat=Some pat; code=Give_exact c })
 
 let make_apply_entry env sigma (eapply,verbose) pri (c,cty) =
   let cty = hnf_constr env sigma cty in
@@ -238,8 +279,8 @@ let make_resolves env sigma flags pri c =
   if ents = [] then
     errorlabstrm "Hint" 
       (pr_lconstr c ++ spc() ++ 
-        (if fst flags then str"cannot be used as a hint"
-	else str "can be used as a hint only for eauto"));
+        (if fst flags then str"cannot be used as a hint."
+	else str "can be used as a hint only for eauto."));
   ents
 
 (* used to add an hypothesis to the local hint database *)
@@ -279,32 +320,23 @@ open Vernacexpr
 (*               declaration of the AUTOHINT library object               *)
 (**************************************************************************)
 
-let add_hint_list hintlist (st,db) =
-  let db' = Hint_db.add_list hintlist db in
-  let st' = 
-    List.fold_left 
-      (fun (ids, csts as st) (_, hint) -> 
-	match hint.code with
-	  | Unfold_nth egr ->
-	      (match egr with
-		| EvalVarRef id -> (Idpred.add id ids, csts)
-		| EvalConstRef cst -> (ids, Cpred.add cst csts))
-	  | _ -> st)
-      st hintlist
-  in (st', db')
-
 (* If the database does not exist, it is created *)
 (* TODO: should a warning be printed in this case ?? *)
 let add_hint dbname hintlist = 
   try 
     let db = searchtable_map dbname in
-    let db' = add_hint_list hintlist db in
+    let db' = Hint_db.add_list hintlist db in
     searchtable_add (dbname,db')
   with Not_found -> 
-    let db = add_hint_list hintlist (empty_transparent_state, Hint_db.empty) in
+    let db = Hint_db.add_list hintlist (Hint_db.empty false) in
     searchtable_add (dbname,db)
 
-let cache_autohint (_,(local,name,hints)) = add_hint name hints
+type hint_action = CreateDB of bool | UpdateDB of (global_reference * pri_auto_tactic) list
+
+let cache_autohint (_,(local,name,hints)) = 
+  match hints with
+  | CreateDB b -> searchtable_add (name, Hint_db.empty b)
+  | UpdateDB hints -> add_hint name hints
 
 let forward_subst_tactic = 
   ref (fun _ -> failwith "subst_tactic is not installed for auto")
@@ -354,12 +386,15 @@ let subst_autohint (_,subst,(local,name,hintlist as obj)) =
       if lab' == lab && data' == data then hint else
 	(lab',data')
   in
-  let hintlist' = list_smartmap subst_hint hintlist in
-    if hintlist' == hintlist then obj else
-      (local,name,hintlist')
-
+    match hintlist with
+    | CreateDB _ -> obj
+    | UpdateDB hintlist ->
+	let hintlist' = list_smartmap subst_hint hintlist in
+	  if hintlist' == hintlist then obj else
+	    (local,name,UpdateDB hintlist')
+	      
 let classify_autohint (_,((local,name,hintlist) as obj)) =
-  if local or hintlist = [] then Dispose else Substitute obj
+  if local or hintlist = (UpdateDB []) then Dispose else Substitute obj
 
 let export_autohint ((local,name,hintlist) as obj) =
   if local then None else Some obj
@@ -373,6 +408,9 @@ let (inAutoHint,outAutoHint) =
                     export_function = export_autohint }
 
 
+let create_hint_db l n b = 
+  Lib.add_anonymous_leaf (inAutoHint (l,n,CreateDB b))
+      
 (**************************************************************************)
 (*                     The "Hint" vernacular command                      *)
 (**************************************************************************)
@@ -381,19 +419,18 @@ let add_resolves env sigma clist local dbnames =
     (fun dbname ->
        Lib.add_anonymous_leaf
 	 (inAutoHint
-	    (local,dbname,
-     	     List.flatten (List.map (fun (x, y) ->
-	       make_resolves env sigma (true,Flags.is_verbose()) x y) clist))))
+	    (local,dbname, UpdateDB
+     	      (List.flatten (List.map (fun (x, y) ->
+		make_resolves env sigma (true,Flags.is_verbose()) x y) clist)))))
     dbnames
 
 
 let add_unfolds l local dbnames =
   List.iter 
     (fun dbname -> Lib.add_anonymous_leaf 
-       (inAutoHint (local,dbname, List.map make_unfold l)))
+       (inAutoHint (local,dbname, UpdateDB (List.map make_unfold l))))
     dbnames
 
-
 let add_extern pri (patmetas,pat) tacast local dbname =
   (* We check that all metas that appear in tacast have at least
      one occurence in the left pattern pat *)
@@ -401,10 +438,10 @@ let add_extern pri (patmetas,pat) tacast local dbname =
   match (list_subtract tacmetas patmetas) with
     | i::_ ->
 	errorlabstrm "add_extern" 
-	  (str "The meta-variable ?" ++ pr_patvar i ++ str" is not bound")
+	  (str "The meta-variable ?" ++ pr_patvar i ++ str" is not bound.")
     | []  ->
 	Lib.add_anonymous_leaf
-	  (inAutoHint(local,dbname, [make_extern pri pat tacast]))
+	  (inAutoHint(local,dbname, UpdateDB [make_extern pri pat tacast]))
 
 let add_externs pri pat tacast local dbnames = 
   List.iter (add_extern pri pat tacast local) dbnames
@@ -413,7 +450,7 @@ let add_trivials env sigma l local dbnames =
   List.iter
     (fun dbname ->
        Lib.add_anonymous_leaf (
-	 inAutoHint(local,dbname, List.map (make_trivial env sigma) l)))
+	 inAutoHint(local,dbname, UpdateDB (List.map (make_trivial env sigma) l))))
     dbnames
 
 let forward_intern_tac = 
@@ -439,7 +476,7 @@ let add_hints local dbnames0 h =
          | _ -> 
            errorlabstrm "evalref_of_ref"
             (str "Cannot coerce" ++ spc () ++ pr_global gr ++ spc () ++
-             str "to an evaluable reference")
+             str "to an evaluable reference.")
         in
 	  if !Flags.dump then Constrintern.add_glob (loc_of_reference r) gr;
 	 (gr,r') in
@@ -493,7 +530,7 @@ let fmt_hint_list_for_head c =
   let dbs = Hintdbmap.to_list !searchtable in
   let valid_dbs = 
     map_succeed 
-      (fun (name,(_,db)) -> (name,db,Hint_db.map_all c db)) 
+      (fun (name,db) -> (name,db,Hint_db.map_all c db)) 
       dbs 
   in
   if valid_dbs = [] then 
@@ -519,11 +556,11 @@ let fmt_hint_term cl =
     let valid_dbs = 
       if occur_existential cl then 
 	map_succeed 
-	  (fun (name, (_, db)) -> (name, db, Hint_db.map_all hd db)) 
+	  (fun (name, db) -> (name, db, Hint_db.map_all hd db)) 
 	  dbs
       else 
 	map_succeed 
-	  (fun (name, (_, db)) -> 
+	  (fun (name, db) -> 
 	     (name, db, Hint_db.map_auto (hd,applist(hdc,args)) db)) 
 	  dbs
     in 
@@ -534,6 +571,9 @@ let fmt_hint_term cl =
 	 hov 0 (prlist fmt_hints_db valid_dbs))
   with Bound | Match_failure _ | Failure _ -> 
     (str "No hint applicable for current goal")
+
+let error_no_such_hint_database x =
+  error ("No such Hint database: "^x^".")
 	  
 let print_hint_term cl = ppnl (fmt_hint_term cl)
 
@@ -544,7 +584,8 @@ let print_applicable_hint () =
   print_hint_term (pf_concl gl)
     
 (* displays the whole hint database db *)
-let print_hint_db ((ids, csts),db) =
+let print_hint_db db =
+  let (ids, csts) = Hint_db.transparent_state db in
   msg (hov 0
 	  (str"Unfoldable variable definitions: " ++ pr_idpred ids ++ fnl () ++
 	   str"Unfoldable constant definitions: " ++ pr_cpred csts ++ fnl ()));
@@ -559,13 +600,13 @@ let print_hint_db_by_name dbname =
   try 
     let db = searchtable_map dbname in print_hint_db db
   with Not_found -> 
-    error (dbname^" : No such Hint database")
+    error_no_such_hint_database dbname
   
 (* displays all the hints of all databases *)
 let print_searchtable () =
   Hintdbmap.iter
     (fun name db ->
-       msg (str "In the database " ++ str name ++ fnl ());
+       msg (str "In the database " ++ str name ++ str ":" ++ fnl ());
        print_hint_db db)
     !searchtable
 
@@ -600,7 +641,7 @@ let unify_resolve_nodelta (c,clenv) gls =
 let unify_resolve flags (c,clenv) gls = 
   let clenv' = connect_clenv gls clenv in
   let _ = clenv_unique_resolver false ~flags clenv' gls in  
-  h_apply true false (c,NoBindings) gls
+  h_apply true false [c,NoBindings] gls
 
 
 (* builds a hint database from a constr signature *)
@@ -610,7 +651,7 @@ let make_local_hint_db eapply lems g =
   let sign = pf_hyps g in
   let hintlist = list_map_append (pf_apply make_resolve_hyp g) sign in
   let hintlist' = list_map_append (pf_apply make_resolves g (eapply,false) None) lems in
-    (empty_transparent_state, Hint_db.add_list hintlist' (Hint_db.add_list hintlist Hint_db.empty))
+    Hint_db.add_list hintlist' (Hint_db.add_list hintlist (Hint_db.empty false))
 
 (* Serait-ce possible de compiler d'abord la tactique puis de faire la
    substitution sans passer par bdize dont l'objectif est de préparer un
@@ -648,7 +689,7 @@ let rec trivial_fail_db mod_delta db_list local_db gl =
     tclTHEN intro 
       (fun g'->
 	 let hintl = make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
-	 in trivial_fail_db mod_delta db_list (add_hint_list hintl local_db) g')
+	 in trivial_fail_db mod_delta db_list (Hint_db.add_list hintl local_db) g')
   in
   tclFIRST 
     (assumption::intro_tac::
@@ -658,12 +699,10 @@ let rec trivial_fail_db mod_delta db_list local_db gl =
 and my_find_search_nodelta db_list local_db hdc concl =
   let tacl = 
     if occur_existential concl then 
-      list_map_append
-	(fun (st, db) -> (Hint_db.map_all hdc db))
+      list_map_append (Hint_db.map_all hdc)
 	(local_db::db_list)
     else
-      list_map_append (fun (_, db) -> 
-	Hint_db.map_auto (hdc,concl) db)
+      list_map_append (Hint_db.map_auto (hdc,concl))
       	(local_db::db_list)
   in
     List.map 
@@ -691,12 +730,13 @@ and my_find_search_delta db_list local_db hdc concl =
   let tacl = 
     if occur_existential concl then 
       list_map_append
-	(fun (st, db) -> 
-	  let st = {flags with modulo_delta = st} in
+	(fun db -> 
+	  let st = {flags with modulo_delta = Hint_db.transparent_state db} in
 	    List.map (fun x -> (st,x)) (Hint_db.map_all hdc db))
 	(local_db::db_list)
     else
-      list_map_append (fun ((ids, csts as st), db) -> 
+      list_map_append (fun db -> 
+	let (ids, csts as st) = Hint_db.transparent_state db in
 	let st, l = 
 	  let l =
 	    if (Idpred.is_empty ids && Cpred.is_empty csts)
@@ -737,7 +777,7 @@ let trivial lems dbnames gl =
 	 try 
 	   searchtable_map x
 	 with Not_found -> 
-	   error ("trivial: "^x^": No such Hint database"))
+	   error_no_such_hint_database x)
       ("core"::dbnames) 
   in
   tclTRY (trivial_fail_db false db_list (make_local_hint_db false lems gl)) gl 
@@ -776,7 +816,7 @@ let decomp_unary_term c gls =
   if Hipattern.is_conjunction hd then 
     simplest_case c gls 
   else 
-    errorlabstrm "Auto.decomp_unary_term" (str "not a unary type") 
+    errorlabstrm "Auto.decomp_unary_term" (str "Not a unary type.")
 
 let decomp_empty_term c gls = 
   let typc = pf_type_of gls c in 
@@ -784,7 +824,7 @@ let decomp_empty_term c gls =
   if Hipattern.is_empty_type hd then 
     simplest_case c gls 
   else 
-    errorlabstrm "Auto.decomp_empty_term" (str "not an empty type") 
+    errorlabstrm "Auto.decomp_empty_term" (str "Not an empty type.")
 
 
 (* decomp is an natural number giving an indication on decomposition 
@@ -817,7 +857,7 @@ let rec search_gen decomp n mod_delta db_list local_db extra_sign goal =
 		(mkVar hid, htyp)]
 	   with Failure _ -> [] 
 	 in
-         search_gen decomp n mod_delta db_list (add_hint_list hintl local_db) [d] g') 
+         search_gen decomp n mod_delta db_list (Hint_db.add_list hintl local_db) [d] g') 
   in
   let rec_tacs = 
     List.map 
@@ -840,7 +880,7 @@ let delta_auto mod_delta n lems dbnames gl =
 	 try 
 	   searchtable_map x
 	 with Not_found -> 
-	   error ("auto: "^x^": No such Hint database"))
+	   error_no_such_hint_database x)
       ("core"::dbnames) 
   in
   let hyps = pf_hyps gl in
@@ -956,7 +996,7 @@ let rec super_search n db_list local_db argl goal =
      (tclTHEN intro 
         (fun g -> 
 	   let hintl = pf_apply make_resolve_any_hyp g (pf_last_hyp g) in
-	   super_search n db_list (add_hint_list hintl local_db)
+	   super_search n db_list (Hint_db.add_list hintl local_db)
 	     argl g))
      ::
      ((List.map 
@@ -974,7 +1014,7 @@ let search_superauto n to_add argl g =
       (fun (id,c) -> add_named_decl (id, None, pf_type_of g c))
       to_add empty_named_context in
   let db0 = list_map_append (make_resolve_hyp (pf_env g) (project g)) sigma in
-  let db = add_hint_list db0 (make_local_hint_db false [] g) in
+  let db = Hint_db.add_list db0 (make_local_hint_db false [] g) in
   super_search n [Hintdbmap.find "core" !searchtable] db argl g
 
 let superauto n to_add argl  = 
diff --git a/tactics/auto.mli b/tactics/auto.mli
index 37406a30..edaaa1c1 100644
--- a/tactics/auto.mli
+++ b/tactics/auto.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: auto.mli 10868 2008-04-29 12:30:25Z msozeau $ i*)
+(*i $Id: auto.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Util
@@ -47,24 +47,30 @@ type search_entry = stored_data list * stored_data list * stored_data Btermdn.t
 module Hint_db :
   sig
     type t
-    val empty : t
+    val empty : bool -> t
     val find : global_reference -> t -> search_entry
     val map_all : global_reference -> t -> pri_auto_tactic list
     val map_auto : global_reference * constr -> t -> pri_auto_tactic list
     val add_one : global_reference * pri_auto_tactic -> t -> t
     val add_list : (global_reference * pri_auto_tactic) list -> t -> t
     val iter : (global_reference -> stored_data list -> unit) -> t -> unit
+
+    val transparent_state : t -> transparent_state
+    val set_transparent_state : t -> transparent_state -> t
+    val set_rigid : t -> constant -> t
   end
 
 type hint_db_name = string
 
-type hint_db = transparent_state * Hint_db.t
+type hint_db = Hint_db.t
 
 val searchtable_map : hint_db_name -> hint_db
 
-val current_db_names : unit -> hint_db_name list
+val searchtable_add : (hint_db_name * hint_db) -> unit
 
-val add_hint_list : (global_reference * pri_auto_tactic) list -> hint_db -> hint_db
+val create_hint_db : bool -> hint_db_name -> bool -> unit
+
+val current_db_names : unit -> hint_db_name list
 
 val add_hints : locality_flag -> hint_db_name list -> hints -> unit
 
@@ -207,3 +213,5 @@ val superauto : int -> (identifier * constr) list -> autoArguments list -> tacti
 *)
 
 val h_superauto : int option -> reference list -> bool -> bool -> tactic
+
+val auto_init : (unit -> unit) ref
diff --git a/tactics/autorewrite.ml b/tactics/autorewrite.ml
index 1d096ec7..4759b6da 100644
--- a/tactics/autorewrite.ml
+++ b/tactics/autorewrite.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: autorewrite.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: autorewrite.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Equality
 open Hipattern
@@ -56,7 +56,7 @@ let print_rewrite_hintdb bas =
  with
   Not_found -> 
    errorlabstrm "AutoRewrite" 
-     (str ("Rewriting base "^(bas)^" does not exist"))
+     (str ("Rewriting base "^(bas)^" does not exist."))
 
 type raw_rew_rule = constr * bool * raw_tactic_expr
 
@@ -67,7 +67,7 @@ let one_base general_rewrite_maybe_in tac_main bas =
       Stringmap.find bas !rewtab
     with Not_found ->
       errorlabstrm "AutoRewrite"
-        (str ("Rewriting base "^(bas)^" does not exist"))
+        (str ("Rewriting base "^(bas)^" does not exist."))
   in
   let lrul = List.map (fun (c,_,b,t) -> (c,b,Tacinterp.eval_tactic t)) lrul in
     tclREPEAT_MAIN (tclPROGRESS (List.fold_left (fun tac (csr,dir,tc) ->
@@ -99,7 +99,7 @@ let autorewrite_multi_in idl tac_main lbas : tactic =
      match (Environ.named_context_of_val gl.Evd.it.Evd.evar_hyps) with
         (last_hyp_id,_,_)::_ -> last_hyp_id
       | _ -> (* even the hypothesis id is missing *)
-             error ("No such hypothesis : " ^ (string_of_id !id))
+             error ("No such hypothesis: " ^ (string_of_id !id) ^".")
     in
     let gl' = general_rewrite_in dir all_occurrences !id cstr false gl in
     let gls = (fst gl').Evd.it in
@@ -140,7 +140,7 @@ let gen_auto_multi_rewrite tac_main lbas cl =
   if cl.concl_occs <> all_occurrences_expr &
      cl.concl_occs <> no_occurrences_expr
   then 
-    error "The \"at\" syntax isn't available yet for the autorewrite tactic"
+    error "The \"at\" syntax isn't available yet for the autorewrite tactic."
   else 
     let compose_tac t1 t2 = 
       match cl.onhyps with 
@@ -170,8 +170,7 @@ let auto_multi_rewrite_with tac_main lbas cl gl =
 	gen_auto_multi_rewrite tac_main  lbas cl gl
     | _ -> 
 	    Util.errorlabstrm "autorewrite" 
-	      (str "autorewrite .. in .. using can only be used either with a unique hypothesis or" ++
-		 str " on the conclusion")
+	      (strbrk "autorewrite .. in .. using can only be used either with a unique hypothesis or on the conclusion.")
 
 
 (* Functions necessary to the library object declaration *)
diff --git a/tactics/btermdn.ml b/tactics/btermdn.ml
index f0b23b8d..a0aecbbc 100644
--- a/tactics/btermdn.ml
+++ b/tactics/btermdn.ml
@@ -6,9 +6,10 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: btermdn.ml 6427 2004-12-07 17:41:10Z sacerdot $ *)
+(* $Id: btermdn.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Term
+open Names
 open Termdn
 open Pattern
 open Libnames
@@ -19,6 +20,23 @@ open Libnames
 
 let dnet_depth = ref 8
 		   
+let bounded_constr_pat_discr_st st (t,depth) =
+  if depth = 0 then 
+    None 
+  else
+    match constr_pat_discr_st st t with
+      | None -> None
+      | Some (c,l) -> Some(c,List.map (fun c -> (c,depth-1)) l)
+	    
+let bounded_constr_val_discr_st st (t,depth) =
+  if depth = 0 then 
+    Dn.Nothing 
+  else
+    match constr_val_discr_st st t with
+      | Dn.Label (c,l) -> Dn.Label(c,List.map (fun c -> (c,depth-1)) l)
+      | Dn.Nothing -> Dn.Nothing
+      | Dn.Everything -> Dn.Everything
+
 let bounded_constr_pat_discr (t,depth) =
   if depth = 0 then 
     None 
@@ -29,24 +47,44 @@ let bounded_constr_pat_discr (t,depth) =
 	    
 let bounded_constr_val_discr (t,depth) =
   if depth = 0 then 
-    None 
+    Dn.Nothing 
   else
     match constr_val_discr t with
-      | None -> None
-      | Some (c,l) -> Some(c,List.map (fun c -> (c,depth-1)) l)
+      | Dn.Label (c,l) -> Dn.Label(c,List.map (fun c -> (c,depth-1)) l)
+      | Dn.Nothing -> Dn.Nothing
+      | Dn.Everything -> Dn.Everything
 
 type 'a t = (global_reference,constr_pattern * int,'a) Dn.t
-
+  
 let create = Dn.create
+  
+let add = function
+  | None -> 
+      (fun dn (c,v) -> 
+	Dn.add dn bounded_constr_pat_discr ((c,!dnet_depth),v))
+  | Some st -> 
+      (fun dn (c,v) -> 
+	Dn.add dn (bounded_constr_pat_discr_st st) ((c,!dnet_depth),v))
 
-let add dn (c,v) = Dn.add dn bounded_constr_pat_discr ((c,!dnet_depth),v)
-
-let rmv dn (c,v) = Dn.rmv dn bounded_constr_pat_discr ((c,!dnet_depth),v)
+let rmv = function
+  | None -> 
+      (fun dn (c,v) -> 
+	Dn.rmv dn bounded_constr_pat_discr ((c,!dnet_depth),v))
+  | Some st -> 
+      (fun dn (c,v) -> 
+	Dn.rmv dn (bounded_constr_pat_discr_st st) ((c,!dnet_depth),v))
 
-let lookup dn t =
-  List.map 
-    (fun ((c,_),v) -> (c,v)) 
-    (Dn.lookup dn bounded_constr_val_discr (t,!dnet_depth))
+let lookup = function
+  | None -> 
+      (fun dn t ->
+	List.map 
+	  (fun ((c,_),v) -> (c,v)) 
+	  (Dn.lookup dn bounded_constr_val_discr (t,!dnet_depth)))
+  | Some st -> 
+      (fun dn t ->
+	List.map 
+	  (fun ((c,_),v) -> (c,v)) 
+	  (Dn.lookup dn (bounded_constr_val_discr_st st) (t,!dnet_depth)))
 
 let app f dn = Dn.app (fun ((c,_),v) -> f(c,v)) dn
 
diff --git a/tactics/btermdn.mli b/tactics/btermdn.mli
index 1ac33557..959f7d10 100644
--- a/tactics/btermdn.mli
+++ b/tactics/btermdn.mli
@@ -6,11 +6,12 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: btermdn.mli 5920 2004-07-16 20:01:26Z herbelin $ i*)
+(*i $Id: btermdn.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Term
 open Pattern
+open Names
 (*i*)
 
 (* Discrimination nets with bounded depth. *)
@@ -19,10 +20,10 @@ type 'a t
 
 val create : unit -> 'a t
 
-val add : 'a t -> (constr_pattern * 'a) -> 'a t
-val rmv : 'a t -> (constr_pattern * 'a) -> 'a t
-
-val lookup : 'a t -> constr -> (constr_pattern * 'a) list
+val add : transparent_state option -> 'a t -> (constr_pattern * 'a) -> 'a t
+val rmv : transparent_state option -> 'a t -> (constr_pattern * 'a) -> 'a t
+  
+val lookup : transparent_state option -> 'a t -> constr -> (constr_pattern * 'a) list
 val app : ((constr_pattern * 'a) -> unit) -> 'a t -> unit
 
 val dnet_depth : int ref
diff --git a/tactics/class_tactics.ml4 b/tactics/class_tactics.ml4
index 9a1a3042..6eb5e359 100644
--- a/tactics/class_tactics.ml4
+++ b/tactics/class_tactics.ml4
@@ -9,7 +9,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: class_tactics.ml4 11150 2008-06-19 11:38:27Z msozeau $ *)
+(* $Id: class_tactics.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -43,11 +43,13 @@ open Evd
 let default_eauto_depth = 100
 let typeclasses_db = "typeclass_instances"
 
+let _ = Auto.auto_init := (fun () -> Auto.create_hint_db false typeclasses_db false)
+
 let check_imported_library d =
   let d' = List.map id_of_string d in
   let dir = make_dirpath (List.rev d') in
   if not (Library.library_is_loaded dir) then
-    error ("Library "^(list_last d)^" has to be imported first")
+    error ("Library "^(list_last d)^" has to be imported first.")
       
 let classes_dirpath =
   make_dirpath (List.map id_of_string ["Classes";"Coq"])
@@ -58,6 +60,17 @@ let init_setoid () =
 
 (** Typeclasses instance search tactic / eauto *)
 
+let evars_of_term init c = 
+  let rec evrec acc c =
+    match kind_of_term c with
+    | Evar (n, _) -> Intset.add n acc
+    | _ -> fold_constr evrec acc c
+  in 
+    evrec init c
+
+let intersects s t =
+  Intset.exists (fun el -> Intset.mem el t) s
+
 open Auto
 
 let e_give_exact c gl = 
@@ -98,7 +111,7 @@ let rec e_trivial_fail_db db_list local_db goal =
 	  let d = pf_last_hyp g' in
 	  let hintl = make_resolve_hyp (pf_env g') (project g') d in
           (e_trivial_fail_db db_list
-	     (add_hint_list hintl local_db) g'))) ::
+	      (Hint_db.add_list hintl local_db) g'))) ::
     (List.map pi1 (e_trivial_resolve db_list local_db (pf_concl goal)) )
   in 
   tclFIRST (List.map tclCOMPLETE tacl) goal 
@@ -108,11 +121,15 @@ and e_my_find_search db_list local_db hdc concl =
   let hintl =
     if occur_existential concl then
       list_map_append
-	(fun (st, db) -> List.map (fun x -> (st, x)) (Hint_db.map_all hdc db))
+	(fun db ->
+	  let st = Hint_db.transparent_state db in
+	    List.map (fun x -> (st, x)) (Hint_db.map_all hdc db))
 	(local_db::db_list)
     else
       list_map_append
-	(fun (st, db) -> List.map (fun x -> (st, x)) (Hint_db.map_auto (hdc,concl) db))
+	(fun db -> 
+	  let st = Hint_db.transparent_state db in
+	    List.map (fun x -> (st, x)) (Hint_db.map_auto (hdc,concl) db))
 	(local_db::db_list)
   in 
   let tac_of_hint = 
@@ -147,15 +164,14 @@ let e_possible_resolve db_list local_db gl =
 
 let find_first_goal gls = 
   try first_goal gls with UserError _ -> assert false
-
-
+    
 type search_state = { 
   depth : int; (*r depth of search before failing *)
   tacres : goal list sigma * validation;
   pri : int;
   last_tactic : std_ppcmds;
   dblist : Auto.hint_db list;
-  localdb :  Auto.hint_db list }
+  localdb : (bool ref * bool ref option * Auto.hint_db) list }
     
 let filter_hyp t = 
   match kind_of_term t with
@@ -167,13 +183,25 @@ let rec catchable = function
   | Stdpp.Exc_located (_, e) -> catchable e
   | e -> Logic.catchable_exception e
 
+let is_dep gl gls =
+  let evs = evars_of_term Intset.empty gl.evar_concl in
+    if evs = Intset.empty then false
+    else
+      List.fold_left
+	(fun b gl -> 
+	  if b then b 
+	  else
+	    let evs' = evars_of_term Intset.empty gl.evar_concl in
+	      intersects evs evs')
+	false gls
+
 module SearchProblem = struct
     
   type state = search_state
 
   let debug = ref false
 
-  let success s = (sig_it (fst s.tacres)) = []
+  let success s = sig_it (fst s.tacres) = []
 
   let pr_ev evs ev = Printer.pr_constr_env (Evd.evar_env ev) (Evarutil.nf_evar evs ev.Evd.evar_concl)
     
@@ -182,23 +210,14 @@ module SearchProblem = struct
       prlist (pr_ev evars) (sig_it gls)
 	
   let filter_tactics (glls,v) l =
-(*     if !debug then *)
-(*       (let _ = Proof_trees.db_pr_goal (List.hd (sig_it glls)) in *)
-(*       let evars = Evarutil.nf_evars (Refiner.project glls) in *)
-(*     	msg (str"Goal: " ++ pr_ev evars (List.hd (sig_it glls)) ++ str"\n")); *)
+    let glls,nv = apply_tac_list tclNORMEVAR glls in
+    let v p = v (nv p) in
     let rec aux = function
       | [] -> []
       | (tac,pri,pptac) :: tacl -> 
 	  try 
-(* 	    if !debug then msg (str"\nTrying tactic: " ++ pptac ++ str"\n"); *)
 	    let (lgls,ptl) = apply_tac_list tac glls in 
 	    let v' p = v (ptl p) in
-(* 	      	      if !debug then *)
-(* 	      		begin *)
-(* 	      		  let evars = Evarutil.nf_evars (Refiner.project glls) in *)
-(* 	      		    msg (str"\nOn goal: " ++ pr_ev evars (List.hd (sig_it glls)) ++ str"\n"); *)
-(* 	      		    msg (hov 1 (pptac ++ str" gives: \n" ++ pr_goals lgls ++ str"\n")) *)
-(* 	      		end; *)
 	      ((lgls,v'),pri,pptac) :: aux tacl
 	  with e when catchable e -> aux tacl
     in aux l
@@ -214,65 +233,83 @@ module SearchProblem = struct
       List.length (sig_it (fst s.tacres)) + 
 	nb_empty_evars (sig_sig (fst s.tacres))
     in
-      if d <> 0 && d <> 1 then d else
+      if d <> 0 then d else
 	let pri = s.pri - s'.pri in
 	  if pri <> 0 then pri
 	  else nbgoals s - nbgoals s'
-
+	  
   let branching s = 
     if s.depth = 0 then 
       []
     else      
-      let lg = fst s.tacres in
-      let nbgl = List.length (sig_it lg) in
-      assert (nbgl > 0);
-      let g = find_first_goal lg in
-      let assumption_tacs = 
-	let l = 
-	  filter_tactics s.tacres
-	    (List.map 
-		(fun id -> (Eauto.e_give_exact_constr (mkVar id), 0,
-			   (str "exact" ++ spc () ++ pr_id id)))
-		(List.filter (fun id -> filter_hyp (pf_get_hyp_typ g id))
-		    (pf_ids_of_hyps g)))
-	in
-	  List.map (fun (res,pri,pp) -> { s with tacres = res; pri = 0;
-	    last_tactic = pp; localdb = List.tl s.localdb }) l
-      in
-(*       let intro_tac =  *)
-(* 	List.map  *)
-(* 	  (fun ((lgls,_) as res,pri,pp) ->  *)
-(* 	     let g' = first_goal lgls in  *)
-(* 	     let hintl =  *)
-(* 	       make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g') *)
-(* 	     in	        *)
-(*              let ldb = Hint_db.add_list hintl (match s.localdb with [] -> assert false | hd :: _ -> hd) in *)
-(* 	       { s with tacres = res;  *)
-(* 		 last_tactic = pp; *)
-(* 		 pri = pri; *)
-(* 		 localdb = ldb :: List.tl s.localdb }) *)
-(* 	  (filter_tactics s.tacres [Tactics.intro,1,(str "intro")]) *)
-(*       in *)
-      let possible_resolve ((lgls,_) as res, pri, pp) =
-	let nbgl' = List.length (sig_it lgls) in
-	  if nbgl' < nbgl then
-	    { s with tacres = res; last_tactic = pp; pri = pri;
-	      localdb = List.tl s.localdb }
-	  else 
-	    { s with 
-	      depth = pred s.depth; tacres = res; 
-	      last_tactic = pp; pri = pri;
-	      localdb = 
-		list_addn (nbgl'-nbgl) (List.hd s.localdb) s.localdb }
-      in
-      let rec_tacs = 
-	let l = 
-	  filter_tactics s.tacres (e_possible_resolve s.dblist (List.hd s.localdb) (pf_concl g))
-	in
-	List.map possible_resolve l
-      in
-      List.sort compare (assumption_tacs (* @intro_tac  @ custom_tac *) @ rec_tacs)
-
+      let (cut, do_cut, ldb as hdldb) = List.hd s.localdb in
+	if !cut then []
+	else begin
+	  Option.iter (fun r -> r := true) do_cut;
+	  let {it=gl; sigma=sigma} = fst s.tacres in 
+	  let nbgl = List.length gl in
+	  let g = { it = List.hd gl ; sigma = sigma } in
+	  let new_db, localdb = 
+	    let tl = List.tl s.localdb in
+	      match tl with
+	      | [] -> hdldb, tl
+	      | (cut', do', ldb') :: rest ->
+		  if not (is_dep (Evarutil.nf_evar_info sigma (List.hd gl)) (List.tl gl)) then
+		    let fresh = ref false in
+		      if do' = None then 
+			(fresh, None, ldb), (cut', Some fresh, ldb') :: rest
+		      else 
+			(cut', None, ldb), tl
+		  else hdldb, tl
+	  in let localdb = new_db :: localdb in
+	  let assumption_tacs = 
+	    let l = 
+	      filter_tactics s.tacres
+		(List.map 
+		    (fun id -> (Eauto.e_give_exact_constr (mkVar id), 0,
+			       (str "exact" ++ spc () ++ pr_id id)))
+		    (List.filter (fun id -> filter_hyp (pf_get_hyp_typ g id))
+			(pf_ids_of_hyps g)))
+	    in
+	      List.map (fun (res,pri,pp) -> { s with tacres = res; pri = 0;
+		last_tactic = pp; localdb = List.tl s.localdb }) l
+	  in
+	  let intro_tac =
+	    List.map
+	      (fun ((lgls,_) as res,pri,pp) ->
+		let g' = first_goal lgls in
+		let hintl =
+		  make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
+		in
+		let ldb = Hint_db.add_list hintl ldb in
+		  { s with tacres = res;
+		    last_tactic = pp;
+		    pri = pri;
+		    localdb = (cut, None, ldb) :: List.tl s.localdb })
+	      (filter_tactics s.tacres [Tactics.intro,1,(str "intro")])
+	  in
+	  let possible_resolve ((lgls,_) as res, pri, pp) =
+	    let nbgl' = List.length (sig_it lgls) in
+	      if nbgl' < nbgl then
+		{ s with 
+		  depth = pred s.depth;
+		  tacres = res; last_tactic = pp; pri = pri;
+		  localdb = List.tl localdb }
+	      else 
+		{ s with depth = pred s.depth; tacres = res; 
+		  last_tactic = pp; pri = pri;
+		  localdb = list_tabulate (fun _ -> new_db) (nbgl'-nbgl) @ localdb }
+	  in
+	  let concl = Evarutil.nf_evar (project g) (pf_concl g) in
+	  let rec_tacs = 
+	    let l = 
+	      filter_tactics s.tacres (e_possible_resolve s.dblist ldb concl)
+	    in
+	      List.map possible_resolve l
+	  in
+	    List.sort compare (assumption_tacs @ intro_tac @ rec_tacs)
+	end
+	  
   let pp s = 
     msg (hov 0 (str " depth=" ++ int s.depth ++ spc () ++ 
 		  s.last_tactic ++ str "\n"))
@@ -340,11 +377,13 @@ let e_breadth_search debug s =
     let tac = 
       if debug then Search.debug_breadth_first else Search.breadth_first 
     in let s = tac s in s.tacres
-  with Not_found -> error "EAuto: breadth first search failed"
+  with Not_found -> error "eauto: breadth first search failed."
 
-let e_search_auto debug (in_depth,p) lems db_list gls = 
+let e_search_auto debug (in_depth,p) lems st db_list gls = 
   let sigma = Evd.sig_sig (fst gls) and gls' = Evd.sig_it (fst gls) in
-  let local_dbs = List.map (fun gl -> make_local_hint_db true lems ({it = gl; sigma = sigma})) gls' in
+  let local_dbs = List.map (fun gl -> 
+    let db = make_local_hint_db true lems ({it = gl; sigma = sigma}) in
+      (ref false, None, Hint_db.set_transparent_state db st)) gls' in
   let state = make_initial_state p gls db_list local_dbs in
   if in_depth then 
     e_depth_search debug state
@@ -355,20 +394,14 @@ let full_eauto debug n lems gls =
   let dbnames = current_db_names () in
   let dbnames =  list_subtract dbnames ["v62"] in
   let db_list = List.map searchtable_map dbnames in
-    e_search_auto debug n lems db_list gls
+    e_search_auto debug n lems empty_transparent_state db_list gls
 
 let nf_goal (gl, valid) =
   { gl with sigma = Evarutil.nf_evars gl.sigma }, valid
 
 let typeclasses_eauto debug n lems gls =
-  let dbnames = [typeclasses_db] in
-  let db_list = List.map
-    (fun x -> 
-      try searchtable_map x 
-      with Not_found -> (empty_transparent_state, Hint_db.empty))
-    dbnames 
-  in
-    e_search_auto debug n lems db_list gls
+  let db = searchtable_map typeclasses_db in
+    e_search_auto debug n lems (Hint_db.transparent_state db) [db] gls
 
 exception Found of evar_map
 
@@ -404,31 +437,23 @@ let resolve_all_evars_once debug (mode, depth) env p evd =
 
 exception FoundTerm of constr
 
-let resolve_one_typeclass env gl =
-  let gls = { it = [ Evd.make_evar (Environ.named_context_val env) gl ] ; sigma = Evd.empty } in
-  let valid x = raise (FoundTerm (fst (Refiner.extract_open_proof Evd.empty (List.hd x)))) in
+let resolve_one_typeclass env ?(sigma=Evd.empty) gl =
+  let gls = { it = [ Evd.make_evar (Environ.named_context_val env) gl ] ; sigma = sigma } in
+  let valid x = raise (FoundTerm (fst (Refiner.extract_open_proof sigma (List.hd x)))) in
   let gls', valid' = typeclasses_eauto false (true, default_eauto_depth) [] (gls, valid) in
     try ignore(valid' []); assert false with FoundTerm t -> 
       let term = Evarutil.nf_evar (sig_sig gls') t in
 	if occur_existential term then raise Not_found else term
 
+let _ = 
+  Typeclasses.solve_instanciation_problem := (fun x y z -> resolve_one_typeclass x ~sigma:y z)
+
 let has_undefined p oevd evd =
   Evd.fold (fun ev evi has -> has ||
     (evi.evar_body = Evar_empty && p ev evi && 
 	(try Typeclasses.is_resolvable (Evd.find oevd ev) with _ -> true)))
     (Evd.evars_of evd) false
 
-let evars_of_term init c = 
-  let rec evrec acc c =
-    match kind_of_term c with
-    | Evar (n, _) -> Intset.add n acc
-    | _ -> fold_constr evrec acc c
-  in 
-    evrec init c
-
-let intersects s t =
-  Intset.exists (fun el -> Intset.mem el t) s
-
 let rec merge_deps deps = function
   | [] -> [deps]
   | hd :: tl -> 
@@ -486,18 +511,21 @@ let resolve_all_evars debug m env p oevd do_split fail =
 	  | Some evd' -> docomp evd' comps
   in docomp oevd split
 
-(* let resolve_all_evars debug m env p oevd = *)
-(*   let oevm = Evd.evars_of oevd in *)
-(*   try *)
-(*     let rec aux n evd = *)
-(*       if has_undefined p oevm evd then *)
-(* 	if n > 0 then *)
-(* 	  let evd' = resolve_all_evars_once debug m env p evd in *)
-(* 	    aux (pred n) evd' *)
-(* 	else None *)
-(*       else Some evd *)
-(*     in aux 3 oevd *)
-(*   with Not_found -> None *)
+let resolve_typeclass_evars d p env evd onlyargs split fail =
+  let pred = 
+    if onlyargs then 
+      (fun ev evi -> Typeclasses.is_implicit_arg (snd (Evd.evar_source ev evd)) &&
+	Typeclasses.is_class_evar evi)
+    else (fun ev evi -> Typeclasses.is_class_evar evi)
+  in resolve_all_evars d p env pred evd split fail
+    
+let solve_inst debug mode depth env evd onlyargs split fail =
+  resolve_typeclass_evars debug (mode, depth) env evd onlyargs split fail
+
+let _ = 
+  Typeclasses.solve_instanciations_problem :=
+    solve_inst false true default_eauto_depth
+
     
 VERNAC COMMAND EXTEND Typeclasses_Unfold_Settings
 | [ "Typeclasses" "unfold" reference_list(cl) ] -> [
@@ -505,6 +533,20 @@ VERNAC COMMAND EXTEND Typeclasses_Unfold_Settings
   ]
 END
 
+VERNAC COMMAND EXTEND Typeclasses_Rigid_Settings
+| [ "Typeclasses" "rigid" reference_list(cl) ] -> [
+    let db = searchtable_map typeclasses_db in
+    let db' = 
+      List.fold_left (fun acc r -> 
+	let gr = Syntax_def.global_with_alias r in
+	  match gr with
+	  | ConstRef c -> Hint_db.set_rigid acc c 
+	  | _ -> acc) db cl
+    in
+      searchtable_add (typeclasses_db,db')
+ ]
+END
+
 (** Typeclass-based rewriting. *)
 
 let respect_proj = lazy (mkConst (snd (List.hd (Lazy.force morphism_class).cl_projs)))
@@ -518,6 +560,7 @@ let try_find_reference dir s =
 let gen_constant dir s = Coqlib.gen_constant "Class_setoid" dir s
 let coq_proj1 = lazy(gen_constant ["Init"; "Logic"] "proj1")
 let coq_proj2 = lazy(gen_constant ["Init"; "Logic"] "proj2")
+let coq_eq = lazy(gen_constant ["Init"; "Logic"] "eq")
 let iff = lazy (gen_constant ["Init"; "Logic"] "iff")
 let coq_all = lazy (gen_constant ["Init"; "Logic"] "all")
 let impl = lazy (gen_constant ["Program"; "Basics"] "impl")
@@ -539,7 +582,7 @@ let coq_inverse = lazy (gen_constant (* ["Classes"; "RelationClasses"] "inverse"
 let inverse car rel = mkApp (Lazy.force coq_inverse, [| car ; car; mkProp; rel |])
 
 let complement = lazy (gen_constant ["Classes"; "RelationClasses"] "complement")
-let pointwise_relation = lazy (gen_constant ["Classes"; "RelationClasses"] "pointwise_relation")
+let pointwise_relation = lazy (gen_constant ["Classes"; "Morphisms"] "pointwise_relation")
 
 let respectful_dep = lazy (gen_constant ["Classes"; "Morphisms"] "respectful_dep")
 let respectful = lazy (gen_constant ["Classes"; "Morphisms"] "respectful")
@@ -556,6 +599,8 @@ let setoid_refl_proj = lazy (gen_constant ["Classes"; "SetoidClass"] "Equivalenc
 let setoid_equiv = lazy (gen_constant ["Classes"; "SetoidClass"] "equiv")
 let setoid_morphism = lazy (gen_constant ["Classes"; "SetoidClass"] "setoid_morphism")
 let setoid_refl_proj = lazy (gen_constant ["Classes"; "SetoidClass"] "Equivalence_Reflexive")
+
+let setoid_relation = lazy (gen_constant ["Classes"; "SetoidTactics"] "SetoidRelation")
   
 let arrow_morphism a b = 
   if isprop a && isprop b then
@@ -570,12 +615,25 @@ let morphism_type = lazy (constr_of_global (Lazy.force morphism_class).cl_impl)
 
 let morphism_proxy_type = lazy (constr_of_global (Lazy.force morphism_proxy_class).cl_impl)
 
+let is_applied_setoid_relation t =
+  match kind_of_term t with
+  | App (c, args) when Array.length args >= 2 ->
+      let head = if isApp c then fst (destApp c) else c in 
+	if eq_constr (Lazy.force coq_eq) head then false
+	else (try      
+	    let evd, evar = Evarutil.new_evar (Evd.create_evar_defs Evd.empty) (Global.env()) (new_Type ()) in
+	    let inst = mkApp (Lazy.force setoid_relation, [| evar; c |]) in
+	      ignore(Typeclasses.resolve_one_typeclass (Global.env()) (Evd.evars_of evd) inst);
+	      true
+	  with _ -> false)
+  | _ -> false
+      
+let _ = 
+  Equality.register_is_applied_setoid_relation is_applied_setoid_relation
+
 exception Found of (constr * constr * (types * types) list * constr * constr array *
 		       (constr * (constr * constr * constr * constr)) option array)
 
-let is_equiv env sigma t = 
-  isConst t && Reductionops.is_conv env sigma (Lazy.force setoid_equiv) t
-
 let split_head = function
     hd :: tl -> hd, tl
   | [] -> assert(false)
@@ -703,13 +761,13 @@ let decompose_setoid_eqhyp env sigma c left2right =
     | [c1;c2] -> [],(c1, c2)
     | x::y::z ->
 	let l,res = split_last_two (y::z) in x::l, res
-    | _ -> error "The term provided is not an applied relation" in
+    | _ -> error "The term provided is not an applied relation." in
   let others,(c1,c2) = split_last_two args in
   let ty1, ty2 = 
     Typing.mtype_of env eqclause.evd c1, Typing.mtype_of env eqclause.evd c2
   in
     if not (evd_convertible env eqclause.evd ty1 ty2) then
-      error "The term does not end with an applied homogeneous relation"
+      error "The term does not end with an applied homogeneous relation."
     else
       { cl=eqclause; prf=(Clenv.clenv_value eqclause);
 	car=ty1; rel=mkApp (equiv, Array.of_list others);
@@ -736,11 +794,11 @@ let allowK = true
 
 let refresh_hypinfo env sigma hypinfo = 
   if !hypinfo.abs = None then
-    let {l2r=l2r; c = c} = !hypinfo in
+    let {l2r=l2r; c = c;cl=cl} = !hypinfo in
       match c with 
 	| Some c ->
 	    (* Refresh the clausenv to not get the same meta twice in the goal. *)
-	    hypinfo := decompose_setoid_eqhyp env sigma c l2r;
+	    hypinfo := decompose_setoid_eqhyp cl.env (Evd.evars_of cl.evd) c l2r;
 	| _ -> ()
   else ()
 
@@ -780,11 +838,12 @@ let unify_eqn env sigma hypinfo t =
 		let mvs = clenv_dependent false env' in
 		  clenv_pose_metas_as_evars env' mvs
 	      in
-	      let c1 = Clenv.clenv_nf_meta env' c1 
-	      and c2 = Clenv.clenv_nf_meta env' c2
-	      and car = Clenv.clenv_nf_meta env' car
-	      and rel = Clenv.clenv_nf_meta env' rel in
-	      let prf = Clenv.clenv_value env' in
+	      let evd' = Typeclasses.resolve_typeclasses env'.env env'.evd in
+	      let env' = { env' with evd = evd' } in
+	      let nf c = Evarutil.nf_evar (Evd.evars_of evd') (Clenv.clenv_nf_meta env' c) in
+	      let c1 = nf c1 and c2 = nf c2
+	      and car = nf car and rel = nf rel 
+	      and prf = nf (Clenv.clenv_value env') in
 	      let ty1 = Typing.mtype_of env'.env env'.evd c1 
 	      and ty2 = Typing.mtype_of env'.env env'.evd c2
 	      in
@@ -974,16 +1033,7 @@ let build_new gl env sigma flags loccs hypinfo concl cstr evars =
   let rest = List.filter (fun o -> o > nbocc_min_1) occs in
   if rest <> [] then error_invalid_occurrence rest;
   eq
-    
-let resolve_typeclass_evars d p env evd onlyargs split fail =
-  let pred = 
-    if onlyargs then 
-      (fun ev evi -> Typeclasses.is_implicit_arg (snd (Evd.evar_source ev evd)) &&
-	class_of_constr evi.Evd.evar_concl <> None)
-    else
-      (fun ev evi -> class_of_constr evi.Evd.evar_concl <> None)
-  in resolve_all_evars d p env pred evd split fail
-      
+          
 let cl_rewrite_clause_aux ?(flags=default_flags) hypinfo goal_meta occs clause gl =
   let concl, is_hyp = 
     match clause with
@@ -1025,7 +1075,7 @@ let cl_rewrite_clause_aux ?(flags=default_flags) hypinfo goal_meta occs clause g
 		| None -> 
 		    let name = next_name_away_with_default "H" Anonymous (pf_ids_of_hyps gl) in
 		      tclTHENLAST
-			(Tacmach.internal_cut_no_check name newt)
+			(Tacmach.internal_cut_no_check false name newt)
 			(tclTHEN (Tactics.revert [name]) (Tactics.refine p))
 		| Some (t, ty) -> 
 		    Tactics.refine
@@ -1057,11 +1107,17 @@ let cl_rewrite_clause_aux ?(flags=default_flags) hypinfo goal_meta occs clause g
   try cl_rewrite_clause_aux ~flags hypinfo goal_meta occs clause gl
   with DependentMorphism -> tclFAIL 0 (str " setoid rewrite failed: cannot handle dependent morphisms") gl
 
-let cl_rewrite_clause c left2right occs clause gl =
+let cl_rewrite_clause (evm,c) left2right occs clause gl =
   init_setoid ();
   let meta = Evarutil.new_meta() in
   let gl = { gl with sigma = Typeclasses.mark_unresolvables gl.sigma } in
-  let hypinfo = ref (decompose_setoid_eqhyp (pf_env gl) (project gl) c left2right) in
+  let env = pf_env gl in
+  let evars = Evd.merge (project gl) evm in
+(*   let c = *)
+(*     let j = Pretyping.Default.understand_judgment_tcc evars env c in *)
+(*       j.Environ.uj_val *)
+(*   in *)
+  let hypinfo = ref (decompose_setoid_eqhyp env evars c left2right) in
     cl_rewrite_clause_aux hypinfo meta occs clause gl
 
 open Genarg
@@ -1071,20 +1127,20 @@ let occurrences_of = function
   | n::_ as nl when n < 0 -> (false,List.map abs nl)
   | nl -> 
       if List.exists (fun n -> n < 0) nl then
-	error "Illegal negative occurrence number";
+	error "Illegal negative occurrence number.";
       (true,nl)
 
 TACTIC EXTEND class_rewrite
-| [ "clrewrite" orient(o) constr(c) "in" hyp(id) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
-| [ "clrewrite" orient(o) constr(c) "at" occurrences(occ) "in" hyp(id) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
-| [ "clrewrite" orient(o) constr(c) "in" hyp(id) ] -> [ cl_rewrite_clause c o all_occurrences (Some (([],id), [])) ]
-| [ "clrewrite" orient(o) constr(c) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) None ]
-| [ "clrewrite" orient(o) constr(c) ] -> [ cl_rewrite_clause c o all_occurrences None ]
+| [ "clrewrite" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
+| [ "clrewrite" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id) ] -> [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), [])) ]
+| [ "clrewrite" orient(o) open_constr(c) "in" hyp(id) ] -> [ cl_rewrite_clause c o all_occurrences (Some (([],id), [])) ]
+| [ "clrewrite" orient(o) open_constr(c) "at" occurrences(occ) ] -> [ cl_rewrite_clause c o (occurrences_of occ) None ]
+| [ "clrewrite" orient(o) open_constr(c) ] -> [ cl_rewrite_clause c o all_occurrences None ]
 END
 
 
 let clsubstitute o c =
-  let is_tac id = match kind_of_term c with Var id' when id' = id -> true | _ -> false in
+  let is_tac id = match kind_of_term (snd c) with Var id' when id' = id -> true | _ -> false in
     Tacticals.onAllClauses 
       (fun cl -> 
 	match cl with
@@ -1092,7 +1148,7 @@ let clsubstitute o c =
 	  | _ -> tclTRY (cl_rewrite_clause c o all_occurrences cl))
 
 TACTIC EXTEND substitute
-| [ "substitute" orient(o) constr(c) ] -> [ clsubstitute o c ]
+| [ "substitute" orient(o) open_constr(c) ] -> [ clsubstitute o c ]
 END
 
 let pr_debug _prc _prlc _prt b =
@@ -1122,13 +1178,6 @@ let pr_depth _prc _prlc _prt = function
 ARGUMENT EXTEND depth TYPED AS int option PRINTED BY pr_depth
 | [ int_or_var_opt(v) ] -> [ match v with Some (ArgArg i) -> Some i | _ -> None ]
 END
-	
-let solve_inst debug mode depth env evd onlyargs split fail =
-  resolve_typeclass_evars debug (mode, depth) env evd onlyargs split fail
-
-let _ = 
-  Typeclasses.solve_instanciations_problem :=
-    solve_inst false true default_eauto_depth
       
 VERNAC COMMAND EXTEND Typeclasses_Settings
  | [ "Typeclasses" "eauto" ":=" debug(d) search_mode(s) depth(depth) ] -> [ 
@@ -1146,7 +1195,8 @@ TACTIC EXTEND typeclasses_eauto
       fun gl -> 
 	let gls = {it = [sig_it gl]; sigma = project gl} in
 	let vals v = List.hd v in
-	  typeclasses_eauto d (mode, depth) [] (gls, vals) ]
+	  try typeclasses_eauto d (mode, depth) [] (gls, vals) 
+	  with Not_found -> tclFAIL 0 (str" typeclasses eauto failed") gl ]
 END
 
 
@@ -1172,15 +1222,15 @@ let _ =
 (* Compatibility with old Setoids *)
   
 TACTIC EXTEND setoid_rewrite
-   [ "setoid_rewrite" orient(o) constr(c) ]
+   [ "setoid_rewrite" orient(o) open_constr(c) ]
    -> [ cl_rewrite_clause c o all_occurrences None ]
- | [ "setoid_rewrite" orient(o) constr(c) "in" hyp(id) ] ->
+ | [ "setoid_rewrite" orient(o) open_constr(c) "in" hyp(id) ] ->
       [ cl_rewrite_clause c o all_occurrences (Some (([],id), []))]
- | [ "setoid_rewrite" orient(o) constr(c) "at" occurrences(occ) ] ->
+ | [ "setoid_rewrite" orient(o) open_constr(c) "at" occurrences(occ) ] ->
       [ cl_rewrite_clause c o (occurrences_of occ) None]
- | [ "setoid_rewrite" orient(o) constr(c) "at" occurrences(occ) "in" hyp(id)] ->
+ | [ "setoid_rewrite" orient(o) open_constr(c) "at" occurrences(occ) "in" hyp(id)] ->
       [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), []))]
- | [ "setoid_rewrite" orient(o) constr(c) "in" hyp(id) "at" occurrences(occ)] ->
+ | [ "setoid_rewrite" orient(o) open_constr(c) "in" hyp(id) "at" occurrences(occ)] ->
       [ cl_rewrite_clause c o (occurrences_of occ) (Some (([],id), []))]
 END
 
@@ -1225,10 +1275,10 @@ let constr_tac = Tacinterp.interp (Tacexpr.TacAtom (dummy_loc, Tacexpr.TacAnyCon
 
 let declare_relation ?(binders=[]) a aeq n refl symm trans = 
   init_setoid ();
+  let instance = declare_instance a aeq (add_suffix n "_relation") "Coq.Classes.SetoidTactics.SetoidRelation"
+  in ignore(anew_instance binders instance []);
   match (refl,symm,trans) with 
-      (None, None, None) -> 
-	let instance = declare_instance a aeq n "Coq.Classes.SetoidTactics.DefaultRelation"
-	in ignore(anew_instance binders instance [])
+      (None, None, None) -> ()
     | (Some lemma1, None, None) -> 
 	ignore (declare_instance_refl binders a aeq n lemma1)
     | (None, Some lemma2, None) -> 
@@ -1577,7 +1627,7 @@ let relation_of_constr c =
     | App (f, args) when Array.length args >= 2 -> 
 	let relargs, args = array_chop (Array.length args - 2) args in
 	  mkApp (f, relargs), args
-    | _ -> error "Not an applied relation"
+    | _ -> error "Not an applied relation."
 
 let is_loaded d =
   let d' = List.map id_of_string d in
@@ -1624,7 +1674,7 @@ let setoid_symmetry_in id gl =
   let rec split_last_two = function
     | [c1;c2] -> [],(c1, c2)
     | x::y::z -> let l,res = split_last_two (y::z) in x::l, res
-    | _ -> error "The term provided is not an equivalence" 
+    | _ -> error "The term provided is not an equivalence."
   in
   let others,(c1,c2) = split_last_two args in
   let he,c1,c2 =  mkApp (equiv, Array.of_list others),c1,c2 in
@@ -1690,3 +1740,18 @@ TACTIC EXTEND apply_typeclasses
 	     Clenvtac.clenv_refine true {cl' with evd = evd'} gl) gl
    ]
 END
+
+let rec head_of_constr t =
+  let t = strip_outer_cast(collapse_appl t) in
+    match kind_of_term t with
+    | Prod (_,_,c2)  -> head_of_constr c2 
+    | LetIn (_,_,_,c2) -> head_of_constr c2
+    | App (f,args)  -> head_of_constr f
+    | _      -> t
+      
+TACTIC EXTEND head_of_constr
+  [ "head_of_constr" ident(h) constr(c) ] -> [
+    let c = head_of_constr c in
+      letin_tac None (Name h) c allHyps
+  ]
+END
diff --git a/tactics/contradiction.ml b/tactics/contradiction.ml
index a2c840a1..313d74a1 100644
--- a/tactics/contradiction.ml
+++ b/tactics/contradiction.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: contradiction.ml 10169 2007-10-03 12:31:45Z herbelin $ *)
+(* $Id: contradiction.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Term
@@ -85,7 +85,7 @@ let contradiction_term (c,lbind as cl) gl =
 	  (fun id -> simplest_elim (mkApp (mkVar id,[|c|]))) gl
       else
 	raise Not_found
-    with Not_found -> error "Not a contradiction"
+    with Not_found -> error "Not a contradiction."
 
 let contradiction = function
   | None -> tclTHEN intros contradiction_context
diff --git a/tactics/decl_interp.ml b/tactics/decl_interp.ml
index d96fa720..97225617 100644
--- a/tactics/decl_interp.ml
+++ b/tactics/decl_interp.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: decl_interp.ml 10739 2008-04-01 14:45:20Z herbelin $ i*)
+(*i $Id: decl_interp.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Util
 open Names
@@ -162,8 +162,8 @@ let decompose_eq env id =
 	App (f,args)->
 	  if eq_constr f _eq && (Array.length args)=3 
 	  then args.(0)
-	  else error "previous step is not an equality"
-      | _ -> error "previous step is not an equality"
+	  else error "Previous step is not an equality."
+      | _ -> error "Previous step is not an equality."
 
 let get_eq_typ info env =
   let typ = decompose_eq env (get_last env) in  
@@ -331,9 +331,9 @@ let interp_cases info sigma env params (pat:cases_pattern_expr) hyps =
     let expected = mib.Declarations.mind_nparams - num_params in
       if List.length params <> expected then
 	errorlabstrm "suppose it is" 
-	  (str "Wrong number of extra arguments : " ++ 
+	  (str "Wrong number of extra arguments: " ++ 
 	     (if expected = 0 then str "none" else int expected) ++ 
-	     str "expected") in
+	     str "expected.") in
   let app_ind =
     let rind = RRef (dummy_loc,Libnames.IndRef pinfo.per_ind) in
     let rparams = List.map detype_ground pinfo.per_params in 
@@ -400,7 +400,7 @@ let interp_suffices_clause sigma env (hyps,cot)=
 	  let nhyps,nc = interp_hyps_gen fst (fun x _ -> x) sigma env hyps c in
 	  nhyps,This nc
       | Thesis Plain as th  -> interp_hyps sigma env hyps,th
-      | Thesis (For n) -> error "\"thesis for\" is not applicable here" in
+      | Thesis (For n) -> error "\"thesis for\" is not applicable here." in
   let push_one hyp env0 =
     match hyp with
 	(Hprop st | Hvar st) ->
diff --git a/tactics/decl_proof_instr.ml b/tactics/decl_proof_instr.ml
index 895b97fe..5356868a 100644
--- a/tactics/decl_proof_instr.ml
+++ b/tactics/decl_proof_instr.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: decl_proof_instr.ml 11072 2008-06-08 16:13:37Z herbelin $ *)
+(* $Id: decl_proof_instr.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -106,6 +106,9 @@ let clean_tmp gls =
   in
     clean_all (tmp_ids gls) gls
 
+let assert_postpone id t =
+  assert_as true (dummy_loc, Genarg.IntroIdentifier id) t
+
 (* start a proof *)
 
 let start_proof_tac gls=
@@ -188,7 +191,7 @@ let close_tactic_mode pts =
     let pts1=  
       try goto_current_focus pts 
       with Not_found -> 
-	error "\"return\" cannot be used outside of Declarative Proof Mode" in
+	error "\"return\" cannot be used outside of Declarative Proof Mode." in
     let pts2 = daimon_subtree pts1 in
     let pts3 = mark_as_done pts2 in 
       goto_current_focus pts3 
@@ -207,18 +210,18 @@ let close_block bt pts =
 	B_claim, Claim::_ | B_focus, Focus_claim::_ | B_proof, [] -> 
 	  daimon_subtree (goto_current_focus pts)
       | _, Claim::_ -> 
-	  error "\"end claim\" expected" 
+	  error "\"end claim\" expected."
       | _, Focus_claim::_ -> 
-	  error "\"end focus\" expected" 
+	  error "\"end focus\" expected."
       | _, [] ->
- 	  error "\"end proof\" expected" 
+ 	  error "\"end proof\" expected."
       | _, (Per (et,_,_,_)::_|Suppose_case::Per (et,_,_,_)::_) ->
 	  begin
 	    match et with
-		ET_Case_analysis -> error "\"end cases\" expected"
-	      | ET_Induction ->  error "\"end induction\" expected"
+		ET_Case_analysis -> error "\"end cases\" expected."
+	      | ET_Induction ->  error "\"end induction\" expected."
 	  end
-      | _,_ -> anomaly "lonely suppose on stack"
+      | _,_ -> anomaly "Lonely suppose on stack."
 
 (* utility for suppose / suppose it is *)
 
@@ -284,10 +287,10 @@ let justification tac gls=
       (tclSOLVE [tclTHEN tac assumption]) 
       (fun gls -> 
 	 if get_strictness () then 
-	   error "insufficient justification" 
+	   error "Insufficient justification."
 	 else
 	   begin
-	     msg_warning (str "insufficient justification");  
+	     msg_warning (str "Insufficient justification.");
 	     daimon_tac gls
 	   end) gls
 
@@ -475,7 +478,7 @@ let thus_tac c ctyp submetas gls =
     try
       find_subsubgoal c ctyp 0 submetas gls
     with Not_found -> 
-      error "I could not relate this statement to the thesis" in
+      error "I could not relate this statement to the thesis." in
   if list = [] then
     exact_check proof gls 
   else
@@ -490,7 +493,7 @@ let anon_id_base = id_of_string "__"
 let mk_stat_or_thesis info gls = function  
     This c -> c
   | Thesis (For _ ) -> 
-      error "\"thesis for ...\" is not applicable here" 
+      error "\"thesis for ...\" is not applicable here."
   | Thesis Plain -> pf_concl gls
 
 let just_tac _then cut info gls0 =
@@ -524,7 +527,7 @@ let instr_cut mkstat _thus _then cut gls0 =
     if _thus then 
       thus_tac (mkVar c_id) c_stat [] gls
     else tclIDTAC gls in
-    tclTHENS (internal_cut c_id c_stat) 
+    tclTHENS (assert_postpone c_id c_stat) 
       [tclTHEN tcl_erase_info (just_tac _then cut info);
        thus_tac] gls0
 
@@ -542,12 +545,12 @@ let decompose_eq id gls =
 	  then (args.(0),
 		args.(1), 
 		args.(2)) 
-	  else error "previous step is not an equality"
-      | _ -> error "previous step is not an equality"
+	  else error "Previous step is not an equality."
+      | _ -> error "Previous step is not an equality."
 	  
 let instr_rew _thus rew_side cut gls0 = 
   let last_id = 
-    try get_last (pf_env gls0) with _ -> error "no previous equality" in
+    try get_last (pf_env gls0) with _ -> error "No previous equality." in
   let typ,lhs,rhs = decompose_eq last_id gls0 in  
   let items_tac gls =
     match cut.cut_by with
@@ -572,14 +575,14 @@ let instr_rew _thus rew_side cut gls0 =
     match rew_side with 
 	Lhs ->
 	  let new_eq = mkApp(_eq,[|typ;cut.cut_stat.st_it;rhs|]) in
-	    tclTHENS (internal_cut c_id new_eq) 
+	    tclTHENS (assert_postpone c_id new_eq) 
 	      [tclTHEN tcl_erase_info 
 		 (tclTHENS (transitivity lhs) 
 		    [just_tac;exact_check (mkVar last_id)]);
 	       thus_tac new_eq] gls0
       | Rhs ->
 	  let new_eq = mkApp(_eq,[|typ;lhs;cut.cut_stat.st_it|]) in
-	    tclTHENS (internal_cut c_id new_eq) 
+	    tclTHENS (assert_postpone c_id new_eq) 
 	      [tclTHEN tcl_erase_info 
 		 (tclTHENS (transitivity rhs) 
 		    [exact_check (mkVar last_id);just_tac]);
@@ -600,7 +603,7 @@ let instr_claim _thus st gls0 =
     else tclIDTAC gls in
   let ninfo1 = {pm_stack=
       (if _thus then Focus_claim else Claim)::info.pm_stack} in
-    tclTHENS (internal_cut id st.st_it) 
+    tclTHENS (assert_postpone id st.st_it) 
       [tcl_change_info ninfo1;
        thus_tac] gls0
 
@@ -691,7 +694,7 @@ let instr_suffices _then cut gls0 =
   let c_term = applist (mkVar c_id,List.map mkMeta metas) in  
   let thus_tac gls= 
     thus_tac c_term c_head c_ctx gls in
-   tclTHENS (internal_cut c_id c_stat) 
+   tclTHENS (assert_postpone c_id c_stat) 
      [tclTHENLIST 
 	 [ assume_tac ctx;   
 	   tcl_erase_info;
@@ -730,7 +733,7 @@ let rec consider_match may_intro introduced available expected gls =
   match available,expected with 
       [],[] ->
 	  tclIDTAC gls
-    | _,[] -> error "last statements do not match a complete hypothesis" 
+    | _,[] -> error "Last statements do not match a complete hypothesis."
 	(* should tell which ones *)
     | [],hyps -> 
 	if may_intro then
@@ -740,11 +743,11 @@ let rec consider_match may_intro introduced available expected gls =
 		(intro_mustbe_force id)
 		(consider_match true [] [id] hyps) 
 		(fun _ -> 
-		   error "not enough sub-hypotheses to match statements")
+		   error "Not enough sub-hypotheses to match statements.")
 		gls 
           end 
 	else
-	  error "not enough sub-hypotheses to match statements" 
+	  error "Not enough sub-hypotheses to match statements."
 	    (* should tell which ones *)
     | id::rest_ids,(Hvar st | Hprop st)::rest ->
 	tclIFTHENELSE (convert_hyp (id,None,st.st_it))
@@ -761,7 +764,7 @@ let rec consider_match may_intro introduced available expected gls =
 	    (fun gls -> 
 	       let nhyps =
 		 try conjunction_arity id gls with 
-		     Not_found -> error "matching hypothesis not found" in 
+		     Not_found -> error "Matching hypothesis not found." in 
 		 tclTHENLIST 
 		   [general_case_analysis false (mkVar id,NoBindings);
 		    intron_then nhyps []
@@ -777,7 +780,7 @@ let consider_tac c hyps gls =
     | _ -> 
 	let id = pf_get_new_id (id_of_string "_tmp") gls in
 	tclTHEN 
-	  (forward None (Genarg.IntroIdentifier id) c)
+	  (forward None (dummy_loc, Genarg.IntroIdentifier id) c)
  	  (consider_match false [] [id] hyps) gls 
 	  
 
@@ -818,7 +821,7 @@ let cast_tac id_or_thesis typ gls =
 	let (_,body,_) = pf_get_hyp gls id in
 	  convert_hyp (id,body,typ) gls
     | Thesis (For _ ) -> 
-	error "\"thesis for ...\" is not applicable here" 
+	error "\"thesis for ...\" is not applicable here."
     | Thesis Plain ->    
           convert_concl typ DEFAULTcast gls
       
@@ -884,7 +887,7 @@ let build_per_info etype casee gls =
     try
       destInd hd 
     with _ -> 
-      error "Case analysis must be done on an inductive object" in
+      error "Case analysis must be done on an inductive object." in
   let mind,oind = Global.lookup_inductive ind in
   let nparams,index =
     match etype with
@@ -955,7 +958,7 @@ let suppose_tac hyps gls0 =
   let ninfo1 = {pm_stack=Suppose_case::info.pm_stack} in
   let old_clauses,stack = register_nodep_subcase id info.pm_stack in
   let ninfo2 = {pm_stack=stack} in
-    tclTHENS (internal_cut id clause) 
+    tclTHENS (assert_postpone id clause) 
       [tclTHENLIST [tcl_change_info ninfo1;
 		    assume_tac hyps;
 		    clear old_clauses];
@@ -1042,7 +1045,7 @@ let rec add_branch ((id,_) as cpl) pats tree=
 		      | Split_patt (_,ind0,_) ->
 			  if (ind <> ind0) then error
 			    (* this can happen with coercions *)
-	                    "Case pattern belongs to wrong inductive type";
+	                    "Case pattern belongs to wrong inductive type.";
 			  let mapi i ati bri =
 			    if i = pred cnum then 
 			      let nargs = 
@@ -1083,12 +1086,12 @@ let thesis_for obj typ per_info env=
   let _ = if ind <> per_info.per_ind then
     errorlabstrm "thesis_for" 
       ((Printer.pr_constr_env env obj) ++ spc () ++ 
-	 str "cannot give an induction hypothesis (wrong inductive type)") in  
+	 str"cannot give an induction hypothesis (wrong inductive type).") in  
   let params,args = list_chop per_info.per_nparams all_args in
   let _ = if not (List.for_all2 eq_constr params per_info.per_params) then
     errorlabstrm "thesis_for" 
       ((Printer.pr_constr_env env obj) ++ spc () ++ 
-	 str "cannot give an induction hypothesis (wrong parameters)") in
+	 str "cannot give an induction hypothesis (wrong parameters).") in
   let hd2 = (applist ((lift (List.length rc) per_info.per_pred),args@[obj])) in
     compose_prod rc (whd_beta hd2)
 
@@ -1161,7 +1164,7 @@ let case_tac params pat_info hyps gls0 =
     register_dep_subcase (id,List.length hyps) (pf_env gls0) per_info 
       pat_info.pat_pat ek in  
   let ninfo2 = {pm_stack=Per(et,per_info,nek,id::old_clauses)::rest} in
-    tclTHENS (internal_cut id clause) 
+    tclTHENS (assert_postpone id clause) 
       [tclTHENLIST 
 	 [tcl_change_info ninfo1; 
 	  assume_st (params@pat_info.pat_vars);
diff --git a/tactics/dhyp.ml b/tactics/dhyp.ml
index 5dd7f5fd..14731b26 100644
--- a/tactics/dhyp.ml
+++ b/tactics/dhyp.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: dhyp.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: dhyp.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (* Chet's comments about this tactic :
  
@@ -246,7 +246,7 @@ let add_destructor_hint local na loc pat pri code =
       | ConclLocation _, _ -> (None, code)
       | _ ->
 	  errorlabstrm "add_destructor_hint"
-          (str "The tactic should be a function of the hypothesis name") end
+          (str "The tactic should be a function of the hypothesis name.") end
   in
   let (_,pat) = Constrintern.interp_constrpattern Evd.empty (Global.env()) pat
   in
@@ -279,13 +279,13 @@ let match_dpat dp cls gls =
               (is_matching concld.d_typ cl) &
               (is_matching concld.d_sort (pf_type_of gls cl)))
             hl)
-        then error "No match"
+        then error "No match."
     | ({onhyps=Some[]},ConclLocation concld) when onconcl ->
         let cl = pf_concl gls in
         if not
           ((is_matching concld.d_typ cl) &
            (is_matching concld.d_sort (pf_type_of gls cl)))
-        then error "No match"
+        then error "No match."
     | _ -> error "ApplyDestructor"
 
 let forward_interp_tactic = 
@@ -304,8 +304,8 @@ let applyDestructor cls discard dd gls =
               ConstrMayEval(ConstrTerm (RRef(dummy_loc,VarRef id),None)) in
             TacLetIn (false, [(dummy_loc, x), arg], tac)
         | None, (None, tac) -> tac
-        | _, (Some _,_) -> error "Destructor expects an hypothesis"
-        | _, (None,_) -> error "Destructor is for conclusion")
+        | _, (Some _,_) -> error "Destructor expects an hypothesis."
+        | _, (None,_) -> error "Destructor is for conclusion.")
       cll in
   let discard_0 =
     List.map (fun cl ->
diff --git a/tactics/dn.ml b/tactics/dn.ml
index ab908ff9..2a8166dc 100644
--- a/tactics/dn.ml
+++ b/tactics/dn.ml
@@ -1,3 +1,4 @@
+(* -*- compile-command: "make -C .. bin/coqtop.byte" -*- *)
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
@@ -6,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: dn.ml 5920 2004-07-16 20:01:26Z herbelin $ *)
+(* $Id: dn.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (* This file implements the basic structure of what Chet called
    ``discrimination nets''. If my understanding is right, it serves
@@ -32,6 +33,10 @@
 
 type ('lbl,'pat) decompose_fun = 'pat -> ('lbl * 'pat list) option
 
+type 'res lookup_res = Label of 'res | Nothing | Everything
+    
+type ('lbl,'tree) lookup_fun = 'tree -> ('lbl * 'tree list) lookup_res
+
 type ('lbl,'pat,'inf) t = (('lbl * int) option,'pat * 'inf) Tlm.t
 
 let create () = Tlm.empty
@@ -46,29 +51,44 @@ let path_of dna =
 	    
   and pathrec deferred t =
     match dna t with
-      | None -> 
-	  None :: (path_of_deferred deferred)
-      | Some (lbl,[]) ->
-	  (Some (lbl,0))::(path_of_deferred deferred)
-      | Some (lbl,(h::def_subl as v)) ->
-	  (Some (lbl,List.length v))::(pathrec (def_subl@deferred) h)
+    | None -> 
+	None :: (path_of_deferred deferred)
+    | Some (lbl,[]) ->
+	(Some (lbl,0))::(path_of_deferred deferred)
+    | Some (lbl,(h::def_subl as v)) ->
+	(Some (lbl,List.length v))::(pathrec (def_subl@deferred) h)
   in 
   pathrec []
     
 let tm_of tm lbl =
-  try [Tlm.map tm lbl] with Not_found -> []
-
+  try [Tlm.map tm lbl, true] with Not_found -> []
+    
+let rec skip_arg n tm =
+  if n = 0 then [tm,true]
+  else
+    List.flatten 
+      (List.map 
+	  (fun a -> match a with
+	  | None -> skip_arg (pred n) (Tlm.map tm a)
+	  | Some (lbl,m) -> 
+	      skip_arg (pred n + m) (Tlm.map tm a)) 
+	  (Tlm.dom tm))
+      
 let lookup tm dna t =
   let rec lookrec t tm =
-    (tm_of tm None)@
-    (match dna t with
-       | None -> []
-       | Some(lbl,v) ->
-	   List.fold_left 
-	     (fun l c -> List.flatten(List.map (lookrec c) l))
-             (tm_of tm (Some(lbl,List.length v))) v)
+    match dna t with
+    | Nothing -> tm_of tm None
+    | Label(lbl,v) ->
+	tm_of tm None@
+	  (List.fold_left 
+	      (fun l c -> 
+		List.flatten(List.map (fun (tm, b) ->
+		  if b then lookrec c tm
+		  else [tm,b]) l))
+              (tm_of tm (Some(lbl,List.length v))) v)
+    | Everything -> skip_arg 1 tm
   in 
-  List.flatten(List.map Tlm.xtract (lookrec t tm))
+    List.flatten (List.map (fun (tm,b) -> Tlm.xtract tm) (lookrec t tm))
 
 let add tm dna (pat,inf) =
   let p = path_of dna pat in Tlm.add tm (p,(pat,inf))
diff --git a/tactics/dn.mli b/tactics/dn.mli
index f8efd053..62e37a73 100644
--- a/tactics/dn.mli
+++ b/tactics/dn.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: dn.mli 5920 2004-07-16 20:01:26Z herbelin $ i*)
+(*i $Id: dn.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (* Discrimination nets. *)
 
@@ -28,13 +28,19 @@ val add : ('lbl,'pat,'inf) t -> ('lbl,'pat) decompose_fun -> 'pat * 'inf
 val rmv : ('lbl,'pat,'inf) t -> ('lbl,'pat) decompose_fun -> 'pat * 'inf 
   -> ('lbl,'pat,'inf) t
 
+type 'res lookup_res = Label of 'res | Nothing | Everything
+    
+type ('lbl,'tree) lookup_fun = 'tree -> ('lbl * 'tree list) lookup_res
+
 (* [lookup t f tree] looks for trees (and their associated
    information) in table [t] such that the structured object [tree]
    matches against them; [f] is used to translated [tree] into its
    prefix decomposition: [f] must decompose any tree into a label
    characterizing its root node and the list of its subtree *)
 
-val lookup : ('lbl,'pat,'inf) t -> ('lbl,'term) decompose_fun -> 'term
+val lookup : ('lbl,'pat,'inf) t -> ('lbl,'term) lookup_fun -> 'term
   -> ('pat * 'inf) list
 
 val app : (('pat * 'inf) -> unit) -> ('lbl,'pat,'inf) t -> unit
+
+val skip_arg : int -> ('lbl,'pat,'inf) t -> (('lbl,'pat,'inf) t * bool) list
diff --git a/tactics/eauto.ml4 b/tactics/eauto.ml4
index 2effe103..1503ca9a 100644
--- a/tactics/eauto.ml4
+++ b/tactics/eauto.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: eauto.ml4 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: eauto.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -74,11 +74,11 @@ let prolog_tac l n gl =
   let n =
     match n with
       |  ArgArg n -> n
-      | _ -> error "Prolog called with a non closed argument"
+      | _ -> error "Prolog called with a non closed argument."
   in
   try (prolog l n gl)
   with UserError ("Refiner.tclFIRST",_) ->
-    errorlabstrm "Prolog.prolog" (str "Prolog failed")
+    errorlabstrm "Prolog.prolog" (str "Prolog failed.")
 
 TACTIC EXTEND prolog
 | [ "prolog" "[" constr_list(l) "]" int_or_var(n) ] -> [ prolog_tac l n ]
@@ -111,7 +111,7 @@ let rec e_trivial_fail_db mod_delta db_list local_db goal =
 	  let d = pf_last_hyp g' in
 	  let hintl = make_resolve_hyp (pf_env g') (project g') d in
           (e_trivial_fail_db mod_delta db_list
-	     (add_hint_list hintl local_db) g'))) ::
+	      (Hint_db.add_list hintl local_db) g'))) ::
     (List.map fst (e_trivial_resolve mod_delta db_list local_db (pf_concl goal)) )
   in 
   tclFIRST (List.map tclCOMPLETE tacl) goal 
@@ -124,10 +124,9 @@ and e_my_find_search_nodelta db_list local_db hdc concl =
   let hdc = head_of_constr_reference hdc in
   let hintl =
     if occur_existential concl then 
-      list_map_append (fun (st, db) -> Hint_db.map_all hdc db) (local_db::db_list)
+      list_map_append (Hint_db.map_all hdc) (local_db::db_list)
     else 
-      list_map_append (fun (st, db) -> 
-	Hint_db.map_auto (hdc,concl) db) (local_db::db_list)
+      list_map_append (Hint_db.map_auto (hdc,concl)) (local_db::db_list)
   in 
   let tac_of_hint = 
     fun {pri=b; pat = p; code=t} -> 
@@ -160,12 +159,12 @@ and e_my_find_search_delta db_list local_db hdc concl =
   let hdc = head_of_constr_reference hdc in
   let hintl =
     if occur_existential concl then 
-      list_map_append (fun (st, db) -> 
-	let flags = {auto_unif_flags with modulo_delta = st} in
+      list_map_append (fun db -> 
+	let flags = {auto_unif_flags with modulo_delta = Hint_db.transparent_state db} in
 	  List.map (fun x -> flags, x) (Hint_db.map_all hdc db)) (local_db::db_list)
     else 
-      list_map_append (fun (st, db) -> 
-	let flags = {auto_unif_flags with modulo_delta = st} in
+      list_map_append (fun db -> 
+	let flags = {auto_unif_flags with modulo_delta = Hint_db.transparent_state db} in
 	  List.map (fun x -> flags, x) (Hint_db.map_auto (hdc,concl) db)) (local_db::db_list)
   in 
   let tac_of_hint = 
@@ -285,8 +284,7 @@ module SearchProblem = struct
 	     let hintl = 
 	       make_resolve_hyp (pf_env g') (project g') (pf_last_hyp g')
 	     in
-	       
-             let ldb = add_hint_list hintl (List.hd s.localdb) in
+             let ldb = Hint_db.add_list hintl (List.hd s.localdb) in
 	     { depth = s.depth; tacres = res; 
 	       last_tactic = pp; dblist = s.dblist;
 	       localdb = ldb :: List.tl s.localdb })
@@ -333,7 +331,7 @@ let e_depth_search debug p db_list local_db gl =
     let tac = if debug then Search.debug_depth_first else Search.depth_first in
     let s = tac (make_initial_state p gl db_list local_db) in
     s.tacres
-  with Not_found -> error "EAuto: depth first search failed"
+  with Not_found -> error "eauto: depth first search failed."
 
 let e_breadth_search debug n db_list local_db gl =
   try
@@ -342,7 +340,7 @@ let e_breadth_search debug n db_list local_db gl =
     in
     let s = tac (make_initial_state n gl db_list local_db) in
     s.tacres
-  with Not_found -> error "EAuto: breadth first search failed"
+  with Not_found -> error "eauto: breadth first search failed."
 
 let e_search_auto debug (in_depth,p) lems db_list gl = 
   let local_db = make_local_hint_db true lems gl in 
@@ -361,7 +359,7 @@ let eauto debug np lems dbnames =
     List.map
       (fun x -> 
 	 try searchtable_map x
-	 with Not_found -> error ("EAuto: "^x^": No such Hint database"))
+	 with Not_found -> error ("No such Hint database: "^x^"."))
       ("core"::dbnames) 
   in
   tclTRY (e_search_auto debug np lems db_list)
@@ -379,12 +377,12 @@ let gen_eauto d np lems = function
 let make_depth = function
   | None -> !default_search_depth 
   | Some (ArgArg d) -> d
-  | _ -> error "EAuto called with a non closed argument"
+  | _ -> error "eauto called with a non closed argument."
 
 let make_dimension n = function
   | None -> (true,make_depth n)
   | Some (ArgArg d) -> (false,d)
-  | _ -> error "EAuto called with a non closed argument"
+  | _ -> error "eauto called with a non closed argument."
 
 open Genarg
 
@@ -452,7 +450,8 @@ let autosimpl db cl =
     else []
   in
   let unfolds = List.concat (List.map (fun dbname -> 
-    let ((ids, csts), _) = searchtable_map dbname in
+    let db = searchtable_map dbname in
+    let (ids, csts) = Hint_db.transparent_state db in
       unfold_of_elts (fun x -> EvalConstRef x) (Cpred.elements csts) @
       unfold_of_elts (fun x -> EvalVarRef x) (Idpred.elements ids)) db)
   in unfold_option unfolds cl
diff --git a/tactics/elim.ml b/tactics/elim.ml
index 889ead5e..55df0f0a 100644
--- a/tactics/elim.ml
+++ b/tactics/elim.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: elim.ml 9842 2007-05-20 17:44:23Z herbelin $ *)
+(* $Id: elim.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -49,8 +49,8 @@ let introCaseAssumsThen tac ba =
     else 
       (ba.branchnames, []),
        if n1 > n2 then snd (list_chop n2 case_thin_sign) else [] in
-  let introCaseAssums = tclTHEN (intros_pattern None l1) (intros_clearing l3)
-  in
+  let introCaseAssums =
+    tclTHEN (intros_pattern no_move l1) (intros_clearing l3) in
   (tclTHEN introCaseAssums (case_on_ba (tac l2) ba))
 
 (* The following tactic Decompose repeatedly applies the
@@ -115,7 +115,7 @@ let inductive_of = function
   | IndRef ity -> ity
   | r ->
       errorlabstrm "Decompose"
-        (Printer.pr_global r ++ str " is not an inductive type")
+        (Printer.pr_global r ++ str " is not an inductive type.")
 
 let decompose_these c l gls =
   let indl = (*List.map inductive_of*) l in 
@@ -182,7 +182,7 @@ let double_ind h1 h2 gls =
   let (abs_i,abs_j) =
     if abs_i < abs_j then (abs_i,abs_j) else
     if abs_i > abs_j then (abs_j,abs_i) else
-      error "Both hypotheses are the same" in
+      error "Both hypotheses are the same." in
   (tclTHEN (tclDO abs_i intro)
      (onLastHyp
        	(fun id ->
diff --git a/tactics/elim.mli b/tactics/elim.mli
index d01d3027..cbbf2f83 100644
--- a/tactics/elim.mli
+++ b/tactics/elim.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: elim.mli 5920 2004-07-16 20:01:26Z herbelin $ i*)
+(*i $Id: elim.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -23,7 +23,7 @@ val introElimAssumsThen :
   (branch_assumptions -> tactic) -> branch_args -> tactic
 
 val introCaseAssumsThen :
-  (intro_pattern_expr list -> branch_assumptions -> tactic) -> 
+  (intro_pattern_expr Util.located list -> branch_assumptions -> tactic) -> 
     branch_args -> tactic
 
 val general_decompose : (identifier * constr -> bool) -> constr -> tactic
diff --git a/tactics/eqdecide.ml4 b/tactics/eqdecide.ml4
index 8e0b2ca3..41f85fa3 100644
--- a/tactics/eqdecide.ml4
+++ b/tactics/eqdecide.ml4
@@ -14,7 +14,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: eqdecide.ml4 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: eqdecide.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Names
@@ -152,14 +152,14 @@ let decideGralEquality g =
     let rectype =
       match kind_of_term headtyp with
         | Ind mi -> mi
-	| _ -> error "This decision procedure only works for inductive objects"
+	| _ -> error"This decision procedure only works for inductive objects."
     in
     (tclTHEN
       (mkBranches c1 c2)
       (tclORELSE (h_solveNoteqBranch eqonleft) (solveEqBranch rectype)))
     g
   with PatternMatchingFailure ->
-    error "The goal must be of the form {x<>y}+{x=y} or {x=y}+{x<>y}"
+    error "The goal must be of the form {x<>y}+{x=y} or {x=y}+{x<>y}."
 
 let decideEqualityGoal = tclTHEN intros decideGralEquality
 
diff --git a/tactics/equality.ml b/tactics/equality.ml
index a475b392..7fb19423 100644
--- a/tactics/equality.ml
+++ b/tactics/equality.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: equality.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: equality.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -76,14 +76,9 @@ let elimination_sort_of_clause = function
 
 (* The next function decides in particular whether to try a regular 
   rewrite or a setoid rewrite. 
-
-  Old approach was: 
-   break everything, if [eq] appears in head position 
-   then regular rewrite else try setoid rewrite
- 
-  New approach is: 
-   if head position is a known setoid relation then setoid rewrite
-   else back to the old approach
+  Approach is to break everything, if [eq] appears in head position 
+  then regular rewrite else try setoid rewrite. 
+  If occurrences are set, use setoid_rewrite.
 *)
 
 let general_s_rewrite_clause = function
@@ -93,45 +88,55 @@ let general_s_rewrite_clause = function
 let general_setoid_rewrite_clause = ref general_s_rewrite_clause
 let register_general_setoid_rewrite_clause = (:=) general_setoid_rewrite_clause
 
+let is_applied_setoid_relation = ref (fun _ -> false)
+let register_is_applied_setoid_relation = (:=) is_applied_setoid_relation
+
+let is_applied_relation t =
+  match kind_of_term t with
+  | App (c, args) when Array.length args >= 2 -> true
+  | _ -> false
+
+let leibniz_rewrite_ebindings_clause cls lft2rgt (c,l) with_evars gl hdcncl =
+  let hdcncls = string_of_inductive hdcncl in 
+  let suffix = elimination_suffix (elimination_sort_of_clause cls gl) in
+  let dir = if cls=None then lft2rgt else not lft2rgt in
+  let rwr_thm = if dir then hdcncls^suffix^"_r" else hdcncls^suffix in
+  let elim =
+    try pf_global gl (id_of_string rwr_thm)
+    with Not_found ->
+      error ("Cannot find rewrite principle "^rwr_thm^".")
+  in general_elim_clause with_evars cls (c,l) (elim,NoBindings) gl
+
+let leibniz_eq = Lazy.lazy_from_fun build_coq_eq
+
 let general_rewrite_ebindings_clause cls lft2rgt occs (c,l) with_evars gl =
-  let ctype = pf_apply get_type_of gl c in 
-  (* A delta-reduction would be here too strong, since it would 
-     break search for a defined setoid relation in head position. *)
-  let t = snd (decompose_prod (whd_betaiotazeta ctype)) in 
-  let head = if isApp t then fst (destApp t) else t in 
-    if relation_table_mem head && l = NoBindings then 
-      !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
-    else 
-      (* Original code. In particular, [splay_prod] performs delta-reduction. *)
-      let env = pf_env gl in
-      let sigma = project gl in 
-      let _,t = splay_prod env sigma ctype in
-	match match_with_equation t with
-	  | None -> 
-	      if l = NoBindings
-	      then !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
-	      else error "The term provided does not end with an equation" 
-	  | Some (hdcncl,_) -> 
-	      if occs <> all_occurrences then (
-		!general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl)
-	      else
-		let hdcncls = string_of_inductive hdcncl in 
-		let suffix = elimination_suffix (elimination_sort_of_clause cls gl) in
-		let dir = if cls=None then lft2rgt else not lft2rgt in
-		let rwr_thm = if dir then hdcncls^suffix^"_r" else hdcncls^suffix in
-		let elim =
-		  try pf_global gl (id_of_string rwr_thm)
-		  with Not_found ->
-		    error ("Cannot find rewrite principle "^rwr_thm)
-		in 
-		  try general_elim_clause with_evars cls (c,l) (elim,NoBindings) gl
-		  with e -> 
-		    let eq = build_coq_eq () in
-		      if not (eq_constr eq head) then
-			try !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
-			with _ -> raise e
-		      else raise e
-			
+  if occs <> all_occurrences then (
+    !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl)
+  else
+    let ctype = pf_apply get_type_of gl c in 
+    let env = pf_env gl in
+    let sigma = project gl in 
+    let rels, t = decompose_prod (whd_betaiotazeta ctype) in
+      match match_with_equation t with
+      | Some (hdcncl,_) -> (* Fast path: direct leibniz rewrite *)
+	  leibniz_rewrite_ebindings_clause cls lft2rgt (c,l) with_evars gl hdcncl
+      | None ->
+	  let env' = List.fold_left (fun env (n,t) -> push_rel (n, None, t) env) env rels in
+	  let _,t' = splay_prod env' sigma t in (* Search for underlying eq *)
+	    match match_with_equation t' with
+	    | Some (hdcncl,_) -> (* Maybe a setoid relation with eq inside *)
+		if l = NoBindings && !is_applied_setoid_relation t then
+		  !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
+		else
+		  (try leibniz_rewrite_ebindings_clause cls lft2rgt (c,l) with_evars gl hdcncl
+		    with e -> 
+		      try !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
+		      with _ -> raise e)
+	    | None -> (* Can't be leibniz, try setoid *)
+		if l = NoBindings
+		then !general_setoid_rewrite_clause cls lft2rgt occs c ~new_goals:[] gl
+		else error "The term provided does not end with an equation."
+
 let general_rewrite_ebindings = 
   general_rewrite_ebindings_clause None
 let general_rewrite_bindings l2r occs (c,bl) = 
@@ -269,7 +274,7 @@ let multi_replace clause c2 c1 unsafe try_prove_eq_opt gl =
 	 ]
       ] gl
   else
-    error "terms do not have convertible types"
+    error "Terms do not have convertible types."
   
 
 let replace c2 c1 gl = multi_replace onConcl c2 c1 false None gl
@@ -494,7 +499,7 @@ let construct_discriminator sigma env dirn c sort =
        *)
       errorlabstrm "Equality.construct_discriminator"
 	(str "Cannot discriminate on inductive constructors with 
-		 dependent types") in
+		 dependent types.") in
   let (ind,_) = dest_ind_family indf in
   let (mib,mip) = lookup_mind_specif env ind in
   let (true_0,false_0,sort_0) = build_coq_True(),build_coq_False(),Prop Null in
@@ -534,7 +539,7 @@ let gen_absurdity id gl =
     simplest_elim (mkVar id) gl
   else
     errorlabstrm "Equality.gen_absurdity" 
-      (str "Not the negation of an equality")
+      (str "Not the negation of an equality.")
 
 (* Precondition: eq is leibniz equality
  
@@ -559,7 +564,7 @@ let apply_on_clause (f,t) clause =
   let argmv = 
     (match kind_of_term (last_arg f_clause.templval.Evd.rebus) with
      | Meta mv -> mv
-     | _  -> errorlabstrm "" (str "Ill-formed clause applicator")) in
+     | _  -> errorlabstrm "" (str "Ill-formed clause applicator.")) in
   clenv_fchain argmv f_clause clause
 
 let discr_positions env sigma (lbeq,(t,t1,t2)) eq_clause cpath dirn sort =
@@ -580,7 +585,7 @@ let discrEq (lbeq,(t,t1,t2) as u) eq_clause gls =
   let env = pf_env gls in
   match find_positions env sigma t1 t2 with
     | Inr _ ->
-	errorlabstrm "discr" (str"Not a discriminable equality")
+	errorlabstrm "discr" (str"Not a discriminable equality.")
     | Inl (cpath, (_,dirn), _) ->
 	let sort = pf_apply get_type_of gls (pf_concl gls) in 
 	discr_positions env sigma u eq_clause cpath dirn sort gls
@@ -594,7 +599,7 @@ let onEquality with_evars tac (c,lbindc) gls =
   let eq =
     try find_eq_data_decompose eqn
     with PatternMatchingFailure ->
-      errorlabstrm "" (str"No primitive equality found") in
+      errorlabstrm "" (str"No primitive equality found.") in
   tclTHEN
     (Refiner.tclEVARS (Evd.evars_of eq_clause'.evd)) 
     (tac eq eq_clause') gls
@@ -607,7 +612,7 @@ let onNegatedEquality with_evars tac gls =
         (onLastHyp (fun id -> 
           onEquality with_evars tac (mkVar id,NoBindings))) gls
   | _ -> 
-      errorlabstrm "" (str "Not a negated primitive equality")
+      errorlabstrm "" (str "Not a negated primitive equality.")
 
 let discrSimpleClause with_evars = function
   | None -> onNegatedEquality with_evars discrEq
@@ -622,7 +627,7 @@ let discrEverywhere with_evars =
     (Tacticals.tryAllClauses
       (fun cl -> tclCOMPLETE (discrSimpleClause with_evars cl)))
     (fun gls -> 
-       errorlabstrm "DiscrEverywhere" (str"No discriminable equalities"))
+       errorlabstrm "DiscrEverywhere" (str"No discriminable equalities."))
 
 let discr_tac with_evars = function
   | None -> discrEverywhere with_evars
@@ -723,7 +728,7 @@ let sig_clausal_form env sigma sort_of_ty siglen ty dflt =
 	(* the_conv_x had a side-effect on evdref *)
 	dflt
       else
-	error "Cannot solve an unification problem"
+	error "Cannot solve an unification problem."
     else
       let (a,p_i_minus_1) = match whd_beta_stack p_i with
 	| (_sigS,[a;p]) -> (a,p)
@@ -865,7 +870,7 @@ let inject_at_positions env sigma (eq,(t,t1,t2)) eq_clause posns =
 	(pf,ty))
       posns in
   if injectors = [] then
-    errorlabstrm "Equality.inj" (str "Failed to decompose the equality");
+    errorlabstrm "Equality.inj" (str "Failed to decompose the equality.");
   tclMAP
     (fun (pf,ty) -> tclTHENS (cut ty) [tclIDTAC; refine pf])
     injectors
@@ -879,10 +884,10 @@ let injEq ipats (eq,(t,t1,t2)) eq_clause =
   match find_positions env sigma t1 t2 with
     | Inl _ ->
 	errorlabstrm "Inj"
-	  (str"Not a projectable equality but a discriminable one")
+	  (str"Not a projectable equality but a discriminable one.")
     | Inr [] ->
 	errorlabstrm "Equality.inj" 
-	   (str"Nothing to do, it is an equality between convertible terms")
+	   (str"Nothing to do, it is an equality between convertible terms.")
     | Inr posns ->
 (* Est-ce utile à partir du moment où les arguments projetés subissent "nf" ?
 	let t1 = try_delta_expand env sigma t1 in
@@ -923,7 +928,7 @@ let injEq ipats (eq,(t,t1,t2)) eq_clause =
         ) with _ ->
 	tclTHEN
 	  (inject_at_positions env sigma (eq,(t,t1,t2)) eq_clause posns)
-	  (intros_pattern None ipats)
+	  (intros_pattern no_move ipats)
 
 let inj ipats with_evars = onEquality with_evars (injEq ipats)
 
@@ -986,7 +991,7 @@ let find_elim sort_of_gl lbeq =
         (match lbeq.rect with
            | Some eq_rect -> eq_rect
            | None -> errorlabstrm "find_elim"
-		 (str "this type of substitution is not allowed"))
+		 (str "This type of substitution is not allowed."))
 
 (* Refine from [|- P e2] to [|- P e1] and [|- e1=e2:>t] (body is P (Rel 1)) *)
 
@@ -1086,11 +1091,10 @@ let try_rewrite tac gls =
     tac gls
   with 
     | PatternMatchingFailure ->
-	errorlabstrm "try_rewrite" (str "Not a primitive equality here")
+	errorlabstrm "try_rewrite" (str "Not a primitive equality here.")
     | e when catchable_exception e -> 
 	errorlabstrm "try_rewrite"
-          (str "Cannot find a well-typed generalization of the goal that" ++
-             str " makes the proof progress")
+          (strbrk "Cannot find a well-typed generalization of the goal that makes the proof progress.")
 
 let cutSubstClause l2r eqn cls gls =
   match cls with
@@ -1145,7 +1149,7 @@ let unfold_body x gl =
     match Sign.lookup_named x hyps with
         (_,Some xval,_) -> xval
       | _ -> errorlabstrm "unfold_body"
-          (pr_id x ++ str" is not a defined hypothesis") in
+          (pr_id x ++ str" is not a defined hypothesis.") in
   let aft = afterHyp x gl in
   let hl = List.fold_right 
     (fun (y,yval,_) cl -> ((all_occurrences_expr,y),InHyp) :: cl) aft [] in
@@ -1182,7 +1186,8 @@ let subst_one x gl =
       let test hyp _ = is_eq_x varx hyp in
       Sign.fold_named_context test ~init:() hyps;
       errorlabstrm "Subst"
-        (str "cannot find any non-recursive equality over " ++ pr_id x)
+        (str "Cannot find any non-recursive equality over " ++ pr_id x ++
+	 str".")
     with FoundHyp res -> res
   in
   (* The set of hypotheses using x *)
@@ -1263,7 +1268,7 @@ let cond_eq_term c t gl =
 
 let rewrite_multi_assumption_cond cond_eq_term cl gl = 
   let rec arec = function 
-    | [] -> error "No such assumption"
+    | [] -> error "No such assumption."
     | (id,_,t) ::rest -> 
 	begin 
 	  try 
@@ -1286,7 +1291,7 @@ let replace_multi_term dir_opt c  =
 (* JF. old version 
 let rewrite_assumption_cond faildir gl =
    let rec arec = function
-      | [] -> error "No such assumption"
+      | [] -> error "No such assumption."
       | (id,_,t)::rest ->
 	  (try let dir = faildir t gl in
 	       general_rewrite dir (mkVar id) gl
@@ -1296,7 +1301,7 @@ let rewrite_assumption_cond faildir gl =
 
 let rewrite_assumption_cond_in faildir hyp gl =
    let rec arec = function
-      | [] -> error "No such assumption"
+      | [] -> error "No such assumption."
       | (id,_,t)::rest ->
 	  (try let dir = faildir t gl in
 	       general_rewrite_in dir hyp (mkVar id) gl
diff --git a/tactics/equality.mli b/tactics/equality.mli
index 42c502be..f05ebc6c 100644
--- a/tactics/equality.mli
+++ b/tactics/equality.mli
@@ -6,9 +6,10 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: equality.mli 11166 2008-06-22 13:23:35Z herbelin $ i*)
+(*i $Id: equality.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
+open Util
 open Names
 open Term
 open Sign
@@ -45,6 +46,7 @@ val rewriteRL   : constr  -> tactic
 val register_general_setoid_rewrite_clause :
   (identifier option -> bool ->
     occurrences -> constr -> new_goals:constr list -> tactic) -> unit
+val register_is_applied_setoid_relation : (constr -> bool) -> unit
 
 val general_rewrite_bindings_in :
   bool -> occurrences -> identifier -> constr with_bindings -> evars_flag -> tactic
@@ -74,9 +76,9 @@ val discrHyp     : identifier -> tactic
 val discrEverywhere : evars_flag -> tactic
 val discr_tac    : evars_flag -> 
   constr with_ebindings induction_arg option -> tactic
-val inj          : intro_pattern_expr list -> evars_flag ->
+val inj          : intro_pattern_expr located list -> evars_flag ->
   constr with_ebindings -> tactic
-val injClause    : intro_pattern_expr list -> evars_flag -> 
+val injClause    : intro_pattern_expr located list -> evars_flag -> 
   constr with_ebindings induction_arg option -> tactic
 val injHyp       : identifier -> tactic
 val injConcl     : tactic
diff --git a/tactics/evar_tactics.ml b/tactics/evar_tactics.ml
index b4a39a24..3c266c51 100644
--- a/tactics/evar_tactics.ml
+++ b/tactics/evar_tactics.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: evar_tactics.ml 11072 2008-06-08 16:13:37Z herbelin $ *)
+(* $Id: evar_tactics.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Term
 open Util
@@ -41,16 +41,16 @@ let instantiate n rawc ido gl =
 		  (match decl with 
 		      (_,None,typ) -> evar_list sigma typ
 		    | _ -> error 
-			"please be more specific : in type or value ?")
+			"Please be more specific: in type or value?")
 	      | InHypTypeOnly ->
 		  let (_, _, typ) = decl in evar_list sigma typ
 	      | InHypValueOnly ->
 		  (match decl with 
 		      (_,Some body,_) -> evar_list sigma body
-		    | _ -> error "not a let .. in  hypothesis") in
+		    | _ -> error "Not a defined hypothesis.") in
     if List.length evl < n then
       error "not enough uninstantiated existential variables";
-    if n <= 0 then error "incorrect existential variable index";
+    if n <= 0 then error "Incorrect existential variable index.";
     let ev,_ =  destEvar (List.nth evl (n-1)) in
     let evd' = w_refine ev rawc (create_goal_evar_defs sigma) in
       tclTHEN
diff --git a/tactics/extratactics.ml4 b/tactics/extratactics.ml4
index 885138e4..66716acd 100644
--- a/tactics/extratactics.ml4
+++ b/tactics/extratactics.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: extratactics.ml4 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: extratactics.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Pcoq
@@ -486,21 +486,29 @@ END
 
 
 TACTIC EXTEND apply_in
-| ["apply" constr_with_bindings(c) "in" hyp(id) ] -> [ apply_in false id [c] ]
-| ["apply" constr_with_bindings(c) "," constr_with_bindings_list_sep(cl,",") 
-   "in" hyp(id) ] -> [ apply_in false id (c::cl) ]
+| ["apply" ne_constr_with_bindings_list_sep(cl,",") "in" hyp(id) ] -> 
+    [ apply_in false id cl ]
 END
 
 
 TACTIC EXTEND eapply_in
-| ["eapply" constr_with_bindings(c) "in" hyp(id) ] -> [ apply_in true id [c] ]
-| ["epply" constr_with_bindings(c) "," constr_with_bindings_list_sep(cl,",") 
-   "in" hyp(id) ] -> [ apply_in true id (c::cl) ]
+| ["eapply" ne_constr_with_bindings_list_sep(cl,",") "in" hyp(id) ] ->
+    [ apply_in true id cl ]
 END
 
 (* sozeau: abs/gen for induction on instantiated dependent inductives, using "Ford" induction as 
   defined by Conor McBride *)
 TACTIC EXTEND generalize_eqs
-| ["generalize_eqs" hyp(id) ] -> [ abstract_generalize id ]
+| ["generalize_eqs" hyp(id) ] -> [ abstract_generalize id ~generalize_vars:false ]
+END
+TACTIC EXTEND generalize_eqs_vars
+| ["generalize_eqs_vars" hyp(id) ] -> [ abstract_generalize id ~generalize_vars:true ]
+END
+
+TACTIC EXTEND conv
+| ["conv" constr(x) constr(y) ] -> [ conv x y ]
 END
 
+TACTIC EXTEND resolve_classes
+| ["resolve_classes" ] -> [ resolve_classes ]
+END
diff --git a/tactics/hiddentac.ml b/tactics/hiddentac.ml
index 190a7ba2..31c1b02f 100644
--- a/tactics/hiddentac.ml
+++ b/tactics/hiddentac.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: hiddentac.ml 11094 2008-06-10 19:35:23Z herbelin $ *)
+(* $Id: hiddentac.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Term
 open Proof_type
@@ -30,8 +30,8 @@ let inj_occ (occ,c) = (occ,inj_open c)
 
 (* Basic tactics *)
 let h_intro_move x y =
-  abstract_tactic (TacIntroMove (x, Option.map inj_id y)) (intro_move x y)
-let h_intro x        = h_intro_move (Some x) None
+  abstract_tactic (TacIntroMove (x, y)) (intro_move x y)
+let h_intro x        = h_intro_move (Some x) no_move
 let h_intros_until x = abstract_tactic (TacIntrosUntil x) (intros_until x)
 let h_assumption     = abstract_tactic TacAssumption assumption
 let h_exact c        = abstract_tactic (TacExact (inj_open c)) (exact_check c)
@@ -40,7 +40,7 @@ let h_exact_no_check c =
 let h_vm_cast_no_check c = 
   abstract_tactic (TacVmCastNoCheck (inj_open c)) (vm_cast_no_check c)
 let h_apply simple ev cb    =
-  abstract_tactic (TacApply (simple,ev,inj_open_wb cb))
+  abstract_tactic (TacApply (simple,ev,List.map inj_open_wb cb))
     (apply_with_ebindings_gen simple ev cb)
 let h_elim ev cb cbo    =
   abstract_tactic (TacElim (ev,inj_open_wb cb,Option.map inj_open_wb cbo))
@@ -70,7 +70,7 @@ let h_generalize cl =
 let h_generalize_dep c =
   abstract_tactic (TacGeneralizeDep (inj_open c))(generalize_dep c)
 let h_let_tac b na c cl =
-  let with_eq = if b then None else Some true in
+  let with_eq = if b then None else Some (true,(dummy_loc,IntroAnonymous)) in
   abstract_tactic (TacLetTac (na,inj_open c,cl,b)) (letin_tac with_eq na c cl)
 let h_instantiate n c ido = 
 (Evar_tactics.instantiate n c ido)
@@ -78,16 +78,19 @@ let h_instantiate n c ido =
     (Evar_refiner.instantiate n c (simple_clause_of cls)) *)
 
 (* Derived basic tactics *)
-let h_simple_induction h =
-  abstract_tactic (TacSimpleInduction h) (simple_induct h)
-let h_simple_destruct h  =
-  abstract_tactic (TacSimpleDestruct h) (simple_destruct h)
-let h_new_induction ev c e idl cl =
-  abstract_tactic (TacNewInduction (ev,List.map inj_ia c,Option.map inj_open_wb e,idl,cl))
-    (new_induct ev c e idl cl)
-let h_new_destruct ev c e idl cl =
-  abstract_tactic (TacNewDestruct (ev,List.map inj_ia c,Option.map inj_open_wb e,idl,cl))
-    (new_destruct ev c e idl cl)
+let h_simple_induction_destruct isrec h =
+  abstract_tactic (TacSimpleInductionDestruct (isrec,h)) 
+    (if isrec then (simple_induct h) else (simple_destruct h))
+let h_simple_induction = h_simple_induction_destruct true
+let h_simple_destruct = h_simple_induction_destruct false
+
+let h_induction_destruct isrec ev l =
+  abstract_tactic (TacInductionDestruct (isrec,ev,List.map (fun (c,e,idl,cl) -> 
+    List.map inj_ia c,Option.map inj_open_wb e,idl,cl) l))
+    (induction_destruct ev isrec l)
+let h_new_induction ev c e idl cl = h_induction_destruct ev true [c,e,idl,cl]
+let h_new_destruct ev c e idl cl = h_induction_destruct ev false [c,e,idl,cl]
+
 let h_specialize n d = abstract_tactic (TacSpecialize (n,inj_open_wb d)) (specialize n d)
 let h_lapply c = abstract_tactic (TacLApply (inj_open c)) (cut_and_apply c)
 
@@ -128,8 +131,8 @@ let h_symmetry c     = abstract_tactic (TacSymmetry c) (intros_symmetry c)
 let h_transitivity c =
   abstract_tactic (TacTransitivity (inj_open c)) (intros_transitivity c)
 
-let h_simplest_apply c  = h_apply false false (c,NoBindings)
-let h_simplest_eapply c = h_apply false true (c,NoBindings)
+let h_simplest_apply c  = h_apply false false [c,NoBindings]
+let h_simplest_eapply c = h_apply false true [c,NoBindings]
 let h_simplest_elim c   = h_elim false (c,NoBindings) None
 let h_simplest_case   c = h_case false (c,NoBindings)
 
diff --git a/tactics/hiddentac.mli b/tactics/hiddentac.mli
index eed3b1da..3e636668 100644
--- a/tactics/hiddentac.mli
+++ b/tactics/hiddentac.mli
@@ -6,10 +6,11 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: hiddentac.mli 11072 2008-06-08 16:13:37Z herbelin $ i*)
+(*i $Id: hiddentac.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
+open Util
 open Term
 open Proof_type
 open Tacmach
@@ -25,7 +26,7 @@ open Clenv
 
 (* Basic tactics *)
 
-val h_intro_move      : identifier option -> identifier option -> tactic
+val h_intro_move      : identifier option -> identifier move_location -> tactic
 val h_intro           : identifier -> tactic
 val h_intros_until    : quantified_hypothesis -> tactic
 
@@ -35,7 +36,7 @@ val h_exact_no_check  : constr -> tactic
 val h_vm_cast_no_check  : constr -> tactic
 
 val h_apply           : advanced_flag -> evars_flag -> 
-                        constr with_ebindings -> tactic
+                        constr with_ebindings list -> tactic
 
 val h_elim            : evars_flag -> constr with_ebindings ->
                         constr with_ebindings option -> tactic
@@ -63,14 +64,20 @@ val h_instantiate     : int -> Rawterm.rawconstr ->
 
 val h_simple_induction   : quantified_hypothesis -> tactic
 val h_simple_destruct    : quantified_hypothesis -> tactic
-val h_new_induction   :
-  evars_flag -> constr with_ebindings induction_arg list ->
-    constr with_ebindings option -> intro_pattern_expr ->
-      Tacticals.clause option -> tactic
-val h_new_destruct    :
-  evars_flag -> constr with_ebindings induction_arg list ->
-    constr with_ebindings option -> intro_pattern_expr ->
-      Tacticals.clause option -> tactic
+val h_simple_induction_destruct : rec_flag -> quantified_hypothesis -> tactic
+val h_new_induction   : evars_flag -> 
+  constr with_ebindings induction_arg list -> constr with_ebindings option ->
+  intro_pattern_expr located option * intro_pattern_expr located option ->
+  Tacticals.clause option -> tactic
+val h_new_destruct    : evars_flag -> 
+  constr with_ebindings induction_arg list -> constr with_ebindings option -> 
+  intro_pattern_expr located option * intro_pattern_expr located option ->
+  Tacticals.clause option -> tactic
+val h_induction_destruct : rec_flag -> evars_flag ->
+  (constr with_ebindings induction_arg list * constr with_ebindings option * 
+   (intro_pattern_expr located option * intro_pattern_expr located option) *
+   Tacticals.clause option) list -> tactic
+
 val h_specialize      : int option -> constr with_ebindings -> tactic
 val h_lapply          : constr -> tactic
 
@@ -80,7 +87,7 @@ val h_lapply          : constr -> tactic
 (* Context management *)
 val h_clear           : bool -> identifier list -> tactic
 val h_clear_body      : identifier list -> tactic
-val h_move            : bool -> identifier -> identifier -> tactic
+val h_move            : bool -> identifier -> identifier move_location -> tactic
 val h_rename          : (identifier*identifier) list -> tactic
 val h_revert          : identifier list -> tactic
 
@@ -110,4 +117,4 @@ val h_simplest_eapply : constr -> tactic
 val h_simplest_elim   : constr -> tactic
 val h_simplest_case   : constr -> tactic
 
-val h_intro_patterns  : intro_pattern_expr list -> tactic
+val h_intro_patterns  : intro_pattern_expr located list -> tactic
diff --git a/tactics/hipattern.ml4 b/tactics/hipattern.ml4
index fca84fd2..de500f89 100644
--- a/tactics/hipattern.ml4
+++ b/tactics/hipattern.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma parsing/q_constr.cmo" i*)
 
-(* $Id: hipattern.ml4 8866 2006-05-28 16:21:04Z herbelin $ *)
+(* $Id: hipattern.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -273,7 +273,7 @@ let dest_nf_eq gls eqn =
   try
     snd (first_match (match_eq_nf gls eqn) equalities)
   with PatternMatchingFailure ->
-    error "Not an equality"
+    error "Not an equality."
 
 (*** Sigma-types *)
 
diff --git a/tactics/inv.ml b/tactics/inv.ml
index 8bd10a4d..68ebfd3c 100644
--- a/tactics/inv.ml
+++ b/tactics/inv.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: inv.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: inv.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -101,7 +101,7 @@ let make_inv_predicate env sigma indf realargs id status concl =
       | Dep dflt_concl ->
 	  if not (occur_var env id concl) then
 	    errorlabstrm "make_inv_predicate"
-              (str "Current goal does not depend on " ++ pr_id id);
+              (str "Current goal does not depend on " ++ pr_id id ++ str".");
           (* We abstract the conclusion of goal with respect to
              realargs and c to * be concl in order to rewrite and have
              c also rewritten when the case * will be done *)
@@ -291,10 +291,10 @@ let generalizeRewriteIntros tac depids id gls =
 let rec tclMAP_i n tacfun = function
   | [] -> tclDO n (tacfun None)
   | a::l -> 
-      if n=0 then error "Too much names"
+      if n=0 then error "Too much names."
       else tclTHEN (tacfun (Some a)) (tclMAP_i (n-1) tacfun l)
 
-let remember_first_eq id x = if !x = None then x := Some id
+let remember_first_eq id x = if !x = no_move then x := MoveAfter id
 
 (* invariant: ProjectAndApply is responsible for erasing the clause
    which it is given as input
@@ -321,7 +321,7 @@ let projectAndApply thin id eqname names depids gls =
       [(if names <> [] then clear [id] else tclIDTAC);
        (tclMAP_i neqns (fun idopt ->
 	 tclTHEN
-	   (intro_move idopt None)
+	   (intro_move idopt no_move)
 	   (* try again to substitute and if still not a variable after *)
 	   (* decomposition, arbitrarily try to rewrite RL !? *)
 	   (tclTRY (onLastHyp (substHypIfVariable (subst_hyp false)))))
@@ -350,7 +350,7 @@ let rewrite_equations_gene othin neqns ba gl =
                         (onLastHyp
                            (fun id ->
                               tclTRY 
-			        (projectAndApply thin id (ref None)
+			        (projectAndApply thin id (ref no_move)
 				  [] depids))));
                  onHyps (compose List.rev (afterHyp last)) bring_hyps;
                  onHyps (afterHyp last)
@@ -375,24 +375,24 @@ let rewrite_equations_gene othin neqns ba gl =
      None: the equations are introduced, but not rewritten
      Some thin: the equations are rewritten, and cleared if thin is true *)
 
-let rec get_names allow_conj = function
+let rec get_names allow_conj (loc,pat) = match pat with
   | IntroWildcard ->
-      error "Discarding pattern not allowed for inversion equations"
+      error "Discarding pattern not allowed for inversion equations."
   | IntroAnonymous ->
-      error "Anonymous pattern not allowed for inversion equations"
-  | IntroFresh _->
-      error "Fresh pattern not allowed for inversion equations"
+      error "Anonymous pattern not allowed for inversion equations."
+  | IntroFresh _ ->
+      error "Fresh pattern not allowed for inversion equations."
   | IntroRewrite _->
-      error "Rewriting pattern not allowed for inversion equations"
+      error "Rewriting pattern not allowed for inversion equations."
   | IntroOrAndPattern [l] -> 
       if allow_conj then
 	if l = [] then (None,[]) else
 	  let l = List.map (fun id -> Option.get (fst (get_names false id))) l in
 	  (Some (List.hd l), l)
       else
-	error "Nested conjunctive patterns not allowed for inversion equations"
+	error"Nested conjunctive patterns not allowed for inversion equations."
   | IntroOrAndPattern l ->
-      error "Disjunctive patterns not allowed for inversion equations"
+      error "Disjunctive patterns not allowed for inversion equations."
   | IntroIdentifier id ->
       (Some id,[id])
 
@@ -404,7 +404,7 @@ let rewrite_equations othin neqns names ba gl =
   let names = List.map (get_names true) names in
   let (depids,nodepids) = split_dep_and_nodep ba.assums gl in
   let rewrite_eqns =
-    let first_eq = ref None in
+    let first_eq = ref no_move in
     match othin with
       | Some thin ->
           tclTHENSEQ
@@ -413,12 +413,12 @@ let rewrite_equations othin neqns names ba gl =
 	     tclMAP_i neqns (fun o ->
 	       let idopt,names = extract_eqn_names o in
                (tclTHEN
-		 (intro_move idopt None)
+		 (intro_move idopt no_move)
 		 (onLastHyp (fun id ->
 		   tclTRY (projectAndApply thin id first_eq names depids)))))
 	       names;
 	     tclMAP (fun (id,_,_) gl ->
-	       intro_move None (if thin then None else !first_eq) gl)
+	       intro_move None (if thin then no_move else !first_eq) gl)
 	       nodepids;
 	     tclMAP (fun (id,_,_) -> tclTRY (clear [id])) depids]
       | None -> tclIDTAC
@@ -453,7 +453,7 @@ let raw_inversion inv_kind id status names gl =
     try pf_reduce_to_atomic_ind gl (pf_type_of gl c)
     with UserError _ -> 
       errorlabstrm "raw_inversion"
-	(str ("The type of "^(string_of_id id)^" is not inductive")) in
+	(str ("The type of "^(string_of_id id)^" is not inductive.")) in
   let indclause = mk_clenv_from gl (c,t) in
   let ccl = clenv_type indclause in
   check_no_metas indclause ccl;
@@ -494,7 +494,7 @@ let not_found_message ids =
 let dep_prop_prop_message id =
   errorlabstrm "Inv"
     (str "Inversion on " ++ pr_id id ++
-       str " would needs dependent elimination Prop-Prop")
+       str " would need dependent elimination from Prop to Prop.")
  
 let not_inductive_here id =
   errorlabstrm "mind_specif_of_mind"
@@ -524,15 +524,15 @@ open Tacexpr
 
 let inv k = inv_gen false k NoDep
 
-let half_inv_tac id  = inv SimpleInversion IntroAnonymous (NamedHyp id)
-let inv_tac id       = inv FullInversion IntroAnonymous (NamedHyp id)
-let inv_clear_tac id = inv FullInversionClear IntroAnonymous (NamedHyp id)
+let half_inv_tac id  = inv SimpleInversion None (NamedHyp id)
+let inv_tac id       = inv FullInversion None (NamedHyp id)
+let inv_clear_tac id = inv FullInversionClear None (NamedHyp id)
 
 let dinv k c = inv_gen false k (Dep c)
 
-let half_dinv_tac id  = dinv SimpleInversion None IntroAnonymous (NamedHyp id)
-let dinv_tac id       = dinv FullInversion None IntroAnonymous (NamedHyp id)
-let dinv_clear_tac id = dinv FullInversionClear None IntroAnonymous (NamedHyp id)
+let half_dinv_tac id  = dinv SimpleInversion None None (NamedHyp id)
+let dinv_tac id       = dinv FullInversion None None (NamedHyp id)
+let dinv_clear_tac id = dinv FullInversionClear None None (NamedHyp id)
 
 (* InvIn will bring the specified clauses into the conclusion, and then
  * perform inversion on the named hypothesis.  After, it will intro them
diff --git a/tactics/inv.mli b/tactics/inv.mli
index bd38d08f..bbb2a322 100644
--- a/tactics/inv.mli
+++ b/tactics/inv.mli
@@ -6,9 +6,10 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: inv.mli 7880 2006-01-16 13:59:08Z herbelin $ i*)
+(*i $Id: inv.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
+open Util
 open Names
 open Term
 open Tacmach
@@ -21,20 +22,20 @@ type inversion_status = Dep of constr option | NoDep
 
 val inv_gen :
   bool -> inversion_kind -> inversion_status ->
-    intro_pattern_expr -> quantified_hypothesis -> tactic
+    intro_pattern_expr located option -> quantified_hypothesis -> tactic
 val invIn_gen :
-  inversion_kind -> intro_pattern_expr -> identifier list -> 
+  inversion_kind -> intro_pattern_expr located option -> identifier list -> 
     quantified_hypothesis -> tactic
 
 val inv_clause :
-  inversion_kind -> intro_pattern_expr -> identifier list ->
+  inversion_kind -> intro_pattern_expr located option -> identifier list ->
     quantified_hypothesis -> tactic
 
-val inv : inversion_kind -> intro_pattern_expr ->
+val inv : inversion_kind -> intro_pattern_expr located option ->
   quantified_hypothesis -> tactic
 
-val dinv : inversion_kind -> constr option -> intro_pattern_expr ->
-  quantified_hypothesis -> tactic
+val dinv : inversion_kind -> constr option ->
+  intro_pattern_expr located option -> quantified_hypothesis -> tactic
 
 val half_inv_tac : identifier -> tactic
 val inv_tac : identifier -> tactic
diff --git a/tactics/leminv.ml b/tactics/leminv.ml
index 70e8c375..5acc5197 100644
--- a/tactics/leminv.ml
+++ b/tactics/leminv.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: leminv.ml 10348 2007-12-06 17:36:14Z aspiwack $ *)
+(* $Id: leminv.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -214,7 +214,7 @@ let inversion_scheme env sigma t sort dep_option inv_op =
        (ids_of_named_context (named_context invEnv)));
   (*
     errorlabstrm "lemma_inversion"
-    (str"Computed inversion goal was not closed in initial signature");
+    (str"Computed inversion goal was not closed in initial signature.");
   *)
   let invSign = named_context_val invEnv in
   let pfs = mk_pftreestate (mk_goal invSign invGoal None) in
@@ -272,7 +272,7 @@ let inversion_lemma_from_goal n na (loc,id) sort dep_option inv_op =
     errorlabstrm "lemma_inversion"
       (str"Cannot compute lemma inversion when there are" ++ spc () ++
 	 str"free variables in the types of an inductive" ++ spc () ++
-	 str"which are not free in its instance"); *)
+	 str"which are not free in its instance."); *)
   add_inversion_lemma na env sigma t sort dep_option inv_op
    
 let add_inversion_lemma_exn na com comsort bool tac =
diff --git a/tactics/nbtermdn.ml b/tactics/nbtermdn.ml
index d9d0a799..b94ae2dd 100644
--- a/tactics/nbtermdn.ml
+++ b/tactics/nbtermdn.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: nbtermdn.ml 10346 2007-12-05 21:11:19Z aspiwack $ *)
+(* $Id: nbtermdn.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -46,14 +46,14 @@ let add dn (na,(pat,valu)) =
   let hkey = Option.map fst (Termdn.constr_pat_discr pat) in 
   dn.table <- Gmap.add na (pat,valu) dn.table;
   let dnm = dn.patterns in
-  dn.patterns <- Gmap.add hkey (Btermdn.add (get_dn dnm hkey) (pat,valu)) dnm
+  dn.patterns <- Gmap.add hkey (Btermdn.add None (get_dn dnm hkey) (pat,valu)) dnm
     
 let rmv dn na =
   let (pat,valu) = Gmap.find na dn.table in
   let hkey = Option.map fst (Termdn.constr_pat_discr pat) in 
   dn.table <- Gmap.remove na dn.table;
   let dnm = dn.patterns in
-  dn.patterns <- Gmap.add hkey (Btermdn.rmv (get_dn dnm hkey) (pat,valu)) dnm
+  dn.patterns <- Gmap.add hkey (Btermdn.rmv None (get_dn dnm hkey) (pat,valu)) dnm
 
 let in_dn dn na = Gmap.mem na dn.table
 			  
@@ -62,8 +62,12 @@ let remap ndn na (pat,valu) =
   add ndn (na,(pat,valu))
 
 let lookup dn valu =
-  let hkey = Option.map fst (Termdn.constr_val_discr valu) in 
-  try Btermdn.lookup (Gmap.find hkey  dn.patterns) valu with Not_found -> []
+  let hkey = 
+    match (Termdn.constr_val_discr valu) with 
+    | Dn.Label(l,_) -> Some l
+    | _ -> None
+  in 
+  try Btermdn.lookup None (Gmap.find hkey dn.patterns) valu with Not_found -> []
 
 let app f dn = Gmap.iter f dn.table
 		       
diff --git a/tactics/refine.ml b/tactics/refine.ml
index 84e9dccc..7ed58f6f 100644
--- a/tactics/refine.ml
+++ b/tactics/refine.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: refine.ml 9841 2007-05-19 21:13:42Z herbelin $ *)
+(* $Id: refine.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 (* JCF -- 6 janvier 1998  EXPERIMENTAL *)
 
@@ -229,7 +229,7 @@ let rec compute_metamap env sigma c = match kind_of_term c with
   (* Produit. Est-ce bien exact ? *)
   | Prod (_,_,_) ->
       if occur_meta c then
-	error "Refine: proof term contains metas in a product"
+	error "refine: proof term contains metas in a product."
       else
       	TH (c,[],[])
 
@@ -330,7 +330,7 @@ let rec tcc_aux subst (TH (c,mm,sgp) as _th) gl =
     | Fix ((ni,_),(fi,ai,_)) , _ ->
 	let out_name = function
 	  | Name id -> id
-          | _ -> error "recursive functions must have names !"
+          | _ -> error "Recursive functions must have names."
 	in
 	let fixes = array_map3 (fun f n c -> (out_name f,succ n,c)) fi ni ai in
 	tclTHENS
@@ -345,7 +345,7 @@ let rec tcc_aux subst (TH (c,mm,sgp) as _th) gl =
     | CoFix (_,(fi,ai,_)) , _ ->
 	let out_name = function
 	  | Name id -> id
-          | _ -> error "recursive functions must have names !"
+          | _ -> error "Recursive functions must have names."
 	in
 	let cofixes = array_map2 (fun f c -> (out_name f,c)) fi ai in
 	tclTHENS
diff --git a/tactics/tacinterp.ml b/tactics/tacinterp.ml
index f4547930..3f8eb0ca 100644
--- a/tactics/tacinterp.ml
+++ b/tactics/tacinterp.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tacinterp.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: tacinterp.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Constrintern
 open Closure
@@ -51,13 +51,13 @@ open Pcoq
 let safe_msgnl s =
     try msgnl s with e -> 
       msgnl 
-	(str "bug in the debugger : " ++
+	(str "bug in the debugger: " ++
          str "an exception is raised while printing debug information")
 
 let error_syntactic_metavariables_not_allowed loc =
   user_err_loc 
     (loc,"out_ident",
-     str "Syntactic metavariables allowed only in quotations")
+     str "Syntactic metavariables allowed only in quotations.")
 
 let error_global_not_found_loc (loc,qid) = error_global_not_found_loc loc qid
 
@@ -72,10 +72,10 @@ type ltac_type =
 
 (* Values for interpretation *)
 type value =
-  | VTactic of loc * tactic  (* For mixed ML/Ltac tactics (e.g. Tauto) *)
   | VRTactic of (goal list sigma * validation) (* For Match results *)
                                                (* Not a true value *)
-  | VFun of (identifier*value) list * identifier option list * glob_tactic_expr
+  | VFun of ltac_trace * (identifier*value) list * 
+      identifier option list * glob_tactic_expr
   | VVoid
   | VInteger of int
   | VIntroPattern of intro_pattern_expr (* includes idents which are not *)
@@ -86,20 +86,20 @@ type value =
   | VList of value list
   | VRec of (identifier*value) list ref * glob_tactic_expr
 
-let locate_tactic_call loc = function
-  | VTactic (_,t) -> VTactic (loc,t)
-  | v -> v
-
-let locate_error_in_file dir = function
-  | Stdpp.Exc_located (loc,e) -> Error_in_file ("",(true,dir,loc),e)
-  | e -> Error_in_file ("",(true,dir,dummy_loc),e)
+let dloc = dummy_loc
 
-let catch_error loc tac g =
-  try tac g
-  with e when loc <> dummy_loc ->
-    match e with
-      |	Stdpp.Exc_located (_,e) -> raise (Stdpp.Exc_located (loc,e))
-      |	e -> raise (Stdpp.Exc_located (loc,e))
+let catch_error call_trace tac g =
+  if call_trace = [] then tac g else try tac g with
+  | LtacLocated _ as e -> raise e
+  | Stdpp.Exc_located (_,LtacLocated _) as e -> raise e
+  | e ->
+    let (loc',c),tail = list_sep_last call_trace in
+    let loc,e' = match e with Stdpp.Exc_located(loc,e) -> loc,e | _ ->dloc,e in
+    if tail = [] then
+      let loc = if loc' = dloc then loc else loc' in
+      raise (Stdpp.Exc_located(loc,e'))
+    else
+      raise (Stdpp.Exc_located(loc',LtacLocated((c,tail,loc),e')))
 
 (* Signature for interpretation: val_interp and interpretation functions *)
 type interp_sign =
@@ -107,11 +107,11 @@ type interp_sign =
       avoid_ids : identifier list; (* ids inherited from the call context
 				      (needed to get fresh ids) *)
       debug : debug_info;
-      last_loc : loc }
+      trace : ltac_trace }
 
 let check_is_value = function
   | VRTactic _ -> (* These are goals produced by Match *)
-   error "Immediate match producing tactics not allowed in local definitions"
+   error "Immediate match producing tactics not allowed in local definitions."
   | _ -> ()
 
 (* For tactic_of_value *)
@@ -121,16 +121,16 @@ exception NotTactic
 let constr_of_VConstr_context = function
   | VConstr_context c -> c
   | _ ->
-    errorlabstrm "constr_of_VConstr_context" (str "not a context variable")
+    errorlabstrm "constr_of_VConstr_context" (str "Not a context variable.")
 
 (* Displays a value *)
 let rec pr_value env = function
   | VVoid -> str "()"
   | VInteger n -> int n
-  | VIntroPattern ipat -> pr_intro_pattern ipat
+  | VIntroPattern ipat -> pr_intro_pattern (dloc,ipat)
   | VConstr c | VConstr_context c ->
       (match env with Some env -> pr_lconstr_env env c | _ -> str "a term")
-  | (VTactic _ | VRTactic _ | VFun _ | VRec _) -> str "a tactic"
+  | (VRTactic _ | VFun _ | VRec _) -> str "a tactic"
   | VList [] -> str "an empty list"
   | VList (a::_) ->
       str "a list (first element is " ++ pr_value env a ++ str")"
@@ -143,24 +143,13 @@ let constr_of_id env id =
   construct_reference (Environ.named_context env) id
 
 (* To embed tactics *)
-let ((tactic_in : (interp_sign -> raw_tactic_expr) -> Dyn.t),
-     (tactic_out : Dyn.t -> (interp_sign -> raw_tactic_expr))) =
+let ((tactic_in : (interp_sign -> glob_tactic_expr) -> Dyn.t),
+     (tactic_out : Dyn.t -> (interp_sign -> glob_tactic_expr))) =
   create "tactic"
 
 let ((value_in : value -> Dyn.t),
      (value_out : Dyn.t -> value)) = create "value"
 
-let tacticIn t = TacArg (TacDynamic (dummy_loc,tactic_in t))
-let tacticOut = function
-  | TacArg (TacDynamic (_,d)) ->
-    if (tag d) = "tactic" then
-      tactic_out d
-    else
-      anomalylabstrm "tacticOut" (str "Dynamic tag should be tactic")
-  | ast ->
-    anomalylabstrm "tacticOut"
-      (str "Not a Dynamic ast: " (* ++ print_ast ast*) )
-
 let valueIn t = TacDynamic (dummy_loc,value_in t)
 let valueOut = function
   | TacDynamic (_,d) ->
@@ -182,8 +171,6 @@ let constrOut = function
   | ast ->
     anomalylabstrm "constrOut" (str "Not a Dynamic ast")
 
-let dloc = dummy_loc
-
 (* Globalizes the identifier *)
 let find_reference env qid =
   (* We first look for a variable of the current proof *)
@@ -195,7 +182,7 @@ let find_reference env qid =
 let error_not_evaluable s =
   errorlabstrm "evalref_of_ref" 
     (str "Cannot coerce" ++ spc ()  ++ s ++ spc () ++
-     str "to an evaluable reference")
+     str "to an evaluable reference.")
 
 (* Table of "pervasives" macros tactics (e.g. auto, simpl, etc.) *)
 let atomic_mactab = ref Idmap.empty
@@ -211,7 +198,7 @@ let _ =
         "hnf", TacReduce(Hnf,nocl);
         "simpl", TacReduce(Simpl None,nocl);
         "compute", TacReduce(Cbv all_flags,nocl);
-        "intro", TacIntroMove(None,None);
+        "intro", TacIntroMove(None,no_move);
         "intros", TacIntroPattern [];
         "assumption", TacAssumption;
         "cofix", TacCofix None;
@@ -263,7 +250,7 @@ let tac_tab = Hashtbl.create 17
 let add_tactic s t =
   if Hashtbl.mem tac_tab s then
     errorlabstrm ("Refiner.add_tactic: ") 
-      (str ("Cannot redeclare tactic "^s));
+      (str ("Cannot redeclare tactic "^s^"."));
   Hashtbl.add tac_tab s t
 
 let overwriting_add_tactic s t =
@@ -278,7 +265,7 @@ let lookup_tactic s =
     Hashtbl.find tac_tab s
   with Not_found -> 
     errorlabstrm "Refiner.lookup_tactic"
-      (str"The tactic " ++ str s ++ str" is not installed")
+      (str"The tactic " ++ str s ++ str" is not installed.")
 (*
 let vernac_tactic (s,args) =
   let tacfun = lookup_tactic s args in
@@ -311,11 +298,17 @@ let lookup_genarg_glob   id = let (f,_,_) = lookup_genarg id in f
 let lookup_interp_genarg id = let (_,f,_) = lookup_genarg id in f
 let lookup_genarg_subst  id = let (_,_,f) = lookup_genarg id in f
 
-(* Dynamically check that an argument is a tactic, possibly unboxing VRec *)
+let propagate_trace ist loc id = function
+  | VFun (_,lfun,it,b) ->
+      let t = if it=[] then b else TacFun (it,b) in
+      VFun ((loc,LtacVarCall (id,t))::ist.trace,lfun,it,b)
+  | x -> x
+
+(* Dynamically check that an argument is a tactic *)
 let coerce_to_tactic loc id = function
-  | VTactic _ | VFun _ | VRTactic _ as a -> a
+  | VFun _ | VRTactic _ as a -> a
   | _ -> user_err_loc 
-  (loc, "", str "variable " ++  pr_id id ++ str " should be bound to a tactic")
+  (loc, "", str "Variable " ++ pr_id id ++ str " should be bound to a tactic.")
 
 (*****************)
 (* Globalization *)
@@ -422,6 +415,11 @@ let intern_constr_reference strict ist = function
       let loc,_ as lqid = qualid_of_reference r in
       RRef (loc,locate_global_with_alias lqid), if strict then None else Some (CRef r)
 
+let intern_move_location ist = function
+  | MoveAfter id -> MoveAfter (intern_hyp_or_metaid ist id)
+  | MoveBefore id -> MoveBefore (intern_hyp_or_metaid ist id)
+  | MoveToEnd toleft as x -> x
+
 (* Internalize an isolated reference in position of tactic *)
 
 let intern_isolated_global_tactic_reference r =
@@ -432,7 +430,7 @@ let intern_isolated_global_tactic_reference r =
   | Ident (_,id) -> Tacexp (lookup_atomic id)
   | _ -> raise Not_found
 
-let intern_isolated_tactic_reference ist r =
+let intern_isolated_tactic_reference strict ist r =
   (* An ltac reference *)
   try Reference (intern_ltac_variable ist r)
   with Not_found ->
@@ -440,7 +438,7 @@ let intern_isolated_tactic_reference ist r =
   try intern_isolated_global_tactic_reference r
   with Not_found ->
   (* Tolerance for compatibility, allow not to use "constr:" *)
-  try ConstrMayEval (ConstrTerm (intern_constr_reference true ist r))
+  try ConstrMayEval (ConstrTerm (intern_constr_reference strict ist r))
   with Not_found ->
   (* Reference not found *)
   error_global_not_found_loc (qualid_of_reference r)
@@ -475,7 +473,7 @@ let intern_non_tactic_reference strict ist r =
   with Not_found ->
   (* By convention, use IntroIdentifier for unbound ident, when not in a def *)
   match r with
-  | Ident (_,id) when not strict -> IntroPattern (IntroIdentifier id)
+  | Ident (loc,id) when not strict -> IntroPattern (loc,IntroIdentifier id)
   | _ ->
   (* Reference not found *)
   error_global_not_found_loc (qualid_of_reference r)
@@ -487,13 +485,14 @@ let intern_message_token ist = function
 let intern_message ist = List.map (intern_message_token ist)
 
 let rec intern_intro_pattern lf ist = function
-  | IntroOrAndPattern l ->
-      IntroOrAndPattern (intern_case_intro_pattern lf ist l)
-  | IntroIdentifier id ->
-      IntroIdentifier (intern_ident lf ist id)
-  | IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _ as x -> x
-
-and intern_case_intro_pattern lf ist =
+  | loc, IntroOrAndPattern l ->
+      loc, IntroOrAndPattern (intern_or_and_intro_pattern lf ist l)
+  | loc, IntroIdentifier id ->
+      loc, IntroIdentifier (intern_ident lf ist id)
+  | loc, (IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _)
+      as x -> x
+
+and intern_or_and_intro_pattern lf ist =
   List.map (List.map (intern_intro_pattern lf ist))
 
 let intern_quantified_hypothesis ist = function
@@ -602,10 +601,10 @@ let intern_red_expr ist = function
 let intern_inversion_strength lf ist = function
   | NonDepInversion (k,idl,ids) ->
       NonDepInversion (k,List.map (intern_hyp_or_metaid ist) idl,
-      intern_intro_pattern lf ist ids)
+      Option.map (intern_intro_pattern lf ist) ids)
   | DepInversion (k,copt,ids) ->
       DepInversion (k, Option.map (intern_constr ist) copt,
-      intern_intro_pattern lf ist ids)
+      Option.map (intern_intro_pattern lf ist) ids)
   | InversionUsing (c,idl) ->
       InversionUsing (intern_constr ist c, List.map (intern_hyp_or_metaid ist) idl)
 
@@ -642,9 +641,9 @@ let internalise_tacarg ch = G_xml.parse_tactic_arg ch
 
 let extern_tacarg ch env sigma = function
   | VConstr c -> !print_xml_term ch env sigma c
-  | VTactic _ | VRTactic _ | VFun _ | VVoid | VInteger _ | VConstr_context _
+  | VRTactic _ | VFun _ | VVoid | VInteger _ | VConstr_context _
   | VIntroPattern _  | VRec _ | VList _ ->
-      error "Only externing of terms is implemented"
+      error "Only externing of terms is implemented."
 
 let extern_request ch req gl la =
   output_string ch "<REQUEST req=\""; output_string ch req;
@@ -652,11 +651,11 @@ let extern_request ch req gl la =
   List.iter (pf_apply (extern_tacarg ch) gl) la;
   output_string ch "</REQUEST>\n"
 
-(* Reads the hypotheses of a Match Context rule *)
-let rec intern_match_context_hyps sigma env lfun = function
+(* Reads the hypotheses of a "match goal" rule *)
+let rec intern_match_goal_hyps sigma env lfun = function
   | (Hyp ((_,na) as locna,mp))::tl ->
       let ido, metas1, pat = intern_pattern sigma env ~as_type:true lfun mp in
-      let lfun, metas2, hyps = intern_match_context_hyps sigma env lfun tl in
+      let lfun, metas2, hyps = intern_match_goal_hyps sigma env lfun tl in
       let lfun' = name_cons na (Option.List.cons ido lfun) in
       lfun', metas1@metas2, Hyp (locna,pat)::hyps
   | [] -> lfun, [], []
@@ -667,7 +666,7 @@ let extract_let_names lrc =
     (fun ((loc,name),_) l ->
       if List.mem name l then
 	user_err_loc
-	  (loc, "glob_tactic", str "This variable is bound several times");
+	  (loc, "glob_tactic", str "This variable is bound several times.");
       name::l)
     lrc []
 
@@ -684,14 +683,15 @@ let rec intern_atomic lf ist x =
   | TacIntroPattern l ->
       TacIntroPattern (List.map (intern_intro_pattern lf ist) l)
   | TacIntrosUntil hyp -> TacIntrosUntil (intern_quantified_hypothesis ist hyp)
-  | TacIntroMove (ido,ido') ->
+  | TacIntroMove (ido,hto) ->
       TacIntroMove (Option.map (intern_ident lf ist) ido,
-          Option.map (intern_hyp ist) ido')
+                    intern_move_location ist hto)
   | TacAssumption -> TacAssumption
   | TacExact c -> TacExact (intern_constr ist c)
   | TacExactNoCheck c -> TacExactNoCheck (intern_constr ist c)
   | TacVmCastNoCheck c -> TacVmCastNoCheck (intern_constr ist c)
-  | TacApply (a,ev,cb) -> TacApply (a,ev,intern_constr_with_bindings ist cb)
+  | TacApply (a,ev,cb) ->
+      TacApply (a,ev,List.map (intern_constr_with_bindings ist) cb)
   | TacElim (ev,cb,cbo) ->
       TacElim (ev,intern_constr_with_bindings ist cb,
                Option.map (intern_constr_with_bindings ist) cbo)
@@ -735,20 +735,15 @@ let rec intern_atomic lf ist x =
         List.map (intern_constr ist) lems)
 
   (* Derived basic tactics *)
-  | TacSimpleInduction h ->
-      TacSimpleInduction (intern_quantified_hypothesis ist h)
-  | TacNewInduction (ev,lc,cbo,ids,cls) ->
-      TacNewInduction (ev,List.map (intern_induction_arg ist) lc,
-               Option.map (intern_constr_with_bindings ist) cbo,
-               intern_intro_pattern lf ist ids,
-               Option.map (clause_app (intern_hyp_location ist)) cls)
-  | TacSimpleDestruct h ->
-      TacSimpleDestruct (intern_quantified_hypothesis ist h)
-  | TacNewDestruct (ev,c,cbo,ids,cls) ->
-      TacNewDestruct (ev,List.map (intern_induction_arg ist) c,
+  | TacSimpleInductionDestruct (isrec,h) ->
+      TacSimpleInductionDestruct (isrec,intern_quantified_hypothesis ist h)
+  | TacInductionDestruct (ev,isrec,l) ->
+      TacInductionDestruct (ev,isrec,List.map (fun (lc,cbo,(ipato,ipats),cls) ->
+	      (List.map (intern_induction_arg ist) lc,
                Option.map (intern_constr_with_bindings ist) cbo,
-	       intern_intro_pattern lf ist ids,
-               Option.map (clause_app (intern_hyp_location ist)) cls)
+               (Option.map (intern_intro_pattern lf ist) ipato,
+	        Option.map (intern_intro_pattern lf ist) ipats),
+               Option.map (clause_app (intern_hyp_location ist)) cls)) l)
   | TacDoubleInduction (h1,h2) ->
       let h1 = intern_quantified_hypothesis ist h1 in
       let h2 = intern_quantified_hypothesis ist h2 in
@@ -764,7 +759,7 @@ let rec intern_atomic lf ist x =
   | TacClear (b,l) -> TacClear (b,List.map (intern_hyp_or_metaid ist) l)
   | TacClearBody l -> TacClearBody (List.map (intern_hyp_or_metaid ist) l)
   | TacMove (dep,id1,id2) ->
-    TacMove (dep,intern_hyp_or_metaid ist id1,intern_hyp_or_metaid ist id2)
+    TacMove (dep,intern_hyp_or_metaid ist id1,intern_move_location ist id2)
   | TacRename l -> 
       TacRename (List.map (fun (id1,id2) -> 
 			     intern_hyp_or_metaid ist id1, 
@@ -812,8 +807,7 @@ let rec intern_atomic lf ist x =
       TacExtend (adjust_loc loc,opn,List.map (intern_genarg ist) l)
   | TacAlias (loc,s,l,(dir,body)) ->
       let l = List.map (fun (id,a) -> (id,intern_genarg ist a)) l in
-      try TacAlias (loc,s,l,(dir,body))
-      with e -> raise (locate_error_in_file (string_of_dirpath dir) e)
+      TacAlias (loc,s,l,(dir,body))
 
 and intern_tactic ist tac = (snd (intern_tactic_seq ist tac) : glob_tactic_expr)
 
@@ -829,8 +823,8 @@ and intern_tactic_seq ist = function
       let l = List.map (fun (n,b) -> 
 	  (n,intern_tacarg !strict_check (if isrec then ist' else ist) b)) l in
       ist.ltacvars, TacLetIn (isrec,l,intern_tactic ist' u)
-  | TacMatchContext (lz,lr,lmr) ->
-      ist.ltacvars, TacMatchContext(lz,lr, intern_match_rule ist lmr)
+  | TacMatchGoal (lz,lr,lmr) ->
+      ist.ltacvars, TacMatchGoal(lz,lr, intern_match_rule ist lmr)
   | TacMatch (lz,c,lmr) ->
       ist.ltacvars, TacMatch (lz,intern_tactic ist c,intern_match_rule ist lmr)
   | TacId l -> ist.ltacvars, TacId (intern_message ist l)
@@ -885,7 +879,7 @@ and intern_tacarg strict ist = function
 	if istac then Reference (ArgVar (adjust_loc loc,id))
 	else ConstrMayEval (ConstrTerm (RVar (adjust_loc loc,id), None))
       else error_syntactic_metavariables_not_allowed loc
-  | TacCall (loc,f,[]) -> intern_isolated_tactic_reference ist f
+  | TacCall (loc,f,[]) -> intern_isolated_tactic_reference strict ist f
   | TacCall (loc,f,l) ->
       TacCall (loc,
         intern_applied_tactic_reference ist f,
@@ -906,7 +900,7 @@ and intern_match_rule ist = function
       All (intern_tactic ist tc) :: (intern_match_rule ist tl)
   | (Pat (rl,mp,tc))::tl ->
       let {ltacvars=(lfun,l2); gsigma=sigma; genv=env} = ist in
-      let lfun',metas1,hyps = intern_match_context_hyps sigma env lfun rl in
+      let lfun',metas1,hyps = intern_match_goal_hyps sigma env lfun rl in
       let ido,metas2,pat = intern_pattern sigma env lfun mp in
       let metas = list_uniquize (metas1@metas2) in
       let ist' = { ist with ltacvars = (metas@(Option.List.cons ido lfun'),l2) } in
@@ -1006,23 +1000,23 @@ let read_pattern lfun = function
 (* Reads the hypotheses of a Match Context rule *)
 let cons_and_check_name id l =
   if List.mem id l then
-    user_err_loc (dloc,"read_match_context_hyps",
-      str ("Hypothesis pattern-matching variable "^(string_of_id id)^
-      " used twice in the same pattern"))
+    user_err_loc (dloc,"read_match_goal_hyps",
+      strbrk ("Hypothesis pattern-matching variable "^(string_of_id id)^
+      " used twice in the same pattern."))
   else id::l
 
-let rec read_match_context_hyps lfun lidh = function
+let rec read_match_goal_hyps lfun lidh = function
   | (Hyp ((loc,na) as locna,mp))::tl ->
       let lidh' = name_fold cons_and_check_name na lidh in
       Hyp (locna,read_pattern lfun mp)::
-	(read_match_context_hyps lfun lidh' tl)
+	(read_match_goal_hyps lfun lidh' tl)
   | [] -> []
 
 (* Reads the rules of a Match Context or a Match *)
 let rec read_match_rule lfun = function
   | (All tc)::tl -> (All tc)::(read_match_rule lfun tl)
   | (Pat (rl,mp,tc))::tl ->
-      Pat (read_match_context_hyps lfun [] rl, read_pattern lfun mp,tc)
+      Pat (read_match_goal_hyps lfun [] rl, read_pattern lfun mp,tc)
       :: read_match_rule lfun tl
   | [] -> []
 
@@ -1110,8 +1104,8 @@ let debugging_exception_step ist signal_anomaly e pp =
 
 let error_ltac_variable loc id env v s =
    user_err_loc (loc, "", str "Ltac variable " ++ pr_id id ++ 
-   str " is bound to" ++ spc () ++ pr_value env v ++ spc () ++ 
-   strbrk "which cannot be coerced to " ++ str s)
+   strbrk " is bound to" ++ spc () ++ pr_value env v ++ spc () ++ 
+   strbrk "which cannot be coerced to " ++ str s ++ str".")
 
 exception CannotCoerceTo of string
 
@@ -1153,8 +1147,8 @@ let coerce_to_intro_pattern env = function
       IntroIdentifier (destVar c)
   | v -> raise (CannotCoerceTo "an introduction pattern")
 
-let interp_intro_pattern_var ist env id =
-  try try_interp_ltac_var (coerce_to_intro_pattern env) ist (Some env)(dloc,id)
+let interp_intro_pattern_var loc ist env id =
+  try try_interp_ltac_var (coerce_to_intro_pattern env) ist (Some env) (loc,id)
   with Not_found -> IntroIdentifier id
 
 let coerce_to_hint_base = function
@@ -1171,8 +1165,9 @@ let coerce_to_int = function
 
 let interp_int ist locid =
   try try_interp_ltac_var coerce_to_int ist None locid
-  with Not_found -> user_err_loc(fst locid,"interp_int",
-				str "Unbound variable"  ++ pr_id (snd locid))
+  with Not_found ->
+    user_err_loc(fst locid,"interp_int",
+      str "Unbound variable "  ++ pr_id (snd locid) ++ str".")
 
 let interp_int_or_var ist = function
   | ArgVar locid -> interp_int ist locid
@@ -1209,7 +1204,7 @@ let interp_hyp ist gl (loc,id as locid) =
   with Not_found -> 
   (* Then look if bound in the proof context at calling time *)
   if is_variable env id then id
-  else user_err_loc (loc,"eval_variable",pr_id id ++ str " not found")
+  else user_err_loc (loc,"eval_variable",pr_id id ++ str " not found.")
 
 let hyp_list_of_VList env = function
   | VList l -> List.map (coerce_to_hyp env) l
@@ -1227,11 +1222,16 @@ let interp_clause_pattern ist gl (l,occl) =
     | (hyp,l) :: rest ->
 	let hyp = interp_hyp ist gl hyp in
 	if List.mem hyp acc then
-	  error ("Hypothesis "^(string_of_id hyp)^" occurs twice");
+	  error ("Hypothesis "^(string_of_id hyp)^" occurs twice.");
 	(hyp,l)::(check (hyp::acc) rest)
     | [] -> []
   in (l,check [] occl)
 
+let interp_move_location ist gl = function
+  | MoveAfter id -> MoveAfter (interp_hyp ist gl id)
+  | MoveBefore id -> MoveBefore (interp_hyp ist gl id)
+  | MoveToEnd toleft as x -> x
+
 (* Interprets a qualified name *)
 let coerce_to_reference env v =
   try match v with
@@ -1309,7 +1309,7 @@ let rec constr_list_aux env = function
 let constr_list ist env = constr_list_aux env ist.lfun
 
 (* Extract the identifier list from lfun: join all branches (what to do else?)*)
-let rec intropattern_ids = function
+let rec intropattern_ids (loc,pat) = match pat with
   | IntroIdentifier id -> [id]
   | IntroOrAndPattern ll -> 
       List.flatten (List.map intropattern_ids (List.flatten ll))
@@ -1317,7 +1317,7 @@ let rec intropattern_ids = function
 
 let rec extract_ids ids = function
   | (id,VIntroPattern ipat)::tl when not (List.mem id ids) ->
-      intropattern_ids ipat @ extract_ids ids tl
+      intropattern_ids (dloc,ipat) @ extract_ids ids tl
   | _::tl -> extract_ids ids tl
   | [] -> []
 
@@ -1388,7 +1388,7 @@ let solve_remaining_evars env initial_sigma evd c =
   proc_rec c
 
 let interp_gen kind ist sigma env (c,ce) =
-  let (ltacvars,unbndltacvars) = constr_list ist env in
+  let (ltacvars,unbndltacvars as vars) = constr_list ist env in
   let typs = retype_list sigma env ltacvars in
   let c = match ce with
   | None -> c
@@ -1398,7 +1398,8 @@ let interp_gen kind ist sigma env (c,ce) =
   | Some c ->
       let ltacdata = (List.map fst ltacvars,unbndltacvars) in
       intern_gen (kind = IsType) ~ltacvars:ltacdata sigma env c in
-  understand_ltac sigma env (typs,unbndltacvars) kind c
+  let trace = (dloc,LtacConstrInterp (c,vars))::ist.trace in
+  catch_error trace (understand_ltac sigma env (typs,unbndltacvars) kind) c
 
 (* Interprets a constr and solve remaining evars with default tactic *)
 let interp_econstr kind ist sigma env cc =
@@ -1532,7 +1533,7 @@ let interp_may_eval f ist gl = function
       with
 	| Not_found ->
 	    user_err_loc (loc, "interp_may_eval",
-	    str "Unbound context identifier" ++ pr_id s))
+	    str "Unbound context identifier" ++ pr_id s ++ str"."))
   | ConstrTypeOf c -> pf_type_of gl (f ist gl c)
   | ConstrTerm c -> 
      try 
@@ -1565,31 +1566,38 @@ let inj_may_eval = function
 let message_of_value = function
   | VVoid -> str "()"
   | VInteger n -> int n
-  | VIntroPattern ipat -> pr_intro_pattern ipat
+  | VIntroPattern ipat -> pr_intro_pattern (dloc,ipat)
   | VConstr_context c | VConstr c -> pr_constr c
-  | VRec _ | VTactic _ | VRTactic _ | VFun _ -> str "<tactic>"
+  | VRec _ | VRTactic _ | VFun _ -> str "<tactic>"
   | VList _ -> str "<list>"
 
-let rec interp_message ist = function
-  | [] -> mt()
-  | MsgString s :: l -> pr_arg str s ++ interp_message ist l
-  | MsgInt n :: l -> pr_arg int n ++ interp_message ist l
-  | MsgIdent (loc,id) :: l ->
+let rec interp_message_token ist = function
+  | MsgString s -> str s
+  | MsgInt n -> int n
+  | MsgIdent (loc,id) ->
       let v =
 	try List.assoc id ist.lfun
-	with Not_found -> user_err_loc (loc,"",pr_id id ++ str" not found") in
-      pr_arg message_of_value v ++ interp_message ist l
+	with Not_found -> user_err_loc (loc,"",pr_id id ++ str" not found.") in
+      message_of_value v
 
 let rec interp_message_nl ist = function
   | [] -> mt()
-  | l -> interp_message ist l ++ fnl()
+  | l -> prlist_with_sep spc (interp_message_token ist) l ++ fnl()
 
-let rec interp_intro_pattern ist gl = function
-  | IntroOrAndPattern l -> IntroOrAndPattern (interp_case_intro_pattern ist gl l)
-  | IntroIdentifier id -> interp_intro_pattern_var ist (pf_env gl) id
-  | IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _ as x -> x
+let interp_message ist l =
+  (* Force evaluation of interp_message_token so that potential errors 
+     are raised now and not at printing time *)
+  prlist (fun x -> spc () ++ x) (List.map (interp_message_token ist) l)
 
-and interp_case_intro_pattern ist gl =
+let rec interp_intro_pattern ist gl = function
+  | loc, IntroOrAndPattern l ->
+      loc, IntroOrAndPattern (interp_or_and_intro_pattern ist gl l)
+  | loc, IntroIdentifier id ->
+      loc, interp_intro_pattern_var loc ist (pf_env gl) id
+  | loc, (IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _)
+      as x -> x
+
+and interp_or_and_intro_pattern ist gl =
   List.map (List.map (interp_intro_pattern ist gl))
 
 (* Quantified named or numbered hypothesis or hypothesis in context *)
@@ -1663,14 +1671,14 @@ let rec val_interp ist gl (tac:glob_tactic_expr) =
 
   let value_interp ist = match tac with
   (* Immediate evaluation *)
-  | TacFun (it,body) -> VFun (ist.lfun,it,body)
+  | TacFun (it,body) -> VFun (ist.trace,ist.lfun,it,body)
   | TacLetIn (true,l,u) -> interp_letrec ist gl l u
   | TacLetIn (false,l,u) -> interp_letin ist gl l u
-  | TacMatchContext (lz,lr,lmr) -> interp_match_context ist gl lz lr lmr 
+  | TacMatchGoal (lz,lr,lmr) -> interp_match_goal ist gl lz lr lmr 
   | TacMatch (lz,c,lmr) -> interp_match ist gl lz c lmr
   | TacArg a -> interp_tacarg ist gl a
   (* Delayed evaluation *)
-  | t -> VTactic (ist.last_loc,eval_tactic ist t)
+  | t -> VFun (ist.trace,ist.lfun,[],t)
 
   in check_for_interrupt (); 
     match ist.debug with
@@ -1679,9 +1687,16 @@ let rec val_interp ist gl (tac:glob_tactic_expr) =
     | _ -> value_interp ist
 
 and eval_tactic ist = function
-  | TacAtom (loc,t) -> fun gl -> catch_error loc (interp_atomic ist gl t) gl
+  | TacAtom (loc,t) ->
+      fun gl ->
+	let box = ref None in abstract_tactic_box := box;
+	let call = LtacAtomCall (t,box) in
+	let tac = (* catch error in the interpretation *)
+	  catch_error ((dloc,call)::ist.trace) (interp_atomic ist gl) t	in
+	(* catch error in the evaluation *)
+	catch_error ((loc,call)::ist.trace) tac gl
   | TacFun _ | TacLetIn _ -> assert false
-  | TacMatchContext _ | TacMatch _ -> assert false
+  | TacMatchGoal _ | TacMatch _ -> assert false
   | TacId s -> tclIDTAC_MESSAGE (interp_message_nl ist s)
   | TacFail (n,s) -> tclFAIL (interp_int_or_var ist n) (interp_message ist s)
   | TacProgress tac -> tclPROGRESS (interp_tactic ist tac)
@@ -1714,31 +1729,33 @@ and force_vrec ist gl = function
   | VRec (lfun,body) -> val_interp {ist with lfun = !lfun} gl body
   | v -> v
 
-and interp_ltac_reference isapplied mustbetac ist gl = function
+and interp_ltac_reference loc' mustbetac ist gl = function
   | ArgVar (loc,id) ->
       let v = List.assoc id ist.lfun in
       let v = force_vrec ist gl v in
+      let v = propagate_trace ist loc id v in
       if mustbetac then coerce_to_tactic loc id v else v
   | ArgArg (loc,r) ->
       let ids = extract_ids [] ist.lfun in
+      let loc_info = ((if loc' = dloc then loc else loc'),LtacNameCall r) in
       let ist = 
         { lfun=[]; debug=ist.debug; avoid_ids=ids;
-          last_loc = if isapplied then ist.last_loc else loc } in
+          trace = loc_info::ist.trace } in
       val_interp ist gl (lookup r)
 
 and interp_tacarg ist gl = function
   | TacVoid -> VVoid
-  | Reference r -> interp_ltac_reference false false ist gl r
+  | Reference r -> interp_ltac_reference dloc false ist gl r
   | Integer n -> VInteger n
-  | IntroPattern ipat -> VIntroPattern (interp_intro_pattern ist gl ipat)
+  | IntroPattern ipat -> VIntroPattern (snd (interp_intro_pattern ist gl ipat))
   | ConstrMayEval c -> VConstr (interp_constr_may_eval ist gl c)
   | MetaIdArg (loc,_,id) -> assert false
-  | TacCall (loc,r,[]) -> interp_ltac_reference false true ist gl r
+  | TacCall (loc,r,[]) -> interp_ltac_reference loc true ist gl r
   | TacCall (loc,f,l) ->
-      let fv = interp_ltac_reference true true ist gl f
+      let fv = interp_ltac_reference loc true ist gl f
       and largs = List.map (interp_tacarg ist gl) l in
       List.iter check_is_value largs;
-      interp_app ist gl fv largs loc
+      interp_app loc ist gl fv largs
   | TacExternal (loc,com,req,la) ->
       interp_external loc ist gl com req (List.map (interp_tacarg ist gl) la)
   | TacFreshId l -> 
@@ -1748,12 +1765,7 @@ and interp_tacarg ist gl = function
   | TacDynamic(_,t) ->
       let tg = (tag t) in
       if tg = "tactic" then
-        let f = (tactic_out t) in 
-        val_interp ist gl
-          (intern_tactic {
-            ltacvars = (List.map fst ist.lfun,[]); ltacrecvars = [];
-            gsigma = project gl; genv = pf_env gl }
-            (f ist))
+        val_interp ist gl (tactic_out t ist)
       else if tg = "value" then
         value_out t
       else if tg = "constr" then
@@ -1763,48 +1775,54 @@ and interp_tacarg ist gl = function
           (str "Unknown dynamic: <" ++ str (Dyn.tag t) ++ str ">"))
 
 (* Interprets an application node *)
-and interp_app ist gl fv largs loc =
+and interp_app loc ist gl fv largs =
   match fv with
-    | VFun(olfun,var,body) ->
+    | VFun(trace,olfun,var,body) ->
       let (newlfun,lvar,lval)=head_with_value (var,largs) in
       if lvar=[] then
 	let v = 
 	  try
-            let lloc = if lval=[] then loc else ist.last_loc in
-	    val_interp { ist with lfun=newlfun@olfun; last_loc=lloc } gl body
+	    catch_error trace
+	      (val_interp { ist with lfun=newlfun@olfun; trace=trace } gl) body
 	  with e ->
             debugging_exception_step ist false e (fun () -> str "evaluation");
 	    raise e in
         debugging_step ist (fun () ->
 	  str "evaluation returns" ++ fnl() ++ pr_value (Some (pf_env gl)) v);
-        if lval=[] then v else interp_app ist gl v lval loc
+        if lval=[] then v else interp_app loc ist gl v lval
       else
-        VFun(newlfun@olfun,lvar,body)
+        VFun(trace,newlfun@olfun,lvar,body)
     | _ ->
 	user_err_loc (loc, "Tacinterp.interp_app",
-          (str"Illegal tactic application"))
+          (str"Illegal tactic application."))
 
 (* Gives the tactic corresponding to the tactic value *)
-and tactic_of_value vle g =
+and tactic_of_value ist vle g =
   match vle with
   | VRTactic res -> res
-  | VTactic (loc,tac) -> catch_error loc tac g
-  | VFun _ -> error "A fully applied tactic is expected"
+  | VFun (trace,lfun,[],t) ->
+      let tac = eval_tactic {ist with lfun=lfun; trace=trace} t in
+      catch_error trace tac g
+  | VFun _ -> error "A fully applied tactic is expected."
   | _ -> raise NotTactic
 
 (* Evaluation with FailError catching *)
 and eval_with_fail ist is_lazy goal tac =
   try
     (match val_interp ist goal tac with
-    | VTactic (loc,tac) when not is_lazy -> VRTactic (catch_error loc tac goal)
+    | VFun (trace,lfun,[],t) when not is_lazy ->
+	let tac = eval_tactic {ist with lfun=lfun; trace=trace} t in
+	VRTactic (catch_error trace tac goal)
     | a -> a)
   with
-    | Stdpp.Exc_located (_,FailError (0,s)) | FailError (0,s) ->
+    | FailError (0,s) | Stdpp.Exc_located(_, FailError (0,s)) 
+    | Stdpp.Exc_located(_,LtacLocated (_,FailError (0,s))) ->
 	raise (Eval_fail s)
-    | Stdpp.Exc_located (s',FailError (lvl,s)) ->
-	raise (Stdpp.Exc_located (s',FailError (lvl - 1, s)))
-    | FailError (lvl,s) ->
-	raise (FailError (lvl - 1, s))
+    | FailError (lvl,s) -> raise (FailError (lvl - 1, s))
+    | Stdpp.Exc_located(s,FailError (lvl,s')) ->
+	raise (Stdpp.Exc_located(s,FailError (lvl - 1, s')))
+    | Stdpp.Exc_located(s,LtacLocated (s'',FailError (lvl,s'))) ->
+	raise (Stdpp.Exc_located(s,LtacLocated (s'',FailError (lvl - 1, s'))))
 
 (* Interprets the clauses of a recursive LetIn *)
 and interp_letrec ist gl llc u =
@@ -1822,14 +1840,14 @@ and interp_letin ist gl llc u =
   val_interp ist gl u
 
 (* Interprets the Match Context expressions *)
-and interp_match_context ist g lz lr lmr =
+and interp_match_goal ist g lz lr lmr =
   let rec apply_goal_sub ist env goal nocc (id,c) csr mt mhyps hyps =
     let (lgoal,ctxt) = match_subterm nocc c csr in
     let lctxt = give_context ctxt id in
       try apply_hyps_context ist env lz goal mt lctxt lgoal mhyps hyps
       with e when is_match_catchable e ->
 	apply_goal_sub ist env goal (nocc + 1) (id,c) csr mt mhyps hyps in
-  let rec apply_match_context ist env goal nrs lex lpt = 
+  let rec apply_match_goal ist env goal nrs lex lpt = 
     begin
       if lex<>[] then db_pattern_rule ist.debug nrs (List.hd lex);
       match lpt with
@@ -1838,7 +1856,7 @@ and interp_match_context ist g lz lr lmr =
               db_mc_pattern_success ist.debug;
               try eval_with_fail ist lz goal t
               with e when is_match_catchable e ->
-		apply_match_context ist env goal (nrs+1) (List.tl lex) tl
+		apply_match_goal ist env goal (nrs+1) (List.tl lex) tl
 	    end
 	| (Pat (mhyps,mgoal,mt))::tl ->
 	    let hyps = make_hyps (pf_hyps goal) in
@@ -1856,21 +1874,21 @@ and interp_match_context ist g lz lr lmr =
 			   | PatternMatchingFailure -> db_matching_failure ist.debug
 			   | Eval_fail s -> db_eval_failure ist.debug s
 			   | _ -> db_logic_failure ist.debug e);
-			apply_match_context ist env goal (nrs+1) (List.tl lex) tl)
+			apply_match_goal ist env goal (nrs+1) (List.tl lex) tl)
 		 | Subterm (id,mg) ->
 		     (try apply_goal_sub ist env goal 0 (id,mg) concl mt mhyps hyps
 		      with
 			| PatternMatchingFailure ->
-			    apply_match_context ist env goal (nrs+1) (List.tl lex) tl))
+			    apply_match_goal ist env goal (nrs+1) (List.tl lex) tl))
 	| _ ->
-	    errorlabstrm "Tacinterp.apply_match_context"
+	    errorlabstrm "Tacinterp.apply_match_goal"
               (v 0 (str "No matching clauses for match goal" ++
 		      (if ist.debug=DebugOff then
 			 fnl() ++ str "(use \"Set Ltac Debug\" for more info)"
-		       else mt())))
+		       else mt()) ++ str"."))
     end in
   let env = pf_env g in
-    apply_match_context ist env g 0 lmr
+    apply_match_goal ist env g 0 lmr
       (read_match_rule (fst (constr_list ist env)) lmr)
 
 (* Tries to match the hypotheses in a Match Context *)
@@ -2023,7 +2041,7 @@ and interp_match ist g lz constr lmr =
          with PatternMatchingFailure -> apply_match ist csr tl)
     | _ ->
       errorlabstrm "Tacinterp.apply_match" (str
-        "No matching clauses for match") in
+        "No matching clauses for match.") in
   let csr = 
       try interp_ltac_constr ist g constr with e ->
         debugging_exception_step ist true e
@@ -2058,9 +2076,8 @@ and interp_ltac_constr ist gl e =
 	  str "offending expression: " ++ fnl() ++
           Pptactic.pr_glob_tactic (pf_env gl) e ++ fnl() ++ str "this is a " ++
           (match result with
-              VTactic _ -> str "VTactic"
             | VRTactic _ -> str "VRTactic"
-            | VFun (il,ul,b) ->
+            | VFun (_,il,ul,b) ->
                 (str "VFun with body " ++ fnl() ++
                     Pptactic.pr_glob_tactic (pf_env gl) b ++ fnl() ++
 		    str "instantiated arguments " ++ fnl() ++
@@ -2074,20 +2091,19 @@ and interp_ltac_constr ist gl e =
                       (match opt_id with
                           Some id -> str (string_of_id id)
                         | None -> str "_") ++ str ", " ++ s)
-                    ul (str ""))
+                    ul (mt()))
             | VVoid -> str "VVoid"
             | VInteger _ -> str "VInteger"
             | VConstr _ -> str "VConstr"
             | VIntroPattern _ -> str "VIntroPattern"
             | VConstr_context _ -> str "VConstrr_context"
             | VRec _ -> str "VRec"
-            | VList _ -> str "VList"))
+            | VList _ -> str "VList") ++ str".")
 
 (* Interprets tactic expressions : returns a "tactic" *)
 and interp_tactic ist tac gl =
-  try tactic_of_value (val_interp ist gl tac) gl
-  with NotTactic ->
-    errorlabstrm "" (str "Must be a command or must give a tactic value")
+  try tactic_of_value ist (val_interp ist gl tac) gl
+  with NotTactic -> errorlabstrm "" (str "Not a tactic.")
 
 (* Interprets a primitive tactic *)
 and interp_atomic ist gl = function
@@ -2096,14 +2112,15 @@ and interp_atomic ist gl = function
       h_intro_patterns (List.map (interp_intro_pattern ist gl) l)
   | TacIntrosUntil hyp ->
       h_intros_until (interp_quantified_hypothesis ist hyp)
-  | TacIntroMove (ido,ido') ->
+  | TacIntroMove (ido,hto) ->
       h_intro_move (Option.map (interp_fresh_ident ist gl) ido)
-      (Option.map (interp_hyp ist gl) ido')
+                   (interp_move_location ist gl hto)
   | TacAssumption -> h_assumption
   | TacExact c -> h_exact (pf_interp_casted_constr ist gl c)
   | TacExactNoCheck c -> h_exact_no_check (pf_interp_constr ist gl c)
   | TacVmCastNoCheck c -> h_vm_cast_no_check (pf_interp_constr ist gl c)
-  | TacApply (a,ev,cb) -> h_apply a ev (interp_constr_with_bindings ist gl cb)
+  | TacApply (a,ev,cb) ->
+      h_apply a ev (List.map (interp_constr_with_bindings ist gl) cb)
   | TacElim (ev,cb,cbo) ->
       h_elim ev (interp_constr_with_bindings ist gl cb)
                 (Option.map (interp_constr_with_bindings ist gl) cbo)
@@ -2149,20 +2166,16 @@ and interp_atomic ist gl = function
       (pf_interp_constr_list ist gl lems)
 
   (* Derived basic tactics *)
-  | TacSimpleInduction h ->
-      h_simple_induction (interp_quantified_hypothesis ist h)
-  | TacNewInduction (ev,lc,cbo,ids,cls) ->
-      h_new_induction ev (List.map (interp_induction_arg ist gl) lc)
-        (Option.map (interp_constr_with_bindings ist gl) cbo)
-        (interp_intro_pattern ist gl ids)
-        (Option.map (interp_clause ist gl) cls)
-  | TacSimpleDestruct h ->
-      h_simple_destruct (interp_quantified_hypothesis ist h)
-  | TacNewDestruct (ev,c,cbo,ids,cls) -> 
-      h_new_destruct ev (List.map (interp_induction_arg ist gl) c)
-        (Option.map (interp_constr_with_bindings ist gl) cbo)
-        (interp_intro_pattern ist gl ids)
-        (Option.map (interp_clause ist gl) cls)
+  | TacSimpleInductionDestruct (isrec,h) ->
+      h_simple_induction_destruct isrec (interp_quantified_hypothesis ist h)
+  | TacInductionDestruct (isrec,ev,l) ->
+      h_induction_destruct ev isrec
+      (List.map (fun (lc,cbo,(ipato,ipats),cls) ->
+	(List.map (interp_induction_arg ist gl) lc,
+         Option.map (interp_constr_with_bindings ist gl) cbo,
+         (Option.map (interp_intro_pattern ist gl) ipato,
+	  Option.map (interp_intro_pattern ist gl) ipats),
+         Option.map (interp_clause ist gl) cls)) l)
   | TacDoubleInduction (h1,h2) ->
       let h1 = interp_quantified_hypothesis ist h1 in
       let h2 = interp_quantified_hypothesis ist h2 in
@@ -2180,7 +2193,7 @@ and interp_atomic ist gl = function
   | TacClear (b,l) -> h_clear b (interp_hyp_list ist gl l)
   | TacClearBody l -> h_clear_body (interp_hyp_list ist gl l)
   | TacMove (dep,id1,id2) ->
-      h_move dep (interp_hyp ist gl id1) (interp_hyp ist gl id2)
+      h_move dep (interp_hyp ist gl id1) (interp_move_location ist gl id2)
   | TacRename l ->
       h_rename (List.map (fun (id1,id2) -> 
 			    interp_hyp ist gl id1, 
@@ -2222,11 +2235,11 @@ and interp_atomic ist gl = function
 	(Option.map (interp_tactic ist) by)
   | TacInversion (DepInversion (k,c,ids),hyp) ->
       Inv.dinv k (Option.map (pf_interp_constr ist gl) c)
-        (interp_intro_pattern ist gl ids)
+        (Option.map (interp_intro_pattern ist gl) ids)
         (interp_declared_or_quantified_hypothesis ist gl hyp)
   | TacInversion (NonDepInversion (k,idl,ids),hyp) ->
       Inv.inv_clause k 
-        (interp_intro_pattern ist gl ids)
+        (Option.map (interp_intro_pattern ist gl) ids)
         (interp_hyp_list ist gl idl)
         (interp_declared_or_quantified_hypothesis ist gl hyp)
   | TacInversion (InversionUsing (c,idl),hyp) ->
@@ -2237,10 +2250,9 @@ and interp_atomic ist gl = function
   (* For extensions *)
   | TacExtend (loc,opn,l) ->
       let tac = lookup_tactic opn in
-      fun gl ->
-        let args = List.map (interp_genarg ist gl) l in
-        abstract_extended_tactic opn args (tac args) gl
-  | TacAlias (loc,_,l,(_,body)) -> fun gl ->
+      let args = List.map (interp_genarg ist gl) l in
+      abstract_extended_tactic opn args (tac args)
+  | TacAlias (loc,s,l,(_,body)) -> fun gl ->
     let rec f x = match genarg_tag x with
     | IntArgType -> 
         VInteger (out_gen globwit_int x)
@@ -2250,7 +2262,7 @@ and interp_atomic ist gl = function
 	failwith "pre-identifiers cannot be bound"
     | IntroPatternArgType ->
 	VIntroPattern 
-	  (interp_intro_pattern ist gl (out_gen globwit_intro_pattern x))
+	  (snd (interp_intro_pattern ist gl (out_gen globwit_intro_pattern x)))
     | IdentArgType -> 
         VIntroPattern 
 	  (IntroIdentifier
@@ -2301,14 +2313,12 @@ and interp_atomic ist gl = function
     | ExtraArgType _ | BindingsArgType 
     | OptArgType _ | PairArgType _ 
     | List0ArgType _ | List1ArgType _ 
-	-> error "This generic type is not supported in alias"
+	-> error "This generic type is not supported in alias."
         
     in
     let lfun = (List.map (fun (x,c) -> (x,f c)) l)@ist.lfun in
-    let v = locate_tactic_call loc (val_interp { ist with lfun=lfun } gl body)
-    in 
-    try tactic_of_value v gl 
-    with NotTactic -> user_err_loc (loc,"",str "not a tactic")
+    let trace = (loc,LtacNotationCall s)::ist.trace in
+    interp_tactic { ist with lfun=lfun; trace=trace } body gl
 
 let make_empty_glob_sign () =
   { ltacvars = ([],[]); ltacrecvars = []; 
@@ -2316,20 +2326,20 @@ let make_empty_glob_sign () =
 
 (* Initial call for interpretation *)
 let interp_tac_gen lfun avoid_ids debug t gl = 
-  interp_tactic { lfun=lfun; avoid_ids=avoid_ids; debug=debug; last_loc=dloc } 
+  interp_tactic { lfun=lfun; avoid_ids=avoid_ids; debug=debug; trace=[] } 
     (intern_tactic {
       ltacvars = (List.map fst lfun, []); ltacrecvars = [];
       gsigma = project gl; genv = pf_env gl } t) gl
 
 let eval_tactic t gls =
-  interp_tactic { lfun=[]; avoid_ids=[]; debug=get_debug(); last_loc=dloc }
+  interp_tactic { lfun=[]; avoid_ids=[]; debug=get_debug(); trace=[] }
     t gls
 
 let interp t = interp_tac_gen [] [] (get_debug()) t
 
 let eval_ltac_constr gl t =
   interp_ltac_constr 
-    { lfun=[]; avoid_ids=[]; debug=get_debug(); last_loc=dloc } gl
+    { lfun=[]; avoid_ids=[]; debug=get_debug(); trace=[] } gl
     (intern_tactic (make_empty_glob_sign ()) t )
 
 (* Hides interpretation for pretty-print *)
@@ -2392,7 +2402,7 @@ let subst_global_reference subst =
  let subst_global ref =
   let ref',t' = subst_global subst ref in
    if not (eq_constr (constr_of_global ref') t') then
-    ppnl (str "Warning: the reference " ++ pr_global ref ++ str " is not " ++
+    ppnl (str "Warning: The reference " ++ pr_global ref ++ str " is not " ++
           str " expanded to \"" ++ pr_lconstr t' ++ str "\", but to " ++
           pr_global ref') ;
    ref'
@@ -2430,10 +2440,10 @@ let subst_match_pattern subst = function
   | Subterm (ido,pc) -> Subterm (ido,subst_pattern subst pc)
   | Term pc -> Term (subst_pattern subst pc)
 
-let rec subst_match_context_hyps subst = function
+let rec subst_match_goal_hyps subst = function
   | Hyp (locs,mp) :: tl ->
       Hyp (locs,subst_match_pattern subst mp)
-      :: subst_match_context_hyps subst tl
+      :: subst_match_goal_hyps subst tl
   | [] -> []
 
 let rec subst_atomic subst (t:glob_atomic_tactic_expr) = match t with
@@ -2443,7 +2453,8 @@ let rec subst_atomic subst (t:glob_atomic_tactic_expr) = match t with
   | TacExact c -> TacExact (subst_rawconstr subst c)
   | TacExactNoCheck c -> TacExactNoCheck (subst_rawconstr subst c)
   | TacVmCastNoCheck c -> TacVmCastNoCheck (subst_rawconstr subst c)
-  | TacApply (a,ev,cb) -> TacApply (a,ev,subst_raw_with_bindings subst cb)
+  | TacApply (a,ev,cb) ->
+      TacApply (a,ev,List.map (subst_raw_with_bindings subst) cb)
   | TacElim (ev,cb,cbo) ->
       TacElim (ev,subst_raw_with_bindings subst cb,
                Option.map (subst_raw_with_bindings subst) cbo)
@@ -2474,14 +2485,11 @@ let rec subst_atomic subst (t:glob_atomic_tactic_expr) = match t with
   | TacDAuto (n,p,lems) -> TacDAuto (n,p,List.map (subst_rawconstr subst) lems)
 
   (* Derived basic tactics *)
-  | TacSimpleInduction h as x -> x
-  | TacNewInduction (ev,lc,cbo,ids,cls) ->
-      TacNewInduction (ev,List.map (subst_induction_arg subst) lc,
-               Option.map (subst_raw_with_bindings subst) cbo, ids, cls)
-  | TacSimpleDestruct h as x -> x
-  | TacNewDestruct (ev,c,cbo,ids,cls) ->
-      TacNewDestruct (ev,List.map (subst_induction_arg subst) c,
-               Option.map (subst_raw_with_bindings subst) cbo, ids, cls)
+  | TacSimpleInductionDestruct (isrec,h) as x -> x
+  | TacInductionDestruct (isrec,ev,l) ->
+      TacInductionDestruct (isrec,ev,List.map (fun (lc,cbo,ids,cls) ->
+	List.map (subst_induction_arg subst) lc,
+        Option.map (subst_raw_with_bindings subst) cbo, ids, cls) l)
   | TacDoubleInduction (h1,h2) as x -> x
   | TacDecomposeAnd c -> TacDecomposeAnd (subst_rawconstr subst c)
   | TacDecomposeOr c -> TacDecomposeOr (subst_rawconstr subst c)
@@ -2540,8 +2548,8 @@ and subst_tactic subst (t:glob_tactic_expr) = match t with
   | TacLetIn (r,l,u) ->
       let l = List.map (fun (n,b) -> (n,subst_tacarg subst b)) l in
       TacLetIn (r,l,subst_tactic subst u)
-  | TacMatchContext (lz,lr,lmr) ->
-      TacMatchContext(lz,lr, subst_match_rule subst lmr)
+  | TacMatchGoal (lz,lr,lmr) ->
+      TacMatchGoal(lz,lr, subst_match_rule subst lmr)
   | TacMatch (lz,c,lmr) ->
       TacMatch (lz,subst_tactic subst c,subst_match_rule subst lmr)
   | TacId _ | TacFail _ as x -> x
@@ -2588,7 +2596,7 @@ and subst_match_rule subst = function
   | (All tc)::tl ->
       (All (subst_tactic subst tc))::(subst_match_rule subst tl)
   | (Pat (rl,mp,tc))::tl ->
-      let hyps = subst_match_context_hyps subst rl in
+      let hyps = subst_match_goal_hyps subst rl in
       let pat = subst_match_pattern subst mp in
       Pat (hyps,pat,subst_tactic subst tc)
       ::(subst_match_rule subst tl)
@@ -2707,12 +2715,12 @@ let print_ltac id =
  try
   let kn = Nametab.locate_tactic id in
   let t = lookup kn in
-   str "Ltac" ++ spc() ++ pr_qualid id ++ str ":=" ++ spc() ++
+   str "Ltac" ++ spc() ++ pr_qualid id ++ str " :=" ++ spc() ++
     Pptactic.pr_glob_tactic (Global.env ()) t
  with
   Not_found ->
    errorlabstrm "print_ltac"
-    (pr_qualid id ++ spc() ++ str "is not a user defined tactic")
+    (pr_qualid id ++ spc() ++ str "is not a user defined tactic.")
 
 open Libnames
 
@@ -2729,14 +2737,14 @@ let make_absolute_name ident repl =
 	if repl then id, kn
 	else
 	  user_err_loc (loc,"Tacinterp.add_tacdef",
-		       str "There is already an Ltac named " ++ pr_reference ident)
+		       str "There is already an Ltac named " ++ pr_reference ident ++ str".")
       else if is_atomic_kn kn then 
 	user_err_loc (loc,"Tacinterp.add_tacdef",
-		     str "Reserved Ltac name " ++ pr_reference ident)
+		     str "Reserved Ltac name " ++ pr_reference ident ++ str".")
       else id, kn
   with Not_found ->
     user_err_loc (loc,"Tacinterp.add_tacdef",
-		 str "There is no Ltac named " ++ pr_reference ident)
+		 str "There is no Ltac named " ++ pr_reference ident ++ str".")
 
 let rec filter_map f l = 
   let rec aux acc = function
@@ -2782,17 +2790,33 @@ let glob_tactic_env l env x =
     x
 
 let interp_redexp env sigma r = 
-  let ist = { lfun=[]; avoid_ids=[]; debug=get_debug (); last_loc=dloc } in
+  let ist = { lfun=[]; avoid_ids=[]; debug=get_debug (); trace=[] } in
   let gist = {(make_empty_glob_sign ()) with genv = env; gsigma = sigma } in
   interp_red_expr ist sigma env (intern_red_expr gist r)
 
+(***************************************************************************)
+(* Embed tactics in raw or glob tactic expr *)
+
+let globTacticIn t = TacArg (TacDynamic (dummy_loc,tactic_in t))
+let tacticIn t = globTacticIn (fun ist -> glob_tactic (t ist))
+
+let tacticOut = function
+  | TacArg (TacDynamic (_,d)) ->
+    if (tag d) = "tactic" then
+      tactic_out d
+    else
+      anomalylabstrm "tacticOut" (str "Dynamic tag should be tactic")
+  | ast ->
+    anomalylabstrm "tacticOut"
+      (str "Not a Dynamic ast: " (* ++ print_ast ast*) )
+
 (***************************************************************************)
 (* Backwarding recursive needs of tactic glob/interp/eval functions *)
 
 let _ = Auto.set_extern_interp
   (fun l -> 
     let l = List.map (fun (id,c) -> (id,VConstr c)) l in
-    interp_tactic {lfun=l;avoid_ids=[];debug=get_debug(); last_loc=dloc})
+    interp_tactic {lfun=l;avoid_ids=[];debug=get_debug(); trace=[]})
 let _ = Auto.set_extern_intern_tac 
   (fun l ->
     Flags.with_option strict_check
diff --git a/tactics/tacinterp.mli b/tactics/tacinterp.mli
index 87aa85dc..928e5914 100644
--- a/tactics/tacinterp.mli
+++ b/tactics/tacinterp.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tacinterp.mli 10919 2008-05-11 22:04:26Z msozeau $ i*)
+(*i $Id: tacinterp.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Dyn
@@ -26,9 +26,9 @@ open Redexpr
 
 (* Values for interpretation *)
 type value =
-  | VTactic of Util.loc * tactic  (* For mixed ML/Ltac tactics (e.g. Tauto) *)
   | VRTactic of (goal list sigma * validation)
-  | VFun of (identifier * value) list * identifier option list * glob_tactic_expr
+  | VFun of ltac_trace * (identifier*value) list * 
+      identifier option list * glob_tactic_expr
   | VVoid
   | VInteger of int
   | VIntroPattern of intro_pattern_expr
@@ -42,18 +42,16 @@ and interp_sign =
   { lfun : (identifier * value) list;
     avoid_ids : identifier list;
     debug : debug_info;
-    last_loc : loc }
+    trace : ltac_trace }
 
 (* Transforms an id into a constr if possible *)
 val constr_of_id : Environ.env -> identifier -> constr
 
 (* To embed several objects in Coqast.t *)
 val tacticIn : (interp_sign -> raw_tactic_expr) -> raw_tactic_expr
-val tacticOut : raw_tactic_expr -> (interp_sign -> raw_tactic_expr)
+val globTacticIn : (interp_sign -> glob_tactic_expr) -> raw_tactic_expr
 val valueIn : value -> raw_tactic_arg
-val valueOut: raw_tactic_arg -> value
 val constrIn : constr -> constr_expr
-val constrOut : constr_expr -> constr
 
 (* Sets the debugger mode *)
 val set_debug : debug_info -> unit
diff --git a/tactics/tacticals.ml b/tactics/tacticals.ml
index eeca6301..3b13d1a0 100644
--- a/tactics/tacticals.ml
+++ b/tactics/tacticals.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tacticals.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: tacticals.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -86,7 +86,7 @@ let tclMAP tacfun l =
 
 let tclNTH_HYP m (tac : constr->tactic) gl =
   tac (try mkVar(let (id,_,_) = List.nth (pf_hyps gl) (m-1) in id) 
-       with Failure _ -> error "No such assumption") gl
+       with Failure _ -> error "No such assumption.") gl
 
 (* apply a tactic to the last element of the signature  *)
 
@@ -94,11 +94,11 @@ let tclLAST_HYP = tclNTH_HYP 1
 
 let tclLAST_NHYPS n tac gl =
   tac (try list_firstn n (pf_ids_of_hyps gl)
-       with Failure _ -> error "No such assumptions") gl
+       with Failure _ -> error "No such assumptions.") gl
 
 let tclTRY_sign (tac : constr->tactic) sign gl =
   let rec arec = function
-    | []      -> tclFAIL 0 (str "no applicable hypothesis")
+    | []      -> tclFAIL 0 (str "No applicable hypothesis.")
     | [s]     -> tac (mkVar s) (*added in order to get useful error messages *)
     | (s::sl) -> tclORELSE (tac (mkVar s)) (arec sl) 
   in 
@@ -218,7 +218,7 @@ let lastHyp gl = List.hd (pf_ids_of_hyps gl)
 
 let nLastHyps n gl =
   try list_firstn n (pf_hyps gl)
-  with Failure "firstn" -> error "Not enough hypotheses in the goal"
+  with Failure "firstn" -> error "Not enough hypotheses in the goal."
 
 
 let onClause t cls gl  = t cls gl
@@ -270,19 +270,28 @@ type branch_args = {
   nassums    : int;         (* the number of assumptions to be introduced *)
   branchsign : bool list;   (* the signature of the branch.
                                true=recursive argument, false=constant *)
-  branchnames : intro_pattern_expr list}
+  branchnames : intro_pattern_expr located list}
 
 type branch_assumptions = {
   ba        : branch_args;     (* the branch args *)
   assums    : named_context}   (* the list of assumptions introduced *)
 
+let check_or_and_pattern_size loc names n =
+  if List.length names <> n then
+    if n = 1 then 
+      user_err_loc (loc,"",str "Expects a conjunctive pattern.")
+    else 
+      user_err_loc (loc,"",str "Expects a disjunctive pattern with " ++ int n 
+	++ str " branches.")
+
 let compute_induction_names n = function
-  | IntroAnonymous ->
+  | None ->
       Array.make n []
-  | IntroOrAndPattern names when List.length names = n ->
+  | Some (loc,IntroOrAndPattern names) ->
+      check_or_and_pattern_size loc names n;
       Array.of_list names
   | _ ->
-      errorlabstrm "" (str "Expects " ++ int n ++ str " lists of names")
+      error "Unexpected introduction pattern."
 
 let compute_construtor_signatures isrec (_,k as ity) =
   let rec analrec c recargs =
@@ -335,7 +344,7 @@ let general_elim_then_using mk_elim
   let indmv = 
     match kind_of_term (last_arg elimclause.templval.Evd.rebus) with
       | Meta mv -> mv
-      | _         -> error "elimination"
+      | _         -> anomaly "elimination"
   in
   let pmv =
     let p, _ = decompose_app elimclause.templtyp.Evd.rebus in
@@ -348,7 +357,7 @@ let general_elim_then_using mk_elim
 	      | Var id -> string_of_id id
 	      | _ -> "\b"
 	  in
-	  error ("The elimination combinator " ^ name_elim ^ " is not known") 
+	  error ("The elimination combinator " ^ name_elim ^ " is unknown.") 
   in
   let elimclause' = clenv_fchain indmv elimclause indclause' in
   let elimclause' = clenv_match_args elimbindings elimclause' in
@@ -393,7 +402,7 @@ let elimination_then_using tac predicate bindings c gl =
   let (ind,t) = pf_reduce_to_quantified_ind gl (pf_type_of gl c) in
   let indclause  = mk_clenv_from gl (c,t) in
   general_elim_then_using gl_make_elim
-    true IntroAnonymous tac predicate bindings ind indclause gl
+    true None tac predicate bindings ind indclause gl
 
 let case_then_using =
   general_elim_then_using gl_make_case_dep false
@@ -423,7 +432,7 @@ let make_elim_branch_assumptions ba gl =
 		   id::constargs,
 		   recargs,
 		   indargs) tl idtl
-      | (_, _) -> error "make_elim_branch_assumptions"
+      | (_, _) -> anomaly "make_elim_branch_assumptions"
   in 
   makerec ([],[],[],[],[]) ba.branchsign
     (try list_firstn ba.nassums (pf_hyps gl)
@@ -447,7 +456,7 @@ let make_case_branch_assumptions ba gl =
 		   id::cargs,
 		   recargs,
 		   id::constargs) tl idtl
-      | (_, _) -> error "make_case_branch_assumptions"
+      | (_, _) -> anomaly "make_case_branch_assumptions"
   in 
   makerec ([],[],[],[]) ba.branchsign
     (try list_firstn ba.nassums (pf_hyps gl)
diff --git a/tactics/tacticals.mli b/tactics/tacticals.mli
index e97abe9f..6826977b 100644
--- a/tactics/tacticals.mli
+++ b/tactics/tacticals.mli
@@ -6,10 +6,11 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tacticals.mli 10785 2008-04-13 21:41:54Z herbelin $ i*)
+(*i $Id: tacticals.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Pp
+open Util
 open Names
 open Term
 open Sign
@@ -124,23 +125,30 @@ type branch_args = {
   nassums    : int;         (* the number of assumptions to be introduced *)
   branchsign : bool list;   (* the signature of the branch.
                                true=recursive argument, false=constant *)
-  branchnames : intro_pattern_expr list}
+  branchnames : intro_pattern_expr located list}
 
 type branch_assumptions = {
   ba        : branch_args;     (* the branch args *)
   assums    : named_context}   (* the list of assumptions introduced *)
 
+(* [check_disjunctive_pattern_size loc pats n] returns an appropriate *)
+(* error message if |pats| <> n *)
+val check_or_and_pattern_size :
+  Util.loc -> or_and_intro_pattern_expr -> int -> unit 
+
 (* Useful for [as intro_pattern] modifier *)
 val compute_induction_names : 
-  int -> intro_pattern_expr -> intro_pattern_expr list array
+  int -> intro_pattern_expr located option -> 
+    intro_pattern_expr located list array
 
 val elimination_sort_of_goal : goal sigma -> sorts_family
 val elimination_sort_of_hyp  : identifier -> goal sigma -> sorts_family
 
 val general_elim_then_using :
-  (inductive -> goal sigma -> constr) -> rec_flag -> intro_pattern_expr ->
-    (branch_args -> tactic) -> constr option -> 
-      (arg_bindings * arg_bindings) -> inductive -> clausenv -> tactic
+  (inductive -> goal sigma -> constr) -> rec_flag ->
+  intro_pattern_expr located option -> (branch_args -> tactic) -> 
+    constr option -> (arg_bindings * arg_bindings) -> inductive -> clausenv ->
+    tactic
 	  
 val elimination_then_using :
   (branch_args -> tactic) -> constr option -> 
@@ -151,12 +159,12 @@ val elimination_then :
     (arg_bindings * arg_bindings) -> constr -> tactic
 
 val case_then_using :
-  intro_pattern_expr -> (branch_args -> tactic) -> 
+  intro_pattern_expr located option -> (branch_args -> tactic) -> 
     constr option -> (arg_bindings * arg_bindings) ->
       inductive -> clausenv -> tactic
 
 val case_nodep_then_using :
-  intro_pattern_expr -> (branch_args -> tactic) -> 
+  intro_pattern_expr located option -> (branch_args -> tactic) -> 
     constr option -> (arg_bindings * arg_bindings) -> 
       inductive -> clausenv -> tactic
 
diff --git a/tactics/tactics.ml b/tactics/tactics.ml
index 88274ef6..b02e84e7 100644
--- a/tactics/tactics.ml
+++ b/tactics/tactics.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: tactics.ml 11166 2008-06-22 13:23:35Z herbelin $ *)
+(* $Id: tactics.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -75,6 +75,8 @@ let inj_ebindings = function
   | ExplicitBindings l -> 
       ExplicitBindings (List.map (fun (l,id,c) -> (l,id,inj_open c)) l)
 
+let dloc = dummy_loc
+
 (*********************************************)
 (*                 Tactics                   *)
 (*********************************************)
@@ -98,7 +100,7 @@ let string_of_inductive c =
       let (mib,mip) = Global.lookup_inductive ind_sp in 
       string_of_id mip.mind_typename
   | _ -> raise Bound
-  with Bound -> error "Bound head variable"
+  with Bound -> error "Bound head variable."
 
 let rec head_constr_bound t l =
   let t = strip_outer_cast(collapse_appl t) in
@@ -114,7 +116,7 @@ let rec head_constr_bound t l =
     | _                -> raise Bound
 
 let head_constr c = 
-  try head_constr_bound c [] with Bound -> error "Bound head variable"
+  try head_constr_bound c [] with Bound -> error "Bound head variable."
 
 (*
 let bad_tactic_args s l =
@@ -126,15 +128,44 @@ let bad_tactic_args s l =
 (******************************************)
 
 let introduction    = Tacmach.introduction 
-let intro_replacing = Tacmach.intro_replacing 
-let internal_cut    = Tacmach.internal_cut
-let internal_cut_rev = Tacmach.internal_cut_rev
 let refine          = Tacmach.refine
 let convert_concl   = Tacmach.convert_concl
 let convert_hyp     = Tacmach.convert_hyp
-let thin            = Tacmach.thin 
 let thin_body       = Tacmach.thin_body
 
+let error_clear_dependency env id = function
+  | Evarutil.OccurHypInSimpleClause None ->
+      errorlabstrm "" (pr_id id ++ str " is used in conclusion.")
+  | Evarutil.OccurHypInSimpleClause (Some id') -> 
+      errorlabstrm ""
+        (pr_id id ++ strbrk " is used in hypothesis " ++ pr_id id' ++ str".")
+  | Evarutil.EvarTypingBreak ev ->
+      errorlabstrm ""
+        (str "Cannot remove " ++ pr_id id ++ 
+	 strbrk " without breaking the typing of " ++ 
+	 Printer.pr_existential env ev ++ str".")
+
+let thin l gl = 
+  try thin l gl
+  with Evarutil.ClearDependencyError (id,err) ->
+    error_clear_dependency (pf_env gl) id err
+
+let internal_cut_gen b d t gl =
+  try internal_cut b d t gl
+  with Evarutil.ClearDependencyError (id,err) ->
+    error_clear_dependency (pf_env gl) id err
+
+let internal_cut = internal_cut_gen false
+let internal_cut_replace = internal_cut_gen true
+
+let internal_cut_rev_gen b d t gl =
+  try internal_cut_rev b d t gl
+  with Evarutil.ClearDependencyError (id,err) ->
+    error_clear_dependency (pf_env gl) id err
+
+let internal_cut_rev = internal_cut_rev_gen false
+let internal_cut_rev_replace = internal_cut_rev_gen true
+
 (* Moving hypotheses *)
 let move_hyp        = Tacmach.move_hyp 
 
@@ -174,7 +205,7 @@ let reduct_in_hyp redfun ((_,id),where) gl =
   match c with
   | None -> 
       if where = InHypValueOnly then
-	errorlabstrm "" (pr_id id ++ str "has no value");
+	errorlabstrm "" (pr_id id ++ str "has no value.");
       convert_hyp_no_check (id,None,redfun' ty) gl
   | Some b ->
       let b' = if where <> InHypTypeOnly then redfun' b else b in
@@ -197,7 +228,7 @@ let change_and_check cv_pb t env sigma c =
   if is_fconv cv_pb env sigma t c then 
     t
   else 
-    errorlabstrm "convert-check-hyp" (str "Not convertible")
+    errorlabstrm "convert-check-hyp" (str "Not convertible.")
 
 (* Use cumulutavity only if changing the conclusion not a subterm *)
 let change_on_subterm cv_pb t = function
@@ -219,7 +250,7 @@ let change occl c cls =
       ({onhyps=(Some(_::_::_)|None)}
       |{onhyps=Some(_::_);concl_occs=((false,_)|(true,_::_))}),
       Some _ ->
-	error "No occurrences expected when changing several hypotheses"
+	error "No occurrences expected when changing several hypotheses."
     | _ -> ());
   onClauses (change_option occl c) cls
 
@@ -273,15 +304,19 @@ let fresh_id_avoid avoid id =
 let fresh_id avoid id gl =
   fresh_id_avoid (avoid@(pf_ids_of_hyps gl)) id
 
-let id_of_name_with_default s = function
-  | Anonymous -> id_of_string s
+let id_of_name_with_default id = function
+  | Anonymous -> id
   | Name id   -> id
 
+let hid = id_of_string "H"
+let xid = id_of_string "X"
+
+let default_id_of_sort = function Prop _ -> hid | Type _ -> xid
+
 let default_id env sigma = function
   | (name,None,t) ->
-      (match Typing.sort_of env sigma t with
-	| Prop _ -> (id_of_name_with_default "H" name)
-	| Type _ -> (id_of_name_with_default "X" name))
+      let dft = default_id_of_sort (Typing.sort_of env sigma t) in
+      id_of_name_with_default dft name
   | (name,Some b,_) -> id_of_name_using_hdchar env b name
 
 (* Non primitive introduction tactics are treated by central_intro
@@ -293,14 +328,14 @@ type intro_name_flag =
   | IntroBasedOn of identifier * identifier list
   | IntroMustBe of identifier
 
-let find_name decl gl = function
+let find_name loc decl gl = function
   | IntroAvoid idl -> 
       (* this case must be compatible with [find_intro_names] below. *)
       let id = fresh_id idl (default_id (pf_env gl) gl.sigma decl) gl in id
   | IntroBasedOn (id,idl) -> fresh_id idl id gl
-  | IntroMustBe id        -> 
+  | IntroMustBe id -> 
       let id' = fresh_id [] id gl in
-      if id' <> id then error ((string_of_id id)^" is already used");
+      if id'<>id then user_err_loc (loc,"",pr_id id ++ str" is already used.");
       id'
 
 (* Returns the names that would be created by intros, without doing
@@ -319,65 +354,72 @@ let find_intro_names ctxt gl =
     ctxt (pf_env gl , []) in
   List.rev res 
 
-
 let build_intro_tac id = function
-  | None      -> introduction id
-  | Some dest -> tclTHEN (introduction id) (move_hyp true id dest)
+  | MoveToEnd true -> introduction id
+  | dest -> tclTHEN (introduction id) (move_hyp true id dest)
 
-let rec intro_gen name_flag move_flag force_flag gl =
+let rec intro_gen loc name_flag move_flag force_flag gl =
   match kind_of_term (pf_concl gl) with
     | Prod (name,t,_) -> 
-	build_intro_tac (find_name (name,None,t) gl name_flag) move_flag gl
+	build_intro_tac (find_name loc (name,None,t) gl name_flag) move_flag gl
     | LetIn (name,b,t,_) ->
-	build_intro_tac (find_name (name,Some b,t) gl name_flag) move_flag gl
+	build_intro_tac (find_name loc (name,Some b,t) gl name_flag) move_flag
+	  gl
     | _ -> 
 	if not force_flag then raise (RefinerError IntroNeedsProduct);
 	try
 	  tclTHEN
 	    (reduce (Red true) onConcl)
-	    (intro_gen name_flag move_flag force_flag) gl
+	    (intro_gen loc name_flag move_flag force_flag) gl
 	with Redelimination ->
-	  errorlabstrm "Intro" (str "No product even after head-reduction")
+	  user_err_loc(loc,"Intro",str "No product even after head-reduction.")
 
-let intro_mustbe_force id = intro_gen (IntroMustBe id) None true
-let intro_using id = intro_gen (IntroBasedOn (id,[])) None false
-let intro_force force_flag = intro_gen (IntroAvoid []) None force_flag
+let intro_mustbe_force id = intro_gen dloc (IntroMustBe id) no_move true
+let intro_using id = intro_gen dloc (IntroBasedOn (id,[])) no_move false
+let intro_force force_flag = intro_gen dloc (IntroAvoid []) no_move force_flag
 let intro = intro_force false
 let introf = intro_force true
 
-let intro_avoiding l = intro_gen (IntroAvoid l) None false 
-
-let introf_move_name destopt = intro_gen (IntroAvoid []) destopt true
+let intro_avoiding l = intro_gen dloc (IntroAvoid l) no_move false 
 
-(* For backwards compatibility *)
-let central_intro = intro_gen
+let introf_move_name destopt = intro_gen dloc (IntroAvoid []) destopt true
 
 (**** Multiple introduction tactics ****)
 
 let rec intros_using = function
-    []      -> tclIDTAC
-   | str::l  -> tclTHEN (intro_using str) (intros_using l)
+  | []     -> tclIDTAC
+  | str::l -> tclTHEN (intro_using str) (intros_using l)
 
 let intros = tclREPEAT (intro_force false)
 
 let intro_erasing id = tclTHEN (thin [id]) (introduction id)
 
+let rec get_next_hyp_position id = function
+  | [] -> error ("No such hypothesis: " ^ string_of_id id)
+  | (hyp,_,_) :: right ->
+      if hyp = id then
+	match right with (id,_,_)::_ -> MoveBefore id | [] -> MoveToEnd true
+      else
+	get_next_hyp_position id right
+
+let intro_replacing id gl =
+  let next_hyp = get_next_hyp_position id (pf_hyps gl) in
+  tclTHENLIST [thin [id]; introduction id; move_hyp true id next_hyp] gl
+
 let intros_replacing ids gl = 
   let rec introrec = function
     | [] -> tclIDTAC
     | id::tl ->
-	(tclTHEN (tclORELSE (intro_replacing id)
-		    (tclORELSE (intro_erasing id)   (* ?? *)
-                       (intro_using id)))
-           (introrec tl))
+	tclTHEN (tclORELSE (intro_replacing id) (intro_using id))
+           (introrec tl)
   in 
   introrec ids gl
 
 (* User-level introduction tactics *)
 
-let intro_move idopt idopt' = match idopt with
-  | None -> intro_gen (IntroAvoid []) idopt' true
-  | Some id -> intro_gen (IntroMustBe id) idopt' true
+let intro_move idopt hto = match idopt with
+  | None -> intro_gen dloc (IntroAvoid []) hto true
+  | Some id -> intro_gen dloc (IntroMustBe id) hto true
 
 let pf_lookup_hypothesis_as_renamed env ccl = function
   | AnonHyp n -> pf_lookup_index_as_renamed env ccl n
@@ -415,7 +457,8 @@ let depth_of_quantified_hypothesis red h gl =
         errorlabstrm "lookup_quantified_hypothesis" 
           (str "No " ++ msg_quantified_hypothesis h ++
 	  strbrk " in current goal" ++
-	  if red then strbrk " even after head-reduction" else mt ())
+	  (if red then strbrk " even after head-reduction" else mt ()) ++
+	  str".")
 
 let intros_until_gen red h g =
   tclDO (depth_of_quantified_hypothesis red h g) intro g
@@ -434,7 +477,7 @@ let try_intros_until tac = function
 let rec intros_move = function
   | [] -> tclIDTAC
   | (hyp,destopt) :: rest ->
-      tclTHEN (intro_gen (IntroMustBe hyp) destopt false)
+      tclTHEN (intro_gen dloc (IntroMustBe hyp) destopt false)
 	(intros_move rest)
 
 let dependent_in_decl a (_,c,t) =
@@ -442,33 +485,6 @@ let dependent_in_decl a (_,c,t) =
     | None -> dependent a t
     | Some body -> dependent a body || dependent a t
 
-let move_to_rhyp rhyp gl =
-  let rec get_lhyp lastfixed depdecls = function
-    | [] ->
-	(match rhyp with
-	   | None -> lastfixed
-      	   | Some h -> anomaly ("Hypothesis should occur: "^ (string_of_id h)))
-    | (hyp,c,typ) as ht :: rest ->
-	if Some hyp = rhyp then 
-	  lastfixed
-	else if List.exists (occur_var_in_decl (pf_env gl) hyp) depdecls then 
-	  get_lhyp lastfixed (ht::depdecls) rest
-        else
-	  get_lhyp (Some hyp) depdecls rest
-  in
-  let sign = pf_hyps gl in
-  let (hyp,c,typ as decl) = List.hd sign in
-  match get_lhyp None [decl] (List.tl sign) with
-    | None -> tclIDTAC gl
-    | Some hypto -> move_hyp true hyp hypto gl
-
-let rec intros_rmove = function
-  | [] -> tclIDTAC
-  | (hyp,destopt) :: rest ->
-      tclTHENLIST [ introduction hyp;
- 		    move_to_rhyp destopt;
-		    intros_rmove rest ]
-
 (* Apply a tactic on a quantified hypothesis, an hypothesis in context
    or a term with bindings *)
 
@@ -515,7 +531,7 @@ let cut c gl =
             (internal_cut_rev id c)
             (tclTHEN (apply_type t [mkVar id]) (thin [id]))
             gl
-    | _  -> error "Not a proposition or a type"
+    | _  -> error "Not a proposition or a type."
 
 let cut_intro t = tclTHENFIRST (cut t) intro
 
@@ -529,9 +545,7 @@ let cut_intro t = tclTHENFIRST (cut t) intro
 (* cut_replacing échoue si l'hypothèse à remplacer apparaît dans le
    but, ou dans une autre hypothèse *)
 let cut_replacing id t tac = 
-  tclTHENS (cut t) [
-      tclORELSE (intro_replacing id) (intro_erasing id); 
-      tac (refine_no_check (mkVar id)) ]
+  tclTHENS (cut t) [ intro_replacing id; tac (refine_no_check (mkVar id)) ]
 
 let cut_in_parallel l = 
   let rec prec = function
@@ -543,7 +557,7 @@ let cut_in_parallel l =
 let error_uninstantiated_metas t clenv =
   let na = meta_name clenv.evd (List.hd (Metaset.elements (metavars_of t))) in
   let id = match na with Name id -> id | _ -> anomaly "unnamed dependent meta"
-  in errorlabstrm "" (str "cannot find an instance for " ++ pr_id id)
+  in errorlabstrm "" (str "Cannot find an instance for " ++ pr_id id ++ str".")
 
 let clenv_refine_in with_evars id clenv gl =
   let clenv = clenv_pose_dependent_evars with_evars clenv in
@@ -577,7 +591,7 @@ let elimination_clause_scheme with_evars allow_K elimclause indclause gl =
     (match kind_of_term (last_arg elimclause.templval.rebus) with
        | Meta mv -> mv
        | _  -> errorlabstrm "elimination_clause"
-             (str "The type of elimination clause is not well-formed")) 
+             (str "The type of elimination clause is not well-formed.")) 
   in
   let elimclause' = clenv_fchain indmv elimclause indclause in 
   res_pf elimclause' ~with_evars:with_evars ~allow_K:allow_K ~flags:elim_flags
@@ -643,22 +657,28 @@ let simplest_elim c = default_elim false (c,NoBindings)
    (e.g. it could replace id:A->B->C by id:C, knowing A/\B)
 *)
 
+let clenv_fchain_in id elim_flags mv elimclause hypclause =
+  try clenv_fchain ~allow_K:false ~flags:elim_flags mv elimclause hypclause
+  with PretypeError (env,NoOccurrenceFound (op,_)) ->
+    (* Set the hypothesis name in the message *)
+    raise (PretypeError (env,NoOccurrenceFound (op,Some id)))
+
 let elimination_in_clause_scheme with_evars id elimclause indclause gl =
   let (hypmv,indmv) = 
     match clenv_independent elimclause with
         [k1;k2] -> (k1,k2)
       | _  -> errorlabstrm "elimination_clause"
-          (str "The type of elimination clause is not well-formed") in
+          (str "The type of elimination clause is not well-formed.") in
   let elimclause'  = clenv_fchain indmv elimclause indclause in 
   let hyp = mkVar id in
   let hyp_typ = pf_type_of gl hyp in
   let hypclause = mk_clenv_from_n gl (Some 0) (hyp, hyp_typ) in
-  let elimclause'' =
-    clenv_fchain ~allow_K:false ~flags:elim_flags hypmv elimclause' hypclause in
+  let elimclause'' = 
+    clenv_fchain_in id elim_flags hypmv elimclause' hypclause in
   let new_hyp_typ  = clenv_type elimclause'' in
   if eq_constr hyp_typ new_hyp_typ then
     errorlabstrm "general_rewrite_in" 
-      (str "Nothing to rewrite in " ++ pr_id id);
+      (str "Nothing to rewrite in " ++ pr_id id ++ str".");
   clenv_refine_in with_evars id elimclause'' gl
 
 let general_elim_in with_evars id =
@@ -688,6 +708,13 @@ let simplest_case c = general_case_analysis false (c,NoBindings)
 (*            Resolution tactics                    *)
 (****************************************************)
 
+let resolve_classes gl =
+  let env = pf_env gl and evd = project gl in
+    if evd = Evd.empty then tclIDTAC gl
+    else
+      let evd' = Typeclasses.resolve_typeclasses env (Evd.create_evar_defs evd) in
+	(tclTHEN (tclEVARS (Evd.evars_of evd')) tclNORMEVAR) gl
+
 (* Resolution with missing arguments *)
 
 let general_apply with_delta with_destruct with_evars (c,lbind) gl =
@@ -701,7 +728,7 @@ let general_apply with_delta with_destruct with_evars (c,lbind) gl =
   let thm_ty0 = nf_betaiota (pf_type_of gl c) in
   let try_apply thm_ty nprod =
     let n = nb_prod thm_ty - nprod in
-    if n<0 then error "Apply: theorem has not enough premisses.";
+    if n<0 then error "Applied theorem has not enough premisses.";
     let clause = make_clenv_binding_apply gl (Some n) (c,thm_ty) lbind in
     Clenvtac.res_pf clause ~with_evars:with_evars ~flags:flags gl in
   try try_apply thm_ty0 concl_nprod
@@ -744,16 +771,22 @@ let general_apply with_delta with_destruct with_evars (c,lbind) gl =
     try_red_apply thm_ty0 in
   try_main_apply c gl
 
-let apply_with_ebindings_gen b = general_apply b b
+let rec apply_with_ebindings_gen b e = function
+  | [] ->
+      tclIDTAC
+  | [cb] ->
+      general_apply b b e cb
+  | cb::cbl -> 
+      tclTHENLAST (general_apply b b e cb) (apply_with_ebindings_gen b e cbl)
 
-let apply_with_ebindings = apply_with_ebindings_gen false false
-let eapply_with_ebindings = apply_with_ebindings_gen false true
+let apply_with_ebindings cb = apply_with_ebindings_gen false false [cb]
+let eapply_with_ebindings cb = apply_with_ebindings_gen false true [cb]
 
 let apply_with_bindings (c,bl) =
   apply_with_ebindings (c,inj_ebindings bl)
 
 let eapply_with_bindings (c,bl) =
-  apply_with_ebindings_gen false true (c,inj_ebindings bl)
+  apply_with_ebindings_gen false true [c,inj_ebindings bl]
 
 let apply c =
   apply_with_ebindings (c,NoBindings)
@@ -788,10 +821,10 @@ let find_matching_clause unifier clause =
 
 let progress_with_clause innerclause clause =
   let ordered_metas = List.rev (clenv_independent clause) in
-  if ordered_metas = [] then error "Statement without assumptions";
+  if ordered_metas = [] then error "Statement without assumptions.";
   let f mv = find_matching_clause (clenv_fchain mv clause) innerclause in
   try list_try_find f ordered_metas
-  with Failure _ -> error "Unable to unify"
+  with Failure _ -> error "Unable to unify."
 
 let apply_in_once gl innerclause (d,lbind) =
   let thm = nf_betaiota (pf_type_of gl d) in
@@ -832,7 +865,7 @@ let cut_and_apply c gl =
 	  tclTHENLAST
 	    (apply_type (mkProd (Anonymous,c2,goal_constr)) [mkMeta(new_meta())])
 	    (apply_term c [mkMeta (new_meta())]) gl
-      | _ -> error "Imp_elim needs a non-dependent product"
+      | _ -> error "lapply needs a non-dependent product."
 
 (********************************************************************)
 (*               Exact tactics                                      *)
@@ -844,7 +877,7 @@ let exact_check c gl =
   if pf_conv_x_leq gl ct concl then  
     refine_no_check c gl 
   else 
-    error "Not an exact proof"
+    error "Not an exact proof."
 
 let exact_no_check = refine_no_check
 
@@ -863,7 +896,7 @@ let (assumption : tactic) = fun gl ->
   let hyps = pf_hyps gl in
   let rec arec only_eq = function
     | [] -> 
-        if only_eq then arec false hyps else error "No such assumption"
+        if only_eq then arec false hyps else error "No such assumption."
     | (id,c,t)::rest -> 
 	if (only_eq & eq_constr t concl) 
           or (not only_eq & pf_conv_x_leq gl t concl)
@@ -881,11 +914,20 @@ let (assumption : tactic) = fun gl ->
  * subsequently used in other hypotheses or in the conclusion of the  
  * goal. *)                                                               
 
-let clear ids gl = (* avant seul dyn_clear n'echouait pas en [] *)
-  if ids=[] then tclIDTAC gl else with_check (thin ids) gl
+let clear ids = (* avant seul dyn_clear n'echouait pas en [] *)
+  if ids=[] then tclIDTAC else thin ids
 
 let clear_body = thin_body
 
+let clear_wildcards ids =
+  tclMAP (fun (loc,id) gl ->
+    try with_check (Tacmach.thin_no_check [id]) gl
+    with ClearDependencyError (id,err) ->
+      (* Intercept standard [thin] error message *)
+      Stdpp.raise_with_loc loc
+        (error_clear_dependency (pf_env gl) (id_of_string "_") err))
+    ids
+
 (*   Takes a list of booleans, and introduces all the variables 
  *  quantified in the goal which are associated with a value
  *  true  in the boolean list. *)
@@ -919,17 +961,17 @@ let specialize mopt (c,lbind) g =
       let term = applist(thd,tstack) in 
       if occur_meta term then
 	errorlabstrm "" (str "Cannot infer an instance for " ++
-          pr_name (meta_name clause.evd (List.hd (collect_metas term))));
+          pr_name (meta_name clause.evd (List.hd (collect_metas term))) ++
+	  str ".");
       Some (evars_of clause.evd), term
   in
   tclTHEN 
     (match evars with Some e -> tclEVARS e | _ -> tclIDTAC)
-    (match kind_of_term (fst (decompose_app c)) with 
-       | Var id when List.exists (fun (i,_,_)-> i=id) (pf_hyps g) ->
-	   let id' = fresh_id [] id g in 
-	   tclTHENS (fun g -> internal_cut id' (pf_type_of g term) g)
-	     [ exact_no_check term; 
-	       tclTHEN (clear [id]) (rename_hyp [id',id]) ]
+    (match kind_of_term (fst(decompose_app (snd(decompose_lam_assum c)))) with
+       | Var id when List.mem id (pf_ids_of_hyps g) ->
+	     tclTHENFIRST
+	       (fun g -> internal_cut_replace id (pf_type_of g term) g)
+	       (exact_no_check term)
        | _ -> tclTHENLAST 
                  (fun g -> cut (pf_type_of g term) g)
                  (exact_no_check term))
@@ -955,14 +997,14 @@ let keep hyps gl =
 (************************)
 
 let check_number_of_constructors expctdnumopt i nconstr =
-  if i=0 then error "The constructors are numbered starting from 1";
+  if i=0 then error "The constructors are numbered starting from 1.";
   begin match expctdnumopt with 
     | Some n when n <> nconstr ->
 	error ("Not an inductive goal with "^
-	       string_of_int n^plural n " constructor")
+	       string_of_int n^plural n " constructor"^".")
     | _ -> ()
   end;
-  if i > nconstr then error "Not enough constructors"
+  if i > nconstr then error "Not enough constructors."
 
 let constructor_tac with_evars expctdnumopt i lbind gl =
   let cl = pf_concl gl in 
@@ -987,7 +1029,7 @@ let any_constructor with_evars tacopt gl =
   let mind = fst (pf_reduce_to_quantified_ind gl (pf_concl gl)) in
   let nconstr =
     Array.length (snd (Global.lookup_inductive mind)).mind_consnames in
-  if nconstr = 0 then error "The type has no constructors";
+  if nconstr = 0 then error "The type has no constructors.";
   tclFIRST
     (List.map
       (fun i -> tclTHEN (constructor_tac with_evars None i NoBindings) t) 
@@ -1025,22 +1067,33 @@ let fix_empty_case nv l =
      and "[ ]" for no clause at all; so we are a bit liberal here *)
   if Array.length nv = 0 & l = [[]] then [] else l
 
-let intro_or_and_pattern ll l' tac =
+let error_unexpected_extra_pattern loc nb pat =
+  let s1,s2,s3 = match pat with
+  | IntroIdentifier _ -> "name", (plural nb " introduction pattern"), "no"
+  | _ -> "introduction pattern", "", "none" in
+  user_err_loc (loc,"",str "Unexpected " ++ str s1 ++ str " (" ++
+    (if nb = 0 then (str s3 ++ str s2) else
+      (str "at most " ++ int nb ++ str s2)) ++ spc () ++
+       str (if nb = 1 then "was" else "were") ++
+      strbrk " expected in the branch).")
+
+let intro_or_and_pattern loc b ll l' tac =
   tclLAST_HYP (fun c gl ->
     let ind,_ = pf_reduce_to_quantified_ind gl (pf_type_of gl c) in
     let nv = mis_constr_nargs ind in
-    let rec adjust_names_length tail n = function
-      | [] when n = 0 or tail -> []
-      | [] -> IntroAnonymous :: adjust_names_length tail (n-1) []
-      | _ :: _ as l when n = 0 -> 
-	  if tail then l else error "Too many names in some branch"
-      | ip :: l -> ip :: adjust_names_length tail (n-1) l in
+    let bracketed = b or not (l'=[]) in
+    let rec adjust_names_length nb n = function
+      | [] when n = 0 or not bracketed -> []
+      | [] -> (dloc,IntroAnonymous) :: adjust_names_length nb (n-1) []
+      | (loc',pat) :: _ as l when n = 0 ->
+	  if bracketed then error_unexpected_extra_pattern loc' nb pat;
+	  l
+      | ip :: l -> ip :: adjust_names_length nb (n-1) l in
     let ll = fix_empty_case nv ll in
-    if List.length ll <> Array.length nv then
-      error "Not the right number of patterns";
+    check_or_and_pattern_size loc ll (Array.length nv);
     tclTHENLASTn
       (tclTHEN case_last clear_last)
-      (array_map2 (fun n l -> tac ((adjust_names_length (l'=[]) n l)@l'))
+      (array_map2 (fun n l -> tac ((adjust_names_length n n l)@l'))
 	nv (Array.of_list ll))
       gl)
 
@@ -1052,11 +1105,11 @@ let clear_if_atomic l2r id gl =
   else tclIDTAC gl
 
 let rec explicit_intro_names = function
-| IntroIdentifier id :: l ->
+| (_, IntroIdentifier id) :: l ->
     id :: explicit_intro_names l
-| (IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _) :: l ->
+| (_, (IntroWildcard | IntroAnonymous | IntroFresh _ | IntroRewrite _)) :: l ->
     explicit_intro_names l
-| IntroOrAndPattern ll :: l' -> 
+| (_, IntroOrAndPattern ll) :: l' -> 
     List.flatten (List.map (fun l -> explicit_intro_names (l@l')) ll)
 | [] ->
     []
@@ -1065,84 +1118,90 @@ let rec explicit_intro_names = function
      to ensure that dependent hypotheses are cleared in the right
      dependency order (see bug #1000); we use fresh names, not used in
      the tactic, for the hyps to clear *)
-let rec intros_patterns avoid thin destopt = function
-  | IntroWildcard :: l ->
+let rec intros_patterns b avoid thin destopt = function
+  | (loc, IntroWildcard) :: l ->
       tclTHEN 
-        (intro_gen (IntroAvoid (avoid@explicit_intro_names l)) None true)
+        (intro_gen loc (IntroAvoid(avoid@explicit_intro_names l)) no_move true)
         (onLastHyp (fun id ->
 	  tclORELSE
-	    (tclTHEN (clear [id]) (intros_patterns avoid thin destopt l))
-	    (intros_patterns avoid (id::thin) destopt l)))
-  | IntroIdentifier id :: l ->
+	    (tclTHEN (clear [id]) (intros_patterns b avoid thin destopt l))
+	    (intros_patterns b avoid ((loc,id)::thin) destopt l)))
+  | (loc, IntroIdentifier id) :: l ->
       tclTHEN
-        (intro_gen (IntroMustBe id) destopt true)
-        (intros_patterns avoid thin destopt l)
-  | IntroAnonymous :: l ->
+        (intro_gen loc (IntroMustBe id) destopt true)
+        (intros_patterns b avoid thin destopt l)
+  | (loc, IntroAnonymous) :: l ->
       tclTHEN
-        (intro_gen (IntroAvoid (avoid@explicit_intro_names l)) destopt true)
-        (intros_patterns avoid thin destopt l)
-  | IntroFresh id :: l ->
+        (intro_gen loc (IntroAvoid (avoid@explicit_intro_names l))
+	  destopt true)
+        (intros_patterns b avoid thin destopt l)
+  | (loc, IntroFresh id) :: l ->
       tclTHEN
-        (intro_gen (IntroBasedOn (id, avoid@explicit_intro_names l)) destopt true)
-        (intros_patterns avoid thin destopt l)
-  | IntroOrAndPattern ll :: l' ->
+        (intro_gen loc (IntroBasedOn (id, avoid@explicit_intro_names l))
+	  destopt true)
+        (intros_patterns b avoid thin destopt l)
+  | (loc, IntroOrAndPattern ll) :: l' ->
       tclTHEN
         introf
-        (intro_or_and_pattern ll l' (intros_patterns avoid thin destopt))
-  | IntroRewrite l2r :: l ->
+        (intro_or_and_pattern loc b ll l'
+	  (intros_patterns b avoid thin destopt))
+  | (loc, IntroRewrite l2r) :: l ->
       tclTHEN 
-        (intro_gen (IntroAvoid (avoid@explicit_intro_names l)) None true)
+        (intro_gen loc (IntroAvoid(avoid@explicit_intro_names l)) no_move true)
         (onLastHyp (fun id ->
 	  tclTHENLIST [
 	    !forward_general_multi_rewrite l2r false (mkVar id,NoBindings) 
 	      allClauses;
 	    clear_if_atomic l2r id;
-	    intros_patterns avoid thin destopt l ]))
-  | [] -> clear thin
+	    intros_patterns b avoid thin destopt l ]))
+  | [] -> clear_wildcards thin
 
-let intros_pattern = intros_patterns [] []
+let intros_pattern = intros_patterns false [] []
 
-let intro_pattern destopt pat = intros_patterns [] [] destopt [pat]
+let intro_pattern destopt pat = intros_patterns false [] [] destopt [dloc,pat]
 
 let intro_patterns = function 
   | [] -> tclREPEAT intro
-  | l  -> intros_pattern None l
+  | l  -> intros_pattern no_move l
 
 (**************************)
 (*   Other cut tactics    *)
 (**************************)
 
-let hid = id_of_string "H"
-let xid = id_of_string "X"
+let make_id s = fresh_id [] (default_id_of_sort s)
 
-let make_id s = fresh_id [] (match s with Prop _ -> hid | Type _ -> xid)
-
-let prepare_intros s ipat gl = match ipat with
+let prepare_intros s (loc,ipat) gl = match ipat with
+  | IntroIdentifier id -> id, tclIDTAC
   | IntroAnonymous -> make_id s gl, tclIDTAC
   | IntroFresh id -> fresh_id [] id gl, tclIDTAC
-  | IntroWildcard -> let id = make_id s gl in id, thin [id]
-  | IntroIdentifier id -> id, tclIDTAC
+  | IntroWildcard -> let id = make_id s gl in id, clear_wildcards [dloc,id]
   | IntroRewrite l2r -> 
       let id = make_id s gl in
       id, !forward_general_multi_rewrite l2r false (mkVar id,NoBindings) allClauses
   | IntroOrAndPattern ll -> make_id s gl, 
-    (tclTHENS 
-      (tclTHEN case_last clear_last)
-      (List.map (intros_pattern None) ll))
+      intro_or_and_pattern loc true ll [] (intros_patterns true [] [] no_move)
 
 let ipat_of_name = function
   | Anonymous -> IntroAnonymous
   | Name id -> IntroIdentifier id
 
+let allow_replace c gl = function (* A rather arbitrary condition... *)
+  | _, IntroIdentifier id ->
+      fst (decompose_app (snd (decompose_lam_assum c))) = mkVar id
+  | _ ->
+      false
+
 let assert_as first ipat c gl =
   match kind_of_term (hnf_type_of gl c) with
   | Sort s ->
       let id,tac = prepare_intros s ipat gl in
-      tclTHENS ((if first then internal_cut else internal_cut_rev) id c)
+      let repl = allow_replace c gl ipat in
+      tclTHENS
+	((if first then internal_cut_gen else internal_cut_rev_gen) repl id c)
 	(if first then [tclIDTAC; tac] else [tac; tclIDTAC]) gl
-  | _  -> error "Not a proposition or a type"
+  | _  -> error "Not a proposition or a type."
 
-let assert_tac first na = assert_as first (ipat_of_name na)
+let assert_tac first na = assert_as first (dloc,ipat_of_name na)
 let true_cut = assert_tac true 
 
 (**************************)
@@ -1341,7 +1400,8 @@ let letin_abstract id c occs gl =
   let ccl = match occurrences_of_goal occs with
     | None -> pf_concl gl
     | Some occ -> subst1 (mkVar id) (subst_term_occ occ c (pf_concl gl)) in
-  let lastlhyp = if depdecls = [] then None else Some(pi1(list_last depdecls)) in
+  let lastlhyp =
+    if depdecls = [] then no_move else MoveAfter(pi1(list_last depdecls)) in
   (depdecls,lastlhyp,ccl)
 
 let letin_tac with_eq name c occs gl =
@@ -1349,23 +1409,29 @@ let letin_tac with_eq name c occs gl =
     let x = id_of_name_using_hdchar (Global.env()) (pf_type_of gl c) name in
     if name = Anonymous then fresh_id [] x gl else
       if not (mem_named_context x (pf_hyps gl)) then x else
-	error ("The variable "^(string_of_id x)^" is already declared") in
+	error ("The variable "^(string_of_id x)^" is already declared.") in
   let (depdecls,lastlhyp,ccl)= letin_abstract id c occs gl in 
   let t = pf_type_of gl c in
   let newcl,eq_tac = match with_eq with
-    | Some lr ->
-      let heq = fresh_id [] (add_prefix "Heq" id) gl in
+    | Some (lr,(loc,ido)) ->
+      let heq = match ido with
+        | IntroAnonymous -> fresh_id [id] (add_prefix "Heq" id) gl
+	| IntroFresh heq_base -> fresh_id [id] heq_base gl
+        | IntroIdentifier id -> id
+	| _ -> error"Expect an introduction pattern naming one hypothesis." in
       let eqdata = build_coq_eq_data () in
       let args = if lr then [t;mkVar id;c] else [t;c;mkVar id]in
       let eq = applist (eqdata.eq,args) in
       let refl = applist (eqdata.refl, [t;mkVar id]) in
       mkNamedLetIn id c t (mkLetIn (Name heq, refl, eq, ccl)),
-      tclTHEN (intro_gen (IntroMustBe heq) lastlhyp true) (thin_body [heq;id])
+      tclTHEN
+	(intro_gen loc (IntroMustBe heq) lastlhyp true)
+	(thin_body [heq;id])
     | None ->
 	mkNamedLetIn id c t ccl, tclIDTAC in
   tclTHENLIST
     [ convert_concl_no_check newcl DEFAULTcast;
-      intro_gen (IntroMustBe id) lastlhyp true;
+      intro_gen dloc (IntroMustBe id) lastlhyp true;
       eq_tac;
       tclMAP convert_hyp_no_check depdecls ] gl
   
@@ -1390,7 +1456,7 @@ let unfold_body x gl =
     match Sign.lookup_named x hyps with
         (_,Some xval,_) -> xval
       | _ -> errorlabstrm "unfold_body"
-          (pr_id x ++ str" is not a defined hypothesis") in
+          (pr_id x ++ str" is not a defined hypothesis.") in
   let aft = afterHyp x gl in
   let hl = List.fold_right (fun (y,yval,_) cl -> (([],y),InHyp) :: cl) aft [] in
   let xvar = mkVar x in
@@ -1445,76 +1511,85 @@ let unfold_all x gl =
 
 let check_unused_names names =
   if names <> [] & Flags.is_verbose () then
-    let s = if List.tl names = [] then " " else "s " in
     msg_warning 
-      (str"Unused introduction pattern" ++ str s ++ 
-       str": " ++ prlist_with_sep spc pr_intro_pattern names)
-
-let rec first_name_buggy = function
-  | IntroOrAndPattern [] -> None
-  | IntroOrAndPattern ([]::l) -> first_name_buggy (IntroOrAndPattern l)
-  | IntroOrAndPattern ((p::_)::_) -> first_name_buggy p
-  | IntroWildcard -> None
-  | IntroRewrite _ -> None
-  | IntroIdentifier id -> Some id
+      (str"Unused introduction " ++ str (plural (List.length names) "pattern")
+       ++ str": " ++ prlist_with_sep spc pr_intro_pattern names)
+
+let rec first_name_buggy avoid gl (loc,pat) = match pat with
+  | IntroOrAndPattern [] -> no_move
+  | IntroOrAndPattern ([]::l) -> 
+      first_name_buggy avoid gl (loc,IntroOrAndPattern l)
+  | IntroOrAndPattern ((p::_)::_) -> first_name_buggy avoid gl p
+  | IntroWildcard -> no_move
+  | IntroRewrite _ -> no_move
+  | IntroIdentifier id -> MoveAfter id
   | IntroAnonymous | IntroFresh _ -> assert false
 
 let consume_pattern avoid id gl = function
-  | [] -> (IntroIdentifier (fresh_id avoid id gl), [])
-  | IntroAnonymous::names ->
+  | [] -> ((dloc, IntroIdentifier (fresh_id avoid id gl)), [])
+  | (loc,IntroAnonymous)::names ->
+      let avoid = avoid@explicit_intro_names names in
+      ((loc,IntroIdentifier (fresh_id avoid id gl)), names)
+  | (loc,IntroFresh id')::names ->
       let avoid = avoid@explicit_intro_names names in
-      (IntroIdentifier (fresh_id avoid id gl), names)
+      ((loc,IntroIdentifier (fresh_id avoid id' gl)), names)
   | pat::names -> (pat,names)
 
 let re_intro_dependent_hypotheses tophyp (lstatus,rstatus) =
   let newlstatus = (* if some IH has taken place at the top of hyps *)
-    List.map (function (hyp,None) -> (hyp,tophyp) | x -> x) lstatus in
+    List.map (function (hyp,MoveToEnd true) -> (hyp,tophyp) | x -> x) lstatus
+  in
   tclTHEN
-    (intros_rmove rstatus)
+    (intros_move rstatus)
     (intros_move newlstatus)
 
+let update destopt tophyp = if destopt = no_move then tophyp else destopt
+
 type elim_arg_kind = RecArg | IndArg | OtherArg
 
 let induct_discharge statuslists destopt avoid' (avoid,ra) names gl =
   let avoid = avoid @ avoid' in
-  let rec peel_tac ra names tophyp gl = match ra with
+  let rec peel_tac ra names tophyp gl =
+    match ra with
     | (RecArg,recvarname) ::
         (IndArg,hyprecname) :: ra' ->
         let recpat,names = match names with
-          | [IntroIdentifier id as pat] ->
-              let id = next_ident_away (add_prefix "IH" id) avoid in
-	      (pat, [IntroIdentifier id])
+          | [loc,IntroIdentifier id as pat] ->
+              let id' = next_ident_away (add_prefix "IH" id) avoid in
+	      (pat, [dloc, IntroIdentifier id'])
           | _ -> consume_pattern avoid recvarname gl names in
         let hyprec,names = consume_pattern avoid hyprecname gl names in
         (* IH stays at top: we need to update tophyp *)
         (* This is buggy for intro-or-patterns with different first hypnames *)
         (* Would need to pass peel_tac as a continuation of intros_patterns *)
         (* (or to have hypotheses classified by blocks...) *)
-        let tophyp = if tophyp=None then first_name_buggy hyprec else tophyp in
+        let newtophyp =
+	  if tophyp=no_move then first_name_buggy avoid gl hyprec else tophyp
+	in
         tclTHENLIST
-	  [ intros_patterns avoid [] destopt [recpat];
-	    intros_patterns avoid [] None [hyprec];
-	    peel_tac ra' names tophyp] gl
+	  [ intros_patterns true avoid [] (update destopt tophyp) [recpat];
+	    intros_patterns true avoid [] no_move [hyprec];
+	    peel_tac ra' names newtophyp] gl
     | (IndArg,hyprecname) :: ra' ->
 	(* Rem: does not happen in Coq schemes, only in user-defined schemes *)
         let pat,names = consume_pattern avoid hyprecname gl names in
-	tclTHEN (intros_patterns avoid [] destopt [pat])
+	tclTHEN (intros_patterns true avoid [] (update destopt tophyp) [pat])
           (peel_tac ra' names tophyp) gl
     | (RecArg,recvarname) :: ra' ->
         let pat,names = consume_pattern avoid recvarname gl names in
-	tclTHEN (intros_patterns avoid [] destopt [pat]) 
+	tclTHEN (intros_patterns true avoid [] (update destopt tophyp) [pat]) 
           (peel_tac ra' names tophyp) gl
     | (OtherArg,_) :: ra' ->
         let pat,names = match names with
-          | [] -> IntroAnonymous, []
+          | [] -> (dloc, IntroAnonymous), []
           | pat::names -> pat,names in
-	tclTHEN (intros_patterns avoid [] destopt [pat])
+	tclTHEN (intros_patterns true avoid [] (update destopt tophyp) [pat])
           (peel_tac ra' names tophyp) gl
     | [] ->
         check_unused_names names;
         re_intro_dependent_hypotheses tophyp statuslists gl
   in
-  peel_tac ra names None gl
+  peel_tac ra names no_move gl
 
 (* - le recalcul de indtyp à chaque itération de atomize_one est pour ne pas
      s'embêter à regarder si un letin_tac ne fait pas des
@@ -1572,7 +1647,7 @@ let find_atomic_param_of_ind nparams indtyp =
   Idset.elements !indvars;
   
 
-   (* [cook_sign] builds the lists [indhyps] of hyps that must be
+(* [cook_sign] builds the lists [indhyps] of hyps that must be
    erased, the lists of hyps to be generalize [(hdeps,tdeps)] on the
    goal together with the places [(lstatus,rstatus)] where to re-intro
    them after induction. To know where to re-intro the dep hyp, we
@@ -1583,7 +1658,7 @@ let find_atomic_param_of_ind nparams indtyp =
    more ancient (on the right) to more recent hyp (on the left) but
    the computation of [lhyp] progresses from the other way, [cook_hyp]
    is in two passes (an alternative would have been to write an
-   higher-order algorithm). We strongly use references to reduce
+   higher-order algorithm). We use references to reduce
    the accumulation of arguments.
 
    To summarize, the situation looks like this
@@ -1635,7 +1710,7 @@ let find_atomic_param_of_ind nparams indtyp =
 
 *)
 
-exception Shunt of identifier option
+exception Shunt of identifier move_location
 
 let cook_sign hyp0_opt indvars_init env =
   let hyp0,indvars = 
@@ -1657,7 +1732,7 @@ let cook_sign hyp0_opt indvars_init env =
       (* If there was no main induction hypotheses, then hyp is one of
          indvars too, so add it to indhyps. *)
       (if hyp0_opt=None then indhyps := hyp::!indhyps); 
-      None (* fake value *)
+      MoveToEnd false (* fake value *)
     end else if List.mem hyp indvars then begin
       (* warning: hyp can still occur after induction *)
       (* e.g. if the goal (t hyp hyp0) with other occs of hyp in t *)
@@ -1673,11 +1748,11 @@ let cook_sign hyp0_opt indvars_init env =
 	  rstatus := (hyp,rhyp)::!rstatus
 	else 
 	  ldeps := hyp::!ldeps; (* status computed in 2nd phase *)
-	Some hyp end
+	MoveBefore hyp end
       else
-	Some hyp
+	MoveBefore hyp
   in
-  let _ = fold_named_context seek_deps env ~init:None in
+  let _ = fold_named_context seek_deps env ~init:(MoveToEnd false) in
   (* 2nd phase from R to L: get left hyp of [hyp0] and [lhyps] *)
   let compute_lstatus lhyp (hyp,_,_) =
     if hyp = hyp0 then raise (Shunt lhyp);
@@ -1685,15 +1760,16 @@ let cook_sign hyp0_opt indvars_init env =
       lstatus := (hyp,lhyp)::!lstatus;
       lhyp
     end else
-      if List.mem hyp !indhyps then lhyp else (Some hyp) 
+      if List.mem hyp !indhyps then lhyp else MoveAfter hyp
   in
   try 
-    let _ = fold_named_context_reverse compute_lstatus ~init:None env in
-(*     anomaly "hyp0 not found" *)
-    raise (Shunt (None)) (* ?? FIXME *)
+    let _ = 
+      fold_named_context_reverse compute_lstatus ~init:(MoveToEnd true) env in
+    raise (Shunt (MoveToEnd true)) (* ?? FIXME *)
   with Shunt lhyp0 ->
     let statuslists = (!lstatus,List.rev !rstatus) in
-    (statuslists, (if hyp0_opt=None then None else lhyp0) , !indhyps, !decldeps)
+    (statuslists, (if hyp0_opt=None then MoveToEnd true else lhyp0),
+     !indhyps, !decldeps)
 
 
 (*
@@ -1764,7 +1840,7 @@ let empty_scheme =
    hypothesis on which the induction is made *)
 let induction_tac with_evars (varname,lbind) typ scheme gl =
   let elimc,lbindelimc = 
-    match scheme.elimc with | Some x -> x | None -> error "No definition of the principle" in
+    match scheme.elimc with | Some x -> x | None -> error "No definition of the principle." in
   let elimt = scheme.elimt in
   let indclause = make_clenv_binding gl (mkVar varname,typ) lbind  in
   let elimclause =
@@ -1779,9 +1855,9 @@ let make_base n id =
     (* digits *)
     id_of_string (atompart_of_id (make_ident (string_of_id id) (Some 0)))
 
-(* Builds tw different names from an optional inductive type and a
+(* Builds two different names from an optional inductive type and a
    number, also deals with a list of names to avoid. If the inductive
-   type is None, then hyprecname is HIi where i is a number. *)
+   type is None, then hyprecname is IHi where i is a number. *)
 let make_up_names n ind_opt cname = 
   let is_hyp = atompart_of_id cname = "H" in
   let base = string_of_id (make_base n cname) in
@@ -1825,7 +1901,7 @@ let chop_context n l =
 
 let error_ind_scheme s =
   let s = if s <> "" then s^" " else s in
-  error ("Cannot recognise "^s^"an induction schema")
+  error ("Cannot recognize "^s^"an induction scheme.")
 
 let mkEq t x y = 
   mkApp (build_coq_eq (), [| t; x; y |])
@@ -1950,29 +2026,23 @@ let abstract_args gl id =
 	       dep, succ (List.length ctx), vars)
     | _ -> None
 
-let abstract_generalize id gl =
+let abstract_generalize id ?(generalize_vars=true) gl =
   Coqlib.check_required_library ["Coq";"Logic";"JMeq"];
-(*   let qualid = (dummy_loc, qualid_of_dirpath (dirpath_of_string "Coq.Logic.JMeq")) in *)
-(*   Library.require_library [qualid] None; *)
   let oldid = pf_get_new_id id gl in
   let newc = abstract_args gl id in
     match newc with
       | None -> tclIDTAC gl
       | Some (newc, dep, n, vars) -> 
-	  if dep then
-	    tclTHENLIST [refine newc;
-			 rename_hyp [(id, oldid)];
-			 tclDO n intro; 
-			 generalize_dep (mkVar oldid);
-			 tclMAP (fun id -> tclTRY (generalize_dep (mkVar id))) vars]
-	      gl
-	  else
-	    tclTHENLIST [refine newc;
-			 clear [id];
-			 tclDO n intro; 
-			 tclMAP (fun id -> tclTRY (generalize_dep (mkVar id))) vars]
-	      gl
-
+	  let tac =
+	    if dep then
+	      tclTHENLIST [refine newc; rename_hyp [(id, oldid)]; tclDO n intro; 
+			   generalize_dep (mkVar oldid)]	      
+	    else
+	      tclTHENLIST [refine newc; clear [id]; tclDO n intro]
+	  in 
+	    if generalize_vars then
+	      tclTHEN tac (tclMAP (fun id -> tclTRY (generalize_dep (mkVar id))) vars) gl
+	    else tac gl
 
 let occur_rel n c = 
   let res = not (noccurn n c) in
@@ -2016,11 +2086,11 @@ let cut_list n l =
   res
 
 
-(* This functions splits the products of the induction scheme [elimt] in three
+(* This function splits the products of the induction scheme [elimt] into four
    parts: 
-    - branches, easily detectable (they are not referred by rels in the subterm)
-    - what was found before branches (acc1) that is: parameters and predicates
-    - what was found after branches (acc3) that is: args and indarg if any
+   - branches, easily detectable (they are not referred by rels in the subterm)
+   - what was found before branches (acc1) that is: parameters and predicates
+   - what was found after branches (acc3) that is: args and indarg if any
    if there is no branch, we try to fill in acc3 with args/indargs.
    We also return the conclusion.
 *)
@@ -2033,13 +2103,13 @@ let decompose_paramspred_branch_args elimt =
 	  then cut_noccur elimt' ((nme,None,tpe)::acc2)
 	  else let acc3,ccl = decompose_prod_assum elimt in acc2 , acc3 , ccl
       | App(_, _) | Rel _ -> acc2 , [] , elimt
-      | _ -> error "cannot recognise an induction schema" in
+      | _ -> error_ind_scheme "" in
   let rec cut_occur elimt acc1 : rel_context * rel_context * rel_context * types =
     match kind_of_term elimt with
       | Prod(nme,tpe,c) when occur_rel 1 c -> cut_occur c ((nme,None,tpe)::acc1)
       | Prod(nme,tpe,c) -> let acc2,acc3,ccl = cut_noccur elimt [] in acc1,acc2,acc3,ccl
       | App(_, _) | Rel _ -> acc1,[],[],elimt
-      | _ -> error "cannot recognise an induction schema" in
+      | _ -> error_ind_scheme "" in
   let acc1, acc2 , acc3, ccl = cut_occur elimt [] in
   (* Particular treatment when dealing with a dependent empty type elim scheme:
      if there is no branch, then acc1 contains all hyps which is wrong (acc1
@@ -2053,8 +2123,7 @@ let decompose_paramspred_branch_args elimt =
     let hd_ccl_pred,_ = decompose_app ccl in
     match kind_of_term hd_ccl_pred with
       | Rel i  -> let acc3,acc1 = cut_list (i-1) hyps in acc1 , [] , acc3 , ccl
-      | _ -> error "cannot recognize an induction schema"
-
+      | _ -> error_ind_scheme ""
 
 
 let exchange_hd_app subst_hd t =
@@ -2064,7 +2133,7 @@ let exchange_hd_app subst_hd t =
 
 (* [rebuild_elimtype_from_scheme scheme] rebuilds the type of an
    eliminator from its [scheme_info]. The idea is to build variants of
-   eliminator by modifying there scheme_info, then rebuild the
+   eliminator by modifying their scheme_info, then rebuild the
    eliminator type, then prove it (with tactics). *)
 let rebuild_elimtype_from_scheme (scheme:elim_scheme): types =
   let hiconcl = 
@@ -2081,7 +2150,7 @@ let rebuild_elimtype_from_scheme (scheme:elim_scheme): types =
 exception NoLastArg
 exception NoLastArgCcl
 
-(* Builds an elim_scheme frome its type and calling form (const+binding) We
+(* Builds an elim_scheme from its type and calling form (const+binding). We
    first separate branches.  We obtain branches, hyps before (params + preds),
    hyps after (args <+ indarg if present>) and conclusion.  Then we proceed as
    follows:
@@ -2131,7 +2200,7 @@ let compute_elim_sig ?elimc elimt =
     (* 3- Look at last arg: is it the indarg? *)
     ignore (
       match List.hd args_indargs with
-	| hiname,Some _,hi -> error "cannot recognize an induction schema"
+	| hiname,Some _,hi -> error_ind_scheme ""
 	| hiname,None,hi -> 
 	    let hi_ind, hi_args = decompose_app hi in
 	    let hi_is_ind = (* hi est d'un type globalisable *)
@@ -2156,11 +2225,11 @@ let compute_elim_sig ?elimc elimt =
   with Exit -> (* Ending by computing indrev: *)
     match !res.indarg with
       | None -> !res (* No indref *)
-      | Some ( _,Some _,_) -> error "Cannot recognise an induction scheme"
+      | Some ( _,Some _,_) -> error_ind_scheme ""
       | Some ( _,None,ind) -> 
 	  let indhd,indargs = decompose_app ind in
 	  try {!res with indref = Some (global_of_constr indhd) }
-	  with _ -> error "Cannot find the inductive type of the inductive schema";;
+	  with _ -> error "Cannot find the inductive type of the inductive scheme.";;
 
 (* Check that the elimination scheme has a form similar to the 
    elimination schemes built by Coq. Schemes may have the standard
@@ -2169,17 +2238,17 @@ let compute_elim_sig ?elimc elimt =
    extra final argument of the form (f x y ...) in the conclusion. In
    the non standard case, naming of generated hypos is slightly
    different. *)
-let compute_elim_signature elimc elimt names_info =
+let compute_elim_signature elimc elimt names_info ind_type_guess =
   let scheme = compute_elim_sig ~elimc:elimc elimt in
   let f,l = decompose_app scheme.concl in
   (* Vérifier que les arguments de Qi sont bien les xi. *)
   match scheme.indarg with
-    | Some (_,Some _,_) -> error "strange letin, cannot recognize an induction schema"
+    | Some (_,Some _,_) -> error "Strange letin, cannot recognize an induction scheme."
     | None -> (* Non standard scheme *)
-	let npred = List.length scheme.predicates in 
 	let is_pred n c = 
 	  let hd = fst (decompose_app c) in match kind_of_term hd with
-	    | Rel q when n < q & q <= n+npred -> IndArg
+	    | Rel q when n < q & q <= n+scheme.npredicates -> IndArg
+	    | _ when hd = ind_type_guess & not scheme.farg_in_concl -> RecArg
 	    | _ -> OtherArg in 
 	let rec check_branch p c = 
 	  match kind_of_term c with
@@ -2208,10 +2277,9 @@ let compute_elim_signature elimc elimt names_info =
 	
     | Some ( _,None,ind) -> (* Standard scheme from an inductive type *)
 	let indhd,indargs = decompose_app ind in
-	let npred = List.length scheme.predicates in
 	let is_pred n c = 
 	  let hd = fst (decompose_app c) in match kind_of_term hd with
-	    | Rel q when n < q & q <= n+npred -> IndArg
+	    | Rel q when n < q & q <= n+scheme.npredicates -> IndArg
 	    | _ when hd = indhd -> RecArg
 	    | _ -> OtherArg in
 	let rec check_branch p c = match kind_of_term c with
@@ -2242,7 +2310,7 @@ let compute_elim_signature elimc elimt names_info =
 		  list_lastn scheme.nargs indargs 
 		  = extended_rel_list 0 scheme.args in
 		if not (ccl_arg_ok & ind_is_ok) then
-		  error "Cannot recognize the conclusion of an induction schema";
+		  error_ind_scheme "the conclusion of";
 		[] 
 	in
 	let indsign = Array.of_list (find_branches 0 (List.rev scheme.branches)) in
@@ -2251,7 +2319,7 @@ let compute_elim_signature elimc elimt names_info =
 
 let find_elim_signature isrec elim hyp0 gl =
   let tmptyp0 =	pf_get_hyp_typ gl hyp0 in
-  let (elimc,elimt) = match elim with
+  let (elimc,elimt),ind = match elim with
     | None ->
 	let mind,_ = pf_reduce_to_quantified_ind gl tmptyp0 in
 	let s = elimination_sort_of_goal gl in
@@ -2259,21 +2327,15 @@ let find_elim_signature isrec elim hyp0 gl =
 	  if isrec then lookup_eliminator mind s
 	  else pf_apply make_case_gen gl mind s in
 	let elimt = pf_type_of gl elimc in
-	((elimc, NoBindings), elimt)
-    | Some (elimc,lbind as e) -> 
-	(e, pf_type_of gl elimc) in
-  let indsign,elim_scheme = compute_elim_signature elimc elimt hyp0 in
+	((elimc, NoBindings), elimt), mkInd mind
+    | Some (elimc,lbind as e) ->
+	let ind_type_guess,_ = decompose_app (snd (decompose_prod tmptyp0)) in
+	(e, pf_type_of gl elimc), ind_type_guess in
+  let indsign,elim_scheme =
+    compute_elim_signature elimc elimt hyp0 ind in
   (indsign,elim_scheme)
 
 
-let mapi f l =
-  let rec mapi_aux f i l =   
-    match l with
-      | [] -> []
-      | e::l' -> f e i :: mapi_aux f (i+1) l' in
-  mapi_aux f 0 l
-
-
 (* Instantiate all meta variables of elimclause using lid, some elts
    of lid are parameters (first ones), the other are
    arguments. Returns the clause obtained.  *)
@@ -2285,19 +2347,20 @@ let recolle_clenv scheme lid elimclause gl =
 	match kind_of_term x with
 	  | Meta mv -> mv
 	  | _  -> errorlabstrm "elimination_clause"
-              (str "The type of elimination clause is not well-formed"))
+              (str "The type of the elimination clause is not well-formed."))
       arr in
   let nmv = Array.length lindmv in
   let lidparams,lidargs = cut_list (scheme.nparams) lid in
   let nidargs = List.length lidargs in
   (* parameters correspond to first elts of lid. *)
   let clauses_params = 
-    mapi (fun id i -> mkVar id , pf_get_hyp_typ gl id , lindmv.(i)) lidparams in
+    list_map_i (fun i id -> mkVar id , pf_get_hyp_typ gl id , lindmv.(i))
+      0 lidparams in
   (* arguments correspond to last elts of lid. *)
   let clauses_args = 
-    mapi 
-      (fun id i -> mkVar id , pf_get_hyp_typ gl id , lindmv.(nmv-nidargs+i))
-      lidargs in
+    list_map_i 
+      (fun i id -> mkVar id , pf_get_hyp_typ gl id , lindmv.(nmv-nidargs+i))
+      0 lidargs in
   let clause_indarg = 
     match scheme.indarg with
       | None -> []
@@ -2321,10 +2384,10 @@ let recolle_clenv scheme lid elimclause gl =
    (elimc ?i ?j ?k...?l). This solves partly meta variables (and may
     produce new ones). Then refine with the resulting term with holes.
 *)
-let induction_tac_felim with_evars indvars (* (elimc,lbindelimc) elimt *) scheme gl = 
+let induction_tac_felim with_evars indvars scheme gl = 
   let elimt = scheme.elimt in
   let elimc,lbindelimc = 
-    match scheme.elimc with | Some x -> x | None -> error "No definition of the principle" in
+    match scheme.elimc with | Some x -> x | None -> error "No definition of the principle." in
   (* elimclause contains this: (elimc ?i ?j ?k...?l) *)
   let elimclause =
     make_clenv_binding gl (mkCast (elimc,DEFAULTcast, elimt),elimt) lbindelimc in
@@ -2334,6 +2397,29 @@ let induction_tac_felim with_evars indvars (* (elimc,lbindelimc) elimt *) scheme
   let resolved = clenv_unique_resolver true elimclause' gl in
   clenv_refine with_evars resolved gl
 
+let apply_induction_in_context isrec hyp0 indsign indvars names induct_tac gl =
+  let env = pf_env gl in
+  let statlists,lhyp0,indhyps,deps = cook_sign hyp0 indvars env in
+  let tmpcl = it_mkNamedProd_or_LetIn (pf_concl gl) deps in
+  let names = compute_induction_names (Array.length indsign) names in
+  let dephyps = List.map (fun (id,_,_) -> id) deps in
+  let deps_cstr =
+    List.fold_left
+      (fun a (id,b,_) -> if b = None then (mkVar id)::a else a) [] deps in
+  tclTHENLIST
+    [ 
+      (* Generalize dependent hyps (but not args) *)
+      if deps = [] then tclIDTAC else apply_type tmpcl deps_cstr;
+      (* clear dependent hyps *)
+      thin dephyps;
+      (* side-conditions in elim (resp case) schemes come last (resp first) *)
+      (if isrec then tclTHENFIRSTn else tclTHENLASTn)
+        (tclTHEN induct_tac (tclTRY (thin (List.rev indhyps))))
+	(array_map2 
+	  (induct_discharge statlists lhyp0 (List.rev dephyps)) indsign names)
+    ]
+    gl
+
 (* Induction with several induction arguments, main differences with
    induction_from_context is that there is no main induction argument,
    so we chose one to be the positioning reference. On the other hand,
@@ -2348,8 +2434,7 @@ let induction_from_context_l isrec with_evars elim_info lid names gl =
     + (if scheme.indarg <> None then 1 else 0) in
   (* Number of given induction args must be exact. *)
   if List.length lid <> nargs_indarg_farg + scheme.nparams then 
-      error "not the right number of arguments given to induction scheme";  
-  let env = pf_env gl in
+      error "Not the right number of arguments given to induction scheme.";
   (* hyp0 is used for re-introducing hyps at the right place afterward.
      We chose the first element of the list of variables on which to
      induct. It is probably the first of them appearing in the
@@ -2361,12 +2446,6 @@ let induction_from_context_l isrec with_evars elim_info lid names gl =
 	  let nargs_without_first = nargs_indarg_farg - 1 in
 	  let ivs,lp = cut_list nargs_without_first l in
 	  e, ivs, lp in
-  let statlists,lhyp0,indhyps,deps = cook_sign None (hyp0::indvars) env in
-  let tmpcl = it_mkNamedProd_or_LetIn (pf_concl gl) deps in
-  let names = compute_induction_names (Array.length indsign) names in
-  let dephyps = List.map (fun (id,_,_) -> id) deps in
-  let deps_cstr =
-    List.fold_left (fun a (id,b,_) -> if b = None then (mkVar id)::a else a) [] deps in
   (* terms to patternify we must patternify indarg or farg if present in concl *)
   let lid_in_pattern = 
     if scheme.indarg <> None & not scheme.indarg_in_concl then List.rev indvars
@@ -2375,68 +2454,32 @@ let induction_from_context_l isrec with_evars elim_info lid names gl =
   let realindvars = (* hyp0 is a real induction arg if it is not the
 		       farg in the conclusion of the induction scheme *)
     List.rev ((if scheme.farg_in_concl then indvars else hyp0::indvars) @ lid_params) in
-  (* Magistral effet de bord: comme dans induction_from_context. *)
-  tclTHENLIST
-    [ 
-      (* Generalize dependent hyps (but not args) *)
-      if deps = [] then tclIDTAC else apply_type tmpcl deps_cstr;
-      thin dephyps; (* clear dependent hyps *)
-      (* pattern to make the predicate appear. *)
-      reduce (Pattern (List.map inj_with_occurrences lidcstr)) onConcl;
-      (* FIXME: Tester ca avec un principe dependant et non-dependant *)
-      (if isrec then tclTHENFIRSTn else tclTHENLASTn)
-       	(tclTHENLIST [ 
-	  (* Induction by "refine (indscheme ?i ?j ?k...)" + resolution of all
-	     possible holes using arguments given by the user (but the
-	     functional one). *)
-	  induction_tac_felim with_evars realindvars scheme;
-          tclTRY (thin (List.rev (indhyps)));
-	])
-	(array_map2 
-	  (induct_discharge statlists lhyp0 (List.rev dephyps)) indsign names)
-    ]
-    gl
-
-
+  let induct_tac = tclTHENLIST [
+    (* pattern to make the predicate appear. *)
+    reduce (Pattern (List.map inj_with_occurrences lidcstr)) onConcl;
+    (* Induction by "refine (indscheme ?i ?j ?k...)" + resolution of all
+       possible holes using arguments given by the user (but the
+       functional one). *)
+    (* FIXME: Tester ca avec un principe dependant et non-dependant *)
+    induction_tac_felim with_evars realindvars scheme
+  ] in
+  apply_induction_in_context isrec
+    None indsign (hyp0::indvars) names induct_tac gl
 
 let induction_from_context isrec with_evars elim_info (hyp0,lbind) names gl =
   let indsign,scheme = elim_info in
   let indref = match scheme.indref with | None -> assert false | Some x -> x in
   let tmptyp0 =	pf_get_hyp_typ gl hyp0 in
   let typ0 = pf_apply reduce_to_quantified_ref gl indref tmptyp0 in
-
-  let env = pf_env gl in
-  let indvars = find_atomic_param_of_ind scheme.nparams (snd (decompose_prod typ0)) in
-  (* induction_from_context_l isrec elim_info (hyp0::List.rev indvars) names gl  *)
-  let statlists,lhyp0,indhyps,deps = cook_sign (Some hyp0) indvars env in
-  let tmpcl = it_mkNamedProd_or_LetIn (pf_concl gl) deps in
-  let names = compute_induction_names (Array.length indsign) names in
-  let dephyps = List.map (fun (id,_,_) -> id) deps in
-  let deps_cstr =
-    List.fold_left
-      (fun a (id,b,_) -> if b = None then (mkVar id)::a else a) [] deps in
-
-  (* Magistral effet de bord: si hyp0 a des arguments, ceux d'entre
-     eux qui ouvrent de nouveaux buts arrivent en premier dans la
-     liste des sous-buts du fait qu'ils sont le plus à gauche dans le
-     combinateur engendré par make_case_gen (un "Cases (hyp0 ?) of
-     ...")  et il faut alors appliquer tclTHENLASTn; en revanche,
-     comme lookup_eliminator renvoie un combinateur de la forme
-     "ind_rec ... (hyp0 ?)", les buts correspondant à des arguments de
-     hyp0 sont maintenant à la fin et c'est tclTHENFIRSTn qui marche !!! *)
-  tclTHENLIST
-    [ if deps = [] then tclIDTAC else apply_type tmpcl deps_cstr;
-      thin dephyps;
-      (if isrec then tclTHENFIRSTn else tclTHENLASTn)
-       	(tclTHENLIST
-	  [ induction_tac with_evars (hyp0,lbind) typ0 scheme;
-	    tclTHEN (tclTRY (unfold_body hyp0)) (thin [hyp0]);
-            tclTRY (thin indhyps) ])
-       	(array_map2
-	   (induct_discharge statlists lhyp0 (List.rev dephyps)) indsign names)
-    ]
-    gl
-
+  let indvars =
+    find_atomic_param_of_ind scheme.nparams (snd (decompose_prod typ0)) in
+  let induct_tac = tclTHENLIST [
+    induction_tac with_evars (hyp0,lbind) typ0 scheme;
+    tclTRY (unfold_body hyp0);
+    thin [hyp0]
+  ] in
+  apply_induction_in_context isrec
+    (Some hyp0) indsign indvars names induct_tac gl
 
 
 exception TryNewInduct of exn
@@ -2466,20 +2509,25 @@ let induction_without_atomization isrec with_evars elim names lid gl =
   in
   let nlid = List.length lid in
   if nlid <> awaited_nargs
-  then error "Not the right number of induction arguments"
+  then error "Not the right number of induction arguments."
   else induction_from_context_l isrec with_evars elim_info lid names gl
 
-let new_induct_gen isrec with_evars elim names (c,lbind) cls gl =
+let new_induct_gen isrec with_evars elim (eqname,names) (c,lbind) cls gl =
   match kind_of_term c with
     | Var id when not (mem_named_context id (Global.named_context()))
-	        & lbind = NoBindings & not with_evars & cls = None ->
+	        & lbind = NoBindings & not with_evars & cls = None
+	        & eqname = None ->
 	induction_with_atomization_of_ind_arg
 	  isrec with_evars elim names (id,lbind) gl
     | _        ->
 	let x = id_of_name_using_hdchar (Global.env()) (pf_type_of gl c) 
 		  Anonymous in
 	let id = fresh_id [] x gl in
-	let with_eq = if cls <> None then Some (not (isVar c)) else None in
+	let with_eq = 
+	  match eqname with
+	  | Some eq -> Some (false,eq)
+	  | _ ->
+	    if cls <> None then Some (false,(dloc,IntroAnonymous)) else None in
 	tclTHEN
 	  (letin_tac with_eq (Name id) c (Option.default allClauses cls))
 	  (induction_with_atomization_of_ind_arg
@@ -2490,7 +2538,10 @@ let new_induct_gen isrec with_evars elim names (c,lbind) cls gl =
    that all arguments and parameters of the scheme are given
    (mandatory for the moment), so we don't need to deal with
     parameters of the inductive type as in new_induct_gen. *)
-let new_induct_gen_l isrec with_evars elim names lc gl =
+let new_induct_gen_l isrec with_evars elim (eqname,names) lc gl =
+  if eqname <> None then
+    errorlabstrm "" (str "Do not know what to do with " ++
+      pr_intro_pattern (Option.get eqname));
   let newlc = ref [] in
   let letids = ref [] in
   let rec atomize_list l gl =
@@ -2532,18 +2583,18 @@ let induct_destruct_l isrec with_evars lc elim names cls =
   let _ = 
     if elim = None
     then 
-      error ("Induction scheme must be given when several induction hypothesis.\n"
-      ^ "Example: induction x1 x2 x3 using my_scheme.") in
+      errorlabstrm "" (strbrk "Induction scheme must be given when several induction hypothesis are given.\n" ++ 
+      str "Example: induction x1 x2 x3 using my_scheme.") in
   let newlc = 
     List.map
       (fun x -> 
 	match x with (* FIXME: should we deal with ElimOnIdent? *)
 	  | ElimOnConstr (x,NoBindings) -> x
-	  | _ -> error "don't know where to find some argument")
+	  | _ -> error "Don't know where to find some argument.")
       lc in
   if cls <> None then
     error
-      "'in' clause not supported when several induction hypothesis are given";
+      "'in' clause not supported when several induction hypothesis are given.";
   new_induct_gen_l isrec with_evars elim names newlc
 
 (* Induction either over a term, over a quantified premisse, or over
@@ -2551,7 +2602,7 @@ let induct_destruct_l isrec with_evars lc elim names cls =
    principles). 
    TODO: really unify induction with one and induction with several
    args *)
-let induct_destruct isrec with_evars lc elim names cls =
+let induct_destruct isrec with_evars (lc,elim,names,cls) =
   assert (List.length lc > 0); (* ensured by syntax, but if called inside caml? *)
   if List.length lc = 1 then (* induction on one arg: use old mechanism *)
     try
@@ -2565,11 +2616,16 @@ let induct_destruct isrec with_evars lc elim names cls =
 	   with _  -> raise x)
   else induct_destruct_l isrec with_evars lc elim names cls
 
+let induction_destruct isrec with_evars = function
+  | [] -> tclIDTAC
+  | [a] -> induct_destruct isrec with_evars a
+  | a::l ->
+      tclTHEN
+        (induct_destruct isrec with_evars a)
+        (tclMAP (induct_destruct false with_evars) l)
 
-      
-
-let new_induct = induct_destruct true
-let new_destruct = induct_destruct false
+let new_induct ev lc e idl cls = induct_destruct true ev (lc,e,idl,cls)
+let new_destruct ev lc e idl cls = induct_destruct false ev (lc,e,idl,cls)
 
 (* The registered tactic, which calls the default elimination
  * if no elimination constant is provided. *)
@@ -2858,7 +2914,7 @@ let abstract_subproof name tac gl =
   let na = next_global_ident_away false name (pf_ids_of_hyps gl) in
   let concl = it_mkNamedProd_or_LetIn (pf_concl gl) sign in
     if occur_existential concl then
-      error "\"abstract\" cannot handle existentials";
+      error "\"abstract\" cannot handle existentials.";
     let lemme =
       start_proof na (Global, Proof Lemma) secsign concl (fun _ _ -> ());
       let _,(const,kind,_) =
@@ -2901,7 +2957,7 @@ let admit_as_an_axiom gl =
   let name = add_suffix (get_current_proof_name ()) "_admitted" in
   let na = next_global_ident_away false name (pf_ids_of_hyps gl) in
   let concl = it_mkNamedProd_or_LetIn (pf_concl gl) sign in
-  if occur_existential concl then error "\"admit\" cannot handle existentials";
+  if occur_existential concl then error"\"admit\" cannot handle existentials.";
   let axiom =
     let cd = Entries.ParameterEntry (concl,false) in
     let con = Declare.declare_internal_constant na (cd,IsAssumption Logical) in
@@ -2911,3 +2967,8 @@ let admit_as_an_axiom gl =
     (applist (axiom, 
               List.rev (Array.to_list (instance_from_named_context sign))))
     gl
+
+let conv x y gl =
+  try let evd = Evarconv.the_conv_x_leq (pf_env gl) x y (Evd.create_evar_defs (project gl)) in
+	tclEVARS (Evd.evars_of evd) gl
+  with _ -> tclFAIL 0 (str"Not convertible") gl
diff --git a/tactics/tactics.mli b/tactics/tactics.mli
index b7ab31c4..d39433d0 100644
--- a/tactics/tactics.mli
+++ b/tactics/tactics.mli
@@ -6,9 +6,10 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: tactics.mli 11166 2008-06-22 13:23:35Z herbelin $ i*)
+(*i $Id: tactics.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
+open Util
 open Names
 open Term
 open Environ
@@ -68,7 +69,8 @@ val find_intro_names : rel_context -> goal sigma -> identifier list
 val intro                : tactic
 val introf               : tactic
 val intro_force          : bool -> tactic
-val intro_move           : identifier option -> identifier option -> tactic
+val intro_move        : identifier option -> identifier move_location -> tactic
+
   (* [intro_avoiding idl] acts as intro but prevents the new identifier
      to belong to [idl] *)
 val intro_avoiding       : identifier list -> tactic
@@ -110,9 +112,10 @@ val onInductionArg :
 
 (*s Introduction tactics with eliminations. *)
 
-val intro_pattern     : identifier option -> intro_pattern_expr      -> tactic
-val intro_patterns    : intro_pattern_expr list -> tactic
-val intros_pattern    : identifier option -> intro_pattern_expr list -> tactic
+val intro_pattern  : identifier move_location -> intro_pattern_expr -> tactic
+val intro_patterns : intro_pattern_expr located list -> tactic
+val intros_pattern :
+  identifier move_location -> intro_pattern_expr located list -> tactic
 
 (*s Exact tactics. *)
 
@@ -167,7 +170,7 @@ val keep          : identifier list -> tactic
 
 val specialize    : int option -> constr with_ebindings -> tactic
 
-val move_hyp      : bool -> identifier -> identifier -> tactic
+val move_hyp      : bool -> identifier -> identifier move_location -> tactic
 val rename_hyp    : (identifier * identifier) list -> tactic
 
 val revert        : identifier list -> tactic
@@ -183,7 +186,7 @@ val apply_without_reduce  : constr      -> tactic
 val apply_list            : constr list -> tactic
 
 val apply_with_ebindings_gen : 
-  advanced_flag -> evars_flag -> constr with_ebindings -> tactic
+  advanced_flag -> evars_flag -> constr with_ebindings list -> tactic
 
 val apply_with_bindings   : constr with_bindings -> tactic
 val eapply_with_bindings  : constr with_bindings -> tactic
@@ -260,7 +263,9 @@ val elim :
 val simple_induct : quantified_hypothesis -> tactic
 
 val new_induct : evars_flag -> constr with_ebindings induction_arg list -> 
-  constr with_ebindings option -> intro_pattern_expr -> clause option -> tactic
+  constr with_ebindings option -> 
+  intro_pattern_expr located option * intro_pattern_expr located option ->
+  clause option -> tactic
 
 (*s Case analysis tactics. *)
 
@@ -269,7 +274,18 @@ val simplest_case         : constr -> tactic
 
 val simple_destruct          : quantified_hypothesis -> tactic
 val new_destruct : evars_flag -> constr with_ebindings induction_arg list -> 
-  constr with_ebindings option -> intro_pattern_expr -> clause option -> tactic
+  constr with_ebindings option -> 
+  intro_pattern_expr located option * intro_pattern_expr located option ->
+  clause option -> tactic
+
+(*s Generic case analysis / induction tactics. *)
+
+val induction_destruct : evars_flag -> rec_flag -> 
+  (constr with_ebindings induction_arg list *
+   constr with_ebindings option *
+   (intro_pattern_expr located option * intro_pattern_expr located option) *
+   clause option) list ->
+    tactic
 
 (*s Eliminations giving the type instead of the proof. *)
 
@@ -330,20 +346,24 @@ val cut_replacing               :
   identifier -> constr -> (tactic -> tactic) -> tactic
 val cut_in_parallel             : constr list -> tactic
 
-val assert_as : bool -> intro_pattern_expr -> constr -> tactic
-val forward   : tactic option -> intro_pattern_expr -> constr -> tactic
-val letin_tac : bool option -> name -> constr -> clause -> tactic
+val assert_as : bool -> intro_pattern_expr located -> constr -> tactic
+val forward   : tactic option -> intro_pattern_expr located -> constr -> tactic
+val letin_tac : (bool * intro_pattern_expr located) option -> name -> 
+  constr -> clause -> tactic
 val true_cut                    : name -> constr -> tactic
 val assert_tac                  : bool -> name -> constr -> tactic
 val generalize      : constr list -> tactic
 val generalize_gen  : ((occurrences * constr) * name) list -> tactic
 val generalize_dep  : constr  -> tactic
 
+val conv            : constr -> constr -> tactic
+val resolve_classes : tactic
+
 val tclABSTRACT : identifier option -> tactic -> tactic
 
 val admit_as_an_axiom : tactic
 
-val abstract_generalize : identifier -> tactic
+val abstract_generalize : identifier -> ?generalize_vars:bool -> tactic
 
 val register_general_multi_rewrite : 
   (bool -> evars_flag -> constr with_ebindings -> clause -> tactic) -> unit
diff --git a/tactics/tauto.ml4 b/tactics/tauto.ml4
index 54094d99..17ea121f 100644
--- a/tactics/tauto.ml4
+++ b/tactics/tauto.ml4
@@ -8,8 +8,9 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(*i $Id: tauto.ml4 10731 2008-03-30 22:30:44Z herbelin $ i*)
+(*i $Id: tauto.ml4 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
+open Term
 open Hipattern
 open Names
 open Libnames
@@ -36,16 +37,35 @@ let is_unit ist =
     <:tactic<idtac>>
   else
     <:tactic<fail>>
-    
+
+let is_record t =
+  let (hdapp,args) = decompose_app t in
+    match (kind_of_term hdapp) with
+      | Ind ind  -> 
+          let (mib,mip) = Global.lookup_inductive ind in
+	    mib.Declarations.mind_record
+      | _ -> false
+
+let is_binary t =
+  let (hdapp,args) = decompose_app t in
+    match (kind_of_term hdapp) with
+    | Ind ind  -> 
+        let (mib,mip) = Global.lookup_inductive ind in
+	  mib.Declarations.mind_nparams = 2
+    | _ -> false
+	
 let is_conj ist =
   let ind = assoc_last ist in
-    if (is_conjunction ind) && (is_nodep_ind ind) then
+    if (is_conjunction ind) && (is_nodep_ind ind) (* && not (is_record ind)  *)
+      && is_binary ind (* for compatibility, as (?X _ _) matches 
+			  applications with 2 or more arguments. *)
+    then
       <:tactic<idtac>>
     else
       <:tactic<fail>>
 
 let is_disj ist =
-  if is_disjunction (assoc_last ist) then
+  if is_disjunction (assoc_last ist) && is_binary (assoc_last ist) then
     <:tactic<idtac>>
   else
     <:tactic<fail>>
@@ -122,7 +142,7 @@ let rec tauto_intuit t_reduce solver ist =
   and t_simplif = tacticIn simplif
   and t_is_disj = tacticIn is_disj
   and t_tauto_intuit = tacticIn (tauto_intuit t_reduce solver) in
-  let t_solver = Tacexpr.TacArg (valueIn (VTactic (dummy_loc,solver))) in
+  let t_solver = globTacticIn (fun _ist -> solver) in
   <:tactic<
    ($t_simplif;$t_axioms
    || match reverse goal with
@@ -145,16 +165,14 @@ let rec tauto_intuit t_reduce solver ist =
     $t_solver
    ) >>
     
-let reduction_not_iff=interp
+let reduction_not_iff _ist =
  <:tactic<repeat 
   match goal with 
   | |- _     => progress unfold Coq.Init.Logic.not, Coq.Init.Logic.iff 
   | H:_ |- _ => progress unfold Coq.Init.Logic.not, Coq.Init.Logic.iff in H
   end >>
 
-
-let t_reduction_not_iff =
-  Tacexpr.TacArg (valueIn (VTactic (dummy_loc,reduction_not_iff)))
+let t_reduction_not_iff = tacticIn reduction_not_iff
 
 let intuition_gen tac =
   interp (tacticIn (tauto_intuit t_reduction_not_iff tac))
@@ -162,12 +180,12 @@ let intuition_gen tac =
 let simplif_gen = interp (tacticIn simplif)
 
 let tauto g =
-  try intuition_gen (interp <:tactic<fail>>) g
+  try intuition_gen <:tactic<fail>> g
   with
     Refiner.FailError _ | UserError _ ->
-      errorlabstrm "tauto" [< str "tauto failed" >]
+      errorlabstrm "tauto" (str "tauto failed.")
 
-let default_intuition_tac = interp <:tactic< auto with * >>
+let default_intuition_tac = <:tactic< auto with * >>
 
 TACTIC EXTEND tauto
 | [ "tauto" ] -> [ tauto ]
@@ -175,5 +193,5 @@ END
 
 TACTIC EXTEND intuition
 | [ "intuition" ] -> [ intuition_gen default_intuition_tac ]
-| [ "intuition" tactic(t) ] -> [ intuition_gen (snd t) ]
+| [ "intuition" tactic(t) ] -> [ intuition_gen (fst t) ]
 END
diff --git a/tactics/termdn.ml b/tactics/termdn.ml
index 65ad1dee..bd439fb4 100644
--- a/tactics/termdn.ml
+++ b/tactics/termdn.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: termdn.ml 7639 2005-12-02 10:01:15Z gregoire $ *)
+(* $Id: termdn.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Util
 open Names
@@ -41,43 +41,54 @@ let decomp_pat =
   decrec []   
 
 let constr_pat_discr t =
-  if not (occur_meta_pattern t) then 
+  if not (occur_meta_pattern t) then
     None
   else
     match decomp_pat t with
-      | PRef ((IndRef _) as ref), args
-      | PRef ((ConstructRef _ ) as ref), args
-      | PRef ((VarRef _) as ref), args -> Some(ref,args)
-      | _ -> None
-
-let constr_val_discr t =
-  let c, l = decomp t in
-  match kind_of_term c with
-    (* Const _,_) -> Some(TERM c,l) *)
-    | Ind ind_sp -> Some(IndRef ind_sp,l)
-    | Construct cstr_sp -> Some(ConstructRef cstr_sp,l)
-    | Var id -> Some(VarRef id,l)
+    | PRef ((IndRef _) as ref), args
+    | PRef ((ConstructRef _ ) as ref), args -> Some (ref,args)
+    | PRef ((VarRef v) as ref), args -> Some(ref,args)
     | _ -> None
 
-(* Les deux fonctions suivantes ecrasaient les precedentes, 
-   ajout d'un suffixe _nil CP 16/08 *) 
-
-let constr_pat_discr_nil t =
-  match constr_pat_discr t with
-    | None -> None
-    | Some (c,_) -> Some(c,[])
-
-let constr_val_discr_nil t =
-  match constr_val_discr t with
-    | None -> None
-    | Some (c,_) -> Some(c,[])
+let constr_pat_discr_st (idpred,cpred) t =
+  match decomp_pat t with
+  | PRef ((IndRef _) as ref), args
+  | PRef ((ConstructRef _ ) as ref), args -> Some (ref,args)
+  | PRef ((VarRef v) as ref), args when not (Idpred.mem v idpred) -> 
+      Some(ref,args)
+  | PVar v, args when not (Idpred.mem v idpred) ->
+      Some(VarRef v,args)
+  | PRef ((ConstRef c) as ref), args when not (Cpred.mem c cpred) ->
+      Some (ref, args)
+  | _ -> None
+
+open Dn
+
+let constr_val_discr t =  
+  let c, l = decomp t in
+    match kind_of_term c with
+    | Ind ind_sp -> Label(IndRef ind_sp,l)
+    | Construct cstr_sp -> Label((ConstructRef cstr_sp),l)
+    | Var id -> Label(VarRef id,l)
+    | Const _ -> Everything
+    | _ -> Nothing
+	
+let constr_val_discr_st (idpred,cpred) t =  
+  let c, l = decomp t in
+    match kind_of_term c with
+    | Const c -> if Cpred.mem c cpred then Everything else Label(ConstRef c,l)
+    | Ind ind_sp -> Label(IndRef ind_sp,l)
+    | Construct cstr_sp -> Label((ConstructRef cstr_sp),l)
+    | Var id when not (Idpred.mem id idpred) -> Label(VarRef id,l)
+    | Evar _ -> Everything
+    | _ -> Nothing
 
 let create = Dn.create 
 
-let add dn = Dn.add dn constr_pat_discr
-
-let rmv dn = Dn.rmv dn constr_pat_discr
+let add dn st = Dn.add dn (constr_pat_discr_st st)
 
-let lookup dn t = Dn.lookup dn constr_val_discr t
+let rmv dn st = Dn.rmv dn (constr_pat_discr_st st)
 
+let lookup dn st t = Dn.lookup dn (constr_val_discr_st st) t
+  
 let app f dn = Dn.app f dn
diff --git a/tactics/termdn.mli b/tactics/termdn.mli
index b65c0eeb..79efd8eb 100644
--- a/tactics/termdn.mli
+++ b/tactics/termdn.mli
@@ -6,12 +6,13 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: termdn.mli 6427 2004-12-07 17:41:10Z sacerdot $ i*)
+(*i $Id: termdn.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Term
 open Pattern
 open Libnames
+open Names
 (*i*)
   
 (* Discrimination nets of terms. *)
@@ -22,7 +23,10 @@ open Libnames
 order in such a way patterns having the same prefix have this common
 prefix shared and the seek for the action associated to the patterns
 that a term matches are found in time proportional to the maximal
-number of nodes of the patterns matching the term *)
+number of nodes of the patterns matching the term. The [transparent_state] 
+indicates which constants and variables can be considered as rigid.
+These dnets are able to cope with existential variables as well, which match
+[Everything]. *)
 
 type 'a t
 
@@ -30,13 +34,13 @@ val create : unit -> 'a t
 
 (* [add t (c,a)] adds to table [t] pattern [c] associated to action [act] *)
 
-val add : 'a t -> (constr_pattern * 'a) -> 'a t
+val add : 'a t -> transparent_state -> (constr_pattern * 'a) -> 'a t
 
-val rmv : 'a t -> (constr_pattern * 'a) -> 'a t
+val rmv : 'a t -> transparent_state -> (constr_pattern * 'a) -> 'a t
 
 (* [lookup t c] looks for patterns (with their action) matching term [c] *)
 
-val lookup : 'a t -> constr -> (constr_pattern * 'a) list
+val lookup : 'a t -> transparent_state -> constr -> (constr_pattern * 'a) list
 
 val app : ((constr_pattern * 'a) -> unit) -> 'a t -> unit
 
@@ -44,9 +48,12 @@ val app : ((constr_pattern * 'a) -> unit) -> 'a t -> unit
 (*i*)
 (* These are for Nbtermdn *)
 
-val constr_pat_discr : 
+val constr_pat_discr_st : transparent_state ->
   constr_pattern -> (global_reference * constr_pattern list) option
-val constr_val_discr :
-  constr -> (global_reference * constr list) option
+val constr_val_discr_st : transparent_state ->
+  constr -> (global_reference * constr list) Dn.lookup_res
+
+val constr_pat_discr : constr_pattern -> (global_reference * constr_pattern list) option
+val constr_val_discr : constr -> (global_reference * constr list) Dn.lookup_res
 
 (*i*)
diff --git a/test-suite/bugs/closed/shouldfail/1915.v b/test-suite/bugs/closed/shouldfail/1915.v
new file mode 100644
index 00000000..a96a482c
--- /dev/null
+++ b/test-suite/bugs/closed/shouldfail/1915.v
@@ -0,0 +1,6 @@
+
+Require Import Setoid.
+
+Goal forall x, impl True (x = 0) -> x = 0 -> False.
+intros x H E.
+rewrite H in E.
\ No newline at end of file
diff --git a/test-suite/bugs/closed/shouldsucceed/1784.v b/test-suite/bugs/closed/shouldsucceed/1784.v
index 616dd26f..5855b168 100644
--- a/test-suite/bugs/closed/shouldsucceed/1784.v
+++ b/test-suite/bugs/closed/shouldsucceed/1784.v
@@ -85,17 +85,17 @@ Program Fixpoint lt_dec (x y:sv) { struct x } : {slt x y}+{~slt x y} :=
       end
   end.
 
-Next Obligation. apply H; inversion H0; subst; trivial. Defined.
-Next Obligation. inversion H. Defined.
-Next Obligation. inversion H. Defined.
-Next Obligation. inversion H; subst. Defined.
+Next Obligation. intro H0. apply H; inversion H0; subst; trivial. Defined.
+Next Obligation. intro H; inversion H. Defined.
+Next Obligation. intro H; inversion H. Defined.
+Next Obligation. intro H; inversion H; subst. Defined.
 Next Obligation.
-  contradict H. inversion H1; subst. assumption. 
+  intro H1; contradict H. inversion H1; subst. assumption. 
   contradict H0; assumption. Defined.
 Next Obligation.
-  contradict H0. inversion H1; subst. assumption. Defined.
+  intro H1; contradict H0. inversion H1; subst. assumption. Defined.
 Next Obligation.
-  contradict H. inversion H0; subst. assumption. Defined.
+  intro H0; contradict H. inversion H0; subst. assumption. Defined.
 Next Obligation.
-  contradict H. inversion H0; subst; auto. Defined.
+  intro H0; contradict H. inversion H0; subst; auto. Defined.
 
diff --git a/test-suite/bugs/closed/shouldsucceed/1905.v b/test-suite/bugs/closed/shouldsucceed/1905.v
new file mode 100644
index 00000000..bd7fd796
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1905.v
@@ -0,0 +1,13 @@
+
+Require Import Setoid.
+
+Axiom t : Set.
+Axiom In : nat -> t -> Prop.
+Axiom InE : forall (x : nat) (s:t), impl (In x s) True.
+
+Goal forall a s, 
+ In a s -> False.
+Proof.
+ intros a s Ia.
+ rewrite InE in Ia.
+Admitted.
\ No newline at end of file
diff --git a/test-suite/bugs/opened/shouldnotfail/1671.v b/test-suite/bugs/opened/shouldnotfail/1671.v
new file mode 100644
index 00000000..800c431e
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1671.v
@@ -0,0 +1,12 @@
+(* Exemple soumis par Pierre Corbineau (bug #1671) *)
+
+CoInductive hdlist : unit -> Type :=
+| cons : hdlist tt -> hdlist tt.
+
+Variable P : forall bo, hdlist bo -> Prop.
+Variable all : forall bo l, P bo l.
+
+Definition F (l:hdlist tt) : P tt l := 
+match l in hdlist u return P u l with
+| cons (cons l') => all tt _
+end.
diff --git a/test-suite/check b/test-suite/check
index f2307d40..571e7a67 100755
--- a/test-suite/check
+++ b/test-suite/check
@@ -54,7 +54,7 @@ test_output() {
         tmpoutput=`mktemp /tmp/coqcheck.XXXXXX`
 	$command $f 2>&1 | grep -v "Welcome to Coq" | grep -v "Skipping rcfile loading" > $tmpoutput
         foutput=`dirname $f`/`basename $f .v`.out
-        diff $tmpoutput $foutput >& /dev/null
+        diff $tmpoutput $foutput > /dev/null 2>&1
 	if [ $? = 0 ]; then 
 	    echo "Ok"
 	    nbtestsok=`expr $nbtestsok + 1`
diff --git a/test-suite/complexity/ring2.v b/test-suite/complexity/ring2.v
index 9f9685dd..e1a799f0 100644
--- a/test-suite/complexity/ring2.v
+++ b/test-suite/complexity/ring2.v
@@ -1,7 +1,7 @@
 (* This example, checks the efficiency of the abstract machine used by ring *)
 (* Expected time < 1.00s *)
 
-Require Import BinInt.
+Require Import BinInt Zbool.
 
 Definition Zplus x y :=
 match x with
@@ -42,7 +42,7 @@ Ltac Zcst t :=
   end.
 
 Add Ring Zr : Zth
-  (decidable Zeqb_ok, constants [Zcst]).
+  (decidable Zeq_bool_eq, constants [Zcst]).
 
 Open Scope Z_scope.
 Infix "+" := Zplus : Z_scope.
diff --git a/test-suite/csdp.cache b/test-suite/csdp.cache
index 59ff450c..6620e52c 100644
--- a/test-suite/csdp.cache
+++ b/test-suite/csdp.cache
@@ -1,94198 +1,5 @@
 *** REQUEST ***
 ""
-3
-3
-4 1 1
-0.10485760000000000000e7 -0.52428800000000000000e6 0.52428800000000000000e6
-0 1 1 2 -0.52428800000000000000e6
-0 1 1 4 0.52428800000000000000e6
-0 1 2 2 -0.10485760000000000000e7
-0 1 4 4 0.10485760000000000000e7
-0 2 1 1 -0.10485760000000000000e7
-1 1 1 1 0.10485760000000000000e7
-1 1 1 2 0.52428800000000000000e6
-1 1 1 4 -0.52428800000000000000e6
-1 1 2 2 0.10485760000000000000e7
-1 1 4 4 -0.10485760000000000000e7
-1 2 1 1 0.10485760000000000000e7
-2 1 1 3 0.10485760000000000000e7
-2 1 1 4 -0.52428800000000000000e6
-2 1 4 4 -0.10485760000000000000e7
-3 1 1 2 -0.52428800000000000000e6
-3 1 1 4 0.52428800000000000000e6
-3 3 1 1 0.10485760000000000000e7
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-8
-4
-4 1 4 1
--0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.10485760000000000000e7
-0 1 1 2 -0.26214400000000000000e6
-0 1 1 4 0.26214400000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 3 1 2 -0.26214400000000000000e6
-0 3 1 4 -0.26214400000000000000e6
-1 1 2 3 0.52428800000000000000e6
-1 1 3 4 -0.52428800000000000000e6
-1 3 1 4 -0.26214400000000000000e6
-1 3 4 4 -0.52428800000000000000e6
-2 1 1 1 0.52428800000000000000e6
-2 1 1 2 0.26214400000000000000e6
-2 1 1 4 -0.26214400000000000000e6
-2 2 1 1 0.52428800000000000000e6
-2 3 1 2 0.26214400000000000000e6
-2 3 1 4 0.26214400000000000000e6
-3 1 1 3 0.52428800000000000000e6
-3 1 1 4 -0.26214400000000000000e6
-3 1 4 4 -0.52428800000000000000e6
-4 1 2 2 0.52428800000000000000e6
-4 1 4 4 -0.52428800000000000000e6
-4 3 1 2 -0.26214400000000000000e6
-4 3 1 4 -0.26214400000000000000e6
-5 1 2 4 0.52428800000000000000e6
-5 1 4 4 -0.10485760000000000000e7
-5 3 1 4 -0.52428800000000000000e6
-6 1 1 2 -0.26214400000000000000e6
-6 1 1 4 0.26214400000000000000e6
-6 3 1 1 0.52428800000000000000e6
-7 1 2 3 -0.52428800000000000000e6
-7 1 3 4 0.52428800000000000000e6
-7 3 1 3 0.52428800000000000000e6
-8 1 1 2 0.26214400000000000000e6
-8 1 1 4 -0.26214400000000000000e6
-8 1 2 3 -0.52428800000000000000e6
-8 1 3 4 0.52428800000000000000e6
-8 3 1 2 0.26214400000000000000e6
-8 3 2 2 0.52428800000000000000e6
-8 4 1 1 0.52428800000000000000e6
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-51
-4
-10 4 4 1
-0.52428800000000000000e6 0.0 0.0 -0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 -0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.0 0.52428800000000000000e6 -0.52428800000000000000e6 0.0 0.0 0.0 0.52428800000000000000e6 0.0 0.0 0.0 -0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.52428800000000000000e6 0.52428800000000000000e6
-0 1 1 2 -0.13107200000000000000e6
-0 1 1 4 0.26214400000000000000e6
-0 1 1 8 -0.13107200000000000000e6
-0 2 1 1 -0.26214400000000000000e6
-0 3 1 2 -0.13107200000000000000e6
-1 1 2 9 -0.26214400000000000000e6
-1 1 7 10 0.13107200000000000000e6
-1 1 10 10 0.26214400000000000000e6
-1 3 3 4 0.26214400000000000000e6
-2 1 2 9 0.13107200000000000000e6
-2 1 6 7 -0.26214400000000000000e6
-2 1 9 10 0.13107200000000000000e6
-2 3 3 4 -0.13107200000000000000e6
-3 1 2 9 -0.26214400000000000000e6
-3 1 7 8 0.13107200000000000000e6
-3 1 8 10 0.13107200000000000000e6
-4 1 2 9 0.26214400000000000000e6
-4 1 3 10 -0.13107200000000000000e6
-4 1 4 7 -0.26214400000000000000e6
-4 1 7 8 -0.13107200000000000000e6
-4 1 7 10 0.13107200000000000000e6
-4 2 4 4 -0.26214400000000000000e6
-4 3 3 4 -0.26214400000000000000e6
-5 1 1 6 -0.13107200000000000000e6
-5 1 3 6 -0.13107200000000000000e6
-5 1 4 5 -0.13107200000000000000e6
-5 1 6 7 0.13107200000000000000e6
-5 1 9 9 0.26214400000000000000e6
-5 2 3 3 -0.26214400000000000000e6
-6 1 2 9 0.13107200000000000000e6
-6 1 4 5 -0.26214400000000000000e6
-6 1 8 9 0.13107200000000000000e6
-7 1 1 6 -0.26214400000000000000e6
-7 1 2 9 0.13107200000000000000e6
-7 1 4 7 0.13107200000000000000e6
-7 3 3 4 -0.13107200000000000000e6
-8 1 1 8 -0.13107200000000000000e6
-8 1 2 5 -0.26214400000000000000e6
-8 1 2 9 0.26214400000000000000e6
-8 1 3 8 -0.13107200000000000000e6
-8 1 3 10 0.13107200000000000000e6
-8 2 2 4 -0.13107200000000000000e6
-9 1 1 4 0.26214400000000000000e6
-9 1 1 6 -0.52428800000000000000e6
-9 1 1 8 0.13107200000000000000e6
-9 1 2 5 0.26214400000000000000e6
-9 1 7 8 0.13107200000000000000e6
-9 2 1 3 0.26214400000000000000e6
-10 1 1 2 0.13107200000000000000e6
-10 1 1 6 -0.52428800000000000000e6
-10 1 1 8 0.13107200000000000000e6
-10 1 2 3 0.13107200000000000000e6
-10 1 2 5 0.26214400000000000000e6
-10 1 3 8 0.13107200000000000000e6
-10 1 3 10 -0.13107200000000000000e6
-10 1 4 7 0.26214400000000000000e6
-10 1 7 8 -0.13107200000000000000e6
-10 2 1 3 0.26214400000000000000e6
-10 2 2 4 0.13107200000000000000e6
-10 2 4 4 -0.26214400000000000000e6
-10 3 1 2 0.13107200000000000000e6
-10 3 3 4 -0.26214400000000000000e6
-10 4 1 1 0.26214400000000000000e6
-11 1 1 1 0.26214400000000000000e6
-11 1 1 2 0.13107200000000000000e6
-11 1 1 4 -0.26214400000000000000e6
-11 1 1 8 0.13107200000000000000e6
-11 2 1 1 0.26214400000000000000e6
-11 3 1 2 0.13107200000000000000e6
-12 1 1 3 0.26214400000000000000e6
-12 1 1 8 -0.26214400000000000000e6
-12 3 1 2 -0.26214400000000000000e6
-13 1 1 4 0.26214400000000000000e6
-13 1 1 5 0.26214400000000000000e6
-13 1 1 6 -0.52428800000000000000e6
-13 1 2 5 0.26214400000000000000e6
-13 2 1 3 0.26214400000000000000e6
-14 1 1 2 -0.26214400000000000000e6
-14 1 1 4 -0.52428800000000000000e6
-14 1 1 6 0.10485760000000000000e7
-14 1 1 7 0.26214400000000000000e6
-14 1 1 8 -0.26214400000000000000e6
-14 1 2 3 -0.26214400000000000000e6
-14 1 2 5 -0.52428800000000000000e6
-14 1 2 9 0.52428800000000000000e6
-14 1 3 8 -0.26214400000000000000e6
-14 1 4 7 -0.52428800000000000000e6
-14 2 1 3 -0.52428800000000000000e6
-14 2 2 4 -0.26214400000000000000e6
-14 3 1 2 -0.26214400000000000000e6
-14 4 1 1 -0.52428800000000000000e6
-15 1 1 9 0.26214400000000000000e6
-15 1 4 7 -0.26214400000000000000e6
-16 1 1 10 0.26214400000000000000e6
-16 1 2 9 -0.52428800000000000000e6
-16 1 3 10 0.26214400000000000000e6
-16 1 7 8 0.26214400000000000000e6
-16 2 4 4 0.52428800000000000000e6
-16 3 3 4 0.52428800000000000000e6
-17 1 1 8 -0.13107200000000000000e6
-17 1 2 2 0.26214400000000000000e6
-17 3 1 2 -0.13107200000000000000e6
-18 1 1 4 0.26214400000000000000e6
-18 1 1 6 -0.52428800000000000000e6
-18 1 2 4 0.26214400000000000000e6
-18 1 2 5 0.26214400000000000000e6
-18 2 1 3 0.26214400000000000000e6
-19 1 2 6 0.26214400000000000000e6
-19 1 4 5 -0.26214400000000000000e6
-20 1 1 8 -0.26214400000000000000e6
-20 1 2 7 0.26214400000000000000e6
-21 1 1 8 0.26214400000000000000e6
-21 1 2 8 0.26214400000000000000e6
-21 1 2 9 -0.52428800000000000000e6
-21 1 3 8 0.26214400000000000000e6
-21 2 2 4 0.26214400000000000000e6
-22 1 2 10 0.26214400000000000000e6
-22 1 7 8 -0.26214400000000000000e6
-23 1 1 8 0.13107200000000000000e6
-23 1 2 3 0.13107200000000000000e6
-23 1 2 5 -0.26214400000000000000e6
-23 1 3 3 0.26214400000000000000e6
-23 2 2 2 0.26214400000000000000e6
-23 3 1 2 0.13107200000000000000e6
-24 1 2 5 -0.26214400000000000000e6
-24 1 3 4 0.26214400000000000000e6
-25 1 1 4 -0.26214400000000000000e6
-25 1 1 6 0.52428800000000000000e6
-25 1 3 5 0.26214400000000000000e6
-25 1 4 5 -0.52428800000000000000e6
-25 2 1 3 -0.26214400000000000000e6
-25 2 2 3 0.26214400000000000000e6
-26 1 1 8 0.26214400000000000000e6
-26 1 2 9 -0.52428800000000000000e6
-26 1 3 7 0.26214400000000000000e6
-26 1 3 8 0.26214400000000000000e6
-26 2 2 4 0.26214400000000000000e6
-27 1 3 9 0.26214400000000000000e6
-27 1 5 8 -0.26214400000000000000e6
-28 1 1 6 -0.13107200000000000000e6
-28 1 4 4 0.26214400000000000000e6
-29 1 1 6 -0.13107200000000000000e6
-29 1 3 6 -0.13107200000000000000e6
-29 1 4 5 -0.13107200000000000000e6
-29 1 4 6 0.26214400000000000000e6
-29 2 3 3 -0.26214400000000000000e6
-30 1 2 9 -0.26214400000000000000e6
-30 1 4 8 0.26214400000000000000e6
-31 1 4 9 0.26214400000000000000e6
-31 1 6 7 -0.26214400000000000000e6
-32 1 2 9 -0.26214400000000000000e6
-32 1 4 10 0.26214400000000000000e6
-32 3 3 4 0.26214400000000000000e6
-33 1 3 6 -0.13107200000000000000e6
-33 1 5 5 0.26214400000000000000e6
-34 1 2 9 -0.26214400000000000000e6
-34 1 5 7 0.26214400000000000000e6
-35 1 5 10 0.26214400000000000000e6
-35 1 8 9 -0.26214400000000000000e6
-36 1 5 9 -0.26214400000000000000e6
-36 1 6 8 0.26214400000000000000e6
-37 1 6 10 0.26214400000000000000e6
-37 1 9 9 -0.52428800000000000000e6
-38 1 2 9 -0.26214400000000000000e6
-38 1 3 10 0.13107200000000000000e6
-38 1 7 7 0.26214400000000000000e6
-38 1 7 8 0.13107200000000000000e6
-38 2 4 4 0.26214400000000000000e6
-38 3 3 4 0.26214400000000000000e6
-39 1 2 9 -0.26214400000000000000e6
-39 1 7 9 0.26214400000000000000e6
-39 3 3 4 0.26214400000000000000e6
-40 1 3 10 -0.13107200000000000000e6
-40 1 8 8 0.26214400000000000000e6
-41 1 1 2 0.26214400000000000000e6
-41 1 1 4 0.52428800000000000000e6
-41 1 1 6 -0.10485760000000000000e7
-41 1 1 8 0.26214400000000000000e6
-41 1 2 3 0.26214400000000000000e6
-41 1 2 5 0.52428800000000000000e6
-41 2 1 2 0.26214400000000000000e6
-41 2 1 3 0.52428800000000000000e6
-41 3 1 2 0.26214400000000000000e6
-42 1 1 2 0.26214400000000000000e6
-42 1 1 4 0.52428800000000000000e6
-42 1 1 6 -0.10485760000000000000e7
-42 1 1 8 0.26214400000000000000e6
-42 1 2 3 0.26214400000000000000e6
-42 1 2 5 0.52428800000000000000e6
-42 2 1 3 0.52428800000000000000e6
-42 2 1 4 0.26214400000000000000e6
-42 3 1 2 0.26214400000000000000e6
-42 4 1 1 0.52428800000000000000e6
-43 1 2 9 0.26214400000000000000e6
-43 1 4 7 0.26214400000000000000e6
-43 1 5 8 0.26214400000000000000e6
-43 1 6 7 -0.52428800000000000000e6
-43 2 3 4 0.26214400000000000000e6
-44 1 1 4 0.26214400000000000000e6
-44 1 1 6 -0.52428800000000000000e6
-44 1 1 8 0.13107200000000000000e6
-44 1 2 3 0.13107200000000000000e6
-44 1 2 5 0.26214400000000000000e6
-44 1 2 9 -0.26214400000000000000e6
-44 1 3 8 0.13107200000000000000e6
-44 1 4 7 0.26214400000000000000e6
-44 2 1 3 0.26214400000000000000e6
-44 2 2 4 0.13107200000000000000e6
-44 3 1 1 0.26214400000000000000e6
-44 3 1 2 0.13107200000000000000e6
-44 4 1 1 0.26214400000000000000e6
-45 1 1 4 0.26214400000000000000e6
-45 1 1 6 -0.52428800000000000000e6
-45 1 2 5 0.26214400000000000000e6
-45 1 4 7 0.26214400000000000000e6
-45 2 1 3 0.26214400000000000000e6
-45 3 1 3 0.26214400000000000000e6
-46 1 1 8 -0.26214400000000000000e6
-46 1 2 9 0.52428800000000000000e6
-46 1 3 10 -0.26214400000000000000e6
-46 1 7 8 -0.26214400000000000000e6
-46 2 4 4 -0.52428800000000000000e6
-46 3 1 4 0.26214400000000000000e6
-46 3 3 4 -0.52428800000000000000e6
-47 1 1 8 -0.13107200000000000000e6
-47 1 2 3 -0.13107200000000000000e6
-47 1 2 9 0.26214400000000000000e6
-47 1 3 8 -0.13107200000000000000e6
-47 2 2 4 -0.13107200000000000000e6
-47 3 2 2 0.26214400000000000000e6
-48 1 2 5 -0.26214400000000000000e6
-48 1 2 9 0.26214400000000000000e6
-48 3 2 3 0.26214400000000000000e6
-49 1 1 8 0.26214400000000000000e6
-49 1 2 9 -0.52428800000000000000e6
-49 1 3 8 0.26214400000000000000e6
-49 1 7 8 0.26214400000000000000e6
-49 2 2 4 0.26214400000000000000e6
-49 3 2 4 0.26214400000000000000e6
-50 1 4 5 -0.13107200000000000000e6
-50 1 6 7 0.13107200000000000000e6
-50 3 3 3 0.26214400000000000000e6
-51 1 7 8 -0.13107200000000000000e6
-51 1 7 10 0.13107200000000000000e6
-51 3 4 4 0.26214400000000000000e6
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-96
-4
-10 4 10 4
--0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 0.26214400000000000000e6 0.0 0.0 -0.52428800000000000000e6 0.0 0.0 0.26214400000000000000e6 -0.52428800000000000000e6 0.0 0.0 0.52428800000000000000e6 0.10485760000000000000e7 0.0 0.0 0.0 -0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.0 0.0 -0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.0 0.0 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.52428800000000000000e6 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.10485760000000000000e7 0.0 -0.52428800000000000000e6
-0 1 1 2 -0.26214400000000000000e6
-0 1 1 4 0.52428800000000000000e6
-0 1 1 8 -0.26214400000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 3 1 2 -0.26214400000000000000e6
-1 1 5 8 0.52428800000000000000e6
-1 1 9 10 -0.52428800000000000000e6
-1 3 7 8 -0.26214400000000000000e6
-1 3 7 10 -0.26214400000000000000e6
-1 3 8 10 -0.26214400000000000000e6
-1 3 10 10 -0.52428800000000000000e6
-2 1 5 8 0.52428800000000000000e6
-2 1 8 9 -0.52428800000000000000e6
-2 3 7 8 -0.26214400000000000000e6
-2 3 8 10 -0.26214400000000000000e6
-3 1 1 10 -0.26214400000000000000e6
-3 2 4 4 -0.52428800000000000000e6
-3 3 1 10 -0.26214400000000000000e6
-3 3 7 8 -0.26214400000000000000e6
-3 3 7 10 -0.26214400000000000000e6
-4 1 5 6 0.52428800000000000000e6
-4 1 6 9 -0.52428800000000000000e6
-4 3 4 9 -0.26214400000000000000e6
-4 3 9 9 -0.52428800000000000000e6
-5 1 8 9 0.26214400000000000000e6
-5 1 9 10 -0.26214400000000000000e6
-5 3 4 9 -0.52428800000000000000e6
-5 3 9 10 0.26214400000000000000e6
-6 1 1 10 0.13107200000000000000e6
-6 1 3 10 0.13107200000000000000e6
-6 1 6 7 -0.52428800000000000000e6
-6 1 7 10 0.13107200000000000000e6
-6 1 9 10 0.26214400000000000000e6
-6 2 4 4 0.26214400000000000000e6
-6 3 1 10 0.13107200000000000000e6
-7 1 2 9 -0.52428800000000000000e6
-7 1 3 10 0.26214400000000000000e6
-7 1 7 10 0.26214400000000000000e6
-7 3 1 10 0.26214400000000000000e6
-7 3 7 8 -0.26214400000000000000e6
-8 1 1 10 0.26214400000000000000e6
-8 1 4 7 -0.52428800000000000000e6
-8 1 7 10 0.26214400000000000000e6
-9 1 1 4 -0.13107200000000000000e6
-9 1 2 5 -0.13107200000000000000e6
-9 1 4 7 -0.13107200000000000000e6
-9 2 1 3 -0.13107200000000000000e6
-9 2 3 3 -0.52428800000000000000e6
-9 3 1 4 -0.13107200000000000000e6
-9 3 1 6 -0.26214400000000000000e6
-9 3 4 5 -0.26214400000000000000e6
-9 3 4 9 -0.26214400000000000000e6
-10 1 5 8 0.26214400000000000000e6
-10 1 9 10 -0.26214400000000000000e6
-10 3 4 5 -0.52428800000000000000e6
-10 3 4 9 -0.52428800000000000000e6
-10 3 5 10 0.26214400000000000000e6
-10 3 9 10 0.26214400000000000000e6
-11 1 2 9 0.26214400000000000000e6
-11 1 6 7 -0.52428800000000000000e6
-11 1 8 9 0.26214400000000000000e6
-11 3 1 6 -0.52428800000000000000e6
-12 1 1 4 -0.26214400000000000000e6
-12 1 1 10 0.13107200000000000000e6
-12 1 2 5 -0.26214400000000000000e6
-12 1 3 10 0.13107200000000000000e6
-12 1 7 10 0.13107200000000000000e6
-12 2 1 3 -0.26214400000000000000e6
-12 2 4 4 0.26214400000000000000e6
-12 3 1 4 -0.26214400000000000000e6
-12 3 1 10 0.13107200000000000000e6
-13 1 1 8 -0.26214400000000000000e6
-13 1 2 9 0.52428800000000000000e6
-13 1 3 10 -0.26214400000000000000e6
-13 1 7 10 -0.26214400000000000000e6
-13 1 8 9 0.52428800000000000000e6
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-96 4 3 4 0.52428800000000000000e6
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-281
-4
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-281 4 3 4 0.26214400000000000000e6
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-468
-4
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-468 4 9 10 0.13107200000000000000e6
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-1024
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-1024 2 6 20 -0.65536000000000000000e5
-1024 2 14 20 0.65536000000000000000e5
-1024 4 9 10 0.65536000000000000000e5
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-1582
-4
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-1578 4 17 20 0.32768000000000000000e5
-1579 1 19 34 0.32768000000000000000e5
-1579 1 30 33 -0.32768000000000000000e5
-1579 3 19 34 0.32768000000000000000e5
-1579 3 20 33 0.32768000000000000000e5
-1579 3 21 34 -0.65536000000000000000e5
-1579 4 18 19 0.32768000000000000000e5
-1580 1 3 34 -0.65536000000000000000e5
-1580 1 4 27 -0.32768000000000000000e5
-1580 1 4 35 -0.32768000000000000000e5
-1580 1 17 24 0.13107200000000000000e6
-1580 1 20 27 -0.65536000000000000000e5
-1580 1 28 35 -0.32768000000000000000e5
-1580 1 30 33 -0.65536000000000000000e5
-1580 1 33 34 0.65536000000000000000e5
-1580 2 4 18 -0.32768000000000000000e5
-1580 2 6 20 -0.65536000000000000000e5
-1580 3 2 31 -0.13107200000000000000e6
-1580 3 3 32 0.32768000000000000000e5
-1580 3 5 26 -0.32768000000000000000e5
-1580 3 17 22 0.65536000000000000000e5
-1580 3 17 30 -0.65536000000000000000e5
-1580 3 18 19 -0.32768000000000000000e5
-1580 3 19 32 -0.32768000000000000000e5
-1580 3 27 32 0.32768000000000000000e5
-1580 3 28 33 0.32768000000000000000e5
-1580 4 13 17 0.32768000000000000000e5
-1580 4 18 20 0.32768000000000000000e5
-1581 4 16 20 -0.16384000000000000000e5
-1581 4 19 19 0.32768000000000000000e5
-1582 1 30 33 0.32768000000000000000e5
-1582 1 33 34 -0.32768000000000000000e5
-1582 3 20 35 0.32768000000000000000e5
-1582 3 22 35 0.32768000000000000000e5
-1582 3 29 34 -0.65536000000000000000e5
-1582 4 19 20 0.32768000000000000000e5
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-2945
-4
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-2945 2 21 35 -0.32768000000000000000e5
-2945 2 29 35 0.32768000000000000000e5
-2945 4 19 20 0.32768000000000000000e5
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-4310
-4
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-4298 1 28 43 -0.26214400000000000000e6
-4298 1 32 47 -0.26214400000000000000e6
-4298 1 33 48 0.13107200000000000000e6
-4298 1 40 55 -0.65536000000000000000e5
-4298 2 2 32 -0.32768000000000000000e5
-4298 2 4 34 0.65536000000000000000e5
-4298 2 16 30 -0.65536000000000000000e5
-4298 2 20 34 -0.13107200000000000000e6
-4298 2 28 34 -0.65536000000000000000e5
-4298 3 5 50 0.65536000000000000000e5
-4298 3 9 38 -0.65536000000000000000e5
-4298 3 10 55 0.13107200000000000000e6
-4298 3 22 35 -0.26214400000000000000e6
-4298 3 22 51 -0.65536000000000000000e5
-4298 3 23 52 0.13107200000000000000e6
-4298 3 26 55 0.65536000000000000000e5
-4298 3 27 40 0.65536000000000000000e5
-4298 3 28 41 -0.26214400000000000000e6
-4298 3 35 48 -0.26214400000000000000e6
-4298 3 38 51 0.65536000000000000000e5
-4298 3 39 52 -0.13107200000000000000e6
-4298 3 40 45 0.13107200000000000000e6
-4298 4 2 30 -0.65536000000000000000e5
-4298 4 6 34 -0.13107200000000000000e6
-4298 4 7 35 -0.65536000000000000000e5
-4298 4 22 34 0.13107200000000000000e6
-4298 4 30 33 0.65536000000000000000e5
-4299 3 40 55 0.65536000000000000000e5
-4299 3 41 54 0.65536000000000000000e5
-4299 3 42 55 -0.13107200000000000000e6
-4299 3 49 50 0.65536000000000000000e5
-4299 4 30 35 0.65536000000000000000e5
-4300 4 15 35 -0.32768000000000000000e5
-4300 4 31 31 0.65536000000000000000e5
-4301 4 23 35 -0.65536000000000000000e5
-4301 4 31 32 0.65536000000000000000e5
-4302 4 30 34 -0.65536000000000000000e5
-4302 4 31 33 0.65536000000000000000e5
-4303 1 44 51 0.65536000000000000000e5
-4303 1 46 53 -0.65536000000000000000e5
-4303 3 19 56 -0.13107200000000000000e6
-4303 3 43 52 0.65536000000000000000e5
-4303 3 45 50 0.65536000000000000000e5
-4303 4 31 34 0.65536000000000000000e5
-4304 1 1 48 0.65536000000000000000e5
-4304 1 2 49 0.13107200000000000000e6
-4304 1 6 53 -0.65536000000000000000e5
-4304 1 8 39 0.13107200000000000000e6
-4304 1 9 40 0.13107200000000000000e6
-4304 1 10 41 -0.26214400000000000000e6
-4304 1 12 43 -0.52428800000000000000e6
-4304 1 23 38 0.65536000000000000000e5
-4304 1 24 39 0.65536000000000000000e5
-4304 1 24 55 0.13107200000000000000e6
-4304 1 25 56 0.65536000000000000000e5
-4304 1 26 41 -0.26214400000000000000e6
-4304 1 28 43 0.26214400000000000000e6
-4304 1 32 47 0.52428800000000000000e6
-4304 1 40 47 0.65536000000000000000e5
-4304 2 2 32 0.65536000000000000000e5
-4304 2 3 33 0.65536000000000000000e5
-4304 2 5 35 -0.65536000000000000000e5
-4304 2 16 30 0.13107200000000000000e6
-4304 2 20 34 0.26214400000000000000e6
-4304 2 33 35 0.65536000000000000000e5
-4304 3 9 38 0.13107200000000000000e6
-4304 3 22 35 0.52428800000000000000e6
-4304 3 22 51 -0.13107200000000000000e6
-4304 3 23 52 0.26214400000000000000e6
-4304 3 24 53 -0.65536000000000000000e5
-4304 3 25 38 0.65536000000000000000e5
-4304 3 25 54 -0.65536000000000000000e5
-4304 3 27 40 0.13107200000000000000e6
-4304 3 28 41 0.52428800000000000000e6
-4304 3 38 51 0.13107200000000000000e6
-4304 3 39 40 -0.65536000000000000000e5
-4304 4 2 30 0.13107200000000000000e6
-4304 4 6 34 0.26214400000000000000e6
-4304 4 7 35 -0.13107200000000000000e6
-4304 4 32 33 0.65536000000000000000e5
-4305 3 27 56 0.65536000000000000000e5
-4305 3 41 54 0.65536000000000000000e5
-4305 3 47 52 -0.13107200000000000000e6
-4305 3 49 50 0.65536000000000000000e5
-4305 4 32 34 0.65536000000000000000e5
-4306 2 33 35 -0.65536000000000000000e5
-4306 2 35 35 0.13107200000000000000e6
-4306 4 32 35 0.65536000000000000000e5
-4307 3 40 55 0.65536000000000000000e5
-4307 3 41 54 0.65536000000000000000e5
-4307 3 42 55 -0.13107200000000000000e6
-4307 3 49 50 0.65536000000000000000e5
-4307 4 33 34 0.65536000000000000000e5
-4308 1 1 48 0.13107200000000000000e6
-4308 1 2 49 0.19660800000000000000e6
-4308 1 6 53 -0.65536000000000000000e5
-4308 1 8 39 0.26214400000000000000e6
-4308 1 9 40 0.26214400000000000000e6
-4308 1 10 41 -0.52428800000000000000e6
-4308 1 12 43 -0.10485760000000000000e7
-4308 1 23 38 0.13107200000000000000e6
-4308 1 24 39 0.65536000000000000000e5
-4308 1 26 41 -0.39321600000000000000e6
-4308 1 28 43 0.78643200000000000000e6
-4308 1 32 47 0.10485760000000000000e7
-4308 1 40 55 -0.13107200000000000000e6
-4308 1 49 56 -0.65536000000000000000e5
-4308 1 54 55 0.13107200000000000000e6
-4308 2 2 32 0.13107200000000000000e6
-4308 2 3 33 0.65536000000000000000e5
-4308 2 4 34 -0.13107200000000000000e6
-4308 2 5 35 -0.65536000000000000000e5
-4308 2 16 30 0.26214400000000000000e6
-4308 2 20 34 0.52428800000000000000e6
-4308 3 5 50 -0.13107200000000000000e6
-4308 3 9 38 0.26214400000000000000e6
-4308 3 22 35 0.10485760000000000000e7
-4308 3 25 38 0.65536000000000000000e5
-4308 3 25 54 -0.65536000000000000000e5
-4308 3 28 41 0.10485760000000000000e7
-4308 3 39 40 -0.65536000000000000000e5
-4308 3 40 53 -0.65536000000000000000e5
-4308 3 48 53 0.65536000000000000000e5
-4308 3 49 50 0.13107200000000000000e6
-4308 3 49 54 0.65536000000000000000e5
-4308 4 2 30 0.26214400000000000000e6
-4308 4 6 34 0.52428800000000000000e6
-4308 4 33 35 0.65536000000000000000e5
-4309 4 31 35 -0.32768000000000000000e5
-4309 4 34 34 0.65536000000000000000e5
-4310 1 40 55 0.65536000000000000000e5
-4310 1 54 55 -0.65536000000000000000e5
-4310 3 41 56 0.65536000000000000000e5
-4310 3 43 56 0.65536000000000000000e5
-4310 3 49 50 -0.65536000000000000000e5
-4310 3 50 55 -0.13107200000000000000e6
-4310 4 34 35 0.65536000000000000000e5
-*** ANSWER ***
-Failure
-*** END ***
-*** REQUEST ***
-""
 1
 3
 1 1 1
@@ -94559,6 +366,98 @@ Failure
 *** END ***
 *** REQUEST ***
 ""
+2
+4
+1 1 1 1
+0.15728640000000000000e7 0.10485760000000000000e7
+0 2 1 1 -0.10485760000000000000e7
+0 4 1 1 -0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.10485760000000000000e7
+1 4 1 1 0.10485760000000000000e7
+2 2 1 1 0.10485760000000000000e7
+2 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+-8.033537119682993312e-10 -8.033532523347130644e-10 
+1 1 1 1 9.639215222160258208e-10 
+1 2 1 1 1.048575999157623970e+06 
+1 3 1 1 1.445882272036933453e-09 
+1 4 1 1 1.048576000000000931e+06 
+2 1 1 1 1.499999999685651009e+00 
+2 2 1 1 1.378900983392931975e-15 
+2 3 1 1 9.999999999999862332e-01 
+2 4 1 1 1.378900796134651217e-15 
+*** END ***
+*** REQUEST ***
+""
+1
+3
+1 1 1
+0.10485760000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 -0.10485760000000000000e7
+1 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+5
+5
+4 1 1 1 1
+0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0
+0 2 1 1 -0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 2 1 1 0.52428800000000000000e6
+2 1 1 3 0.52428800000000000000e6
+2 1 1 4 -0.52428800000000000000e6
+2 2 1 1 -0.10485760000000000000e7
+2 4 1 1 0.10485760000000000000e7
+3 1 1 2 -0.52428800000000000000e6
+3 1 1 4 0.26214400000000000000e6
+3 1 3 3 0.52428800000000000000e6
+3 2 1 1 0.52428800000000000000e6
+3 4 1 1 -0.52428800000000000000e6
+4 2 1 1 0.52428800000000000000e6
+4 3 1 1 0.52428800000000000000e6
+4 4 1 1 -0.52428800000000000000e6
+5 1 1 2 -0.52428800000000000000e6
+5 1 1 4 0.26214400000000000000e6
+5 1 3 4 0.52428800000000000000e6
+5 1 4 4 -0.52428800000000000000e6
+5 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-1.338594917701584393e-10 -4.876570677399720908e-12 -8.432248596379257249e-11 -1.376003305176662146e-10 6.303077531793304895e-11 
+1 1 1 1 1.961387163584582007e-06 
+1 1 1 2 1.116298839109634367e-05 
+1 1 1 3 -2.556727487312544875e-06 
+1 1 1 4 -3.024766708235593078e-06 
+1 1 2 2 7.214231238477719979e-05 
+1 1 3 3 2.793304486379264481e-05 
+1 1 3 4 3.304627912988848237e-05 
+1 1 4 4 3.909603325488893426e-05 
+1 2 1 1 5.242879998907233821e+05 
+1 3 1 1 1.102983309069068926e-10 
+1 4 1 1 1.833803270175834998e-04 
+1 5 1 1 1.051885915146662243e-04 
+2 1 1 1 1.999999999825280872e+00 
+2 1 1 2 -3.095056099254819282e-01 
+2 1 1 3 8.388821521212311283e-02 
+2 1 1 4 8.388917358587567874e-02 
+2 1 2 2 4.789927494245199008e-02 
+2 1 2 3 -1.307058076260208049e-02 
+2 1 2 4 -1.290714134044862460e-02 
+2 1 3 3 2.971005649372479018e-01 
+2 1 3 4 -2.447309307272341194e-01 
+2 1 4 4 2.134402019028047992e-01 
+2 2 1 1 2.103712716147778344e-16 
+2 3 1 1 1.000000958427416542e+00 
+2 4 1 1 9.583793370118670507e-07 
+2 5 1 1 1.669900717227676154e-06 
+*** END ***
+*** REQUEST ***
+""
 1
 2
 2 1
@@ -105175,481 +11074,143 @@ Infeasible
 *** END ***
 *** REQUEST ***
 ""
-5
-5
-4 1 1 1 1
-0.15728640000000000000e7 -0.10485760000000000000e7 -0.52428800000000000000e6 -0.15728640000000000000e7 0.10485760000000000000e7
-0 1 2 2 -0.52428800000000000000e6
-0 1 4 4 0.52428800000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 4 1 1 -0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 1 2 2 0.52428800000000000000e6
-1 1 4 4 -0.52428800000000000000e6
-1 2 1 1 0.52428800000000000000e6
-1 4 1 1 0.52428800000000000000e6
-2 1 1 2 0.52428800000000000000e6
-2 1 1 4 -0.52428800000000000000e6
-2 4 1 1 -0.10485760000000000000e7
-3 1 1 3 0.52428800000000000000e6
-3 1 1 4 -0.26214400000000000000e6
-3 1 4 4 -0.52428800000000000000e6
-4 1 2 2 -0.52428800000000000000e6
-4 1 2 4 0.52428800000000000000e6
-4 1 4 4 -0.52428800000000000000e6
-4 5 1 1 -0.52428800000000000000e6
-5 3 1 1 0.52428800000000000000e6
-5 4 1 1 0.52428800000000000000e6
-*** ANSWER ***
-Failure
-*** END ***
-*** REQUEST ***
-""
-20
-7
-4 1 4 1 4 1 1
--0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.52428800000000000000e6
-0 1 1 2 -0.26214400000000000000e6
-0 1 1 4 0.26214400000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 3 1 2 0.26214400000000000000e6
-0 5 1 4 -0.26214400000000000000e6
-1 1 2 3 0.52428800000000000000e6
-1 1 3 4 -0.52428800000000000000e6
-1 5 1 4 -0.26214400000000000000e6
-1 5 4 4 -0.52428800000000000000e6
-2 1 1 1 0.52428800000000000000e6
-2 1 1 2 0.26214400000000000000e6
-2 1 1 4 -0.26214400000000000000e6
-2 2 1 1 0.52428800000000000000e6
-2 3 1 2 -0.26214400000000000000e6
-2 5 1 4 0.26214400000000000000e6
-3 1 1 3 0.52428800000000000000e6
-3 1 1 4 -0.26214400000000000000e6
-3 1 4 4 -0.52428800000000000000e6
-4 1 2 2 0.52428800000000000000e6
-4 1 4 4 -0.52428800000000000000e6
-4 3 1 2 0.26214400000000000000e6
-4 5 1 4 -0.26214400000000000000e6
-5 1 2 4 0.52428800000000000000e6
-5 1 4 4 -0.10485760000000000000e7
-5 5 1 4 -0.52428800000000000000e6
-6 1 1 2 0.26214400000000000000e6
-6 1 1 4 -0.26214400000000000000e6
-6 3 1 1 0.52428800000000000000e6
-7 1 2 3 0.52428800000000000000e6
-7 1 3 4 -0.52428800000000000000e6
-7 3 1 3 0.52428800000000000000e6
-8 3 1 4 0.52428800000000000000e6
-8 5 1 4 0.52428800000000000000e6
-9 1 1 2 -0.26214400000000000000e6
-9 1 1 4 0.26214400000000000000e6
-9 1 2 3 0.52428800000000000000e6
-9 1 3 4 -0.52428800000000000000e6
-9 3 1 2 0.26214400000000000000e6
-9 3 2 2 0.52428800000000000000e6
-9 4 1 1 0.52428800000000000000e6
-10 3 3 3 0.52428800000000000000e6
-10 5 3 3 0.52428800000000000000e6
-11 3 4 4 0.52428800000000000000e6
-11 5 4 4 0.52428800000000000000e6
-12 1 1 2 -0.26214400000000000000e6
-12 1 1 4 0.26214400000000000000e6
-12 5 1 1 0.52428800000000000000e6
-13 3 1 2 0.52428800000000000000e6
-13 5 1 2 0.52428800000000000000e6
-14 1 2 3 -0.52428800000000000000e6
-14 1 3 4 0.52428800000000000000e6
-14 5 1 3 0.52428800000000000000e6
-15 1 1 2 0.26214400000000000000e6
-15 1 1 4 -0.26214400000000000000e6
-15 1 2 3 -0.52428800000000000000e6
-15 1 3 4 0.52428800000000000000e6
-15 3 1 2 -0.26214400000000000000e6
-15 4 1 1 -0.52428800000000000000e6
-15 5 2 2 0.52428800000000000000e6
-16 3 2 3 0.52428800000000000000e6
-16 5 2 3 0.52428800000000000000e6
-17 3 2 4 0.52428800000000000000e6
-17 5 2 4 0.52428800000000000000e6
-18 3 3 4 0.52428800000000000000e6
-18 5 3 4 0.52428800000000000000e6
-19 4 1 1 0.52428800000000000000e6
-19 6 1 1 0.52428800000000000000e6
-20 3 1 2 -0.26214400000000000000e6
-20 5 1 4 -0.26214400000000000000e6
-20 7 1 1 0.52428800000000000000e6
+2
+3
+2 1 1
+0.10485760000000000000e7 0.10485760000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 2 2 0.10485760000000000000e7
+1 2 1 1 0.10485760000000000000e7
+2 1 1 1 0.10485760000000000000e7
+2 1 1 2 -0.52428800000000000000e6
+2 3 1 1 0.10485760000000000000e7
 *** ANSWER ***
-1.408782135629833379e-09 -1.602915007691423680e-09 -2.114475652645426357e-10 1.060506410792219022e-09 2.087517963511041579e-10 7.735026962533785022e-02 -6.083346056031729135e-10 -1.056624336133169251e-01 1.443375650931139342e-01 -1.043524718501323747e-09 1.443375655752403564e-01 1.077350266300642900e+00 3.943375640054703757e-01 2.270314905788526486e-09 1.443375636846789267e-01 8.310024292703551422e-10 1.443375652667335807e-01 8.309943070227691571e-10 -1.341153069964939011e-09 -1.043513950273019921e-09 
-1 1 1 1 1.330530909011591600e-04 
-1 1 1 2 8.214146408166717733e-05 
-1 1 1 3 -1.108594210974165294e-04 
-1 1 1 4 -2.671176437533311163e-05 
-1 1 2 2 1.529452979555114694e-03 
-1 1 2 3 -3.220826912303867418e-05 
-1 1 2 4 1.094460618053276968e-04 
-1 1 3 3 9.734421944536802984e-04 
-1 1 3 4 3.220826912303867418e-05 
-1 1 4 4 3.093987068390115919e-04 
-1 2 1 1 5.242880001330530504e+05 
-1 3 1 1 4.055381913477132912e+04 
-1 3 1 2 -5.539754590173628094e+04 
-1 3 1 3 -3.189425337024763205e-04 
-1 3 1 4 -5.539754599425870401e+04 
-1 3 2 2 7.567445430098070938e+04 
-1 3 2 3 4.356846016372959568e-04 
-1 3 2 4 7.567445341856521554e+04 
-1 3 3 3 4.263347068400591411e-04 
-1 3 3 4 4.356803432403535958e-04 
-1 3 4 4 7.567445455375382153e+04 
-1 4 1 1 1.008717294824084537e-03 
-1 5 1 1 5.648418173916736851e+05 
-1 5 1 2 2.067464527573000523e+05 
-1 5 1 3 1.190298861326054974e-03 
-1 5 1 4 2.067464531023424352e+05 
-1 5 2 2 7.567445356255515071e+04 
-1 5 2 3 4.356846016372959568e-04 
-1 5 2 4 7.567445341856521554e+04 
-1 5 3 3 4.263347068400591411e-04 
-1 5 3 4 4.356803432403535958e-04 
-1 5 4 4 7.567445381514624751e+04 
-1 6 1 1 2.702917337079049562e-04 
-1 7 1 1 4.263403524929400973e-04 
-2 1 1 1 3.732050805139194516e+00 
-2 1 1 2 -2.205738821003602190e-01 
-2 1 1 3 5.137913895681569532e-01 
-2 1 1 4 3.567764144417457928e-01 
-2 1 2 2 5.161058552875832373e-01 
-2 1 2 3 1.025309974541342359e-02 
-2 1 2 4 9.345607328673936898e-02 
-2 1 3 3 8.811272737592539261e-01 
-2 1 3 4 1.025319705650454272e-02 
-2 1 4 4 1.670806364694566115e+00 
-2 2 1 1 8.098913424095950693e-10 
-2 3 1 1 1.577350296542103125e+00 
-2 3 1 2 5.773502179991568672e-01 
-2 3 1 3 9.731109131778280951e-08 
-2 3 1 4 5.773502914078277870e-01 
-2 3 2 2 4.226500930909230513e-01 
-2 3 2 3 -1.505172222580337775e-03 
-2 3 2 4 -2.930749631858512249e-07 
-2 3 3 3 1.009116009161232563e+00 
-2 3 3 4 1.505025171725787349e-03 
-2 3 4 4 4.226499032143540280e-01 
-2 4 1 1 4.226495869899917768e-01 
-2 5 1 1 4.226497034578927114e-01 
-2 5 1 2 -5.773502179991555350e-01 
-2 5 1 3 -9.731109217953321892e-08 
-2 5 1 4 -5.773502914078278980e-01 
-2 5 2 2 1.577349906909068178e+00 
-2 5 2 3 1.505172222581506979e-03 
-2 5 2 4 2.930749610850833078e-07 
-2 5 3 3 9.908839908387667705e-01 
-2 5 3 4 -1.505025171724929745e-03 
-2 5 4 4 1.577350096785647304e+00 
-2 6 1 1 1.577350413010008445e+00 
-2 7 1 1 9.999999265913281921e-01 
+1.170818692744000744e+00 1.447215295915970978e+00 
+1 1 1 1 4.689392261611652211e+05 
+1 1 1 2 -7.587576130651925923e+05 
+1 1 2 2 1.227692381593513535e+06 
+1 2 1 1 1.227692381593513535e+06 
+1 3 1 1 1.517515226161165396e+06 
+2 1 1 1 2.618033982848464447e+00 
+2 1 1 2 1.618033984214826360e+00 
+2 1 2 2 9.999999983112128898e-01 
+2 2 1 1 1.688748897052140516e-09 
+2 3 1 1 1.366359508118386529e-09 
 *** END ***
 *** REQUEST ***
 ""
-5
-5
-4 1 1 1 1
-0.52428800000000000000e6 -0.10485760000000000000e7 -0.52428800000000000000e6 -0.15728640000000000000e7 0.10485760000000000000e7
-0 1 2 2 0.52428800000000000000e6
-0 1 4 4 -0.52428800000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 4 1 1 0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 1 2 2 -0.52428800000000000000e6
-1 1 4 4 0.52428800000000000000e6
-1 2 1 1 0.52428800000000000000e6
-1 4 1 1 -0.52428800000000000000e6
-2 1 1 2 0.52428800000000000000e6
-2 1 1 4 -0.52428800000000000000e6
-2 4 1 1 -0.10485760000000000000e7
-3 1 1 3 0.52428800000000000000e6
-3 1 1 4 -0.26214400000000000000e6
-3 1 4 4 -0.52428800000000000000e6
-4 1 2 2 -0.52428800000000000000e6
-4 1 2 4 0.52428800000000000000e6
-4 1 4 4 -0.52428800000000000000e6
-4 5 1 1 -0.52428800000000000000e6
-5 3 1 1 0.52428800000000000000e6
-5 4 1 1 0.52428800000000000000e6
+11
+1
+9
+-0.20000000000000000000e1 -0.40000000000000000000e1 0.0 -0.20000000000000000000e1 0.0 0.0 -0.40000000000000000000e1 0.0 0.0 0.0 0.0
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 0.20000000000000000000e1
+0 1 4 4 -0.10000000000000000000e1
+0 1 5 5 0.20000000000000000000e1
+0 1 6 6 0.30000000000000000000e1
+0 1 7 7 -0.10000000000000000000e1
+0 1 8 8 -0.10000000000000000000e1
+0 1 9 9 -0.10000000000000000000e1
+1 1 1 4 0.10000000000000000000e1
+1 1 2 2 -0.20000000000000000000e1
+2 1 1 6 0.10000000000000000000e1
+2 1 3 3 -0.20000000000000000000e1
+2 1 4 6 0.10000000000000000000e1
+2 1 5 5 -0.20000000000000000000e1
+3 1 1 8 -0.10000000000000000000e1
+3 1 2 7 0.10000000000000000000e1
+3 1 2 8 0.10000000000000000000e1
+3 1 4 7 -0.10000000000000000000e1
+4 1 2 9 0.10000000000000000000e1
+4 1 6 6 -0.20000000000000000000e1
+5 1 1 5 0.10000000000000000000e1
+5 1 2 3 -0.10000000000000000000e1
+5 1 2 5 -0.10000000000000000000e1
+5 1 3 4 0.10000000000000000000e1
+6 1 2 6 -0.10000000000000000000e1
+6 1 3 5 0.10000000000000000000e1
+7 1 3 8 0.10000000000000000000e1
+7 1 5 7 0.10000000000000000000e1
+7 1 6 6 -0.40000000000000000000e1
+8 1 1 9 0.10000000000000000000e1
+8 1 3 7 -0.10000000000000000000e1
+8 1 4 9 0.10000000000000000000e1
+8 1 5 8 -0.10000000000000000000e1
+9 1 1 8 -0.10000000000000000000e1
+9 1 3 6 0.10000000000000000000e1
+9 1 4 7 -0.10000000000000000000e1
+9 1 5 6 0.10000000000000000000e1
+10 1 3 9 -0.10000000000000000000e1
+10 1 5 9 -0.10000000000000000000e1
+10 1 6 7 0.10000000000000000000e1
+10 1 6 8 0.10000000000000000000e1
+11 1 6 9 -0.10000000000000000000e1
+11 1 7 8 0.10000000000000000000e1
 *** ANSWER ***
-Failure
+5.000179462710149236e-01 -1.499910088781482242e+00 0.000000000000000000e+00 -9.999820571239961264e-01 0.000000000000000000e+00 0.000000000000000000e+00 -9.999100882951448277e-01 0.000000000000000000e+00 0.000000000000000000e+00 0.000000000000000000e+00 0.000000000000000000e+00 
+1 1 1 1 1.000000003557179440e+00 
+1 1 1 4 5.000179462710149236e-01 
+1 1 1 6 -1.499910088781482242e+00 
+1 1 2 2 9.999641110151495926e-01 
+1 1 2 9 -9.999820571239961264e-01 
+1 1 3 3 9.998201811201439249e-01 
+1 1 3 8 -9.999100882951448277e-01 
+1 1 4 4 1.000000003557179440e+00 
+1 1 4 6 -1.499910088781482242e+00 
+1 1 5 5 9.998201811201439249e-01 
+1 1 5 7 -9.999100882951448277e-01 
+1 1 6 6 2.999604470985750559e+00 
+1 1 7 7 1.000000003557179440e+00 
+1 1 8 8 1.000000003557179440e+00 
+1 1 9 9 1.000000003557179440e+00 
+2 1 1 1 1.184220387763170584e+04 
+2 1 1 4 1.184220399462378919e+04 
+2 1 1 6 1.184309073001916113e+04 
+2 1 2 2 1.184320399458401334e+04 
+2 1 2 9 1.184297764883485434e+04 
+2 1 3 3 1.184409078860287264e+04 
+2 1 3 8 1.184297764886539881e+04 
+2 1 4 4 1.184220411189475271e+04 
+2 1 4 6 1.184309084718016129e+04 
+2 1 5 5 1.184409078860287264e+04 
+2 1 5 7 1.184297764886539881e+04 
+2 1 6 6 1.184397764896266563e+04 
+2 1 7 7 1.184186461389191209e+04 
+2 1 8 8 1.184186461389191209e+04 
+2 1 9 9 1.184275130749586242e+04 
 *** END ***
 *** REQUEST ***
 ""
-20
-7
-4 1 4 1 4 1 1
--0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.10485760000000000000e7 0.52428800000000000000e6
-0 1 1 2 0.26214400000000000000e6
-0 1 1 4 -0.26214400000000000000e6
-0 2 1 1 -0.52428800000000000000e6
-0 3 1 2 -0.26214400000000000000e6
-0 5 1 4 0.26214400000000000000e6
+4
+2
+3 1
+-0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 0.10485760000000000000e7
+0 1 3 3 -0.10485760000000000000e7
+0 2 1 1 -0.10485760000000000000e7
 1 1 2 3 0.52428800000000000000e6
-1 1 3 4 -0.52428800000000000000e6
-1 5 1 4 -0.26214400000000000000e6
-1 5 4 4 -0.52428800000000000000e6
-2 1 1 1 0.52428800000000000000e6
-2 1 1 2 -0.26214400000000000000e6
-2 1 1 4 0.26214400000000000000e6
-2 2 1 1 0.52428800000000000000e6
-2 3 1 2 0.26214400000000000000e6
-2 5 1 4 -0.26214400000000000000e6
-3 1 1 3 0.52428800000000000000e6
-3 1 1 4 -0.26214400000000000000e6
-3 1 4 4 -0.52428800000000000000e6
-4 1 2 2 0.52428800000000000000e6
-4 1 4 4 -0.52428800000000000000e6
-4 3 1 2 0.26214400000000000000e6
-4 5 1 4 -0.26214400000000000000e6
-5 1 2 4 0.52428800000000000000e6
-5 1 4 4 -0.10485760000000000000e7
-5 5 1 4 -0.52428800000000000000e6
-6 1 1 2 0.26214400000000000000e6
-6 1 1 4 -0.26214400000000000000e6
-6 3 1 1 0.52428800000000000000e6
-7 1 2 3 0.52428800000000000000e6
-7 1 3 4 -0.52428800000000000000e6
-7 3 1 3 0.52428800000000000000e6
-8 3 1 4 0.52428800000000000000e6
-8 5 1 4 0.52428800000000000000e6
-9 1 1 2 0.26214400000000000000e6
-9 1 1 4 -0.26214400000000000000e6
-9 1 2 3 0.52428800000000000000e6
-9 1 3 4 -0.52428800000000000000e6
-9 3 1 2 0.26214400000000000000e6
-9 3 2 2 0.52428800000000000000e6
-9 4 1 1 -0.52428800000000000000e6
-10 3 3 3 0.52428800000000000000e6
-10 5 3 3 0.52428800000000000000e6
-11 3 4 4 0.52428800000000000000e6
-11 5 4 4 0.52428800000000000000e6
-12 1 1 2 -0.26214400000000000000e6
-12 1 1 4 0.26214400000000000000e6
-12 5 1 1 0.52428800000000000000e6
-13 3 1 2 0.52428800000000000000e6
-13 5 1 2 0.52428800000000000000e6
-14 1 2 3 -0.52428800000000000000e6
-14 1 3 4 0.52428800000000000000e6
-14 5 1 3 0.52428800000000000000e6
-15 1 1 2 -0.26214400000000000000e6
-15 1 1 4 0.26214400000000000000e6
-15 1 2 3 -0.52428800000000000000e6
-15 1 3 4 0.52428800000000000000e6
-15 3 1 2 -0.26214400000000000000e6
-15 4 1 1 0.52428800000000000000e6
-15 5 2 2 0.52428800000000000000e6
-16 3 2 3 0.52428800000000000000e6
-16 5 2 3 0.52428800000000000000e6
-17 3 2 4 0.52428800000000000000e6
-17 5 2 4 0.52428800000000000000e6
-18 3 3 4 0.52428800000000000000e6
-18 5 3 4 0.52428800000000000000e6
-19 4 1 1 0.52428800000000000000e6
-19 6 1 1 0.52428800000000000000e6
-20 3 1 2 -0.26214400000000000000e6
-20 5 1 4 -0.26214400000000000000e6
-20 7 1 1 0.52428800000000000000e6
+1 1 3 3 -0.10485760000000000000e7
+2 1 2 2 0.10485760000000000000e7
+2 1 2 3 -0.52428800000000000000e6
+3 1 1 1 0.10485760000000000000e7
+3 1 2 2 -0.10485760000000000000e7
+3 1 3 3 0.10485760000000000000e7
+3 2 1 1 0.10485760000000000000e7
+4 1 1 2 -0.10485760000000000000e7
+4 1 1 3 0.10485760000000000000e7
 *** ANSWER ***
--1.342746526345061715e-09 -2.443492977315052222e-10 2.208950819456293398e-11 -1.532357985106601546e-10 -3.139233416116088887e-11 1.077350268749094120e+00 7.009852277455727232e-10 3.943375659685520174e-01 1.443375671349989564e-01 -5.878340507562113329e-11 1.443375661877718541e-01 7.735026948774698097e-02 -1.056624327919023082e-01 -1.878285492550673151e-10 1.443375666874154029e-01 2.565781949174762027e-10 1.443375668147542368e-01 2.565786864113415496e-10 2.942145218318752536e-10 -5.878238521589696054e-11 
-1 1 1 1 3.819403205883547918e-05 
-1 1 1 2 -1.224733049205359824e-05 
-1 1 1 3 1.158126407231101153e-05 
-1 1 1 4 6.456704127512840957e-06 
-1 1 2 2 8.596374633833324744e-05 
-1 1 2 3 -3.328802848049413742e-06 
-1 1 2 4 -1.645862409268672010e-05 
-1 1 3 3 1.663034366678906723e-04 
-1 1 3 4 3.328802848049413742e-06 
-1 1 4 4 2.679791111105120707e-04 
-1 2 1 1 5.242880000381940044e+05 
-1 3 1 1 5.648418178682285361e+05 
-1 3 1 2 2.067464544649153540e+05 
-1 3 1 3 3.675181430842708319e-04 
-1 3 1 4 2.067464537865202001e+05 
-1 3 2 2 7.567445456437776738e+04 
-1 3 2 3 1.345208686568937634e-04 
-1 3 2 4 7.567445423017386929e+04 
-1 3 3 3 1.354840027876034331e-04 
-1 3 3 4 1.345211263412294384e-04 
-1 3 4 4 7.567445406775796437e+04 
-1 4 1 1 8.589389131903515245e-05 
-1 5 1 1 4.055381825549533096e+04 
-1 5 1 2 -5.539754556360087736e+04 
-1 5 1 3 -9.847625443184073249e-05 
-1 5 1 4 -5.539754572539421497e+04 
-1 5 2 2 7.567445432971508126e+04 
-1 5 2 3 1.345208686568937634e-04 
-1 5 2 4 7.567445423017386929e+04 
-1 5 3 3 1.354840027876034331e-04 
-1 5 3 4 1.345211263412294384e-04 
-1 5 4 4 7.567445477174385451e+04 
-1 6 1 1 3.205565798900817526e-04 
-1 7 1 1 1.354845374878180936e-04 
-2 1 1 1 3.732050806982203373e+00 
-2 1 1 2 4.978949133196186594e-01 
-2 1 1 3 -1.308568436669261814e-01 
-2 1 1 4 -7.945535675086745631e-02 
-2 1 2 2 1.972442206524292363e+00 
-2 1 2 3 6.164317095563820459e-02 
-2 1 2 4 3.950919296356215638e-01 
-2 1 3 3 1.074614358661167834e+00 
-2 1 3 4 6.164314293620330037e-02 
-2 1 4 4 8.177416694170173139e-01 
-2 2 1 1 1.955575535633660102e-10 
-2 3 1 1 4.226497299295132737e-01 
-2 3 1 2 -5.773502768886704661e-01 
-2 3 1 3 -2.801943794662026982e-08 
-2 3 1 4 -5.773502602186049160e-01 
-2 3 2 2 1.577350183915906534e+00 
-2 3 2 3 -5.093597884469405757e-03 
-2 3 2 4 7.563155554311366017e-08 
-2 3 3 3 1.000664225665719220e+00 
-2 3 3 4 5.093637134632639923e-03 
-2 3 4 4 1.577350204179726045e+00 
-2 4 1 1 1.577350233136592728e+00 
-2 5 1 1 1.577350270070483784e+00 
-2 5 1 2 5.773502768886699110e-01 
-2 5 1 3 2.801943516876615048e-08 
-2 5 1 4 5.773502602186050270e-01 
-2 5 2 2 4.226498160840916896e-01 
-2 5 2 3 5.093597884469902755e-03 
-2 5 2 4 -7.563155467628118543e-08 
-2 5 3 3 9.993357743342811128e-01 
-2 5 3 4 -5.093637134632782171e-03 
-2 5 4 4 4.226497958202757865e-01 
-2 6 1 1 4.226497668634069393e-01 
-2 7 1 1 9.999999833299334506e-01 
-*** END ***
-*** REQUEST ***
-""
-2
-4
-1 1 1 1
-0.15728640000000000000e7 0.10485760000000000000e7
-0 2 1 1 -0.10485760000000000000e7
-0 4 1 1 -0.10485760000000000000e7
-1 1 1 1 0.10485760000000000000e7
-1 2 1 1 0.10485760000000000000e7
-1 4 1 1 0.10485760000000000000e7
-2 2 1 1 0.10485760000000000000e7
-2 3 1 1 0.10485760000000000000e7
-*** ANSWER ***
--8.033537119682993312e-10 -8.033532523347130644e-10 
-1 1 1 1 9.639215222160258208e-10 
-1 2 1 1 1.048575999157623970e+06 
-1 3 1 1 1.445882272036933453e-09 
-1 4 1 1 1.048576000000000931e+06 
-2 1 1 1 1.499999999685651009e+00 
-2 2 1 1 1.378900983392931975e-15 
-2 3 1 1 9.999999999999862332e-01 
-2 4 1 1 1.378900796134651217e-15 
-*** END ***
-*** REQUEST ***
-""
-1
-3
-1 1 1
-0.10485760000000000000e7
-0 1 1 1 0.10485760000000000000e7
-1 1 1 1 0.10485760000000000000e7
-1 2 1 1 -0.10485760000000000000e7
-1 3 1 1 0.10485760000000000000e7
-*** ANSWER ***
-Infeasible
-*** END ***
-*** REQUEST ***
-""
-5
-5
-4 1 1 1 1
-0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0
-0 2 1 1 -0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 2 1 1 0.52428800000000000000e6
-2 1 1 3 0.52428800000000000000e6
-2 1 1 4 -0.52428800000000000000e6
-2 2 1 1 -0.10485760000000000000e7
-2 4 1 1 0.10485760000000000000e7
-3 1 1 2 -0.52428800000000000000e6
-3 1 1 4 0.26214400000000000000e6
-3 1 3 3 0.52428800000000000000e6
-3 2 1 1 0.52428800000000000000e6
-3 4 1 1 -0.52428800000000000000e6
-4 2 1 1 0.52428800000000000000e6
-4 3 1 1 0.52428800000000000000e6
-4 4 1 1 -0.52428800000000000000e6
-5 1 1 2 -0.52428800000000000000e6
-5 1 1 4 0.26214400000000000000e6
-5 1 3 4 0.52428800000000000000e6
-5 1 4 4 -0.52428800000000000000e6
-5 5 1 1 0.52428800000000000000e6
-*** ANSWER ***
--1.338594917701584393e-10 -4.876570677399720908e-12 -8.432248596379257249e-11 -1.376003305176662146e-10 6.303077531793304895e-11 
-1 1 1 1 1.961387163584582007e-06 
-1 1 1 2 1.116298839109634367e-05 
-1 1 1 3 -2.556727487312544875e-06 
-1 1 1 4 -3.024766708235593078e-06 
-1 1 2 2 7.214231238477719979e-05 
-1 1 3 3 2.793304486379264481e-05 
-1 1 3 4 3.304627912988848237e-05 
-1 1 4 4 3.909603325488893426e-05 
-1 2 1 1 5.242879998907233821e+05 
-1 3 1 1 1.102983309069068926e-10 
-1 4 1 1 1.833803270175834998e-04 
-1 5 1 1 1.051885915146662243e-04 
-2 1 1 1 1.999999999825280872e+00 
-2 1 1 2 -3.095056099254819282e-01 
-2 1 1 3 8.388821521212311283e-02 
-2 1 1 4 8.388917358587567874e-02 
-2 1 2 2 4.789927494245199008e-02 
-2 1 2 3 -1.307058076260208049e-02 
-2 1 2 4 -1.290714134044862460e-02 
-2 1 3 3 2.971005649372479018e-01 
-2 1 3 4 -2.447309307272341194e-01 
-2 1 4 4 2.134402019028047992e-01 
-2 2 1 1 2.103712716147778344e-16 
-2 3 1 1 1.000000958427416542e+00 
-2 4 1 1 9.583793370118670507e-07 
-2 5 1 1 1.669900717227676154e-06 
-*** END ***
-*** REQUEST ***
-""
-4
-2
-3 1
--0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0
-0 1 2 2 0.10485760000000000000e7
-0 1 3 3 -0.10485760000000000000e7
-0 2 1 1 -0.10485760000000000000e7
-1 1 2 3 0.52428800000000000000e6
-1 1 3 3 -0.10485760000000000000e7
-2 1 2 2 0.10485760000000000000e7
-2 1 2 3 -0.52428800000000000000e6
-3 1 1 1 0.10485760000000000000e7
-3 1 2 2 -0.10485760000000000000e7
-3 1 3 3 0.10485760000000000000e7
-3 2 1 1 0.10485760000000000000e7
-4 1 1 2 -0.10485760000000000000e7
-4 1 1 3 0.10485760000000000000e7
-*** ANSWER ***
-9.999995669872646653e-01 9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00 
-1 1 1 1 3.962767353149487803e-08 
-1 1 2 2 4.540467642000610149e-01 
-1 1 2 3 4.540466709859902750e-01 
-1 1 3 3 4.540468014726645185e-01 
-1 2 1 1 1.048576000000039581e+06 
-2 1 1 1 9.999999999999281686e-01 
-2 1 2 2 2.500000307927105481e-01 
-2 1 2 3 -2.499999692072846225e-01 
-2 1 3 3 2.500000307927234822e-01 
-2 2 1 1 5.333451642288094782e-14 
+9.999995669872646653e-01 9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00 
+1 1 1 1 3.962767353149487803e-08 
+1 1 2 2 4.540467642000610149e-01 
+1 1 2 3 4.540466709859902750e-01 
+1 1 3 3 4.540468014726645185e-01 
+1 2 1 1 1.048576000000039581e+06 
+2 1 1 1 9.999999999999281686e-01 
+2 1 2 2 2.500000307927105481e-01 
+2 1 2 3 -2.499999692072846225e-01 
+2 1 3 3 2.500000307927234822e-01 
+2 2 1 1 5.333451642288094782e-14 
 *** END ***
 *** REQUEST ***
 ""
@@ -106175,374 +11736,9508 @@ Infeasible
 *** END ***
 *** REQUEST ***
 ""
-10
+10
+8
+5 1 1 1 1 1 1 1
+0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.10485760000000000000e7 0.0 0.26214400000000000000e6 0.52428800000000000000e6
+0 1 3 3 0.10485760000000000000e7
+0 1 4 4 -0.52428800000000000000e6
+0 2 1 1 -0.52428800000000000000e6
+1 1 3 3 0.10485760000000000000e7
+1 1 4 4 -0.52428800000000000000e6
+2 1 1 1 0.52428800000000000000e6
+2 1 3 3 -0.10485760000000000000e7
+2 1 4 4 0.52428800000000000000e6
+2 2 1 1 0.52428800000000000000e6
+3 1 1 2 0.52428800000000000000e6
+3 4 1 1 -0.10485760000000000000e7
+4 1 1 3 0.52428800000000000000e6
+4 6 1 1 -0.10485760000000000000e7
+5 1 2 2 0.52428800000000000000e6
+5 1 4 4 -0.52428800000000000000e6
+6 1 2 3 0.52428800000000000000e6
+6 8 1 1 -0.10485760000000000000e7
+7 1 2 4 0.52428800000000000000e6
+7 4 1 1 -0.10485760000000000000e7
+7 5 1 1 -0.10485760000000000000e7
+8 1 3 3 -0.52428800000000000000e6
+8 1 5 5 0.52428800000000000000e6
+9 1 1 4 -0.26214400000000000000e6
+9 1 3 3 0.10485760000000000000e7
+9 1 4 4 -0.52428800000000000000e6
+9 2 1 1 -0.52428800000000000000e6
+9 3 1 1 0.52428800000000000000e6
+10 1 3 4 -0.26214400000000000000e6
+10 6 1 1 0.52428800000000000000e6
+10 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+9.999999992564915230e-01 -3.810695576889143537e-10 -6.735625426342454187e-12 -5.444777627013238453e-12 4.367506358700158526e-11 1.227413030293301348e-10 1.401229005084607075e-10 -1.886153909364574320e-10 1.964397041031435087e-10 -2.684354364726813310e-10 
+1 1 1 1 6.957817438412523987e-05 
+1 1 1 2 -3.531407583526232621e-06 
+1 1 1 3 -2.854631572511516762e-06 
+1 1 1 4 -5.149548979241445196e-05 
+1 1 2 2 2.922666823836324659e-04 
+1 1 2 3 6.435179228264143771e-05 
+1 1 2 4 7.346475526177984744e-05 
+1 1 3 3 1.941943637436432425e-04 
+1 1 3 4 7.036873905869457484e-05 
+1 1 4 4 3.335015036236895630e-04 
+1 1 5 5 1.704795845624373744e-04 
+1 2 1 1 5.242879999665871728e+05 
+1 3 1 1 3.723593502305598893e-04 
+1 4 1 1 1.295016752892227258e-04 
+1 5 1 1 1.224388601221695558e-04 
+1 6 1 1 1.343401556733645440e-04 
+1 7 1 1 1.286308925283409683e-04 
+1 8 1 1 1.406647860804472426e-04 
+2 1 1 1 9.999999999048075905e-01 
+2 1 1 2 -9.795735713603917483e-02 
+2 1 1 3 -7.486315305695728783e-02 
+2 1 1 4 1.760541517543041112e-01 
+2 1 2 2 2.860587828470143590e-01 
+2 1 2 3 -6.792434344894913989e-02 
+2 1 2 4 -1.175060159893176470e-01 
+2 1 3 3 3.930293914235066244e-01 
+2 1 3 4 -1.011994963720127400e-01 
+2 1 4 4 2.860587828470145255e-01 
+2 1 5 5 3.930293914235067909e-01 
+2 2 1 1 9.519167358025126290e-11 
+2 3 1 1 1.760541518494961044e-01 
+2 4 1 1 4.020426428639607419e-01 
+2 5 1 1 4.804513411467217221e-01 
+2 6 1 1 4.251368469430427677e-01 
+2 7 1 1 4.736636566849445895e-01 
+2 8 1 1 4.320756565510509017e-01 
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+*** ANSWER ***
+5.000000006943153830e-01 
+1 1 1 1 1.290417214877562224e-03 
+1 2 1 1 2.621440009263960528e+05 
+1 3 1 1 2.621440009263960528e+05 
+1 4 1 1 5.623748076465434273e-04 
+2 1 1 1 9.999999999999984457e-01 
+2 2 1 1 1.665972352747017299e-15 
+2 3 1 1 1.665972352747017299e-15 
+2 4 1 1 1.637537031929143128e+00 
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.15728640000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.10485760000000000000e7
+1 4 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+0.10485760000000000000e7 0.52428800000000000000e6 0.26214400000000000000e6 0.10485760000000000000e7 0.13107200000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 1 0.10485760000000000000e7
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+2 1 1 2 -0.10485760000000000000e7
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+3 1 2 2 0.10485760000000000000e7
+3 1 2 3 -0.52428800000000000000e6
+3 6 1 1 -0.52428800000000000000e6
+4 1 2 3 -0.52428800000000000000e6
+4 1 3 3 0.10485760000000000000e7
+4 2 1 1 0.52428800000000000000e6
+4 4 1 1 0.52428800000000000000e6
+5 1 1 1 0.10485760000000000000e7
+5 1 1 2 -0.52428800000000000000e6
+5 2 1 1 0.52428800000000000000e6
+5 3 1 1 0.10485760000000000000e7
+6 1 1 2 -0.52428800000000000000e6
+6 5 1 1 0.10485760000000000000e7
+7 1 1 2 0.52428800000000000000e6
+7 1 2 3 -0.52428800000000000000e6
+7 7 1 1 0.10485760000000000000e7
+*** ANSWER ***
+9.999999985586283113e-01 -9.282233207833762598e-10 2.416410040619999275e-09 7.287384010613641448e-10 1.000000001150653572e+00 -1.678412777448631064e-10 9.999999957510178339e-01 
+1 1 1 1 2.123588660274164375e-03 
+1 1 1 2 -1.769654364154091275e-03 
+1 1 1 3 -9.733126968137495449e-04 
+1 1 2 2 3.450830535535617805e-03 
+1 1 2 3 -1.769670706440063662e-04 
+1 1 3 3 1.681178558413772006e-03 
+1 2 1 1 1.048576000173377106e+06 
+1 3 1 1 1.048576002123588696e+06 
+1 4 1 1 5.242880005434158957e+05 
+1 5 1 1 7.410466251298562790e-04 
+1 6 1 1 1.048575998138758354e+06 
+1 7 1 1 1.048575996461660252e+06 
+2 1 1 1 2.749999992995243225e+00 
+2 1 1 2 1.499999995096669370e+00 
+2 1 1 3 1.749999994396194358e+00 
+2 1 2 2 1.249999997198100399e+00 
+2 1 2 3 9.999999964976236111e-01 
+2 1 3 3 1.999999994396199687e+00 
+2 2 1 1 1.400950902881645464e-09 
+2 3 1 1 1.400951113825400542e-09 
+2 4 1 1 2.801898309253689249e-09 
+2 5 1 1 1.999999995096668037e+00 
+2 6 1 1 1.400952195814864889e-09 
+2 7 1 1 1.400955085529339772e-09 
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+-0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 2 1 1 -0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+1 4 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+-0.15728640000000000000e7 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 0.10485760000000000000e7 0.78643200000000000000e6 0.26214400000000000000e6
+0 1 1 1 0.10485760000000000000e7
+1 1 2 3 -0.52428800000000000000e6
+1 2 1 1 -0.10485760000000000000e7
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+1 6 1 1 -0.10485760000000000000e7
+2 1 1 2 -0.52428800000000000000e6
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+2 2 1 1 0.10485760000000000000e7
+3 1 2 2 0.10485760000000000000e7
+3 1 2 3 -0.10485760000000000000e7
+3 2 1 1 -0.10485760000000000000e7
+3 4 1 1 -0.10485760000000000000e7
+4 1 2 3 -0.26214400000000000000e6
+4 1 3 3 0.10485760000000000000e7
+4 6 1 1 0.52428800000000000000e6
+5 1 1 1 0.10485760000000000000e7
+5 1 1 2 -0.52428800000000000000e6
+5 3 1 1 0.10485760000000000000e7
+6 1 1 2 -0.26214400000000000000e6
+6 2 1 1 0.52428800000000000000e6
+6 5 1 1 0.10485760000000000000e7
+7 1 1 2 0.26214400000000000000e6
+7 1 2 3 -0.52428800000000000000e6
+7 2 1 1 -0.52428800000000000000e6
+7 7 1 1 0.10485760000000000000e7
+*** ANSWER ***
+-2.122682326267485209e+00 7.752558743508156103e-02 1.165856920741376257e+00 9.814639206878961880e-03 1.612372975707343281e+00 -5.204790215550311268e-10 3.519523024615122119e-08 
+1 1 1 1 6.421196079141121591e+05 
+1 1 1 2 -8.859935285101566697e+05 
+1 1 1 3 8.129147037032808294e+04 
+1 1 2 2 1.222489589062118437e+06 
+1 1 2 3 -1.121655822818670131e+05 
+1 1 3 3 1.029139765980135235e+04 
+1 2 1 1 1.084595610608764226e+06 
+1 3 1 1 1.690695607914112275e+06 
+1 4 1 1 1.003304158963754307e+06 
+1 5 1 1 1.993047227803988741e-03 
+1 6 1 1 2.230939443047560286e+06 
+1 7 1 1 3.944368278889842649e-02 
+2 1 1 1 4.259591772956758504e+00 
+2 1 1 2 3.259591775595432228e+00 
+2 1 1 3 1.879795885741197825e+00 
+2 1 2 2 2.499999987441589688e+00 
+2 1 2 3 1.499999989441199277e+00 
+2 1 3 3 1.499999993720805946e+00 
+2 2 1 1 4.113025632613441975e-09 
+2 3 1 1 2.638667510379978050e-09 
+2 4 1 1 4.446179952225849587e-09 
+2 5 1 1 2.379795885741203598e+00 
+2 6 1 1 1.999588384178727381e-09 
+2 7 1 1 1.202041036999986628e-01 
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.15728640000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+1 4 1 1 -0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+0.10485760000000000000e7 0.10485760000000000000e7 0.78643200000000000000e6 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 -0.26214400000000000000e6
+0 1 1 2 -0.39321600000000000000e6
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+2 1 1 2 0.26214400000000000000e6
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+2 1 2 3 0.26214400000000000000e6
+2 2 1 1 0.52428800000000000000e6
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+2 6 1 1 0.10485760000000000000e7
+3 1 1 2 0.26214400000000000000e6
+3 1 2 2 0.52428800000000000000e6
+3 1 2 3 -0.26214400000000000000e6
+3 2 1 1 0.52428800000000000000e6
+3 4 1 1 0.52428800000000000000e6
+4 1 1 2 0.13107200000000000000e6
+4 1 2 3 -0.13107200000000000000e6
+4 1 3 3 0.52428800000000000000e6
+4 2 1 1 0.26214400000000000000e6
+4 4 1 1 0.26214400000000000000e6
+5 1 1 2 -0.65536000000000000000e6
+5 1 2 3 -0.13107200000000000000e6
+5 2 1 1 -0.78643200000000000000e6
+5 3 1 1 0.52428800000000000000e6
+5 4 1 1 -0.26214400000000000000e6
+5 6 1 1 -0.52428800000000000000e6
+6 1 1 2 0.13107200000000000000e6
+6 1 2 3 0.13107200000000000000e6
+6 2 1 1 0.26214400000000000000e6
+6 4 1 1 0.26214400000000000000e6
+6 5 1 1 0.52428800000000000000e6
+6 6 1 1 0.52428800000000000000e6
+7 1 1 2 -0.13107200000000000000e6
+7 1 2 3 -0.39321600000000000000e6
+7 2 1 1 -0.26214400000000000000e6
+7 4 1 1 -0.26214400000000000000e6
+7 6 1 1 -0.52428800000000000000e6
+7 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-7.608360275419644920e-10 -7.798072457369716546e-11 -8.013859884436968844e-10 -7.171668043536295414e-10 5.714285702070482920e-01 -7.988172012271727674e-10 1.428571434699175968e-01 
+1 1 1 1 5.560274682077934530e-05 
+1 1 1 2 -8.176870375087877353e-06 
+1 1 1 3 -4.088435812529453948e-05 
+1 1 2 2 3.434288891953024645e-05 
+1 1 2 3 -1.635386148034894142e-06 
+1 1 3 3 7.849799650774358199e-05 
+1 2 1 1 2.995931426548591116e+05 
+1 3 1 1 2.995931426712128450e+05 
+1 4 1 1 7.489828527046926320e+04 
+1 5 1 1 3.568967323170778479e-05 
+1 6 1 1 1.497965713027546590e+05 
+1 7 1 1 7.489828649005611078e+04 
+2 1 1 1 1.357142856728937641e+00 
+2 1 1 2 3.571428568738232445e-01 
+2 1 1 3 7.142857137476383844e-01 
+2 1 2 2 1.357142856728940306e+00 
+2 1 2 3 2.142857143271021947e-01 
+2 1 3 3 9.285714283644747047e-01 
+2 2 1 1 1.448673344637826035e-10 
+2 3 1 1 1.448673288269433621e-10 
+2 4 1 1 5.794697349261452038e-10 
+2 5 1 1 1.214285713747635498e+00 
+2 6 1 1 2.897347029504898006e-10 
+2 7 1 1 5.794683254243045175e-10 
+*** END ***
+*** REQUEST ***
+""
+5
+5
+3 1 1 1 1
+0.10485760000000000000e7 -0.10485760000000000000e7 -0.52428800000000000000e6 0.0 0.10485760000000000000e7
+0 2 1 1 -0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 2 1 1 0.52428800000000000000e6
+2 1 1 2 0.52428800000000000000e6
+2 4 1 1 -0.10485760000000000000e7
+3 1 2 2 -0.10485760000000000000e7
+3 1 3 3 0.52428800000000000000e6
+4 1 1 3 -0.26214400000000000000e6
+4 2 1 1 -0.52428800000000000000e6
+4 3 1 1 0.52428800000000000000e6
+5 1 2 3 -0.26214400000000000000e6
+5 4 1 1 0.52428800000000000000e6
+5 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-4.457229613295930973e-10 6.115897346811394566e-17 1.833869924093994424e-10 -3.451031505601001684e-16 -4.457225765264029824e-10 
+1 1 1 1 1.376100633449915924e-10 
+1 1 1 2 3.206491588165052434e-11 
+1 1 1 3 9.046672030042689854e-11 
+1 1 2 2 4.139213860695481126e-05 
+1 1 2 3 1.168434991009373834e-04 
+1 1 3 3 3.298349370359715885e-04 
+1 2 1 1 5.242880000000003492e+05 
+1 3 1 1 2.336871566261909672e-04 
+1 4 1 1 2.752279266958520360e-10 
+1 5 1 1 3.393577580175436896e-10 
+2 1 1 1 2.000000000038513637e+00 
+2 1 1 2 1.679352122297247312e-04 
+2 1 1 3 2.183096486070790850e-06 
+2 1 2 2 5.333764953618103100e-01 
+2 1 2 3 -1.886894755874139185e-01 
+2 1 3 3 6.675299065681922217e-02 
+2 2 1 1 5.248430535658322443e-16 
+2 3 1 1 2.183106356807534618e-06 
+2 4 1 1 1.000167935332526570e+00 
+2 5 1 1 8.111425888609598012e-01 
+*** END ***
+*** REQUEST ***
+""
+1
+1
+7
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 -0.10000000000000000000e1
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.0
+0 1 6 6 0.10000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.10000000000000000000e1
+1 1 3 3 0.0
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.10000000000000000000e1
+1 1 6 6 0.0
+1 1 7 7 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+1
+1
+7
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.10000000000000000000e1
+0 1 3 3 0.0
+0 1 4 4 0.10000000000000000000e1
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+0 1 6 6 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 -0.10000000000000000000e1
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.0
+1 1 6 6 0.10000000000000000000e1
+1 1 7 7 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 0.0
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+0 1 5 5 0.0
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+1 1 2 2 -0.10000000000000000000e1
+1 1 3 3 0.0
+1 1 4 4 0.10000000000000000000e1
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+1 1 6 6 0.0
+1 1 7 7 0.10000000000000000000e1
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+2 1 2 2 0.0
+2 1 3 3 -0.10000000000000000000e1
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.0
+2 1 6 6 0.10000000000000000000e1
+2 1 8 8 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 -0.20000000000000000000e1
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+0 1 5 5 0.0
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+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.10000000000000000000e1
+1 1 3 3 0.0
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+1 1 6 6 0.0
+1 1 7 7 0.10000000000000000000e1
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+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.0
+2 1 6 6 0.10000000000000000000e1
+2 1 8 8 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 0.0
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.20000000000000000000e1
+0 1 6 6 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.10000000000000000000e1
+1 1 3 3 0.0
+1 1 4 4 0.10000000000000000000e1
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+1 1 6 6 0.0
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+2 1 2 2 0.0
+2 1 3 3 -0.10000000000000000000e1
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.0
+2 1 6 6 0.10000000000000000000e1
+2 1 8 8 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
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+0 1 4 4 0.10000000000000000000e1
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+0 1 6 6 0.20000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.10000000000000000000e1
+1 1 3 3 0.0
+1 1 4 4 0.10000000000000000000e1
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+1 1 6 6 0.0
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 0.0
+2 1 3 3 -0.10000000000000000000e1
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.0
+2 1 6 6 0.10000000000000000000e1
+2 1 8 8 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+1
+1
+5
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 0.10000000000000000000e1
+0 1 4 4 0.20000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 0.10000000000000000000e1
+1 1 4 4 0.0
+1 1 5 5 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+1
+1
+5
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
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+0 1 4 4 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.20000000000000000000e1
+1 1 3 3 0.10000000000000000000e1
+1 1 4 4 0.20000000000000000000e1
+1 1 5 5 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+6
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.10000000000000000000e1
+0 1 3 3 0.10000000000000000000e1
+0 1 4 4 0.10000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 0.10000000000000000000e1
+1 1 4 4 0.0
+1 1 5 5 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.10000000000000000000e1
+2 1 4 4 0.20000000000000000000e1
+2 1 6 6 0.10000000000000000000e1
+*** ANSWER ***
+4.999999992068303034e-01 4.999999999999717448e-01 
+1 1 1 1 2.234855962115750234e-09 
+1 1 2 2 1.441714466032480548e-09 
+1 1 3 3 6.484598716445790825e-10 
+1 1 4 4 1.441601382173089094e-09 
+1 1 5 5 5.000000006484882631e-01 
+1 1 6 6 5.000000014416297045e-01 
+2 1 1 1 2.430636066597300915e-01 
+2 1 2 2 6.491689746068749489e-01 
+2 1 3 3 1.243063605282559214e+00 
+2 1 4 4 6.491689746068740607e-01 
+2 1 5 5 1.377170993508608760e-09 
+2 1 6 6 1.377172611291298374e-09 
+*** END ***
+*** REQUEST ***
+""
+2
+1
+6
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 0.10000000000000000000e1
+0 1 4 4 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 0.10000000000000000000e1
+1 1 4 4 0.0
+1 1 5 5 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.10000000000000000000e1
+2 1 4 4 0.20000000000000000000e1
+2 1 6 6 0.10000000000000000000e1
+*** ANSWER ***
+9.999999994936811243e-01 9.682230762383211618e-11 
+1 1 1 1 1.309904697678035410e-09 
+1 1 2 2 7.067635777442771991e-10 
+1 1 3 3 4.909117361428470945e-10 
+1 1 4 4 1.094052808239612281e-09 
+1 1 5 5 1.000000000394089428e+00 
+1 1 6 6 9.972305006157776836e-10 
+2 1 1 1 4.222498665480665103e-01 
+2 1 2 2 1.100973461369222361e+00 
+2 1 3 3 1.422249865900061749e+00 
+2 1 4 4 7.109544607945516015e-01 
+2 1 5 5 6.480049172985338255e-10 
+2 1 6 6 7.800380017973469471e-01 
+*** END ***
+*** REQUEST ***
+""
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+*** REQUEST ***
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+*** END ***
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+Infeasible
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+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
+""
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+Infeasible
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+*** REQUEST ***
+""
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
+""
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+Infeasible
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+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+Infeasible
+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+*** END ***
+*** REQUEST ***
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+Infeasible
+*** END ***
+*** REQUEST ***
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+Infeasible
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+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+Infeasible
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+*** REQUEST ***
+""
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+Infeasible
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+*** REQUEST ***
+""
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+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+-5.556890788244735801e-11 9.999999998126090084e-01 
+1 1 1 1 1.371766850022979014e-09 
+1 1 2 2 1.239944655225034812e-09 
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+2 1 7 7 9.036829141458061487e-01 
+2 1 8 8 8.319933258656564673e-10 
+*** END ***
+*** REQUEST ***
+""
+2
+1
 8
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 *** ANSWER ***
-9.999999992564915230e-01 -3.810695576889143537e-10 -6.735625426342454187e-12 -5.444777627013238453e-12 4.367506358700158526e-11 1.227413030293301348e-10 1.401229005084607075e-10 -1.886153909364574320e-10 1.964397041031435087e-10 -2.684354364726813310e-10 
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+2 1 7 7 8.319966659598644703e-10 
+2 1 8 8 9.036829867678720651e-01 
 *** END ***
 *** REQUEST ***
 ""
+2
 1
-4
-1 1 1 1
-0.10485760000000000000e7
-0 1 1 1 0.52428800000000000000e6
-1 1 1 1 0.10485760000000000000e7
-1 2 1 1 0.52428800000000000000e6
-1 3 1 1 0.52428800000000000000e6
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 -0.20000000000000000000e1
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.20000000000000000000e1
+0 1 6 6 0.20000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 -0.20000000000000000000e1
+1 1 3 3 0.0
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.20000000000000000000e1
+1 1 6 6 0.0
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 0.0
+2 1 3 3 -0.20000000000000000000e1
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.0
+2 1 6 6 0.20000000000000000000e1
+2 1 8 8 0.10000000000000000000e1
 *** ANSWER ***
-5.000000006943153830e-01 
-1 1 1 1 1.290417214877562224e-03 
-1 2 1 1 2.621440009263960528e+05 
-1 3 1 1 2.621440009263960528e+05 
-1 4 1 1 5.623748076465434273e-04 
-2 1 1 1 9.999999999999984457e-01 
-2 2 1 1 1.665972352747017299e-15 
-2 3 1 1 1.665972352747017299e-15 
-2 4 1 1 1.637537031929143128e+00 
+Infeasible
 *** END ***
 *** REQUEST ***
 ""
+2
 1
-4
-1 1 1 1
-0.15728640000000000000e7
-0 1 1 1 0.10485760000000000000e7
-1 1 1 1 0.10485760000000000000e7
-1 2 1 1 0.52428800000000000000e6
-1 3 1 1 0.10485760000000000000e7
-1 4 1 1 -0.10485760000000000000e7
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 0.0
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.0
+0 1 6 6 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 -0.20000000000000000000e1
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.0
+1 1 6 6 0.20000000000000000000e1
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.0
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.20000000000000000000e1
+2 1 6 6 0.0
+2 1 8 8 0.10000000000000000000e1
 *** ANSWER ***
 Infeasible
 *** END ***
 *** REQUEST ***
 ""
-7
-7
-3 1 1 1 1 1 1
-0.10485760000000000000e7 0.52428800000000000000e6 0.26214400000000000000e6 0.10485760000000000000e7 0.13107200000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
-0 1 1 1 0.10485760000000000000e7
-1 1 2 3 0.52428800000000000000e6
-1 2 1 1 0.52428800000000000000e6
-1 4 1 1 0.52428800000000000000e6
-1 6 1 1 0.10485760000000000000e7
-2 1 1 2 -0.10485760000000000000e7
-2 1 1 3 0.10485760000000000000e7
-2 2 1 1 0.10485760000000000000e7
-3 1 2 2 0.10485760000000000000e7
-3 1 2 3 -0.52428800000000000000e6
-3 6 1 1 -0.52428800000000000000e6
-4 1 2 3 -0.52428800000000000000e6
-4 1 3 3 0.10485760000000000000e7
-4 2 1 1 0.52428800000000000000e6
-4 4 1 1 0.52428800000000000000e6
-5 1 1 1 0.10485760000000000000e7
-5 1 1 2 -0.52428800000000000000e6
-5 2 1 1 0.52428800000000000000e6
-5 3 1 1 0.10485760000000000000e7
-6 1 1 2 -0.52428800000000000000e6
-6 5 1 1 0.10485760000000000000e7
-7 1 1 2 0.52428800000000000000e6
-7 1 2 3 -0.52428800000000000000e6
-7 7 1 1 0.10485760000000000000e7
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 0.0
+0 1 3 3 -0.20000000000000000000e1
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.0
+0 1 6 6 0.20000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 -0.20000000000000000000e1
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.0
+1 1 6 6 0.20000000000000000000e1
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.0
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.20000000000000000000e1
+2 1 6 6 0.0
+2 1 8 8 0.10000000000000000000e1
+*** ANSWER ***
+9.999999998126088974e-01 -5.556900459200294288e-11 
+1 1 1 1 1.371768075283454030e-09 
+1 1 2 2 1.239945918359582213e-09 
+1 1 3 3 1.503590213300041686e-09 
+1 1 4 4 8.858478070408223231e-10 
+1 1 5 5 1.017669899991571269e-09 
+1 1 6 6 7.540257960484817367e-10 
+1 1 7 7 1.000000000941416722e+00 
+1 1 8 8 1.073238904583577314e-09 
+2 1 1 1 8.264668397480413597e-01 
+2 1 2 2 9.284018756793208649e-01 
+2 1 3 3 7.440682187553763205e-01 
+2 1 4 4 1.003750962326673601e+00 
+2 1 5 5 8.879183499986768036e-01 
+2 1 6 6 1.155426157050063019e+00 
+2 1 7 7 8.319939589806611944e-10 
+2 1 8 8 9.036829287826558810e-01 
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 0.0
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.20000000000000000000e1
+0 1 6 6 0.0
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 -0.20000000000000000000e1
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.0
+1 1 6 6 0.20000000000000000000e1
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.0
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.20000000000000000000e1
+2 1 6 6 0.0
+2 1 8 8 0.10000000000000000000e1
 *** ANSWER ***
-9.999999985586283113e-01 -9.282233207833762598e-10 2.416410040619999275e-09 7.287384010613641448e-10 1.000000001150653572e+00 -1.678412777448631064e-10 9.999999957510178339e-01 
-1 1 1 1 2.123588660274164375e-03 
-1 1 1 2 -1.769654364154091275e-03 
-1 1 1 3 -9.733126968137495449e-04 
-1 1 2 2 3.450830535535617805e-03 
-1 1 2 3 -1.769670706440063662e-04 
-1 1 3 3 1.681178558413772006e-03 
-1 2 1 1 1.048576000173377106e+06 
-1 3 1 1 1.048576002123588696e+06 
-1 4 1 1 5.242880005434158957e+05 
-1 5 1 1 7.410466251298562790e-04 
-1 6 1 1 1.048575998138758354e+06 
-1 7 1 1 1.048575996461660252e+06 
-2 1 1 1 2.749999992995243225e+00 
-2 1 1 2 1.499999995096669370e+00 
-2 1 1 3 1.749999994396194358e+00 
-2 1 2 2 1.249999997198100399e+00 
-2 1 2 3 9.999999964976236111e-01 
-2 1 3 3 1.999999994396199687e+00 
-2 2 1 1 1.400950902881645464e-09 
-2 3 1 1 1.400951113825400542e-09 
-2 4 1 1 2.801898309253689249e-09 
-2 5 1 1 1.999999995096668037e+00 
-2 6 1 1 1.400952195814864889e-09 
-2 7 1 1 1.400955085529339772e-09 
+-5.556891800422891315e-11 9.999999998126090084e-01 
+1 1 1 1 1.371766834908556190e-09 
+1 1 2 2 1.503588811560894002e-09 
+1 1 3 3 1.239944722019174444e-09 
+1 1 4 4 8.858468417542438861e-10 
+1 1 5 5 7.540251988850989329e-10 
+1 1 6 6 1.017669050002260653e-09 
+1 1 7 7 1.073237968006482483e-09 
+1 1 8 8 1.000000000941415834e+00 
+2 1 1 1 8.264668205471025209e-01 
+2 1 2 2 7.440682022098322745e-01 
+2 1 3 3 9.284018576700705516e-01 
+2 1 4 4 1.003750951780127076e+00 
+2 1 5 5 1.155426136177322816e+00 
+2 1 6 6 8.879183348606732862e-01 
+2 1 7 7 9.036829143857701974e-01 
+2 1 8 8 8.319933256754810271e-10 
 *** END ***
 *** REQUEST ***
 ""
+2
 1
-4
-1 1 1 1
--0.10485760000000000000e7
-0 1 1 1 0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 2 1 1 -0.52428800000000000000e6
-1 3 1 1 0.52428800000000000000e6
-1 4 1 1 -0.10485760000000000000e7
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
+0 1 1 1 -0.10000000000000000000e1
+0 1 2 2 -0.20000000000000000000e1
+0 1 3 3 -0.20000000000000000000e1
+0 1 4 4 0.10000000000000000000e1
+0 1 5 5 0.20000000000000000000e1
+0 1 6 6 0.20000000000000000000e1
+1 1 1 1 -0.10000000000000000000e1
+1 1 2 2 0.0
+1 1 3 3 -0.20000000000000000000e1
+1 1 4 4 0.10000000000000000000e1
+1 1 5 5 0.0
+1 1 6 6 0.20000000000000000000e1
+1 1 7 7 0.10000000000000000000e1
+2 1 1 1 -0.10000000000000000000e1
+2 1 2 2 -0.20000000000000000000e1
+2 1 3 3 0.0
+2 1 4 4 0.10000000000000000000e1
+2 1 5 5 0.20000000000000000000e1
+2 1 6 6 0.0
+2 1 8 8 0.10000000000000000000e1
 *** ANSWER ***
 Infeasible
 *** END ***
 *** REQUEST ***
 ""
-7
-7
-3 1 1 1 1 1 1
--0.15728640000000000000e7 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 0.10485760000000000000e7 0.78643200000000000000e6 0.26214400000000000000e6
-0 1 1 1 0.10485760000000000000e7
-1 1 2 3 -0.52428800000000000000e6
-1 2 1 1 -0.10485760000000000000e7
-1 4 1 1 -0.10485760000000000000e7
-1 6 1 1 -0.10485760000000000000e7
-2 1 1 2 -0.52428800000000000000e6
-2 1 1 3 0.10485760000000000000e7
-2 2 1 1 0.10485760000000000000e7
-3 1 2 2 0.10485760000000000000e7
-3 1 2 3 -0.10485760000000000000e7
-3 2 1 1 -0.10485760000000000000e7
-3 4 1 1 -0.10485760000000000000e7
-4 1 2 3 -0.26214400000000000000e6
-4 1 3 3 0.10485760000000000000e7
-4 6 1 1 0.52428800000000000000e6
-5 1 1 1 0.10485760000000000000e7
-5 1 1 2 -0.52428800000000000000e6
-5 3 1 1 0.10485760000000000000e7
-6 1 1 2 -0.26214400000000000000e6
-6 2 1 1 0.52428800000000000000e6
-6 5 1 1 0.10485760000000000000e7
-7 1 1 2 0.26214400000000000000e6
-7 1 2 3 -0.52428800000000000000e6
-7 2 1 1 -0.52428800000000000000e6
-7 7 1 1 0.10485760000000000000e7
+5
+5
+4 1 1 1 1
+0.16384000000000000000e6 0.98304000000000000000e6 -0.19660800000000000000e6 -0.14745600000000000000e7 0.98304000000000000000e6
+0 1 2 2 -0.32768000000000000000e6
+0 1 4 4 0.32768000000000000000e6
+0 2 1 1 -0.32768000000000000000e6
+0 4 1 1 0.98304000000000000000e6
+1 1 1 1 0.98304000000000000000e6
+1 1 2 2 0.32768000000000000000e6
+1 1 4 4 -0.32768000000000000000e6
+1 2 1 1 0.32768000000000000000e6
+1 4 1 1 -0.98304000000000000000e6
+2 1 1 2 0.98304000000000000000e6
+2 1 1 4 -0.98304000000000000000e6
+2 4 1 1 0.19660800000000000000e7
+3 1 1 3 0.98304000000000000000e6
+3 1 1 4 -0.58982400000000000000e6
+3 1 4 4 -0.39321600000000000000e6
+4 1 2 2 -0.98304000000000000000e6
+4 1 2 4 0.98304000000000000000e6
+4 1 4 4 -0.98304000000000000000e6
+4 5 1 1 -0.98304000000000000000e6
+5 3 1 1 0.98304000000000000000e6
+5 4 1 1 0.98304000000000000000e6
 *** ANSWER ***
--2.122682326267485209e+00 7.752558743508156103e-02 1.165856920741376257e+00 9.814639206878961880e-03 1.612372975707343281e+00 -5.204790215550311268e-10 3.519523024615122119e-08 
-1 1 1 1 6.421196079141121591e+05 
-1 1 1 2 -8.859935285101566697e+05 
-1 1 1 3 8.129147037032808294e+04 
-1 1 2 2 1.222489589062118437e+06 
-1 1 2 3 -1.121655822818670131e+05 
-1 1 3 3 1.029139765980135235e+04 
-1 2 1 1 1.084595610608764226e+06 
-1 3 1 1 1.690695607914112275e+06 
-1 4 1 1 1.003304158963754307e+06 
-1 5 1 1 1.993047227803988741e-03 
-1 6 1 1 2.230939443047560286e+06 
-1 7 1 1 3.944368278889842649e-02 
-2 1 1 1 4.259591772956758504e+00 
-2 1 1 2 3.259591775595432228e+00 
-2 1 1 3 1.879795885741197825e+00 
-2 1 2 2 2.499999987441589688e+00 
-2 1 2 3 1.499999989441199277e+00 
-2 1 3 3 1.499999993720805946e+00 
-2 2 1 1 4.113025632613441975e-09 
-2 3 1 1 2.638667510379978050e-09 
-2 4 1 1 4.446179952225849587e-09 
-2 5 1 1 2.379795885741203598e+00 
-2 6 1 1 1.999588384178727381e-09 
-2 7 1 1 1.202041036999986628e-01 
+Failure
 *** END ***
 *** REQUEST ***
 ""
-1
-4
-1 1 1 1
-0.15728640000000000000e7
-0 1 1 1 0.52428800000000000000e6
-1 1 1 1 0.10485760000000000000e7
-1 2 1 1 0.52428800000000000000e6
-1 3 1 1 0.52428800000000000000e6
-1 4 1 1 -0.52428800000000000000e6
+20
+7
+4 1 4 1 4 1 1
+0.98304000000000000000e6 0.13107200000000000000e7 -0.39321600000000000000e6 0.0 -0.19660800000000000000e7 0.98304000000000000000e6 0.0 0.0 0.19660800000000000000e7 0.19660800000000000000e7 0.19660800000000000000e7 0.98304000000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.19660800000000000000e7 0.98304000000000000000e6
+0 1 1 2 -0.24576000000000000000e6
+0 1 1 4 0.24576000000000000000e6
+0 2 1 1 -0.16384000000000000000e6
+0 3 1 2 -0.81920000000000000000e5
+0 5 1 4 0.81920000000000000000e5
+1 1 2 3 0.12288000000000000000e7
+1 1 3 4 -0.12288000000000000000e7
+1 5 1 4 0.73728000000000000000e6
+1 5 4 4 0.49152000000000000000e6
+2 1 1 1 0.49152000000000000000e6
+2 1 1 2 0.24576000000000000000e6
+2 1 1 4 -0.24576000000000000000e6
+2 2 1 1 0.16384000000000000000e6
+2 3 1 2 0.81920000000000000000e5
+2 5 1 4 -0.81920000000000000000e5
+3 1 1 3 0.49152000000000000000e6
+3 1 1 4 -0.29491200000000000000e6
+3 1 4 4 -0.19660800000000000000e6
+4 1 2 2 0.49152000000000000000e6
+4 1 4 4 -0.49152000000000000000e6
+4 3 1 2 -0.24576000000000000000e6
+4 5 1 4 0.24576000000000000000e6
+5 1 2 4 0.49152000000000000000e6
+5 1 4 4 -0.98304000000000000000e6
+5 5 1 4 0.49152000000000000000e6
+6 1 1 2 -0.24576000000000000000e6
+6 1 1 4 0.24576000000000000000e6
+6 3 1 1 0.49152000000000000000e6
+7 1 2 3 -0.49152000000000000000e6
+7 1 3 4 0.49152000000000000000e6
+7 3 1 3 0.49152000000000000000e6
+8 3 1 4 0.49152000000000000000e6
+8 5 1 4 0.49152000000000000000e6
+9 1 1 2 0.73728000000000000000e6
+9 1 1 4 -0.73728000000000000000e6
+9 1 2 3 -0.12288000000000000000e7
+9 1 3 4 0.12288000000000000000e7
+9 3 1 2 0.73728000000000000000e6
+9 3 2 2 0.49152000000000000000e6
+9 4 1 1 0.49152000000000000000e6
+10 3 3 3 0.49152000000000000000e6
+10 5 3 3 0.49152000000000000000e6
+11 3 4 4 0.49152000000000000000e6
+11 5 4 4 0.49152000000000000000e6
+12 1 1 2 0.24576000000000000000e6
+12 1 1 4 -0.24576000000000000000e6
+12 5 1 1 0.49152000000000000000e6
+13 3 1 2 0.49152000000000000000e6
+13 5 1 2 0.49152000000000000000e6
+14 1 2 3 0.49152000000000000000e6
+14 1 3 4 -0.49152000000000000000e6
+14 5 1 3 0.49152000000000000000e6
+15 1 1 2 -0.73728000000000000000e6
+15 1 1 4 0.73728000000000000000e6
+15 1 2 3 0.12288000000000000000e7
+15 1 3 4 -0.12288000000000000000e7
+15 3 1 2 -0.73728000000000000000e6
+15 4 1 1 -0.49152000000000000000e6
+15 5 2 2 0.49152000000000000000e6
+16 3 2 3 0.49152000000000000000e6
+16 5 2 3 0.49152000000000000000e6
+17 3 2 4 0.49152000000000000000e6
+17 5 2 4 0.49152000000000000000e6
+18 3 3 4 0.49152000000000000000e6
+18 5 3 4 0.49152000000000000000e6
+19 4 1 1 0.49152000000000000000e6
+19 6 1 1 0.49152000000000000000e6
+20 3 1 2 0.24576000000000000000e6
+20 5 1 4 0.24576000000000000000e6
+20 7 1 1 0.49152000000000000000e6
 *** ANSWER ***
-Infeasible
+Failure
 *** END ***
 *** REQUEST ***
 ""
-7
-7
-3 1 1 1 1 1 1
-0.10485760000000000000e7 0.10485760000000000000e7 0.78643200000000000000e6 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 -0.26214400000000000000e6
-0 1 1 2 -0.39321600000000000000e6
-0 1 2 3 -0.13107200000000000000e6
-0 2 1 1 -0.78643200000000000000e6
-0 4 1 1 -0.26214400000000000000e6
-0 6 1 1 -0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 1 1 2 0.39321600000000000000e6
-1 1 2 3 0.13107200000000000000e6
-1 2 1 1 0.78643200000000000000e6
-1 4 1 1 0.26214400000000000000e6
-1 6 1 1 0.52428800000000000000e6
-2 1 1 2 0.26214400000000000000e6
-2 1 1 3 0.52428800000000000000e6
-2 1 2 3 0.26214400000000000000e6
-2 2 1 1 0.52428800000000000000e6
-2 4 1 1 0.52428800000000000000e6
-2 6 1 1 0.10485760000000000000e7
-3 1 1 2 0.26214400000000000000e6
-3 1 2 2 0.52428800000000000000e6
-3 1 2 3 -0.26214400000000000000e6
-3 2 1 1 0.52428800000000000000e6
-3 4 1 1 0.52428800000000000000e6
-4 1 1 2 0.13107200000000000000e6
-4 1 2 3 -0.13107200000000000000e6
-4 1 3 3 0.52428800000000000000e6
-4 2 1 1 0.26214400000000000000e6
-4 4 1 1 0.26214400000000000000e6
-5 1 1 2 -0.65536000000000000000e6
-5 1 2 3 -0.13107200000000000000e6
-5 2 1 1 -0.78643200000000000000e6
-5 3 1 1 0.52428800000000000000e6
-5 4 1 1 -0.26214400000000000000e6
-5 6 1 1 -0.52428800000000000000e6
-6 1 1 2 0.13107200000000000000e6
-6 1 2 3 0.13107200000000000000e6
-6 2 1 1 0.26214400000000000000e6
-6 4 1 1 0.26214400000000000000e6
-6 5 1 1 0.52428800000000000000e6
-6 6 1 1 0.52428800000000000000e6
-7 1 1 2 -0.13107200000000000000e6
-7 1 2 3 -0.39321600000000000000e6
-7 2 1 1 -0.26214400000000000000e6
-7 4 1 1 -0.26214400000000000000e6
-7 6 1 1 -0.52428800000000000000e6
-7 7 1 1 0.52428800000000000000e6
+2
+3
+2 1 1
+0.78643200000000000000e6 -0.18350080000000000000e7
+0 1 2 2 -0.26214400000000000000e6
+0 2 1 1 -0.26214400000000000000e6
+1 1 1 1 0.26214400000000000000e6
+1 1 2 2 0.26214400000000000000e6
+1 2 1 1 0.26214400000000000000e6
+2 1 1 2 -0.13107200000000000000e6
+2 1 2 2 -0.10485760000000000000e7
+2 2 1 1 -0.10485760000000000000e7
+2 3 1 1 0.26214400000000000000e6
 *** ANSWER ***
--7.608360275419644920e-10 -7.798072457369716546e-11 -8.013859884436968844e-10 -7.171668043536295414e-10 5.714285702070482920e-01 -7.988172012271727674e-10 1.428571434699175968e-01 
-1 1 1 1 5.560274682077934530e-05 
-1 1 1 2 -8.176870375087877353e-06 
-1 1 1 3 -4.088435812529453948e-05 
-1 1 2 2 3.434288891953024645e-05 
-1 1 2 3 -1.635386148034894142e-06 
-1 1 3 3 7.849799650774358199e-05 
-1 2 1 1 2.995931426548591116e+05 
-1 3 1 1 2.995931426712128450e+05 
-1 4 1 1 7.489828527046926320e+04 
-1 5 1 1 3.568967323170778479e-05 
-1 6 1 1 1.497965713027546590e+05 
-1 7 1 1 7.489828649005611078e+04 
-2 1 1 1 1.357142856728937641e+00 
-2 1 1 2 3.571428568738232445e-01 
-2 1 1 3 7.142857137476383844e-01 
-2 1 2 2 1.357142856728940306e+00 
-2 1 2 3 2.142857143271021947e-01 
-2 1 3 3 9.285714283644747047e-01 
-2 2 1 1 1.448673344637826035e-10 
-2 3 1 1 1.448673288269433621e-10 
-2 4 1 1 5.794697349261452038e-10 
-2 5 1 1 1.214285713747635498e+00 
-2 6 1 1 2.897347029504898006e-10 
-2 7 1 1 5.794683254243045175e-10 
+1.127570111857972568e-01 2.449355441053016891e-01 
+1 1 1 1 2.955857394028963608e+04 
+1 1 1 2 -3.210419163697010299e+04 
+1 1 2 2 3.486904084452883399e+04 
+1 2 1 1 3.486904084452883399e+04 
+1 3 1 1 6.420838327394020598e+04 
+2 1 1 1 1.623722218783865356e+00 
+2 1 1 2 1.494888884982461086e+00 
+2 1 2 2 1.376277763118065600e+00 
+2 2 1 1 1.809839237968250559e-08 
+2 3 1 1 9.854620231493015123e-09 
 *** END ***
 *** REQUEST ***
 ""
-5
-5
-3 1 1 1 1
-0.10485760000000000000e7 -0.10485760000000000000e7 -0.52428800000000000000e6 0.0 0.10485760000000000000e7
+4
+2
+3 1
+-0.78643200000000000000e6 0.78643200000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 0.52428800000000000000e6
+0 1 3 3 -0.52428800000000000000e6
 0 2 1 1 -0.52428800000000000000e6
-1 1 1 1 0.52428800000000000000e6
-1 2 1 1 0.52428800000000000000e6
-2 1 1 2 0.52428800000000000000e6
-2 4 1 1 -0.10485760000000000000e7
-3 1 2 2 -0.10485760000000000000e7
+1 1 2 3 0.78643200000000000000e6
+1 1 3 3 -0.15728640000000000000e7
+2 1 2 2 0.15728640000000000000e7
+2 1 2 3 -0.78643200000000000000e6
+3 1 1 1 0.15728640000000000000e7
+3 1 2 2 -0.52428800000000000000e6
 3 1 3 3 0.52428800000000000000e6
-4 1 1 3 -0.26214400000000000000e6
-4 2 1 1 -0.52428800000000000000e6
-4 3 1 1 0.52428800000000000000e6
-5 1 2 3 -0.26214400000000000000e6
-5 4 1 1 0.52428800000000000000e6
-5 5 1 1 0.52428800000000000000e6
+3 2 1 1 0.52428800000000000000e6
+4 1 1 2 -0.15728640000000000000e7
+4 1 1 3 0.15728640000000000000e7
 *** ANSWER ***
--4.457229613295930973e-10 6.115897346811394566e-17 1.833869924093994424e-10 -3.451031505601001684e-16 -4.457225765264029824e-10 
-1 1 1 1 1.376100633449915924e-10 
-1 1 1 2 3.206491588165052434e-11 
-1 1 1 3 9.046672030042689854e-11 
-1 1 2 2 4.139213860695481126e-05 
-1 1 2 3 1.168434991009373834e-04 
-1 1 3 3 3.298349370359715885e-04 
-1 2 1 1 5.242880000000003492e+05 
-1 3 1 1 2.336871566261909672e-04 
-1 4 1 1 2.752279266958520360e-10 
-1 5 1 1 3.393577580175436896e-10 
-2 1 1 1 2.000000000038513637e+00 
-2 1 1 2 1.679352122297247312e-04 
-2 1 1 3 2.183096486070790850e-06 
-2 1 2 2 5.333764953618103100e-01 
-2 1 2 3 -1.886894755874139185e-01 
-2 1 3 3 6.675299065681922217e-02 
-2 2 1 1 5.248430535658322443e-16 
-2 3 1 1 2.183106356807534618e-06 
-2 4 1 1 1.000167935332526570e+00 
-2 5 1 1 8.111425888609598012e-01 
+Failure
 *** END ***
diff --git a/test-suite/failure/evarclear1.v b/test-suite/failure/evarclear1.v
new file mode 100644
index 00000000..2e9fa0f3
--- /dev/null
+++ b/test-suite/failure/evarclear1.v
@@ -0,0 +1,10 @@
+Set Printing Existential Instances.
+Set Printing All.
+Goal forall y, let z := S y in exists x, x = 0.
+intros.
+eexists.
+unfold z.
+clear y z.
+(* should fail because the evar should no longer be allowed to depend on z *)
+instantiate (1:=z).
+
diff --git a/test-suite/failure/evarclear2.v b/test-suite/failure/evarclear2.v
new file mode 100644
index 00000000..e606a06f
--- /dev/null
+++ b/test-suite/failure/evarclear2.v
@@ -0,0 +1,9 @@
+Set Printing Existential Instances.
+Set Printing All.
+Goal let y:=0 in exists x:y=y, x = x.
+intros.
+eexists.
+rename y into z.
+unfold z at 1 2.
+(* should fail because the evar type depends on z *)
+clear z.
diff --git a/test-suite/micromega/bertot.v b/test-suite/micromega/bertot.v
index 6951fcd3..bcf222f9 100644
--- a/test-suite/micromega/bertot.v
+++ b/test-suite/micromega/bertot.v
@@ -7,7 +7,7 @@
 (************************************************************************)
 
 Require Import ZArith.
-Require Import Micromegatac.
+Require Import Psatz.
 
 Open Scope Z_scope.
 
@@ -17,6 +17,6 @@ Goal (forall x y n,
   (x < n /\ x <= n /\ 2 * y = x * (x+1) -> x + 1 <= n /\ 2 *(x+1+y) = (x+1)*(x+2))).
 Proof.
   intros.
-  micromega Z.
+  psatz Z 3.
 Qed.
 
diff --git a/test-suite/micromega/example.v b/test-suite/micromega/example.v
index dc78ace5..751fe91e 100644
--- a/test-suite/micromega/example.v
+++ b/test-suite/micromega/example.v
@@ -7,7 +7,7 @@
 (************************************************************************)
 
 Require Import ZArith.
-Require Import Micromegatac.
+Require Import Psatz.
 Require Import Ring_normalize.
 Open Scope Z_scope.
 Require Import ZMicromega.
@@ -19,7 +19,7 @@ Lemma not_so_easy : forall x n : Z,
   2*x + 1 <= 2 *n -> x <= n-1.
 Proof.
   intros.
-  zfarkas. 
+  lia. 
 Qed.
 
 
@@ -28,14 +28,14 @@ Qed.
 Lemma some_pol : forall x, 4 * x ^ 2 + 3 * x + 2 >= 0.
 Proof.
   intros. 
-  micromega Z. 
+  psatz Z 2. 
 Qed.
 
 
 Lemma Zdiscr: forall a b c x, 
   a * x ^ 2 + b * x + c = 0 -> b ^ 2 - 4 * a * c >= 0.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 4.
 Qed.
 
 
@@ -43,7 +43,7 @@ Lemma plus_minus : forall x y,
   0 = x + y -> 0 =  x -y -> 0 = x /\ 0 = y.
 Proof.
   intros.
-  zfarkas.
+  lia.
 Qed.
 
 
@@ -51,13 +51,13 @@ Qed.
 Lemma mplus_minus : forall x y, 
   x + y >= 0 -> x -y >= 0 -> x^2 - y^2 >= 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma pol3: forall x y, 0 <= x + y ->  
   x^3 + 3*x^2*y + 3*x* y^2 + y^3 >= 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 4.
 Qed.
 
 
@@ -96,7 +96,7 @@ Proof.
   generalize (H8 _ _ _ (conj H5 H4)).
   generalize (H10 _ _ _ (conj H5 H4)).
   generalize rho_ge.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
 (* Rule of signs *)
@@ -104,55 +104,55 @@ Qed.
 Lemma sign_pos_pos: forall x y,
   x > 0 -> y > 0 -> x*y > 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_pos_zero: forall x y,
   x > 0 -> y = 0 -> x*y = 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_pos_neg: forall x y,
   x > 0 -> y < 0 -> x*y < 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_zer_pos: forall x y,
   x = 0 -> y > 0 -> x*y = 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_zero_zero: forall x y,
   x = 0 -> y = 0 -> x*y = 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_zero_neg: forall x y,
   x = 0 -> y < 0 -> x*y = 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_neg_pos: forall x y,
   x < 0 -> y > 0 -> x*y < 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_neg_zero: forall x y,
   x < 0 -> y = 0 -> x*y = 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma sign_neg_neg: forall x y,
   x < 0 -> y < 0 -> x*y > 0.
 Proof.
-  intros; micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 
@@ -161,26 +161,26 @@ Qed.
 Lemma binomial : forall x y, (x+y)^2 = x^2 + 2*x*y + y^2.
 Proof.
   intros.
-  zfarkas.
+  lia.
 Qed.
 
 Lemma product : forall x y, x >= 0 -> y >= 0 -> x * y >= 0.
 Proof.
   intros.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
 
 Lemma product_strict : forall x y, x > 0 -> y > 0 -> x * y > 0.
 Proof.
   intros.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
 
 Lemma pow_2_pos : forall x, x ^ 2 + 1 = 0 ->  False.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 2.
 Qed.
 
 (* Found in Parrilo's talk *)
@@ -188,10 +188,9 @@ Qed.
 Lemma parrilo_ex : forall x y, x - y^2 + 3 >= 0 -> y + x^2 + 2 = 0 -> False.
 Proof.
   intros.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
-
 (* from hol_light/Examples/sos.ml *)
 
 Lemma hol_light1 : forall a1 a2 b1 b2,
@@ -199,26 +198,26 @@ Lemma hol_light1 : forall a1 a2 b1 b2,
    (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) -> 
    (a1 * b1 + a2 * b2 = 0) -> a1 * a2 - b1 * b2 >= 0.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 4.
 Qed.
 
 
 Lemma hol_light2 : forall x a,
         3 * x + 7 * a < 4 -> 3 < 2 * x -> a < 0.
 Proof.
- intros ; micromega Z.
+ intros ; psatz Z 2.
 Qed.
 
 Lemma hol_light3 : forall b a c x,
   b ^ 2 < 4 * a * c -> (a * x ^2  + b * x + c = 0) -> False.
 Proof.
-intros ; micromega Z.
+intros ; psatz Z 4.
 Qed.
 
 Lemma hol_light4 : forall a c b x,
   a * x ^ 2 + b * x + c = 0 -> b ^ 2 >= 4 * a * c.
 Proof.
-intros ; micromega Z.
+intros ; psatz Z 4.
 Qed.
 
 Lemma hol_light5 : forall x y,
@@ -228,7 +227,7 @@ Lemma hol_light5 : forall x y,
       x ^ 2 + (y - 1) ^ 2 < 1 \/
       (x - 1) ^ 2 + (y - 1) ^ 2 < 1.
 Proof.
-intros; micromega Z.
+intros; psatz Z 3.
 Qed.
 
 
@@ -237,32 +236,32 @@ Lemma hol_light7 : forall x y z,
  0<= x /\ 0 <= y /\ 0 <= z /\ x + y + z <= 3
   -> x * y + x * z + y * z >= 3 * x * y * z.
 Proof.
-intros ; micromega Z.
+intros ; psatz Z 3.
 Qed.
 
 Lemma hol_light8 : forall x y z,
  x ^ 2 + y ^ 2 + z ^ 2 = 1 -> (x + y + z) ^ 2 <= 3.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 2.
 Qed.
 
 Lemma hol_light9 : forall w x y z,
  w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 = 1
   -> (w + x + y + z) ^ 2 <= 4.
 Proof.
-  intros;micromega Z.
+  intros; psatz Z 2.
 Qed.
 
 Lemma hol_light10 : forall x y,
  x >= 1 /\ y >= 1 -> x * y >= x + y - 1.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 2.
 Qed.
 
 Lemma hol_light11 : forall x y,
  x > 1 /\ y > 1 -> x * y > x + y - 1.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 2.
 Qed.
 
 
@@ -274,14 +273,14 @@ Lemma hol_light12: forall x y z,
 Proof.
   intros x y z ; set (e:= (125841 / 50000)).
   compute in e.
-  unfold e ; intros ; micromega Z.
+  unfold e ; intros ; psatz Z 2.
 Qed.
 
 Lemma hol_light14 : forall x y z,
  2 <= x /\ x <= 4 /\ 2 <= y /\ y <= 4 /\ 2 <= z /\ z <= 4
   -> 12 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z).
 Proof.
-  intros ;micromega Z.
+  intros ;psatz Z 2.
 Qed.
 
 (* ------------------------------------------------------------------------- *)
@@ -292,20 +291,20 @@ Lemma hol_light16 : forall x y,
   0 <= x /\ 0 <= y /\ (x * y = 1)
    -> x + y <= x ^ 2 + y ^ 2.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 2.
 Qed.
 
 Lemma hol_light17 : forall x y,
   0 <= x /\ 0 <= y /\ (x * y = 1)
    -> x * y * (x + y) <= x ^ 2 + y ^ 2.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 3.
 Qed.
 
 Lemma hol_light18 : forall x y,
   0 <= x /\ 0 <= y -> x * y * (x + y) ^ 2 <= (x ^ 2 + y ^ 2) ^ 2.
 Proof.
-  intros ; micromega Z.
+  intros ; psatz Z 4.
 Qed.
 
 (* ------------------------------------------------------------------------- *)
@@ -314,13 +313,13 @@ Qed.
 
 Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m.
 Proof.
-  intros ; zfarkas.
+  intros ; lia.
 Qed.
 
 Lemma hol_light22 : forall n, n >= 0 -> n <= n * n.
 Proof.
   intros.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
 
@@ -329,12 +328,12 @@ Lemma hol_light24 : forall x1 y1 x2 y2, x1 >= 0 -> x2 >= 0 -> y1 >= 0 -> y2 >= 0
                 -> (x1 + y1 = x2 + y2).
 Proof.
   intros.
-  micromega Z.
+  psatz Z 2.
 Qed.
 
 Lemma motzkin' : forall x y, (x^2+y^2+1)*(x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2) >= 0.
 Proof.
-  intros ; sos Z.
+  intros ; psatz Z.
 Qed.
 
 
@@ -343,5 +342,5 @@ Lemma motzkin : forall x y, (x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2)  >= 0.
 Proof.
   intros.
   generalize (motzkin' x y).
-  micromega Z.
+  psatz Z 8.
 Qed.
diff --git a/test-suite/micromega/heap3_vcgen_25.v b/test-suite/micromega/heap3_vcgen_25.v
index ec88b68d..0298303f 100644
--- a/test-suite/micromega/heap3_vcgen_25.v
+++ b/test-suite/micromega/heap3_vcgen_25.v
@@ -7,7 +7,7 @@
 (************************************************************************)
 
 Require Import ZArith.
-Require Import Micromegatac.
+Require Import Psatz.
 
 Open Scope Z_scope.
 
@@ -34,5 +34,5 @@ Lemma vcgen_25 : forall
   (H13 : 0 <= 121 * i + 810 * j + -7465 * m + 64350),
   (1 = -2 * i + it).
 Proof.
-  intros ; zfarkas.
+  intros ; lia.
 Qed.
diff --git a/test-suite/micromega/qexample.v b/test-suite/micromega/qexample.v
index 42aff5a4..1fa250e0 100644
--- a/test-suite/micromega/qexample.v
+++ b/test-suite/micromega/qexample.v
@@ -6,7 +6,7 @@
 (*                                                                      *)
 (************************************************************************)
 
-Require Import Micromegatac.
+Require Import Psatz.
 Require Import QArith.
 Require Import Ring_normalize.
 
@@ -14,22 +14,25 @@ Lemma plus_minus : forall x y,
   0 == x + y -> 0 ==  x -y -> 0 == x /\ 0 == y.
 Proof.
   intros.
-  omicron Q.
+  psatzl Q.
 Qed.
 
+
+
+
 (* Other (simple) examples *)
 Open Scope Q_scope.
 
 Lemma binomial : forall x y:Q, ((x+y)^2 == x^2 + (2 # 1) *x*y + y^2).
 Proof.
   intros.
-  omicron Q.
+  psatzl Q.
 Qed.
 
 
 Lemma hol_light19 : forall m n, (2 # 1) * m + n == (n + m) + m.
 Proof.
-  intros ; omicron Q.
+  intros ; psatzl Q.
 Qed.
 Open Scope Z_scope.
 Open Scope Q_scope.
@@ -58,5 +61,19 @@ Lemma vcgen_25 : forall
   (( 1# 1) == (-2 # 1) * i + it).
 Proof.
   intros.
-  omicron Q.
+  psatzl Q.
+Qed.
+
+Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False.
+Proof.
+  intros.
+  psatz Q 2.
 Qed.
+
+Lemma motzkin' : forall x y, (x^2+y^2+1)*(x^2*y^4 + x^4*y^2 + 1 - (3 # 1) *x^2*y^2) >= 0.
+Proof.
+  intros ; psatz Q.
+Qed.
+
+
+
diff --git a/test-suite/micromega/rexample.v b/test-suite/micromega/rexample.v
index 5132dc4e..d7386a4e 100644
--- a/test-suite/micromega/rexample.v
+++ b/test-suite/micromega/rexample.v
@@ -6,17 +6,17 @@
 (*                                                                      *)
 (************************************************************************)
 
-Require Import Micromegatac.
+Require Import Psatz.
 Require Import Reals.
 Require Import Ring_normalize.
 
 Open Scope R_scope.
 
-Lemma plus_minus : forall x y, 
+Lemma yplus_minus : forall x y, 
   0 = x + y -> 0 =  x -y -> 0 = x /\ 0 = y.
 Proof.
   intros.
-  omicron R.
+  psatzl R.
 Qed.
 
 (* Other (simple) examples *)
@@ -24,13 +24,13 @@ Qed.
 Lemma binomial : forall x y, ((x+y)^2 = x^2 + 2 *x*y + y^2).
 Proof.
   intros.
-  omicron R.
+  psatzl R.
 Qed.
 
 
 Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m.
 Proof.
-  intros ; omicron R.
+  intros ; psatzl R.
 Qed.
 
 
@@ -58,5 +58,20 @@ Lemma vcgen_25 : forall
   (( 1 ) = (-2  ) * i + it).
 Proof.
   intros.
-  omicron R.
+  psatzl R.
 Qed.
+
+Goal forall x, -x^2 >= 0 -> x - 1 >= 0 -> False.
+Proof.
+  intros.
+  psatz R 2.
+Qed.
+
+Lemma motzkin' : forall x y, (x^2+y^2+1)*(x^2*y^4 + x^4*y^2 + 1 - (3 ) *x^2*y^2) >= 0.
+Proof.
+  intros ; psatz R.
+Qed.
+
+Lemma l1 : forall x y z : R, Rabs (x - z) <= Rabs (x - y) + Rabs (y - z).
+intros; split_Rabs; psatzl R.
+Qed.
\ No newline at end of file
diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v
index 30c72e8c..b78bba25 100644
--- a/test-suite/micromega/square.v
+++ b/test-suite/micromega/square.v
@@ -6,12 +6,12 @@
 (*                                                                      *)
 (************************************************************************)
 
-Require Import ZArith Zwf Micromegatac QArith.
+Require Import ZArith Zwf Psatz QArith.
 Open Scope Z_scope.
 
 Lemma Zabs_square : forall x,  (Zabs  x)^2 = x^2.
 Proof.
- intros ; case (Zabs_dec x) ; intros ; micromega Z.
+ intros ; case (Zabs_dec x) ; intros ; psatz Z 2.
 Qed.
 Hint Resolve Zabs_pos Zabs_square.
 
@@ -21,11 +21,11 @@ intros [n [p [Heq Hnz]]]; pose (n' := Zabs n); pose (p':=Zabs p).
 assert (facts : 0 <= Zabs n /\ 0 <= Zabs p /\ Zabs n^2=n^2
          /\ Zabs p^2 = p^2) by auto.
 assert (H : (0 < n' /\ 0 <= p' /\ n' ^2 = 2* p' ^2)) by 
-  (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; micromega Z).
+  (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; psatz Z 2).
 generalize p' H; elim n' using (well_founded_ind (Zwf_well_founded 0)); clear.
 intros n IHn p [Hn [Hp Heq]].
-assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; micromega Z).
-assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by micromega Z.
+assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; psatz Z 2).
+assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by psatz Z 2.
 apply (IHn (2*p-n) Hzwf (n-p) Hdecr).
 Qed.
 
@@ -44,7 +44,9 @@ Lemma QdenZpower : forall x : Q, ' Qden (x ^ 2)%Q = ('(Qden x) ^ 2) %Z.
 Proof.
   intros.
   destruct x.
-  cbv beta  iota zeta delta - [Pmult].
+  simpl.
+  unfold Zpower_pos.
+  simpl.
   rewrite Pmult_1_r.
   reflexivity.
 Qed.
diff --git a/test-suite/micromega/zomicron.v b/test-suite/micromega/zomicron.v
index b13654d6..2b40f6c9 100644
--- a/test-suite/micromega/zomicron.v
+++ b/test-suite/micromega/zomicron.v
@@ -1,27 +1,27 @@
 Require Import ZArith.
-Require Import Micromegatac.
+Require Import Psatz.
 Open Scope Z_scope.
 
 Lemma two_x_eq_1 : forall x, 2 * x = 1 -> False.
 Proof.
   intros.
-  omicron Z.
+  lia.
 Qed.
 
 Lemma two_x_y_eq_1 : forall x y, 2 * x + 2 * y = 1 -> False.
 Proof.
   intros.
-  omicron Z.
+  lia.
 Qed.
 
 Lemma two_x_y_z_eq_1 : forall x y z, 2 * x + 2 * y + 2 * z= 1 -> False.
 Proof.
   intros.
-  omicron Z.
+  lia.
 Qed.
 
 Lemma omega_nightmare : forall x y, 27 <= 11 * x + 13 * y <= 45 -> 7 * x - 9 * y = 4 -> -10 <= 7 * x - 9 * y <= 4 -> False.
 Proof.
   intros ; intuition auto.
-  omicron Z.
+  lia.
 Qed.  
diff --git a/test-suite/output/ArgumentsScope.out b/test-suite/output/ArgumentsScope.out
new file mode 100644
index 00000000..6643c142
--- /dev/null
+++ b/test-suite/output/ArgumentsScope.out
@@ -0,0 +1,56 @@
+a : bool -> bool
+
+Argument scope is [bool_scope]
+Expands to: Variable a
+b : bool -> bool
+
+Argument scope is [bool_scope]
+Expands to: Variable b
+negb'' : bool -> bool
+
+Argument scope is [bool_scope]
+negb'' is transparent
+Expands to: Constant Top.A.B.negb''
+negb' : bool -> bool
+
+Argument scope is [bool_scope]
+negb' is transparent
+Expands to: Constant Top.A.negb'
+negb : bool -> bool
+
+Argument scope is [bool_scope]
+negb is transparent
+Expands to: Constant Coq.Init.Datatypes.negb
+a : bool -> bool
+
+Expands to: Variable a
+b : bool -> bool
+
+Expands to: Variable b
+negb : bool -> bool
+
+negb is transparent
+Expands to: Constant Coq.Init.Datatypes.negb
+negb' : bool -> bool
+
+negb' is transparent
+Expands to: Constant Top.A.negb'
+negb'' : bool -> bool
+
+negb'' is transparent
+Expands to: Constant Top.A.B.negb''
+a : bool -> bool
+
+Expands to: Variable a
+negb : bool -> bool
+
+negb is transparent
+Expands to: Constant Coq.Init.Datatypes.negb
+negb' : bool -> bool
+
+negb' is transparent
+Expands to: Constant Top.negb'
+negb'' : bool -> bool
+
+negb'' is transparent
+Expands to: Constant Top.negb''
diff --git a/test-suite/output/ArgumentsScope.v b/test-suite/output/ArgumentsScope.v
new file mode 100644
index 00000000..13b5e13d
--- /dev/null
+++ b/test-suite/output/ArgumentsScope.v
@@ -0,0 +1,29 @@
+(* A few tests to check Argument Scope Global command *)
+
+Section A.
+Variable a : bool -> bool.
+Definition negb' := negb.
+Section B.
+Variable b : bool -> bool.
+Definition negb'' := negb.
+About a.
+About b.
+About negb''.
+About negb'.
+About negb.
+Arguments Scope Global negb'' [ _ ].
+Arguments Scope Global negb' [ _ ].
+Arguments Scope Global negb [ _ ].
+Arguments Scope Global a [ _ ].
+Arguments Scope Global b [ _ ].
+About a.
+About b.
+About negb.
+About negb'.
+About negb''.
+End B.
+About a.
+End A.
+About negb.
+About negb'.
+About negb''.
diff --git a/test-suite/output/Cases.out b/test-suite/output/Cases.out
index 9d0d0658..995754a6 100644
--- a/test-suite/output/Cases.out
+++ b/test-suite/output/Cases.out
@@ -21,7 +21,7 @@ Argument scopes are [nat_scope nat_scope _ _ _]
 foo = 
 fix foo (A : Type) (l : list A) {struct l} : option A :=
   match l with
-  | nil => None (A:=A)
+  | nil => None
   | x0 :: nil => Some x0
   | x0 :: (_ :: _) as l0 => foo A l0
   end
diff --git a/test-suite/output/Fixpoint.out b/test-suite/output/Fixpoint.out
index f4270d3d..c69d31f4 100644
--- a/test-suite/output/Fixpoint.out
+++ b/test-suite/output/Fixpoint.out
@@ -1,6 +1,6 @@
 fix F (A B : Set) (f : A -> B) (l : list A) {struct l} : 
 list B := match l with
-          | nil => nil (A:=B)
+          | nil => nil
           | a :: l0 => f a :: F A B f l0
           end
      : forall A B : Set, (A -> B) -> list A -> list B
@@ -13,13 +13,13 @@ fix even_pos_odd_pos 2
  with (odd_pos_even_pos (n:_) (H:odd n) {struct H} : n >= 1).
  intros.
  destruct H.
-   omega.
+  omega.
   
-   apply odd_pos_even_pos in H.
-   omega.
+  apply odd_pos_even_pos in H.
+  omega.
   
  intros.
  destruct H.
-  apply even_pos_odd_pos in H.
-  omega.
+ apply even_pos_odd_pos in H.
+ omega.
  
diff --git a/test-suite/output/Match_subterm.out b/test-suite/output/Match_subterm.out
new file mode 100644
index 00000000..951a98db
--- /dev/null
+++ b/test-suite/output/Match_subterm.out
@@ -0,0 +1,8 @@
+(0 = 1)
+eq
+nat
+0
+1
+S
+0
+2
diff --git a/test-suite/output/Match_subterm.v b/test-suite/output/Match_subterm.v
new file mode 100644
index 00000000..2c44b187
--- /dev/null
+++ b/test-suite/output/Match_subterm.v
@@ -0,0 +1,6 @@
+Goal 0 = 1.
+match goal with
+| |- context [?v] =>
+  idtac v ; fail
+| _ => idtac 2
+end.
diff --git a/test-suite/output/Tactics.out b/test-suite/output/Tactics.out
index 287e8488..ac5eedc1 100644
--- a/test-suite/output/Tactics.out
+++ b/test-suite/output/Tactics.out
@@ -1,4 +1,4 @@
-intro H; split; [  a H |  e H ].
+intro H; split; [ a H | e H ].
 
 intros; match goal with
         | |- context [if ?X then _ else _] => case X
diff --git a/test-suite/success/CanonicalStructure.v b/test-suite/success/CanonicalStructure.v
index 44d21b83..b8cae471 100644
--- a/test-suite/success/CanonicalStructure.v
+++ b/test-suite/success/CanonicalStructure.v
@@ -12,3 +12,20 @@ Record Silly (X : Set) : Set := mkSilly { x : X }.
 Definition anotherMk := mkSilly.
 Definition struct := anotherMk nat 3.
 Canonical Structure struct.
+
+(* Intertwinning canonical structures and delta-expansion *)
+(* Assia's short example *)
+
+Open Scope bool_scope.
+
+Set Implicit Arguments.
+
+Structure test_struct : Type := mk_test {dom :> Type; f : dom -> dom -> bool}.
+
+Notation " x != y":= (f _ x y)(at level 10).
+
+Canonical Structure bool_test := mk_test (fun x y => x || y).
+
+Definition b := bool.
+
+Check (fun x : b => x != x).
diff --git a/test-suite/success/ImplicitArguments.v b/test-suite/success/ImplicitArguments.v
index e7795733..84ec298d 100644
--- a/test-suite/success/ImplicitArguments.v
+++ b/test-suite/success/ImplicitArguments.v
@@ -2,6 +2,8 @@ Inductive vector {A : Type} : nat -> Type :=
 | vnil : vector 0
 | vcons : A -> forall {n'}, vector n' -> vector (S n').
 
+Implicit Arguments vector [].
+
 Require Import Coq.Program.Program.
 
 Program Definition head {A : Type} {n : nat} (v : vector A (S n)) : vector A n :=
diff --git a/test-suite/success/Notations.v b/test-suite/success/Notations.v
index facd5509..6dce0401 100644
--- a/test-suite/success/Notations.v
+++ b/test-suite/success/Notations.v
@@ -21,3 +21,8 @@ Definition marker := O.
 Notation "x +1" := (S x) (at level 8, left associativity).
 Reset marker.
 Notation "x +1" := (S x) (at level 8, right associativity).
+
+(* Check that empty levels (here 8 and 2 in pattern) are added in the
+   right order *)
+
+Notation "' 'C_' G ( A )" := (A,G) (at level 8, G at level 2).
diff --git a/test-suite/success/setoid_test2.v b/test-suite/success/setoid_test2.v
index 34fff9d1..b89787bb 100644
--- a/test-suite/success/setoid_test2.v
+++ b/test-suite/success/setoid_test2.v
@@ -120,7 +120,7 @@ Axiom eqS1: S1 -> S1 -> Prop.
 Axiom SetoidS1 : Setoid_Theory S1 eqS1.
 Add Setoid S1 eqS1 SetoidS1 as S1setoid.
 
-Instance eqS1_default : DefaultRelation S1 eqS1.
+Instance eqS1_default : DefaultRelation eqS1.
 
 Axiom eqS1': S1 -> S1 -> Prop.
 Axiom SetoidS1' : Setoid_Theory S1 eqS1'.
@@ -220,7 +220,7 @@ Axiom eqS1_test8: S1_test8 -> S1_test8 -> Prop.
 Axiom SetoidS1_test8 : Setoid_Theory S1_test8 eqS1_test8.
 Add Setoid S1_test8 eqS1_test8 SetoidS1_test8 as S1_test8setoid.
 
-Instance eqS1_test8_default : DefaultRelation S1_test8 eqS1_test8.
+Instance eqS1_test8_default : DefaultRelation eqS1_test8.
 
 Axiom f_test8 : S2 -> S1_test8.
 Add Morphism f_test8 : f_compat_test8. Admitted.
diff --git a/theories/Classes/EquivDec.v b/theories/Classes/EquivDec.v
index debe953a..1e58d05d 100644
--- a/theories/Classes/EquivDec.v
+++ b/theories/Classes/EquivDec.v
@@ -13,7 +13,7 @@
  * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
  *              91405 Orsay, France *)
 
-(* $Id: EquivDec.v 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: EquivDec.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Set Implicit Arguments.
 Unset Strict Implicit.
@@ -40,7 +40,7 @@ Class [ equiv : Equivalence A ] => EqDec :=
 (** We define the [==] overloaded notation for deciding equality. It does not take precedence
    of [==] defined in the type scope, hence we can have both at the same time. *)
 
-Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70).
+Notation " x == y " := (equiv_dec (x :>) (y :>)) (no associativity, at level 70) : equiv_scope.
 
 Definition swap_sumbool {A B} (x : { A } + { B }) : { B } + { A } :=
   match x with
@@ -58,7 +58,7 @@ Program Definition nequiv_dec [ EqDec A ] (x y : A) : { x =/= y } + { x === y }
 
 (** Overloaded notation for inequality. *)
 
-Infix "=/=" := nequiv_dec (no associativity, at level 70).
+Infix "<>" := nequiv_dec (no associativity, at level 70) : equiv_scope.
 
 (** Define boolean versions, losing the logical information. *)
 
@@ -155,4 +155,4 @@ Program Instance list_eqdec [ eqa : EqDec A eq ] : ! EqDec (list A) eq :=
   Next Obligation.
   Proof. clear aux. red in H0. subst. 
     destruct y; intuition (discriminate || eauto).
-  Defined.
\ No newline at end of file
+  Defined.
diff --git a/theories/Classes/Equivalence.v b/theories/Classes/Equivalence.v
index 70bf3483..d52eed47 100644
--- a/theories/Classes/Equivalence.v
+++ b/theories/Classes/Equivalence.v
@@ -13,7 +13,7 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *) 
 
-(* $Id: Equivalence.v 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: Equivalence.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Require Export Coq.Program.Basics.
 Require Import Coq.Program.Tactics.
@@ -116,7 +116,7 @@ Section Respecting.
   Definition respecting [ Equivalence A (R : relation A), Equivalence B (R' : relation B) ] : Type := 
     { morph : A -> B | respectful R R' morph morph }.
   
-  Program Instance respecting_equiv [ Equivalence A R, Equivalence B R' ] :
+  Program Instance respecting_equiv [ eqa : Equivalence A R, eqb : Equivalence B R' ] :
     Equivalence respecting
     (fun (f g : respecting) => forall (x y : A), R x y -> R' (proj1_sig f x) (proj1_sig g y)).
 
@@ -124,18 +124,17 @@ Section Respecting.
 
   Next Obligation.
   Proof. 
-    unfold respecting in *. program_simpl. red in H2,H3,H4. 
-    transitivity (y x0) ; auto.
-    transitivity (y y0) ; auto.
-    symmetry. auto.
+    unfold respecting in *. program_simpl. transitivity (y y0); auto. apply H0. reflexivity.
   Qed.
 
 End Respecting.
 
 (** The default equivalence on function spaces, with higher-priority than [eq]. *)
 
-Program Instance pointwise_equivalence [ Equivalence A eqA ] :
-  Equivalence (B -> A) (pointwise_relation eqA) | 9.
+Program Instance pointwise_equivalence [ eqb : Equivalence B eqB ] :
+  Equivalence (A -> B) (pointwise_relation eqB) | 9.
+
+  Solve Obligations using simpl_relation ; first [ reflexivity | (symmetry ; auto) ].
 
   Next Obligation.
   Proof.
diff --git a/theories/Classes/Functions.v b/theories/Classes/Functions.v
index 49fc4f89..4c844911 100644
--- a/theories/Classes/Functions.v
+++ b/theories/Classes/Functions.v
@@ -13,7 +13,7 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *)
 
-(* $Id: Functions.v 10739 2008-04-01 14:45:20Z herbelin $ *)
+(* $Id: Functions.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Require Import Coq.Classes.RelationClasses.
 Require Import Coq.Classes.Morphisms.
@@ -21,22 +21,22 @@ Require Import Coq.Classes.Morphisms.
 Set Implicit Arguments.
 Unset Strict Implicit.
 
-Class [ m : Morphism (A -> B) (RA ++> RB) f ] => Injective : Prop :=
+Class Injective ((m : Morphism (A -> B) (RA ++> RB) f)) : Prop :=
   injective : forall x y : A, RB (f x) (f y) -> RA x y.
 
-Class [ m : Morphism (A -> B) (RA ++> RB) f ] => Surjective : Prop :=
+Class ((m : Morphism (A -> B) (RA ++> RB) f)) => Surjective : Prop :=
   surjective : forall y, exists x : A, RB y (f x).
 
-Definition Bijective [ m : Morphism (A -> B) (RA ++> RB) (f : A -> B) ] :=
+Definition Bijective ((m : Morphism (A -> B) (RA ++> RB) (f : A -> B))) :=
   Injective m /\ Surjective m.
 
-Class [ m : Morphism (A -> B) (eqA ++> eqB) ] => MonoMorphism :=
+Class MonoMorphism (( m : Morphism (A -> B) (eqA ++> eqB) )) :=
   monic :> Injective m.
 
-Class [ m : Morphism (A -> B) (eqA ++> eqB) ] => EpiMorphism :=
+Class EpiMorphism ((m : Morphism (A -> B) (eqA ++> eqB))) :=
   epic :> Surjective m.
 
-Class [ m : Morphism (A -> B) (eqA ++> eqB) ] => IsoMorphism :=
+Class IsoMorphism ((m : Morphism (A -> B) (eqA ++> eqB))) :=
   monomorphism :> MonoMorphism m ; epimorphism :> EpiMorphism m.
 
-Class [ m : Morphism (A -> A) (eqA ++> eqA), ! IsoMorphism m ] => AutoMorphism.
+Class ((m : Morphism (A -> A) (eqA ++> eqA))) [ ! IsoMorphism m ] => AutoMorphism.
diff --git a/theories/Classes/Init.v b/theories/Classes/Init.v
index 6ba0c61e..e5f951d0 100644
--- a/theories/Classes/Init.v
+++ b/theories/Classes/Init.v
@@ -13,9 +13,22 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *)
 
-(* $Id: Init.v 10739 2008-04-01 14:45:20Z herbelin $ *)
+(* $Id: Init.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (* Ltac typeclass_instantiation := typeclasses eauto || eauto. *)
 
 Tactic Notation "clapply" ident(c) :=
   eapply @c ; eauto with typeclass_instances.
+
+(** The unconvertible typeclass, to test that two objects of the same type are 
+   actually different. *)
+
+Class Unconvertible (A : Type) (a b : A).
+
+Ltac unconvertible :=
+  match goal with
+    | |- @Unconvertible _ ?x ?y => conv x y ; fail 1 "Convertible"
+    | |- _ => apply Build_Unconvertible 
+  end.
+
+Hint Extern 0 (@Unconvertible _ _ _) => unconvertible : typeclass_instances.
\ No newline at end of file
diff --git a/theories/Classes/Morphisms.v b/theories/Classes/Morphisms.v
index f21c68a6..c2ae026d 100644
--- a/theories/Classes/Morphisms.v
+++ b/theories/Classes/Morphisms.v
@@ -1,4 +1,4 @@
-(* -*- coq-prog-args: ("-emacs-U" "-top" "Coq.Classes.Morphisms"); compile-command: "make -C ../.. TIME='time'" -*- *)
+(* -*- coq-prog-name: "~/research/coq/trunk/bin/coqtop.byte"; coq-prog-args: ("-emacs-U" "-top" "Coq.Classes.Morphisms"); compile-command: "make -C ../.. TIME='time'" -*- *)
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
@@ -13,7 +13,7 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *)
 
-(* $Id: Morphisms.v 11092 2008-06-10 18:28:26Z msozeau $ *)
+(* $Id: Morphisms.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Require Import Coq.Program.Basics.
 Require Import Coq.Program.Tactics.
@@ -39,10 +39,6 @@ Class Morphism A (R : relation A) (m : A) : Prop :=
 
 Implicit Arguments Morphism [A].
 
-(** We allow to unfold the [relation] definition while doing morphism search. *)
-
-Typeclasses unfold relation.
-
 (** Respectful morphisms. *)
 
 (** The fully dependent version, not used yet. *)
@@ -79,9 +75,22 @@ Arguments Scope respectful [type_scope type_scope signature_scope signature_scop
 
 Open Local Scope signature_scope.
 
+(** Pointwise lifting is just respect with leibniz equality on the left. *)
+
+Definition pointwise_relation {A B : Type} (R : relation B) : relation (A -> B) := 
+  fun f g => forall x : A, R (f x) (g x).
+
+Lemma pointwise_pointwise A B (R : relation B) : 
+  relation_equivalence (pointwise_relation R) (@eq A ==> R).
+Proof. intros. split. simpl_relation. firstorder. Qed.
+
 (** We can build a PER on the Coq function space if we have PERs on the domain and
    codomain. *)
 
+Hint Unfold Reflexive : core.
+Hint Unfold Symmetric : core.
+Hint Unfold Transitive : core.
+
 Program Instance respectful_per [ PER A (R : relation A), PER B (R' : relation B) ] : 
   PER (A -> B) (R ==> R').
 
@@ -92,24 +101,26 @@ Program Instance respectful_per [ PER A (R : relation A), PER B (R' : relation B
     transitivity (y x0)...
   Qed.
 
-(** Subrelations induce a morphism on the identity, not used for morphism search yet. *)
+(** Subrelations induce a morphism on the identity. *)
 
-Lemma subrelation_id_morphism [ subrelation A R� R₂ ] : Morphism (R� ==> R₂) id.
+Instance subrelation_id_morphism [ subrelation A R� R₂ ] : Morphism (R� ==> R₂) id.
 Proof. firstorder. Qed.
 
 (** The subrelation property goes through products as usual. *)
 
-Instance morphisms_subrelation [ sub : subrelation A R� R₂ ] :
-  ! subrelation (B -> A) (R ==> R�) (R ==> R₂).
-Proof. firstorder. Qed.
+Instance morphisms_subrelation_respectful [ subl : subrelation A R₂ R�, subr : subrelation B S� S₂ ] :
+  subrelation (R� ==> S�) (R₂ ==> S₂).
+Proof. simpl_relation. apply subr. apply H. apply subl. apply H0. Qed.
 
-Instance morphisms_subrelation_left [ sub : subrelation A R₂ R� ] :
-  ! subrelation (A -> B) (R� ==> R) (R₂ ==> R) | 3.
-Proof. firstorder. Qed.
+(** And of course it is reflexive. *)
+
+Instance morphisms_subrelation_refl : ! subrelation A R R | 10.
+Proof. simpl_relation. Qed.
 
 (** [Morphism] is itself a covariant morphism for [subrelation]. *)
 
-Lemma subrelation_morphism [ sub : subrelation A R� R₂, mor : Morphism A R� m ] : Morphism R₂ m.
+Lemma subrelation_morphism [ mor : Morphism A R� m, unc : Unconvertible (relation A) R� R₂,
+  sub : subrelation A R� R₂ ] : Morphism R₂ m.
 Proof.
   intros. apply sub. apply mor.
 Qed.
@@ -121,8 +132,9 @@ Proof. reduce. subst. firstorder. Qed.
 (** We use an external tactic to manage the application of subrelation, which is otherwise
    always applicable. We allow its use only once per branch. *)
 
-Inductive subrelation_done : Prop :=
-  did_subrelation : subrelation_done.
+Inductive subrelation_done : Prop := did_subrelation : subrelation_done.
+
+Inductive normalization_done : Prop := did_normalization.
 
 Ltac subrelation_tac := 
   match goal with
@@ -131,7 +143,7 @@ Ltac subrelation_tac :=
       set(H:=did_subrelation) ; eapply @subrelation_morphism
   end.
 
-Hint Extern 4 (@Morphism _ _ _) => subrelation_tac : typeclass_instances.
+Hint Extern 5 (@Morphism _ _ _) => subrelation_tac : typeclass_instances.
 
 (** Essential subrelation instances for [iff], [impl] and [pointwise_relation]. *)
 
@@ -181,20 +193,10 @@ Program Instance trans_contra_co_morphism
     transitivity x0...
   Qed.
 
-(* (** Dually... *) *)
-
-(* Program Instance [ Transitive A R ] => *)
-(*   trans_co_contra_inv_impl_morphism : Morphism (R ++> R --> inverse impl) R. *)
-  
-(*   Next Obligation. *)
-(*   Proof with auto. *)
-(*     apply* trans_contra_co_morphism ; eauto. eauto. *)
-(*   Qed. *)
-
 (** Morphism declarations for partial applications. *)
 
 Program Instance trans_contra_inv_impl_morphism
-  [ Transitive A R ] : Morphism (R --> inverse impl) (R x).
+  [ Transitive A R ] : Morphism (R --> inverse impl) (R x) | 3.
 
   Next Obligation.
   Proof with auto.
@@ -202,7 +204,7 @@ Program Instance trans_contra_inv_impl_morphism
   Qed.
 
 Program Instance trans_co_impl_morphism
-  [ Transitive A R ] : Morphism (R ==> impl) (R x).
+  [ Transitive A R ] : Morphism (R ==> impl) (R x) | 3.
 
   Next Obligation.
   Proof with auto.
@@ -210,23 +212,23 @@ Program Instance trans_co_impl_morphism
   Qed.
 
 Program Instance trans_sym_co_inv_impl_morphism
-  [ Transitive A R, Symmetric A R ] : Morphism (R ==> inverse impl) (R x).
+  [ PER A R ] : Morphism (R ==> inverse impl) (R x) | 2.
 
   Next Obligation.
   Proof with auto.
-    transitivity y...
+    transitivity y... symmetry...
   Qed.
 
 Program Instance trans_sym_contra_impl_morphism
-  [ Transitive A R, Symmetric _ R ] : Morphism (R --> impl) (R x).
+  [ PER A R ] : Morphism (R --> impl) (R x) | 2.
 
   Next Obligation.
   Proof with auto.
-    transitivity x0...
+    transitivity x0... symmetry...
   Qed.
 
-Program Instance equivalence_partial_app_morphism
-  [ Equivalence A R ] : Morphism (R ==> iff) (R x).
+Program Instance per_partial_app_morphism
+  [ PER A R ] : Morphism (R ==> iff) (R x) | 1.
 
   Next Obligation.
   Proof with auto.
@@ -240,36 +242,16 @@ Program Instance equivalence_partial_app_morphism
    to get an [R y z] goal. *)
 
 Program Instance trans_co_eq_inv_impl_morphism
-  [ Transitive A R ] : Morphism (R ==> (@eq A) ==> inverse impl) R.
+  [ Transitive A R ] : Morphism (R ==> (@eq A) ==> inverse impl) R | 2.
 
   Next Obligation.
   Proof with auto.
     transitivity y...
   Qed.
 
-(* Program Instance [ Transitive A R ] =>  *)
-(*   trans_contra_eq_impl_morphism : Morphism (R --> (@eq A) ==> impl) R. *)
-
-(*   Next Obligation. *)
-(*   Proof with auto. *)
-(*     transitivity x... *)
-(*   Qed. *)
-
 (** Every Symmetric and Transitive relation gives rise to an equivariant morphism. *)
 
-Program Instance trans_sym_morphism
-  [ Transitive A R, Symmetric _ R ] : Morphism (R ==> R ==> iff) R.
-
-  Next Obligation.
-  Proof with auto.
-    split ; intros.
-    transitivity x0... transitivity x...
-  
-    transitivity y... transitivity y0... 
-  Qed.
-
-Program Instance equiv_morphism [ Equivalence A R ] :
-  Morphism (R ==> R ==> iff) R.
+Program Instance PER_morphism [ PER A R ] : Morphism (R ==> R ==> iff) R | 1.
 
   Next Obligation.
   Proof with auto.
@@ -279,27 +261,21 @@ Program Instance equiv_morphism [ Equivalence A R ] :
     transitivity y... transitivity y0... symmetry...
   Qed.
 
-(** In case the rewrite happens at top level. *)
-
-Program Instance iff_inverse_impl_id :
-  Morphism (iff ==> inverse impl) id.
-
-Program Instance inverse_iff_inverse_impl_id :
-  Morphism (iff --> inverse impl) id.
+Lemma symmetric_equiv_inverse [ Symmetric A R ] : relation_equivalence R (flip R).
+Proof. firstorder. Qed.
   
-Program Instance iff_impl_id :
-  Morphism (iff ==> impl) id.
+Program Instance compose_morphism A B C R₀ R� R₂ :
+  Morphism ((R� ==> R₂) ==> (R₀ ==> R�) ==> (R₀ ==> R₂)) (@compose A B C).
+
+  Next Obligation.
+  Proof.
+    simpl_relation.
+    unfold compose. apply H. apply H0. apply H1.
+  Qed.
 
-Program Instance inverse_iff_impl_id :
-  Morphism (iff --> impl) id.
-  
 (** Coq functions are morphisms for leibniz equality, 
    applied only if really needed. *)
 
-(* Instance (A : Type) [ Reflexive B R ] => *)
-(*   eq_reflexive_morphism : Morphism (@Logic.eq A ==> R) m | 3. *)
-(* Proof. simpl_relation. Qed. *)
-
 Instance reflexive_eq_dom_reflexive (A : Type) [ Reflexive B R' ] :
   Reflexive (@Logic.eq A ==> R').
 Proof. simpl_relation. Qed.
@@ -335,49 +311,81 @@ Class MorphismProxy A (R : relation A) (m : A) : Prop :=
   respect_proxy : R m m.
 
 Instance reflexive_morphism_proxy
-  [ Reflexive A R ] (x : A) : MorphismProxy A R x | 1.
+  [ Reflexive A R ] (x : A) : MorphismProxy R x | 1.
 Proof. firstorder. Qed.
 
 Instance morphism_morphism_proxy
-  [ Morphism A R x ] : MorphismProxy A R x | 2.
+  [ Morphism A R x ] : MorphismProxy R x | 2.
 Proof. firstorder. Qed.
 
-(* Instance (A : Type) [ Reflexive B R ] => *)
-(*   eq_reflexive_morphism : Morphism (@Logic.eq A ==> R) m | 3. *)
-(* Proof. simpl_relation. Qed. *)
-
 (** [R] is Reflexive, hence we can build the needed proof. *)
 
 Lemma Reflexive_partial_app_morphism [ Morphism (A -> B) (R ==> R') m, MorphismProxy A R x ] :
    Morphism R' (m x).
 Proof. simpl_relation. Qed.
 
+Class Params {A : Type} (of : A) (arity : nat).
+
+Class PartialApplication.
+
 Ltac partial_application_tactic := 
-  let tac x :=
-    match type of x with
-      | Type => fail 1
-      | _ => eapply @Reflexive_partial_app_morphism
+  let rec do_partial_apps H m :=
+    match m with
+      | ?m' ?x => eapply @Reflexive_partial_app_morphism ; [do_partial_apps H m'|clear H]
+      | _ => idtac
     end
   in
-  let on_morphism m :=
-    match m with
-      | ?m' ?x => tac x
-      | ?m' _ ?x => tac x
-      | ?m' _ _ ?x => tac x
-      | ?m' _ _ _ ?x => tac x
-      | ?m' _ _ _ _ ?x => tac x
-      | ?m' _ _ _ _ _ ?x => tac x
-      | ?m' _ _ _ _ _ _ ?x => tac x
-      | ?m' _ _ _ _ _ _ _ ?x => tac x
-      | ?m' _ _ _ _ _ _ _ _ ?x => tac x
+  let rec do_partial H ar m :=
+    match ar with
+      | 0 => do_partial_apps H m
+      | S ?n' => 
+        match m with
+          ?m' ?x => do_partial H n' m'
+        end
     end
   in
+  let on_morphism m :=
+    let m' := fresh in head_of_constr m' m ;
+    let n := fresh in evar (n:nat) ;
+    let v := eval compute in n in clear n ;
+    let H := fresh in
+      assert(H:Params m' v) by typeclasses eauto ;
+      let v' := eval compute in v in 
+      do_partial H v' m
+ in
   match goal with
-    | [ |- @Morphism _ _ ?m ] => on_morphism m
+    | [ _ : subrelation_done |- _ ] => fail 1
+    | [ _ : normalization_done |- _ ] => fail 1
+    | [ _ : @Params _ _ _ |- _ ] => fail 1
+    | [ |- @Morphism ?T _ (?m ?x) ] => 
+      match goal with 
+        | [ _ : PartialApplication |- _ ] => 
+          eapply @Reflexive_partial_app_morphism
+        | _ => 
+          on_morphism (m x) || 
+            (eapply @Reflexive_partial_app_morphism ;
+              [ pose Build_PartialApplication | idtac ])
+      end
   end.
 
-(* Program Instance [ Morphism (A -> B) (R ==> R') m, Reflexive A R ] (x : A) => *)
-(*   reflexive_partial_app_morphism : Morphism R' (m x). *)
+Section PartialAppTest.
+  Instance and_ar : Params and 0.
+
+  Goal Morphism (iff) (and True True).
+    partial_application_tactic.
+  Admitted.
+
+  Goal Morphism (iff) (or True True).
+    partial_application_tactic.
+    partial_application_tactic. 
+  Admitted.
+
+  Goal Morphism (iff ==> iff) (iff True).
+    partial_application_tactic.
+    (*partial_application_tactic. *)
+   Admitted.
+
+End PartialAppTest.
 
 Hint Extern 4 (@Morphism _ _ _) => partial_application_tactic : typeclass_instances.
 
@@ -395,19 +403,19 @@ Class (A : Type) => Normalizes (m : relation A) (m' : relation A) : Prop :=
   normalizes : relation_equivalence m m'.
 
 Instance inverse_respectful_norm : 
-  Normalizes (A -> B) (inverse R ==> inverse R') (inverse (R ==> R')) .
+  ! Normalizes (A -> B) (inverse R ==> inverse R') (inverse (R ==> R')) .
 Proof. firstorder. Qed.
 
 (* If not an inverse on the left, do a double inverse. *)
 
 Instance not_inverse_respectful_norm : 
-  Normalizes (A -> B) (R ==> inverse R') (inverse (inverse R ==> R')) | 4.
+  ! Normalizes (A -> B) (R ==> inverse R') (inverse (inverse R ==> R')) | 4.
 Proof. firstorder. Qed.
 
 Instance inverse_respectful_rec_norm [ Normalizes B R' (inverse R'') ] :
-  Normalizes (A -> B) (inverse R ==> R') (inverse (R ==> R'')).
-Proof. red ; intros.  
-  pose normalizes as r.
+  ! Normalizes (A -> B) (inverse R ==> R') (inverse (R ==> R'')).
+Proof. red ; intros. 
+  assert(r:=normalizes).
   setoid_rewrite r.
   setoid_rewrite inverse_respectful.
   reflexivity.
@@ -415,8 +423,14 @@ Qed.
 
 (** Once we have normalized, we will apply this instance to simplify the problem. *)
 
-Program Instance morphism_inverse_morphism
-  [ Morphism A R m ] : Morphism (inverse R) m | 2.
+Definition morphism_inverse_morphism [ mor : Morphism A R m ] : Morphism (inverse R) m := mor.
+
+Ltac morphism_inverse :=
+  match goal with
+    [ |- @Morphism _ (flip _) _ ] => eapply @morphism_inverse_morphism
+  end.
+
+Hint Extern 2 (@Morphism _ _ _) => morphism_inverse : typeclass_instances.
 
 (** Bootstrap !!! *)
 
@@ -434,16 +448,16 @@ Qed.
 Lemma morphism_releq_morphism [ Normalizes A R R', Morphism _ R' m ] : Morphism R m.
 Proof.
   intros.
+
   pose respect as r.
   pose normalizes as norm.
   setoid_rewrite norm.
   assumption.
 Qed.
 
-Inductive normalization_done : Prop := did_normalization.
-
 Ltac morphism_normalization := 
   match goal with
+    | [ _ : subrelation_done |- _ ] => fail 1
     | [ _ : normalization_done |- _ ] => fail 1
     | [ |- @Morphism _ _ _ ] => let H := fresh "H" in
       set(H:=did_normalization) ; eapply @morphism_releq_morphism
@@ -464,4 +478,4 @@ Ltac morphism_reflexive :=
     | [ |- @Morphism _ _ _ ] => eapply @reflexive_morphism
   end.
 
-Hint Extern 4 (@Morphism _ _ _) => morphism_reflexive : typeclass_instances.
\ No newline at end of file
+Hint Extern 7 (@Morphism _ _ _) => morphism_reflexive : typeclass_instances.
diff --git a/theories/Classes/Morphisms_Prop.v b/theories/Classes/Morphisms_Prop.v
index 7dc1f95e..ec62e12e 100644
--- a/theories/Classes/Morphisms_Prop.v
+++ b/theories/Classes/Morphisms_Prop.v
@@ -29,7 +29,7 @@ Program Instance not_iff_morphism :
 
 (** Logical conjunction. *)
 
-Program Instance and_impl_iff_morphism :
+Program Instance and_impl_morphism :
   Morphism (impl ==> impl ==> impl) and.
 
 (* Program Instance and_impl_iff_morphism :  *)
@@ -49,7 +49,7 @@ Program Instance and_iff_morphism :
 
 (** Logical disjunction. *)
 
-Program Instance or_impl_iff_morphism : 
+Program Instance or_impl_morphism : 
   Morphism (impl ==> impl ==> impl) or.
 
 (* Program Instance or_impl_iff_morphism :  *)
diff --git a/theories/Classes/Morphisms_Relations.v b/theories/Classes/Morphisms_Relations.v
index 5018fa01..1b389667 100644
--- a/theories/Classes/Morphisms_Relations.v
+++ b/theories/Classes/Morphisms_Relations.v
@@ -48,3 +48,11 @@ Proof. intro. apply (predicate_equivalence_pointwise (cons A (cons A nil))). Qed
 Instance subrelation_pointwise :
   Morphism (subrelation ==> pointwise_relation (A:=A) (pointwise_relation (A:=A) impl)) id.
 Proof. intro. apply (predicate_implication_pointwise (cons A (cons A nil))). Qed.
+
+
+Lemma inverse_pointwise_relation A (R : relation A) : 
+  relation_equivalence (pointwise_relation (inverse R)) (inverse (pointwise_relation (A:=A) R)).
+Proof. intros. split; firstorder. Qed.
+
+
+
diff --git a/theories/Classes/RelationClasses.v b/theories/Classes/RelationClasses.v
index a9a53068..9a43a1ba 100644
--- a/theories/Classes/RelationClasses.v
+++ b/theories/Classes/RelationClasses.v
@@ -1,4 +1,4 @@
-(* -*- coq-prog-args: ("-emacs-U" "-top" "Coq.Classes.RelationClasses") -*- *)
+(* -*- coq-prog-name: "coqtop.byte"; coq-prog-args: ("-emacs-U" "-top" "Coq.Classes.RelationClasses") -*- *)
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
@@ -14,20 +14,21 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *)
 
-(* $Id: RelationClasses.v 11092 2008-06-10 18:28:26Z msozeau $ *)
+(* $Id: RelationClasses.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Require Export Coq.Classes.Init.
 Require Import Coq.Program.Basics.
 Require Import Coq.Program.Tactics.
 Require Export Coq.Relations.Relation_Definitions.
 
+(** We allow to unfold the [relation] definition while doing morphism search. *)
+
+Typeclasses unfold relation.
+
 Notation inverse R := (flip (R:relation _) : relation _).
 
 Definition complement {A} (R : relation A) : relation A := fun x y => R x y -> False.
 
-Definition pointwise_relation {A B : Type} (R : relation B) : relation (A -> B) := 
-  fun f g => forall x : A, R (f x) (g x).
-
 (** These are convertible. *)
 
 Lemma complement_inverse : forall A (R : relation A), complement (inverse R) = inverse (complement R).
@@ -42,7 +43,7 @@ Class Reflexive A (R : relation A) :=
   reflexivity : forall x, R x x.
 
 Class Irreflexive A (R : relation A) := 
-  irreflexivity :> Reflexive A (complement R).
+  irreflexivity :> Reflexive (complement R).
 
 Class Symmetric A (R : relation A) := 
   symmetry : forall x y, R x y -> R y x.
@@ -53,12 +54,6 @@ Class Asymmetric A (R : relation A) :=
 Class Transitive A (R : relation A) := 
   transitivity : forall x y z, R x y -> R y z -> R x z.
 
-Implicit Arguments Reflexive [A].
-Implicit Arguments Irreflexive [A].
-Implicit Arguments Symmetric [A].
-Implicit Arguments Asymmetric [A].
-Implicit Arguments Transitive [A].
-
 Hint Resolve @irreflexivity : ord.
 
 Unset Implicit Arguments.
@@ -91,7 +86,7 @@ Program Instance Reflexive_complement_Irreflexive [ Reflexive A (R : relation A)
     unfold complement.
     red. intros H.
     intros H' ; apply H'.
-    apply (reflexivity H).
+    apply reflexivity.
   Qed.
 
 
@@ -129,7 +124,7 @@ Ltac simpl_relation :=
   unfold flip, impl, arrow ; try reduce ; program_simpl ;
     try ( solve [ intuition ]).
 
-Ltac obligations_tactic ::= simpl_relation.
+Ltac obligation_tactic ::= simpl_relation.
 
 (** Logical implication. *)
 
@@ -171,17 +166,17 @@ Class Equivalence (carrier : Type) (equiv : relation carrier) : Prop :=
 
 (** An Equivalence is a PER plus reflexivity. *)
 
-Instance Equivalence_PER [ Equivalence A R ] : PER A R :=
+Instance Equivalence_PER [ Equivalence A R ] : PER A R | 10 :=
   PER_Symmetric := Equivalence_Symmetric ;
   PER_Transitive := Equivalence_Transitive.
 
 (** We can now define antisymmetry w.r.t. an equivalence relation on the carrier. *)
 
-Class [ Equivalence A eqA ] => Antisymmetric (R : relation A) := 
+Class Antisymmetric ((equ : Equivalence A eqA)) (R : relation A) := 
   antisymmetry : forall x y, R x y -> R y x -> eqA x y.
 
-Program Instance flip_antiSymmetric [ eq : Equivalence A eqA, ! Antisymmetric eq R ] :
-  Antisymmetric eq (flip R).
+Program Instance flip_antiSymmetric {{Antisymmetric A eqA R}} :
+  ! Antisymmetric A eqA (flip R).
 
 (** Leibinz equality [eq] is an equivalence relation.
    The instance has low priority as it is always applicable 
@@ -372,7 +367,7 @@ Proof. intro A. exact (@predicate_implication_preorder (cons A (cons A nil))). Q
    We give an equivalent definition, up-to an equivalence relation 
    on the carrier. *)
 
-Class [ equ : Equivalence A eqA, PreOrder A R ] => PartialOrder :=
+Class [ equ : Equivalence A eqA, preo : PreOrder A R ] => PartialOrder :=
   partial_order_equivalence : relation_equivalence eqA (relation_conjunction R (inverse R)).
 
 (** The equivalence proof is sufficient for proving that [R] must be a morphism 
@@ -394,7 +389,3 @@ Program Instance subrelation_partial_order :
   Proof.
     unfold relation_equivalence in *. firstorder.
   Qed.
-
-Lemma inverse_pointwise_relation A (R : relation A) : 
-  relation_equivalence (pointwise_relation (inverse R)) (inverse (pointwise_relation (A:=A) R)).
-Proof. reflexivity. Qed.
diff --git a/theories/Classes/SetoidClass.v b/theories/Classes/SetoidClass.v
index a9bdaa8f..178d5333 100644
--- a/theories/Classes/SetoidClass.v
+++ b/theories/Classes/SetoidClass.v
@@ -13,7 +13,7 @@
    Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
    91405 Orsay, France *)
 
-(* $Id: SetoidClass.v 11065 2008-06-06 22:39:43Z msozeau $ *)
+(* $Id: SetoidClass.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Set Implicit Arguments.
 Unset Strict Implicit.
@@ -41,13 +41,13 @@ Typeclasses unfold equiv.
 (** Shortcuts to make proof search easier. *)
 
 Definition setoid_refl [ sa : Setoid A ] : Reflexive equiv.
-Proof. eauto with typeclass_instances. Qed.
+Proof. typeclasses eauto. Qed.
 
 Definition setoid_sym [ sa : Setoid A ] : Symmetric equiv.
-Proof. eauto with typeclass_instances. Qed.
+Proof. typeclasses eauto. Qed.
 
 Definition setoid_trans [ sa : Setoid A ] : Transitive equiv.
-Proof. eauto with typeclass_instances. Qed.
+Proof. typeclasses eauto. Qed.
 
 Existing Instance setoid_refl.
 Existing Instance setoid_sym.
@@ -123,7 +123,7 @@ Ltac setoidify := repeat setoidify_tac.
 (** Every setoid relation gives rise to a morphism, in fact every partial setoid does. *)
 
 Program Definition setoid_morphism [ sa : Setoid A ] : Morphism (equiv ++> equiv ++> iff) equiv :=
-  trans_sym_morphism.
+  PER_morphism.
 
 (** Add this very useful instance in the database. *)
 
@@ -142,7 +142,7 @@ Program Instance type_equivalence : Equivalence Type type_eq.
 
 Ltac morphism_tac := try red ; unfold arrow ; intros ; program_simpl ; try tauto.
 
-Ltac obligations_tactic ::= morphism_tac.
+Ltac obligation_tactic ::= morphism_tac.
 
 (** These are morphisms used to rewrite at the top level of a proof, 
    using [iff_impl_id_morphism] if the proof is in [Prop] and
@@ -178,4 +178,4 @@ Infix "=~=" := pequiv (at level 70, no associativity) : type_scope.
 
 (** Reset the default Program tactic. *)
 
-Ltac obligations_tactic ::= program_simpl.
+Ltac obligation_tactic ::= program_simpl.
diff --git a/theories/Classes/SetoidDec.v b/theories/Classes/SetoidDec.v
index cf3d202d..8a069343 100644
--- a/theories/Classes/SetoidDec.v
+++ b/theories/Classes/SetoidDec.v
@@ -13,7 +13,7 @@
  * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
  *              91405 Orsay, France *)
 
-(* $Id: SetoidDec.v 10919 2008-05-11 22:04:26Z msozeau $ *)
+(* $Id: SetoidDec.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Set Implicit Arguments.
 Unset Strict Implicit.
@@ -27,12 +27,12 @@ Require Export Coq.Classes.SetoidClass.
 
 Require Import Coq.Logic.Decidable.
 
-Class [ Setoid A ] => DecidableSetoid :=
+Class DecidableSetoid A [ Setoid A ] :=
   setoid_decidable : forall x y : A, decidable (x == y).
 
 (** The [EqDec] class gives a decision procedure for a particular setoid equality. *)
 
-Class [ Setoid A ] => EqDec :=
+Class (( s : Setoid A )) => EqDec :=
   equiv_dec : forall x y : A, { x == y } + { x =/= y }.
 
 (** We define the [==] overloaded notation for deciding equality. It does not take precedence
@@ -75,18 +75,18 @@ Require Import Coq.Arith.Arith.
 
 (** The equiv is burried inside the setoid, but we can recover it by specifying which setoid we're talking about. *)
 
-Program Instance eq_setoid : Setoid A :=
+Program Instance eq_setoid A : Setoid A :=
   equiv := eq ; setoid_equiv := eq_equivalence.
 
-Program Instance nat_eq_eqdec : EqDec (@eq_setoid nat) :=
+Program Instance nat_eq_eqdec : EqDec (eq_setoid nat) :=
   equiv_dec := eq_nat_dec.
 
 Require Import Coq.Bool.Bool.
 
-Program Instance bool_eqdec : EqDec (@eq_setoid bool) :=
+Program Instance bool_eqdec : EqDec (eq_setoid bool) :=
   equiv_dec := bool_dec.
 
-Program Instance unit_eqdec : EqDec (@eq_setoid unit) :=
+Program Instance unit_eqdec : EqDec (eq_setoid unit) :=
   equiv_dec x y := in_left.
 
   Next Obligation.
@@ -95,7 +95,7 @@ Program Instance unit_eqdec : EqDec (@eq_setoid unit) :=
     reflexivity.
   Qed.
 
-Program Instance prod_eqdec [ ! EqDec (@eq_setoid A), ! EqDec (@eq_setoid B) ] : EqDec (@eq_setoid (prod A B)) :=
+Program Instance prod_eqdec [ ! EqDec (eq_setoid A), ! EqDec (eq_setoid B) ] : EqDec (eq_setoid (prod A B)) :=
   equiv_dec x y := 
     let '(x1, x2) := x in 
     let '(y1, y2) := y in 
@@ -110,7 +110,7 @@ Program Instance prod_eqdec [ ! EqDec (@eq_setoid A), ! EqDec (@eq_setoid B) ] :
 
 Require Import Coq.Program.FunctionalExtensionality.
 
-Program Instance bool_function_eqdec [ ! EqDec (@eq_setoid A) ] : EqDec (@eq_setoid (bool -> A)) :=
+Program Instance bool_function_eqdec [ ! EqDec (eq_setoid A) ] : EqDec (eq_setoid (bool -> A)) :=
   equiv_dec f g := 
     if f true == g true then
       if f false == g false then in_left
diff --git a/theories/Classes/SetoidTactics.v b/theories/Classes/SetoidTactics.v
index b29a52cc..6398b125 100644
--- a/theories/Classes/SetoidTactics.v
+++ b/theories/Classes/SetoidTactics.v
@@ -13,7 +13,7 @@
  * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
  *              91405 Orsay, France *)
 
-(* $Id: SetoidTactics.v 10921 2008-05-12 12:27:25Z msozeau $ *)
+(* $Id: SetoidTactics.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 Require Export Coq.Classes.RelationClasses.
 Require Export Coq.Classes.Morphisms.
@@ -24,11 +24,22 @@ Require Export Coq.Relations.Relation_Definitions.
 Set Implicit Arguments.
 Unset Strict Implicit.
 
+(** Setoid relation on a given support: declares a relation as a setoid
+   for use with rewrite. It helps choosing if a rewrite should be handled
+   by setoid_rewrite or the regular rewrite using leibniz equality.
+   Users can declare an [SetoidRelation A RA] anywhere to declare default 
+   relations. This is also done automatically by the [Declare Relation A RA]
+   commands. *)
+
+Class SetoidRelation A (R : relation A).
+
+Instance impl_setoid_relation : SetoidRelation impl.
+Instance iff_setoid_relation : SetoidRelation iff.
+
 (** Default relation on a given support. Can be used by tactics
    to find a sensible default relation on any carrier. Users can 
-   declare an [Instance A RA] anywhere to declare default relations.
-   This is also done by the [Declare Relation A RA] command with no
-   parameters for backward compatibility. *)
+   declare an [Instance def : DefaultRelation A RA] anywhere to 
+   declare default relations. *)
 
 Class DefaultRelation A (R : relation A).
 
@@ -38,7 +49,7 @@ Definition default_relation [ DefaultRelation A R ] := R.
 
 (** Every [Equivalence] gives a default relation, if no other is given (lowest priority). *)
 
-Instance equivalence_default [ Equivalence A R ] : DefaultRelation A R | 4.
+Instance equivalence_default [ Equivalence A R ] : DefaultRelation R | 4.
 
 (** The setoid_replace tactics in Ltac, defined in terms of default relations and
    the setoid_rewrite tactic. *)
@@ -174,3 +185,5 @@ Ltac default_add_morphism_tactic :=
   end.
 
 Ltac add_morphism_tactic := default_add_morphism_tactic.
+
+Ltac obligation_tactic ::= program_simpl.
diff --git a/theories/FSets/FMapFacts.v b/theories/FSets/FMapFacts.v
index b307efe3..94444f5b 100644
--- a/theories/FSets/FMapFacts.v
+++ b/theories/FSets/FMapFacts.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1       *)
 (***********************************************************************)
 
-(* $Id: FMapFacts.v 10782 2008-04-12 16:08:04Z msozeau $ *)
+(* $Id: FMapFacts.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (** * Finite maps library *)
 
@@ -660,6 +660,8 @@ Add Relation key E.eq
  transitivity proved by E.eq_trans 
  as KeySetoid.
 
+Typeclasses unfold key.
+
 Implicit Arguments Equal [[elt]].
 
 Add Parametric Relation (elt : Type) : (t elt) Equal  
diff --git a/theories/FSets/FSetFacts.v b/theories/FSets/FSetFacts.v
index b4b834b1..d77d9c60 100644
--- a/theories/FSets/FSetFacts.v
+++ b/theories/FSets/FSetFacts.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1       *)
 (***********************************************************************)
 
-(* $Id: FSetFacts.v 10765 2008-04-08 16:15:23Z msozeau $ *)
+(* $Id: FSetFacts.v 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 (** * Finite sets library *)
 
@@ -309,6 +309,8 @@ Add Relation elt E.eq
  transitivity proved by E.eq_trans 
  as EltSetoid.
 
+Typeclasses unfold elt.
+
 Add Relation t Equal 
  reflexivity proved by eq_refl 
  symmetry proved by eq_sym
diff --git a/theories/Init/Tactics.v b/theories/Init/Tactics.v
index afe8297e..10555fc0 100644
--- a/theories/Init/Tactics.v
+++ b/theories/Init/Tactics.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Tactics.v 11072 2008-06-08 16:13:37Z herbelin $ i*)
+(*i $Id: Tactics.v 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 Require Import Notations.
 Require Import Logic.
@@ -115,7 +115,7 @@ lazymatch T with
     evar (a : t); pose proof (H a) as H1; unfold a in H1;
     clear a; clear H; rename H1 into H; find_equiv H
 | ?A <-> ?B => idtac
-| _ => fail "The given statement does not seem to end with an equivalence"
+| _ => fail "The given statement does not seem to end with an equivalence."
 end.
 
 Ltac bapply lemma todo :=
@@ -141,7 +141,7 @@ t;
 match goal with
 | H : _ |- _ => solve [inversion H]
 | _ => solve [trivial | reflexivity | symmetry; trivial | discriminate | split]
-| _ => fail 1 "Cannot solve this goal"
+| _ => fail 1 "Cannot solve this goal."
 end.
 
 (** A tactic to document or check what is proved at some point of a script *)
diff --git a/theories/Init/Wf.v b/theories/Init/Wf.v
index f46b2b11..d3f8f1ab 100644
--- a/theories/Init/Wf.v
+++ b/theories/Init/Wf.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Wf.v 10712 2008-03-23 11:38:38Z herbelin $ i*)
+(*i $Id: Wf.v 11251 2008-07-24 08:28:40Z herbelin $ i*)
 
 (** * This module proves the validity of
     - well-founded recursion (also known as course of values)
@@ -27,6 +27,7 @@ Section Well_founded.
  Variable R : A -> A -> Prop.
 
  (** The accessibility predicate is defined to be non-informative *)
+ (** (Acc_rect is automatically defined because Acc is a singleton type) *)
 
  Inductive Acc (x: A) : Prop :=
      Acc_intro : (forall y:A, R y x -> Acc y) -> Acc x.
@@ -35,22 +36,6 @@ Section Well_founded.
   destruct 1; trivial.
  Defined.
 
-  (** Informative elimination :
-     [let Acc_rec F = let rec wf x = F x wf in wf] *)
-
- Section AccRecType.
-
-  Variable P : A -> Type.
-  Variable F : forall x:A,
-    (forall y:A, R y x -> Acc y) -> (forall y:A, R y x -> P y) -> P x.
-
-  Fixpoint Acc_rect (x:A) (a:Acc x) {struct a} : P x :=
-    F (Acc_inv a) (fun (y:A) (h:R y x) => Acc_rect (Acc_inv a h)).
-
- End AccRecType.
-
- Definition Acc_rec (P:A -> Set) := Acc_rect P.
-
  (** A relation is well-founded if every element is accessible *)
 
  Definition well_founded := forall a:A, Acc a.
diff --git a/theories/Logic/ClassicalDescription.v b/theories/Logic/ClassicalDescription.v
index 3737abf6..d15e2c96 100644
--- a/theories/Logic/ClassicalDescription.v
+++ b/theories/Logic/ClassicalDescription.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: ClassicalDescription.v 10170 2007-10-03 14:41:25Z herbelin $ i*)
+(*i $Id: ClassicalDescription.v 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 (** This file provides classical logic and definite description, which is
     equivalent to providing classical logic and Church's iota operator *)
@@ -21,7 +21,7 @@ Set Implicit Arguments.
 Require Export Classical.
 Require Import ChoiceFacts.
 
-Notation Local "'inhabited' A" := A (at level 200, only parsing).
+Notation Local inhabited A := A.
 
 Axiom constructive_definite_description :
   forall (A : Type) (P : A->Prop), (exists! x : A, P x) -> { x : A | P x }.
diff --git a/theories/Logic/ClassicalFacts.v b/theories/Logic/ClassicalFacts.v
index 734de52d..8a045ec8 100644
--- a/theories/Logic/ClassicalFacts.v
+++ b/theories/Logic/ClassicalFacts.v
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: ClassicalFacts.v 10156 2007-09-30 19:02:14Z herbelin $ i*)
+(*i $Id: ClassicalFacts.v 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 (** Some facts and definitions about classical logic
 
@@ -119,7 +119,7 @@ Qed.
 
 *)
 
-Definition inhabited (A:Prop) := A.
+Notation Local inhabited A := A.
 
 Lemma prop_ext_A_eq_A_imp_A :
   prop_extensionality -> forall A:Prop, inhabited A -> (A -> A) = A.
@@ -514,8 +514,6 @@ Qed.
     344 of Lecture Notes in Mathematics, Springer-Verlag, 1973.
 *)
 
-Notation Local "'inhabited' A" := A (at level 10, only parsing).
-
 Definition IndependenceOfGeneralPremises :=
   forall (A:Type) (P:A -> Prop) (Q:Prop),
     inhabited A -> (Q -> exists x, P x) -> exists x, Q -> P x.
diff --git a/theories/Logic/ConstructiveEpsilon.v b/theories/Logic/ConstructiveEpsilon.v
index f1503d24..3753b97b 100644
--- a/theories/Logic/ConstructiveEpsilon.v
+++ b/theories/Logic/ConstructiveEpsilon.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: ConstructiveEpsilon.v 10739 2008-04-01 14:45:20Z herbelin $ i*)
+(*i $Id: ConstructiveEpsilon.v 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 (** This module proves the constructive description schema, which
 infers the sigma-existence (i.e., [Set]-existence) of a witness to a
@@ -53,7 +53,7 @@ of our searching algorithm. *)
 
 Let R (x y : nat) : Prop := x = S y /\ ~ P y.
 
-Notation Local "'acc' x" := (Acc R x) (at level 10).
+Notation Local acc x := (Acc R x).
 
 Lemma P_implies_acc : forall x : nat, P x -> acc x.
 Proof.
diff --git a/theories/Logic/Diaconescu.v b/theories/Logic/Diaconescu.v
index 5f139f35..880ef7e2 100644
--- a/theories/Logic/Diaconescu.v
+++ b/theories/Logic/Diaconescu.v
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Diaconescu.v 9245 2006-10-17 12:53:34Z notin $ i*)
+(*i $Id: Diaconescu.v 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 (** Diaconescu showed that the Axiom of Choice entails Excluded-Middle
    in topoi [Diaconescu75]. Lacas and Werner adapted the proof to show
@@ -267,7 +267,7 @@ End ProofIrrel_RelChoice_imp_EqEM.
 
 (** Proof sketch from Bell [Bell93] (with thanks to P. Castéran) *)
 
-Notation Local "'inhabited' A" := A (at level 10, only parsing).
+Notation Local inhabited A := A.
 
 Section ExtensionalEpsilon_imp_EM.
 
diff --git a/theories/Numbers/BigNumPrelude.v b/theories/Numbers/BigNumPrelude.v
index 9669eacd..83ecd10d 100644
--- a/theories/Numbers/BigNumPrelude.v
+++ b/theories/Numbers/BigNumPrelude.v
@@ -8,7 +8,7 @@
 (*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
 (************************************************************************)
 
-(*i $Id: BigNumPrelude.v 11013 2008-05-28 18:17:30Z letouzey $ i*)
+(*i $Id: BigNumPrelude.v 11207 2008-07-04 16:50:32Z letouzey $ i*)
 
 (** * BigNumPrelude *)
 
@@ -277,7 +277,7 @@ Theorem Zmod_le_first: forall a b, 0 <= a -> 0 < b -> 0 <= a mod b <= a.
  Qed.
 
 
- Lemma shift_unshift_mod_2 : forall n p a, (0<=p<=n)%Z -> 
+ Lemma shift_unshift_mod_2 : forall n p a, 0 <= p <= n -> 
    ((a * 2 ^ (n - p)) mod (2^n) / 2 ^ (n - p)) mod (2^n) = 
    a mod 2 ^ p.
  Proof.
@@ -329,7 +329,7 @@ Theorem Zmod_le_first: forall a b, 0 <= a -> 0 < b -> 0 <= a mod b <= a.
  Qed.
 
  Theorem Zgcd_div_pos a b:
-   (0 < b)%Z -> (0 < Zgcd a b)%Z -> (0 < b / Zgcd a b)%Z.
+   0 < b -> 0 < Zgcd a b -> 0 < b / Zgcd a b.
  Proof.
  intros a b Ha Hg.
  case (Zle_lt_or_eq 0 (b/Zgcd a b)); auto.
@@ -340,6 +340,72 @@ Theorem Zmod_le_first: forall a b, 0 <= a -> 0 < b -> 0 <= a mod b <= a.
  assert (F := (Zgcd_is_gcd a b)); inversion F; auto.
  Qed.
 
+ Theorem Zdiv_neg a b:
+   a < 0 -> 0 < b -> a / b < 0.
+ Proof.
+ intros a b Ha Hb.
+ assert (b > 0) by omega.
+ generalize (Z_mult_div_ge a _ H); intros.
+ assert (b * (a / b) < 0)%Z.
+  apply Zle_lt_trans with a; auto with zarith.
+ destruct b; try (compute in Hb; discriminate).
+ destruct (a/Zpos p)%Z.
+ compute in H1; discriminate.
+ compute in H1; discriminate.
+ compute; auto.
+ Qed.
+ 
+ Lemma Zgcd_Zabs : forall z z', Zgcd (Zabs z) z' = Zgcd z z'.
+ Proof.
+ destruct z; simpl; auto.
+ Qed.
+
+ Lemma Zgcd_sym : forall p q, Zgcd p q = Zgcd q p.
+ Proof.
+ intros.
+ apply Zis_gcd_gcd.
+ apply Zgcd_is_pos.
+ apply Zis_gcd_sym.
+ apply Zgcd_is_gcd.
+ Qed.
+
+ Lemma Zdiv_gcd_zero : forall a b, b / Zgcd a b = 0 -> b <> 0 -> 
+  Zgcd a b = 0.
+ Proof.
+ intros.
+ generalize (Zgcd_is_gcd a b); destruct 1.
+ destruct H2 as (k,Hk).
+ generalize H; rewrite Hk at 1.
+ destruct (Z_eq_dec (Zgcd a b) 0) as [H'|H']; auto.
+ rewrite Z_div_mult_full; auto.
+ intros; subst k; simpl in *; subst b; elim H0; auto.
+ Qed.
+
+ Lemma Zgcd_1 : forall z, Zgcd z 1 = 1.
+ Proof.
+ intros; apply Zis_gcd_gcd; auto with zarith; apply Zis_gcd_1.
+ Qed.
+ Hint Resolve Zgcd_1.
+
+ Lemma Zgcd_mult_rel_prime : forall a b c, 
+  Zgcd a c = 1 -> Zgcd b c = 1 -> Zgcd (a*b) c = 1.
+ Proof.
+ intros.
+ rewrite Zgcd_1_rel_prime in *.
+ apply rel_prime_sym; apply rel_prime_mult; apply rel_prime_sym; auto.
+ Qed.
+
+ Lemma Zcompare_gt : forall (A:Type)(a a':A)(p q:Z),
+  match (p?=q)%Z with Gt => a | _ => a' end = 
+  if Z_le_gt_dec p q then a' else a.
+ Proof.
+ intros.
+ destruct Z_le_gt_dec as [H|H].
+ red in H.
+ destruct (p?=q)%Z; auto; elim H; auto.
+ rewrite H; auto.
+ Qed.
+
 Theorem Zbounded_induction :
   (forall Q : Z -> Prop, forall b : Z,
     Q 0 ->
diff --git a/theories/Numbers/Cyclic/Abstract/NZCyclic.v b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
index 22f6d95b..fb3f0cef 100644
--- a/theories/Numbers/Cyclic/Abstract/NZCyclic.v
+++ b/theories/Numbers/Cyclic/Abstract/NZCyclic.v
@@ -8,7 +8,7 @@
 (*                      Evgeny Makarov, INRIA, 2007                     *)
 (************************************************************************)
 
-(*i $Id: NZCyclic.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: NZCyclic.v 11238 2008-07-19 09:34:03Z herbelin $ i*)
 
 Require Export NZAxioms.
 Require Import BigNumPrelude.
@@ -89,8 +89,8 @@ Open Local Scope IntScope.
 Notation "x == y"  := (NZeq x y) (at level 70) : IntScope.
 Notation "x ~= y" := (~ NZeq x y) (at level 70) : IntScope.
 Notation "0" := NZ0 : IntScope.
-Notation "'S'" := NZsucc : IntScope.
-Notation "'P'" := NZpred : IntScope.
+Notation S x := (NZsucc x).
+Notation P x := (NZpred x).
 (*Notation "1" := (S 0) : IntScope.*)
 Notation "x + y" := (NZadd x y) : IntScope.
 Notation "x - y" := (NZsub x y) : IntScope.
diff --git a/theories/Numbers/Integer/BigZ/BigZ.v b/theories/Numbers/Integer/BigZ/BigZ.v
index 09abf424..cb920124 100644
--- a/theories/Numbers/Integer/BigZ/BigZ.v
+++ b/theories/Numbers/Integer/BigZ/BigZ.v
@@ -8,7 +8,7 @@
 (*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
 (************************************************************************)
 
-(*i $Id: BigZ.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: BigZ.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Export BigN.
 Require Import ZMulOrder.
@@ -42,25 +42,27 @@ Infix "?=" := BigZ.compare : bigZ_scope.
 Infix "==" := BigZ.eq (at level 70, no associativity) : bigZ_scope.
 Infix "<" := BigZ.lt : bigZ_scope.
 Infix "<=" := BigZ.le : bigZ_scope.
+Notation "x > y" := (BigZ.lt y x)(only parsing) : bigZ_scope.
+Notation "x >= y" := (BigZ.le y x)(only parsing) : bigZ_scope.
 Notation "[ i ]" := (BigZ.to_Z i) : bigZ_scope.
 
 Open Scope bigZ_scope.
 
 (** Some additional results about [BigZ] *)
 
-Theorem spec_to_Z: forall n:bigZ, 
+Theorem spec_to_Z: forall n:bigZ,
   BigN.to_Z (BigZ.to_N n) = ((Zsgn [n]) * [n])%Z.
 Proof.
-intros n; case n; simpl; intros p; 
+intros n; case n; simpl; intros p;
   generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
 intros p1 H1; case H1; auto.
 intros p1 H1; case H1; auto.
 Qed.
 
-Theorem spec_to_N n: 
+Theorem spec_to_N n:
  ([n] = Zsgn [n] * (BigN.to_Z (BigZ.to_N n)))%Z.
 Proof.
-intros n; case n; simpl; intros p; 
+intros n; case n; simpl; intros p;
   generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
 intros p1 H1; case H1; auto.
 intros p1 H1; case H1; auto.
@@ -69,7 +71,7 @@ Qed.
 Theorem spec_to_Z_pos: forall n, (0 <= [n])%Z ->
   BigN.to_Z (BigZ.to_N n) = [n].
 Proof.
-intros n; case n; simpl; intros p; 
+intros n; case n; simpl; intros p;
   generalize (BigN.spec_pos p); case (BigN.to_Z p); auto.
 intros p1 _ H1; case H1; auto.
 intros p1 H1; case H1; auto.
@@ -87,7 +89,7 @@ Qed.
 
 (** [BigZ] is a ring *)
 
-Lemma BigZring : 
+Lemma BigZring :
  ring_theory BigZ.zero BigZ.one BigZ.add BigZ.mul BigZ.sub BigZ.opp BigZ.eq.
 Proof.
 constructor.
@@ -102,6 +104,8 @@ exact sub_opp.
 exact add_opp.
 Qed.
 
+Typeclasses unfold NZadd NZmul NZsub NZeq.
+
 Add Ring BigZr : BigZring.
 
 (** Todo: tactic translating from [BigZ] to [Z] + omega *)
diff --git a/theories/Numbers/Integer/BigZ/ZMake.v b/theories/Numbers/Integer/BigZ/ZMake.v
index 1f2b12bb..6305156b 100644
--- a/theories/Numbers/Integer/BigZ/ZMake.v
+++ b/theories/Numbers/Integer/BigZ/ZMake.v
@@ -8,7 +8,7 @@
 (*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
 (************************************************************************)
 
-(*i $Id: ZMake.v 11027 2008-06-01 13:28:59Z letouzey $ i*)
+(*i $Id: ZMake.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Import ZArith.
 Require Import BigNumPrelude.
@@ -30,6 +30,7 @@ Module Make (N:NType) <: ZType.
   | Neg : N.t -> t_.
  
  Definition t := t_.
+ Typeclasses unfold t.
 
  Definition zero := Pos N.zero.
  Definition one  := Pos N.one.
diff --git a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
index d7c56267..aceb8984 100644
--- a/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
+++ b/theories/Numbers/Integer/SpecViaZ/ZSigZAxioms.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: ZSigZAxioms.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: ZSigZAxioms.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Import ZArith.
 Require Import ZAxioms.
@@ -216,7 +216,7 @@ Qed.
 Add Morphism Z.compare with signature Z.eq ==> Z.eq ==> (@eq comparison) as compare_wd.
 Proof. 
 intros x x' Hx y y' Hy.
-rewrite 2 spec_compare_alt; rewrite Hx, Hy; intuition.
+rewrite 2 spec_compare_alt; unfold Z.eq in *; rewrite Hx, Hy; intuition.
 Qed.
 
 Add Morphism Z.lt with signature Z.eq ==> Z.eq ==> iff as NZlt_wd.
diff --git a/theories/Numbers/Natural/Abstract/NOrder.v b/theories/Numbers/Natural/Abstract/NOrder.v
index 826ffa2c..15aed7ab 100644
--- a/theories/Numbers/Natural/Abstract/NOrder.v
+++ b/theories/Numbers/Natural/Abstract/NOrder.v
@@ -8,7 +8,7 @@
 (*                      Evgeny Makarov, INRIA, 2007                     *)
 (************************************************************************)
 
-(*i $Id: NOrder.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: NOrder.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Export NMul.
 
@@ -309,13 +309,12 @@ Proof NZgt_wf.
 
 Theorem lt_wf_0 : well_founded lt.
 Proof.
-assert (H : relations_eq lt (fun n m : N => 0 <= n /\ n < m)).
+setoid_replace lt with (fun n m : N => 0 <= n /\ n < m) 
+  using relation (@relations_eq N N).
+apply lt_wf.
 intros x y; split.
 intro H; split; [apply le_0_l | assumption]. now intros [_ H].
-rewrite H; apply lt_wf.
-(* does not work:
-setoid_replace lt with (fun n m : N => 0 <= n /\ n < m) using relation relations_eq.*)
-Qed.
+Defined.
 
 (* Theorems that are true for natural numbers but not for integers *)
 
diff --git a/theories/Numbers/Natural/BigN/BigN.v b/theories/Numbers/Natural/BigN/BigN.v
index 0574c09f..41c255b1 100644
--- a/theories/Numbers/Natural/BigN/BigN.v
+++ b/theories/Numbers/Natural/BigN/BigN.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: BigN.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: BigN.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (** * Natural numbers in base 2^31 *)
 
@@ -47,6 +47,8 @@ Infix "?=" := BigN.compare : bigN_scope.
 Infix "==" := BigN.eq (at level 70, no associativity) : bigN_scope.
 Infix "<" := BigN.lt : bigN_scope.
 Infix "<=" := BigN.le : bigN_scope.
+Notation "x > y" := (BigN.lt y x)(only parsing) : bigN_scope.
+Notation "x >= y" := (BigN.le y x)(only parsing) : bigN_scope.
 Notation "[ i ]" := (BigN.to_Z i) : bigN_scope.
 
 Open Scope bigN_scope.
@@ -62,7 +64,7 @@ Qed.
 
 (** [BigN] is a semi-ring *)
 
-Lemma BigNring : 
+Lemma BigNring :
  semi_ring_theory BigN.zero BigN.one BigN.add BigN.mul BigN.eq.
 Proof.
 constructor.
@@ -76,6 +78,8 @@ exact mul_assoc.
 exact mul_add_distr_r.
 Qed.
 
+Typeclasses unfold NZadd NZsub NZmul.
+
 Add Ring BigNr : BigNring.
 
 (** Todo: tactic translating from [BigN] to [Z] + omega *)
diff --git a/theories/Numbers/Natural/BigN/NMake_gen.ml b/theories/Numbers/Natural/BigN/NMake_gen.ml
index bd0fb5b1..4d6b45c5 100644
--- a/theories/Numbers/Natural/BigN/NMake_gen.ml
+++ b/theories/Numbers/Natural/BigN/NMake_gen.ml
@@ -8,7 +8,7 @@
 (*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
 (************************************************************************)
 
-(*i $Id: NMake_gen.ml 11136 2008-06-18 10:41:34Z herbelin $ i*)
+(*i $Id: NMake_gen.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*S NMake_gen.ml : this file generates NMake.v *)
 
@@ -139,7 +139,7 @@ let _ =
   pr "";
   pr " Definition %s := %s_." t t;
   pr "";
-
+  pr " Typeclasses unfold %s." t;
   pr " Definition w_0 := w0_op.(znz_0).";
   pr "";
 
diff --git a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
index fe068437..84836268 100644
--- a/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
+++ b/theories/Numbers/Natural/SpecViaZ/NSigNAxioms.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: NSigNAxioms.v 11040 2008-06-03 00:04:16Z letouzey $ i*)
+(*i $Id: NSigNAxioms.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Import ZArith.
 Require Import Nnat.
@@ -223,7 +223,7 @@ Qed.
 Add Morphism N.compare with signature N.eq ==> N.eq ==> (@eq comparison) as compare_wd.
 Proof. 
 intros x x' Hx y y' Hy.
-rewrite 2 spec_compare_alt; rewrite Hx, Hy; intuition.
+rewrite 2 spec_compare_alt. unfold N.eq in *. rewrite Hx, Hy; intuition.
 Qed.
 
 Add Morphism N.lt with signature N.eq ==> N.eq ==> iff as NZlt_wd.
diff --git a/theories/Numbers/Rational/BigQ/BigQ.v b/theories/Numbers/Rational/BigQ/BigQ.v
index 39e120f7..21f2513f 100644
--- a/theories/Numbers/Rational/BigQ/BigQ.v
+++ b/theories/Numbers/Rational/BigQ/BigQ.v
@@ -8,19 +8,35 @@
 (*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
 (************************************************************************)
 
-(*i $Id: BigQ.v 11028 2008-06-01 17:34:19Z letouzey $ i*)
+(*i $Id: BigQ.v 11208 2008-07-04 16:57:46Z letouzey $ i*)
 
-Require Export QMake_base.
-Require Import QpMake.
-Require Import QvMake.
-Require Import Q0Make.
-Require Import QifMake.
-Require Import QbiMake.
+Require Import Field Qfield BigN BigZ QSig QMake.
 
-(* We choose for Q the implemention with
-   multiple representation of 0: 0, 1/0, 2/0 etc *)
+(** We choose for BigQ an implemention with
+    multiple representation of 0: 0, 1/0, 2/0 etc.
+    See [QMake.v] *)
 
-Module BigQ <: QSig.QType := Q0.
+(** First, we provide translations functions between [BigN] and [BigZ] *)
+
+Module BigN_BigZ <: NType_ZType BigN.BigN BigZ.
+ Definition Z_of_N := BigZ.Pos.
+ Lemma spec_Z_of_N : forall n, BigZ.to_Z (Z_of_N n) = BigN.to_Z n.
+ Proof.
+ reflexivity.
+ Qed.
+ Definition Zabs_N := BigZ.to_N.
+ Lemma spec_Zabs_N : forall z, BigN.to_Z (Zabs_N z) = Zabs (BigZ.to_Z z).
+ Proof.
+ unfold Zabs_N; intros.
+ rewrite BigZ.spec_to_Z, Zmult_comm; apply Zsgn_Zabs.
+ Qed.
+End BigN_BigZ.
+
+(** This allows to build [BigQ] out of [BigN] and [BigQ] via [QMake] *)
+
+Module BigQ <: QSig.QType := QMake.Make BigN BigZ BigN_BigZ.
+
+(** Notations about [BigQ] *)
 
 Notation bigQ := BigQ.t.
 
@@ -28,8 +44,150 @@ Delimit Scope bigQ_scope with bigQ.
 Bind Scope bigQ_scope with bigQ.
 Bind Scope bigQ_scope with BigQ.t.
 
-Notation " i + j " := (BigQ.add i j) : bigQ_scope.
-Notation " i - j " := (BigQ.sub i j) : bigQ_scope.
-Notation " i * j " := (BigQ.mul i j) : bigQ_scope.
-Notation " i / j " := (BigQ.div i j) : bigQ_scope.
-Notation " i ?= j " := (BigQ.compare i j) : bigQ_scope.
+Infix "+" := BigQ.add : bigQ_scope.
+Infix "-" := BigQ.sub : bigQ_scope.
+Notation "- x" := (BigQ.opp x) : bigQ_scope.
+Infix "*" := BigQ.mul : bigQ_scope.
+Infix "/" := BigQ.div : bigQ_scope.
+Infix "^" := BigQ.power : bigQ_scope.
+Infix "?=" := BigQ.compare : bigQ_scope.
+Infix "==" := BigQ.eq : bigQ_scope.
+Infix "<" := BigQ.lt : bigQ_scope.
+Infix "<=" := BigQ.le : bigQ_scope.
+Notation "x > y" := (BigQ.lt y x)(only parsing) : bigQ_scope.
+Notation "x >= y" := (BigQ.le y x)(only parsing) : bigQ_scope.
+Notation "[ q ]" := (BigQ.to_Q q) : bigQ_scope.
+
+Open Scope bigQ_scope.
+
+(** [BigQ] is a setoid *)
+
+Add Relation BigQ.t BigQ.eq
+ reflexivity proved by (fun x => Qeq_refl [x])
+ symmetry proved by (fun x y => Qeq_sym [x] [y])
+ transitivity proved by (fun x y z => Qeq_trans [x] [y] [z])
+as BigQeq_rel.
+
+Add Morphism BigQ.add with signature BigQ.eq ==> BigQ.eq ==> BigQ.eq as BigQadd_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_add; rewrite H, H0; apply Qeq_refl.
+Qed.
+
+Add Morphism BigQ.opp with signature BigQ.eq ==> BigQ.eq as BigQopp_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_opp; rewrite H; apply Qeq_refl.
+Qed.
+
+Add Morphism BigQ.sub with signature BigQ.eq ==> BigQ.eq ==> BigQ.eq as BigQsub_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_sub; rewrite H, H0; apply Qeq_refl.
+Qed.
+
+Add Morphism BigQ.mul with signature BigQ.eq ==> BigQ.eq ==> BigQ.eq as BigQmul_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_mul; rewrite H, H0; apply Qeq_refl.
+Qed.
+
+Add Morphism BigQ.inv with signature BigQ.eq ==> BigQ.eq as BigQinv_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_inv; rewrite H; apply Qeq_refl.
+Qed.
+
+Add Morphism BigQ.div with signature BigQ.eq ==> BigQ.eq ==> BigQ.eq as BigQdiv_wd.
+Proof.
+ unfold BigQ.eq; intros; rewrite !BigQ.spec_div; rewrite H, H0; apply Qeq_refl.
+Qed.
+
+(* TODO : fix this. For the moment it's useless (horribly slow)
+Hint Rewrite
+ BigQ.spec_0 BigQ.spec_1 BigQ.spec_m1 BigQ.spec_compare
+ BigQ.spec_red BigQ.spec_add BigQ.spec_sub BigQ.spec_opp
+ BigQ.spec_mul BigQ.spec_inv BigQ.spec_div BigQ.spec_power_pos
+ BigQ.spec_square : bigq. *)
+
+
+(** [BigQ] is a field *)
+
+Lemma BigQfieldth :
+ field_theory BigQ.zero BigQ.one BigQ.add BigQ.mul BigQ.sub BigQ.opp BigQ.div BigQ.inv BigQ.eq.
+Proof.
+constructor.
+constructor; intros; red.
+rewrite BigQ.spec_add, BigQ.spec_0; ring.
+rewrite ! BigQ.spec_add; ring.
+rewrite ! BigQ.spec_add; ring.
+rewrite BigQ.spec_mul, BigQ.spec_1; ring.
+rewrite ! BigQ.spec_mul; ring.
+rewrite ! BigQ.spec_mul; ring.
+rewrite BigQ.spec_add, ! BigQ.spec_mul, BigQ.spec_add; ring.
+unfold BigQ.sub; apply Qeq_refl.
+rewrite BigQ.spec_add, BigQ.spec_0, BigQ.spec_opp; ring.
+compute; discriminate.
+intros; red.
+unfold BigQ.div; apply Qeq_refl.
+intros; red.
+rewrite BigQ.spec_mul, BigQ.spec_inv, BigQ.spec_1; field.
+rewrite <- BigQ.spec_0; auto.
+Qed.
+
+Lemma BigQpowerth :
+ power_theory BigQ.one BigQ.mul BigQ.eq Z_of_N BigQ.power.
+Proof.
+constructor.
+intros; red.
+rewrite BigQ.spec_power.
+replace ([r] ^ Z_of_N n)%Q with (pow_N 1 Qmult [r] n)%Q.
+destruct n.
+simpl; compute; auto.
+induction p; simpl; auto; try rewrite !BigQ.spec_mul, !IHp; apply Qeq_refl.
+destruct n; reflexivity.
+Qed.
+
+Lemma BigQ_eq_bool_correct :
+ forall x y, BigQ.eq_bool x y = true -> x==y.
+Proof.
+intros; generalize (BigQ.spec_eq_bool x y); rewrite H; auto.
+Qed.
+
+Lemma BigQ_eq_bool_complete :
+ forall x y, x==y -> BigQ.eq_bool x y = true.
+Proof.
+intros; generalize (BigQ.spec_eq_bool x y).
+destruct BigQ.eq_bool; auto.
+Qed.
+
+(* TODO : improve later the detection of constants ... *)
+
+Ltac BigQcst t :=
+ match t with
+   | BigQ.zero => BigQ.zero
+   | BigQ.one => BigQ.one
+   | BigQ.minus_one => BigQ.minus_one
+   | _ => NotConstant
+ end.
+
+Add Field BigQfield : BigQfieldth
+ (decidable BigQ_eq_bool_correct,
+  completeness BigQ_eq_bool_complete,
+  constants [BigQcst],
+  power_tac BigQpowerth [Qpow_tac]).
+
+Section Examples.
+
+Let ex1 : forall x y z, (x+y)*z ==  (x*z)+(y*z).
+  intros.
+  ring.
+Qed.
+
+Let ex8 : forall x, x ^ 1 == x.
+  intro.
+  ring.
+Qed.
+
+Let ex10 : forall x y, ~(y==BigQ.zero) -> (x/y)*y == x.
+intros.
+field.
+auto.
+Qed.
+
+End Examples.
\ No newline at end of file
diff --git a/theories/Numbers/Rational/BigQ/Q0Make.v b/theories/Numbers/Rational/BigQ/Q0Make.v
deleted file mode 100644
index 93f52c03..00000000
--- a/theories/Numbers/Rational/BigQ/Q0Make.v
+++ /dev/null
@@ -1,1412 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(*i $Id: Q0Make.v 11028 2008-06-01 17:34:19Z letouzey $ i*)
-
-Require Import Bool.
-Require Import ZArith.
-Require Import Znumtheory.
-Require Import BigNumPrelude.
-Require Import Arith.
-Require Export BigN.
-Require Export BigZ.
-Require Import QArith.
-Require Import Qcanon.
-Require Import Qpower.
-Require Import QSig.
-Require Import QMake_base.
-
-Module Q0 <: QType.
-
- Import BinInt Zorder.
-
- (** The notation of a rational number is either an integer x,
-     interpreted as itself or a pair (x,y) of an integer x and a natural
-     number y interpreted as x/y. The pairs (x,0) and (0,y) are all
-     interpreted as 0. *)
-
- Definition t := q_type.
-
- (** Specification with respect to [QArith] *) 
-
- Open Local Scope Q_scope.
-
- Definition of_Z x: t := Qz (BigZ.of_Z x).
-
- Definition of_Q q: t := 
- match q with x # y =>
-  Qq (BigZ.of_Z x) (BigN.of_N (Npos y))
- end.
-
- Definition to_Q (q: t) := 
- match q with 
-  Qz x => BigZ.to_Z x # 1
- |Qq x y => if BigN.eq_bool y BigN.zero then 0
-            else BigZ.to_Z x # Z2P (BigN.to_Z y)
- end.
-
- Notation "[ x ]" := (to_Q x).
-
- Theorem strong_spec_of_Q: forall q: Q, [of_Q q] = q.
- Proof.
- intros (x,y); simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
-   rewrite BigN.spec_of_pos; intros HH; discriminate HH.
- rewrite BigZ.spec_of_Z; simpl.
- rewrite (BigN.spec_of_pos); auto.
- Qed.
-
- Theorem spec_of_Q: forall q: Q, [of_Q q] == q.
- Proof.
- intros; rewrite strong_spec_of_Q; red; auto.
- Qed.
-
- Definition eq x y := [x] == [y].
-
- Definition zero: t := Qz BigZ.zero.
- Definition one: t := Qz BigZ.one.
- Definition minus_one: t := Qz BigZ.minus_one.
-
- Lemma spec_0: [zero] == 0.
- Proof.
- reflexivity.
- Qed.
-
- Lemma spec_1: [one] == 1.
- Proof.
- reflexivity.
- Qed.
-
- Lemma spec_m1: [minus_one] == -(1).
- Proof.
- reflexivity.
- Qed.
-
- Definition opp (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.opp zx)
-  | Qq nx dx => Qq (BigZ.opp nx) dx
-  end.
-
- Theorem strong_spec_opp: forall q, [opp q] = -[q].
- Proof.
- intros [z | x y]; simpl.
- rewrite BigZ.spec_opp; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- rewrite BigZ.spec_opp; auto.
- Qed.
-
- Theorem spec_opp : forall q, [opp q] == -[q].
- Proof.
- intros; rewrite strong_spec_opp; red; auto.
- Qed.
-
- Definition compare (x y: t) :=
-  match x, y with
-  | Qz zx, Qz zy => BigZ.compare zx zy
-  | Qz zx, Qq ny dy => 
-    if BigN.eq_bool dy BigN.zero then BigZ.compare zx BigZ.zero
-    else BigZ.compare (BigZ.mul zx (BigZ.Pos dy)) ny
-  | Qq nx dx, Qz zy => 
-    if BigN.eq_bool dx BigN.zero then BigZ.compare BigZ.zero zy 
-    else BigZ.compare nx (BigZ.mul zy (BigZ.Pos dx))
-  | Qq nx dx, Qq ny dy =>
-    match BigN.eq_bool dx BigN.zero, BigN.eq_bool dy BigN.zero with
-    | true, true => Eq
-    | true, false => BigZ.compare BigZ.zero ny
-    | false, true => BigZ.compare nx BigZ.zero
-    | false, false => BigZ.compare (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx))
-    end
-  end.
-
- Theorem spec_compare: forall q1 q2, (compare q1 q2) = ([q1] ?= [q2]).
- Proof.
- intros [z1 | x1 y1] [z2 | x2 y2]; 
-   unfold Qcompare, compare, to_Q, Qnum, Qden.
- repeat rewrite Zmult_1_r.
- generalize (BigZ.spec_compare z1 z2); case BigZ.compare; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- rewrite Zmult_1_r.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_1_r; generalize (BigZ.spec_compare z1 BigZ.zero);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite HH1; rewrite Zcompare_refl; auto.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (z1 * BigZ.Pos y2) x2)%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero z2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite <- HH1; rewrite Zcompare_refl; auto.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
- rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 (z2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zcompare_refl; auto.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero x2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 BigZ.zero)%bigZ; case BigZ.compare;
-   auto; rewrite BigZ.spec_0.
- intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- repeat rewrite Z2P_correct.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (x1 * BigZ.Pos y2) 
-                               (x2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   repeat rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- Qed.
-
- Definition lt n m := compare n m = Lt.
- Definition le n m := compare n m <> Gt.
- Definition min n m := match compare n m with Gt => m | _ => n end.
- Definition max n m := match compare n m with Lt => m | _ => n end.
-
-(* Je pense que cette fonction normalise bien ... *)
- Definition norm n d: t :=
-  let gcd := BigN.gcd (BigZ.to_N n) d in 
-  match BigN.compare BigN.one gcd with
-  | Lt => 
-    let n := BigZ.div n (BigZ.Pos gcd) in
-    let d := BigN.div d gcd in
-    match BigN.compare d BigN.one with
-    | Gt => Qq n d
-    | Eq => Qz n
-    | Lt => zero
-    end
-  | Eq => Qq n d
-  | Gt => zero (* gcd = 0 => both numbers are 0 *)
-  end.
-
- Theorem spec_norm: forall n q, [norm n q] == [Qq n q].
- Proof.
- intros p q; unfold norm.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_gcd; intros H1.
-   apply Qeq_refl.
- generalize (BigN.spec_pos (q / BigN.gcd (BigZ.to_N p) q)%bigN).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith; intros H2 HH.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl;
-  rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd;
-  auto with zarith.
- generalize H2; rewrite H3; 
-   rewrite Zdiv_0_l; auto with zarith.
- generalize H1 H2 H3 (BigN.spec_pos q); clear H1 H2 H3.
- rewrite spec_to_N.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4; rewrite Z2P_correct; auto with zarith.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl.
- case H3.
- generalize H1 H2 H3 HH; clear H1 H2 H3 HH.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 HH.
-  rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto with zarith.
- case (Zle_lt_or_eq _ _ HH); auto with zarith.
- intros HH1; rewrite <- HH1; ring.
- generalize (Zgcd_is_gcd a b); intros HH1; inversion HH1; auto.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_div;
-   rewrite BigN.spec_gcd; auto with zarith; intros H3.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H4.
- case H3; rewrite H4;  rewrite Zdiv_0_l; auto with zarith.
- simpl.
- assert (FF := BigN.spec_pos q).
- rewrite Z2P_correct; auto with zarith.
- rewrite <- BigN.spec_gcd; rewrite <- BigN.spec_div; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; auto with zarith.
- simpl; rewrite BigZ.spec_div; simpl.
- rewrite BigN.spec_gcd; auto with zarith.
- generalize H1 H2 H3 H4 HH FF; clear H1 H2 H3 H4 HH FF.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4 HH FF.
- rewrite spec_to_N; fold a.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- case (Zle_lt_or_eq _ _ 
-   (BigN.spec_pos (BigN.gcd (BigZ.to_N p) q)));
-  rewrite BigN.spec_gcd; auto with zarith.
- intros; apply False_ind; auto with zarith.
- intros HH2; assert (FF1 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- assert (FF2 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2; simpl.
- rewrite spec_to_N.
- rewrite FF2; ring.
- Qed.
-
-   
- Definition add (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy => 
-      if BigN.eq_bool dy BigN.zero then x 
-      else Qq (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => Qq (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-       let d := BigN.mul dx dy in
-       Qq n d
-    end
-  end.
-
- Theorem spec_add : forall x y, [add x y] == [x] + [y].
- Proof.
- intros [x | nx dx] [y | ny dy]; unfold Qplus; simpl.
- rewrite BigZ.spec_add; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- assert (F1:= BigN.spec_pos dy).
- rewrite Zmult_1_r; red; simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- rewrite Zmult_1_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- assert (F1:= BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- case HH2; auto.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH2; auto.
- case HH1; auto.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH; auto.
- rewrite Zmult_1_r; rewrite Zplus_0_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- simpl.
- generalize (BigN.spec_eq_bool (dx * dy)%bigN BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_mul;
-   rewrite BigN.spec_0; intros HH2.
- (case (Zmult_integral _ _ HH2); intros HH3);
-  [case HH| case HH1]; auto.
- rewrite BigZ.spec_add; repeat rewrite BigZ.spec_mul; simpl.
- assert (Fx: (0 < BigN.to_Z dx)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- assert (Fy: (0 < BigN.to_Z dy)%Z).
-   generalize (BigN.spec_pos dy); auto with zarith.
- red; simpl; rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- apply Zmult_lt_0_compat; auto.
- Qed.
-
- Definition add_norm (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy =>  
-      if BigN.eq_bool dy BigN.zero then x 
-      else norm (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => norm (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-       let d := BigN.mul dx dy in
-       norm n d
-    end
-  end.
-
- Theorem spec_add_norm : forall x y, [add_norm x y] == [x] + [y].
- Proof.
- intros x y; rewrite <- spec_add; auto.
- case x; case y; clear x y; unfold add_norm, add.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- simpl.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- apply Qeq_refl.
- intros p1 p2 n.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- apply Qeq_refl.
- intros p1 q1 p2 q2.
- generalize (BigN.spec_eq_bool q2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- generalize (BigN.spec_eq_bool q1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- apply Qeq_refl.
- Qed.
-
- Definition sub x y := add x (opp y).
-
- Theorem spec_sub : forall x y, [sub x y] == [x] - [y].
- Proof.
- intros x y; unfold sub; rewrite spec_add; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Definition sub_norm x y := add_norm x (opp y).
-
- Theorem spec_sub_norm : forall x y, [sub_norm x y] == [x] - [y].
- Proof.
- intros x y; unfold sub_norm; rewrite spec_add_norm; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Definition mul (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => Qq (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
- Theorem spec_mul : forall x y, [mul x y] == [x] * [y].
- Proof.
- intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl.
- rewrite BigZ.spec_mul; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end;  rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; rewrite Pmult_1_r.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0;  rewrite BigN.spec_mul;
-      intros HH1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- red; simpl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- red; simpl; ring.
- case (Zmult_integral _ _ HH1); intros HH.
-   case HH2; auto.
-   case HH3; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- case HH1; rewrite HH2; ring.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- case HH1; rewrite HH3; ring.
- rewrite BigZ.spec_mul.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- apply Qeq_refl.
-  generalize (BigN.spec_pos dx); auto with zarith.
-  generalize (BigN.spec_pos dy); auto with zarith.
- Qed.
-
-Definition mul_norm (x y: t): t := 
- match x, y with
- | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
- | Qz zx, Qq ny dy =>
-   if BigZ.eq_bool zx BigZ.zero then zero
-   else	
-     let gcd := BigN.gcd (BigZ.to_N zx) dy in
-     match BigN.compare gcd BigN.one with
-       Gt => 
-       let zx := BigZ.div zx (BigZ.Pos gcd) in
-       let d := BigN.div dy gcd in
-       if BigN.eq_bool d BigN.one then Qz (BigZ.mul zx ny)
-       else Qq (BigZ.mul zx ny) d
-      | _  => Qq (BigZ.mul zx ny) dy
-     end
- | Qq nx dx, Qz zy =>   
-   if BigZ.eq_bool zy BigZ.zero then zero
-   else	
-     let gcd := BigN.gcd (BigZ.to_N zy) dx in
-     match BigN.compare gcd BigN.one with
-       Gt => 
-       let zy := BigZ.div zy (BigZ.Pos gcd) in
-       let d := BigN.div dx gcd in
-       if BigN.eq_bool d BigN.one then Qz (BigZ.mul zy nx)
-       else Qq (BigZ.mul zy nx) d
-     | _ =>  Qq (BigZ.mul zy nx) dx
-     end
- | Qq nx dx, Qq ny dy => 
-     let (nx, dy) := 
-       let gcd := BigN.gcd (BigZ.to_N nx) dy in
-       match BigN.compare gcd BigN.one with 
-        Gt => (BigZ.div nx (BigZ.Pos gcd), BigN.div dy gcd)
-       | _ => (nx, dy)
-       end in
-     let (ny, dx) := 
-       let gcd := BigN.gcd (BigZ.to_N ny) dx in
-       match BigN.compare gcd BigN.one with 
-        Gt =>  (BigZ.div ny (BigZ.Pos gcd), BigN.div dx gcd) 
-       | _ =>  (ny, dx)
-       end in 
-     let d := (BigN.mul dx dy) in
-     if BigN.eq_bool d BigN.one then Qz (BigZ.mul ny nx) 
-     else Qq (BigZ.mul ny nx) d
- end.
-
- Theorem spec_mul_norm : forall x y, [mul_norm x y] == [x] * [y].
- Proof.
- intros x y; rewrite <- spec_mul; auto.
- unfold mul_norm, mul; case x; case y; clear x y.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- set (a := BigN.to_Z (BigZ.to_N p2)).
- set (b := BigN.to_Z n).
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- case BigN.eq_bool; try apply Qeq_refl.
- rewrite BigZ.spec_mul; rewrite H.
- red; simpl; ring.
- assert (F: (0 < a)%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p2))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; rewrite BigN.spec_gcd;
-      fold a b; intros H1.
- apply Qeq_refl.
- apply Qeq_refl.
- assert (F0 : (0 < (Zgcd a b))%Z).
-   apply Zlt_trans with 1%Z.
-   red; auto.
-   apply Zgt_lt; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; rewrite BigN.spec_div;
- rewrite BigN.spec_gcd; auto with zarith; 
- fold a b; intros H2.
- assert (F1: b = Zgcd a b).
-   pattern b at 1; rewrite (Zdivide_Zdiv_eq (Zgcd a b) b);
-   auto with zarith.
-   rewrite H2; ring.
-   assert (FF := Zgcd_is_gcd a b); inversion FF; auto.
- assert (F2: (0 < b)%Z).
-   rewrite F1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros H3.
- rewrite H3 in F2; discriminate F2.
- rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; 
-  fold a b; auto with zarith.
- rewrite BigZ.spec_mul.
- red; simpl; rewrite Z2P_correct; auto.
- rewrite Zmult_1_r; rewrite spec_to_N; fold a b.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; rewrite BigN.spec_div;
- rewrite BigN.spec_gcd; fold a b; auto; intros H3.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- apply Qeq_refl.
- case H4; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite H3; ring.
- assert (FF := Zgcd_is_gcd a b); inversion FF; auto.
- simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros H4.
- case H3; rewrite H4; rewrite Zdiv_0_l; auto.
- rewrite BigZ.spec_mul; rewrite BigZ.spec_div; simpl;
-  rewrite BigN.spec_gcd; fold a b; auto with zarith.
- assert (F1: (0 < b)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos n)); fold b; auto with zarith.
- red; simpl.
- rewrite BigZ.spec_mul.
- repeat rewrite Z2P_correct; auto.
- rewrite spec_to_N; fold a.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- ring.
- apply Zgcd_div_pos; auto.
- intros p1 p2 n.
- set (a := BigN.to_Z (BigZ.to_N p1)).
- set (b := BigN.to_Z n).
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- case BigN.eq_bool; try apply Qeq_refl.
- rewrite BigZ.spec_mul; rewrite H.
- red; simpl; ring.
- assert (F: (0 < a)%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p1))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; rewrite BigN.spec_gcd;
-      fold a b; intros H1.
- repeat rewrite BigZ.spec_mul; rewrite Zmult_comm.
- apply Qeq_refl.
- repeat rewrite BigZ.spec_mul; rewrite Zmult_comm.
- apply Qeq_refl.
- assert (F0 : (0 < (Zgcd a b))%Z).
-   apply Zlt_trans with 1%Z.
-   red; auto.
-   apply Zgt_lt; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; rewrite BigN.spec_div;
- rewrite BigN.spec_gcd; auto with zarith; 
- fold a b; intros H2.
- assert (F1: b = Zgcd a b).
-   pattern b at 1; rewrite (Zdivide_Zdiv_eq (Zgcd a b) b);
-   auto with zarith.
-   rewrite H2; ring.
-   assert (FF := Zgcd_is_gcd a b); inversion FF; auto.
- assert (F2: (0 < b)%Z).
-   rewrite F1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros H3.
- rewrite H3 in F2; discriminate F2.
- rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; 
-  fold a b; auto with zarith.
- rewrite BigZ.spec_mul.
- red; simpl; rewrite Z2P_correct; auto.
- rewrite Zmult_1_r; rewrite spec_to_N; fold a b.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; rewrite BigN.spec_div;
- rewrite BigN.spec_gcd; fold a b; auto; intros H3.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- apply Qeq_refl.
- case H4; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite H3; ring.
- assert (FF := Zgcd_is_gcd a b); inversion FF; auto.
- simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros H4.
- case H3; rewrite H4; rewrite Zdiv_0_l; auto.
- rewrite BigZ.spec_mul; rewrite BigZ.spec_div; simpl;
-  rewrite BigN.spec_gcd; fold a b; auto with zarith.
- assert (F1: (0 < b)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos n)); fold b; auto with zarith.
- red; simpl.
- rewrite BigZ.spec_mul.
- repeat rewrite Z2P_correct; auto.
- rewrite spec_to_N; fold a.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- ring.
- apply Zgcd_div_pos; auto.
- set (f := fun p t =>
-        match (BigN.gcd (BigZ.to_N p) t ?= BigN.one)%bigN with
-       | Eq => (p, t)
-       | Lt => (p, t)
-       | Gt =>
-         ((p / BigZ.Pos (BigN.gcd (BigZ.to_N p) t))%bigZ,
-           (t / BigN.gcd (BigZ.to_N p) t)%bigN)
-       end).
- assert (F: forall p t,
-   let (n, d) := f p t in [Qq p t] == [Qq n d]).
- intros p t1; unfold f.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; rewrite BigN.spec_gcd; intros H1.
- apply Qeq_refl.
- apply Qeq_refl.
- set (a := BigN.to_Z (BigZ.to_N p)).
- set (b := BigN.to_Z t1).
- fold a b in H1.
- assert (F0 : (0 < (Zgcd a b))%Z).
-   apply Zlt_trans with 1%Z.
-   red; auto.
-   apply Zgt_lt; auto.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros HH1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; fold b; intros HH2.
- simpl; ring.
- case HH2.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a b; auto.
- rewrite HH1; rewrite Zdiv_0_l; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0;
-   rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a b; auto;
-   intros HH2.
- case HH1.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite HH2; ring.
- assert (FF := Zgcd_is_gcd a b); inversion FF; auto.
- simpl.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; fold a b; auto with zarith.
- assert (F1: (0 < b)%Z).
-    case (Zle_lt_or_eq _ _ (BigN.spec_pos t1)); fold b; auto with zarith.
-    intros HH; case HH1; auto.
- repeat rewrite Z2P_correct; auto.
- rewrite spec_to_N; fold a.
- rewrite Zgcd_div_swap; auto.
- apply Zgcd_div_pos; auto.
- intros HH; rewrite HH in F0; discriminate F0.
- intros p1 n1 p2 n2.
- change ([let (nx , dy) := f p2 n1 in
-         let (ny, dx) := f p1 n2 in
-  if BigN.eq_bool (dx * dy)%bigN BigN.one
-   then Qz (ny * nx)
-  else Qq (ny * nx) (dx * dy)] == [Qq (p2 * p1) (n2 * n1)]).
-  generalize (F p2 n1) (F p1 n2).
- case f; case f.
- intros u1 u2 v1 v2 Hu1 Hv1.
- apply Qeq_trans with [mul (Qq p2 n1) (Qq p1 n2)].
- rewrite spec_mul; rewrite Hu1; rewrite Hv1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; rewrite BigN.spec_mul; intros HH1.
- assert (F1: BigN.to_Z u2 = 1%Z).
-  case (Zmult_1_inversion_l _ _ HH1); auto.
-  generalize (BigN.spec_pos u2); auto with zarith.
- assert (F2: BigN.to_Z v2 = 1%Z).
-  rewrite Zmult_comm in HH1.
-  case (Zmult_1_inversion_l _ _ HH1); auto.
-  generalize (BigN.spec_pos v2); auto with zarith.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- rewrite H1 in F2; discriminate F2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2.
- rewrite H2 in F1; discriminate F1.
- simpl; rewrite BigZ.spec_mul.
- rewrite F1; rewrite F2; simpl; ring.
- rewrite Qmult_comm; rewrite <- spec_mul.
- apply Qeq_refl.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; rewrite BigN.spec_mul;
- rewrite Zmult_comm; intros H1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; rewrite BigN.spec_mul; intros H2; auto.
- case H2; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; rewrite BigN.spec_mul; intros H2; auto.
- case H1; auto.
- Qed.
-
-
-Definition inv (x: t): t := 
- match x with
- | Qz (BigZ.Pos n) => Qq BigZ.one n
- | Qz (BigZ.Neg n) => Qq BigZ.minus_one n
- | Qq (BigZ.Pos n) d => Qq (BigZ.Pos d) n
- | Qq (BigZ.Neg n) d => Qq (BigZ.Neg d) n
- end.
-
- Theorem spec_inv : forall x, [inv x] == /[x].
- Proof.
- intros [ [x | x] | [nx | nx] dx]; unfold inv, Qinv; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- Qed.
-
-Definition inv_norm (x: t): t := 
- match x with
- | Qz (BigZ.Pos n) => 
-   match BigN.compare n BigN.one with
-     Gt => Qq BigZ.one n
-   | _ =>  x
-   end
- | Qz (BigZ.Neg n) => 
-   match BigN.compare n BigN.one with
-     Gt => Qq BigZ.minus_one n
-   | _ =>  x
-   end
- | Qq (BigZ.Pos n) d =>
-   match BigN.compare n BigN.one with
-     Gt => Qq (BigZ.Pos d) n
-   | Eq =>  Qz (BigZ.Pos d) 
-   | Lt => Qz (BigZ.zero)
-   end
- | Qq (BigZ.Neg n) d => 
-   match BigN.compare n BigN.one with
-     Gt => Qq (BigZ.Neg d) n
-   | Eq =>  Qz (BigZ.Neg d) 
-   | Lt => Qz (BigZ.zero)
-   end
- end.
-
- Theorem spec_inv_norm : forall x, [inv_norm x] == /[x].
- Proof.
- intros [ [x | x] | [nx | nx] dx]; unfold inv_norm, Qinv.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H.
- simpl; rewrite H; apply Qeq_refl.
- case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); simpl.
- generalize H; case BigN.to_Z.
- intros _ HH; discriminate HH.
- intros p; case p; auto.
-   intros p1 HH; discriminate HH.
-   intros p1 HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; discriminate HH.
- intros HH; rewrite <- HH.
-   apply Qeq_refl.
- generalize H; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- rewrite H1; intros HH; discriminate.
- generalize H; case BigN.to_Z.
- intros HH; discriminate HH.
- intros; red; simpl; auto.
- intros p HH; discriminate HH.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H.
- simpl; rewrite H; apply Qeq_refl.
- case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); simpl.
- generalize H; case BigN.to_Z.
- intros _ HH; discriminate HH.
- intros p; case p; auto.
-   intros p1 HH; discriminate HH.
-   intros p1 HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; discriminate HH.
- intros HH; rewrite <- HH.
-   apply Qeq_refl.
- generalize H; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- rewrite H1; intros HH; discriminate.
- generalize H; case BigN.to_Z.
- intros HH; discriminate HH.
- intros; red; simpl; auto.
- intros p HH; discriminate HH.
- simpl Qnum.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; simpl.
- case BigN.compare; red; simpl; auto.
- rewrite H1; auto.
- case BigN.eq_bool; auto.
- simpl; rewrite H1; auto.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H2.
- rewrite H2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- red; simpl.
- rewrite Zmult_1_r; rewrite Pmult_1_r; rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- generalize H2 (BigN.spec_pos nx); case (BigN.to_Z nx).
- intros; apply Qeq_refl.
- intros p; case p; clear p.
- intros p HH; discriminate HH.
- intros p HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- simpl; generalize H2; case (BigN.to_Z nx).
- intros HH; discriminate HH.
- intros p Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- rewrite H4 in H2; discriminate H2.
- red; simpl.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p HH; discriminate HH.
- simpl Qnum.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; simpl.
- case BigN.compare; red; simpl; auto.
- rewrite H1; auto.
- case BigN.eq_bool; auto.
- simpl; rewrite H1; auto.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H2.
- rewrite H2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zmult_1_r; rewrite Pmult_1_r; rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- generalize H2 (BigN.spec_pos nx); case (BigN.to_Z nx).
- intros; apply Qeq_refl.
- intros p; case p; clear p.
- intros p HH; discriminate HH.
- intros p HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- simpl; generalize H2; case (BigN.to_Z nx).
- intros HH; discriminate HH.
- intros p Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- rewrite H4 in H2; discriminate H2.
- red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p HH; discriminate HH.
- Qed.
-
- Definition div x y := mul x (inv y).
-
- Theorem spec_div x y: [div x y] == [x] / [y].
- Proof.
- intros x y; unfold div; rewrite spec_mul; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Definition div_norm x y := mul_norm x (inv y).
-
- Theorem spec_div_norm x y: [div_norm x y] == [x] / [y].
- Proof.
- intros x y; unfold div_norm; rewrite spec_mul_norm; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Definition square (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.square zx)
-  | Qq nx dx => Qq (BigZ.square nx) (BigN.square dx)
-  end.
-
- Theorem spec_square : forall x, [square x] == [x] ^ 2.
- Proof.
- intros [ x | nx dx]; unfold square.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- simpl Qpower.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H1; rewrite H; auto.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H; case (Zmult_integral _ _ H1); auto.
- simpl.
- rewrite BigZ.spec_square.
- rewrite Zpos_mult_morphism.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_pos dx); auto with zarith.
- Qed.
-
- Definition power_pos (x: t) p: t :=
-  match x with
-  | Qz zx => Qz (BigZ.power_pos zx p)
-  | Qq nx dx => Qq (BigZ.power_pos nx p) (BigN.power_pos dx p)
-  end.
-
- Theorem spec_power_pos : forall x p, [power_pos x p] == [x] ^ Zpos p.
- Proof.
- intros [x | nx dx] p; unfold power_pos.
-   unfold power_pos; red; simpl.
-   generalize (Qpower_decomp p (BigZ.to_Z x) 1).
-   unfold Qeq; simpl.
-   rewrite Zpower_pos_1_l; simpl Z2P.
-   rewrite Zmult_1_r.
-   intros H; rewrite H.
-   rewrite BigZ.spec_power_pos; simpl; ring.
- simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_power_pos; intros H1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2.
- elim p; simpl.
- intros; red; simpl; auto.
- intros p1 Hp1; rewrite <- Hp1; red; simpl; auto.
- apply Qeq_refl.
- case H2; generalize H1.
- elim p; simpl.
- intros p1 Hrec.
- change (xI p1) with (1 + (xO p1))%positive.
- rewrite Zpower_pos_is_exp; rewrite Zpower_pos_1_r.
- intros HH; case (Zmult_integral _ _ HH); auto.
- rewrite <- Pplus_diag.
- rewrite Zpower_pos_is_exp.
- intros HH1; case (Zmult_integral _ _ HH1); auto.
- intros p1 Hrec.
- rewrite <- Pplus_diag.
- rewrite Zpower_pos_is_exp.
- intros HH1; case (Zmult_integral _ _ HH1); auto.
- rewrite Zpower_pos_1_r; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2.
- case H1; rewrite H2; auto.
- simpl; rewrite Zpower_pos_0_l; auto.
- assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
- assert (F2: (0 < BigN.to_Z dx  ^ ' p)%Z).
-  unfold Zpower; apply Zpower_pos_pos; auto.
- unfold power_pos; red; simpl.
- generalize (Qpower_decomp p (BigZ.to_Z nx) 
-               (Z2P (BigN.to_Z dx))).
- unfold Qeq; simpl.
- repeat rewrite Z2P_correct; auto.
- unfold Qeq; simpl; intros HH.
- rewrite HH.
- rewrite BigZ.spec_power_pos; simpl; ring.
- Qed.
-
- (** Interaction with [Qcanon.Qc] *)
- 
- Open Scope Qc_scope.
-
- Definition of_Qc q := of_Q (this q).
-
- Definition to_Qc q := !!(to_Q q).
-
- Notation "[[ x ]]" := (to_Qc x).
-
- Theorem spec_of_Qc: forall q, [[of_Qc q]] = q.
- Proof.
- intros (x, Hx); unfold of_Qc, to_Qc; simpl.
- apply Qc_decomp; simpl.
- intros.
- rewrite <- H0 at 2; apply Qred_complete.
- apply spec_of_Q.
- Qed.
-
- Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
- Proof.
- intros q; unfold Qcopp, to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- rewrite spec_opp.
- rewrite <- Qred_opp.
- rewrite Qred_correct; red; auto.
- Qed.
-
- Theorem spec_comparec: forall q1 q2,
-  compare q1 q2 = ([[q1]] ?= [[q2]]).
- Proof.
- unfold Qccompare, to_Qc. 
- intros q1 q2; rewrite spec_compare; simpl; auto.
- apply Qcompare_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_addc x y:
-  [[add x y]] = [[x]] + [[y]].
- Proof.
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_add_normc x y:
-  [[add_norm x y]] = [[x]] + [[y]].
- Proof.
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add_norm; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_subc x y:  [[sub x y]] = [[x]] - [[y]].
- Proof.
- intros x y; unfold sub; rewrite spec_addc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Theorem spec_sub_normc x y:
-   [[sub_norm x y]] = [[x]] - [[y]].
- intros x y; unfold sub_norm; rewrite spec_add_normc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Theorem spec_mulc x y:
-  [[mul x y]] = [[x]] * [[y]].
- Proof.
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_mul_normc x y:
-   [[mul_norm x y]] = [[x]] * [[y]].
- Proof.
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul_norm; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_invc x:
-   [[inv x]] =  /[[x]].
- Proof.
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_inv_normc x:
-   [[inv_norm x]] =  /[[x]].
- Proof.
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv_norm; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_divc x y: [[div x y]] = [[x]] / [[y]].
- Proof.
- intros x y; unfold div; rewrite spec_mulc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto. 
- Qed.
-
- Theorem spec_div_normc x y: [[div_norm x y]] = [[x]] / [[y]].
- Proof.
- intros x y; unfold div_norm; rewrite spec_mul_normc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto.
- Qed.
-
- Theorem spec_squarec x: [[square x]] =  [[x]]^2.
- Proof.
- intros x; unfold to_Qc.
- apply trans_equal with (!! ([x]^2)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_square; auto.
- simpl Qcpower.
- replace (!! [x] * 1) with (!![x]); try ring.
- simpl.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Theorem spec_power_posc x p:
-   [[power_pos x p]] = [[x]] ^ nat_of_P p.
- Proof.
- intros x p; unfold to_Qc.
- apply trans_equal with (!! ([x]^Zpos p)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_power_pos; auto.
- pattern p; apply Pind; clear p.
- simpl; ring.
- intros p Hrec.
- rewrite nat_of_P_succ_morphism; simpl Qcpower.
- rewrite <- Hrec.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _;
- unfold this.
- apply Qred_complete.
- assert (F: [x] ^ ' Psucc p == [x] *   [x] ^ ' p).
-  simpl; case x; simpl; clear x Hrec.
-  intros x; simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  intros nx dx.
-  match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-  end; auto; rewrite BigN.spec_0.
-  unfold Qpower_positive.
-  assert (tmp: forall p, pow_pos Qmult 0%Q p = 0%Q).
-    intros p1; elim p1; simpl; auto; clear p1.
-    intros p1 Hp1; rewrite Hp1; auto.
-    intros p1 Hp1; rewrite Hp1; auto.
-  repeat rewrite tmp; intros; red; simpl; auto.
-  intros H1.
-  assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
-  simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  repeat rewrite Zpos_mult_morphism.
-  repeat rewrite Z2P_correct; auto.
-  2: apply Zpower_pos_pos; auto.
-  2: apply Zpower_pos_pos; auto.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
- rewrite F.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-End Q0.
diff --git a/theories/Numbers/Rational/BigQ/QMake.v b/theories/Numbers/Rational/BigQ/QMake.v
new file mode 100644
index 00000000..494420bd
--- /dev/null
+++ b/theories/Numbers/Rational/BigQ/QMake.v
@@ -0,0 +1,1345 @@
+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
+(************************************************************************)
+
+(*i $Id: QMake.v 11208 2008-07-04 16:57:46Z letouzey $ i*)
+
+Require Import BigNumPrelude ROmega.
+Require Import QArith Qcanon Qpower.
+Require Import NSig ZSig QSig.
+
+Module Type NType_ZType (N:NType)(Z:ZType).
+ Parameter Z_of_N : N.t -> Z.t.
+ Parameter spec_Z_of_N : forall n, Z.to_Z (Z_of_N n) = N.to_Z n.
+ Parameter Zabs_N : Z.t -> N.t.
+ Parameter spec_Zabs_N : forall z, N.to_Z (Zabs_N z) = Zabs (Z.to_Z z).
+End NType_ZType.
+
+Module Make (N:NType)(Z:ZType)(Import NZ:NType_ZType N Z) <: QType.
+
+ (** The notation of a rational number is either an integer x,
+     interpreted as itself or a pair (x,y) of an integer x and a natural
+     number y interpreted as x/y. The pairs (x,0) and (0,y) are all
+     interpreted as 0. *)
+
+ Inductive t_ := 
+  | Qz : Z.t -> t_
+  | Qq : Z.t -> N.t -> t_.
+
+ Definition t := t_.
+
+ (** Specification with respect to [QArith] *) 
+
+ Open Local Scope Q_scope.
+
+ Definition of_Z x: t := Qz (Z.of_Z x).
+
+ Definition of_Q (q:Q) : t := 
+  let (x,y) := q in 
+  match y with 
+    | 1%positive => Qz (Z.of_Z x)
+    | _ => Qq (Z.of_Z x) (N.of_N (Npos y))
+  end.
+
+ Definition to_Q (q: t) := 
+ match q with 
+   | Qz x => Z.to_Z x # 1
+   | Qq x y => if N.eq_bool y N.zero then 0
+               else Z.to_Z x # Z2P (N.to_Z y)
+ end.
+
+ Notation "[ x ]" := (to_Q x).
+
+ Theorem strong_spec_of_Q: forall q: Q, [of_Q q] = q.
+ Proof.
+ intros(x,y); destruct y; simpl; rewrite Z.spec_of_Z; auto.
+ generalize (N.spec_eq_bool (N.of_N (Npos y~1)) N.zero); 
+  case N.eq_bool; auto; rewrite N.spec_0.
+ rewrite N.spec_of_N; intros; discriminate.
+ rewrite N.spec_of_N; auto.
+ generalize (N.spec_eq_bool (N.of_N (Npos y~0)) N.zero); 
+  case N.eq_bool; auto; rewrite N.spec_0.
+ rewrite N.spec_of_N; intros; discriminate.
+ rewrite N.spec_of_N; auto.
+ Qed.
+
+ Theorem spec_of_Q: forall q: Q, [of_Q q] == q.
+ Proof.
+ intros; rewrite strong_spec_of_Q; red; auto.
+ Qed.
+
+ Definition eq x y := [x] == [y].
+
+ Definition zero: t := Qz Z.zero.
+ Definition one: t := Qz Z.one.
+ Definition minus_one: t := Qz Z.minus_one.
+
+ Lemma spec_0: [zero] == 0.
+ Proof.
+ simpl; rewrite Z.spec_0; reflexivity.
+ Qed.
+
+ Lemma spec_1: [one] == 1.
+ Proof.
+ simpl; rewrite Z.spec_1; reflexivity.
+ Qed.
+
+ Lemma spec_m1: [minus_one] == -(1).
+ Proof.
+ simpl; rewrite Z.spec_m1; reflexivity.
+ Qed.
+
+ Definition compare (x y: t) :=
+  match x, y with
+  | Qz zx, Qz zy => Z.compare zx zy
+  | Qz zx, Qq ny dy => 
+    if N.eq_bool dy N.zero then Z.compare zx Z.zero
+    else Z.compare (Z.mul zx (Z_of_N dy)) ny
+  | Qq nx dx, Qz zy => 
+    if N.eq_bool dx N.zero then Z.compare Z.zero zy 
+    else Z.compare nx (Z.mul zy (Z_of_N dx))
+  | Qq nx dx, Qq ny dy =>
+    match N.eq_bool dx N.zero, N.eq_bool dy N.zero with
+    | true, true => Eq
+    | true, false => Z.compare Z.zero ny
+    | false, true => Z.compare nx Z.zero
+    | false, false => Z.compare (Z.mul nx (Z_of_N dy)) 
+                                (Z.mul ny (Z_of_N dx))
+    end
+  end.
+
+ Lemma Zcompare_spec_alt : 
+  forall z z', Z.compare z z' = (Z.to_Z z ?= Z.to_Z z')%Z.
+ Proof.
+ intros; generalize (Z.spec_compare z z'); destruct Z.compare; auto.
+ intro H; rewrite H; symmetry; apply Zcompare_refl.
+ Qed.
+ 
+ Lemma Ncompare_spec_alt : 
+  forall n n', N.compare n n' = (N.to_Z n ?= N.to_Z n')%Z.
+ Proof.
+ intros; generalize (N.spec_compare n n'); destruct N.compare; auto.
+ intro H; rewrite H; symmetry; apply Zcompare_refl.
+ Qed.
+
+ Lemma N_to_Z2P : forall n, N.to_Z n <> 0%Z -> 
+  Zpos (Z2P (N.to_Z n)) = N.to_Z n.
+ Proof.
+ intros; apply Z2P_correct.
+ generalize (N.spec_pos n); romega.
+ Qed.
+
+ Hint Rewrite 
+  Zplus_0_r Zplus_0_l Zmult_0_r Zmult_0_l Zmult_1_r Zmult_1_l 
+  Z.spec_0 N.spec_0 Z.spec_1 N.spec_1 Z.spec_m1 Z.spec_opp
+  Zcompare_spec_alt Ncompare_spec_alt
+  Z.spec_add N.spec_add Z.spec_mul N.spec_mul 
+  Z.spec_gcd N.spec_gcd Zgcd_Zabs
+  spec_Z_of_N spec_Zabs_N
+ : nz.
+ Ltac nzsimpl := autorewrite with nz in *.
+
+ Ltac destr_neq_bool := repeat
+ (match goal with |- context [N.eq_bool ?x ?y] => 
+   generalize (N.spec_eq_bool x y); case N.eq_bool
+  end).
+ 
+ Ltac destr_zeq_bool := repeat
+ (match goal with |- context [Z.eq_bool ?x ?y] => 
+   generalize (Z.spec_eq_bool x y); case Z.eq_bool
+  end).
+
+ Ltac simpl_ndiv := rewrite N.spec_div by (nzsimpl; romega).
+ Tactic Notation "simpl_ndiv" "in" "*" := 
+   rewrite N.spec_div in * by (nzsimpl; romega).
+
+ Ltac simpl_zdiv := rewrite Z.spec_div by (nzsimpl; romega).
+ Tactic Notation "simpl_zdiv" "in" "*" := 
+   rewrite Z.spec_div in * by (nzsimpl; romega).
+
+ Ltac qsimpl := try red; unfold to_Q; simpl; intros; 
+  destr_neq_bool; destr_zeq_bool; simpl; nzsimpl; auto; intros.
+
+ Theorem spec_compare: forall q1 q2, (compare q1 q2) = ([q1] ?= [q2]).
+ Proof.
+ intros [z1 | x1 y1] [z2 | x2 y2]; 
+   unfold Qcompare, compare; qsimpl; rewrite ! N_to_Z2P; auto.
+ Qed.
+
+ Definition lt n m := compare n m = Lt.
+ Definition le n m := compare n m <> Gt.
+ Definition min n m := match compare n m with Gt => m | _ => n end.
+ Definition max n m := match compare n m with Lt => m | _ => n end.
+
+ Definition eq_bool n m := 
+  match compare n m with Eq => true | _ => false end.
+
+ Theorem spec_eq_bool: forall x y,
+  if eq_bool x y then [x] == [y] else ~([x] == [y]).
+ Proof.
+ intros.
+ unfold eq_bool.
+ rewrite spec_compare.
+ generalize (Qeq_alt [x] [y]).
+ destruct Qcompare.
+ intros H; rewrite H; auto.
+ intros H H'; rewrite H in H'; discriminate.
+ intros H H'; rewrite H in H'; discriminate.
+ Qed.
+
+ (** Normalisation function *)
+
+ Definition norm n d : t :=
+  let gcd := N.gcd (Zabs_N n) d in 
+  match N.compare N.one gcd with
+  | Lt => 
+    let n := Z.div n (Z_of_N gcd) in
+    let d := N.div d gcd in
+    match N.compare d N.one with
+    | Gt => Qq n d
+    | Eq => Qz n
+    | Lt => zero
+    end
+  | Eq => Qq n d
+  | Gt => zero (* gcd = 0 => both numbers are 0 *)
+  end.
+
+ Theorem spec_norm: forall n q, [norm n q] == [Qq n q].
+ Proof.
+ intros p q; unfold norm.
+ assert (Hp := N.spec_pos (Zabs_N p)).
+ assert (Hq := N.spec_pos q).
+ nzsimpl.
+ destr_zcompare.
+ qsimpl.
+
+ simpl_ndiv.
+ destr_zcompare.
+ qsimpl.
+ rewrite H1 in *; rewrite Zdiv_0_l in H0; discriminate.
+ rewrite N_to_Z2P; auto.
+ simpl_zdiv; nzsimpl.
+ rewrite Zgcd_div_swap0, H0; romega.
+
+ qsimpl.
+ assert (0 < N.to_Z q / Zgcd (Z.to_Z p) (N.to_Z q))%Z.
+  apply Zgcd_div_pos; romega.
+ romega.
+
+ qsimpl.
+ simpl_ndiv in *; nzsimpl; romega.
+ simpl_ndiv in *.
+ rewrite H1, Zdiv_0_l in H2; elim H2; auto.
+ rewrite 2 N_to_Z2P; auto.
+ simpl_ndiv; simpl_zdiv; nzsimpl.
+ apply Zgcd_div_swap0; romega.
+
+ qsimpl.
+ assert (H' : Zgcd (Z.to_Z p) (N.to_Z q) = 0%Z).
+  generalize (Zgcd_is_pos (Z.to_Z p) (N.to_Z q)); romega.
+ symmetry; apply (Zgcd_inv_0_l _ _ H'); auto.
+ Qed.
+
+ Theorem strong_spec_norm : forall p q, [norm p q] = Qred [Qq p q].
+ Proof.
+ intros.
+ replace (Qred [Qq p q]) with (Qred [norm p q]) by 
+  (apply Qred_complete; apply spec_norm).
+ symmetry; apply Qred_identity.
+ unfold norm.
+ assert (Hp := N.spec_pos (Zabs_N p)).
+ assert (Hq := N.spec_pos q).
+ nzsimpl.
+ destr_zcompare.
+ (* Eq *)
+ simpl.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ intros.
+ rewrite N_to_Z2P; auto.
+ (* Lt *)
+ simpl_ndiv.
+ destr_zcompare.
+ qsimpl; auto.
+ qsimpl.
+ qsimpl.
+ simpl_zdiv; nzsimpl.
+ rewrite N_to_Z2P; auto.
+ clear H1.
+ simpl_ndiv; nzsimpl.
+ rewrite Zgcd_1_rel_prime.
+ destruct (Z_lt_le_dec 0 (N.to_Z q)).
+ apply Zis_gcd_rel_prime; auto with zarith.
+ apply Zgcd_is_gcd.
+ replace (N.to_Z q) with 0%Z in * by romega.
+ rewrite Zdiv_0_l in H0; discriminate.
+ (* Gt *)
+ simpl; auto.
+ Qed.
+
+ (** Reduction function : producing irreducible fractions *) 
+
+ Definition red (x : t) : t := 
+  match x with 
+   | Qz z => x
+   | Qq n d => norm n d
+  end.
+
+ Definition Reduced x := [red x] = [x].
+
+ Theorem spec_red : forall x, [red x] == [x].
+ Proof.
+ intros [ z | n d ].
+ auto with qarith.
+ unfold red.
+ apply spec_norm.
+ Qed.
+
+ Theorem strong_spec_red : forall x, [red x] = Qred [x].
+ Proof.
+ intros [ z | n d ].
+ unfold red.
+ symmetry; apply Qred_identity; simpl; auto.
+ unfold red; apply strong_spec_norm.
+ Qed.
+   
+ Definition add (x y: t): t :=
+  match x with
+  | Qz zx =>
+    match y with
+    | Qz zy => Qz (Z.add zx zy)
+    | Qq ny dy => 
+      if N.eq_bool dy N.zero then x 
+      else Qq (Z.add (Z.mul zx (Z_of_N dy)) ny) dy
+    end
+  | Qq nx dx =>
+    if N.eq_bool dx N.zero then y 
+    else match y with
+    | Qz zy => Qq (Z.add nx (Z.mul zy (Z_of_N dx))) dx
+    | Qq ny dy =>
+      if N.eq_bool dy N.zero then x
+      else
+       let n := Z.add (Z.mul nx (Z_of_N dy)) (Z.mul ny (Z_of_N dx)) in
+       let d := N.mul dx dy in
+       Qq n d
+    end
+  end.
+
+ Theorem spec_add : forall x y, [add x y] == [x] + [y].
+ Proof.
+ intros [x | nx dx] [y | ny dy]; unfold Qplus; qsimpl.
+ intuition.
+ rewrite N_to_Z2P; auto.
+ intuition.
+ rewrite Pmult_1_r, N_to_Z2P; auto.
+ intuition.
+ rewrite Pmult_1_r, N_to_Z2P; auto.
+ destruct (Zmult_integral _ _ H); intuition.
+ rewrite Zpos_mult_morphism, 2 N_to_Z2P; auto.
+ rewrite (Z2P_correct (N.to_Z dx * N.to_Z dy)); auto.
+ apply Zmult_lt_0_compat.
+  generalize (N.spec_pos dx); romega.
+  generalize (N.spec_pos dy); romega.
+ Qed.
+
+ Definition add_norm (x y: t): t :=
+  match x with
+  | Qz zx =>
+    match y with
+    | Qz zy => Qz (Z.add zx zy)
+    | Qq ny dy =>  
+      if N.eq_bool dy N.zero then x 
+      else norm (Z.add (Z.mul zx (Z_of_N dy)) ny) dy
+    end
+  | Qq nx dx =>
+    if N.eq_bool dx N.zero then y 
+    else match y with
+    | Qz zy => norm (Z.add nx (Z.mul zy (Z_of_N dx))) dx
+    | Qq ny dy =>
+      if N.eq_bool dy N.zero then x
+      else
+       let n := Z.add (Z.mul nx (Z_of_N dy)) (Z.mul ny (Z_of_N dx)) in
+       let d := N.mul dx dy in
+       norm n d
+    end
+  end.
+
+ Theorem spec_add_norm : forall x y, [add_norm x y] == [x] + [y].
+ Proof.
+ intros x y; rewrite <- spec_add.
+ destruct x; destruct y; unfold add_norm, add; 
+ destr_neq_bool; auto using Qeq_refl, spec_norm.
+ Qed.
+
+ Theorem strong_spec_add_norm : forall x y : t, 
+   Reduced x -> Reduced y -> Reduced (add_norm x y).
+ Proof.
+ unfold Reduced; intros.
+ rewrite strong_spec_red.
+ rewrite <- (Qred_complete [add x y]); 
+  [ | rewrite spec_add, spec_add_norm; apply Qeq_refl ].
+ rewrite <- strong_spec_red.
+ destruct x as [zx|nx dx]; destruct y as [zy|ny dy].
+ simpl in *; auto.
+ simpl; intros.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ simpl; intros.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ simpl; intros.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ Qed.
+
+ Definition opp (x: t): t :=
+  match x with
+  | Qz zx => Qz (Z.opp zx)
+  | Qq nx dx => Qq (Z.opp nx) dx
+  end.
+
+ Theorem strong_spec_opp: forall q, [opp q] = -[q].
+ Proof.
+ intros [z | x y]; simpl.
+ rewrite Z.spec_opp; auto.
+ match goal with  |- context[N.eq_bool ?X ?Y] => 
+  generalize (N.spec_eq_bool X Y); case N.eq_bool
+ end; auto; rewrite N.spec_0.
+ rewrite Z.spec_opp; auto.
+ Qed.
+
+ Theorem spec_opp : forall q, [opp q] == -[q].
+ Proof.
+ intros; rewrite strong_spec_opp; red; auto.
+ Qed.
+
+ Theorem strong_spec_opp_norm : forall q, Reduced q -> Reduced (opp q).
+ Proof.
+ unfold Reduced; intros.
+ rewrite strong_spec_opp, <- H, !strong_spec_red, <- Qred_opp.
+ apply Qred_complete; apply spec_opp.
+ Qed.
+
+ Definition sub x y := add x (opp y).
+
+ Theorem spec_sub : forall x y, [sub x y] == [x] - [y].
+ Proof.
+ intros x y; unfold sub; rewrite spec_add; auto.
+ rewrite spec_opp; ring.
+ Qed.
+
+ Definition sub_norm x y := add_norm x (opp y).
+
+ Theorem spec_sub_norm : forall x y, [sub_norm x y] == [x] - [y].
+ Proof.
+ intros x y; unfold sub_norm; rewrite spec_add_norm; auto.
+ rewrite spec_opp; ring.
+ Qed.
+
+ Theorem strong_spec_sub_norm : forall x y, 
+  Reduced x -> Reduced y -> Reduced (sub_norm x y).
+ Proof.
+ intros.
+ unfold sub_norm.
+ apply strong_spec_add_norm; auto.
+ apply strong_spec_opp_norm; auto.
+ Qed.
+
+ Definition mul (x y: t): t :=
+  match x, y with
+  | Qz zx, Qz zy => Qz (Z.mul zx zy)
+  | Qz zx, Qq ny dy => Qq (Z.mul zx ny) dy
+  | Qq nx dx, Qz zy => Qq (Z.mul nx zy) dx
+  | Qq nx dx, Qq ny dy => Qq (Z.mul nx ny) (N.mul dx dy)
+  end.
+
+ Theorem spec_mul : forall x y, [mul x y] == [x] * [y].
+ Proof.
+ intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl; qsimpl.
+ rewrite Pmult_1_r, N_to_Z2P; auto.
+ destruct (Zmult_integral _ _ H1); intuition.
+ rewrite H0 in H1; elim H1; auto.
+ rewrite H0 in H1; elim H1; auto.
+ rewrite H in H1; nzsimpl; elim H1; auto.
+ rewrite Zpos_mult_morphism, 2 N_to_Z2P; auto.
+ rewrite (Z2P_correct (N.to_Z dx * N.to_Z dy)); auto.
+ apply Zmult_lt_0_compat.
+  generalize (N.spec_pos dx); omega.
+  generalize (N.spec_pos dy); omega.
+ Qed.
+
+ Lemma norm_denum : forall n d, 
+  [if N.eq_bool d N.one then Qz n else Qq n d] == [Qq n d].
+ Proof.
+ intros; simpl; qsimpl.
+ rewrite H0 in H; discriminate.
+ rewrite N_to_Z2P, H0; auto with zarith.
+ Qed.
+
+ Definition irred n d :=        
+   let gcd := N.gcd (Zabs_N n) d in
+   match N.compare gcd N.one with 
+     | Gt => (Z.div n (Z_of_N gcd), N.div d gcd)
+     | _ => (n, d)
+   end.
+
+ Lemma spec_irred : forall n d, exists g, 
+  let (n',d') := irred n d in 
+  (Z.to_Z n' * g = Z.to_Z n)%Z /\ (N.to_Z d' * g = N.to_Z d)%Z.
+ Proof.
+ intros.
+ unfold irred; nzsimpl; simpl.
+ destr_zcompare.
+ exists 1%Z; nzsimpl; auto.
+ exists 0%Z; nzsimpl.
+ assert (Zgcd (Z.to_Z n) (N.to_Z d) = 0%Z).
+  generalize (Zgcd_is_pos (Z.to_Z n) (N.to_Z d)); romega.
+ clear H.
+ split.
+ symmetry; apply (Zgcd_inv_0_l _ _ H0).
+ symmetry; apply (Zgcd_inv_0_r _ _ H0).
+ exists (Zgcd (Z.to_Z n) (N.to_Z d)).
+ simpl.
+ split.
+ simpl_zdiv; nzsimpl.
+ destruct (Zgcd_is_gcd (Z.to_Z n) (N.to_Z d)).
+ rewrite Zmult_comm; symmetry; apply Zdivide_Zdiv_eq; auto with zarith.
+ simpl_ndiv; nzsimpl.
+ destruct (Zgcd_is_gcd (Z.to_Z n) (N.to_Z d)).
+ rewrite Zmult_comm; symmetry; apply Zdivide_Zdiv_eq; auto with zarith.
+ Qed.
+
+ Lemma spec_irred_zero : forall n d, 
+   (N.to_Z d = 0)%Z <-> (N.to_Z (snd (irred n d)) = 0)%Z.
+ Proof.
+ intros.
+ unfold irred.
+ split.
+ nzsimpl; intros.
+ destr_zcompare; auto.
+ simpl.
+ simpl_ndiv; nzsimpl.
+ rewrite H, Zdiv_0_l; auto.
+ nzsimpl; destr_zcompare; simpl; auto.
+ simpl_ndiv; nzsimpl.
+ intros.
+ generalize (N.spec_pos d); intros.
+ destruct (N.to_Z d); auto.
+ assert (0 < 0)%Z.
+  rewrite <- H0 at 2.
+  apply Zgcd_div_pos; auto with zarith.
+  compute; auto.
+ discriminate.
+ compute in H1; elim H1; auto.
+ Qed.
+
+ Lemma strong_spec_irred : forall n d, 
+  (N.to_Z d <> 0%Z) -> 
+  let (n',d') := irred n d in Zgcd (Z.to_Z n') (N.to_Z d') = 1%Z.
+ Proof.
+ unfold irred; intros.
+ nzsimpl.
+ destr_zcompare; simpl; auto.
+ elim H.
+ apply (Zgcd_inv_0_r (Z.to_Z n)).
+ generalize (Zgcd_is_pos (Z.to_Z n) (N.to_Z d)); romega.
+
+ simpl_ndiv; simpl_zdiv; nzsimpl.
+ rewrite Zgcd_1_rel_prime.
+ apply Zis_gcd_rel_prime.
+ generalize (N.spec_pos d); romega.
+ generalize (Zgcd_is_pos (Z.to_Z n) (N.to_Z d)); romega.
+ apply Zgcd_is_gcd; auto.
+ Qed.
+
+ Definition mul_norm_Qz_Qq z n d := 
+   if Z.eq_bool z Z.zero then zero 
+   else
+    let gcd := N.gcd (Zabs_N z) d in
+    match N.compare gcd N.one with
+      | Gt => 
+        let z := Z.div z (Z_of_N gcd) in
+        let d := N.div d gcd in
+        if N.eq_bool d N.one then Qz (Z.mul z n) else Qq (Z.mul z n) d
+      | _  => Qq (Z.mul z n) d
+    end.
+
+ Definition mul_norm (x y: t): t := 
+ match x, y with
+ | Qz zx, Qz zy => Qz (Z.mul zx zy)
+ | Qz zx, Qq ny dy => mul_norm_Qz_Qq zx ny dy
+ | Qq nx dx, Qz zy => mul_norm_Qz_Qq zy nx dx
+ | Qq nx dx, Qq ny dy => 
+    let (nx, dy) := irred nx dy in 
+    let (ny, dx) := irred ny dx in 
+    let d := N.mul dx dy in
+    if N.eq_bool d N.one then Qz (Z.mul ny nx) else Qq (Z.mul ny nx) d
+ end.
+
+ Lemma spec_mul_norm_Qz_Qq : forall z n d, 
+   [mul_norm_Qz_Qq z n d] == [Qq (Z.mul z n) d].
+ Proof.
+ intros z n d; unfold mul_norm_Qz_Qq; nzsimpl; rewrite Zcompare_gt.
+ destr_zeq_bool; intros Hz; nzsimpl.
+ qsimpl; rewrite Hz; auto.
+ assert (Hd := N.spec_pos d).
+ destruct Z_le_gt_dec.
+ qsimpl.
+ rewrite norm_denum.
+ qsimpl.
+ simpl_ndiv in *; nzsimpl.
+ rewrite (Zdiv_gcd_zero _ _ H0 H) in z0; discriminate.
+ simpl_ndiv in *; nzsimpl.
+ rewrite H, Zdiv_0_l in H0; elim H0; auto.
+ rewrite 2 N_to_Z2P; auto.
+ simpl_ndiv; simpl_zdiv; nzsimpl.
+ rewrite (Zmult_comm (Z.to_Z z)), <- 2 Zmult_assoc.
+ rewrite <- Zgcd_div_swap0; auto with zarith; ring.
+ Qed.
+
+ Lemma strong_spec_mul_norm_Qz_Qq : forall z n d, 
+   Reduced (Qq n d) -> Reduced (mul_norm_Qz_Qq z n d).
+ Proof.
+ unfold Reduced; intros z n d.
+ rewrite 2 strong_spec_red, 2 Qred_iff.
+ simpl; nzsimpl.
+ destr_neq_bool; intros Hd H; simpl in *; nzsimpl.
+ 
+ unfold mul_norm_Qz_Qq; nzsimpl; rewrite Zcompare_gt.
+ destr_zeq_bool; intros Hz; simpl; nzsimpl; simpl; auto.
+ destruct Z_le_gt_dec.
+ simpl; nzsimpl.
+ destr_neq_bool; simpl; nzsimpl; auto.
+ intros H'; elim H'; auto.
+ destr_neq_bool; simpl; nzsimpl.
+ simpl_ndiv; nzsimpl; rewrite Hd, Zdiv_0_l; intros; discriminate.
+ intros _.
+ destr_neq_bool; simpl; nzsimpl; auto.
+ simpl_ndiv; nzsimpl; rewrite Hd, Zdiv_0_l; intro H'; elim H'; auto.
+
+ rewrite N_to_Z2P in H; auto.
+ unfold mul_norm_Qz_Qq; nzsimpl; rewrite Zcompare_gt.
+ destr_zeq_bool; intros Hz; simpl; nzsimpl; simpl; auto.
+ destruct Z_le_gt_dec as [H'|H'].
+ simpl; nzsimpl.
+ destr_neq_bool; simpl; nzsimpl; auto.
+ intros.
+ rewrite N_to_Z2P; auto.
+ apply Zgcd_mult_rel_prime; auto.
+  generalize (Zgcd_inv_0_l (Z.to_Z z) (N.to_Z d))
+    (Zgcd_is_pos (Z.to_Z z) (N.to_Z d)); romega.
+ destr_neq_bool; simpl; nzsimpl; auto.
+ simpl_ndiv; simpl_zdiv; nzsimpl.
+ intros.
+ destr_neq_bool; simpl; nzsimpl; auto.
+ simpl_ndiv in *; nzsimpl.
+ intros.
+ rewrite Z2P_correct.
+ apply Zgcd_mult_rel_prime.
+ rewrite Zgcd_1_rel_prime.
+ apply Zis_gcd_rel_prime.
+ generalize (N.spec_pos d); romega.
+ generalize (Zgcd_is_pos (Z.to_Z z) (N.to_Z d)); romega.
+ apply Zgcd_is_gcd.
+ destruct (Zgcd_is_gcd (Z.to_Z z) (N.to_Z d)) as [ (z0,Hz0) (d0,Hd0) Hzd].
+ replace (N.to_Z d / Zgcd (Z.to_Z z) (N.to_Z d))%Z with d0.
+ rewrite Zgcd_1_rel_prime in *.
+ apply bezout_rel_prime.
+ destruct (rel_prime_bezout _ _ H) as [u v Huv].
+ apply Bezout_intro with u (v*(Zgcd (Z.to_Z z) (N.to_Z d)))%Z.
+ rewrite <- Huv; rewrite Hd0 at 2; ring.
+ rewrite Hd0 at 1.
+ symmetry; apply Z_div_mult_full; auto with zarith.
+ apply Zgcd_div_pos.
+ generalize (N.spec_pos d); romega.
+ generalize (Zgcd_is_pos (Z.to_Z z) (N.to_Z d)); romega.
+ Qed.
+
+ Theorem spec_mul_norm : forall x y, [mul_norm x y] == [x] * [y].
+ Proof.
+ intros x y; rewrite <- spec_mul; auto.
+ unfold mul_norm, mul; destruct x; destruct y.
+ apply Qeq_refl.
+ apply spec_mul_norm_Qz_Qq.
+ rewrite spec_mul_norm_Qz_Qq; qsimpl; ring.
+
+ rename t0 into nx, t3 into dy, t2 into ny, t1 into dx.
+ destruct (spec_irred nx dy) as (g & Hg).
+ destruct (spec_irred ny dx) as (g' & Hg').
+ assert (Hz := spec_irred_zero nx dy).
+ assert (Hz':= spec_irred_zero ny dx).
+ destruct irred as (n1,d1); destruct irred as (n2,d2). 
+ simpl snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2'].
+ rewrite norm_denum.
+ qsimpl.
+
+ elim H; destruct (Zmult_integral _ _ H0) as [Eq|Eq].
+ rewrite <- Hz' in Eq; rewrite Eq; simpl; auto.
+ rewrite <- Hz in Eq; rewrite Eq; nzsimpl; auto.
+
+ elim H0; destruct (Zmult_integral _ _ H) as [Eq|Eq].
+ rewrite Hz' in Eq; rewrite Eq; simpl; auto.
+ rewrite Hz in Eq; rewrite Eq; nzsimpl; auto.
+
+ rewrite 2 Z2P_correct.
+ rewrite <- Hg1, <- Hg2, <- Hg1', <- Hg2'; ring.
+
+ assert (0 <= N.to_Z d2 * N.to_Z d1)%Z 
+  by (apply Zmult_le_0_compat; apply N.spec_pos).
+ romega.
+ assert (0 <= N.to_Z dx * N.to_Z dy)%Z 
+  by (apply Zmult_le_0_compat; apply N.spec_pos).
+ romega.
+ Qed.
+
+ Theorem strong_spec_mul_norm : forall x y,
+  Reduced x -> Reduced y -> Reduced (mul_norm x y).
+ Proof.
+ unfold Reduced; intros.
+ rewrite strong_spec_red, Qred_iff.
+ destruct x as [zx|nx dx]; destruct y as [zy|ny dy].
+ simpl in *; auto.
+ simpl.
+ rewrite <- Qred_iff, <- strong_spec_red, strong_spec_mul_norm_Qz_Qq; auto.
+ simpl.
+ rewrite <- Qred_iff, <- strong_spec_red, strong_spec_mul_norm_Qz_Qq; auto.
+ simpl.
+ destruct (spec_irred nx dy) as [g Hg].
+ destruct (spec_irred ny dx) as [g' Hg'].
+ assert (Hz := spec_irred_zero nx dy).
+ assert (Hz':= spec_irred_zero ny dx).
+ assert (Hgc := strong_spec_irred nx dy).
+ assert (Hgc' := strong_spec_irred ny dx).
+ destruct irred as (n1,d1); destruct irred as (n2,d2). 
+ simpl snd in *; destruct Hg as [Hg1 Hg2]; destruct Hg' as [Hg1' Hg2'].
+ destr_neq_bool; simpl; nzsimpl; intros.
+ apply Zis_gcd_gcd; auto with zarith; apply Zis_gcd_1.
+ destr_neq_bool; simpl; nzsimpl; intros.
+ auto.
+
+ revert H H0.
+ rewrite 2 strong_spec_red, 2 Qred_iff; simpl.
+ destr_neq_bool; simpl; nzsimpl; intros.
+ rewrite Hz in H; rewrite H in H2; nzsimpl; elim H2; auto.
+ rewrite Hz' in H0; rewrite H0 in H2; nzsimpl; elim H2; auto.
+ rewrite Hz in H; rewrite H in H2; nzsimpl; elim H2; auto.
+
+ rewrite N_to_Z2P in *; auto.
+ rewrite Z2P_correct.
+
+ apply Zgcd_mult_rel_prime; rewrite Zgcd_sym; 
+  apply Zgcd_mult_rel_prime; rewrite Zgcd_sym; auto.
+ 
+ rewrite Zgcd_1_rel_prime in *.
+ apply bezout_rel_prime.
+ destruct (rel_prime_bezout _ _ H4) as [u v Huv].
+ apply Bezout_intro with (u*g')%Z (v*g)%Z.
+ rewrite <- Huv, <- Hg1', <- Hg2. ring.
+
+ rewrite Zgcd_1_rel_prime in *.
+ apply bezout_rel_prime.
+ destruct (rel_prime_bezout _ _ H3) as [u v Huv].
+ apply Bezout_intro with (u*g)%Z (v*g')%Z.
+ rewrite <- Huv, <- Hg2', <- Hg1. ring.
+
+ assert (0 <= N.to_Z d2 * N.to_Z d1)%Z.
+  apply Zmult_le_0_compat; apply N.spec_pos.
+ romega.
+ Qed.
+
+ Definition inv (x: t): t := 
+ match x with
+ | Qz z => 
+   match Z.compare Z.zero z with 
+     | Eq => zero
+     | Lt => Qq Z.one (Zabs_N z)
+     | Gt => Qq Z.minus_one (Zabs_N z)
+   end
+ | Qq n d => 
+   match Z.compare Z.zero n with
+     | Eq => zero
+     | Lt => Qq (Z_of_N d) (Zabs_N n)
+     | Gt => Qq (Z.opp (Z_of_N d)) (Zabs_N n)
+   end
+ end.
+
+ Theorem spec_inv : forall x, [inv x] == /[x].
+ Proof.
+ destruct x as [ z | n d ].
+ (* Qz z *)
+ simpl.
+ rewrite Zcompare_spec_alt; destr_zcompare.
+ (* 0 = z *)
+ rewrite <- H.
+ simpl; nzsimpl; compute; auto.
+ (* 0 < z *)
+ simpl.
+ destr_neq_bool; nzsimpl; [ intros; rewrite Zabs_eq in *; romega | intros _ ].
+ set (z':=Z.to_Z z) in *; clearbody z'.
+ red; simpl.
+ rewrite Zabs_eq by romega.
+ rewrite Z2P_correct by auto.
+ unfold Qinv; simpl; destruct z'; simpl; auto; discriminate.
+ (* 0 > z *)
+ simpl.
+ destr_neq_bool; nzsimpl; [ intros; rewrite Zabs_non_eq in *; romega | intros _ ].
+ set (z':=Z.to_Z z) in *; clearbody z'.
+ red; simpl.
+ rewrite Zabs_non_eq by romega.
+ rewrite Z2P_correct by romega.
+ unfold Qinv; simpl; destruct z'; simpl; auto; discriminate.
+ (* Qq n d *)
+ simpl.
+ rewrite Zcompare_spec_alt; destr_zcompare.
+ (* 0 = n *)
+ rewrite <- H.
+ simpl; nzsimpl.
+ destr_neq_bool; intros; compute; auto.
+ (* 0 < n *)
+ simpl.
+ destr_neq_bool; nzsimpl; intros.
+ intros; rewrite Zabs_eq in *; romega.
+ intros; rewrite Zabs_eq in *; romega.
+ clear H1.
+ rewrite H0.
+ compute; auto.
+ clear H1.
+ set (n':=Z.to_Z n) in *; clearbody n'.
+ rewrite Zabs_eq by romega.
+ red; simpl.
+ rewrite Z2P_correct by auto.
+ unfold Qinv; simpl; destruct n'; simpl; auto; try discriminate.
+ rewrite Zpos_mult_morphism, N_to_Z2P; auto.
+ (* 0 > n *)
+ simpl.
+ destr_neq_bool; nzsimpl; intros.
+ intros; rewrite Zabs_non_eq in *; romega.
+ intros; rewrite Zabs_non_eq in *; romega.
+ clear H1.
+ red; nzsimpl; rewrite H0; compute; auto.
+ clear H1.
+ set (n':=Z.to_Z n) in *; clearbody n'.
+ red; simpl; nzsimpl.
+ rewrite Zabs_non_eq by romega.
+ rewrite Z2P_correct by romega.
+ unfold Qinv; simpl; destruct n'; simpl; auto; try discriminate.
+ assert (T : forall x, Zneg x = Zopp (Zpos x)) by auto.
+ rewrite T, Zpos_mult_morphism, N_to_Z2P; auto; ring.
+ Qed.
+
+ Definition inv_norm (x: t): t := 
+   match x with
+     | Qz z => 
+       match Z.compare Z.zero z with 
+         | Eq => zero
+         | Lt => Qq Z.one (Zabs_N z)
+         | Gt => Qq Z.minus_one (Zabs_N z)
+       end
+     | Qq n d => 
+       if N.eq_bool d N.zero then zero else 
+       match Z.compare Z.zero n with 
+         | Eq => zero
+         | Lt => 
+           match Z.compare n Z.one with 
+             | Gt => Qq (Z_of_N d) (Zabs_N n)
+             | _ => Qz (Z_of_N d)
+           end
+         | Gt => 
+           match Z.compare n Z.minus_one with 
+             | Lt => Qq (Z.opp (Z_of_N d)) (Zabs_N n)
+             | _ => Qz (Z.opp (Z_of_N d))
+           end
+       end
+   end.
+
+ Theorem spec_inv_norm : forall x, [inv_norm x] == /[x].
+ Proof.
+ intros.
+ rewrite <- spec_inv.
+ destruct x as [ z | n d ].
+ (* Qz z *)
+ simpl.
+ rewrite Zcompare_spec_alt; destr_zcompare; auto with qarith.
+ (* Qq n d *)
+ simpl; nzsimpl; destr_neq_bool.
+ destr_zcompare; simpl; auto with qarith.
+ destr_neq_bool; nzsimpl; auto with qarith.
+ intros _ Hd; rewrite Hd; auto with qarith.
+ destr_neq_bool; nzsimpl; auto with qarith.
+ intros _ Hd; rewrite Hd; auto with qarith.
+ (* 0 < n *)
+ destr_zcompare; auto with qarith.
+ destr_zcompare; nzsimpl; simpl; auto with qarith; intros.
+ destr_neq_bool; nzsimpl; [ intros; rewrite Zabs_eq in *; romega | intros _ ].
+ rewrite H0; auto with qarith.
+ romega.
+ (* 0 > n *)
+ destr_zcompare; nzsimpl; simpl; auto with qarith.
+ destr_neq_bool; nzsimpl; [ intros; rewrite Zabs_non_eq in *; romega | intros _ ].
+ rewrite H0; auto with qarith.
+ romega.
+ Qed.
+
+ Theorem strong_spec_inv_norm : forall x, Reduced x -> Reduced (inv_norm x).
+ Proof.
+ unfold Reduced. 
+ intros.
+ destruct x as [ z | n d ].
+ (* Qz *)
+ simpl; nzsimpl.
+ rewrite strong_spec_red, Qred_iff.
+ destr_zcompare; simpl; nzsimpl; auto.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ (* Qq n d *)
+ rewrite strong_spec_red, Qred_iff in H; revert H.
+ simpl; nzsimpl.
+ destr_neq_bool; nzsimpl; auto with qarith.
+ destr_zcompare; simpl; nzsimpl; auto; intros.
+ (* 0 < n *)
+ destr_zcompare; simpl; nzsimpl; auto.
+ destr_neq_bool; nzsimpl; simpl; auto.
+ rewrite Zabs_eq; romega.
+ intros _.
+ rewrite strong_spec_norm; simpl; nzsimpl.
+ destr_neq_bool; nzsimpl.
+ rewrite Zabs_eq; romega.
+ intros _.
+ rewrite Qred_iff.
+ simpl.
+ rewrite Zabs_eq; auto with zarith.
+ rewrite N_to_Z2P in *; auto.
+ rewrite Z2P_correct; auto with zarith.
+ rewrite Zgcd_sym; auto.
+ (* 0 > n *)
+ destr_neq_bool; nzsimpl; simpl; auto; intros.
+ destr_zcompare; simpl; nzsimpl; auto.
+ destr_neq_bool; nzsimpl.
+ rewrite Zabs_non_eq; romega.
+ intros _.
+ rewrite strong_spec_norm; simpl; nzsimpl.
+ destr_neq_bool; nzsimpl.
+ rewrite Zabs_non_eq; romega.
+ intros _.
+ rewrite Qred_iff.
+ simpl.
+ rewrite N_to_Z2P in *; auto.
+ rewrite Z2P_correct; auto with zarith.
+ intros.
+ rewrite Zgcd_sym, Zgcd_Zabs, Zgcd_sym.
+ apply Zis_gcd_gcd; auto with zarith.
+ apply Zis_gcd_minus.
+ rewrite Zopp_involutive, <- H1; apply Zgcd_is_gcd.
+ rewrite Zabs_non_eq; romega.
+ Qed.
+
+ Definition div x y := mul x (inv y).
+
+ Theorem spec_div x y: [div x y] == [x] / [y].
+ Proof.
+ intros x y; unfold div; rewrite spec_mul; auto.
+ unfold Qdiv; apply Qmult_comp.
+ apply Qeq_refl.
+ apply spec_inv; auto.
+ Qed.
+
+ Definition div_norm x y := mul_norm x (inv_norm y).
+
+ Theorem spec_div_norm x y: [div_norm x y] == [x] / [y].
+ Proof.
+ intros x y; unfold div_norm; rewrite spec_mul_norm; auto.
+ unfold Qdiv; apply Qmult_comp.
+ apply Qeq_refl.
+ apply spec_inv_norm; auto.
+ Qed.
+ 
+ Theorem strong_spec_div_norm : forall x y, 
+   Reduced x -> Reduced y -> Reduced (div_norm x y).
+ Proof.
+ intros; unfold div_norm.
+ apply strong_spec_mul_norm; auto.
+ apply strong_spec_inv_norm; auto.
+ Qed.
+
+ Definition square (x: t): t :=
+  match x with
+  | Qz zx => Qz (Z.square zx)
+  | Qq nx dx => Qq (Z.square nx) (N.square dx)
+  end.
+
+ Theorem spec_square : forall x, [square x] == [x] ^ 2.
+ Proof.
+ destruct x as [ z | n d ].
+ simpl; rewrite Z.spec_square; red; auto.
+ simpl.
+ destr_neq_bool; nzsimpl; intros.
+ apply Qeq_refl.
+ rewrite N.spec_square in *; nzsimpl.
+ contradict H; elim (Zmult_integral _ _ H0); auto.
+ rewrite N.spec_square in *; nzsimpl.
+ rewrite H in H0; simpl in H0; elim H0; auto.
+ assert (0 < N.to_Z d)%Z by (generalize (N.spec_pos d); romega).
+ clear H H0.
+ rewrite Z.spec_square, N.spec_square.  
+ red; simpl.
+ rewrite Zpos_mult_morphism; rewrite !Z2P_correct; auto.
+ apply Zmult_lt_0_compat; auto.
+ Qed.
+
+ Definition power_pos (x : t) p : t :=
+  match x with
+  | Qz zx => Qz (Z.power_pos zx p)
+  | Qq nx dx => Qq (Z.power_pos nx p) (N.power_pos dx p)
+  end.
+ 
+ Theorem spec_power_pos : forall x p, [power_pos x p] == [x] ^ Zpos p.
+ Proof.
+ intros [ z | n d ] p; unfold power_pos.
+ (* Qz *)
+ simpl.
+ rewrite Z.spec_power_pos.
+ rewrite Qpower_decomp.
+ red; simpl; f_equal.
+ rewrite Zpower_pos_1_l; auto.
+ (* Qq *)
+ simpl.
+ rewrite Z.spec_power_pos.
+ destr_neq_bool; nzsimpl; intros.
+ apply Qeq_sym; apply Qpower_positive_0.
+ rewrite N.spec_power_pos in *.
+ assert (0 < N.to_Z d ^ ' p)%Z.
+  apply Zpower_gt_0; auto with zarith.
+  generalize (N.spec_pos d); romega.
+ romega.
+ rewrite N.spec_power_pos, H in *.
+ rewrite Zpower_0_l in H0; [ elim H0; auto | discriminate ].
+ rewrite Qpower_decomp.
+ red; simpl; do 3 f_equal.
+ rewrite Z2P_correct by (generalize (N.spec_pos d); romega).
+ rewrite N.spec_power_pos. auto.
+ Qed.
+
+ Theorem strong_spec_power_pos : forall x p, 
+  Reduced x -> Reduced (power_pos x p).
+ Proof.
+ destruct x as [z | n d]; simpl; intros.
+ red; simpl; auto.
+ red; simpl; intros.
+ rewrite strong_spec_norm; simpl.
+ destr_neq_bool; nzsimpl; intros.
+ simpl; auto.
+ rewrite Qred_iff.
+ revert H.
+ unfold Reduced; rewrite strong_spec_red, Qred_iff; simpl.
+ destr_neq_bool; nzsimpl; simpl; intros.
+ rewrite N.spec_power_pos in H0.
+ elim H0; rewrite H; rewrite Zpower_0_l; auto; discriminate.
+ rewrite N_to_Z2P in *; auto.
+ rewrite N.spec_power_pos, Z.spec_power_pos; auto.
+ rewrite Zgcd_1_rel_prime in *.
+ apply rel_prime_Zpower; auto with zarith.
+ Qed.
+
+ Definition power (x : t) (z : Z) : t := 
+   match z with 
+     | Z0 => one
+     | Zpos p => power_pos x p
+     | Zneg p => inv (power_pos x p)
+   end.
+
+ Theorem spec_power : forall x z, [power x z] == [x]^z.
+ Proof.
+ destruct z.
+ simpl; nzsimpl; red; auto.
+ apply spec_power_pos.
+ simpl.
+ rewrite spec_inv, spec_power_pos; apply Qeq_refl.
+ Qed.
+
+ Definition power_norm (x : t) (z : Z) : t := 
+   match z with 
+     | Z0 => one
+     | Zpos p => power_pos x p
+     | Zneg p => inv_norm (power_pos x p)
+   end.
+
+ Theorem spec_power_norm : forall x z, [power_norm x z] == [x]^z.
+ Proof.
+ destruct z.
+ simpl; nzsimpl; red; auto.
+ apply spec_power_pos.
+ simpl.
+ rewrite spec_inv_norm, spec_power_pos; apply Qeq_refl.
+ Qed.
+
+ Theorem strong_spec_power_norm : forall x z, 
+   Reduced x -> Reduced (power_norm x z).
+ Proof.
+ destruct z; simpl.
+ intros _; unfold Reduced; rewrite strong_spec_red.
+ unfold one.
+ simpl to_Q; nzsimpl; auto.
+ intros; apply strong_spec_power_pos; auto.
+ intros; apply strong_spec_inv_norm; apply strong_spec_power_pos; auto.
+ Qed.
+
+
+ (** Interaction with [Qcanon.Qc] *)
+ 
+ Open Scope Qc_scope.
+
+ Definition of_Qc q := of_Q (this q).
+
+ Definition to_Qc q := !! [q].
+
+ Notation "[[ x ]]" := (to_Qc x).
+
+ Theorem strong_spec_of_Qc : forall q, [of_Qc q] = q.
+ Proof.
+ intros (q,Hq); intros.
+ unfold of_Qc; rewrite strong_spec_of_Q; auto.
+ Qed.
+
+ Lemma strong_spec_of_Qc_bis : forall q, Reduced (of_Qc q).
+ Proof.
+ intros; red; rewrite strong_spec_red, strong_spec_of_Qc.
+ destruct q; simpl; auto.
+ Qed.
+
+ Theorem spec_of_Qc: forall q, [[of_Qc q]] = q.
+ Proof.
+ intros; apply Qc_decomp; simpl; intros.
+ rewrite strong_spec_of_Qc; auto.
+ Qed.
+
+ Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
+ Proof.
+ intros q; unfold Qcopp, to_Qc, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ rewrite spec_opp, <- Qred_opp, Qred_correct.
+ apply Qeq_refl.
+ Qed.
+
+ Theorem spec_oppc_bis : forall q : Qc, [opp (of_Qc q)] = - q.
+ Proof.
+ intros.
+ rewrite <- strong_spec_opp_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (-q)%Q).
+ rewrite spec_opp, strong_spec_of_Qc; auto with qarith.
+ Qed.
+
+ Theorem spec_comparec: forall q1 q2,
+  compare q1 q2 = ([[q1]] ?= [[q2]]).
+ Proof.
+ unfold Qccompare, to_Qc.
+ intros q1 q2; rewrite spec_compare; simpl; auto.
+ apply Qcompare_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_addc x y:
+  [[add x y]] = [[x]] + [[y]].
+ Proof.
+ intros x y; unfold to_Qc.
+ apply trans_equal with (!! ([x] + [y])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_add; auto.
+ unfold Qcplus, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_add_normc x y:
+  [[add_norm x y]] = [[x]] + [[y]].
+ Proof.
+ intros x y; unfold to_Qc.
+ apply trans_equal with (!! ([x] + [y])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_add_norm; auto.
+ unfold Qcplus, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_add_normc_bis : forall x y : Qc, 
+   [add_norm (of_Qc x) (of_Qc y)] = x+y.
+ Proof.
+ intros.
+ rewrite <- strong_spec_add_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (x+y)%Q).
+ rewrite spec_add_norm, ! strong_spec_of_Qc; auto with qarith.
+ Qed.
+
+ Theorem spec_subc x y:  [[sub x y]] = [[x]] - [[y]].
+ Proof.
+ intros x y; unfold sub; rewrite spec_addc; auto.
+ rewrite spec_oppc; ring.
+ Qed.
+
+ Theorem spec_sub_normc x y:
+   [[sub_norm x y]] = [[x]] - [[y]].
+ Proof.
+ intros x y; unfold sub_norm; rewrite spec_add_normc; auto.
+ rewrite spec_oppc; ring.
+ Qed.
+
+ Theorem spec_sub_normc_bis : forall x y : Qc, 
+   [sub_norm (of_Qc x) (of_Qc y)] = x-y.
+ Proof.
+ intros.
+ rewrite <- strong_spec_sub_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (x+(-y)%Qc)%Q).
+ rewrite spec_sub_norm, ! strong_spec_of_Qc.
+ unfold Qcopp, Q2Qc; rewrite Qred_correct; auto with qarith.
+ Qed.
+
+ Theorem spec_mulc x y:
+  [[mul x y]] = [[x]] * [[y]].
+ Proof.
+ intros x y; unfold to_Qc.
+ apply trans_equal with (!! ([x] * [y])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_mul; auto.
+ unfold Qcmult, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_mul_normc x y:
+   [[mul_norm x y]] = [[x]] * [[y]].
+ Proof.
+ intros x y; unfold to_Qc.
+ apply trans_equal with (!! ([x] * [y])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_mul_norm; auto.
+ unfold Qcmult, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_mul_normc_bis : forall x y : Qc, 
+   [mul_norm (of_Qc x) (of_Qc y)] = x*y.
+ Proof.
+ intros.
+ rewrite <- strong_spec_mul_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (x*y)%Q).
+ rewrite spec_mul_norm, ! strong_spec_of_Qc; auto with qarith.
+ Qed.
+
+ Theorem spec_invc x:
+   [[inv x]] =  /[[x]].
+ Proof.
+ intros x; unfold to_Qc.
+ apply trans_equal with (!! (/[x])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_inv; auto.
+ unfold Qcinv, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_inv_normc x:
+   [[inv_norm x]] =  /[[x]].
+ Proof.
+ intros x; unfold to_Qc.
+ apply trans_equal with (!! (/[x])).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_inv_norm; auto.
+ unfold Qcinv, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_inv_normc_bis : forall x : Qc, 
+   [inv_norm (of_Qc x)] = /x.
+ Proof.
+ intros.
+ rewrite <- strong_spec_inv_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (/x)%Q).
+ rewrite spec_inv_norm, ! strong_spec_of_Qc; auto with qarith.
+ Qed.
+
+ Theorem spec_divc x y: [[div x y]] = [[x]] / [[y]].
+ Proof.
+ intros x y; unfold div; rewrite spec_mulc; auto.
+ unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
+ apply spec_invc; auto. 
+ Qed.
+
+ Theorem spec_div_normc x y: [[div_norm x y]] = [[x]] / [[y]].
+ Proof.
+ intros x y; unfold div_norm; rewrite spec_mul_normc; auto.
+ unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
+ apply spec_inv_normc; auto.
+ Qed.
+
+ Theorem spec_div_normc_bis : forall x y : Qc, 
+   [div_norm (of_Qc x) (of_Qc y)] = x/y.
+ Proof.
+ intros.
+ rewrite <- strong_spec_div_norm by apply strong_spec_of_Qc_bis.
+ rewrite strong_spec_red.
+ symmetry; apply (Qred_complete (x*(/y)%Qc)%Q).
+ rewrite spec_div_norm, ! strong_spec_of_Qc.
+ unfold Qcinv, Q2Qc; rewrite Qred_correct; auto with qarith.
+ Qed.
+
+ Theorem spec_squarec x: [[square x]] =  [[x]]^2.
+ Proof.
+ intros x; unfold to_Qc.
+ apply trans_equal with (!! ([x]^2)).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_square; auto.
+ simpl Qcpower.
+ replace (!! [x] * 1) with (!![x]); try ring.
+ simpl.
+ unfold Qcmult, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
+ Qed.
+
+ Theorem spec_power_posc x p:
+   [[power_pos x p]] = [[x]] ^ nat_of_P p.
+ Proof.
+ intros x p; unfold to_Qc.
+ apply trans_equal with (!! ([x]^Zpos p)).
+ unfold Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete; apply spec_power_pos; auto.
+ induction p using Pind.
+ simpl; ring.
+ rewrite nat_of_P_succ_morphism; simpl Qcpower.
+ rewrite <- IHp; clear IHp.
+ unfold Qcmult, Q2Qc.
+ apply Qc_decomp; intros _ _; unfold this.
+ apply Qred_complete.
+ setoid_replace ([x] ^ ' Psucc p)%Q with ([x] * [x] ^ ' p)%Q.
+ apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
+ simpl.
+ rewrite Pplus_one_succ_l.
+ rewrite Qpower_plus_positive; simpl; apply Qeq_refl.
+ Qed.
+
+End Make.
+
diff --git a/theories/Numbers/Rational/BigQ/QMake_base.v b/theories/Numbers/Rational/BigQ/QMake_base.v
deleted file mode 100644
index 547e74b7..00000000
--- a/theories/Numbers/Rational/BigQ/QMake_base.v
+++ /dev/null
@@ -1,34 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(* $Id: QMake_base.v 10964 2008-05-22 11:08:13Z letouzey $ *)
-
-(** * An implementation of rational numbers based on big integers *)
-
-Require Export BigN.
-Require Export BigZ.
-
-(* Basic type for Q: a Z or a pair of a Z and an N *)
-
-Inductive q_type := 
- | Qz : BigZ.t -> q_type
- | Qq : BigZ.t -> BigN.t -> q_type.
-
-Definition print_type x := 
- match x with
- | Qz _ => Z
- | _ => (Z*Z)%type
- end.
-
-Definition print x :=
- match x return print_type x with
- | Qz zx => BigZ.to_Z zx
- | Qq nx dx => (BigZ.to_Z nx, BigN.to_Z dx)
- end.
diff --git a/theories/Numbers/Rational/BigQ/QbiMake.v b/theories/Numbers/Rational/BigQ/QbiMake.v
deleted file mode 100644
index 699f383e..00000000
--- a/theories/Numbers/Rational/BigQ/QbiMake.v
+++ /dev/null
@@ -1,1066 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(*i $Id: QbiMake.v 11027 2008-06-01 13:28:59Z letouzey $ i*)
-
-Require Import Bool.
-Require Import ZArith.
-Require Import Znumtheory.
-Require Import BigNumPrelude.
-Require Import Arith.
-Require Export BigN.
-Require Export BigZ.
-Require Import QArith.
-Require Import Qcanon.
-Require Import Qpower.
-Require Import QMake_base.	
-
-Module Qbi.
-
- Import BinInt Zorder.
- Open Local Scope Q_scope.
- Open Local Scope Qc_scope.
-
- (** The notation of a rational number is either an integer x,
-     interpreted as itself or a pair (x,y) of an integer x and a naturel
-     number y interpreted as x/y. The pairs (x,0) and (0,y) are all
-     interpreted as 0. *)
-
- Definition t := q_type.
-
- Definition zero: t := Qz BigZ.zero.
- Definition one: t  := Qz BigZ.one.
- Definition minus_one: t := Qz BigZ.minus_one.
-
- Definition of_Z x: t := Qz (BigZ.of_Z x).
-
-
- Definition of_Q q: t := 
- match q with x # y =>
-  Qq (BigZ.of_Z x) (BigN.of_N (Npos y))
- end.
-
- Definition of_Qc q := of_Q (this q).
-
- Definition to_Q (q: t) := 
- match q with 
-  Qz x => BigZ.to_Z x # 1
- |Qq x y => if BigN.eq_bool y BigN.zero then 0%Q
-            else BigZ.to_Z x # Z2P (BigN.to_Z y)
- end.
-
- Definition to_Qc q := !!(to_Q q).
-
- Notation "[[ x ]]" := (to_Qc x).
-
- Notation "[ x ]" := (to_Q x).
-
- Theorem spec_to_Q: forall q: Q, [of_Q q] = q.
- intros (x,y); simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
-   rewrite BigN.spec_of_pos; intros HH; discriminate HH.
- rewrite BigZ.spec_of_Z; simpl.
- rewrite (BigN.spec_of_pos); auto.
- Qed.
-
- Theorem spec_to_Qc: forall q, [[of_Qc q]] = q.
- intros (x, Hx); unfold of_Qc, to_Qc; simpl.
- apply Qc_decomp; simpl.
- intros; rewrite spec_to_Q; auto.
- Qed.
-
- Definition opp (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.opp zx)
-  | Qq nx dx => Qq (BigZ.opp nx) dx
-  end.
-
- Theorem spec_opp: forall q, ([opp q] = -[q])%Q.
- intros [z | x y]; simpl.
- rewrite BigZ.spec_opp; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- rewrite BigZ.spec_opp; auto.
- Qed.
-
- Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
- intros q; unfold Qcopp, to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- rewrite spec_opp.
- rewrite <- Qred_opp.
- rewrite Qred_involutive; auto.
- Qed.
-
-
- Definition compare (x y: t) :=
-  match x, y with
-  | Qz zx, Qz zy => BigZ.compare zx zy
-  | Qz zx, Qq ny dy => 
-    if BigN.eq_bool dy BigN.zero then BigZ.compare zx BigZ.zero
-    else
-      match BigZ.cmp_sign zx ny with
-      | Lt => Lt 
-      | Gt => Gt
-      | Eq => BigZ.compare (BigZ.mul zx (BigZ.Pos dy)) ny
-      end
-  | Qq nx dx, Qz zy =>
-    if BigN.eq_bool dx BigN.zero then BigZ.compare BigZ.zero zy     
-    else
-      match BigZ.cmp_sign nx zy with
-      | Lt => Lt
-      | Gt => Gt
-      | Eq => BigZ.compare nx (BigZ.mul zy (BigZ.Pos dx))
-      end
-  | Qq nx dx, Qq ny dy =>
-    match BigN.eq_bool dx BigN.zero, BigN.eq_bool dy BigN.zero with
-    | true, true => Eq
-    | true, false => BigZ.compare BigZ.zero ny
-    | false, true => BigZ.compare nx BigZ.zero
-    | false, false =>
-      match BigZ.cmp_sign nx ny with
-      | Lt => Lt
-      | Gt => Gt
-      | Eq => BigZ.compare (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx))
-      end
-    end
-  end.
-
- Theorem spec_compare: forall q1 q2, 
-  compare q1 q2 = ([q1] ?= [q2])%Q.
- intros [z1 | x1 y1] [z2 | x2 y2]; 
-   unfold Qcompare, compare, to_Q, Qnum, Qden.
- repeat rewrite Zmult_1_r.
- generalize (BigZ.spec_compare z1 z2); case BigZ.compare; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- rewrite Zmult_1_r.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_1_r; generalize (BigZ.spec_compare z1 BigZ.zero);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite HH1; rewrite Zcompare_refl; auto.
- set (a := BigZ.to_Z z1); set (b := BigZ.to_Z x2);
-   set (c := BigN.to_Z y2); fold c in HH.
- assert (F: (0 < c)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos  y2)); fold c; auto.
-   intros H1; case HH; rewrite <- H1; auto.
- rewrite Z2P_correct; auto with zarith.
- generalize (BigZ.spec_cmp_sign z1 x2); case BigZ.cmp_sign; fold a b c.
- intros _; generalize (BigZ.spec_compare (z1 * BigZ.Pos y2)%bigZ x2); 
-   case BigZ.compare; rewrite BigZ.spec_mul; simpl; fold a b c; auto.
- intros H1; rewrite H1; rewrite Zcompare_refl; auto.
- intros (H1, H2); apply sym_equal; change (a * c < b)%Z.
- apply Zlt_le_trans with (2 := H2).
- change 0%Z with (0 * c)%Z.
- apply Zmult_lt_compat_r; auto with zarith.
- intros (H1, H2); apply sym_equal; change (a * c > b)%Z.
- apply Zlt_gt.
- apply Zlt_le_trans with (1 := H2).
- change 0%Z with (0 * c)%Z.
- apply Zmult_le_compat_r; auto with zarith.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero z2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite <- HH1; rewrite Zcompare_refl; auto.
- set (a := BigZ.to_Z z2); set (b := BigZ.to_Z x1);
-   set (c := BigN.to_Z y1); fold c in HH.
- assert (F: (0 < c)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos  y1)); fold c; auto.
-   intros H1; case HH; rewrite <- H1; auto.
- rewrite Zmult_1_r; rewrite Z2P_correct; auto with zarith.
- generalize (BigZ.spec_cmp_sign x1 z2); case BigZ.cmp_sign; fold a b c.
- intros _; generalize (BigZ.spec_compare x1 (z2 * BigZ.Pos y1)%bigZ); 
-   case BigZ.compare; rewrite BigZ.spec_mul; simpl; fold a b c; auto.
- intros H1; rewrite H1; rewrite Zcompare_refl; auto.
- intros (H1, H2); apply sym_equal; change (b < a * c)%Z.
- apply Zlt_le_trans with (1 := H1).
- change 0%Z with (0 * c)%Z.
- apply Zmult_le_compat_r; auto with zarith.
- intros (H1, H2); apply sym_equal; change (b > a * c)%Z.
- apply Zlt_gt.
- apply Zlt_le_trans with (2 := H1).
- change 0%Z with (0 * c)%Z.
- apply Zmult_lt_compat_r; auto with zarith.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zcompare_refl; auto.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero x2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 BigZ.zero)%bigZ; case BigZ.compare;
-   auto; rewrite BigZ.spec_0.
- intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- set (a := BigZ.to_Z x1); set (b := BigZ.to_Z x2);
-   set (c1 := BigN.to_Z y1); set (c2 := BigN.to_Z y2).
- fold c1 in HH; fold c2 in HH1.
- assert (F1: (0 < c1)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos  y1)); fold c1; auto.
-   intros H1; case HH; rewrite <- H1; auto.
- assert (F2: (0 < c2)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos  y2)); fold c2; auto.
-   intros H1; case HH1; rewrite <- H1; auto.
- repeat rewrite Z2P_correct; auto.
- generalize (BigZ.spec_cmp_sign x1 x2); case BigZ.cmp_sign.
- intros _; generalize (BigZ.spec_compare (x1 * BigZ.Pos y2)%bigZ
-                          (x2 * BigZ.Pos y1)%bigZ); 
-   case BigZ.compare; rewrite BigZ.spec_mul; simpl; fold a b c1 c2; auto.
- rewrite BigZ.spec_mul; simpl; fold a b c1; intros HH2; rewrite HH2;
-  rewrite Zcompare_refl; auto.
- rewrite BigZ.spec_mul; simpl; auto.
- rewrite BigZ.spec_mul; simpl; auto.
- fold a b; intros (H1, H2); apply sym_equal; change (a * c2 < b * c1)%Z.
- apply Zlt_le_trans with 0%Z.
-   change 0%Z with (0 * c2)%Z.
- apply Zmult_lt_compat_r; auto with zarith.
- apply Zmult_le_0_compat; auto with zarith.
- fold a b; intros (H1, H2); apply sym_equal; change (a * c2 > b * c1)%Z.
- apply Zlt_gt; apply Zlt_le_trans with 0%Z.
- change 0%Z with (0 * c1)%Z.
- apply Zmult_lt_compat_r; auto with zarith.
- apply Zmult_le_0_compat; auto with zarith.
- Qed.
-
-
- Definition do_norm_n n := 
-  match n with
-  | BigN.N0 _ => false
-  | BigN.N1 _ => false
-  | BigN.N2 _ => false
-  | BigN.N3 _ => false
-  | BigN.N4 _ => false
-  | BigN.N5 _ => false
-  | BigN.N6 _ => false
-  | _         => true 
-  end.
- 
- Definition do_norm_z z :=
-  match z with
-  | BigZ.Pos n => do_norm_n n
-  | BigZ.Neg n => do_norm_n n
-  end.
-
-(* Je pense que cette fonction normalise bien ... *)
- Definition norm n d: t :=
-  if andb (do_norm_z n) (do_norm_n d) then
-  let gcd := BigN.gcd (BigZ.to_N n) d in 
-  match BigN.compare BigN.one gcd with
-  | Lt => 
-    let n := BigZ.div n (BigZ.Pos gcd) in
-    let d := BigN.div d gcd in
-    match BigN.compare d BigN.one with
-    | Gt => Qq n d
-    | Eq => Qz n
-    | Lt => zero
-    end
-  | Eq => Qq n d
-  | Gt => zero (* gcd = 0 => both numbers are 0 *)
-  end
- else Qq n d.
-
- Theorem spec_norm: forall n q, 
-     ([norm n q] == [Qq n q])%Q.
- intros p q; unfold norm.
- case do_norm_z; simpl andb.
- 2: apply Qeq_refl.
- case do_norm_n.
- 2: apply Qeq_refl.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_gcd; intros H1.
-   apply Qeq_refl.
- generalize (BigN.spec_pos (q / BigN.gcd (BigZ.to_N p) q)%bigN).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith; intros H2 HH.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl;
-  rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd;
-  auto with zarith.
- generalize H2; rewrite H3; 
-   rewrite Zdiv_0_l; auto with zarith.
- generalize H1 H2 H3 (BigN.spec_pos q); clear H1 H2 H3.
- rewrite spec_to_N.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4; rewrite Z2P_correct; auto with zarith.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl.
- case H3.
- generalize H1 H2 H3 HH; clear H1 H2 H3 HH.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 HH.
-  rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto with zarith.
- case (Zle_lt_or_eq _ _ HH); auto with zarith.
- intros HH1; rewrite <- HH1; ring.
- generalize (Zgcd_is_gcd a b); intros HH1; inversion HH1; auto.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_div;
-   rewrite BigN.spec_gcd; auto with zarith; intros H3.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H4.
- case H3; rewrite H4;  rewrite Zdiv_0_l; auto with zarith.
- simpl.
- assert (FF := BigN.spec_pos q).
- rewrite Z2P_correct; auto with zarith.
- rewrite <- BigN.spec_gcd; rewrite <- BigN.spec_div; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; auto with zarith.
- simpl; rewrite BigZ.spec_div; simpl.
- rewrite BigN.spec_gcd; auto with zarith.
- generalize H1 H2 H3 H4 HH FF; clear H1 H2 H3 H4 HH FF.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4 HH FF.
- rewrite spec_to_N; fold a.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- case (Zle_lt_or_eq _ _ 
-   (BigN.spec_pos (BigN.gcd (BigZ.to_N p) q)));
-  rewrite BigN.spec_gcd; auto with zarith.
- intros; apply False_ind; auto with zarith.
- intros HH2; assert (FF1 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- assert (FF2 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2; simpl.
- rewrite spec_to_N.
- rewrite FF2; ring.
- Qed.
-   
- Definition add (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy => 
-      if BigN.eq_bool dy BigN.zero then x 
-      else Qq (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => Qq (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       if BigN.eq_bool dx dy then
-         let n := BigZ.add nx ny in
-         Qq n dx
-       else
-         let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-         let d := BigN.mul dx dy in
-         Qq n d
-    end
-  end.
-
-
-
- Theorem spec_add x y: 
-  ([add x y] == [x] + [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qplus; simpl.
- rewrite BigZ.spec_add; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- assert (F1:= BigN.spec_pos dy).
- rewrite Zmult_1_r; red; simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- rewrite Zmult_1_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- assert (F1:= BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- case HH2; auto.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH2; auto.
- case HH1; auto.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH; auto.
- rewrite Zmult_1_r; rewrite Zplus_0_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- simpl.
- generalize (BigN.spec_eq_bool (dx * dy)%bigN BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_mul;
-   rewrite BigN.spec_0; intros HH2.
- (case (Zmult_integral _ _ HH2); intros HH3);
-  [case HH| case HH1]; auto.
- generalize (BigN.spec_eq_bool dx dy);
-   case BigN.eq_bool; intros HH3.
- rewrite <- HH3.
- assert (Fx: (0 < BigN.to_Z dx)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- red; simpl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH4.
- case HH; auto.
- simpl; rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; repeat rewrite BigZ.spec_mul; simpl.
- ring.
- assert (Fx: (0 < BigN.to_Z dx)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- assert (Fy: (0 < BigN.to_Z dy)%Z).
-   generalize (BigN.spec_pos dy); auto with zarith.
- red; simpl; rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_mul;
-    rewrite BigN.spec_0; intros H3; simpl.
- absurd (0 < 0)%Z; auto with zarith.
- rewrite BigZ.spec_add; repeat rewrite BigZ.spec_mul; simpl.
- repeat rewrite Z2P_correct; auto with zarith.
- apply Zmult_lt_0_compat; auto.
- Qed.
-
- Theorem spec_addc x y:
-  [[add x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition add_norm (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy =>  
-      if BigN.eq_bool dy BigN.zero then x 
-      else 
-        norm (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => norm (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       if BigN.eq_bool dx dy then
-         let n := BigZ.add nx ny in
-         norm n dx
-       else
-         let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-         let d := BigN.mul dx dy in
-         norm n d
-    end
-  end.
-
- Theorem spec_add_norm x y:
-  ([add_norm x y] == [x] + [y])%Q.
- intros x y; rewrite <- spec_add; auto.
- case x; case y; clear x y; unfold add_norm, add.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- simpl.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- apply Qeq_refl.
- intros p1 p2 n.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- apply Qeq_refl.
- intros p1 q1 p2 q2.
- generalize (BigN.spec_eq_bool q2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- generalize (BigN.spec_eq_bool q1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; intros HH3;
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; apply Qeq_refl.
- Qed.
-
- Theorem spec_add_normc x y:
-  [[add_norm x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add_norm; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
- 
- Definition sub x y := add x (opp y).
-
- Theorem spec_sub x y:
-  ([sub x y] == [x] - [y])%Q.
- intros x y; unfold sub; rewrite spec_add; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_subc x y:  [[sub x y]] = [[x]] - [[y]].
- intros x y; unfold sub; rewrite spec_addc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Definition sub_norm x y := add_norm x (opp y).
-
- Theorem spec_sub_norm x y: 
-  ([sub_norm x y] == [x] - [y])%Q.
- intros x y; unfold sub_norm; rewrite spec_add_norm; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_sub_normc x y:
-   [[sub_norm x y]] = [[x]] - [[y]].
- intros x y; unfold sub_norm; rewrite spec_add_normc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Definition mul (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => Qq (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
- Theorem spec_mul x y: ([mul x y] == [x] * [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl.
- rewrite BigZ.spec_mul; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end;  rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; rewrite Pmult_1_r.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0;  rewrite BigN.spec_mul;
-      intros HH1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- red; simpl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- red; simpl; ring.
- case (Zmult_integral _ _ HH1); intros HH.
-   case HH2; auto.
-   case HH3; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- case HH1; rewrite HH2; ring.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- case HH1; rewrite HH3; ring.
- rewrite BigZ.spec_mul.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- apply Qeq_refl.
-  generalize (BigN.spec_pos dx); auto with zarith.
-  generalize (BigN.spec_pos dy); auto with zarith.
- Qed.
-
- Theorem spec_mulc x y:
-  [[mul x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition mul_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => mul (Qz ny) (norm zx dy)
-  | Qq nx dx, Qz zy => mul (Qz nx) (norm zy dx)
-  | Qq nx dx, Qq ny dy => mul (norm nx dy) (norm ny dx)
-  end.
-
- Theorem spec_mul_norm x y:
-  ([mul_norm x y] == [x] * [y])%Q.
- intros x y; rewrite <- spec_mul; auto.
- unfold mul_norm; case x; case y; clear x y.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- repeat rewrite spec_mul.
- match goal with |- ?Z == _ =>
-   match Z with context id [norm ?X ?Y] =>
-   let y := context id [Qq X Y] in
-   apply Qeq_trans with y; [repeat apply Qmult_comp;
-   repeat apply Qplus_comp; repeat apply Qeq_refl;
-   apply spec_norm | idtac]
-   end
- end.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH; simpl; ring.
- intros p1 p2 n.
- repeat rewrite spec_mul.
- match goal with |- ?Z == _ =>
-   match Z with context id [norm ?X ?Y] =>
-   let y := context id [Qq X Y] in
-   apply Qeq_trans with y; [repeat apply Qmult_comp;
-   repeat apply Qplus_comp; repeat apply Qeq_refl;
-   apply spec_norm | idtac]
-   end
- end.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH; simpl; try ring.
- rewrite Pmult_1_r; auto.
- intros p1 n1 p2 n2.
- repeat rewrite spec_mul.
- repeat match goal with |- ?Z == _ =>
-   match Z with context id [norm ?X ?Y] =>
-   let y := context id [Qq X Y] in
-   apply Qeq_trans with y; [repeat apply Qmult_comp;
-   repeat apply Qplus_comp; repeat apply Qeq_refl;
-   apply spec_norm | idtac]
-   end
- end.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1;
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; try ring.
- repeat rewrite Zpos_mult_morphism; ring.
- Qed.
-
- Theorem spec_mul_normc x y:
-   [[mul_norm x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul_norm; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition inv (x: t): t := 
-  match x with
-  | Qz (BigZ.Pos n) => Qq BigZ.one n
-  | Qz (BigZ.Neg n) => Qq BigZ.minus_one n
-  | Qq (BigZ.Pos n) d => Qq (BigZ.Pos d) n
-  | Qq (BigZ.Neg n) d => Qq (BigZ.Neg d) n
-  end.
-
-
- Theorem spec_inv x:
-   ([inv x] == /[x])%Q.
- intros [ [x | x] | [nx | nx] dx]; unfold inv, Qinv; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- Qed.
-
- Theorem spec_invc x:
-   [[inv x]] =  /[[x]].
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition inv_norm (x: t): t := 
-  match x with
-  | Qz (BigZ.Pos n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.one n
-  | Qz (BigZ.Neg n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.minus_one n
-  | Qq (BigZ.Pos n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Pos d) n
-  | Qq (BigZ.Neg n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Neg d) n
-  end.
-
- Theorem spec_inv_norm x: ([inv_norm x] == /[x])%Q.
- intros x; rewrite <- spec_inv; generalize x; clear x.
- intros [ [x | x] | [nx | nx] dx]; unfold inv_norm, inv;
-   match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-     generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-   end; rewrite BigN.spec_0; intros H1; try apply Qeq_refl;
-   red; simpl;
-   match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-     generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-   end; rewrite BigN.spec_0; intros H2; auto;
-   case H2; auto.
- Qed.
-
- Theorem spec_inv_normc x:
-   [[inv_norm x]] =  /[[x]].
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv_norm; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
- Definition div x y := mul x (inv y).
-
- Theorem spec_div x y: ([div x y] == [x] / [y])%Q.
- intros x y; unfold div; rewrite spec_mul; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_divc x y: [[div x y]] = [[x]] / [[y]].
- intros x y; unfold div; rewrite spec_mulc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto. 
- Qed.
-
- Definition div_norm x y := mul_norm x (inv y).
-
- Theorem spec_div_norm x y: ([div_norm x y] == [x] / [y])%Q.
- intros x y; unfold div_norm; rewrite spec_mul_norm; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_div_normc x y: [[div_norm x y]] = [[x]] / [[y]].
- intros x y; unfold div_norm; rewrite spec_mul_normc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto.
- Qed.
-
-
- Definition square (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.square zx)
-  | Qq nx dx => Qq (BigZ.square nx) (BigN.square dx)
-  end.
-
-
- Theorem spec_square x: ([square x] == [x] ^ 2)%Q.
- intros [ x | nx dx]; unfold square.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- simpl Qpower.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H1; rewrite H; auto.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H; case (Zmult_integral _ _ H1); auto.
- simpl.
- rewrite BigZ.spec_square.
- rewrite Zpos_mult_morphism.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_pos dx); auto with zarith.
- Qed.
-
- Theorem spec_squarec x: [[square x]] =  [[x]]^2.
- intros x; unfold to_Qc.
- apply trans_equal with (!! ([x]^2)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_square; auto.
- simpl Qcpower.
- replace (!! [x] * 1) with (!![x]); try ring.
- simpl.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition power_pos (x: t) p: t :=
-  match x with
-  | Qz zx => Qz (BigZ.power_pos zx p)
-  | Qq nx dx => Qq (BigZ.power_pos nx p) (BigN.power_pos dx p)
-  end.
-
- Theorem spec_power_pos x p: ([power_pos x p] == [x] ^ Zpos p)%Q.
- Proof.
- intros [x | nx dx] p; unfold power_pos.
-   unfold power_pos; red; simpl.
-   generalize (Qpower_decomp p (BigZ.to_Z x) 1).
-   unfold Qeq; simpl.
-   rewrite Zpower_pos_1_l; simpl Z2P.
-   rewrite Zmult_1_r.
-   intros H; rewrite H.
-   rewrite BigZ.spec_power_pos; simpl; ring.
- simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_power_pos; intros H1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2.
- elim p; simpl.
- intros; red; simpl; auto.
- intros p1 Hp1; rewrite <- Hp1; red; simpl; auto.
- apply Qeq_refl.
- case H2; generalize H1.
- elim p; simpl.
- intros p1 Hrec.
- change (xI p1) with (1 + (xO p1))%positive.
- rewrite Zpower_pos_is_exp; rewrite Zpower_pos_1_r.
- intros HH; case (Zmult_integral _ _ HH); auto.
- rewrite <- Pplus_diag.
- rewrite Zpower_pos_is_exp.
- intros HH1; case (Zmult_integral _ _ HH1); auto.
- intros p1 Hrec.
- rewrite <- Pplus_diag.
- rewrite Zpower_pos_is_exp.
- intros HH1; case (Zmult_integral _ _ HH1); auto.
- rewrite Zpower_pos_1_r; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2.
- case H1; rewrite H2; auto.
- simpl; rewrite Zpower_pos_0_l; auto.
- assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
- assert (F2: (0 < BigN.to_Z dx  ^ ' p)%Z).
-  unfold Zpower; apply Zpower_pos_pos; auto.
- unfold power_pos; red; simpl.
- generalize (Qpower_decomp p (BigZ.to_Z nx) 
-               (Z2P (BigN.to_Z dx))).
- unfold Qeq; simpl.
- repeat rewrite Z2P_correct; auto.
- unfold Qeq; simpl; intros HH.
- rewrite HH.
- rewrite BigZ.spec_power_pos; simpl; ring.
- Qed.
-
- Theorem spec_power_posc x p:
-   [[power_pos x p]] = [[x]] ^ nat_of_P p.
- intros x p; unfold to_Qc.
- apply trans_equal with (!! ([x]^Zpos p)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_power_pos; auto.
- pattern p; apply Pind; clear p.
- simpl; ring.
- intros p Hrec.
- rewrite nat_of_P_succ_morphism; simpl Qcpower.
- rewrite <- Hrec.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _;
- unfold this.
- apply Qred_complete.
- assert (F: [x] ^ ' Psucc p == [x] *   [x] ^ ' p).
-  simpl; case x; simpl; clear x Hrec.
-  intros x; simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  intros nx dx.
-  match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-  end; auto; rewrite BigN.spec_0.
-  unfold Qpower_positive.
-  assert (tmp: forall p, pow_pos Qmult 0%Q p = 0%Q).
-    intros p1; elim p1; simpl; auto; clear p1.
-    intros p1 Hp1; rewrite Hp1; auto.
-    intros p1 Hp1; rewrite Hp1; auto.
-  repeat rewrite tmp; intros; red; simpl; auto.
-  intros H1.
-  assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
-  simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  repeat rewrite Zpos_mult_morphism.
-  repeat rewrite Z2P_correct; auto.
-  2: apply Zpower_pos_pos; auto.
-  2: apply Zpower_pos_pos; auto.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
- rewrite F.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-End Qbi.
diff --git a/theories/Numbers/Rational/BigQ/QifMake.v b/theories/Numbers/Rational/BigQ/QifMake.v
deleted file mode 100644
index 1d8ecc94..00000000
--- a/theories/Numbers/Rational/BigQ/QifMake.v
+++ /dev/null
@@ -1,979 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(*i $Id: QifMake.v 11027 2008-06-01 13:28:59Z letouzey $ i*)
-
-Require Import Bool.
-Require Import ZArith.
-Require Import Znumtheory.
-Require Import BigNumPrelude.
-Require Import Arith.
-Require Export BigN.
-Require Export BigZ.
-Require Import QArith.
-Require Import Qcanon.
-Require Import Qpower.
-Require Import QMake_base.
-
-Module Qif.
-
- Import BinInt.
- Open Local Scope Q_scope.
- Open Local Scope Qc_scope.
-
- (** The notation of a rational number is either an integer x,
-     interpreted as itself or a pair (x,y) of an integer x and a naturel
-     number y interpreted as x/y. The pairs (x,0) and (0,y) are all
-     interpreted as 0. *)
-
- Definition t := q_type.
-
- Definition zero: t := Qz BigZ.zero.
- Definition one: t := Qz BigZ.one.
- Definition minus_one: t := Qz BigZ.minus_one.
-
- Definition of_Z x: t := Qz (BigZ.of_Z x).
-
- Definition of_Q q: t := 
- match q with x # y =>
-  Qq (BigZ.of_Z x) (BigN.of_N (Npos y))
- end.
-
- Definition of_Qc q := of_Q (this q).
-
- Definition to_Q (q: t) := 
- match q with 
-  Qz x => BigZ.to_Z x # 1
- |Qq x y => if BigN.eq_bool y BigN.zero then 0%Q
-            else BigZ.to_Z x # Z2P (BigN.to_Z y)
- end.
-
- Definition to_Qc q := !!(to_Q q).
-
- Notation "[[ x ]]" := (to_Qc x).
-
- Notation "[ x ]" := (to_Q x).
-
- Theorem spec_to_Q: forall q: Q, [of_Q q] = q.
- intros (x,y); simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
-   rewrite BigN.spec_of_pos; intros HH; discriminate HH.
- rewrite BigZ.spec_of_Z; simpl.
- rewrite (BigN.spec_of_pos); auto.
- Qed.
-
- Theorem spec_to_Qc: forall q, [[of_Qc q]] = q.
- intros (x, Hx); unfold of_Qc, to_Qc; simpl.
- apply Qc_decomp; simpl.
- intros; rewrite spec_to_Q; auto.
- Qed.
-
- Definition opp (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.opp zx)
-  | Qq nx dx => Qq (BigZ.opp nx) dx
-  end.
-
- Theorem spec_opp: forall q, ([opp q] = -[q])%Q.
- intros [z | x y]; simpl.
- rewrite BigZ.spec_opp; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-  generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- rewrite BigZ.spec_opp; auto.
- Qed.
-
- Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
- intros q; unfold Qcopp, to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- rewrite spec_opp.
- rewrite <- Qred_opp.
- rewrite Qred_involutive; auto.
- Qed.
-
- Definition compare (x y: t) :=
-  match x, y with
-  | Qz zx, Qz zy => BigZ.compare zx zy
-  | Qz zx, Qq ny dy => 
-    if BigN.eq_bool dy BigN.zero then BigZ.compare zx BigZ.zero
-    else BigZ.compare (BigZ.mul zx (BigZ.Pos dy)) ny
-  | Qq nx dx, Qz zy => 
-    if BigN.eq_bool dx BigN.zero then BigZ.compare BigZ.zero zy 
-    else BigZ.compare nx (BigZ.mul zy (BigZ.Pos dx))
-  | Qq nx dx, Qq ny dy =>
-    match BigN.eq_bool dx BigN.zero, BigN.eq_bool dy BigN.zero with
-    | true, true => Eq
-    | true, false => BigZ.compare BigZ.zero ny
-    | false, true => BigZ.compare nx BigZ.zero
-    | false, false => BigZ.compare (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx))
-    end
-  end.
-
- Theorem spec_compare: forall q1 q2, 
-  compare q1 q2 = ([q1] ?= [q2])%Q.
- intros [z1 | x1 y1] [z2 | x2 y2]; 
-   unfold Qcompare, compare, to_Q, Qnum, Qden.
- repeat rewrite Zmult_1_r.
- generalize (BigZ.spec_compare z1 z2); case BigZ.compare; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- rewrite Zmult_1_r.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_1_r; generalize (BigZ.spec_compare z1 BigZ.zero);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite HH1; rewrite Zcompare_refl; auto.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (z1 * BigZ.Pos y2) x2)%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero z2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH1; rewrite <- HH1; rewrite Zcompare_refl; auto.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
- rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 (z2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zcompare_refl; auto.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare BigZ.zero x2);
-  case BigZ.compare; auto.
- rewrite BigZ.spec_0; intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- rewrite Zmult_0_l; rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 BigZ.zero)%bigZ; case BigZ.compare;
-   auto; rewrite BigZ.spec_0.
- intros HH2; rewrite <- HH2; rewrite Zcompare_refl; auto.
- repeat rewrite Z2P_correct.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (x1 * BigZ.Pos y2) 
-                               (x2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   repeat rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- Qed.
-
- Definition do_norm_n n := 
-  match n with
-  | BigN.N0 _ => false
-  | BigN.N1 _ => false
-  | BigN.N2 _ => false
-  | BigN.N3 _ => false
-  | BigN.N4 _ => false
-  | BigN.N5 _ => false
-  | BigN.N6 _ => false
-  | _         => true 
-  end.
-
- Definition do_norm_z z :=
-  match z with
-  | BigZ.Pos n => do_norm_n n
-  | BigZ.Neg n => do_norm_n n
-  end.
-
-(* Je pense que cette fonction normalise bien ... *)
- Definition norm n d: t :=
-  if andb (do_norm_z n) (do_norm_n d) then
-  let gcd := BigN.gcd (BigZ.to_N n) d in 
-  match BigN.compare BigN.one gcd with
-  | Lt => 
-    let n := BigZ.div n (BigZ.Pos gcd) in
-    let d := BigN.div d gcd in
-    match BigN.compare d BigN.one with
-    | Gt => Qq n d
-    | Eq => Qz n
-    | Lt => zero
-    end
-  | Eq => Qq n d
-  | Gt => zero (* gcd = 0 => both numbers are 0 *)
-  end
- else Qq n d.
-
- Theorem spec_norm: forall n q, 
-     ([norm n q] == [Qq n q])%Q.
- intros p q; unfold norm.
- case do_norm_z; simpl andb.
- 2: apply Qeq_refl.
- case do_norm_n.
- 2: apply Qeq_refl.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_gcd; intros H1.
-   apply Qeq_refl.
- generalize (BigN.spec_pos (q / BigN.gcd (BigZ.to_N p) q)%bigN).
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; auto; rewrite BigN.spec_1; rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith; intros H2 HH.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl;
-  rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd;
-  auto with zarith.
- generalize H2; rewrite H3; 
-   rewrite Zdiv_0_l; auto with zarith.
- generalize H1 H2 H3 (BigN.spec_pos q); clear H1 H2 H3.
- rewrite spec_to_N.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4; rewrite Z2P_correct; auto with zarith.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H3; simpl.
- case H3.
- generalize H1 H2 H3 HH; clear H1 H2 H3 HH.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 HH.
-  rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto with zarith.
- case (Zle_lt_or_eq _ _ HH); auto with zarith.
- intros HH1; rewrite <- HH1; ring.
- generalize (Zgcd_is_gcd a b); intros HH1; inversion HH1; auto.
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_div;
-   rewrite BigN.spec_gcd; auto with zarith; intros H3.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H4.
- case H3; rewrite H4;  rewrite Zdiv_0_l; auto with zarith.
- simpl.
- assert (FF := BigN.spec_pos q).
- rewrite Z2P_correct; auto with zarith.
- rewrite <- BigN.spec_gcd; rewrite <- BigN.spec_div; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; auto with zarith.
- simpl; rewrite BigZ.spec_div; simpl.
- rewrite BigN.spec_gcd; auto with zarith.
- generalize H1 H2 H3 H4 HH FF; clear H1 H2 H3 H4 HH FF.
- set (a := (BigN.to_Z (BigZ.to_N p))).
- set (b := (BigN.to_Z q)).
- intros H1 H2 H3 H4 HH FF.
- rewrite spec_to_N; fold a.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_div; 
-   rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_gcd; auto with zarith.
- case (Zle_lt_or_eq _ _ 
-   (BigN.spec_pos (BigN.gcd (BigZ.to_N p) q)));
-  rewrite BigN.spec_gcd; auto with zarith.
- intros; apply False_ind; auto with zarith.
- intros HH2; assert (FF1 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- assert (FF2 := Zgcd_inv_0_l _ _ (sym_equal HH2)).
- red; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H2; simpl.
- rewrite spec_to_N.
- rewrite FF2; ring.
- Qed.
-
-   
- Definition add (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy => 
-      if BigN.eq_bool dy BigN.zero then x 
-      else Qq (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => Qq (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-       let d := BigN.mul dx dy in
-       Qq n d
-    end
-  end.
-
-
- Theorem spec_add x y: 
-  ([add x y] == [x] + [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qplus; simpl.
- rewrite BigZ.spec_add; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- assert (F1:= BigN.spec_pos dy).
- rewrite Zmult_1_r; red; simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH; simpl; try ring.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool;
-   rewrite BigN.spec_0; intros HH1; simpl; try ring.
- case HH; auto.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl; auto.
- rewrite Zmult_1_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- assert (F1:= BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- case HH2; auto.
- simpl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH2; auto.
- case HH1; auto.
- rewrite Zmult_1_r; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- simpl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- case HH; auto.
- rewrite Zmult_1_r; rewrite Zplus_0_r; rewrite Pmult_1_r.
- apply Qeq_refl.
- simpl.
- generalize (BigN.spec_eq_bool (dx * dy)%bigN BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_mul;
-   rewrite BigN.spec_0; intros HH2.
- (case (Zmult_integral _ _ HH2); intros HH3);
-  [case HH| case HH1]; auto.
- rewrite BigZ.spec_add; repeat rewrite BigZ.spec_mul; simpl.
- assert (Fx: (0 < BigN.to_Z dx)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- assert (Fy: (0 < BigN.to_Z dy)%Z).
-   generalize (BigN.spec_pos dy); auto with zarith.
- red; simpl; rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- apply Zmult_lt_0_compat; auto.
- Qed.
-
- Theorem spec_addc x y:
-  [[add x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition add_norm (x y: t): t :=
-  match x with
-  | Qz zx =>
-    match y with
-    | Qz zy => Qz (BigZ.add zx zy)
-    | Qq ny dy =>  
-      if BigN.eq_bool dy BigN.zero then x 
-      else norm (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-    end
-  | Qq nx dx =>
-    if BigN.eq_bool dx BigN.zero then y 
-    else match y with
-    | Qz zy => norm (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-    | Qq ny dy =>
-      if BigN.eq_bool dy BigN.zero then x
-      else
-       let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-       let d := BigN.mul dx dy in
-       norm n d
-    end
-  end.
-
- Theorem spec_add_norm x y:
-  ([add_norm x y] == [x] + [y])%Q.
- intros x y; rewrite <- spec_add; auto.
- case x; case y; clear x y; unfold add_norm, add.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- simpl.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- apply Qeq_refl.
- intros p1 p2 n.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- apply Qeq_refl.
- intros p1 q1 p2 q2.
- generalize (BigN.spec_eq_bool q2 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH1.
- apply Qeq_refl.
- generalize (BigN.spec_eq_bool q1 BigN.zero);
-   case BigN.eq_bool; rewrite BigN.spec_0; intros HH2.
- apply Qeq_refl.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- apply Qeq_refl.
- Qed.
-
- Theorem spec_add_normc x y:
-  [[add_norm x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add_norm; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition sub x y := add x (opp y).
-
-
- Theorem spec_sub x y:
-  ([sub x y] == [x] - [y])%Q.
- intros x y; unfold sub; rewrite spec_add; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_subc x y:  [[sub x y]] = [[x]] - [[y]].
- intros x y; unfold sub; rewrite spec_addc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Definition sub_norm x y := add_norm x (opp y).
-
- Theorem spec_sub_norm x y: 
-  ([sub_norm x y] == [x] - [y])%Q.
- intros x y; unfold sub_norm; rewrite spec_add_norm; auto.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_sub_normc x y:
-   [[sub_norm x y]] = [[x]] - [[y]].
- intros x y; unfold sub_norm; rewrite spec_add_normc; auto.
- rewrite spec_oppc; ring.
- Qed.
-
- Definition mul (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => Qq (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
-
- Theorem spec_mul x y: ([mul x y] == [x] * [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl.
- rewrite BigZ.spec_mul; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end;  rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH1.
- red; simpl; ring.
- rewrite BigZ.spec_mul; rewrite Pmult_1_r.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0;  rewrite BigN.spec_mul;
-      intros HH1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- red; simpl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- red; simpl; ring.
- case (Zmult_integral _ _ HH1); intros HH.
-   case HH2; auto.
-   case HH3; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH2.
- case HH1; rewrite HH2; ring.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros HH3.
- case HH1; rewrite HH3; ring.
- rewrite BigZ.spec_mul.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- apply Qeq_refl.
-  generalize (BigN.spec_pos dx); auto with zarith.
-  generalize (BigN.spec_pos dy); auto with zarith.
- Qed.
-
- Theorem spec_mulc x y:
-  [[mul x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
- Definition mul_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => norm (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => norm (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => norm (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
- Theorem spec_mul_norm x y:
-  ([mul_norm x y] == [x] * [y])%Q.
- intros x y; rewrite <- spec_mul; auto.
- unfold mul_norm, mul; case x; case y; clear x y.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; apply Qeq_refl.
- intros p1 p2 n.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; apply Qeq_refl.
- intros p1 n1 p2 n2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; apply Qeq_refl.
- Qed.
-
- Theorem spec_mul_normc x y:
-   [[mul_norm x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul_norm; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-
- Definition inv (x: t): t := 
-  match x with
-  | Qz (BigZ.Pos n) => Qq BigZ.one n
-  | Qz (BigZ.Neg n) => Qq BigZ.minus_one n
-  | Qq (BigZ.Pos n) d => Qq (BigZ.Pos d) n
-  | Qq (BigZ.Neg n) d => Qq (BigZ.Neg d) n
-  end.
-
- Theorem spec_inv x:
-   ([inv x] == /[x])%Q.
- intros [ [x | x] | [nx | nx] dx]; unfold inv, Qinv; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- rewrite H1; apply Qeq_refl.
- generalize H1 (BigN.spec_pos x); case (BigN.to_Z x); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl; auto.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- apply Qeq_refl.
- rewrite H1; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H2; simpl; auto.
- rewrite H2; red; simpl; auto.
- generalize H1 (BigN.spec_pos nx); case (BigN.to_Z nx); simpl;
-   auto.
- intros HH; case HH; auto.
- intros; red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p _ HH; case HH; auto.
- Qed.
-
- Theorem spec_invc x:
-   [[inv x]] =  /[[x]].
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-Definition inv_norm (x: t): t := 
- match x with
- | Qz (BigZ.Pos n) => 
-   match BigN.compare n BigN.one with
-     Gt => Qq BigZ.one n
-   | _ =>  x
-   end
- | Qz (BigZ.Neg n) => 
-   match BigN.compare n BigN.one with
-     Gt => Qq BigZ.minus_one n
-   | _ =>  x
-   end
- | Qq (BigZ.Pos n) d =>
-   match BigN.compare n BigN.one with
-     Gt => Qq (BigZ.Pos d) n
-   | Eq =>  Qz (BigZ.Pos d) 
-   | Lt => Qz (BigZ.zero)
-   end
- | Qq (BigZ.Neg n) d => 
-   match BigN.compare n BigN.one with
-     Gt => Qq (BigZ.Neg d) n
-   | Eq =>  Qz (BigZ.Neg d) 
-   | Lt => Qz (BigZ.zero)
-   end
- end.
-
- Theorem spec_inv_norm x: ([inv_norm x] == /[x])%Q.
- intros [ [x | x] | [nx | nx] dx]; unfold inv_norm, Qinv.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H.
- simpl; rewrite H; apply Qeq_refl.
- case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); simpl.
- generalize H; case BigN.to_Z.
- intros _ HH; discriminate HH.
- intros p; case p; auto.
-   intros p1 HH; discriminate HH.
-   intros p1 HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; discriminate HH.
- intros HH; rewrite <- HH.
-   apply Qeq_refl.
- generalize H; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- rewrite H1; intros HH; discriminate.
- generalize H; case BigN.to_Z.
- intros HH; discriminate HH.
- intros; red; simpl; auto.
- intros p HH; discriminate HH.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H.
- simpl; rewrite H; apply Qeq_refl.
- case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); simpl.
- generalize H; case BigN.to_Z.
- intros _ HH; discriminate HH.
- intros p; case p; auto.
-   intros p1 HH; discriminate HH.
-   intros p1 HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; discriminate HH.
- intros HH; rewrite <- HH.
-   apply Qeq_refl.
- generalize H; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- rewrite H1; intros HH; discriminate.
- generalize H; case BigN.to_Z.
- intros HH; discriminate HH.
- intros; red; simpl; auto.
- intros p HH; discriminate HH.
- simpl Qnum.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; simpl.
- case BigN.compare; red; simpl; auto.
- rewrite H1; auto.
- case BigN.eq_bool; auto.
- simpl; rewrite H1; auto.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H2.
- rewrite H2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- red; simpl.
- rewrite Zmult_1_r; rewrite Pmult_1_r; rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- generalize H2 (BigN.spec_pos nx); case (BigN.to_Z nx).
- intros; apply Qeq_refl.
- intros p; case p; clear p.
- intros p HH; discriminate HH.
- intros p HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- simpl; generalize H2; case (BigN.to_Z nx).
- intros HH; discriminate HH.
- intros p Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- rewrite H4 in H2; discriminate H2.
- red; simpl.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p HH; discriminate HH.
- simpl Qnum.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1; simpl.
- case BigN.compare; red; simpl; auto.
- rewrite H1; auto.
- case BigN.eq_bool; auto.
- simpl; rewrite H1; auto.
- match goal with  |- context[BigN.compare ?X ?Y] => 
-   generalize (BigN.spec_compare X Y); case BigN.compare
- end; rewrite BigN.spec_1; intros H2.
- rewrite H2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zmult_1_r; rewrite Pmult_1_r; rewrite Z2P_correct; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- generalize H2 (BigN.spec_pos nx); case (BigN.to_Z nx).
- intros; apply Qeq_refl.
- intros p; case p; clear p.
- intros p HH; discriminate HH.
- intros p HH; discriminate HH.
- intros HH; discriminate HH.
- intros p _ HH; case HH; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H3.
- case H1; auto.
- simpl; generalize H2; case (BigN.to_Z nx).
- intros HH; discriminate HH.
- intros p Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H4.
- rewrite H4 in H2; discriminate H2.
- red; simpl.
- assert (tmp: forall x, Zneg x = Zopp (Zpos x)); auto.
- rewrite tmp.
- rewrite Zpos_mult_morphism.
- rewrite Z2P_correct; auto.
- ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p HH; discriminate HH.
- Qed.
-
- Theorem spec_inv_normc x:
-   [[inv_norm x]] =  /[[x]].
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv_norm; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
- Definition div x y := mul x (inv y).
-
- Theorem spec_div x y: ([div x y] == [x] / [y])%Q.
- intros x y; unfold div; rewrite spec_mul; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_divc x y: [[div x y]] = [[x]] / [[y]].
- intros x y; unfold div; rewrite spec_mulc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto. 
- Qed.
-
- Definition div_norm x y := mul_norm x (inv y).
-
- Theorem spec_div_norm x y: ([div_norm x y] == [x] / [y])%Q.
- intros x y; unfold div_norm; rewrite spec_mul_norm; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_div_normc x y: [[div_norm x y]] = [[x]] / [[y]].
- intros x y; unfold div_norm; rewrite spec_mul_normc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto.
- Qed.
-
-
- Definition square (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.square zx)
-  | Qq nx dx => Qq (BigZ.square nx) (BigN.square dx)
-  end.
-
- Theorem spec_square x: ([square x] == [x] ^ 2)%Q.
- intros [ x | nx dx]; unfold square.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- simpl Qpower.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; intros H.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H1; rewrite H; auto.
- red; simpl.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_square;
-   intros H1.
- case H; case (Zmult_integral _ _ H1); auto.
- simpl.
- rewrite BigZ.spec_square.
- rewrite Zpos_mult_morphism.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- generalize (BigN.spec_pos dx); auto with zarith.
- generalize (BigN.spec_pos dx); auto with zarith.
- Qed.
-
- Theorem spec_squarec x: [[square x]] =  [[x]]^2.
- intros x; unfold to_Qc.
- apply trans_equal with (!! ([x]^2)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_square; auto.
- simpl Qcpower.
- replace (!! [x] * 1) with (!![x]); try ring.
- simpl.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-End Qif.
diff --git a/theories/Numbers/Rational/BigQ/QpMake.v b/theories/Numbers/Rational/BigQ/QpMake.v
deleted file mode 100644
index ac3ca47a..00000000
--- a/theories/Numbers/Rational/BigQ/QpMake.v
+++ /dev/null
@@ -1,901 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(*i $Id: QpMake.v 11027 2008-06-01 13:28:59Z letouzey $ i*)
-
-Require Import Bool.
-Require Import ZArith.
-Require Import Znumtheory.
-Require Import BigNumPrelude.
-Require Import Arith.
-Require Export BigN.
-Require Export BigZ.
-Require Import QArith.
-Require Import Qcanon.
-Require Import Qpower.
-Require Import QMake_base.
-
-Notation Nspec_lt := BigNAxiomsMod.NZOrdAxiomsMod.spec_lt.
-Notation Nspec_le := BigNAxiomsMod.NZOrdAxiomsMod.spec_le.
-
-Module Qp.
-
- (** The notation of a rational number is either an integer x,
-     interpreted as itself or a pair (x,y) of an integer x and a naturel
-     number y interpreted as x/(y+1). *)
-
- Definition t := q_type.
-
- Definition zero: t := Qz BigZ.zero.
- Definition one: t := Qz BigZ.one.
- Definition minus_one: t := Qz BigZ.minus_one.
-
- Definition of_Z x: t := Qz (BigZ.of_Z x).
-
- Definition d_to_Z d := BigZ.Pos (BigN.succ d).
-
- Definition of_Q q: t := 
- match q with x # y =>
-  Qq (BigZ.of_Z x) (BigN.pred (BigN.of_N (Npos y)))
- end.
-
- Definition of_Qc q := of_Q (this q).
-
- Definition to_Q (q: t) := 
- match q with 
-  Qz x => BigZ.to_Z x # 1
- |Qq x y => BigZ.to_Z x # Z2P (BigN.to_Z (BigN.succ y))
- end.
-
- Definition to_Qc q := !!(to_Q q).
-
- Notation "[[ x ]]" := (to_Qc x).
-
- Notation "[ x ]" := (to_Q x).
-
- Theorem spec_to_Q: forall q: Q, [of_Q q] = q.
- intros (x,y); simpl.
- rewrite BigZ.spec_of_Z; auto.
- rewrite BigN.spec_succ; simpl. simpl.
- rewrite BigN.spec_pred; rewrite (BigN.spec_of_pos).
- replace (Zpos y - 1 + 1)%Z with (Zpos y); auto; ring.
- red; auto.
- Qed.
-
- Theorem spec_to_Qc: forall q, [[of_Qc q]] = q.
- intros (x, Hx); unfold of_Qc, to_Qc; simpl.
- apply Qc_decomp; simpl.
- intros; rewrite spec_to_Q; auto.
- Qed.
-
- Definition opp (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.opp zx)
-  | Qq nx dx => Qq (BigZ.opp nx) dx
-  end.
-
-
- Theorem spec_opp: forall q, ([opp q] = -[q])%Q.
- intros [z | x y]; simpl.
- rewrite BigZ.spec_opp; auto.
- rewrite BigZ.spec_opp; auto.
- Qed.
-
-
- Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
- intros q; unfold Qcopp, to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- rewrite spec_opp.
- rewrite <- Qred_opp.
- rewrite Qred_involutive; auto.
- Qed.
-
- Definition compare (x y: t) :=
-  match x, y with
-  | Qz zx, Qz zy => BigZ.compare zx zy
-  | Qz zx, Qq ny dy => BigZ.compare (BigZ.mul zx (d_to_Z dy)) ny
-  | Qq nx dy, Qz zy => BigZ.compare nx (BigZ.mul zy (d_to_Z dy))
-  | Qq nx dx, Qq ny dy =>
-    BigZ.compare (BigZ.mul nx (d_to_Z dy)) (BigZ.mul ny (d_to_Z dx))
-  end.
-
- Theorem spec_compare: forall q1 q2,
-  compare q1 q2 = ([q1] ?= [q2])%Q.
- intros [z1 | x1 y1] [z2 | x2 y2]; unfold Qcompare; simpl.
- repeat rewrite Zmult_1_r.
- generalize (BigZ.spec_compare z1 z2); case BigZ.compare; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- rewrite Zmult_1_r.
- rewrite BigN.spec_succ.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (z1 * d_to_Z y2) x2)%bigZ; case BigZ.compare; 
-   intros H; rewrite <- H.
- rewrite BigZ.spec_mul; unfold d_to_Z; simpl.
- rewrite BigN.spec_succ.
- rewrite Zcompare_refl; auto.
- rewrite BigZ.spec_mul; unfold d_to_Z; simpl.
- rewrite BigN.spec_succ; auto.
- rewrite BigZ.spec_mul; unfold d_to_Z; simpl.
- rewrite BigN.spec_succ; auto.
- rewrite Zmult_1_r.
- rewrite BigN.spec_succ.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
- generalize (BigZ.spec_compare x1 (z2 * d_to_Z y1))%bigZ; case BigZ.compare;
-    rewrite BigZ.spec_mul; unfold d_to_Z; simpl;  
-    rewrite BigN.spec_succ; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- repeat rewrite BigN.spec_succ; auto.
- repeat rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (x1 * d_to_Z  y2)
-                  (x2 * d_to_Z y1))%bigZ; case BigZ.compare;
-    repeat rewrite BigZ.spec_mul; unfold d_to_Z; simpl;  
-    repeat rewrite BigN.spec_succ; intros H; auto.
- rewrite H; auto.
- rewrite Zcompare_refl; auto.
- Qed.
-
-
- Theorem spec_comparec: forall q1 q2,
-  compare q1 q2 = ([[q1]] ?= [[q2]]).
- unfold Qccompare, to_Qc. 
- intros q1 q2; rewrite spec_compare; simpl.
- apply Qcompare_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-(* Inv d > 0, Pour la forme normal unique on veut d > 1 *)
- Definition norm n d: t :=
-  if BigZ.eq_bool n BigZ.zero then zero
-  else
-    let gcd := BigN.gcd (BigZ.to_N n) d in
-    if BigN.eq_bool gcd BigN.one then Qq n (BigN.pred d)
-    else	
-      let n := BigZ.div n (BigZ.Pos gcd) in
-      let d := BigN.div d gcd in
-      if BigN.eq_bool d BigN.one then Qz n
-      else Qq n (BigN.pred d).
-
- Theorem spec_norm: forall n q, 
-    ((0 < BigN.to_Z q)%Z -> [norm n q] == [Qq n (BigN.pred q)])%Q.
- intros p q; unfold norm; intros Hq.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto; rewrite BigZ.spec_0; intros H1.
-   red; simpl; rewrite H1; ring.
- case (Zle_lt_or_eq _ _ Hp); clear Hp; intros Hp.
- case (Zle_lt_or_eq _ _ 
-      (Zgcd_is_pos (BigN.to_Z (BigZ.to_N p)) (BigN.to_Z q))); intros H4.
- 2: generalize Hq; rewrite (Zgcd_inv_0_r _ _ (sym_equal H4)); auto with zarith.
- 2: red; simpl; auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1; intros H2.
-   apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1.
- red; simpl.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Zmult_1_r.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N; intros; rewrite Zgcd_div_swap; auto.
- rewrite H; ring.
- intros H3.
- red; simpl.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- assert (F: (0 < BigN.to_Z (q / BigN.gcd (BigZ.to_N p) q)%bigN)%Z).
-   rewrite BigN.spec_div; auto with zarith.
-   rewrite BigN.spec_gcd.
-   apply Zgcd_div_pos; auto.
-   rewrite BigN.spec_gcd; auto.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite Z2P_correct; auto.
- rewrite Z2P_correct; auto.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite spec_to_N; apply Zgcd_div_swap; auto.
- case H1; rewrite spec_to_N; rewrite <- Hp; ring.
- Qed.
-
- Theorem spec_normc: forall n q, 
-    (0 < BigN.to_Z q)%Z -> [[norm n q]] = [[Qq n (BigN.pred q)]].
- intros n q H; unfold to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_norm; auto.
- Qed.
-   
- Definition add (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.add zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.add (BigZ.mul zx (d_to_Z dy)) ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.add nx (BigZ.mul zy (d_to_Z dx))) dx
-  | Qq nx dx, Qq ny dy => 
-    let dx' := BigN.succ dx in
-    let dy' := BigN.succ dy in
-    let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy')) (BigZ.mul ny (BigZ.Pos dx')) in
-    let d := BigN.pred (BigN.mul dx' dy') in
-    Qq n d
-  end. 
-
- Theorem spec_d_to_Z: forall dy,
-     (BigZ.to_Z (d_to_Z dy) = BigN.to_Z dy + 1)%Z.
- intros dy; unfold d_to_Z; simpl.
- rewrite BigN.spec_succ; auto.
- Qed.
-
- Theorem spec_succ_pos: forall p,
-  (0 < BigN.to_Z (BigN.succ p))%Z.
- intros p; rewrite BigN.spec_succ;
-   generalize (BigN.spec_pos p); auto with zarith.
- Qed.
-
- Theorem spec_add x y: ([add x y] == [x] + [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qplus; simpl.
- rewrite BigZ.spec_add; repeat rewrite Zmult_1_r; auto.
-  apply Qeq_refl; auto.
- assert (F1:= BigN.spec_pos dy).
- rewrite Zmult_1_r.
- simpl; rewrite Z2P_correct; rewrite BigN.spec_succ; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul.
- rewrite spec_d_to_Z; apply Qeq_refl.
- assert (F1:= BigN.spec_pos dx).
- rewrite Zmult_1_r; rewrite Pmult_1_r.
- simpl; rewrite Z2P_correct; rewrite BigN.spec_succ; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul.
- rewrite spec_d_to_Z; apply Qeq_refl.
- repeat rewrite BigN.spec_succ.
- assert (Fx: (0 < BigN.to_Z dx + 1)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- assert (Fy: (0 < BigN.to_Z dy + 1)%Z).
-   generalize (BigN.spec_pos dy); auto with zarith.
- repeat rewrite BigN.spec_pred.
- rewrite BigZ.spec_add; repeat rewrite BigN.spec_mul;
-   repeat rewrite BigN.spec_succ.
- assert (tmp: forall x, (x-1+1 = x)%Z); [intros; ring | rewrite tmp; clear tmp].
- repeat rewrite Z2P_correct; auto.
- repeat rewrite BigZ.spec_mul; simpl.
- repeat rewrite BigN.spec_succ.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto; apply Qeq_refl.
- rewrite BigN.spec_mul; repeat rewrite BigN.spec_succ; auto with zarith.
- apply Zmult_lt_0_compat; auto.
- Qed.
-
- Theorem spec_addc x y: [[add x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition add_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.add zx zy)
-  | Qz zx, Qq ny dy => 
-    let d := BigN.succ dy in
-    norm (BigZ.add (BigZ.mul zx (BigZ.Pos d)) ny) d 
-  | Qq nx dx, Qz zy =>
-    let d := BigN.succ dx in
-    norm (BigZ.add (BigZ.mul zy (BigZ.Pos d)) nx) d
-  | Qq nx dx, Qq ny dy =>
-    let dx' := BigN.succ dx in
-    let dy' := BigN.succ dy in
-    let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy')) (BigZ.mul ny (BigZ.Pos dx')) in
-    let d := BigN.mul dx' dy' in
-    norm n d 
-  end.
-
- Theorem spec_add_norm x y: ([add_norm x y] == [x] + [y])%Q.
- intros x y; rewrite <- spec_add.
- unfold add_norm, add; case x; case y.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X (BigN.pred Y)]);
-  [apply spec_norm | idtac]
- end.
- rewrite BigN.spec_succ; generalize (BigN.spec_pos n); auto with zarith.
- simpl.
- repeat rewrite BigZ.spec_add.
- repeat rewrite BigZ.spec_mul; simpl.
- rewrite BigN.succ_pred; try apply Qeq_refl; apply lt_0_succ.
- intros p1 n p2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X (BigN.pred Y)]);
-  [apply spec_norm | idtac]
- end.
- rewrite BigN.spec_succ; generalize (BigN.spec_pos p2); auto with zarith.
- simpl.
- repeat rewrite BigZ.spec_add.
- repeat rewrite BigZ.spec_mul; simpl.
- rewrite BinInt.Zplus_comm.
- rewrite BigN.succ_pred; try apply Qeq_refl; apply lt_0_succ.
- intros p1 q1 p2 q2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X (BigN.pred Y)]);
-  [apply spec_norm | idtac]
- end; try apply Qeq_refl.
- rewrite BigN.spec_mul.
- apply Zmult_lt_0_compat; apply spec_succ_pos.
- Qed.
-
- Theorem spec_add_normc x y: [[add_norm x y]] = [[x]] + [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add_norm.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
- 
- Definition sub (x y: t): t := add x (opp y).
-
- Theorem spec_sub x y: ([sub x y] == [x] - [y])%Q.
- intros x y; unfold sub; rewrite spec_add.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_subc x y: [[sub x y]] = [[x]] - [[y]].
- intros x y; unfold sub; rewrite spec_addc.
- rewrite spec_oppc; ring.
- Qed.
-
- Definition sub_norm x y := add_norm x (opp y).
-
- Theorem spec_sub_norm x y: ([sub_norm x y] == [x] - [y])%Q.
- intros x y; unfold sub_norm; rewrite spec_add_norm.
- rewrite spec_opp; ring.
- Qed.
-
- Theorem spec_sub_normc x y: [[sub_norm x y]] = [[x]] - [[y]].
- intros x y; unfold sub_norm; rewrite spec_add_normc.
- rewrite spec_oppc; ring.
- Qed.
-
-
- Definition mul (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => 
-    Qq (BigZ.mul nx ny) (BigN.pred (BigN.mul (BigN.succ dx) (BigN.succ dy)))
-  end.
-
- Theorem spec_mul x y: ([mul x y] == [x] * [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl.
- rewrite BigZ.spec_mul; repeat rewrite Zmult_1_r; auto.
-  apply Qeq_refl; auto.
- rewrite BigZ.spec_mul; apply Qeq_refl.
- rewrite BigZ.spec_mul; rewrite Pmult_1_r; auto.
-  apply Qeq_refl; auto.
- assert (F1:= spec_succ_pos dx).
- assert (F2:= spec_succ_pos dy).
- rewrite BigN.succ_pred.
- rewrite BigN.spec_mul; rewrite BigZ.spec_mul.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto; apply Qeq_refl.
- rewrite Nspec_lt, BigN.spec_0, BigN.spec_mul; auto.
- apply Zmult_lt_0_compat; apply spec_succ_pos.
- Qed.
-
- Theorem spec_mulc x y: [[mul x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition mul_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy =>
-    if BigZ.eq_bool zx BigZ.zero then zero
-    else	
-      let d := BigN.succ dy in
-      let gcd := BigN.gcd (BigZ.to_N zx) d in
-      if BigN.eq_bool gcd BigN.one then Qq (BigZ.mul zx ny) dy
-      else 
-        let zx := BigZ.div zx (BigZ.Pos gcd) in
-        let d := BigN.div d gcd in
-        if BigN.eq_bool d BigN.one then Qz (BigZ.mul zx ny)
-        else Qq (BigZ.mul zx ny) (BigN.pred d)
-  | Qq nx dx, Qz zy =>   
-    if BigZ.eq_bool zy BigZ.zero then zero
-    else	
-      let d := BigN.succ dx in
-      let gcd := BigN.gcd (BigZ.to_N zy) d in
-      if BigN.eq_bool gcd BigN.one then Qq (BigZ.mul zy nx) dx
-      else 
-        let zy := BigZ.div zy (BigZ.Pos gcd) in
-        let d := BigN.div d gcd in
-        if BigN.eq_bool d BigN.one then Qz (BigZ.mul zy nx)
-        else Qq (BigZ.mul zy nx) (BigN.pred d)
-  | Qq nx dx, Qq ny dy => 
-    norm (BigZ.mul nx ny) (BigN.mul (BigN.succ dx) (BigN.succ dy))
-  end.
-
- Theorem spec_mul_norm x y: ([mul_norm x y] == [x] * [y])%Q.
- intros x y; rewrite <- spec_mul.
- unfold mul_norm, mul; case x; case y.
-  intros; apply Qeq_refl.
- intros p1 n p2.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- rewrite BigZ.spec_mul; rewrite H; red; auto.
- assert (F: (0 < BigN.to_Z (BigZ.to_N p2))%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p2))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- assert (F1: (0 < BigN.to_Z (BigN.succ n))%Z).
-  rewrite BigN.spec_succ; generalize (BigN.spec_pos n); auto with zarith.
- assert (F2: (0 < Zgcd (BigN.to_Z (BigZ.to_N p2)) (BigN.to_Z (BigN.succ n)))%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos (BigN.to_Z (BigZ.to_N p2))
-                                       (BigN.to_Z (BigN.succ n)))); intros H3; auto.
-   generalize F; rewrite (Zgcd_inv_0_l _ _ (sym_equal H3)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
-  intros; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith.
- intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N.
- rewrite Zmult_1_r; repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite (spec_to_N p2).
- case (Zle_lt_or_eq _ _
-       (BigN.spec_pos  (BigN.succ n / 
-                         BigN.gcd (BigZ.to_N p2) 
-                                  (BigN.succ n)))%bigN); intros F3.
- rewrite BigN.succ_pred; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto; try ring.
- rewrite Nspec_lt, BigN.spec_0; auto.
- apply False_ind; generalize F1.
- rewrite (Zdivide_Zdiv_eq
-          (Zgcd (BigN.to_Z (BigZ.to_N p2)) (BigN.to_Z (BigN.succ n)))
-           (BigN.to_Z (BigN.succ n))); auto.
- generalize F3; rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith.
- intros HH; rewrite <- HH; auto with zarith.
- assert (FF:= Zgcd_is_gcd (BigN.to_Z (BigZ.to_N p2))
-           (BigN.to_Z (BigN.succ n))); inversion FF; auto.
- intros p1 p2 n.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- rewrite BigZ.spec_mul; rewrite H; red; simpl; ring.
- assert (F: (0 < BigN.to_Z (BigZ.to_N p1))%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p1))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- assert (F1: (0 < BigN.to_Z (BigN.succ n))%Z).
-  rewrite BigN.spec_succ; generalize (BigN.spec_pos n); auto with zarith.
- assert (F2: (0 < Zgcd (BigN.to_Z (BigZ.to_N p1)) (BigN.to_Z (BigN.succ n)))%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos (BigN.to_Z (BigZ.to_N p1))
-                                       (BigN.to_Z (BigN.succ n)))); intros H3; auto.
-   generalize F; rewrite (Zgcd_inv_0_l _ _ (sym_equal H3)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
-  intros; repeat rewrite BigZ.spec_mul; rewrite Zmult_comm; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith.
- intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N.
- rewrite Zmult_1_r; repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite (spec_to_N p1).
- case (Zle_lt_or_eq _ _
-       (BigN.spec_pos  (BigN.succ n / 
-                         BigN.gcd (BigZ.to_N p1) 
-                                  (BigN.succ n)))%bigN); intros F3.
- rewrite BigN.succ_pred; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto; try ring.
- rewrite Nspec_lt, BigN.spec_0; auto.
- apply False_ind; generalize F1.
- rewrite (Zdivide_Zdiv_eq
-          (Zgcd (BigN.to_Z (BigZ.to_N p1)) (BigN.to_Z (BigN.succ n)))
-           (BigN.to_Z (BigN.succ n))); auto.
- generalize F3; rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith.
- intros HH; rewrite <- HH; auto with zarith.
- assert (FF:= Zgcd_is_gcd (BigN.to_Z (BigZ.to_N p1))
-           (BigN.to_Z (BigN.succ n))); inversion FF; auto.
- intros p1 n1 p2 n2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X (BigN.pred Y)]);
-  [apply spec_norm | idtac]
- end; try  apply Qeq_refl.
- rewrite BigN.spec_mul.
- apply Zmult_lt_0_compat; rewrite BigN.spec_succ;
-    generalize (BigN.spec_pos n1) (BigN.spec_pos n2); auto with zarith.
- Qed.
-
- Theorem spec_mul_normc x y: [[mul_norm x y]] = [[x]] * [[y]].
- intros x y; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul_norm.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition inv (x: t): t := 
-  match x with
-  | Qz (BigZ.Pos n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.one (BigN.pred n)
-  | Qz (BigZ.Neg n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.minus_one (BigN.pred n)
-  | Qq (BigZ.Pos n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Pos (BigN.succ d)) (BigN.pred n)
-  | Qq (BigZ.Neg n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Neg (BigN.succ d)) (BigN.pred n)
-  end.
-
- Theorem spec_inv x: ([inv x] == /[x])%Q.
- intros [ [x | x] | [nx | nx] dx]; unfold inv.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- unfold to_Q; rewrite BigZ.spec_1.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- red; unfold Qinv; simpl.
- generalize F; case BigN.to_Z; auto with zarith.
- intros p Hp; discriminate Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- red; unfold Qinv; simpl.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- generalize F; case BigN.to_Z; simpl; auto with zarith.
- intros p Hp; discriminate Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z nx)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos nx)); auto with zarith.
- red; unfold Qinv; simpl.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite BigN.spec_succ; rewrite Z2P_correct; auto with zarith.
- generalize F; case BigN.to_Z; auto with zarith.
- intros p Hp; discriminate Hp.
- generalize (BigN.spec_pos dx); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z nx)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos nx)); auto with zarith.
- red; unfold Qinv; simpl.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite BigN.spec_succ; rewrite Z2P_correct; auto with zarith.
- generalize F; case BigN.to_Z; auto with zarith.
- simpl; intros.
- match goal with  |- (?X = Zneg ?Y)%Z => 
-   replace (Zneg Y) with (-(Zpos Y))%Z;
-   try rewrite Z2P_correct; auto with zarith
- end.
- rewrite Zpos_mult_morphism; 
-   rewrite Z2P_correct; auto with zarith; try ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p Hp; discriminate Hp.
- generalize (BigN.spec_pos dx); auto with zarith.
- Qed.
-
- Theorem spec_invc x: [[inv x]] =  /[[x]].
- intros x; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-Definition inv_norm x := 
- match x with
- | Qz (BigZ.Pos n) => 
-      if BigN.eq_bool n BigN.zero then zero else
-      if BigN.eq_bool n BigN.one then x else Qq BigZ.one (BigN.pred n)
- | Qz (BigZ.Neg n) => 
-      if BigN.eq_bool n BigN.zero then zero  else
-      if BigN.eq_bool n BigN.one then x else Qq BigZ.minus_one (BigN.pred n)
- | Qq (BigZ.Pos n) d => let d := BigN.succ d in 
-                  if BigN.eq_bool n BigN.zero then zero else
-                  if BigN.eq_bool n BigN.one then Qz (BigZ.Pos d) 
-                     else Qq (BigZ.Pos d) (BigN.pred n)
- | Qq (BigZ.Neg n) d => let d := BigN.succ d in 
-                  if BigN.eq_bool n BigN.zero then zero else
-                  if BigN.eq_bool n BigN.one then Qz (BigZ.Neg d) 
-                     else Qq (BigZ.Neg d) (BigN.pred n)
- end.
-
- Theorem spec_inv_norm x: ([inv_norm x] == /[x])%Q.
- intros x; rewrite <- spec_inv.
- (case x; clear x); [intros [x | x] | intros nx dx];
-  unfold inv_norm, inv.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
- red; simpl.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite Z2P_correct; try rewrite H1; auto with zarith.
-  apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
- red; simpl.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite Z2P_correct; try rewrite H1; auto with zarith.
-  apply Qeq_refl.
- case nx; clear nx; intros nx.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
- red; simpl.
- rewrite BigN.succ_pred; try rewrite H1; auto with zarith.
- rewrite Nspec_lt, BigN.spec_0, H1; auto with zarith.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; intros H1.
- red; simpl.
- rewrite BigN.succ_pred; try rewrite H1; auto with zarith.
- rewrite Nspec_lt, BigN.spec_0, H1; auto with zarith.
- apply Qeq_refl.
- Qed.
-
-
- Definition div x y := mul x (inv y).
-
- Theorem spec_div x y: ([div x y] == [x] / [y])%Q.
- intros x y; unfold div; rewrite spec_mul; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_divc x y: [[div x y]] = [[x]] / [[y]].
- intros x y; unfold div; rewrite spec_mulc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto. 
- Qed.
-
- Definition div_norm x y := mul_norm x (inv y).
-
- Theorem spec_div_norm x y: ([div_norm x y] == [x] / [y])%Q.
- intros x y; unfold div_norm; rewrite spec_mul_norm; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- Qed.
-
- Theorem spec_div_normc x y: [[div_norm x y]] = [[x]] / [[y]].
- intros x y; unfold div_norm; rewrite spec_mul_normc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto.
- Qed.
-
-
- Definition square (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.square zx)
-  | Qq nx dx => Qq (BigZ.square nx) (BigN.pred (BigN.square (BigN.succ dx)))
-  end.
-
- Theorem spec_square x: ([square x] == [x] ^ 2)%Q.
- intros [ x | nx dx]; unfold square.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- assert (F: (0 < BigN.to_Z (BigN.succ dx))%Z).
-   rewrite BigN.spec_succ;
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos dx)); auto with zarith.
- assert (F1 : (0 < BigN.to_Z (BigN.square (BigN.succ dx)))%Z).
-   rewrite BigN.spec_square; apply Zmult_lt_0_compat;
-     auto with zarith.
- rewrite BigN.succ_pred by (rewrite Nspec_lt, BigN.spec_0; auto).
- rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- repeat rewrite BigN.spec_succ; auto with zarith.
- rewrite BigN.spec_square; auto with zarith.
- repeat rewrite BigN.spec_succ; auto with zarith.
- Qed.
-
- Theorem spec_squarec x: [[square x]] =  [[x]]^2.
- intros x; unfold to_Qc.
- apply trans_equal with (!! ([x]^2)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_square.
- simpl Qcpower.
- replace (!! [x] * 1) with (!![x]); try ring.
- simpl.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition power_pos (x: t) p: t :=
-  match x with
-  | Qz zx => Qz (BigZ.power_pos zx p)
-  | Qq nx dx => Qq (BigZ.power_pos nx p) (BigN.pred (BigN.power_pos (BigN.succ dx) p))
-  end.
-
-
- Theorem spec_power_pos x p: ([power_pos x p] == [x] ^ Zpos p)%Q.
- Proof.
- intros [x | nx dx] p; unfold power_pos.
-   unfold power_pos; red; simpl.
-   generalize (Qpower_decomp p (BigZ.to_Z x) 1).
-   unfold Qeq; simpl.
-   rewrite Zpower_pos_1_l; simpl Z2P.
-   rewrite Zmult_1_r.
-   intros H; rewrite H.
-   rewrite BigZ.spec_power_pos; simpl; ring.
- assert (F1: (0 < BigN.to_Z (BigN.succ dx))%Z).
-     rewrite BigN.spec_succ;
-     generalize (BigN.spec_pos dx); auto with zarith.
- assert (F2: (0 < BigN.to_Z (BigN.succ dx) ^ ' p)%Z).
-  unfold Zpower; apply Zpower_pos_pos; auto.
- unfold power_pos; red; simpl.
- rewrite BigN.succ_pred, BigN.spec_power_pos.
- rewrite Z2P_correct; auto.
- generalize (Qpower_decomp p (BigZ.to_Z nx) 
-               (Z2P (BigN.to_Z (BigN.succ dx)))).
- unfold Qeq; simpl.
- repeat rewrite Z2P_correct; auto.
- unfold Qeq; simpl; intros HH.
- rewrite HH.
- rewrite BigZ.spec_power_pos; simpl; ring.
- rewrite Nspec_lt, BigN.spec_0, BigN.spec_power_pos; auto.
- Qed.
-
- Theorem spec_power_posc x p: [[power_pos x p]] = [[x]] ^ nat_of_P p.
- intros x p; unfold to_Qc.
- apply trans_equal with (!! ([x]^Zpos p)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_power_pos.
- pattern p; apply Pind; clear p.
- simpl; ring.
- intros p Hrec.
- rewrite nat_of_P_succ_morphism; simpl Qcpower.
- rewrite <- Hrec.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _;
- unfold this.
- apply Qred_complete.
- assert (F: [x] ^ ' Psucc p == [x] *   [x] ^ ' p).
-  simpl; case x; simpl; clear x Hrec.
-  intros x; simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  intros nx dx; simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  assert (F1: (0 < BigN.to_Z (BigN.succ dx))%Z).
-    rewrite BigN.spec_succ; generalize (BigN.spec_pos dx); 
-      auto with zarith.
-  repeat rewrite Zpos_mult_morphism.
-  repeat rewrite Z2P_correct; auto.
-  2: apply Zpower_pos_pos; auto.
-  2: apply Zpower_pos_pos; auto.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
- rewrite F.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
-End Qp.
diff --git a/theories/Numbers/Rational/BigQ/QvMake.v b/theories/Numbers/Rational/BigQ/QvMake.v
deleted file mode 100644
index 4523e241..00000000
--- a/theories/Numbers/Rational/BigQ/QvMake.v
+++ /dev/null
@@ -1,1151 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-(*            Benjamin Gregoire, Laurent Thery, INRIA, 2007             *)
-(************************************************************************)
-
-(*i $Id: QvMake.v 11027 2008-06-01 13:28:59Z letouzey $ i*)
-
-Require Import Bool.
-Require Import ZArith.
-Require Import Znumtheory.
-Require Import BigNumPrelude.
-Require Import Arith.
-Require Export BigN.
-Require Export BigZ.
-Require Import QArith.
-Require Import Qcanon.
-Require Import Qpower.
-Require Import QMake_base.
-
-Module Qv.
-
- Import BinInt Zorder.
- Open Local Scope Q_scope.
- Open Local Scope Qc_scope.
-
- (** The notation of a rational number is either an integer x,
-     interpreted as itself or a pair (x,y) of an integer x and a naturel
-     number y interpreted as x/y. All functions maintain the invariant
-     that y is never zero. *)
-
- Definition t := q_type.
-
- Definition zero: t := Qz BigZ.zero.
- Definition one: t := Qz BigZ.one.
- Definition minus_one: t := Qz BigZ.minus_one.
-
- Definition of_Z x: t := Qz (BigZ.of_Z x).
-
- Definition wf x := 
-  match x with
-  | Qz _ => True
-  | Qq n d => if BigN.eq_bool d BigN.zero then False else True
-  end.
-
- Definition of_Q q: t := 
- match q with x # y =>
-  Qq (BigZ.of_Z x) (BigN.of_N (Npos y))
- end.
-
- Definition of_Qc q := of_Q (this q).
-
- Definition to_Q (q: t) := 
- match q with 
-  Qz x => BigZ.to_Z x # 1
- |Qq x y => BigZ.to_Z x # Z2P (BigN.to_Z y)
- end.
-
- Definition to_Qc q := !!(to_Q q).
-
- Notation "[[ x ]]" := (to_Qc x).
-
- Notation "[ x ]" := (to_Q x).
-
- Theorem spec_to_Q: forall q: Q, [of_Q q] = q.
- intros (x,y); simpl.
- rewrite BigZ.spec_of_Z; simpl.
- rewrite (BigN.spec_of_pos); auto.
- Qed.
-
- Theorem spec_to_Qc: forall q, [[of_Qc q]] = q.
- intros (x, Hx); unfold of_Qc, to_Qc; simpl.
- apply Qc_decomp; simpl.
- intros; rewrite spec_to_Q; auto.
- Qed.
-
- Definition opp (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.opp zx)
-  | Qq nx dx => Qq (BigZ.opp nx) dx
-  end.
-
- Theorem wf_opp: forall x, wf x -> wf (opp x).
- intros [zx | nx dx]; unfold opp, wf; auto.
- Qed.
-
- Theorem spec_opp: forall q, ([opp q] = -[q])%Q.
- intros [z | x y]; simpl.
- rewrite BigZ.spec_opp; auto.
- rewrite BigZ.spec_opp; auto.
- Qed.
-
- Theorem spec_oppc: forall q, [[opp q]] = -[[q]].
- intros q; unfold Qcopp, to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- rewrite spec_opp.
- rewrite <- Qred_opp.
- rewrite Qred_involutive; auto.
- Qed.
-
- (* Les fonctions doivent assurer que si leur arguments sont valides alors
-    le resultat est correct et valide (si c'est un Q) 
- *)
-
- Definition compare (x y: t) :=
-  match x, y with
-  | Qz zx, Qz zy => BigZ.compare zx zy
-  | Qz zx, Qq ny dy => BigZ.compare (BigZ.mul zx (BigZ.Pos dy)) ny
-  | Qq nx dx, Qz zy => BigZ.compare nx (BigZ.mul zy (BigZ.Pos dx))  
-  | Qq nx dx, Qq ny dy => BigZ.compare (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx))
-  end.
-
- Theorem spec_compare: forall q1 q2, wf q1 -> wf q2 ->
-  compare q1 q2 = ([q1] ?= [q2])%Q.
- intros [z1 | x1 y1] [z2 | x2 y2]; 
-   unfold Qcompare, compare, to_Q, Qnum, Qden, wf.
- repeat rewrite Zmult_1_r.
- generalize (BigZ.spec_compare z1 z2); case BigZ.compare; intros H; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- rewrite Zmult_1_r.
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool.
-   intros _ _ HH; case HH.
- rewrite BigN.spec_0; intros HH _ _.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (z1 * BigZ.Pos y2) x2)%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH _ _.
- rewrite Z2P_correct; auto with zarith.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
- rewrite Zmult_1_r.
- generalize (BigZ.spec_compare x1 (z2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- generalize (BigN.spec_eq_bool y1 BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH1. 
- generalize (BigN.spec_eq_bool y2 BigN.zero);
-   case BigN.eq_bool.
-   intros _ _ HH; case HH.
- rewrite BigN.spec_0; intros HH2 _ _.
- repeat rewrite Z2P_correct.
-  2: generalize (BigN.spec_pos y1); auto with zarith.
-  2: generalize (BigN.spec_pos y2); auto with zarith.
- generalize (BigZ.spec_compare (x1 * BigZ.Pos y2) 
-                               (x2 * BigZ.Pos y1))%bigZ; case BigZ.compare;
-   repeat rewrite BigZ.spec_mul; simpl; intros H; apply sym_equal; auto.
- rewrite H; rewrite Zcompare_refl; auto.
- Qed.
-
- Theorem spec_comparec: forall q1 q2, wf q1 -> wf q2 ->
-  compare q1 q2 = ([[q1]] ?= [[q2]]).
- unfold Qccompare, to_Qc. 
- intros q1 q2 Hq1 Hq2; rewrite spec_compare; simpl; auto.
- apply Qcompare_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition norm n d: t :=
-  if BigZ.eq_bool n BigZ.zero then zero
-  else
-    let gcd := BigN.gcd (BigZ.to_N n) d in
-    if BigN.eq_bool gcd BigN.one then Qq n d
-    else	
-      let n := BigZ.div n (BigZ.Pos gcd) in
-      let d := BigN.div d gcd in
-      if BigN.eq_bool d BigN.one then Qz n
-      else Qq n d.
-
- Theorem wf_norm: forall n q,
-   (BigN.to_Z q <> 0)%Z -> wf (norm n q).
- intros p q; unfold norm, wf; intros Hq.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto; rewrite BigZ.spec_0; intros H1.
- simpl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- set (a := BigN.to_Z (BigZ.to_N p)).
- set (b := (BigN.to_Z q)).
- assert (F: (0 < Zgcd a b)%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos a b)); auto.
-   intros HH1; case Hq; apply (Zgcd_inv_0_r _ _ (sym_equal HH1)).
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; auto; fold a; fold b.
- intros H; case Hq; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite H; auto with zarith.
- assert (F1:= Zgcd_is_gcd a b); inversion F1; auto.
- Qed.
- 
- Theorem spec_norm: forall n q, 
-    ((0 < BigN.to_Z q)%Z -> [norm n q] == [Qq n q])%Q.
- intros p q; unfold norm; intros Hq.
- assert (Hp := BigN.spec_pos (BigZ.to_N p)).
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto; rewrite BigZ.spec_0; intros H1.
-   red; simpl; rewrite H1; ring.
- case (Zle_lt_or_eq _ _ Hp); clear Hp; intros Hp.
- case (Zle_lt_or_eq _ _ 
-      (Zgcd_is_pos (BigN.to_Z (BigZ.to_N p)) (BigN.to_Z q))); intros H4.
- 2: generalize Hq; rewrite (Zgcd_inv_0_r _ _ (sym_equal H4)); auto with zarith.
- 2: red; simpl; auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1; intros H2.
-   apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_1.
- red; simpl.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite Zmult_1_r.
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N; intros; rewrite Zgcd_div_swap; auto.
- rewrite H; ring.
- intros H3.
- red; simpl.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- assert (F: (0 < BigN.to_Z (q / BigN.gcd (BigZ.to_N p) q)%bigN)%Z).
-   rewrite BigN.spec_div; auto with zarith.
-   rewrite BigN.spec_gcd.
-   apply Zgcd_div_pos; auto.
-   rewrite BigN.spec_gcd; auto.
- rewrite Z2P_correct; auto.
- rewrite Z2P_correct; auto.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; auto with zarith.
- rewrite spec_to_N; apply Zgcd_div_swap; auto.
- case H1; rewrite spec_to_N; rewrite <- Hp; ring.
- Qed.
-
- Theorem spec_normc: forall n q, 
-    (0 < BigN.to_Z q)%Z -> [[norm n q]] = [[Qq n q]].
- intros n q H; unfold to_Qc, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_norm; auto.
- Qed.
-      
- Definition add (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.add zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.add nx (BigZ.mul zy (BigZ.Pos dx))) dx
-  | Qq nx dx, Qq ny dy => 
-    let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-    let d := BigN.mul dx dy in
-    Qq n d
-  end.
-
- Theorem wf_add: forall x y, wf x -> wf y -> wf (add x y).
- intros [zx | nx dx] [zy | ny dy]; unfold add, wf; auto.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_mul.
- intros H1 H2 H3.
- case (Zmult_integral _ _ H1); auto with zarith.
- Qed.
-
- Theorem spec_add x y: wf x -> wf y ->
-  ([add x y] == [x] + [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qplus; simpl.
- rewrite BigZ.spec_add; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- assert (F1:= BigN.spec_pos dy).
- rewrite Zmult_1_r.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool.
-   intros _ _ HH; case HH.
- rewrite BigN.spec_0; intros HH _ _.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul.
- simpl; apply Qeq_refl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH _ _.
- assert (F1:= BigN.spec_pos dx).
- rewrite Zmult_1_r; rewrite Pmult_1_r.
- simpl; rewrite Z2P_correct; auto with zarith.
- rewrite BigZ.spec_add; rewrite BigZ.spec_mul; simpl.
- apply Qeq_refl.
- generalize (BigN.spec_eq_bool dx BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH1.
- generalize (BigN.spec_eq_bool dy BigN.zero);
-   case BigN.eq_bool.
-   intros _ _ HH; case HH.
- rewrite BigN.spec_0; intros HH2 _ _.
- assert (Fx: (0 < BigN.to_Z dx)%Z).
-   generalize (BigN.spec_pos dx); auto with zarith.
- assert (Fy: (0 < BigN.to_Z dy)%Z).
-   generalize (BigN.spec_pos dy); auto with zarith.
- rewrite BigZ.spec_add; repeat rewrite BigN.spec_mul.
- red; simpl.
- rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto.
- repeat rewrite BigZ.spec_mul; simpl; auto.
- apply Zmult_lt_0_compat; auto.
- Qed.
-
- Theorem spec_addc x y: wf x -> wf y ->
-  [[add x y]] = [[x]] + [[y]].
- intros x y H1 H2; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition add_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.add zx zy)
-  | Qz zx, Qq ny dy => 
-    norm (BigZ.add (BigZ.mul zx (BigZ.Pos dy)) ny) dy 
-  | Qq nx dx, Qz zy =>
-    norm (BigZ.add (BigZ.mul zy (BigZ.Pos dx)) nx) dx
-  | Qq nx dx, Qq ny dy =>
-    let n := BigZ.add (BigZ.mul nx (BigZ.Pos dy)) (BigZ.mul ny (BigZ.Pos dx)) in
-    let d := BigN.mul dx dy in
-    norm n d 
-  end.
-
- Theorem wf_add_norm: forall x y, wf x -> wf y -> wf (add_norm x y).
- intros [zx | nx dx] [zy | ny dy]; unfold add_norm; auto.
- intros HH1 HH2; apply wf_norm.
- generalize HH2; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros HH1 HH2; apply wf_norm.
- generalize HH1; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros HH1 HH2; apply wf_norm.
- rewrite BigN.spec_mul; intros HH3.
- case (Zmult_integral _ _ HH3).
- generalize HH1; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- generalize HH2; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- Qed.
-
- Theorem spec_add_norm x y: wf x -> wf y ->
-  ([add_norm x y] == [x] + [y])%Q.
- intros x y H1 H2; rewrite <- spec_add; auto.
- generalize H1 H2; unfold add_norm, add, wf; case x; case y; clear H1 H2.
-  intros; apply Qeq_refl.
- intros p1 n p2 _.
- generalize (BigN.spec_eq_bool n BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH _.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- generalize (BigN.spec_pos n); auto with zarith.
- simpl.
- repeat rewrite BigZ.spec_add.
- repeat rewrite BigZ.spec_mul; simpl.
- apply Qeq_refl.
- intros p1 n p2.
- generalize (BigN.spec_eq_bool p2 BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH _ _.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end.
- generalize (BigN.spec_pos p2); auto with zarith.
- simpl.
- repeat rewrite BigZ.spec_add.
- repeat rewrite BigZ.spec_mul; simpl.
- rewrite Zplus_comm.
- apply Qeq_refl.
- intros p1 q1 p2 q2.
- generalize (BigN.spec_eq_bool q2 BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH1 _.
- generalize (BigN.spec_eq_bool q1 BigN.zero);
-   case BigN.eq_bool.
-   intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH2 _.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; try apply Qeq_refl.
- rewrite BigN.spec_mul.
- apply Zmult_lt_0_compat.
-  generalize (BigN.spec_pos q2); auto with zarith.
-  generalize (BigN.spec_pos q1); auto with zarith.
- Qed.
-
- Theorem spec_add_normc x y: wf x -> wf y ->
-  [[add_norm x y]] = [[x]] + [[y]].
- intros x y Hx Hy; unfold to_Qc.
- apply trans_equal with (!! ([x] + [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_add_norm; auto.
- unfold Qcplus, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qplus_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition sub x y := add x (opp y).
-
- Theorem wf_sub x y: wf x -> wf y -> wf (sub x y).
- intros x y Hx Hy; unfold sub; apply wf_add; auto.
- apply wf_opp; auto.
- Qed.
-
- Theorem spec_sub x y: wf x -> wf y ->
-  ([sub x y] == [x] - [y])%Q.
- intros x y Hx Hy; unfold sub; rewrite spec_add; auto.
- rewrite spec_opp; ring.
- apply wf_opp; auto.
- Qed.
-
- Theorem spec_subc x y: wf x -> wf y ->
-   [[sub x y]] = [[x]] - [[y]].
- intros x y Hx Hy; unfold sub; rewrite spec_addc; auto.
- rewrite spec_oppc; ring.
- apply wf_opp; auto.
- Qed.
-
- Definition sub_norm x y := add_norm x (opp y).
-
- Theorem wf_sub_norm x y: wf x -> wf y -> wf (sub_norm x y).
- intros x y Hx Hy; unfold sub_norm; apply wf_add_norm; auto.
- apply wf_opp; auto.
- Qed.
-
- Theorem spec_sub_norm x y: wf x -> wf y ->
-  ([sub_norm x y] == [x] - [y])%Q.
- intros x y Hx Hy; unfold sub_norm; rewrite spec_add_norm; auto.
- rewrite spec_opp; ring.
- apply wf_opp; auto.
- Qed.
-
- Theorem spec_sub_normc x y: wf x -> wf y ->
-   [[sub_norm x y]] = [[x]] - [[y]].
- intros x y Hx Hy; unfold sub_norm; rewrite spec_add_normc; auto.
- rewrite spec_oppc; ring.
- apply wf_opp; auto.
- Qed.
-
- Definition mul (x y: t): t :=
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy => Qq (BigZ.mul zx ny) dy
-  | Qq nx dx, Qz zy => Qq (BigZ.mul nx zy) dx
-  | Qq nx dx, Qq ny dy => 
-    Qq (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
- Theorem wf_mul: forall x y, wf x -> wf y -> wf (mul x y).
- intros [zx | nx dx] [zy | ny dy]; unfold mul, wf; auto.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_mul.
- intros H1 H2 H3.
- case (Zmult_integral _ _ H1); auto with zarith.
- Qed.
-
- Theorem spec_mul x y: wf x -> wf y -> ([mul x y] == [x] * [y])%Q.
- intros [x | nx dx] [y | ny dy]; unfold Qmult; simpl.
- rewrite BigZ.spec_mul; repeat rewrite Zmult_1_r; auto.
-  intros; apply Qeq_refl; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros _ _ HH; case HH.
- rewrite BigN.spec_0; intros HH1 _ _.
- rewrite BigZ.spec_mul; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros _ HH; case HH.
- rewrite BigN.spec_0; intros HH1 _ _.
- rewrite BigZ.spec_mul; rewrite Pmult_1_r.
- apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros _ HH; case HH.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- intros _ _ _ HH; case HH.
- rewrite BigN.spec_0; intros H1 H2 _ _.
- rewrite BigZ.spec_mul; rewrite BigN.spec_mul.
- assert (tmp: 
-  (forall a b, 0 < a -> 0 < b -> Z2P (a * b) = (Z2P a * Z2P b)%positive)%Z).
-  intros [|a|a] [|b|b]; simpl; auto; intros; apply False_ind; auto with zarith.
- rewrite tmp; auto.
- apply Qeq_refl.
-  generalize (BigN.spec_pos dx); auto with zarith.
-  generalize (BigN.spec_pos dy); auto with zarith.
- Qed.
-
- Theorem spec_mulc x y: wf x -> wf y ->
-  [[mul x y]] = [[x]] * [[y]].
- intros x y Hx Hy; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition mul_norm (x y: t): t := 
-  match x, y with
-  | Qz zx, Qz zy => Qz (BigZ.mul zx zy)
-  | Qz zx, Qq ny dy =>
-    if BigZ.eq_bool zx BigZ.zero then zero
-    else	
-      let gcd := BigN.gcd (BigZ.to_N zx) dy in
-      if BigN.eq_bool gcd BigN.one then Qq (BigZ.mul zx ny) dy
-      else 
-        let zx := BigZ.div zx (BigZ.Pos gcd) in
-        let d := BigN.div dy gcd in
-        if BigN.eq_bool d BigN.one then Qz (BigZ.mul zx ny)
-        else Qq (BigZ.mul zx ny) d
-  | Qq nx dx, Qz zy =>   
-    if BigZ.eq_bool zy BigZ.zero then zero
-    else	
-      let gcd := BigN.gcd (BigZ.to_N zy) dx in
-      if BigN.eq_bool gcd BigN.one then Qq (BigZ.mul zy nx) dx
-      else 
-        let zy := BigZ.div zy (BigZ.Pos gcd) in
-        let d := BigN.div dx gcd in
-        if BigN.eq_bool d BigN.one then Qz (BigZ.mul zy nx)
-        else Qq (BigZ.mul zy nx) d
-  | Qq nx dx, Qq ny dy => norm (BigZ.mul nx ny) (BigN.mul dx dy)
-  end.
-
- Theorem wf_mul_norm: forall x y, wf x -> wf y -> wf (mul_norm x y).
- intros [zx | nx dx] [zy | ny dy]; unfold mul_norm; auto.
- intros HH1 HH2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto;
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_1; rewrite BigZ.spec_0.
- intros H1 H2; unfold wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_0.
- set (a := BigN.to_Z (BigZ.to_N zx)).
- set (b := (BigN.to_Z dy)).
- assert (F: (0 < Zgcd a b)%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos a b)); auto.
-   intros HH3; case H2; rewrite spec_to_N; fold a.
-   rewrite (Zgcd_inv_0_l _ _ (sym_equal HH3)); try ring.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a; fold b; auto.
- intros H.
- generalize HH2; simpl wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_0; intros HH; case HH; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite H; auto with zarith.
- assert (F1:= Zgcd_is_gcd a b); inversion F1; auto.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_1; rewrite BigN.spec_gcd.
- intros HH1 H1 H2.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto.
- rewrite BigN.spec_1; rewrite BigN.spec_gcd.
- intros HH1 H1 H2.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; auto.
- rewrite BigZ.spec_0.
- intros HH2.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- set (a := BigN.to_Z (BigZ.to_N zy)).
- set (b := (BigN.to_Z dx)).
- assert (F: (0 < Zgcd a b)%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos a b)); auto.
-   intros HH3; case HH2; rewrite spec_to_N; fold a.
-   rewrite (Zgcd_inv_0_l _ _ (sym_equal HH3)); try ring.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a; fold b; auto.
- intros H; unfold wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_0.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a; fold b; auto.
- intros HH; generalize H1; simpl wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- rewrite BigN.spec_0.
- intros HH3; case HH3; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite HH; auto with zarith.
- assert (F1:= Zgcd_is_gcd a b); inversion F1; auto.
- intros HH1 HH2; apply wf_norm.
- rewrite BigN.spec_mul; intros HH3.
- case (Zmult_integral _ _ HH3).
- generalize HH1; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- generalize HH2; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto.
- Qed.
-
- Theorem spec_mul_norm x y: wf x -> wf y ->
-  ([mul_norm x y] == [x] * [y])%Q.
- intros x y Hx Hy; rewrite <- spec_mul; auto.
- unfold mul_norm, mul; generalize Hx Hy; case x; case y; clear Hx Hy.
-  intros; apply Qeq_refl.
- intros p1 n p2 Hx Hy.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- rewrite BigZ.spec_mul; rewrite H; red; auto.
- assert (F: (0 < BigN.to_Z (BigZ.to_N p2))%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p2))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- assert (F1: (0 < BigN.to_Z n)%Z).
-  generalize Hy; simpl.
-  match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-    generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-  end; auto.
-  intros _ HH; case HH.
-  rewrite BigN.spec_0; generalize (BigN.spec_pos n); auto with zarith.
- set (a := BigN.to_Z (BigZ.to_N p2)).
- set (b := BigN.to_Z n).
- assert (F2: (0 < Zgcd a b )%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos a b)); intros H3; auto.
-   generalize F; fold a; rewrite (Zgcd_inv_0_l _ _ (sym_equal H3)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; try rewrite BigN.spec_gcd; 
-  fold a b; intros H1.
-  intros; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith; fold a b; intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N; fold a; fold b.
- rewrite Zmult_1_r; repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- intros H2; red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite Z2P_correct; auto with zarith.
- rewrite (spec_to_N p2); fold a b.
- rewrite Z2P_correct; auto with zarith.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p1)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto; try ring.
- case (Zle_lt_or_eq _ _
-       (BigN.spec_pos  (n / 
-                         BigN.gcd (BigZ.to_N p2) 
-                                  n))%bigN);
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- intros H3.
- apply False_ind; generalize F1.
- generalize Hy; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; auto with zarith.
- intros HH; case HH; fold b.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- rewrite <- H3; ring.
- assert (FF:= Zgcd_is_gcd a b); inversion FF; auto.
- intros p1 p2 n Hx Hy.
- match goal with  |- context[BigZ.eq_bool ?X ?Y] => 
-   generalize (BigZ.spec_eq_bool X Y); case BigZ.eq_bool
- end; unfold zero, to_Q; repeat rewrite BigZ.spec_0; intros H.
- rewrite BigZ.spec_mul; rewrite H; red; simpl; ring.
- set (a := BigN.to_Z (BigZ.to_N p1)).
- set (b := BigN.to_Z n).
- assert (F: (0 < a)%Z).
-  case (Zle_lt_or_eq _ _ (BigN.spec_pos (BigZ.to_N p1))); auto.
-  intros H1; case H; rewrite spec_to_N; rewrite <- H1; ring.
- assert (F1: (0 < b)%Z).
-  generalize Hx; unfold wf.
-  match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-    generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-  end; rewrite BigN.spec_0; auto with zarith.
-  generalize (BigN.spec_pos n); fold b; auto with zarith.
- assert (F2: (0 < Zgcd a b)%Z).
-   case (Zle_lt_or_eq _ _ (Zgcd_is_pos a b)); intros H3; auto.
-   generalize F; rewrite (Zgcd_inv_0_l _ _ (sym_equal H3)); auto with zarith.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1; rewrite BigN.spec_gcd; fold a b; intros H1.
-  intros; repeat rewrite BigZ.spec_mul; rewrite Zmult_comm; apply Qeq_refl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_1.
- rewrite BigN.spec_div; rewrite BigN.spec_gcd;
-   auto with zarith.
- fold a b; intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd;
-   fold a b; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite spec_to_N; fold a b.
- rewrite Zmult_1_r; repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto with zarith.
- rewrite H2; ring.
- intros H2.
- red; simpl.
- repeat rewrite BigZ.spec_mul.
- rewrite BigZ.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- rewrite Z2P_correct; auto with zarith.
- rewrite (spec_to_N p1); fold a b.
- case (Zle_lt_or_eq _ _
-       (BigN.spec_pos  (n / BigN.gcd (BigZ.to_N p1) n))%bigN); intros F3.
- rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_div; simpl; rewrite BigN.spec_gcd; 
-   fold a b; auto with zarith.
- repeat rewrite <- Zmult_assoc.
- rewrite (Zmult_comm (BigZ.to_Z p2)).
- repeat rewrite Zmult_assoc.
- rewrite Zgcd_div_swap; auto; try ring.
- apply False_ind; generalize F1.
- rewrite (Zdivide_Zdiv_eq (Zgcd a b) b); auto.
- generalize F3; rewrite BigN.spec_div; rewrite BigN.spec_gcd; fold a b;
-   auto with zarith.
- intros HH; rewrite <- HH; auto with zarith.
- assert (FF:= Zgcd_is_gcd a b); inversion FF; auto.
- intros p1 n1 p2 n2 Hn1 Hn2.
- match goal with |- [norm ?X ?Y] == _ =>
-  apply Qeq_trans with ([Qq X Y]);
-  [apply spec_norm | idtac]
- end; try  apply Qeq_refl.
- rewrite BigN.spec_mul.
- apply Zmult_lt_0_compat.
- generalize Hn1; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; auto with zarith.
- generalize (BigN.spec_pos n1) (BigN.spec_pos n2); auto with zarith.
- generalize Hn2; simpl.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; auto with zarith.
- generalize (BigN.spec_pos n1) (BigN.spec_pos n2); auto with zarith.
- Qed.
-
- Theorem spec_mul_normc x y: wf x -> wf y ->
-   [[mul_norm x y]] = [[x]] * [[y]].
- intros x y Hx Hy; unfold to_Qc.
- apply trans_equal with (!! ([x] * [y])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_mul_norm; auto.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
- Definition inv (x: t): t := 
-  match x with
-  | Qz (BigZ.Pos n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.one n
-  | Qz (BigZ.Neg n) => 
-    if BigN.eq_bool n BigN.zero then zero else Qq BigZ.minus_one n
-  | Qq (BigZ.Pos n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Pos d) n
-  | Qq (BigZ.Neg n) d => 
-    if BigN.eq_bool n BigN.zero then zero else Qq (BigZ.Neg d) n
-  end.
-
-
- Theorem wf_inv: forall x, wf x -> wf (inv x).
- intros [ zx | nx dx]; unfold inv, wf; auto.
- case zx; clear zx.
- intros nx.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_mul.
- intros nx.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0; rewrite BigN.spec_mul.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- intros _ HH; case HH.
- intros H1 _.
- case nx; clear nx.
- intros nx.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; simpl; auto.
- intros nx.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; simpl; auto.
- Qed.
-
- Theorem spec_inv x: wf x ->
-   ([inv x] == /[x])%Q.
- intros [ [x | x] _ | [nx | nx] dx]; unfold inv.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- unfold to_Q; rewrite BigZ.spec_1.
- red; unfold Qinv; simpl.
- generalize F; case BigN.to_Z; auto with zarith.
- intros p Hp; discriminate Hp.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z x)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos x)); auto with zarith.
- red; unfold Qinv; simpl.
- generalize F; case BigN.to_Z; simpl; auto with zarith.
- intros p Hp; discriminate Hp.
- simpl wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- intros HH; case HH.
- intros _.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z nx)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos nx)); auto with zarith.
- red; unfold Qinv; simpl.
- rewrite Z2P_correct; auto with zarith.
- generalize F; case BigN.to_Z; auto with zarith.
- intros p Hp; discriminate Hp.
- generalize (BigN.spec_pos dx); auto with zarith.
- simpl wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H1.
- intros HH; case HH.
- intros _.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; rewrite BigN.spec_0; intros H.
-  unfold zero, to_Q; rewrite BigZ.spec_0.
- unfold BigZ.to_Z; rewrite H; apply Qeq_refl.
- assert (F: (0 < BigN.to_Z nx)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos nx)); auto with zarith.
- red; unfold Qinv; simpl.
- rewrite Z2P_correct; auto with zarith.
- generalize F; case BigN.to_Z; auto with zarith.
- simpl; intros. 
- match goal with  |- (?X = Zneg ?Y)%Z => 
-   replace (Zneg Y) with (Zopp (Zpos Y));
-   try rewrite Z2P_correct; auto with zarith
- end.
- rewrite Zpos_mult_morphism; 
-   rewrite Z2P_correct; auto with zarith; try ring.
- generalize (BigN.spec_pos dx); auto with zarith.
- intros p Hp; discriminate Hp.
- generalize (BigN.spec_pos dx); auto with zarith.
- Qed.
-
- Theorem spec_invc x: wf x ->
-   [[inv x]] =  /[[x]].
- intros x Hx; unfold to_Qc.
- apply trans_equal with (!! (/[x])).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_inv; auto.
- unfold Qcinv, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qinv_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
- Definition div x y := mul x (inv y).
-
- Theorem wf_div x y: wf x -> wf y -> wf (div x y).
- intros x y Hx Hy; unfold div; apply wf_mul; auto.
- apply wf_inv; auto.
- Qed.
-
- Theorem spec_div x y: wf x -> wf y ->
-  ([div x y] == [x] / [y])%Q.
- intros x y Hx Hy; unfold div; rewrite spec_mul; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- apply wf_inv; auto.
- Qed.
-
- Theorem spec_divc x y: wf x -> wf y ->
-   [[div x y]] = [[x]] / [[y]].
- intros x y Hx Hy; unfold div; rewrite spec_mulc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto. 
- apply wf_inv; auto.
- Qed.
-
- Definition div_norm x y := mul_norm x (inv y).
-
- Theorem wf_div_norm x y: wf x -> wf y -> wf (div_norm x y).
- intros x y Hx Hy; unfold div_norm; apply wf_mul_norm; auto.
- apply wf_inv; auto.
- Qed.
-
- Theorem spec_div_norm x y: wf x -> wf y ->
-  ([div_norm x y] == [x] / [y])%Q.
- intros x y Hx Hy; unfold div_norm; rewrite spec_mul_norm; auto.
- unfold Qdiv; apply Qmult_comp.
- apply Qeq_refl.
- apply spec_inv; auto.
- apply wf_inv; auto.
- Qed.
-
- Theorem spec_div_normc x y: wf x -> wf y ->
-   [[div_norm x y]] = [[x]] / [[y]].
- intros x y Hx Hy; unfold div_norm; rewrite spec_mul_normc; auto.
- unfold Qcdiv; apply f_equal2 with (f := Qcmult); auto.
- apply spec_invc; auto.
- apply wf_inv; auto.
- Qed.
-
- Definition square (x: t): t :=
-  match x with
-  | Qz zx => Qz (BigZ.square zx)
-  | Qq nx dx => Qq (BigZ.square nx) (BigN.square dx)
-  end.
-
- Theorem wf_square: forall x, wf x -> wf (square x).
- intros [ zx | nx dx]; unfold square, wf; auto.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- rewrite BigN.spec_square; intros H1 H2; case H2.
- case (Zmult_integral _ _ H1); auto.
- Qed.
-
- Theorem spec_square x: wf x -> ([square x] == [x] ^ 2)%Q.
- intros [ x | nx dx]; unfold square.
- intros _.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- unfold wf.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- intros _ HH; case HH.
- intros H1 _.
- red; simpl; rewrite BigZ.spec_square; auto with zarith.
- assert (F: (0 < BigN.to_Z dx)%Z).
-   case (Zle_lt_or_eq _ _ (BigN.spec_pos dx)); auto with zarith.
- assert (F1 : (0 < BigN.to_Z (BigN.square dx))%Z).
-   rewrite BigN.spec_square; apply Zmult_lt_0_compat;
-     auto with zarith.
- rewrite Zpos_mult_morphism.
- repeat rewrite Z2P_correct; auto with zarith.
- rewrite BigN.spec_square; auto with zarith.
- Qed.
-
- Theorem spec_squarec x: wf x -> [[square x]] =  [[x]]^2.
- intros x Hx; unfold to_Qc.
- apply trans_equal with (!! ([x]^2)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_square; auto.
- simpl Qcpower.
- replace (!! [x] * 1) with (!![x]); try ring.
- simpl.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-
- Definition power_pos (x: t) p: t :=
-  match x with
-  | Qz zx => Qz (BigZ.power_pos zx p)
-  | Qq nx dx => Qq (BigZ.power_pos nx p) (BigN.power_pos dx p)
-  end.
-
- Theorem wf_power_pos: forall x p, wf x -> wf (power_pos x p).
- intros [ zx | nx dx] p; unfold power_pos, wf; auto.
- repeat match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- rewrite BigN.spec_power_pos; simpl.
- intros H1 H2 _.
- case (Zle_lt_or_eq _ _ (BigN.spec_pos dx)); auto with zarith.
- intros H3; generalize (Zpower_pos_pos _ p H3); auto with zarith.
- Qed.
-
- Theorem spec_power_pos x p: wf x -> ([power_pos x p] == [x] ^ Zpos p)%Q.
- Proof.
- intros [x | nx dx] p; unfold power_pos.
-   intros _; unfold power_pos; red; simpl.
-   generalize (Qpower_decomp p (BigZ.to_Z x) 1).
-   unfold Qeq; simpl.
-   rewrite Zpower_pos_1_l; simpl Z2P.
-   rewrite Zmult_1_r.
-   intros H; rewrite H.
-   rewrite BigZ.spec_power_pos; simpl; ring.
- unfold wf.
- match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
- end; auto; rewrite BigN.spec_0.
- intros _ HH; case HH.
- intros H1 _.
- assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
- assert (F2: (0 < BigN.to_Z dx  ^ ' p)%Z).
-  unfold Zpower; apply Zpower_pos_pos; auto.
- unfold power_pos; red; simpl.
- rewrite Z2P_correct; rewrite BigN.spec_power_pos; auto.
- generalize (Qpower_decomp p (BigZ.to_Z nx) 
-               (Z2P (BigN.to_Z dx))).
- unfold Qeq; simpl.
- repeat rewrite Z2P_correct; auto.
- unfold Qeq; simpl; intros HH.
- rewrite HH.
- rewrite BigZ.spec_power_pos; simpl; ring.
- Qed.
-
- Theorem spec_power_posc x p: wf x ->
-   [[power_pos x p]] = [[x]] ^ nat_of_P p.
- intros x p Hx; unfold to_Qc.
- apply trans_equal with (!! ([x]^Zpos p)).
- unfold Q2Qc.
- apply Qc_decomp; intros _ _; unfold this.
- apply Qred_complete; apply spec_power_pos; auto.
- pattern p; apply Pind; clear p.
- simpl; ring.
- intros p Hrec.
- rewrite nat_of_P_succ_morphism; simpl Qcpower.
- rewrite <- Hrec.
- unfold Qcmult, Q2Qc.
- apply Qc_decomp; intros _ _;
- unfold this.
- apply Qred_complete.
- assert (F: [x] ^ ' Psucc p == [x] *   [x] ^ ' p).
-  simpl; generalize Hx; case x; simpl; clear x Hx Hrec.
-  intros x _; simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  intros nx dx.
-  match goal with  |- context[BigN.eq_bool ?X ?Y] => 
-   generalize (BigN.spec_eq_bool X Y); case BigN.eq_bool
-  end; auto; rewrite BigN.spec_0.
-  intros _ HH; case HH.
-  intros H1 _.
-  assert (F1: (0 < BigN.to_Z dx)%Z).
-     generalize (BigN.spec_pos dx); auto with zarith.
-  simpl; repeat rewrite Qpower_decomp; simpl.
-  red; simpl; repeat rewrite Zpower_pos_1_l; simpl Z2P.
-  rewrite Pplus_one_succ_l.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
-  repeat rewrite Zpos_mult_morphism.
-  repeat rewrite Z2P_correct; auto.
-  2: apply Zpower_pos_pos; auto.
-  2: apply Zpower_pos_pos; auto.
-  rewrite Zpower_pos_is_exp.
-  rewrite Zpower_pos_1_r; auto.
- rewrite F.
- apply Qmult_comp; apply Qeq_sym; apply Qred_correct.
- Qed.
-
-End Qv.
-
diff --git a/theories/Numbers/Rational/SpecViaQ/QSig.v b/theories/Numbers/Rational/SpecViaQ/QSig.v
index a488c7c6..be9b2d4e 100644
--- a/theories/Numbers/Rational/SpecViaQ/QSig.v
+++ b/theories/Numbers/Rational/SpecViaQ/QSig.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: QSig.v 11028 2008-06-01 17:34:19Z letouzey $ i*)
+(*i $Id: QSig.v 11207 2008-07-04 16:50:32Z letouzey $ i*)
 
 Require Import QArith Qpower.
 
@@ -40,14 +40,24 @@ Module Type QType.
 
  Parameter compare : t -> t -> comparison.
 
- Parameter spec_compare: forall x y, compare x y = ([x] ?= [y]).
+ Parameter spec_compare : forall x y, compare x y = ([x] ?= [y]).
 
  Definition lt n m := compare n m = Lt.
  Definition le n m := compare n m <> Gt.
  Definition min n m := match compare n m with Gt => m | _ => n end.
  Definition max n m := match compare n m with Lt => m | _ => n end.
 
- Parameter add  : t -> t -> t.
+ Parameter eq_bool : t -> t -> bool.
+ 
+ Parameter spec_eq_bool : forall x y, 
+  if eq_bool x y then [x]==[y] else ~([x]==[y]).
+
+ Parameter red : t -> t.
+ 
+ Parameter spec_red : forall x, [red x] == [x].
+ Parameter strong_spec_red : forall x, [red x] = Qred [x].
+
+ Parameter add : t -> t -> t.
 
  Parameter spec_add: forall x y, [add x y] == [x] + [y].
 
@@ -75,10 +85,13 @@ Module Type QType.
 
  Parameter spec_div: forall x y, [div x y] == [x] / [y].
 
- Parameter power_pos : t -> positive -> t.
+ Parameter power : t -> Z -> t.
 
- Parameter spec_power_pos: forall x n, [power_pos x n] == [x] ^ Zpos n.
+ Parameter spec_power: forall x z, [power x z] == [x] ^ z.
 
 End QType.
 
-(* TODO: add norm function and variants, add eq_bool, what about Qc ? *)
\ No newline at end of file
+(** NB: several of the above functions come with [..._norm] variants
+     that expect reduced arguments and return reduced results. *)
+
+(** TODO : also speak of specifications via Qcanon ... *)
diff --git a/theories/Program/Equality.v b/theories/Program/Equality.v
index d19f29c3..c776070a 100644
--- a/theories/Program/Equality.v
+++ b/theories/Program/Equality.v
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Equality.v 11023 2008-05-30 11:08:39Z msozeau $ i*)
+(*i $Id: Equality.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (** Tactics related to (dependent) equality and proof irrelevance. *)
 
@@ -82,7 +82,7 @@ Ltac simpl_uip :=
 
 (** Simplify equalities appearing in the context and goal. *)
 
-Ltac simpl_eq := simpl ; repeat (elim_eq_rect ; simpl) ; repeat (simpl_uip ; simpl).
+Ltac simpl_eq := simpl ; unfold eq_rec_r, eq_rec ; repeat (elim_eq_rect ; simpl) ; repeat (simpl_uip ; simpl).
 
 (** Try to abstract a proof of equality, if no proof of the same equality is present in the context. *)
 
@@ -235,30 +235,43 @@ Ltac simpl_depind := subst* ; autoinjections ; try discriminates ;
    and starts a dependent induction using this tactic. *)
 
 Ltac do_depind tac H :=
+  generalize_eqs_vars H ; tac H ; repeat progress simpl_depind.
+
+(** A variant where generalized variables should be given by the user. *)
+
+Ltac do_depind' tac H :=
   generalize_eqs H ; tac H ; repeat progress simpl_depind.
 
 (** Calls [destruct] on the generalized hypothesis, results should be similar to inversion. *)
 
 Tactic Notation "dependent" "destruction" ident(H) := 
-  do_depind ltac:(fun H => destruct H ; intros) H ; subst*.
+  do_depind ltac:(fun hyp => destruct hyp ; intros) H ; subst*.
 
 Tactic Notation "dependent" "destruction" ident(H) "using" constr(c) := 
-  do_depind ltac:(fun H => destruct H using c ; intros) H.
+  do_depind ltac:(fun hyp => destruct hyp using c ; intros) H.
+
+(** This tactic also generalizes the goal by the given variables before the induction. *)
+
+Tactic Notation "dependent" "destruction" ident(H) "generalizing" ne_hyp_list(l) := 
+  do_depind' ltac:(fun hyp => revert l ; destruct hyp ; intros) H.
+
+Tactic Notation "dependent" "destruction" ident(H) "generalizing" ne_hyp_list(l) "using" constr(c) := 
+  do_depind' ltac:(fun hyp => revert l ; destruct hyp using c ; intros) H.
 
 (** Then we have wrappers for usual calls to induction. One can customize the induction tactic by 
    writting another wrapper calling do_depind. *)
 
 Tactic Notation "dependent" "induction" ident(H) := 
-  do_depind ltac:(fun H => induction H ; intros) H.
+  do_depind ltac:(fun hyp => induction hyp ; intros) H.
 
 Tactic Notation "dependent" "induction" ident(H) "using" constr(c) := 
-  do_depind ltac:(fun H => induction H using c ; intros) H.
+  do_depind ltac:(fun hyp => induction hyp using c ; intros) H.
 
 (** This tactic also generalizes the goal by the given variables before the induction. *)
 
 Tactic Notation "dependent" "induction" ident(H) "generalizing" ne_hyp_list(l) := 
-  do_depind ltac:(fun H => generalize l ; clear l ; induction H ; intros) H.
+  do_depind' ltac:(fun hyp => generalize l ; clear l ; induction hyp ; intros) H.
 
 Tactic Notation "dependent" "induction" ident(H) "generalizing" ne_hyp_list(l) "using" constr(c) := 
-  do_depind ltac:(fun H => generalize l ; clear l ; induction H using c ; intros) H.
+  do_depind' ltac:(fun hyp => generalize l ; clear l ; induction hyp using c ; intros) H.
 
diff --git a/theories/Program/Tactics.v b/theories/Program/Tactics.v
index 41b170c9..bb5054b4 100644
--- a/theories/Program/Tactics.v
+++ b/theories/Program/Tactics.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Tactics.v 11122 2008-06-13 14:18:44Z msozeau $ i*)
+(*i $Id: Tactics.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (** This module implements various tactics used to simplify the goals produced by Program,
    which are also generally useful. *)
@@ -77,10 +77,10 @@ Ltac clear_dup :=
   match goal with 
     | [ H : ?X |- _ ] => 
       match goal with
-        | [ H' : X |- _ ] =>
-          match H' with
-            | H => fail 2 
-            | _ => clear H' || clear H
+        | [ H' : ?Y |- _ ] =>
+          match H with
+            | H' => fail 2
+            | _ => conv X Y ; (clear H' || clear H)
           end
       end
   end.
@@ -158,14 +158,6 @@ Ltac autoinjection :=
   let tac H := progress (inversion H ; subst ; clear_dups) ; clear H in
     match goal with
       | [ H : ?f ?a = ?f' ?a' |- _ ] => tac H
-      | [ H : ?f ?a ?b = ?f' ?a' ?b'  |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c = ?f' ?a' ?b' ?c' |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d= ?f' ?a' ?b' ?c' ?d' |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d ?e= ?f' ?a' ?b' ?c' ?d' ?e' |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d ?e ?g= ?f' ?a' ?b' ?c' ?d' ?e' ?g'  |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d ?e ?g ?h= ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d ?e ?g ?h ?i = ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' ?i' |- _ ] => tac H
-      | [ H : ?f ?a ?b ?c ?d ?e ?g ?h ?i ?j = ?f' ?a' ?b' ?c' ?d' ?e'?g' ?h' ?i' ?j' |- _ ] => tac H
     end.
 
 Ltac autoinjections := repeat autoinjection.
@@ -222,7 +214,7 @@ Ltac refine_hyp c :=
     end.
 
 (** The default simplification tactic used by Program is defined by [program_simpl], sometimes [auto]
-   is not enough, better rebind using [Obligations Tactic := tac] in this case, 
+   is not enough, better rebind using [Obligation Tactic := tac] in this case, 
    possibly using [program_simplify] to use standard goal-cleaning tactics. *)
 
 Ltac program_simplify :=
@@ -231,4 +223,4 @@ Ltac program_simplify :=
 
 Ltac program_simpl := program_simplify ; auto.
 
-Ltac obligations_tactic := program_simpl.
+Ltac obligation_tactic := program_simpl.
diff --git a/theories/Program/Utils.v b/theories/Program/Utils.v
index 21eee0ca..fcd85f41 100644
--- a/theories/Program/Utils.v
+++ b/theories/Program/Utils.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Utils.v 10919 2008-05-11 22:04:26Z msozeau $ i*)
+(*i $Id: Utils.v 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 Require Export Coq.Program.Tactics.
 
@@ -42,8 +42,8 @@ Notation dec := sumbool_of_bool.
 
 (** Hide proofs and generates obligations when put in a term. *)
 
-Notation "'in_left'" := (@left _ _ _) : program_scope.
-Notation "'in_right'" := (@right _ _ _) : program_scope.
+Notation in_left := (@left _ _ _).
+Notation in_right := (@right _ _ _).
 
 (** Extraction directives *)
 (*
diff --git a/theories/QArith/QArith_base.v b/theories/QArith/QArith_base.v
index 304fbf77..78cf2892 100644
--- a/theories/QArith/QArith_base.v
+++ b/theories/QArith/QArith_base.v
@@ -6,11 +6,11 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: QArith_base.v 10765 2008-04-08 16:15:23Z msozeau $ i*)
+(*i $Id: QArith_base.v 11301 2008-08-04 19:41:18Z herbelin $ i*)
 
 Require Export ZArith.
 Require Export ZArithRing.
-Require Export Setoid.
+Require Export Setoid Bool.
 
 (** * Definition of [Q] and basic properties *)
 
@@ -28,24 +28,24 @@ Ltac simpl_mult := repeat rewrite Zpos_mult_morphism.
 
 Notation "a # b" := (Qmake a b) (at level 55, no associativity) : Q_scope.
 
-Definition inject_Z (x : Z) := Qmake x 1. 
+Definition inject_Z (x : Z) := Qmake x 1.
 Arguments Scope inject_Z [Z_scope].
 
-Notation " 'QDen'  p " := (Zpos (Qden p)) (at level 20, no associativity) : Q_scope.
+Notation QDen p := (Zpos (Qden p)).
 Notation " 0 " := (0#1) : Q_scope.
 Notation " 1 " := (1#1) : Q_scope.
 
 Definition Qeq (p q : Q) := (Qnum p * QDen q)%Z = (Qnum q * QDen p)%Z.
 Definition Qle (x y : Q) := (Qnum x * QDen y <= Qnum y * QDen x)%Z.
 Definition Qlt (x y : Q) := (Qnum x * QDen y < Qnum y * QDen x)%Z.
-Notation Qgt := (fun a b : Q => Qlt b a).
-Notation Qge := (fun a b : Q => Qle b a).
+Notation Qgt a b := (Qlt b a) (only parsing).
+Notation Qge a b := (Qle b a) (only parsing).
 
-Infix "==" := Qeq (at level 70, no associativity) : Q_scope. 
+Infix "==" := Qeq (at level 70, no associativity) : Q_scope.
 Infix "<" := Qlt : Q_scope.
-Infix ">" := Qgt : Q_scope.
 Infix "<=" := Qle : Q_scope.
-Infix ">=" := Qge : Q_scope.
+Notation "x > y" := (Qlt y x)(only parsing) : Q_scope.
+Notation "x >= y" := (Qle y x)(only parsing) : Q_scope.
 Notation "x <= y <= z" := (x<=y/\y<=z) : Q_scope.
 
 (** Another approach : using Qcompare for defining order relations. *)
@@ -84,7 +84,7 @@ rewrite Zcompare_Gt_Lt_antisym; auto.
 rewrite Zcompare_Gt_Lt_antisym in H; auto.
 Qed.
 
-Hint Unfold Qeq Qlt Qle: qarith.
+Hint Unfold Qeq Qlt Qle : qarith.
 Hint Extern 5 (?X1 <> ?X2) => intro; discriminate: qarith.
 
 (** * Properties of equality. *)
@@ -94,7 +94,7 @@ Proof.
  auto with qarith.
 Qed.
 
-Theorem Qeq_sym : forall x y, x == y -> y == x. 
+Theorem Qeq_sym : forall x y, x == y -> y == x.
 Proof.
  auto with qarith.
 Qed.
@@ -102,7 +102,7 @@ Qed.
 Theorem Qeq_trans : forall x y z, x == y -> y == z -> x == z.
 Proof.
 unfold Qeq in |- *; intros.
-apply Zmult_reg_l with (QDen y). 
+apply Zmult_reg_l with (QDen y).
 auto with qarith.
 transitivity (Qnum x * QDen y * QDen z)%Z; try ring.
 rewrite H.
@@ -117,6 +117,44 @@ Proof.
  intros; case (Z_eq_dec (Qnum x * QDen y) (Qnum y * QDen x)); auto.
 Defined.
 
+Definition Qeq_bool x y :=
+  (Zeq_bool (Qnum x * QDen y) (Qnum y * QDen x))%Z.
+
+Definition Qle_bool x y := 
+  (Zle_bool (Qnum x * QDen y) (Qnum y * QDen x))%Z.
+
+Lemma Qeq_bool_iff : forall x y, Qeq_bool x y = true <-> x == y.
+Proof.
+  unfold Qeq_bool, Qeq; intros. 
+  symmetry; apply Zeq_is_eq_bool.
+Qed.
+
+Lemma Qeq_bool_eq : forall x y, Qeq_bool x y = true -> x == y.
+Proof.
+  intros; rewrite <- Qeq_bool_iff; auto.
+Qed.
+
+Lemma Qeq_eq_bool : forall x y, x == y -> Qeq_bool x y = true.
+Proof.
+  intros; rewrite Qeq_bool_iff; auto.
+Qed.
+
+Lemma Qeq_bool_neq : forall x y, Qeq_bool x y = false -> ~ x == y.
+Proof.
+  intros x y H; rewrite <- Qeq_bool_iff, H; discriminate.
+Qed.
+
+Lemma Qle_bool_iff : forall x y, Qle_bool x y = true <-> x <= y.
+Proof.
+  unfold Qle_bool, Qle; intros.
+  symmetry; apply Zle_is_le_bool.
+Qed.
+
+Lemma Qle_bool_imp_le : forall x y, Qle_bool x y = true -> x <= y.
+Proof.
+  intros; rewrite <- Qle_bool_iff; auto.
+Qed.
+
 (** We now consider [Q] seen as a setoid. *)
 
 Definition Q_Setoid : Setoid_Theory Q Qeq.
@@ -130,7 +168,7 @@ Hint Resolve (Seq_refl Q Qeq Q_Setoid): qarith.
 Hint Resolve (Seq_sym Q Qeq Q_Setoid): qarith.
 Hint Resolve (Seq_trans Q Qeq Q_Setoid): qarith.
 
-Theorem Qnot_eq_sym : forall x y, ~x == y -> ~y == x. 
+Theorem Qnot_eq_sym : forall x y, ~x == y -> ~y == x.
 Proof.
  auto with qarith.
 Qed.
@@ -139,13 +177,13 @@ Hint Resolve Qnot_eq_sym : qarith.
 
 (** * Addition, multiplication and opposite *)
 
-(** The addition, multiplication and opposite are defined 
+(** The addition, multiplication and opposite are defined
    in the straightforward way: *)
 
 Definition Qplus (x y : Q) :=
   (Qnum x * QDen y + Qnum y * QDen x) # (Qden x * Qden y).
 
-Definition Qmult (x y : Q) := (Qnum x * Qnum y) # (Qden x * Qden y). 
+Definition Qmult (x y : Q) := (Qnum x * Qnum y) # (Qden x * Qden y).
 
 Definition Qopp (x : Q) := (- Qnum x) # (Qden x).
 
@@ -164,8 +202,8 @@ Infix "+" := Qplus : Q_scope.
 Notation "- x" := (Qopp x) : Q_scope.
 Infix "-" := Qminus : Q_scope.
 Infix "*" := Qmult : Q_scope.
-Notation "/ x" := (Qinv x) : Q_scope. 
-Infix "/" := Qdiv : Q_scope. 
+Notation "/ x" := (Qinv x) : Q_scope.
+Infix "/" := Qdiv : Q_scope.
 
 (** A light notation for [Zpos] *)
 
@@ -181,7 +219,7 @@ Qed.
 
 (** * Setoid compatibility results *)
 
-Add Morphism Qplus : Qplus_comp. 
+Add Morphism Qplus : Qplus_comp.
 Proof.
   unfold Qeq, Qplus; simpl.
   Open Scope Z_scope.
@@ -208,7 +246,7 @@ Qed.
 Add Morphism Qminus : Qminus_comp.
 Proof.
   intros.
-  unfold Qminus. 
+  unfold Qminus.
   rewrite H; rewrite H0; auto with qarith.
 Qed.
 
@@ -232,11 +270,11 @@ Proof.
   Open Scope Z_scope.
   intros (p1, p2) (q1, q2); simpl.
   case p1; simpl.
-  intros. 
+  intros.
   assert (q1 = 0).
   elim (Zmult_integral q1 ('p2)); auto with zarith.
   intros; discriminate.
-  subst; auto. 
+  subst; auto.
   case q1; simpl; intros; try discriminate.
   rewrite (Pmult_comm p2 p); rewrite (Pmult_comm q2 p0); auto.
   case q1; simpl; intros; try discriminate.
@@ -254,7 +292,7 @@ Add Morphism Qle with signature Qeq ==> Qeq ==> iff as Qle_comp.
 Proof.
   cut (forall x1 x2, x1==x2 -> forall x3 x4, x3==x4 -> x1<=x3 -> x2<=x4).
   split; apply H; assumption || (apply Qeq_sym ; assumption).
-  
+
   unfold Qeq, Qle; simpl.
   Open Scope Z_scope.
   intros (p1, p2) (q1, q2) H (r1, r2) (s1, s2) H0 H1; simpl in *.
@@ -289,14 +327,26 @@ Proof.
   replace (s1 * 'q2 * 'p2 * 'r2) with (s1 * 'r2 * 'q2 * 'p2) by ring.
   rewrite <- H0.
   replace (p1 * 'q2 * 's2 * 'r2) with ('q2 * 's2 * (p1 * 'r2)) by ring.
-  replace (r1 * 's2 * 'q2 * 'p2) with ('q2 * 's2 * (r1 * 'p2)) by ring. 
+  replace (r1 * 's2 * 'q2 * 'p2) with ('q2 * 's2 * (r1 * 'p2)) by ring.
   apply Zlt_gt.
   apply Zmult_gt_0_lt_compat_l; auto with zarith.
   Close Scope Z_scope.
 Qed.
 
+Add Morphism Qeq_bool with signature Qeq ==> Qeq ==> (@eq bool) as Qeqb_comp.
+Proof.
+ intros; apply eq_true_iff_eq.
+ rewrite 2 Qeq_bool_iff, H, H0; split; auto with qarith.
+Qed.
+
+Add Morphism Qle_bool with signature Qeq ==> Qeq ==> (@eq bool) as Qleb_comp.
+Proof.
+ intros; apply eq_true_iff_eq.
+ rewrite 2 Qle_bool_iff, H, H0.
+ split; auto with qarith.
+Qed.
 
-Lemma Qcompare_egal_dec: forall n m p q : Q, 
+Lemma Qcompare_egal_dec: forall n m p q : Q,
   (n<m -> p<q) -> (n==m -> p==q) -> (n>m -> p>q) -> ((n?=m) = (p?=q)).
 Proof.
   intros.
@@ -306,7 +356,6 @@ Proof.
   omega.
 Qed.
 
-
 Add Morphism Qcompare : Qcompare_comp.
 Proof.
   intros; apply Qcompare_egal_dec; rewrite H; rewrite H0; auto.
@@ -341,7 +390,7 @@ Lemma Qplus_0_r : forall x, x+0 == x.
 Proof.
   intros (x1, x2); unfold Qeq, Qplus; simpl.
   rewrite Pmult_comm; simpl; ring.
-Qed. 
+Qed.
 
 (** Commutativity of addition: *)
 
@@ -374,6 +423,18 @@ Proof.
   intros; red; simpl; rewrite Pmult_assoc; ring.
 Qed.
 
+(** multiplication and zero *)
+
+Lemma Qmult_0_l : forall x , 0*x == 0.
+Proof.
+  intros; compute; reflexivity.
+Qed.
+
+Lemma Qmult_0_r : forall x , x*0 == 0.
+Proof.
+  intros; red; simpl; ring.
+Qed.
+
 (** [1] is a neutral element for multiplication: *)
 
 Lemma Qmult_1_l : forall n, 1*n == n.
@@ -385,7 +446,7 @@ Theorem Qmult_1_r : forall n, n*1==n.
 Proof.
   intro; red; simpl.
   rewrite Zmult_1_r with (n := Qnum n).
-  rewrite Pmult_comm; simpl; trivial. 
+  rewrite Pmult_comm; simpl; trivial.
 Qed.
 
 (** Commutativity of multiplication *)
@@ -427,7 +488,7 @@ Proof.
   rewrite <- H0; ring.
 Qed.
 
-(** * Inverse and division. *) 
+(** * Inverse and division. *)
 
 Lemma Qinv_involutive : forall q, (/ / q) == q.
 Proof.
@@ -438,13 +499,13 @@ Theorem Qmult_inv_r : forall x, ~ x == 0 -> x*(/x) == 1.
 Proof.
   intros (x1, x2); unfold Qeq, Qdiv, Qmult; case x1; simpl;
     intros; simpl_mult; try ring.
-  elim H; auto. 
+  elim H; auto.
 Qed.
 
 Lemma Qinv_mult_distr : forall p q, / (p * q) == /p * /q.
 Proof.
   intros (x1,x2) (y1,y2); unfold Qeq, Qinv, Qmult; simpl.
-  destruct x1; simpl; auto; 
+  destruct x1; simpl; auto;
     destruct y1; simpl; auto.
 Qed.
 
@@ -485,10 +546,10 @@ Proof.
   red; trivial.
   apply Zle_trans with (y1 * 'x2 * 'z2).
   replace (x1 * 'z2 * 'y2) with (x1 * 'y2 * 'z2) by ring.
-  apply Zmult_le_compat_r; auto with zarith. 
+  apply Zmult_le_compat_r; auto with zarith.
   replace (y1 * 'x2 * 'z2) with (y1 * 'z2 * 'x2) by ring.
   replace (z1 * 'x2 * 'y2) with (z1 * 'y2 * 'x2) by ring.
-  apply Zmult_le_compat_r; auto with zarith. 
+  apply Zmult_le_compat_r; auto with zarith.
   Close Scope Z_scope.
 Qed.
 
@@ -516,9 +577,9 @@ Proof.
   apply Zgt_le_trans with (y1 * 'x2 * 'z2).
   replace (y1 * 'x2 * 'z2) with (y1 * 'z2 * 'x2) by ring.
   replace (z1 * 'x2 * 'y2) with (z1 * 'y2 * 'x2) by ring.
-  apply Zmult_gt_compat_r; auto with zarith. 
+  apply Zmult_gt_compat_r; auto with zarith.
   replace (x1 * 'z2 * 'y2) with (x1 * 'y2 * 'z2) by ring.
-  apply Zmult_le_compat_r; auto with zarith. 
+  apply Zmult_le_compat_r; auto with zarith.
   Close Scope Z_scope.
 Qed.
 
@@ -532,9 +593,9 @@ Proof.
   apply Zle_gt_trans with (y1 * 'x2 * 'z2).
   replace (y1 * 'x2 * 'z2) with (y1 * 'z2 * 'x2) by ring.
   replace (z1 * 'x2 * 'y2) with (z1 * 'y2 * 'x2) by ring.
-  apply Zmult_le_compat_r; auto with zarith. 
+  apply Zmult_le_compat_r; auto with zarith.
   replace (x1 * 'z2 * 'y2) with (x1 * 'y2 * 'z2) by ring.
-  apply Zmult_gt_compat_r; auto with zarith. 
+  apply Zmult_gt_compat_r; auto with zarith.
   Close Scope Z_scope.
 Qed.
 
@@ -572,7 +633,7 @@ Proof.
   unfold Qle, Qlt, Qeq; intros; apply Zle_lt_or_eq; auto.
 Qed.
 
-Hint Resolve Qle_not_lt Qlt_not_le Qnot_le_lt Qnot_lt_le 
+Hint Resolve Qle_not_lt Qlt_not_le Qnot_le_lt Qnot_lt_le
  Qlt_le_weak Qlt_not_eq Qle_antisym Qle_refl: qartih.
 
 (** Some decidability results about orders. *)
@@ -679,7 +740,7 @@ Proof.
 intros [[|n|n] d] Ha; assumption.
 Qed.
 
-Lemma Qle_shift_div_l : forall a b c, 
+Lemma Qle_shift_div_l : forall a b c,
  0 < c -> a*c <= b -> a <= b/c.
 Proof.
 intros a b c Hc H.
@@ -690,7 +751,7 @@ rewrite Qmult_div_r; try assumption.
 auto with *.
 Qed.
 
-Lemma Qle_shift_inv_l : forall a c, 
+Lemma Qle_shift_inv_l : forall a c,
  0 < c -> a*c <= 1 -> a <= /c.
 Proof.
 intros a c Hc H.
@@ -699,7 +760,7 @@ change (a <= 1/c).
 apply Qle_shift_div_l; assumption.
 Qed.
 
-Lemma Qle_shift_div_r : forall a b c, 
+Lemma Qle_shift_div_r : forall a b c,
  0 < b -> a <= c*b -> a/b <= c.
 Proof.
 intros a b c Hc H.
@@ -710,7 +771,7 @@ rewrite Qmult_div_r; try assumption.
 auto with *.
 Qed.
 
-Lemma Qle_shift_inv_r : forall b c, 
+Lemma Qle_shift_inv_r : forall b c,
  0 < b -> 1 <= c*b -> /b <= c.
 Proof.
 intros b c Hc H.
@@ -772,7 +833,7 @@ Qed.
 
 (** * Rational to the n-th power *)
 
-Definition Qpower_positive (q:Q)(p:positive) : Q := 
+Definition Qpower_positive (q:Q)(p:positive) : Q :=
  pow_pos Qmult q p.
 
 Add Morphism Qpower_positive with signature Qeq ==> @eq _ ==> Qeq as Qpower_positive_comp.
diff --git a/theories/QArith/Qfield.v b/theories/QArith/Qfield.v
index 5d548aea..9841ef89 100644
--- a/theories/QArith/Qfield.v
+++ b/theories/QArith/Qfield.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Qfield.v 10739 2008-04-01 14:45:20Z herbelin $ i*)
+(*i $Id: Qfield.v 11208 2008-07-04 16:57:46Z letouzey $ i*)
 
 Require Export Field.
 Require Export QArith_base.
@@ -14,23 +14,8 @@ Require Import NArithRing.
 
 (** * field and ring tactics for rational numbers *)
 
-Definition Qeq_bool (x y : Q) :=
-  if Qeq_dec x y then true else false.
-
-Lemma Qeq_bool_correct : forall x y : Q, Qeq_bool x y = true -> x==y.
-Proof.
-  intros x y; unfold Qeq_bool in |- *; case (Qeq_dec x y); simpl in |- *; auto.
-  intros _ H; inversion H.
-Qed.
-
-Lemma Qeq_bool_complete : forall x y : Q, x==y -> Qeq_bool x y = true.
-Proof.
-  intros x y; unfold Qeq_bool in |- *; case (Qeq_dec x y); simpl in |- *; auto.
-Qed.
-
-Definition Qsft : field_theory 0 1 Qplus Qmult Qminus Qopp Qdiv Qinv Qeq.
+Definition Qsrt : ring_theory 0 1 Qplus Qmult Qminus Qopp Qeq.
 Proof.
-  constructor.
   constructor.
   exact Qplus_0_l.
   exact Qplus_comm.
@@ -41,6 +26,12 @@ Proof.
   exact Qmult_plus_distr_l.
   reflexivity.
   exact Qplus_opp_r.
+Qed.
+
+Definition Qsft : field_theory 0 1 Qplus Qmult Qminus Qopp Qdiv Qinv Qeq.
+Proof.
+  constructor.
+  exact Qsrt.
   discriminate.
   reflexivity.
   intros p Hp.
@@ -83,8 +74,8 @@ Ltac Qpow_tac t :=
   end.
 
 Add Field Qfield : Qsft 
- (decidable Qeq_bool_correct, 
-  completeness Qeq_bool_complete,
+ (decidable Qeq_bool_eq, 
+  completeness Qeq_eq_bool,
   constants [Qcst], 
   power_tac Qpower_theory [Qpow_tac]).
 
diff --git a/theories/Strings/String.v b/theories/Strings/String.v
index 53260480..00f28a9c 100644
--- a/theories/Strings/String.v
+++ b/theories/Strings/String.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: String.v 10855 2008-04-27 11:16:15Z msozeau $ *)
+(* $Id: String.v 11206 2008-07-04 16:21:28Z letouzey $ *)
 
 (** Contributed by Laurent Théry (INRIA);
     Adapted to Coq V8 by the Coq Development Team *)
@@ -225,7 +225,7 @@ Fixpoint index (n : nat) (s1 s2 : string) {struct s2} : option nat :=
       end
   end.
 
-(* Dirty trick to evaluate locally that prefix reduces itself *)
+(* Dirty trick to avoid locally that prefix reduces itself *)
 Opaque prefix.
 
 (** If the result of [index] is [Some m], [s1] in [s2] at position [m] *)
diff --git a/theories/ZArith/Zbool.v b/theories/ZArith/Zbool.v
index 34114d46..71befa4a 100644
--- a/theories/ZArith/Zbool.v
+++ b/theories/ZArith/Zbool.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: Zbool.v 10063 2007-08-08 14:21:03Z emakarov $ *)
+(* $Id: Zbool.v 11208 2008-07-04 16:57:46Z letouzey $ *)
 
 Require Import BinInt.
 Require Import Zeven.
@@ -16,7 +16,7 @@ Require Import ZArith_dec.
 Require Import Sumbool.
 
 Unset Boxed Definitions.
-
+Open Local Scope Z_scope.
 
 (** * Boolean operations from decidabilty of order *)
 (** The decidability of equality and order relations over
@@ -37,80 +37,82 @@ Definition Zeven_odd_bool (x:Z) := bool_of_sumbool (Zeven_odd_dec x).
 (** * Boolean comparisons of binary integers *)
 
 Definition Zle_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Gt => false
     | _ => true
   end.
 
 Definition Zge_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Lt => false
     | _ => true
   end.
 
 Definition Zlt_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Lt => true
     | _ => false
   end.
 
 Definition Zgt_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Gt => true
     | _ => false
   end.
 
 Definition Zeq_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Eq => true
     | _ => false
   end.
 
 Definition Zneq_bool (x y:Z) :=
-  match (x ?= y)%Z with
+  match x ?= y with
     | Eq => false
     | _ => true
   end.
 
+(** Properties in term of [if ... then ... else ...] *)
+
 Lemma Zle_cases :
-  forall n m:Z, if Zle_bool n m then (n <= m)%Z else (n > m)%Z.
+  forall n m:Z, if Zle_bool n m then (n <= m) else (n > m).
 Proof.
   intros x y; unfold Zle_bool, Zle, Zgt in |- *.
-  case (x ?= y)%Z; auto; discriminate.
+  case (x ?= y); auto; discriminate.
 Qed.
 
 Lemma Zlt_cases :
-  forall n m:Z, if Zlt_bool n m then (n < m)%Z else (n >= m)%Z.
+  forall n m:Z, if Zlt_bool n m then (n < m) else (n >= m).
 Proof.
   intros x y; unfold Zlt_bool, Zlt, Zge in |- *.
-  case (x ?= y)%Z; auto; discriminate.
+  case (x ?= y); auto; discriminate.
 Qed.
 
 Lemma Zge_cases :
-  forall n m:Z, if Zge_bool n m then (n >= m)%Z else (n < m)%Z.
+  forall n m:Z, if Zge_bool n m then (n >= m) else (n < m).
 Proof.
   intros x y; unfold Zge_bool, Zge, Zlt in |- *.
-  case (x ?= y)%Z; auto; discriminate.
+  case (x ?= y); auto; discriminate.
 Qed.
 
 Lemma Zgt_cases :
-  forall n m:Z, if Zgt_bool n m then (n > m)%Z else (n <= m)%Z.
+  forall n m:Z, if Zgt_bool n m then (n > m) else (n <= m).
 Proof.
   intros x y; unfold Zgt_bool, Zgt, Zle in |- *.
-  case (x ?= y)%Z; auto; discriminate.
+  case (x ?= y); auto; discriminate.
 Qed.
 
 (** Lemmas on [Zle_bool] used in contrib/graphs *)
 
-Lemma Zle_bool_imp_le : forall n m:Z, Zle_bool n m = true -> (n <= m)%Z.
+Lemma Zle_bool_imp_le : forall n m:Z, Zle_bool n m = true -> (n <= m).
 Proof.
   unfold Zle_bool, Zle in |- *. intros x y. unfold not in |- *.
-  case (x ?= y)%Z; intros; discriminate.
+  case (x ?= y); intros; discriminate.
 Qed.
 
-Lemma Zle_imp_le_bool : forall n m:Z, (n <= m)%Z -> Zle_bool n m = true.
+Lemma Zle_imp_le_bool : forall n m:Z, (n <= m) -> Zle_bool n m = true.
 Proof.
-  unfold Zle, Zle_bool in |- *. intros x y. case (x ?= y)%Z; trivial. intro. elim (H (refl_equal _)).
+  unfold Zle, Zle_bool in |- *. intros x y. case (x ?= y); trivial. intro. elim (H (refl_equal _)).
 Qed.
 
 Lemma Zle_bool_refl : forall n:Z, Zle_bool n n = true.
@@ -136,8 +138,8 @@ Qed.
 Definition Zle_bool_total :
   forall x y:Z, {Zle_bool x y = true} + {Zle_bool y x = true}.
 Proof.
-  intros x y; intros. unfold Zle_bool in |- *. cut ((x ?= y)%Z = Gt <-> (y ?= x)%Z = Lt).
-  case (x ?= y)%Z. left. reflexivity.
+  intros x y; intros. unfold Zle_bool in |- *. cut ((x ?= y) = Gt <-> (y ?= x) = Lt).
+  case (x ?= y). left. reflexivity.
   left. reflexivity.
   right. rewrite (proj1 H (refl_equal _)). reflexivity.
   apply Zcompare_Gt_Lt_antisym.
@@ -159,39 +161,40 @@ Qed.
 
 Lemma Zone_min_pos : forall n:Z, Zle_bool n 0 = false -> Zle_bool 1 n = true.
 Proof.
-  intros x; intros. apply Zle_imp_le_bool. change (Zsucc 0 <= x)%Z in |- *. apply Zgt_le_succ. generalize H.
-  unfold Zle_bool, Zgt in |- *. case (x ?= 0)%Z. intro H0. discriminate H0.
+  intros x; intros. apply Zle_imp_le_bool. change (Zsucc 0 <= x) in |- *. apply Zgt_le_succ. generalize H.
+  unfold Zle_bool, Zgt in |- *. case (x ?= 0). intro H0. discriminate H0.
   intro H0. discriminate H0.
   reflexivity.
 Qed.
 
+(** Properties in term of [iff] *)
 
-Lemma Zle_is_le_bool : forall n m:Z, (n <= m)%Z <-> Zle_bool n m = true.
+Lemma Zle_is_le_bool : forall n m:Z, (n <= m) <-> Zle_bool n m = true.
 Proof.
   intros. split. intro. apply Zle_imp_le_bool. assumption.
   intro. apply Zle_bool_imp_le. assumption.
 Qed.
 
-Lemma Zge_is_le_bool : forall n m:Z, (n >= m)%Z <-> Zle_bool m n = true.
+Lemma Zge_is_le_bool : forall n m:Z, (n >= m) <-> Zle_bool m n = true.
 Proof.
   intros. split. intro. apply Zle_imp_le_bool. apply Zge_le. assumption.
   intro. apply Zle_ge. apply Zle_bool_imp_le. assumption.
 Qed.
 
-Lemma Zlt_is_lt_bool : forall n m:Z, (n < m)%Z <-> Zlt_bool n m = true.
+Lemma Zlt_is_lt_bool : forall n m:Z, (n < m) <-> Zlt_bool n m = true.
 Proof.
 intros n m; unfold Zlt_bool, Zlt.
-destruct (n ?= m)%Z; simpl; split; now intro.
+destruct (n ?= m); simpl; split; now intro.
 Qed.
 
-Lemma Zgt_is_gt_bool : forall n m:Z, (n > m)%Z <-> Zgt_bool n m = true.
+Lemma Zgt_is_gt_bool : forall n m:Z, (n > m) <-> Zgt_bool n m = true.
 Proof.
 intros n m; unfold Zgt_bool, Zgt.
-destruct (n ?= m)%Z; simpl; split; now intro.
+destruct (n ?= m); simpl; split; now intro.
 Qed.
 
 Lemma Zlt_is_le_bool :
-  forall n m:Z, (n < m)%Z <-> Zle_bool n (m - 1) = true.
+  forall n m:Z, (n < m) <-> Zle_bool n (m - 1) = true.
 Proof.
   intros x y. split. intro. apply Zle_imp_le_bool. apply Zlt_succ_le. rewrite (Zsucc_pred y) in H.
   assumption.
@@ -199,9 +202,29 @@ Proof.
 Qed.
 
 Lemma Zgt_is_le_bool :
-  forall n m:Z, (n > m)%Z <-> Zle_bool m (n - 1) = true.
+  forall n m:Z, (n > m) <-> Zle_bool m (n - 1) = true.
 Proof.
-  intros x y. apply iff_trans with (y < x)%Z. split. exact (Zgt_lt x y).
+  intros x y. apply iff_trans with (y < x). split. exact (Zgt_lt x y).
   exact (Zlt_gt y x).
   exact (Zlt_is_le_bool y x).
 Qed.
+
+Lemma Zeq_is_eq_bool : forall x y, x = y <-> Zeq_bool x y = true.
+Proof.
+  intros; unfold Zeq_bool.
+  generalize (Zcompare_Eq_iff_eq x y); destruct Zcompare; intuition;
+   try discriminate.
+Qed.
+
+Lemma Zeq_bool_eq : forall x y, Zeq_bool x y = true -> x = y.
+Proof.
+  intros x y H; apply <- Zeq_is_eq_bool; auto.
+Qed.
+
+Lemma Zeq_bool_neq : forall x y, Zeq_bool x y = false -> x <> y.
+Proof.
+  unfold Zeq_bool; red ; intros; subst.
+  rewrite Zcompare_refl in H.
+  discriminate.
+Qed.
+
diff --git a/theories/ZArith/Zcompare.v b/theories/ZArith/Zcompare.v
index 6c5b07d2..8244d4ce 100644
--- a/theories/ZArith/Zcompare.v
+++ b/theories/ZArith/Zcompare.v
@@ -40,6 +40,15 @@ Proof.
 	    | destruct ((x' ?= y')%positive Eq); reflexivity || discriminate ] ].
 Qed.
 
+Ltac destr_zcompare := 
+ match goal with |- context [Zcompare ?x ?y] => 
+  let H := fresh "H" in 
+  case_eq (Zcompare x y); intro H;
+   [generalize (Zcompare_Eq_eq _ _ H); clear H; intro H |
+    change (x<y)%Z in H | 
+    change (x>y)%Z in H ]
+ end.
+
 Lemma Zcompare_Eq_iff_eq : forall n m:Z, (n ?= m) = Eq <-> n = m.
 Proof.
   intros x y; split; intro E;
diff --git a/theories/ZArith/Znumtheory.v b/theories/ZArith/Znumtheory.v
index e77475e0..9be372a3 100644
--- a/theories/ZArith/Znumtheory.v
+++ b/theories/ZArith/Znumtheory.v
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: Znumtheory.v 10295 2007-11-06 22:46:21Z letouzey $ i*)
+(*i $Id: Znumtheory.v 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 Require Import ZArith_base.
 Require Import ZArithRing.
@@ -522,7 +522,7 @@ Lemma Zis_gcd_mult :
   forall a b c d:Z, Zis_gcd a b d -> Zis_gcd (c * a) (c * b) (c * d).
 Proof.
   intros a b c d; simple induction 1; constructor; intuition.
-  elim (Zis_gcd_bezout a b d H); intros.
+  elim (Zis_gcd_bezout a b d H). intros.
   elim H3; intros.
   elim H4; intros.
   apply Zdivide_intro with (u * q + v * q0).
diff --git a/tools/coq_makefile.ml4 b/tools/coq_makefile.ml4
index 77dbcc47..d1d0d854 100644
--- a/tools/coq_makefile.ml4
+++ b/tools/coq_makefile.ml4
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coq_makefile.ml4 11136 2008-06-18 10:41:34Z herbelin $ *)
+(* $Id: coq_makefile.ml4 11255 2008-07-24 16:57:13Z notin $ *)
 
 (* créer un Makefile pour un développement Coq automatiquement *)
 
@@ -156,7 +156,6 @@ let variables l =
     | _ :: r -> var_aux r
   in
     section "Variables definitions.";
-    print "CAMLP4LIB:=$(shell $(CAMLBIN)camlp5 -where 2> /dev/null || $(CAMLBIN)camlp4 -where)\n";
     print "CAMLP4:=$(notdir $(CAMLP4LIB))\n"; 
     if Coq_config.local then
       (print "COQSRC:=$(COQTOP)\n";
@@ -175,7 +174,7 @@ let variables l =
   -I $(COQTOP)/contrib/subtac -I $(COQTOP)/contrib/xml \\
   -I $(CAMLP4LIB)\n")
     else
-      (print "COQSRC:=$(shell $(COQTOP)coqc -where)\n"; 
+      (print "COQSRC:=$(shell $(COQBIN)coqc -where)\n"; 
        print "COQSRCLIBS:=-I $(COQSRC)\n");
     print "ZFLAGS:=$(OCAMLLIBS) $(COQSRCLIBS)\n";
     if !opt = "-byte" then 
@@ -255,7 +254,8 @@ let include_dirs l =
   let str_i' = parse_includes inc_i' in
   let str_r = parse_includes inc_r in
     section "Libraries definition.";
-    print "OCAMLLIBS:="; print_list "\\\n  " str_i; print "\n";
+    print "CAMLP4LIB:=$(shell $(CAMLBIN)camlp5 -where 2> /dev/null || $(CAMLBIN)camlp4 -where)\n";
+    print "OCAMLLIBS:=-I $(CAMLP4LIB) "; print_list "\\\n  " str_i; print "\n";
     print "COQLIBS:="; print_list "\\\n  " str_i'; print " "; print_list "\\\n  " str_r; print "\n";
     print "COQDOCLIBS:=";   print_list "\\\n  " str_r; print "\n\n"
 
diff --git a/tools/coqdep.ml b/tools/coqdep.ml
index dc80476b..b4b161f5 100644
--- a/tools/coqdep.ml
+++ b/tools/coqdep.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coqdep.ml 10746 2008-04-03 15:45:25Z notin $ *)
+(* $Id: coqdep.ml 11282 2008-07-28 11:51:53Z msozeau $ *)
 
 open Printf
 open Coqdep_lexer
@@ -442,8 +442,8 @@ let rec add_directory recur add_file phys_dir log_dir =
   try
     while true do
       let f = readdir dirh in
-      (* we avoid . .. and all hidden files and subdirs (e.g. .svn) *)
-      if f.[0] <> '.' then
+      (* we avoid . .. and all hidden files and subdirs (e.g. .svn, _darcs) *)
+      if f.[0] <> '.' && f.[0] <> '_' then
         let phys_f = phys_dir//f in
 	match try (stat phys_f).st_kind with _ -> S_BLK with
 	  | S_DIR when recur -> add_directory recur add_file phys_f (log_dir@[f])
diff --git a/tools/coqdoc/cdglobals.ml b/tools/coqdoc/cdglobals.ml
index 44b9bd3c..3339b1db 100644
--- a/tools/coqdoc/cdglobals.ml
+++ b/tools/coqdoc/cdglobals.ml
@@ -32,6 +32,13 @@ let open_out_file f =
 let close_out_file () = close_out !out_channel
 
 
+type glob_source_t =
+    | NoGlob
+    | DotGlob
+    | GlobFile of string
+
+let glob_source = ref DotGlob 
+
 let header_trailer = ref true
 let header_file = ref ""
 let header_file_spec = ref false
diff --git a/tools/coqdoc/main.ml b/tools/coqdoc/main.ml
index 7111187f..81560259 100644
--- a/tools/coqdoc/main.ml
+++ b/tools/coqdoc/main.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: main.ml 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: main.ml 11236 2008-07-18 15:58:12Z notin $ i*)
 
 (* Modified by Lionel Elie Mamane <lionel@mamane.lu> on 9 & 10 Mar 2004:
  *  - handling of absolute filenames (function coq_module)
@@ -50,6 +50,7 @@ let usage () =
   prerr_endline "  --tex <file>         consider <file> as a .tex file";
   prerr_endline "  -p <string>          insert <string> in LaTeX preamble";
   prerr_endline "  --files-from <file>  read file names to process in <file>";
+  prerr_endline "  --glob-from <file>   read globalization information from <file>";
   prerr_endline "  --quiet              quiet mode (default)";
   prerr_endline "  --verbose            verbose mode";  
   prerr_endline "  --no-externals       no links to Coq standard library";
@@ -300,7 +301,7 @@ let parse () =
     | "-R" :: ([] | [_]) ->
 	usage ()
     | ("-glob-from" | "--glob-from") :: f :: rem ->
-	obsolete "glob-from"; parse_rec rem
+	glob_source := GlobFile f; parse_rec rem
     | ("-glob-from" | "--glob-from") :: [] ->
 	usage ()
     | ("--no-externals" | "-no-externals" | "-noexternals") :: rem ->
@@ -436,7 +437,10 @@ let produce_document l =
 	  Filename.concat !output_dir "coqdoc.sty" 
 	else "coqdoc.sty" in
 	copy src dst);
-  let l = List.map read_glob l in
+  (match !Cdglobals.glob_source with
+    | NoGlob -> ()
+    | DotGlob -> ignore (List.map read_glob l)
+    | GlobFile f -> ignore (Index.read_glob f));
   List.iter index_module l;
   match !out_to with
     | StdOut -> 
diff --git a/tools/coqdoc/pretty.mll b/tools/coqdoc/pretty.mll
index 8be3e0b0..baace5ba 100644
--- a/tools/coqdoc/pretty.mll
+++ b/tools/coqdoc/pretty.mll
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: pretty.mll 11154 2008-06-19 18:42:19Z msozeau $ i*)
+(*i $Id: pretty.mll 11255 2008-07-24 16:57:13Z notin $ i*)
 
 (*s Utility functions for the scanners *)
 
@@ -56,6 +56,7 @@
 
   let formatted = ref false
   let brackets = ref 0
+  let comment_level = ref 0
 
   let backtrack lexbuf = lexbuf.lex_curr_pos <- lexbuf.lex_start_pos
 
@@ -93,7 +94,8 @@
 
   let reset () =
     formatted := false;
-    brackets := 0
+    brackets := 0;
+    comment_level := 0
 
   (* erasing of Section/End *)
 
@@ -385,6 +387,7 @@ rule coq_bol = parse
   | space* "(**" space+ "printing" space+
       { eprintf "warning: bad 'printing' command at character %d\n" 
 	  (lexeme_start lexbuf); flush stderr;
+	comment_level := 1;
 	ignore (comment lexbuf);
 	coq_bol lexbuf }
   | space* "(**" space+ "remove" space+ "printing" space+ 
@@ -394,10 +397,12 @@ rule coq_bol = parse
   | space* "(**" space+ "remove" space+ "printing" space+
       { eprintf "warning: bad 'remove printing' command at character %d\n" 
 	  (lexeme_start lexbuf); flush stderr;
+	comment_level := 1;
 	ignore (comment lexbuf);
 	coq_bol lexbuf }
   | space* "(*"
-      { let eol = comment lexbuf in
+      { comment_level := 1; 
+	let eol = comment lexbuf in
 	  if eol then coq_bol lexbuf else coq lexbuf }
   | eof 
       { () }
@@ -421,7 +426,8 @@ and coq = parse
 	  Output.end_doc (); Output.start_coq (); 
 	  if eol then coq_bol lexbuf else coq lexbuf }
   | "(*"
-      { let eol = comment lexbuf in
+      { comment_level := 1;
+	let eol = comment lexbuf in
 	  if eol then begin Output.line_break(); coq_bol lexbuf end 
           else coq lexbuf
       }
@@ -556,7 +562,7 @@ and escaped_coq = parse
   | "["
       { incr brackets; Output.char '['; escaped_coq lexbuf }
   | "(*"
-      { ignore (comment lexbuf); escaped_coq lexbuf }
+      { comment_level := 1; ignore (comment lexbuf); escaped_coq lexbuf }
   | "*)"
       { (* likely to be a syntax error: we escape *) backtrack lexbuf }
   | eof
@@ -591,16 +597,16 @@ and comments = parse
 (*s Skip comments *)
 
 and comment = parse
-  | "(*" { comment lexbuf }
-  | "*)" space* nl { true }
-  | "*)" { false }
-  | eof  { false }
-  | _    { comment lexbuf }
+  | "(*" { incr comment_level; comment lexbuf }
+  | "*)" space* nl { decr comment_level; if !comment_level > 0 then comment lexbuf else true }
+  | "*)" { decr comment_level; if !comment_level > 0 then comment lexbuf else false }
+  | eof  {  false }
+  | _    {  comment lexbuf }
 
 and skip_to_dot = parse
   | '.' space* nl { true }
   | eof | '.' space+ { false}
-  | "(*" { ignore (comment lexbuf); skip_to_dot lexbuf }
+  | "(*" { comment_level := 1; ignore (comment lexbuf); skip_to_dot lexbuf }
   | _ { skip_to_dot lexbuf }
 
 and body_bol = parse
@@ -616,7 +622,8 @@ and body = parse
   | '.' space* nl | '.' space* eof { Output.char '.'; Output.line_break(); true }      
   | '.' space+ { Output.char '.'; Output.char ' '; false }
   | '"' { Output.char '"'; ignore(notation lexbuf); body lexbuf }
-  | "(*" { let eol = comment lexbuf in 
+  | "(*" { comment_level := 1; 
+	   let eol = comment lexbuf in 
 	     if eol 
 	     then begin Output.line_break(); body_bol lexbuf end
 	     else body lexbuf }
diff --git a/tools/gallina_lexer.mll b/tools/gallina_lexer.mll
index 0b769dbd..7eaec2a8 100644
--- a/tools/gallina_lexer.mll
+++ b/tools/gallina_lexer.mll
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: gallina_lexer.mll 5920 2004-07-16 20:01:26Z herbelin $ *)
+(* $Id: gallina_lexer.mll 11301 2008-08-04 19:41:18Z herbelin $ *)
 
 {
  open Lexing
@@ -51,7 +51,7 @@ rule action = parse
 		cRcpt := 0; action lexbuf }
   | [' ' '\t']* '\n'      { if !cRcpt < 2 then print "\n";
       	       	       	    cRcpt := !cRcpt+1; action lexbuf}
-  | eof       { raise Fin_fichier}
+  | eof       { (raise Fin_fichier : unit)}
   | _         { print (Lexing.lexeme lexbuf); cRcpt := 0; action lexbuf }
 
 and comment = parse
diff --git a/toplevel/auto_ind_decl.ml b/toplevel/auto_ind_decl.ml
index 094a77ff..49b9ce7a 100644
--- a/toplevel/auto_ind_decl.ml
+++ b/toplevel/auto_ind_decl.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: auto_ind_decl.ml 11166 2008-06-22 13:23:35Z herbelin $ i*)
+(*i $Id: auto_ind_decl.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 open Tacmach
 open Util
@@ -55,6 +55,8 @@ let subst_in_constr (_,subst,(ind,const)) =
 exception EqNotFound of string 
 exception EqUnknown of string
 
+let dl = dummy_loc
+
 (* Some pre declaration of constant we are going to use *)
 let bb = constr_of_global Coqlib.glob_bool
 
@@ -514,13 +516,13 @@ let compute_bl_tact ind lnamesparrec nparrec  =
                      new_induct false [ (Tacexpr.ElimOnConstr ((mkVar freshn),
                                         Rawterm.NoBindings))]
                                 None
-                                Genarg.IntroAnonymous
+                                (None,None)
 		                None;
                      intro_using freshm;
                      new_destruct false [ (Tacexpr.ElimOnConstr ((mkVar freshm),
                                     Rawterm.NoBindings))]
                                 None
-                                Genarg.IntroAnonymous
+                                (None,None)
 		                None;
                      intro_using freshz;
                      intros;
@@ -542,9 +544,9 @@ repeat ( apply andb_prop in z;let z1:= fresh "Z" in destruct z as [z1 z]).
                             (new_destruct false [Tacexpr.ElimOnConstr
                                       ((mkVar freshz,Rawterm.NoBindings))]
                                   None
-                                  ( Genarg.IntroOrAndPattern [[
-                                    Genarg.IntroIdentifier fresht;
-                                    Genarg.IntroIdentifier freshz]]) None) gl
+                                  (None, Some (dl,Genarg.IntroOrAndPattern [[
+                                    dl,Genarg.IntroIdentifier fresht;
+                                    dl,Genarg.IntroIdentifier freshz]])) None) gl
                         ]);
 (*
   Ci a1 ... an = Ci b1 ... bn 
@@ -632,13 +634,13 @@ let compute_lb_tact ind lnamesparrec nparrec =
                      new_induct false [Tacexpr.ElimOnConstr 
                                     ((mkVar freshn),Rawterm.NoBindings)] 
                                 None
-                                Genarg.IntroAnonymous
+                                (None,None)
 		                None;
                      intro_using freshm;
                      new_destruct false [Tacexpr.ElimOnConstr 
                                     ((mkVar freshm),Rawterm.NoBindings)]
                                 None
-                                Genarg.IntroAnonymous
+                                (None,None)
 		                None;
                      intro_using freshz;
                      intros;
@@ -746,7 +748,7 @@ let compute_dec_tact ind lnamesparrec nparrec =
       Pfedit.by ( tclTHENSEQ [
                         intros_using fresh_first_intros;
                         intros_using [freshn;freshm];
-                        assert_as true (Genarg.IntroIdentifier freshH) (
+                        assert_as true (dl,Genarg.IntroIdentifier freshH) (
                     mkApp(sumbool(),[|eqtrue eqbnm; eqfalse eqbnm|])
                   ) ]); 
 (*we do this so we don't have to prove the same goal twice *)
@@ -754,7 +756,7 @@ let compute_dec_tact ind lnamesparrec nparrec =
                    (new_destruct false [Tacexpr.ElimOnConstr
                                   (eqbnm,Rawterm.NoBindings)]
                                 None
-                                Genarg.IntroAnonymous
+                                (None,None)
 		                None)
                   Auto.default_auto
                 );
@@ -764,9 +766,9 @@ let compute_dec_tact ind lnamesparrec nparrec =
                     new_destruct false [Tacexpr.ElimOnConstr 
                                     ((mkVar freshH),Rawterm.NoBindings)] 
                                 None
-                                (Genarg.IntroOrAndPattern [
-                                    [Genarg.IntroAnonymous];
-                                    [Genarg.IntroIdentifier freshH2]]) None
+                                (None,Some (dl,Genarg.IntroOrAndPattern [
+                                    [dl,Genarg.IntroAnonymous];
+                                    [dl,Genarg.IntroIdentifier freshH2]])) None
       );
       let arfresh = Array.of_list fresh_first_intros in
         let xargs = Array.sub arfresh 0 (2*nparrec) in
@@ -793,7 +795,7 @@ let compute_dec_tact ind lnamesparrec nparrec =
                       unfold_constr (Lazy.force Coqlib.coq_not_ref);
                       intro;
                       Equality.subst_all;
-                assert_as true (Genarg.IntroIdentifier freshH3) 
+                assert_as true (dl,Genarg.IntroIdentifier freshH3) 
                 (mkApp(eq,[|bb;mkApp(eqI,[|mkVar freshm;mkVar freshm|]);tt|]))
           ]);
           Pfedit.by 
diff --git a/toplevel/cerrors.ml b/toplevel/cerrors.ml
index 40d74256..0983463a 100644
--- a/toplevel/cerrors.ml
+++ b/toplevel/cerrors.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: cerrors.ml 10410 2007-12-31 13:11:55Z msozeau $ *)
+(* $Id: cerrors.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -34,21 +34,21 @@ let rec explain_exn_default_aux anomaly_string report_fn = function
   | Stream.Failure -> 
       hov 0 (anomaly_string () ++ str "uncaught Stream.Failure.")
   | Stream.Error txt -> 
-      hov 0 (str "Syntax error: " ++ str txt)
+      hov 0 (str "Syntax error: " ++ str txt ++ str ".")
   | Token.Error txt -> 
-      hov 0 (str "Syntax error: " ++ str txt)
+      hov 0 (str "Syntax error: " ++ str txt ++ str ".")
   | Sys_error msg -> 
       hov 0 (anomaly_string () ++ str "uncaught exception Sys_error " ++ str (guill msg) ++ report_fn ())
   | UserError(s,pps) -> 
-      hov 1 (str "User error: " ++ where s ++ pps)
+      hov 0 (str "Error: " ++ where s ++ pps)
   | Out_of_memory -> 
-      hov 0 (str "Out of memory")
+      hov 0 (str "Out of memory.")
   | Stack_overflow -> 
-      hov 0 (str "Stack overflow")
+      hov 0 (str "Stack overflow.")
   | Anomaly (s,pps) -> 
-      hov 1 (anomaly_string () ++ where s ++ pps ++ report_fn ())
+      hov 0 (anomaly_string () ++ where s ++ pps ++ report_fn ())
   | Match_failure(filename,pos1,pos2) ->
-      hov 1 (anomaly_string () ++ str "Match failure in file " ++ str (guill filename) ++ 
+      hov 0 (anomaly_string () ++ str "Match failure in file " ++ str (guill filename) ++ 
       if Sys.ocaml_version = "3.06" then
 		   (str " from character " ++ int pos1 ++ 
                     str " to " ++ int pos2)
@@ -83,6 +83,11 @@ let rec explain_exn_default_aux anomaly_string report_fn = function
       hov 0 (str "Error:" ++ spc () ++ Himsg.explain_inductive_error e)
   | RecursionSchemeError e -> 
       hov 0 (str "Error:" ++ spc () ++ Himsg.explain_recursion_scheme_error e)
+  | Proof_type.LtacLocated (_,(Refiner.FailError (i,s) as exc)) when s <> mt () ->
+      explain_exn_default_aux anomaly_string report_fn exc
+  | Proof_type.LtacLocated (s,exc) ->
+      hov 0 (Himsg.explain_ltac_call_trace s ++ fnl ()
+             ++ explain_exn_default_aux anomaly_string report_fn exc)
   | Cases.PatternMatchingError (env,e) -> 
       hov 0
 	(str "Error:" ++ spc () ++ Himsg.explain_pattern_matching_error env e)
@@ -94,13 +99,15 @@ let rec explain_exn_default_aux anomaly_string report_fn = function
       hov 0 (str "Error:" ++ spc () ++
 	       str "The reference" ++ spc () ++ Libnames.pr_qualid q ++
 	       spc () ++ str "was not found" ++ 
-	       spc () ++ str "in the current" ++ spc () ++ str "environment")
+	       spc () ++ str "in the current" ++ spc () ++ str "environment.")
   | Nametab.GlobalizationConstantError q ->
       hov 0 (str "Error:" ++ spc () ++
-	       str "No constant of this name:" ++ spc () ++ Libnames.pr_qualid q)
+	       str "No constant of this name:" ++ spc () ++ 
+               Libnames.pr_qualid q ++ str ".")
   | Refiner.FailError (i,s) ->
-      hov 0 (str "Error: Tactic failure" ++ s ++
-             if i=0 then mt () else str " (level " ++ int i ++ str").")
+      hov 0 (str "Error: Tactic failure" ++ 
+                (if s <> mt() then str ":" ++ s else mt ()) ++
+                if i=0 then str "." else str " (level " ++ int i ++ str").")
   | Stdpp.Exc_located (loc,exc) ->
       hov 0 ((if loc = dummy_loc then (mt ())
                else (str"At location " ++ print_loc loc ++ str":" ++ fnl ()))
@@ -145,7 +152,7 @@ let raise_if_debug e =
 let _ = Tactic_debug.explain_logic_error := explain_exn_default
 
 let _ = Tactic_debug.explain_logic_error_no_anomaly :=
-          explain_exn_default_aux (fun () -> mt()) (fun () -> mt())
+          explain_exn_default_aux (fun () -> mt()) (fun () -> str ".")
 
 let explain_exn_function = ref explain_exn_default
 
diff --git a/toplevel/class.ml b/toplevel/class.ml
index 92fd2d4c..2c6a63b0 100644
--- a/toplevel/class.ml
+++ b/toplevel/class.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: class.ml 11085 2008-06-10 08:54:43Z herbelin $ *)
+(* $Id: class.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -119,7 +119,7 @@ let class_of_global = function
   | ConstructRef _ as c -> 
       errorlabstrm "class_of_global"
 	(str "Constructors, such as " ++ Printer.pr_global c ++ 
-	   str " cannot be used as class")
+	   str ", cannot be used as a class.")
 
 (* 
 lp est la liste (inverse'e) des arguments de la coercion
@@ -189,7 +189,7 @@ let ident_key_of_class = function
 
 let error_not_transparent source =
   errorlabstrm "build_id_coercion"
-    (pr_class source ++ str " must be a transparent constant")
+    (pr_class source ++ str " must be a transparent constant.")
 
 let build_id_coercion idf_opt source =
   let env = Global.env () in
@@ -218,8 +218,8 @@ let build_id_coercion idf_opt source =
       (Reductionops.is_conv_leq env Evd.empty
 	(Typing.type_of env Evd.empty val_f) typ_f)
     then
-      error ("cannot be defined as coercion - "^
-             "maybe a bad number of arguments") 
+      errorlabstrm "" (strbrk
+	"Cannot be defined as coercion (maybe a bad number of arguments).")
   in
   let idf =
     match idf_opt with
@@ -283,7 +283,8 @@ let add_new_coercion_core coef stre source target isid =
 let try_add_new_coercion_core ref b c d e =
   try add_new_coercion_core ref b c d e
   with CoercionError e ->
-      errorlabstrm "try_add_new_coercion_core" (explain_coercion_error ref e)
+      errorlabstrm "try_add_new_coercion_core"
+        (explain_coercion_error ref e ++ str ".")
 
 let try_add_new_coercion ref stre =
   try_add_new_coercion_core ref stre None None false
diff --git a/toplevel/classes.ml b/toplevel/classes.ml
index 8ed99cbd..511befd8 100644
--- a/toplevel/classes.ml
+++ b/toplevel/classes.ml
@@ -7,7 +7,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: classes.ml 11161 2008-06-21 14:32:47Z msozeau $ i*)
+(*i $Id: classes.ml 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Names
@@ -50,22 +50,23 @@ let declare_instance_cst glob con =
   let _, r = decompose_prod_assum instance in
     match class_of_constr r with
       | Some tc -> add_instance (new_instance tc None glob con)
-      | None -> error "Constant does not build instances of a declared type class"
+      | None -> errorlabstrm "" (Pp.strbrk "Constant does not build instances of a declared type class.")
 
 let declare_instance glob idl =
   let con = 
     try (match global (Ident idl) with
       | ConstRef x -> x
       | _ -> raise Not_found)
-    with _ -> error "Instance definition not found"
+    with _ -> error "Instance definition not found."
   in declare_instance_cst glob con
 	  
 let mismatched_params env n m = mismatched_ctx_inst env Parameters n m
-(* let mismatched_defs env n m = mismatched_ctx_inst env Definitions n m *)
 let mismatched_props env n m = mismatched_ctx_inst env Properties n m
 
 type binder_list = (identifier located * bool * constr_expr) list
 
+(* Calls to interpretation functions. *)
+
 let interp_binders_evars isevars env avoid l =
   List.fold_left
     (fun (env, ids, params) ((loc, i), t) -> 
@@ -87,111 +88,6 @@ let interp_typeclass_context_evars isevars env avoid l =
 	(push_named d env, i :: ids, d::params))
     (env, avoid, []) l
 
-let interp_constrs_evars isevars env avoid l =
-  List.fold_left
-    (fun (env, ids, params) t -> 
-      let t' = interp_binder_evars isevars env Anonymous t in
-      let id = Nameops.next_name_away (Termops.named_hd env t' Anonymous) ids in
-      let d = (id,None,t') in
-	(push_named d env, id :: ids, d::params))
-    (env, avoid, []) l
-
-let raw_assum_of_binders k = 
-  List.map (fun ((loc,i),t) -> LocalRawAssum ([(loc, Name i)], k, t))
-
-let raw_assum_of_constrs k = 
-  List.map2 (fun t (n,_,_) -> LocalRawAssum ([(dummy_loc, Name n)], k, t))
-
-let raw_assum_of_anonymous_constrs k = 
-  List.map (fun t -> LocalRawAssum ([(dummy_loc, Anonymous)], k, t))
-
-let decl_expr_of_binders = 
-  List.map (fun ((loc,i),t) -> false, Vernacexpr.AssumExpr ((loc, Name i), t))
-      
-let rec unfold n f acc = 
-  match n with 
-    | 0 -> f 0 acc
-    | n -> unfold (n - 1) f (f n acc)
-
-(* Declare everything in the parameters as implicit, and the class instance as well *)
-open Topconstr
-
-let declare_implicit_proj c proj imps sub =
-  let len = List.length c.cl_context in
-  let (ctx, _) = decompose_prod_n (len + 1) (Typeops.type_of_constant (Global.env()) (snd proj)) in
-  let expls =
-    let rec aux i expls = function
-	[] -> expls
-      | (Name n, _) :: tl -> 
-	  let impl = ExplByPos (i, Some n), (true, true) in
-	    aux (succ i) (impl :: List.remove_assoc (ExplByName n) expls) tl
-      | (Anonymous,_) :: _ -> assert(false)
-    in
-      aux 1 [] (List.rev ctx)
-  in 
-  let expls = expls @ List.map (function (ExplByPos (i, n), f) -> (ExplByPos (succ len + i, n)), f | _ -> assert(false)) imps in
-    if sub then 
-      declare_instance_cst true (snd proj);
-    Impargs.declare_manual_implicits false (ConstRef (snd proj)) true expls
-      
-let declare_implicits impls subs cl =
-  Util.list_iter3 (fun p imps sub -> declare_implicit_proj cl p imps sub)
-    cl.cl_projs impls subs;
-  let len = List.length cl.cl_context in
-  let indimps = 
-    list_fold_left_i 
-      (fun i acc (is, (na, b, t)) -> 
-	if len - i <= cl.cl_params then acc
-	else 
-	  match is with
-	      None | Some (_, false) -> (ExplByPos (i, Some na), (false, true)) :: acc
-	    | _ -> acc)
-      1 [] (List.rev cl.cl_context)
-  in
-    Impargs.declare_manual_implicits false cl.cl_impl false indimps
-      
-let rel_of_named_context subst l = 
-  List.fold_right
-    (fun (id, _, t) (ctx, acc) -> (Name id, None, subst_vars acc t) :: ctx, id :: acc)
-    l ([], subst)
-
-let ids_of_rel_context subst l = 
-  List.fold_right
-    (fun (id, _, t) acc -> Nameops.out_name id :: acc)
-    l subst
-
-let degenerate_decl (na,b,t) =
-  let id = match na with
-    | Name id -> id
-    | Anonymous -> anomaly "Unnamed record variable" in 
-  match b with
-    | None -> (id, Entries.LocalAssum t)
-    | Some b -> (id, Entries.LocalDef b)
-
-
-let declare_structure env id idbuild params arity fields =
-  let nparams = List.length params and nfields = List.length fields in
-  let args = extended_rel_list nfields params in
-  let ind = applist (mkRel (1+nparams+nfields), args) in
-  let type_constructor = it_mkProd_or_LetIn ind fields in
-  let mie_ind =
-    { mind_entry_typename = id;
-      mind_entry_arity = arity;
-      mind_entry_consnames = [idbuild];
-      mind_entry_lc = [type_constructor] } in
-  let mie =
-    { mind_entry_params = List.map degenerate_decl params;
-      mind_entry_record = true;
-      mind_entry_finite = true;
-      mind_entry_inds = [mie_ind] } in
-  let kn = Command.declare_mutual_with_eliminations true mie [] in
-  let rsp = (kn,0) in (* This is ind path of idstruc *)
-  let id = Nameops.next_ident_away id (ids_of_context (Global.env())) in
-  let kinds,sp_projs = Record.declare_projections rsp ~kind:Method ~name:id (List.map (fun _ -> false) fields) fields in
-  let _build = ConstructRef (rsp,1) in
-    Recordops.declare_structure(rsp,idbuild,List.rev kinds,List.rev sp_projs);
-    rsp
-
 let interp_type_evars evdref env ?(impls=([],[])) typ =
   let typ' = intern_gen true ~impls (Evd.evars_of !evdref) env typ in
   let imps = Implicit_quantifiers.implicits_of_rawterm typ' in
@@ -202,15 +98,6 @@ let mk_interning_data env na impls typ =
   in (na, ([], impl, Notation.compute_arguments_scope typ))
     
 let interp_fields_evars isevars env avoid l =
-  List.fold_left
-    (fun (env, uimpls, ids, params, impls) ((loc, i), _, t) -> 
-      let impl, t' = interp_type_evars isevars env ~impls t in
-      let data = mk_interning_data env i impl t' in
-      let d = (i,None,t') in
-	(push_named d env, impl :: uimpls, Idset.add i ids, d::params, ([], data :: snd impls)))
-    (env, [], avoid, [], ([], [])) l    
-
-let interp_fields_rel_evars isevars env avoid l =
   List.fold_left
     (fun (env, uimpls, ids, params, impls) ((loc, i), _, t) -> 
       let impl, t' = interp_type_evars isevars env ~impls t in
@@ -219,6 +106,27 @@ let interp_fields_rel_evars isevars env avoid l =
 	(push_rel d env, impl :: uimpls, Idset.add i ids, d::params, ([], data :: snd impls)))
     (env, [], avoid, [], ([], [])) l    
 
+(* Declare everything in the parameters as implicit, and the class instance as well *)
+
+open Topconstr
+
+let implicits_of_context ctx =
+  list_map_i (fun i name ->
+    let explname = 
+      match name with 
+      | Name n -> Some n
+      | Anonymous -> None
+    in ExplByPos (i, explname), (true, true))
+    1 (List.rev (Anonymous :: (List.map pi1 ctx)))
+
+let degenerate_decl (na,b,t) =
+  let id = match na with
+    | Name id -> id
+    | Anonymous -> anomaly "Unnamed record variable" in 
+  match b with
+    | None -> (id, Entries.LocalAssum t)
+    | Some b -> (id, Entries.LocalDef b)
+
 let name_typeclass_binder avoid = function
   | LocalRawAssum ([loc, Anonymous], bk, c) ->
       let name = 
@@ -237,33 +145,7 @@ let name_typeclass_binders avoid l =
 				   b' :: binders, avoid)
       ([], avoid) l
   in List.rev l', avoid
-
-let decompose_named_assum = 
-  let rec prodec_rec subst l c =
-    match kind_of_term c with
-      | Prod (Name na,t,c) -> 
-	let decl = (na,None,substl subst t) in
-	let subst' = mkVar na :: subst in
-	  prodec_rec subst' (add_named_decl decl l) (substl subst' c)
-      | LetIn (Name na, b, t, c) ->
-	let decl = (na,Some (substl subst b),substl subst t) in
-	let subst' = mkVar na :: subst in
-	  prodec_rec subst' (add_named_decl decl l) (substl subst' c)
-      | Cast (c,_,_)      -> prodec_rec subst l c
-      | _               -> l,c
-  in prodec_rec [] []
       
-let push_named_context = 
-  List.fold_right push_named
-
-let named_of_rel_context (subst, ids, env as init) ctx =
-  Sign.fold_rel_context
-    (fun (na,c,t) (subst, avoid, env) ->
-      let id = Nameops.next_name_away na avoid in
-      let d = (id,Option.map (substl subst) c,substl subst t) in
-	(mkVar id :: subst, id::avoid, d::env))
-    ctx ~init
-    
 let new_class id par ar sup props =
   let env0 = Global.env() in
   let isevars = ref (Evd.create_evar_defs Evd.empty) in
@@ -294,7 +176,7 @@ let new_class id par ar sup props =
     
   (* Interpret the definitions and propositions *)
   let env_props, prop_impls, bound, ctx_props, _ = 
-    interp_fields_rel_evars isevars env_params bound props 
+    interp_fields_evars isevars env_params bound props 
   in
   let subs = List.map (fun ((loc, id), b, _) -> b) props in
   (* Instantiate evars and check all are resolved *)
@@ -305,6 +187,12 @@ let new_class id par ar sup props =
   let ctx_props = Evarutil.nf_rel_context_evar sigma ctx_props in
   let arity = Reductionops.nf_evar sigma arity in
   let ce t = Evarutil.check_evars env0 Evd.empty isevars t in
+  let fieldimpls = 
+    (* Make the class and all params implicits in the projections *)
+    let ctx_impls = implicits_of_context ctx_params in
+    let len = succ (List.length ctx_params) in
+      List.map (fun x -> ctx_impls @ Impargs.lift_implicits len x) prop_impls
+  in
   let impl, projs = 
     let params = ctx_params and fields = ctx_props in
       List.iter (fun (_,c,t) -> ce t; match c with Some c -> ce c | None -> ()) (params @ fields);
@@ -337,31 +225,34 @@ let new_class id par ar sup props =
 	    let proj_cst = Declare.declare_constant proj_name
 	      (DefinitionEntry proj_entry, IsDefinition Definition) 
 	    in
-	      ConstRef cst, [proj_name, proj_cst]
+	    let cref = ConstRef cst in
+	      Impargs.declare_manual_implicits false cref (Impargs.is_implicit_args()) arity_imps;
+	      Impargs.declare_manual_implicits false (ConstRef proj_cst) (Impargs.is_implicit_args()) (List.hd fieldimpls);
+	      cref, [proj_name, proj_cst]
 	| _ ->
 	    let idb = id_of_string ("Build_" ^ (string_of_id (snd id))) in
-	    let kn = declare_structure env0 (snd id) idb params arity fields in
-	      IndRef kn, (List.map2 (fun (id, _, _) y -> Nameops.out_name id, Option.get y)
-			     fields (Recordops.lookup_projections kn))
+	    let idarg = Nameops.next_ident_away (snd id) (ids_of_context (Global.env())) in
+	    let kn = Record.declare_structure (snd id) idb arity_imps
+	      params arity fieldimpls fields ~kind:Method ~name:idarg false (List.map (fun _ -> false) fields)
+	    in
+	      IndRef (kn,0), (List.map2 (fun (id, _, _) y -> Nameops.out_name id, Option.get y)
+			     fields (Recordops.lookup_projections (kn,0)))
   in
-  let ids = List.map pi1 (named_context env0) in
-  let (subst, ids, named_ctx_params) = named_of_rel_context ([], ids, []) ctx_params in
-  let (_, _, named_ctx_props) = named_of_rel_context (subst, ids, []) ctx_props in
   let ctx_context =
     List.map (fun ((na, b, t) as d) -> 
       match Typeclasses.class_of_constr t with
-      | Some cl -> (Some (cl.cl_impl, List.exists (fun (_, n) -> n = Name na) supnames), d)
+      | Some cl -> (Some (cl.cl_impl, List.exists (fun (_, n) -> n = na) supnames), d)
       | None -> (None, d))
-      named_ctx_params
+      ctx_params
   in
   let k =
     { cl_impl = impl;
-      cl_params = List.length par;
       cl_context = ctx_context;
-      cl_props = named_ctx_props;
+      cl_props = ctx_props;
       cl_projs = projs }
   in
-    declare_implicits (List.rev prop_impls) subs k;
+    List.iter2 (fun p sub -> if sub then declare_instance_cst true (snd p))
+      k.cl_projs subs;
     add_class k
     
 type binder_def_list = (identifier located * identifier located list * constr_expr) list
@@ -369,63 +260,16 @@ type binder_def_list = (identifier located * identifier located list * constr_ex
 let binders_of_lidents l =
   List.map (fun (loc, id) -> LocalRawAssum ([loc, Name id], Default Rawterm.Implicit, CHole (loc, None))) l
 
-let subst_ids_in_named_context subst l =
-  let x, _ = 
-    List.fold_right
-      (fun (id, _, t) (ctx, k) -> (id, None, substn_vars k subst t) :: ctx, succ k)
-      l ([], 1)
-  in x
-    
-let subst_one_named inst ids t =
-  substnl inst 0 (substn_vars 1 ids t)
-      
-let subst_named inst subst ctx =
-  let ids = List.map (fun (id, _, _) -> id) subst in
-  let ctx' = subst_ids_in_named_context ids ctx in
-  let ctx', _ =
-    List.fold_right
-      (fun (id, _, t) (ctx, k) -> (id, None, substnl inst k t) :: ctx, succ k)
-      ctx' ([], 0)
-  in ctx'
-(*
-let infer_super_instances env params params_ctx super =
-  let super = subst_named params params_ctx super in
-    List.fold_right 
-      (fun (na, _, t) (sups, ids, supctx) -> 
-	let t = subst_one_named sups ids t in
-	let inst = 
-	  try resolve_one_typeclass env t 
-	  with Not_found -> 
-	    let cl, args = destClass t in
-	      no_instance (push_named_context supctx env) (dummy_loc, cl.cl_name) (Array.to_list args)
-	in
-	let d = (na, Some inst, t) in
-	  inst :: sups, na :: ids, d :: supctx)
-      super ([], [], [])*)
-      
-(* let evars_of_context ctx id n env = *)
-(*   List.fold_right (fun (na, _, t) (n, env, nc) ->  *)
-(*     let b = Evarutil.e_new_evar isevars env ~src:(dummy_loc, ImplicitArg (Ident id, (n * Some na))) t in *)
-(*     let d = (na, Some b, t) in *)
-(*       (succ n, push_named d env, d :: nc)) *)
-(*     ctx (n, env, []) *)
-
 let type_ctx_instance isevars env ctx inst subst =
-  List.fold_left2
-    (fun (subst, instctx) (na, _, t) ce ->
-      let t' = replace_vars subst t in
-      let c = interp_casted_constr_evars isevars env ce t' in
-      let d = na, Some c, t' in
-	(na, c) :: subst, d :: instctx)
-    (subst, []) (List.rev ctx) inst
-
-let substitution_of_constrs ctx cstrs =
-  List.fold_right2 (fun c (na, _, _) acc -> (na, c) :: acc) cstrs ctx []
-
-let destClassApp cl =
-  match cl with
-    | CApp (loc, (None,CRef (Ident f)), l) -> f, List.map fst l
-    | _ -> raise Not_found
+  let (s, _) = 
+    List.fold_left2
+      (fun (subst, instctx) (na, _, t) ce ->
+	let t' = substl subst t in
+	let c = interp_casted_constr_evars isevars env ce t' in
+	let d = na, Some c, t' in
+	  c :: subst, d :: instctx)
+      (subst, []) (List.rev ctx) inst
+  in s
 
 let refine_ref = ref (fun _ -> assert(false))
 
@@ -521,31 +365,31 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=defau
   let k, ctx', imps, subst = 
     let c = Command.generalize_constr_expr tclass ctx in
     let imps, c' = interp_type_evars isevars env c in
-    let ctx, c = decompose_named_assum c' in
+    let ctx, c = decompose_prod_assum c' in
     let cl, args = Typeclasses.dest_class_app c in
-      cl, ctx, imps, substitution_of_constrs (List.map snd cl.cl_context) (List.rev (Array.to_list args))
+      cl, ctx, imps, List.rev (Array.to_list args)
   in
   let id = 
     match snd instid with
 	Name id -> 
 	  let sp = Lib.make_path id in
 	    if Nametab.exists_cci sp then
-	      errorlabstrm "new_instance" (Nameops.pr_id id ++ Pp.str " already exists");
+	      errorlabstrm "new_instance" (Nameops.pr_id id ++ Pp.str " already exists.");
 	    id
       | Anonymous -> 
 	  let i = Nameops.add_suffix (id_of_class k) "_instance_0" in
 	    Termops.next_global_ident_away false i (Termops.ids_of_context env)
   in
-  let env' = push_named_context ctx' env in
+  let env' = push_rel_context ctx' env in
   isevars := Evarutil.nf_evar_defs !isevars;
   isevars := resolve_typeclasses env !isevars;
   let sigma = Evd.evars_of !isevars in
-  let substctx = Typeclasses.nf_substitution sigma subst in
+  let substctx = List.map (Evarutil.nf_evar sigma) subst in
     if Lib.is_modtype () then
       begin
-	let _, ty_constr = instance_constructor k (List.rev_map snd substctx) in
+	let _, ty_constr = instance_constructor k (List.rev subst) in
 	let termtype = 
-	  let t = it_mkNamedProd_or_LetIn ty_constr ctx' in
+	  let t = it_mkProd_or_LetIn ty_constr ctx' in
 	    Evarutil.nf_isevar !isevars t
 	in
 	Evarutil.check_evars env Evd.empty !isevars termtype;
@@ -555,7 +399,7 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=defau
       end
     else
       begin
-	let subst, _propsctx = 
+	let subst = 
 	  let props = 
 	    List.map (fun (x, l, d) -> 
 	      x, Topconstr.abstract_constr_expr d (binders_of_lidents l))
@@ -567,8 +411,8 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=defau
 	      List.fold_left
 		(fun (props, rest) (id,_,_) -> 
 		  try 
-		    let ((loc, mid), c) = List.find (fun ((_,id'), c) -> id' = id) rest in
-		    let rest' = List.filter (fun ((_,id'), c) -> id' <> id) rest in
+		    let ((loc, mid), c) = List.find (fun ((_,id'), c) -> Name id' = id) rest in
+		    let rest' = List.filter (fun ((_,id'), c) -> Name id' <> id) rest in
 		      Constrintern.add_glob loc (ConstRef (List.assoc mid k.cl_projs));
 		      c :: props, rest'
 		  with Not_found -> (CHole (Util.dummy_loc, None) :: props), rest)
@@ -579,12 +423,12 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=defau
 	      else
 		type_ctx_instance isevars env' k.cl_props props substctx
 	in
-	let app, ty_constr = instance_constructor k (List.rev_map snd subst) in
+	let app, ty_constr = instance_constructor k (List.rev subst) in
 	let termtype = 
-	  let t = it_mkNamedProd_or_LetIn ty_constr ctx' in
+	  let t = it_mkProd_or_LetIn ty_constr ctx' in
 	    Evarutil.nf_isevar !isevars t
 	in
-	let term = Termops.it_mkNamedLambda_or_LetIn app ctx' in
+	let term = Termops.it_mkLambda_or_LetIn app ctx' in
 	isevars := Evarutil.nf_evar_defs !isevars;
 	let term = Evarutil.nf_isevar !isevars term in
 	let evm = Evd.evars_of (undefined_evars !isevars) in
@@ -607,31 +451,26 @@ let new_instance ?(global=false) ctx (instid, bk, cl) props ?(on_free_vars=defau
 	  end
       end
 
-let goal_kind = Decl_kinds.Global, Decl_kinds.DefinitionBody Decl_kinds.Definition
-
-let solve_by_tac env evd evar evi t =
-  let goal = {it = evi; sigma = (Evd.evars_of evd) } in
-  let (res, valid) = t goal in 
-    if res.it = [] then 
-      let prooftree = valid [] in
-      let proofterm, obls = Refiner.extract_open_proof res.sigma prooftree in
-	if obls = [] then 
-	  let evd' = evars_reset_evd res.sigma evd in
-	  let evd' = evar_define evar proofterm evd' in
-	    evd', true
-	else evd, false
-    else evd, false
+let named_of_rel_context l =
+  let acc, ctx = 
+    List.fold_right 
+      (fun (na, b, t) (subst, ctx) ->
+	let id = match na with Anonymous -> raise (Invalid_argument "named_of_rel_context") | Name id -> id in
+	let d = (id, Option.map (substl subst) b, substl subst t) in
+	  (mkVar id :: subst, d :: ctx))
+      l ([], [])
+  in ctx
 
 let context ?(hook=fun _ -> ()) l =
   let env = Global.env() in
-  let isevars = ref (Evd.create_evar_defs Evd.empty) in
-  let avoid = Termops.ids_of_context env in
-  let ctx, l = Implicit_quantifiers.resolve_class_binders (vars_of_env env) l in
-  let env', avoid, ctx = interp_binders_evars isevars env avoid ctx in
-  let env', avoid, l = interp_typeclass_context_evars isevars env' avoid l in
-  isevars := Evarutil.nf_evar_defs !isevars;
-  let sigma = Evd.evars_of !isevars in
-  let fullctx = Evarutil.nf_named_context_evar sigma (l @ ctx) in
+  let evars = ref (Evd.create_evar_defs Evd.empty) in
+  let (env', fullctx), impls = interp_context_evars evars env l in
+  let fullctx = Evarutil.nf_rel_context_evar (Evd.evars_of !evars) fullctx in
+  let ce t = Evarutil.check_evars env Evd.empty !evars t in
+  List.iter (fun (n, b, t) -> Option.iter ce b; ce t) fullctx;
+  let ctx = try named_of_rel_context fullctx with _ -> 
+    error "Anonymous variables not allowed in contexts."
+  in
     List.iter (function (id,_,t) -> 
       if Lib.is_modtype () then 
 	let cst = Declare.declare_internal_constant id
@@ -642,96 +481,12 @@ let context ?(hook=fun _ -> ()) l =
 		add_instance (Typeclasses.new_instance tc None false cst);
 		hook (ConstRef cst)
 	    | None -> ()
-      else
-	(Command.declare_one_assumption false (Local (* global *), Definitional) t
-	    [] true (* implicit *) true (* always kept *) false (* inline *) (dummy_loc, id);
-	 match class_of_constr t with
-	     None -> ()
-	   | Some tc -> hook (VarRef id)))
-      (List.rev fullctx)
-
-open Libobject
-
-let module_qualid = qualid_of_dirpath (dirpath_of_string "Coq.Classes.Init")
-let tactic_qualid = make_qualid (dirpath_of_string "Coq.Classes.Init") (id_of_string "typeclass_instantiation")
-  
-let tactic_expr = Tacexpr.TacArg (Tacexpr.Reference (Qualid (dummy_loc, tactic_qualid)))
-let tactic = lazy (Tacinterp.interp tactic_expr)
-
-let _ =
-  Typeclasses.solve_instanciation_problem :=
-    (fun env evd ev evi -> 
-      Library.require_library [(dummy_loc, module_qualid)] None; (* may be inefficient *)
-      solve_by_tac env evd ev evi (Lazy.force tactic))
-
-(* let prod = lazy_fun Coqlib.build_prod *)
-
-(* let build_conjunction evm = *)
-(*   List.fold_left *)
-(*     (fun (acc, evs) (ev, evi)  -> *)
-(*       if class_of_constr evi.evar_concl <> None then *)
-(* 	mkApp ((Lazy.force prod).Coqlib.typ, [|evi.evar_concl; acc |]), evs *)
-(*       else acc, Evd.add evs ev evi) *)
-(*     (Coqlib.build_coq_True (), Evd.empty) evm *)
-
-(* let destruct_conjunction evm_list evm evm' term = *)
-(*   let _, evm = *)
-(*     List.fold_right *)
-(*       (fun (ev, evi) (term, evs) -> *)
-(* 	if class_of_constr evi.evar_concl <> None then *)
-(* 	  match kind_of_term term with *)
-(* 	    | App (x, [| _ ; _ ; proof ; term |]) -> *)
-(* 		let evs' = Evd.define evs ev proof in *)
-(* 		  (term, evs') *)
-(* 	    | _ -> assert(false) *)
-(* 	else *)
-(* 	  match (Evd.find evm' ev).evar_body with *)
-(* 	      Evar_empty -> raise Not_found *)
-(* 	    | Evar_defined c -> *)
-(* 		let evs' = Evd.define evs ev c in *)
-(* 		  (term, evs')) *)
-(*       evm_list (term, evm) *)
-(*   in evm *)
- 
-(* let solve_by_tac env evd evar evi t = *)
-(*   let goal = {it = evi; sigma = (Evd.evars_of evd) } in *)
-(*   let (res, valid) = t goal in *)
-(*     if res.it = [] then *)
-(*       let prooftree = valid [] in *)
-(*       let proofterm, obls = Refiner.extract_open_proof res.sigma prooftree in *)
-(* 	if obls = [] then *)
-(* 	  let evd' = evars_reset_evd res.sigma evd in *)
-(* 	  let evd' = evar_define evar proofterm evd' in *)
-(* 	    evd', true *)
-(* 	else evd, false *)
-(*     else evd, false *)
-
-(* let resolve_all_typeclasses env evd = *)
-(*   let evm = Evd.evars_of evd in *)
-(*   let evm_list = Evd.to_list evm in *)
-(*   let goal, typesevm = build_conjunction evm_list in *)
-(*   let evars = ref (Evd.create_evar_defs typesevm) in *)
-(*   let term = resolve_one_typeclass_evd env evars goal in *)
-(*   let evm' = destruct_conjunction evm_list evm (Evd.evars_of !evars) term in *)
-(*     Evd.create_evar_defs evm' *)
-
-(* let _ = *)
-(*   Typeclasses.solve_instanciations_problem := *)
-(*     (fun env evd ->  *)
-(*       Library.require_library [(dummy_loc, module_qualid)] None; (\* may be inefficient *\) *)
-(*       resolve_all_typeclasses env evd) *)
-
-let solve_evars_by_tac env evd t =
-  let ev = make_evar empty_named_context_val mkProp in
-  let goal = {it = ev; sigma = (Evd.evars_of evd) } in
-  let (res, valid) = t goal in 
-  let evd' = evars_reset_evd res.sigma evd in
-    evd'
-(*       Library.require_library [(dummy_loc, module_qualid)] None (a\* may be inefficient *\); *)
-
-(* let _ = *)
-(*   Typeclasses.solve_instanciations_problem := *)
-(*     (fun env evd ->  *)
-(*       Eauto.resolve_all_evars false (true, 15) env  *)
-(* 	(fun ev evi -> is_implicit_arg (snd (evar_source ev evd)) *)
-(* 	  && class_of_constr evi.evar_concl <> None) evd) *)
+      else (
+	let impl = List.exists (fun (x,_) -> match x with ExplByPos (_, Some id') -> id = id' | _ -> false) impls
+	in
+	  Command.declare_one_assumption false (Local (* global *), Definitional) t
+	    [] impl (* implicit *) true (* always kept *) false (* inline *) (dummy_loc, id);
+	  match class_of_constr t with
+	  | None -> ()
+	  | Some tc -> hook (VarRef id)))
+      (List.rev ctx)
diff --git a/toplevel/classes.mli b/toplevel/classes.mli
index f3cb0c58..f149ac72 100644
--- a/toplevel/classes.mli
+++ b/toplevel/classes.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: classes.mli 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: classes.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -23,17 +23,21 @@ open Typeclasses
 open Implicit_quantifiers
 (*i*)
 
+(* Errors *)
+
+val mismatched_params : env -> constr_expr list -> rel_context -> 'a
+
+val mismatched_props : env -> constr_expr list -> rel_context -> 'a
+
 type binder_list = (identifier located * bool * constr_expr) list
 type binder_def_list = (identifier located * identifier located list * constr_expr) list
  
 val binders_of_lidents : identifier located list -> local_binder list
 
-val declare_implicit_proj : typeclass -> (identifier * constant) -> 
-  Impargs.manual_explicitation list -> bool -> unit
-(*
-val infer_super_instances : env -> constr list ->
-  named_context -> named_context -> types list * identifier list * named_context
-*)
+val name_typeclass_binders : Idset.t ->
+    Topconstr.local_binder list ->
+    Topconstr.local_binder list * Idset.t
+
 val new_class : identifier located ->
   local_binder list ->
   Vernacexpr.sort_expr located option ->
@@ -46,6 +50,10 @@ val default_on_free_vars : identifier list -> unit
 
 val fail_on_free_vars : identifier list -> unit
 
+(* Instance declaration *)
+
+val declare_instance : bool -> identifier located -> unit
+
 val declare_instance_constant :
   typeclass ->
   int option -> (* priority *)
@@ -69,35 +77,15 @@ val new_instance :
   identifier
 
 (* For generation on names based on classes only *)
-val id_of_class : typeclass -> identifier
-    
-val context : ?hook:(Libnames.global_reference -> unit) -> typeclass_context -> unit
-
-val declare_instance : bool -> identifier located -> unit
 
-val mismatched_params : env -> constr_expr list -> named_context -> 'a
+val id_of_class : typeclass -> identifier
 
-val mismatched_props : env -> constr_expr list -> named_context -> 'a
+(* Context command *)    
 
-val solve_by_tac :     env ->
-    Evd.evar_defs ->
-    Evd.evar ->
-  evar_info ->
-  Proof_type.tactic ->
-    Evd.evar_defs * bool
+val context : ?hook:(Libnames.global_reference -> unit) -> 
+  local_binder list -> unit
 
-val solve_evars_by_tac :     env ->
-    Evd.evar_defs ->
-  Proof_type.tactic ->
-  Evd.evar_defs
+(* Forward ref for refine *)
 
 val refine_ref : (open_constr -> Proof_type.tactic) ref
 
-val decompose_named_assum : types -> named_context * types
-
-val push_named_context : named_context -> env -> env
-
-val name_typeclass_binders : Idset.t ->
-    Topconstr.local_binder list ->
-    Topconstr.local_binder list * Idset.t
-
diff --git a/toplevel/command.ml b/toplevel/command.ml
index 531eadb3..3688c347 100644
--- a/toplevel/command.ml
+++ b/toplevel/command.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: command.ml 11169 2008-06-24 14:37:18Z notin $ *)
+(* $Id: command.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -88,8 +88,8 @@ let rec complete_conclusion a cs = function
       let (has_no_args,name,params) = a in
       if not has_no_args then
 	user_err_loc (loc,"",
-	  str "Cannot infer the non constant arguments of the conclusion of "
-	  ++ pr_id cs);
+	  strbrk"Cannot infer the non constant arguments of the conclusion of "
+	  ++ pr_id cs ++ str ".");
       let args = List.map (fun id -> CRef(Ident(loc,id))) params in
       CAppExpl (loc,(None,Ident(loc,name)),List.rev args)
   | c -> c
@@ -310,7 +310,7 @@ let declare_eq_scheme sp =
           definition_message nam
     done
   with Not_found -> 
-    error "Your type contains Parameters without a boolean equality"
+    error "Your type contains Parameters without a boolean equality."
 
 (* decidability of eq *)
 
@@ -473,7 +473,7 @@ type inductive_expr = {
 }
 
 let minductive_message = function
-  | []  -> error "no inductive definition"
+  | []  -> error "No inductive definition."
   | [x] -> (pr_id x ++ str " is defined")
   | l   -> hov 0  (prlist_with_sep pr_coma pr_id l ++
 		     spc () ++ str "are defined")
@@ -556,12 +556,18 @@ let interp_mutual paramsl indl notations finite =
     mind_entry_consnames = cnames;
     mind_entry_lc = ctypes
   }) indl arities constructors in
-
+  let impls = 
+    let len = List.length ctx_params in
+      List.map (fun (_,_,impls) ->
+	userimpls, List.map (fun impls -> 
+	  userimpls @ (lift_implicits len impls)) impls) constructors
+  in
   (* Build the mutual inductive entry *)
   { mind_entry_params = List.map prepare_param ctx_params;
     mind_entry_record = false; 
     mind_entry_finite = finite; 
-    mind_entry_inds = entries }, (List.map (fun (_,_,impls) -> userimpls, impls) constructors)
+    mind_entry_inds = entries }, 
+    impls
 
 let eq_constr_expr c1 c2 =
   try let _ = Constrextern.check_same_type c1 c2 in true with _ -> false
@@ -591,7 +597,7 @@ let extract_params indl =
   | [] -> anomaly "empty list of inductive types"
   | params::paramsl ->
       if not (List.for_all (eq_local_binders params) paramsl) then error 
-	"Parameters should be syntactically the same for each inductive type";
+	"Parameters should be syntactically the same for each inductive type.";
       params
 
 let prepare_inductive ntnl indl =
@@ -613,23 +619,17 @@ let _ =
       optread  = (fun () -> !elim_flag) ;
       optwrite = (fun b -> elim_flag := b) }
 
-
-let lift_implicits n = 
-  List.map (fun x -> 
-    match fst x with 
-	ExplByPos (k, id) -> ExplByPos (k + n, id), snd x
-      | _ -> x)
-
 let declare_mutual_with_eliminations isrecord mie impls =
   let names = List.map (fun e -> e.mind_entry_typename) mie.mind_entry_inds in
-  let params = List.length mie.mind_entry_params in
   let (_,kn) = declare_mind isrecord mie in    
     list_iter_i (fun i (indimpls, constrimpls) -> 
       let ind = (kn,i) in
+	maybe_declare_manual_implicits false (IndRef ind)
+	  (is_implicit_args()) indimpls;
 	list_iter_i
 	  (fun j impls -> 
 	    maybe_declare_manual_implicits false (ConstructRef (ind, succ j))
-	      (is_implicit_args()) (indimpls @ (lift_implicits params impls)))
+	      (is_implicit_args()) impls)
 	  constrimpls)
       impls;
     if_verbose ppnl (minductive_message names);
@@ -672,7 +672,7 @@ let recursive_message indexes = function
 		    | None -> mt ())
 
 let corecursive_message _ = function
-  | [] -> error "no corecursive definition"
+  | [] -> error "No corecursive definition."
   | [id] -> pr_id id ++ str " is corecursively defined"
   | l -> hov 0 (prlist_with_sep pr_coma pr_id l ++
                     spc () ++ str "are corecursively defined")
@@ -827,6 +827,7 @@ let interp_recursive fixkind l boxed =
     List.split (List.map (interp_fix_context evdref env) fixl) in
   let fixccls = List.map2 (interp_fix_ccl evdref) fixctxs fixl in
   let fixtypes = List.map2 build_fix_type fixctxs fixccls in
+  let fixtypes = List.map (nf_evar (evars_of !evdref)) fixtypes in
   let env_rec = push_named_types env fixnames fixtypes in
 
   (* Get interpretation metadatas *)
@@ -1005,7 +1006,7 @@ let build_combined_scheme name schemes =
 		let qualid = qualid_of_reference refe in
 		let cst = try 
                     Nametab.locate_constant (snd qualid) 
-                with Not_found -> error ((string_of_qualid (snd qualid))^" is not declared")
+                with Not_found -> error ((string_of_qualid (snd qualid))^" is not declared.")
                 in
 		let ty = Typeops.type_of_constant env cst in
 		  qualid, cst, ty)
@@ -1051,15 +1052,21 @@ let retrieve_first_recthm = function
               (Option.map Declarations.force body,opaq)
           | _ -> assert false
 
+let default_thm_id = id_of_string "Unnamed_thm"
+
 let compute_proof_name = function
   | Some (loc,id) ->
       (* We check existence here: it's a bit late at Qed time *)
       if Nametab.exists_cci (Lib.make_path id) or is_section_variable id then
-        user_err_loc (loc,"",pr_id id ++ str " already exists");
+        user_err_loc (loc,"",pr_id id ++ str " already exists.");
       id
   | None ->
-      next_global_ident_away false (id_of_string "Unnamed_thm")
- 	(Pfedit.get_all_proof_names ())
+      let rec next avoid id =
+        let id = next_global_ident_away false id avoid in
+        if Nametab.exists_cci (Lib.make_path id) then next (id::avoid) id 
+        else id
+      in
+      next (Pfedit.get_all_proof_names ()) default_thm_id
 
 let save_remaining_recthms (local,kind) body opaq i (id,(t_i,imps)) =
   match body with
@@ -1207,7 +1214,7 @@ let start_proof_com kind thms hook =
 
 let check_anonymity id save_ident =
   if atompart_of_id id <> "Unnamed_thm" then
-    error "This command can only be used for unnamed theorem"
+    error "This command can only be used for unnamed theorem."
 (*
     message("Overriding name "^(string_of_id id)^" and using "^save_ident)
 *)
diff --git a/toplevel/command.mli b/toplevel/command.mli
index 26526a5f..8ac8c234 100644
--- a/toplevel/command.mli
+++ b/toplevel/command.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: command.mli 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: command.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Util
@@ -56,18 +56,16 @@ val declare_assumption : identifier located list ->
 val declare_interning_data : 'a * Constrintern.implicits_env ->
     string * Topconstr.constr_expr * Topconstr.scope_name option -> unit
 
-
-val compute_interning_datas :  Environ.env ->
-    'a list ->
-    'b list ->
-    Term.types list ->
-    Impargs.manual_explicitation list list ->
+val compute_interning_datas :  Environ.env -> 'a list -> 'b list ->
+  Term.types list ->Impargs.manual_explicitation list list ->
   'a list *
-    ('b *
-	(Names.identifier list * Impargs.implicits_list *
-	    Topconstr.scope_name option list))
+    ('b * (Names.identifier list * Impargs.implicits_list *
+	      Topconstr.scope_name option list))
     list
 
+val check_mutuality : Environ.env -> definition_object_kind ->
+  (identifier * types) list -> unit
+
 val build_mutual : (inductive_expr * decl_notation) list -> bool -> unit
 
 val declare_mutual_with_eliminations :
@@ -87,10 +85,10 @@ type fixpoint_expr = {
   fix_type : constr_expr
 }
 
-val recursive_message : Decl_kinds.definition_object_kind ->
-  int array option -> Names.identifier list -> Pp.std_ppcmds
+val recursive_message : definition_object_kind ->
+  int array option -> identifier list -> Pp.std_ppcmds
   
-val declare_fix : bool -> Decl_kinds.definition_object_kind -> identifier ->
+val declare_fix : bool -> definition_object_kind -> identifier ->
   constr -> types -> Impargs.manual_explicitation list -> global_reference
 
 val build_recursive : (Topconstr.fixpoint_expr * decl_notation) list -> bool -> unit
diff --git a/toplevel/coqtop.ml b/toplevel/coqtop.ml
index e6d2deec..f8c57ad2 100644
--- a/toplevel/coqtop.ml
+++ b/toplevel/coqtop.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: coqtop.ml 11062 2008-06-06 14:19:50Z notin $ *)
+(* $Id: coqtop.ml 11209 2008-07-05 10:17:49Z herbelin $ *)
 
 open Pp
 open Util
@@ -72,10 +72,12 @@ let check_coq_overwriting p =
   if string_of_id (list_last (repr_dirpath p)) = "Coq" then
     error "The \"Coq\" logical root directory is reserved for the Coq library"
 
-let set_include d p = push_include (d,p)
-let set_rec_include d p = check_coq_overwriting p; push_rec_include (d,p)
-let set_default_include d = set_include d Nameops.default_root_prefix
-let set_default_rec_include d = set_rec_include d Nameops.default_root_prefix
+let set_default_include d = push_include (d,Nameops.default_root_prefix)
+let set_default_rec_include d = push_rec_include(d,Nameops.default_root_prefix)
+let set_include d p =
+  let p = dirpath_of_string p in check_coq_overwriting p; push_include (d,p)
+let set_rec_include d p =
+  let p = dirpath_of_string p in check_coq_overwriting p; push_rec_include(d,p)
  
 let load_vernacular_list = ref ([] : (string * bool) list)
 let add_load_vernacular verb s =
@@ -187,15 +189,22 @@ let parse_args is_ide =
     | "-impredicative-set" :: rem -> 
         set_engagement Declarations.ImpredicativeSet; parse rem
 
+    | ("-I"|"-include") :: d :: "-as" :: p :: rem -> set_include d p; parse rem
+    | ("-I"|"-include") :: d :: "-as" :: [] -> usage ()
     | ("-I"|"-include") :: d :: rem -> set_default_include d; parse rem
     | ("-I"|"-include") :: []       -> usage ()
 
-    | "-R" :: d :: p :: rem ->set_rec_include d (dirpath_of_string p);parse rem
+    | "-R" :: d :: "-as" :: p :: rem -> set_rec_include d p;parse rem
+    | "-R" :: d :: "-as" :: [] -> usage ()
+    | "-R" :: d :: p :: rem -> set_rec_include d p;parse rem
     | "-R" :: ([] | [_]) -> usage ()
 
     | "-top" :: d :: rem -> set_toplevel_name (dirpath_of_string d); parse rem
     | "-top" :: [] -> usage ()
 
+    | "-exclude-dir" :: f :: rem -> exclude_search_in_dirname f; parse rem
+    | "-exclude-dir" :: [] -> usage ()
+
     | "-notop" :: rem -> unset_toplevel_name (); parse rem
     | "-q" :: rem -> no_load_rc (); parse rem
 
diff --git a/toplevel/fhimsg.ml b/toplevel/fhimsg.ml
deleted file mode 100644
index 4ef5d5fd..00000000
--- a/toplevel/fhimsg.ml
+++ /dev/null
@@ -1,355 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(* $Id: fhimsg.ml 7837 2006-01-11 09:47:32Z herbelin $ *)
-
-open Pp
-open Util
-open Names
-open Term
-open Sign
-open Environ
-open Type_errors
-open Reduction
-open G_minicoq
-
-module type Printer = sig
-  val pr_term : path_kind -> env -> constr -> std_ppcmds
-end
-
-module Make = functor (P : Printer) -> struct
-
-  let print_decl k env (s,typ) =
-    let ptyp = P.pr_term k env typ in 
-    (spc () ++ pr_id s ++ str" : " ++ ptyp)
-  
-  let print_binding k env = function
-    | Anonymous,ty -> 
-	(spc () ++ str"_" ++ str" : " ++ P.pr_term k env ty)
-    | Name id,ty -> 
-	(spc () ++ pr_id id ++ str" : " ++ P.pr_term k env ty)
-
-(****
-  let sign_it_with f sign e =
-    snd (fold_named_context
-	   (fun (id,v,t) (sign,e) -> (add_named_decl (id,v,t) sign, f id t sign e))
-           sign (empty_named_context,e))
-
-  let dbenv_it_with f env e =
-    snd (dbenv_it 
-	   (fun na t (env,e) -> (add_rel_decl (na,t) env, f na t env e))
-           env (gLOB(get_globals env),e))
-****)
-      
-  let pr_env k env =
-    let sign_env =
-      fold_named_context
-	(fun env (id,_,t) pps ->
-           let pidt =  print_decl k env (id,t) in (pps ++ fnl () ++ pidt))
-	env (mt ()) 
-    in
-    let db_env =
-      fold_rel_context
-	(fun env (na,_,t) pps ->
-           let pnat = print_binding k env (na,t) in (pps ++ fnl () ++ pnat))
-	env (mt ())
-    in 
-    (sign_env ++ db_env)
-    
-  let pr_ne_ctx header k env =
-    if rel_context env = [] && named_context env = [] then
-      (mt ())
-    else
-      (header ++ pr_env k env)
-
-
-let explain_unbound_rel k ctx n =
-  let pe = pr_ne_ctx (str"in environment") k ctx in
-  (str"Unbound reference: " ++ pe ++ fnl () ++
-     str"The reference " ++ int n ++ str" is free")
-
-let explain_not_type k ctx c =
-  let pe = pr_ne_ctx (str"In environment") k ctx in
-  let pc = P.pr_term k ctx c in
-  (pe ++ cut () ++ str "the term" ++ brk(1,1) ++ pc ++ spc () ++
-     str"should be typed by Set, Prop or Type.");;
-
-let explain_bad_assumption k ctx c =
-  let pc = P.pr_term k ctx c in
-  (str "Cannot declare a variable or hypothesis over the term" ++
-     brk(1,1) ++ pc ++ spc () ++ str "because this term is not a type.");;
-
-let explain_reference_variables id =
-  (str "the constant" ++ spc () ++ pr_id id ++ spc () ++ 
-     str "refers to variables which are not in the context")
-
-let msg_bad_elimination ctx k = function
-  | Some(ki,kp,explanation) ->
-      let pki = P.pr_term k ctx ki in
-      let pkp = P.pr_term k ctx kp in
-      (hov 0 
-         (fnl () ++ str "Elimination of an inductive object of sort : " ++
-            pki ++ brk(1,0) ++
-            str "is not allowed on a predicate in sort : " ++ pkp ++fnl () ++
-            str "because" ++ spc () ++ str explanation))
-  | None -> 
-      (mt ())
-
-let explain_elim_arity k ctx ind aritylst c pj okinds = 
-  let pi = P.pr_term k ctx ind in
-  let ppar = prlist_with_sep pr_coma (P.pr_term k ctx) aritylst in
-  let pc = P.pr_term k ctx c in
-  let pp = P.pr_term k ctx pj.uj_val in
-  let ppt = P.pr_term k ctx pj.uj_type in
-  (str "Incorrect elimination of" ++ brk(1,1) ++ pc ++ spc () ++
-     str "in the inductive type" ++ brk(1,1) ++ pi ++ fnl () ++
-     str "The elimination predicate" ++ brk(1,1) ++ pp ++ spc () ++
-     str "has type" ++ brk(1,1) ++ ppt ++ fnl () ++
-     str "It should be one of :" ++ brk(1,1) ++ hov 0 ppar ++ fnl () ++
-     msg_bad_elimination ctx k okinds)
-
-let explain_case_not_inductive k ctx cj =
-  let pc = P.pr_term k ctx cj.uj_val in
-  let pct = P.pr_term k ctx cj.uj_type in
-  (str "In Cases expression" ++ brk(1,1) ++ pc ++ spc () ++ 
-     str "has type" ++ brk(1,1) ++ pct ++ spc () ++ 
-     str "which is not an inductive definition")
-  
-let explain_number_branches k ctx cj expn =
-  let pc = P.pr_term k ctx cj.uj_val in
-  let pct = P.pr_term k ctx cj.uj_val in
-  (str "Cases on term" ++ brk(1,1) ++ pc ++ spc () ++
-     str "of type" ++ brk(1,1) ++ pct ++ spc () ++
-     str "expects " ++  int expn ++ str " branches")
-
-let explain_ill_formed_branch k ctx c i actty expty =
-  let pc = P.pr_term k ctx c in
-  let pa = P.pr_term k ctx actty in
-  let pe = P.pr_term k ctx expty in
-  (str "In Cases expression on term" ++ brk(1,1) ++ pc ++
-     spc () ++ str "the branch " ++ int (i+1) ++
-     str " has type" ++ brk(1,1) ++ pa ++ spc () ++ 
-     str "which should be:" ++ brk(1,1) ++ pe)
-
-let explain_generalization k ctx (name,var) c =
-  let pe = pr_ne_ctx (str"in environment") k ctx in
-  let pv = P.pr_term k ctx var in
-  let pc = P.pr_term k (push_rel (name,None,var) ctx) c in
-  (str"Illegal generalization: " ++ pe ++ fnl () ++
-     str"Cannot generalize" ++ brk(1,1) ++ pv ++ spc () ++
-     str"over" ++ brk(1,1) ++ pc ++ spc () ++
-     str"which should be typed by Set, Prop or Type.")
-
-let explain_actual_type k ctx c ct pt =
-  let pe = pr_ne_ctx (str"In environment") k ctx in
-  let pc = P.pr_term k ctx c in
-  let pct = P.pr_term k ctx ct in
-  let pt = P.pr_term k ctx pt in
-  (pe ++ fnl () ++
-     str"The term" ++ brk(1,1) ++ pc ++ spc () ++
-     str"does not have type" ++ brk(1,1) ++ pt ++ fnl () ++
-     str"Actually, it has type" ++ brk(1,1) ++ pct)
-
-let explain_cant_apply_bad_type k ctx (n,exptyp,actualtyp) rator randl =
-  let ctx = make_all_name_different ctx in
-  let pe = pr_ne_ctx (str"in environment") k ctx in
-  let pr = pr_term k ctx rator.uj_val in
-  let prt = pr_term k ctx rator.uj_type in
-  let term_string = if List.length randl > 1 then "terms" else "term" in
-  let many = match n mod 10 with 1 -> "st" | 2 -> "nd" | _ -> "th" in
-  let appl = prlist_with_sep pr_fnl 
-	       (fun c ->
-		  let pc = pr_term k ctx c.uj_val in
-		  let pct = pr_term k ctx c.uj_type in
-		  hov 2 (pc ++ spc () ++ str": " ++ pct)) randl
-  in
-  (str"Illegal application (Type Error): " ++ pe ++ fnl () ++
-     str"The term" ++ brk(1,1) ++ pr ++ spc () ++
-     str"of type" ++ brk(1,1) ++ prt ++ spc () ++
-     str("cannot be applied to the "^term_string) ++ fnl () ++ 
-     str" " ++ v 0 appl ++ fnl () ++
-     str"The " ++int n ++ str (many^" term of type ") ++
-     pr_term k ctx actualtyp ++
-     str" should be of type " ++ pr_term k ctx exptyp)
-
-let explain_cant_apply_not_functional k ctx rator randl =
-  let ctx = make_all_name_different ctx in
-  let pe = pr_ne_ctx (str"in environment") k ctx in
-  let pr = pr_term k ctx rator.uj_val in
-  let prt = pr_term k ctx rator.uj_type in
-  let term_string = if List.length randl > 1 then "terms" else "term" in
-  let appl = prlist_with_sep pr_fnl 
-	       (fun c ->
-		  let pc = pr_term k ctx c.uj_val in
-		  let pct = pr_term k ctx c.uj_type in
-		  hov 2 (pc ++ spc () ++ str": " ++ pct)) randl
-  in
-  (str"Illegal application (Non-functional construction): " ++ pe ++ fnl () ++
-     str"The term" ++ brk(1,1) ++ pr ++ spc () ++
-     str"of type" ++ brk(1,1) ++ prt ++ spc () ++
-     str("cannot be applied to the "^term_string) ++ fnl () ++ 
-     str" " ++ v 0 appl ++ fnl ())
-
-(* (co)fixpoints *)
-let explain_ill_formed_rec_body k ctx err names i vdefs =
-  let str = match err with
-
-  (* Fixpoint guard errors *)
-  | NotEnoughAbstractionInFixBody ->
-      (str "Not enough abstractions in the definition")
-  | RecursionNotOnInductiveType ->
-      (str "Recursive definition on a non inductive type")
-  | RecursionOnIllegalTerm ->
-      (str "Recursive call applied to an illegal term")
-  | NotEnoughArgumentsForFixCall ->
-      (str "Not enough arguments for the recursive call")
-
-  (* CoFixpoint guard errors *)
-  (* TODO : récupérer le contexte des termes pour pouvoir les afficher *)
-  | CodomainNotInductiveType c ->
-      (str "The codomain is" ++ spc () ++ P.pr_term k ctx c ++ spc () ++
-	 str "which should be a coinductive type")
-  | NestedRecursiveOccurrences ->
-      (str "Nested recursive occurrences")
-  | UnguardedRecursiveCall c ->
-      (str "Unguarded recursive call")
-  | RecCallInTypeOfAbstraction c ->
-      (str "Not allowed recursive call in the domain of an abstraction")
-  | RecCallInNonRecArgOfConstructor c ->
-      (str "Not allowed recursive call in a non-recursive argument of constructor")
-  | RecCallInTypeOfDef c ->
-      (str "Not allowed recursive call in the type of a recursive definition")
-  | RecCallInCaseFun c ->
-      (str "Not allowed recursive call in a branch of cases")
-  | RecCallInCaseArg c -> 
-      (str "Not allowed recursive call in the argument of cases")
-  | RecCallInCasePred c ->
-      (str "Not allowed recursive call in the type of cases in")
-  | NotGuardedForm c ->
-      str "Sub-expression " ++ pr_lconstr_env ctx c ++ spc() ++
-      str "not in guarded form (should be a constructor, Cases or CoFix)"
-in
-  let pvd = P.pr_term k ctx vdefs.(i) in
-  let s =
-    match names.(i) with Name id -> string_of_id id | Anonymous -> "_" in
-  (str ++ fnl () ++ str"The " ++
-     if Array.length vdefs = 1 then (mt ()) else (int (i+1) ++ str "-th ") ++
-     str"recursive definition" ++ spc () ++ str s ++
-	 spc () ++ str":=" ++ spc () ++ pvd ++ spc () ++
-     str "is not well-formed")
-    
-let explain_ill_typed_rec_body k ctx i lna vdefj vargs =
-  let pvd = P.pr_term k ctx (vdefj.(i)).uj_val in
-  let pvdt = P.pr_term k ctx (vdefj.(i)).uj_type in
-  let pv = P.pr_term k ctx vargs.(i) in
-  (str"The " ++
-     if Array.length vdefj = 1 then (mt ()) else (int (i+1) ++ str "-th") ++
-     str"recursive definition" ++ spc () ++ pvd ++ spc () ++
-     str "has type" ++ spc () ++ pvdt ++spc () ++ str "it should be" ++ spc () ++ pv)
-
-let explain_not_inductive k ctx c =
-  let pc = P.pr_term k ctx c in
-  (str"The term" ++ brk(1,1) ++ pc ++ spc () ++
-     str "is not an inductive definition")
-
-let explain_ml_case k ctx mes c ct br brt =
-  let pc = P.pr_term k ctx c in
-  let pct = P.pr_term k ctx ct in
-  let expln =
-    match mes with
-      | "Inductive" -> (pct ++ str "is not an inductive definition")
-      | "Predicate" -> (str "ML case not allowed on a predicate")
-      | "Absurd" -> (str "Ill-formed case expression on an empty type")
-      | "Decomp" ->
-          let plf = P.pr_term k ctx br in
-          let pft = P.pr_term k ctx brt in
-          (str "The branch " ++ plf ++ ws 1 ++ cut () ++ str "has type " ++ pft ++
-             ws 1 ++ cut () ++
-             str "does not correspond to the inductive definition")
-      | "Dependent" ->
-          (str "ML case not allowed for a dependent case elimination")
-      | _ -> (mt ())
-  in
-  hov 0 (str "In ML case expression on " ++ pc ++ ws 1 ++ cut () ++
-           str "of type" ++  ws 1 ++ pct ++ ws 1 ++ cut () ++ 
-           str "which is an inductive predicate." ++ fnl () ++ expln)
-
-let explain_type_error k ctx = function
-  | UnboundRel n -> 
-      explain_unbound_rel k ctx n
-  | NotAType c -> 
-      explain_not_type k ctx c.uj_val
-  | BadAssumption c -> 
-      explain_bad_assumption k ctx c
-  | ReferenceVariables id -> 
-      explain_reference_variables id
-  | ElimArity (ind, aritylst, c, pj, okinds) ->
-      explain_elim_arity k ctx (mkMutInd ind) aritylst c pj okinds 
-  | CaseNotInductive cj -> 
-      explain_case_not_inductive k ctx cj
-  | NumberBranches (cj, n) -> 
-      explain_number_branches k ctx cj n
-  | IllFormedBranch (c, i, actty, expty) -> 
-      explain_ill_formed_branch k ctx c i actty expty 
-  | Generalization (nvar, c) ->
-      explain_generalization k ctx nvar c.uj_val
-  | ActualType (c, ct, pt) -> 
-      explain_actual_type k ctx c ct pt
-  | CantApplyBadType (s, rator, randl) ->
-      explain_cant_apply_bad_type k ctx s rator randl
-  | CantApplyNonFunctional (rator, randl) ->
-      explain_cant_apply_not_functional k ctx rator randl
-  | IllFormedRecBody (i, lna, vdefj, vargs) ->
-      explain_ill_formed_rec_body k ctx i lna vdefj vargs
-  | IllTypedRecBody (i, lna, vdefj, vargs) ->
-      explain_ill_typed_rec_body k ctx i lna vdefj vargs
-(*
-  | NotInductive c ->
-      explain_not_inductive k ctx c
-  | MLCase (mes,c,ct,br,brt) ->
-      explain_ml_case k ctx mes c ct br brt
-*)
-  | _ -> 
-      (str "Unknown type error (TODO)")
-
-let explain_refiner_bad_type k ctx arg ty conclty =
-  errorlabstrm "Logic.conv_leq_goal"
-    (str"refiner was given an argument" ++ brk(1,1) ++ 
-       P.pr_term k ctx arg ++ spc () ++
-       str"of type" ++ brk(1,1) ++ P.pr_term k ctx ty ++ spc () ++
-       str"instead of" ++ brk(1,1) ++ P.pr_term k ctx conclty)
-
-let explain_refiner_occur_meta k ctx t =
-  errorlabstrm "Logic.mk_refgoals"
-    (str"cannot refine with term" ++ brk(1,1) ++ P.pr_term k ctx t ++
-       spc () ++ str"because there are metavariables, and it is" ++
-       spc () ++ str"neither an application nor a Case")
-
-let explain_refiner_cannot_applt k ctx t harg =
-  errorlabstrm "Logic.mkARGGOALS"
-    (str"in refiner, a term of type " ++ brk(1,1) ++
-       P.pr_term k ctx t ++ spc () ++ str"could not be applied to" ++ brk(1,1) ++
-       P.pr_term k ctx harg)
-
-let explain_occur_check k ctx ev rhs =
-  let id = "?" ^ string_of_int ev in
-  let pt = P.pr_term k ctx rhs in
-  errorlabstrm "Trad.occur_check"
-    (str"Occur check failed: tried to define " ++ str id ++
-      str" with term" ++ brk(1,1) ++ pt)
-
-let explain_not_clean k ctx sp t =
-  let c = mkRel (Intset.choose (free_rels t)) in
-  let id = string_of_id (Names.basename sp) in
-  let var = P.pr_term k ctx c in
-  errorlabstrm "Trad.not_clean"
-    (str"Tried to define " ++ str id ++
-       str" with a term using variable " ++ var ++ spc () ++
-       str"which is not in its scope.")
-
-end
diff --git a/toplevel/himsg.ml b/toplevel/himsg.ml
index 579acffa..41783faa 100644
--- a/toplevel/himsg.ml
+++ b/toplevel/himsg.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: himsg.ml 11150 2008-06-19 11:38:27Z msozeau $ *)
+(* $Id: himsg.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -392,7 +392,7 @@ let explain_cannot_unify env m n =
   let pm = pr_lconstr_env env m in
   let pn = pr_lconstr_env env n in
   str "Impossible to unify" ++ brk(1,1) ++ pm ++ spc () ++
-  str "with" ++ brk(1,1) ++ pn
+  str "with" ++ brk(1,1) ++ pn ++ str "."
 
 let explain_cannot_unify_local env m n subn =
   let pm = pr_lconstr_env env m in
@@ -400,34 +400,31 @@ let explain_cannot_unify_local env m n subn =
   let psubn = pr_lconstr_env env subn in
     str "Impossible to unify" ++ brk(1,1) ++ pm ++ spc () ++
       str "with" ++ brk(1,1) ++ pn ++ spc () ++ str "as" ++ brk(1,1) ++
-      psubn ++ str " contains local variables"
+      psubn ++ str " contains local variables."
 
 let explain_refiner_cannot_generalize env ty =
   str "Cannot find a well-typed generalisation of the goal with type: " ++
-  pr_lconstr_env env ty
+  pr_lconstr_env env ty ++ str "."
 
 let explain_no_occurrence_found env c id =
   str "Found no subterm matching " ++ pr_lconstr_env env c ++
   str " in " ++ 
     (match id with
       | Some id -> pr_id id
-      | None -> str"the current goal")
+      | None -> str"the current goal") ++ str "."
 
 let explain_cannot_unify_binding_type env m n =
   let pm = pr_lconstr_env env m in
   let pn = pr_lconstr_env env n in
   str "This binding has type" ++ brk(1,1) ++ pm ++ spc () ++
-  str "which should be unifiable with" ++ brk(1,1) ++ pn
+  str "which should be unifiable with" ++ brk(1,1) ++ pn ++ str "."
 
 let explain_cannot_find_well_typed_abstraction env p l =
-  let la,lc = list_chop (List.length l - 1) l in
   str "Abstracting over the " ++
   str (plural (List.length l) "term") ++ spc () ++ 
-  hov 0 (prlist_with_sep pr_coma (pr_lconstr_env env) la ++
-         (if la<>[] then str " and" ++ spc () else mt()) ++ 
-         pr_lconstr_env env (List.hd lc)) ++ spc () ++
+  hov 0 (pr_enum (pr_lconstr_env env) l) ++ spc () ++
   str "leads to a term" ++ spc () ++ pr_lconstr_env env p ++ spc () ++ 
-  str "which is ill-typed"
+  str "which is ill-typed."
 
 let explain_type_error env err =
   let env = make_all_name_different env in
@@ -487,11 +484,11 @@ let explain_pretype_error env err =
 (* Typeclass errors *)
 
 let explain_not_a_class env c =
-  pr_constr_env env c ++ str" is not a declared type class"
+  pr_constr_env env c ++ str" is not a declared type class."
 
 let explain_unbound_method env cid id =
   str "Unbound method name " ++ Nameops.pr_id (snd id) ++ spc () ++ str"of class" ++ spc () ++ 
-    pr_global cid
+    pr_global cid ++ str "."
 
 let pr_constr_exprs exprs = 
   hv 0 (List.fold_right 
@@ -532,7 +529,7 @@ let explain_unsatisfiable_constraints env evd constr =
 	
 let explain_mismatched_contexts env c i j = 
   str"Mismatched contexts while declaring instance: " ++ brk (1,1) ++
-    hov 1 (str"Expected:" ++ brk (1, 1) ++ pr_named_context env j) ++ fnl () ++ brk (1,1) ++ 
+    hov 1 (str"Expected:" ++ brk (1, 1) ++ pr_rel_context env j) ++ fnl () ++ brk (1,1) ++ 
     hov 1 (str"Found:" ++ brk (1, 1) ++ pr_constr_exprs i)
 
 let explain_typeclass_error env err = 
@@ -549,21 +546,20 @@ let explain_refiner_bad_type arg ty conclty =
   str "Refiner was given an argument" ++ brk(1,1) ++
   pr_lconstr arg ++ spc () ++
   str "of type" ++ brk(1,1) ++ pr_lconstr ty ++ spc () ++
-  str "instead of" ++ brk(1,1) ++ pr_lconstr conclty
+  str "instead of" ++ brk(1,1) ++ pr_lconstr conclty ++ str "."
 
 let explain_refiner_unresolved_bindings l =
-  let l = map_succeed (function Name id -> id | _ -> failwith "") l in
   str "Unable to find an instance for the " ++ 
   str (plural (List.length l) "variable") ++ spc () ++
-  prlist_with_sep pr_coma pr_id l
+  prlist_with_sep pr_coma pr_name l ++ str"."
 
 let explain_refiner_cannot_apply t harg =
-  str "In refiner, a term of type " ++ brk(1,1) ++
+  str "In refiner, a term of type" ++ brk(1,1) ++
   pr_lconstr t ++ spc () ++ str "could not be applied to" ++ brk(1,1) ++
-  pr_lconstr harg
+  pr_lconstr harg ++ str "."
 
 let explain_refiner_not_well_typed c =
-  str "The term " ++ pr_lconstr c ++ str " is not well-typed"
+  str "The term " ++ pr_lconstr c ++ str " is not well-typed."
 
 let explain_intro_needs_product () =
   str "Introduction tactics needs products."
@@ -706,7 +702,7 @@ let explain_bad_constructor env cstr ind =
   str "is expected."
 
 let decline_string n s =
-  if n = 0 then "no "^s
+  if n = 0 then "no "^s^"s"
   else if n = 1 then "1 "^s
   else (string_of_int n^" "^s^"s")
 
@@ -781,3 +777,40 @@ let explain_reduction_tactic_error = function
       str "The abstracted term" ++ spc () ++ pr_lconstr_env_at_top env c ++
       spc () ++ str "is not well typed." ++ fnl () ++
       explain_type_error env' e
+
+let explain_ltac_call_trace (last,trace,loc) =
+  let calls = last :: List.rev (List.map snd trace) in
+  let pr_call = function
+  | Proof_type.LtacNotationCall s -> quote (str s)
+  | Proof_type.LtacNameCall cst -> quote (Pptactic.pr_ltac_constant cst)
+  | Proof_type.LtacVarCall (id,t) ->
+      quote (Nameops.pr_id id) ++ strbrk " (bound to " ++ 
+      Pptactic.pr_glob_tactic (Global.env()) t ++ str ")"
+  | Proof_type.LtacAtomCall (te,otac) -> quote
+      (Pptactic.pr_glob_tactic (Global.env())
+	(Tacexpr.TacAtom (dummy_loc,te)))
+      ++ (match !otac with
+      | Some te' when (Obj.magic te' <> te) ->
+	  strbrk " (expanded to " ++ quote
+	  (Pptactic.pr_tactic (Global.env())
+	    (Tacexpr.TacAtom (dummy_loc,te')))
+	++ str ")"
+      | _ -> mt ())
+  | Proof_type.LtacConstrInterp (c,(vars,unboundvars)) ->
+      let filter =
+	function (id,None) -> None | (id,Some id') -> Some(id,mkVar id') in
+      let unboundvars = list_map_filter filter unboundvars in
+      quote (pr_rawconstr_env (Global.env()) c) ++
+      (if unboundvars <> [] or vars <> [] then
+	strbrk " (with " ++ prlist_with_sep pr_coma (fun (id,c) -> 
+	pr_id id ++ str ":=" ++ Printer.pr_lconstr c)
+	  (List.rev vars @ unboundvars)
+       else mt()) ++ str ")" in
+  if calls <> [] then
+    let kind_of_last_call = match list_last calls with
+    | Proof_type.LtacConstrInterp _ -> ", last term evaluation failed."
+    | _ -> ", last call failed." in
+    hov 0 (str "In nested Ltac calls to " ++ 
+           pr_enum pr_call calls ++ strbrk kind_of_last_call)
+  else
+    mt ()
diff --git a/toplevel/himsg.mli b/toplevel/himsg.mli
index 1b9e38ce..ff5991de 100644
--- a/toplevel/himsg.mli
+++ b/toplevel/himsg.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: himsg.mli 10410 2007-12-31 13:11:55Z msozeau $ i*)
+(*i $Id: himsg.mli 11309 2008-08-06 10:30:35Z herbelin $ i*)
 
 (*i*)
 open Pp
@@ -40,3 +40,6 @@ val explain_pattern_matching_error :
 
 val explain_reduction_tactic_error :
   Tacred.reduction_tactic_error -> std_ppcmds
+
+val explain_ltac_call_trace : 
+  Proof_type.ltac_call_kind * Proof_type.ltac_trace * Util.loc -> std_ppcmds
diff --git a/toplevel/metasyntax.ml b/toplevel/metasyntax.ml
index fbeaea34..89ba6aac 100644
--- a/toplevel/metasyntax.ml
+++ b/toplevel/metasyntax.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: metasyntax.ml 11121 2008-06-12 21:15:49Z herbelin $ *)
+(* $Id: metasyntax.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -127,7 +127,7 @@ let print_grammar = function
       Gram.Entry.print Pcoq.Vernac_.gallina;
       msgnl (str "Entry gallina_ext is");
       Gram.Entry.print Pcoq.Vernac_.gallina_ext;
-  | _ -> error "Unknown or unprintable grammar entry"
+  | _ -> error "Unknown or unprintable grammar entry."
 
 (**********************************************************************)
 (* Parse a format (every terminal starting with a letter or a single
@@ -143,11 +143,11 @@ let parse_format (loc,str) =
     if n = 0 then l else push_token (UnpTerminal (String.make n ' ')) l in
   let close_box i b = function
     | a::(_::_ as l) -> push_token (UnpBox (b,a)) l
-    | _ -> error "Non terminated box in format" in
+    | _ -> error "Non terminated box in format." in
   let close_quotation i =
     if i < String.length str & str.[i] = '\'' & (i+1 = l or str.[i+1] = ' ')
     then i+1
-    else error "Incorrectly terminated quoted expression" in
+    else error "Incorrectly terminated quoted expression." in
   let rec spaces n i =
     if i < String.length str & str.[i] = ' ' then spaces (n+1) (i+1)
     else n in
@@ -155,10 +155,10 @@ let parse_format (loc,str) =
     if i < String.length str & str.[i] <> ' ' then
       if str.[i] = '\'' & quoted &
         (i+1 >= String.length str or str.[i+1] = ' ')
-      then if n=0 then error "Empty quoted token" else n
+      then if n=0 then error "Empty quoted token." else n
       else nonspaces quoted (n+1) (i+1)
     else
-      if quoted then error "Spaces are not allowed in (quoted) symbols"
+      if quoted then error "Spaces are not allowed in (quoted) symbols."
       else n in
   let rec parse_non_format i =
     let n = nonspaces false 0 i in
@@ -189,8 +189,8 @@ let parse_format (loc,str) =
 		(* Parse " [ .. ",  *)
 	    | ' ' | '\'' ->
 		parse_box (fun n -> PpHOVB n) (i+1)
-	    | _ -> error "\"v\", \"hv\", \" \" expected after \"[\" in format"
-	  else error "\"v\", \"hv\" or \" \" expected after \"[\" in format"
+	    | _ -> error "\"v\", \"hv\", \" \" expected after \"[\" in format."
+	  else error "\"v\", \"hv\" or \" \" expected after \"[\" in format."
       (* Parse "]"  *)
       | ']' ->
 	  ([] :: parse_token (close_quotation (i+1)))
@@ -201,7 +201,7 @@ let parse_format (loc,str) =
 	    (parse_token (close_quotation (i+n))))
     else
       if n = 0 then []
-      else error "Ending spaces non part of a format annotation"
+      else error "Ending spaces non part of a format annotation."
   and parse_box box i =
     let n = spaces 0 i in
     close_box i (box n) (parse_token (close_quotation (i+n)))
@@ -223,9 +223,9 @@ let parse_format (loc,str) =
   try
     if str <> "" then match parse_token 0 with
       | [l] -> l
-      | _ -> error "Box closed without being opened in format"
+      | _ -> error "Box closed without being opened in format."
     else
-      error "Empty format"
+      error "Empty format."
   with e ->
     Stdpp.raise_with_loc loc e
 
@@ -274,11 +274,11 @@ let rec find_pattern xl = function
   | [NonTerminal x], NonTerminal x' :: l' ->
       (x,x',xl),l'
   | [NonTerminal _], Terminal s :: _ | Terminal s :: _, _ ->
-      error ("The token "^s^" occurs on one side of \"..\" but not on the other side")
+      error ("The token "^s^" occurs on one side of \"..\" but not on the other side.")
   | [NonTerminal _], Break s :: _ | Break s :: _, _ ->
-      error ("A break occurs on one side of \"..\" but not on the other side")
+      error ("A break occurs on one side of \"..\" but not on the other side.")
   | ((SProdList _ | NonTerminal _) :: _ | []), _ -> 
-      error ("The special symbol \"..\" must occur in a configuration of the form\n\"x symbs .. symbs y\"")
+      error ("The special symbol \"..\" must occur in a configuration of the form\n\"x symbs .. symbs y\".")
 
 let rec interp_list_parser hd = function
   | [] -> [], List.rev hd
@@ -320,12 +320,13 @@ let rec raw_analyse_notation_tokens = function
   | String ".." :: sl ->
       let (vars,l) = raw_analyse_notation_tokens sl in
       (list_add_set ldots_var vars, NonTerminal ldots_var :: l)
+  | String "_" :: _ -> error "_ must be quoted."
   | String x :: sl when is_normal_token x ->
       Lexer.check_ident x;
       let id = Names.id_of_string x in
       let (vars,l) = raw_analyse_notation_tokens sl in
       if List.mem id vars then
-	error ("Variable "^x^" occurs more than once");
+	error ("Variable "^x^" occurs more than once.");
       (id::vars, NonTerminal id :: l)
   | String s :: sl ->
       Lexer.check_keyword s;
@@ -481,10 +482,10 @@ let make_hunks etyps symbols from =
 
 (* Build default printing rules from explicit format *)
 
-let error_format () = error "The format does not match the notation"
+let error_format () = error "The format does not match the notation."
 
 let rec split_format_at_ldots hd = function
-  | UnpTerminal s :: fmt when id_of_string s = ldots_var -> List.rev hd, fmt
+  | UnpTerminal s :: fmt when s = string_of_id ldots_var -> List.rev hd, fmt
   | u :: fmt -> 
       check_no_ldots_in_box u;
       split_format_at_ldots (u::hd) fmt
@@ -494,7 +495,7 @@ and check_no_ldots_in_box = function
   | UnpBox (_,fmt) ->
       (try 
         let _ = split_format_at_ldots [] fmt in
-        error ("The special symbol \"..\" must occur at the same formatting depth than the variables of which it is the ellipse")
+        error ("The special symbol \"..\" must occur at the same formatting depth than the variables of which it is the ellipse.")
       with Exit -> ())
   | _ -> ()
 
@@ -512,7 +513,7 @@ let read_recursive_format sl fmt =
   let rec get_tail = function
     | a :: sepfmt, b :: fmt when a = b -> get_tail (sepfmt, fmt)
     | [], tail -> skip_var_in_recursive_format tail
-    | _ -> error "The format is not the same on the right and left hand side of the special token \"..\"" in
+    | _ -> error "The format is not the same on the right and left hand side of the special token \"..\"." in
   let slfmt, fmt = get_head fmt in
   slfmt, get_tail (slfmt, fmt)
 
@@ -594,7 +595,7 @@ let make_production etyps symbols =
 	    let y = match List.assoc x etyps with
               | ETConstr x -> x
               | _ ->
-                  error "Component of recursive patterns in notation must be constr" in
+                  error "Component of recursive patterns in notation must be constr." in
             let typ = ETConstrList (y,sl) in
             NonTerm (typ, Some (x,typ)) :: l)
       symbols [] in
@@ -640,7 +641,7 @@ let error_incompatible_level ntn oldprec prec =
     (str ("Notation "^ntn^" is already defined") ++ spc() ++ 
     pr_level ntn oldprec ++ 
     spc() ++ str "while it is now required to be" ++ spc() ++ 
-    pr_level ntn prec)
+    pr_level ntn prec ++ str ".")
 
 let cache_one_syntax_extension (prec,ntn,gr,pp) =
   try 
@@ -692,34 +693,34 @@ let interp_modifiers modl =
     | SetEntryType (s,typ) :: l ->
 	let id = id_of_string s in
 	if List.mem_assoc id etyps then
-	  error (s^" is already assigned to an entry or constr level");
+	  error (s^" is already assigned to an entry or constr level.");
 	interp assoc level ((id,typ)::etyps) format l
     | SetItemLevel ([],n) :: l ->
 	interp assoc level etyps format l
     | SetItemLevel (s::idl,n) :: l ->
 	let id = id_of_string s in
 	if List.mem_assoc id etyps then
-	  error (s^" is already assigned to an entry or constr level");
+	  error (s^" is already assigned to an entry or constr level.");
 	let typ = ETConstr (n,()) in
 	interp assoc level ((id,typ)::etyps) format (SetItemLevel (idl,n)::l)
     | SetLevel n :: l ->
-	if level <> None then error "A level is given more than once";
+	if level <> None then error "A level is given more than once.";
 	interp assoc (Some n) etyps format l
     | SetAssoc a :: l ->
-	if assoc <> None then error "An associativity is given more than once";
+	if assoc <> None then error"An associativity is given more than once.";
 	interp (Some a) level etyps format l
     | SetOnlyParsing :: l ->
 	onlyparsing := true;
 	interp assoc level etyps format l
     | SetFormat s :: l ->
-	if format <> None then error "A format is given more than once";
+	if format <> None then error "A format is given more than once.";
 	interp assoc level etyps (Some s) l
   in interp None None [] None modl
 
 let check_infix_modifiers modifiers =
   let (assoc,level,t,b,fmt) = interp_modifiers modifiers in
   if t <> [] then
-    error "explicit entry level or type unexpected in infix notation"
+    error "explicit entry level or type unexpected in infix notation."
 
 let no_syntax_modifiers modifiers = 
   modifiers = [] or modifiers = [SetOnlyParsing]
@@ -739,9 +740,9 @@ let set_entry_type etyps (x,typ) =
 
 let check_rule_productivity l = 
   if List.for_all (function NonTerminal _ -> true | _ -> false) l then
-    error "A notation must include at least one symbol";
+    error "A notation must include at least one symbol.";
   if (match l with SProdList _ :: _ -> true | _ -> false) then
-    error "A recursive notation must start with at least one symbol"
+    error "A recursive notation must start with at least one symbol."
 
 let is_not_printable = function
   | AVar _ -> warning "This notation won't be used for printing as it is bound to a \nsingle variable"; true
@@ -752,38 +753,38 @@ let find_precedence lev etyps symbols =
   | NonTerminal x :: _ ->
       (try match List.assoc x etyps with
 	| ETConstr _ ->
-	    error "The level of the leftmost non-terminal cannot be changed"
+	    error "The level of the leftmost non-terminal cannot be changed."
 	| ETIdent | ETBigint | ETReference -> 
 	    if lev = None then 
-	      Flags.if_verbose msgnl (str "Setting notation at level 0")
+	      Flags.if_verbose msgnl (str "Setting notation at level 0.")
 	    else
 	    if lev <> Some 0 then
-	      error "A notation starting with an atomic expression must be at level 0";
+	      error "A notation starting with an atomic expression must be at level 0.";
 	    0
 	| ETPattern | ETOther _ -> (* Give a default ? *)
 	    if lev = None then
-	      error "Need an explicit level"
+	      error "Need an explicit level."
 	    else Option.get lev
         | ETConstrList _ -> assert false (* internally used in grammar only *)
       with Not_found -> 
 	if lev = None then
-	  error "A left-recursive notation must have an explicit level"
+	  error "A left-recursive notation must have an explicit level."
 	else Option.get lev)
   | Terminal _ ::l when
       (match list_last symbols with Terminal _ -> true |_ -> false)
       -> 
       if lev = None then
-	(Flags.if_verbose msgnl (str "Setting notation at level 0"); 0)
+	(Flags.if_verbose msgnl (str "Setting notation at level 0."); 0)
       else Option.get lev
   | _ ->
-      if lev = None then error "Cannot determine the level";
+      if lev = None then error "Cannot determine the level.";
       Option.get lev
 
 let check_curly_brackets_notation_exists () =
   try let _ = Notation.level_of_notation "{ _ }" in ()
   with Not_found -> 
     error "Notations involving patterns of the form \"{ _ }\" are treated \n\
-specially and require that the notation \"{ _ }\" is already reserved"
+specially and require that the notation \"{ _ }\" is already reserved."
 
 (* Remove patterns of the form "{ _ }", unless it is the "{ _ }" notation *)
 let remove_curly_brackets l = 
@@ -970,7 +971,7 @@ let add_syntax_extension local mv =
 let add_notation_interpretation df names c sc =
   try add_notation_interpretation_core false df names c sc false
   with NoSyntaxRule ->
-    error "Parsing rule for this notation has to be previously declared"
+    error "Parsing rule for this notation has to be previously declared."
 
 (* Main entry point *)
 
diff --git a/toplevel/minicoq.ml b/toplevel/minicoq.ml
deleted file mode 100644
index e688d50e..00000000
--- a/toplevel/minicoq.ml
+++ /dev/null
@@ -1,149 +0,0 @@
-(************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
-(************************************************************************)
-
-(* $Id: minicoq.ml 10346 2007-12-05 21:11:19Z aspiwack $ *)
-
-open Pp
-open Util
-open Names
-open Term
-open Sign
-open Declarations
-open Inductive
-open Type_errors
-open Safe_typing
-open G_minicoq
-
-let (env : safe_environment ref) = ref empty_environment
-
-let locals () =
-  List.map (fun (id,b,t) -> (id, make_path [] id CCI))
-    (named_context !env)
-
-let lookup_named id =
-  let rec look n = function
-    | [] -> mkVar id
-    | (Name id')::_ when id = id' -> mkRel n
-    | _::r -> look (succ n) r
-  in
-  look 1
-
-let args sign = Array.of_list (instance_from_section_context sign)
-
-let rec globalize bv c = match kind_of_term c with
-  | Var id -> lookup_named id bv
-  | Const (sp, _) ->
-      let cb = lookup_constant sp !env in mkConst (sp, args cb.const_hyps)
-  | Ind (sp,_ as spi, _) ->
-      let mib = lookup_mind sp !env in mkMutInd (spi, args mib.mind_hyps)
-  | Construct ((sp,_),_ as spc, _) ->
-      let mib = lookup_mind sp !env in mkMutConstruct (spc, args mib.mind_hyps)
-  | _ -> map_constr_with_named_binders (fun na l -> na::l) globalize bv c
-
-let check c = 
-  let c = globalize [] c in
-  let (j,u) = safe_infer !env c in
-  let ty = j_type j in
-  let pty = pr_term CCI (env_of_safe_env !env) ty in
-  mSGNL (hov 0 (str"  :" ++ spc () ++ hov 0 pty ++ fnl ()))
-
-let definition id ty c =
-  let c = globalize [] c in
-  let ty = Option.map (globalize []) ty in
-  let ce = { const_entry_body = c; const_entry_type = ty } in
-  let sp = make_path [] id CCI in
-  env := add_constant sp ce (locals()) !env;
-  mSGNL (hov 0 (pr_id id ++ spc () ++ str"is defined" ++ fnl ()))
-
-let parameter id t =
-  let t = globalize [] t in
-  let sp = make_path [] id CCI in
-  env := add_parameter sp t (locals()) !env;
-  mSGNL (hov 0 (str"parameter" ++ spc () ++ pr_id id ++ 
-		  spc () ++ str"is declared" ++ fnl ()))
-
-let variable id t =
-  let t = globalize [] t in
-  env := push_named_assum (id,t) !env;
-  mSGNL (hov 0 (str"variable" ++ spc () ++ pr_id id ++ 
-		  spc () ++ str"is declared" ++ fnl ()))
-
-let inductive par inds =
-  let nparams = List.length par in
-  let bvpar = List.rev (List.map (fun (id,_) -> Name id) par) in
-  let name_inds = List.map (fun (id,_,_) -> Name id) inds in
-  let bv = bvpar @  List.rev name_inds in
-  let npar = List.map (fun (id,c) -> (Name id, globalize [] c)) par in
-  let one_inductive (id,ar,cl) =
-    let cv = List.map (fun (_,c) -> prod_it (globalize bv c) npar) cl in
-    { mind_entry_nparams = nparams;
-      mind_entry_params = List.map (fun (id,c) -> (id, LocalAssum c)) par;
-      mind_entry_typename = id;
-      mind_entry_arity = prod_it (globalize bvpar ar) npar;
-      mind_entry_consnames = List.map fst cl;
-      mind_entry_lc = cv }
-  in
-  let inds = List.map one_inductive inds in
-  let mie = { 
-    mind_entry_finite = true;
-    mind_entry_inds = inds }
-  in
-  let sp =
-    let mi1 = List.hd inds in
-    make_path [] mi1.mind_entry_typename CCI in
-  env := add_mind sp mie (locals()) !env;
-  mSGNL (hov 0 (str"inductive type(s) are declared" ++ fnl ()))
-
-
-let execute = function
-  | Check c -> check c
-  | Definition (id, ty, c) -> definition id ty c
-  | Parameter (id, t) -> parameter id t
-  | Variable (id, t) -> variable id t
-  | Inductive (par,inds) -> inductive par inds
-
-let parse_file f =
-  let c = open_in f in
-  let cs = Stream.of_channel c in
-  try
-    while true do
-      let c = Grammar.Entry.parse command cs in execute c
-    done
-  with 
-    | End_of_file | Stdpp.Exc_located (_, End_of_file) -> close_in c; exit 0
-    | exn -> close_in c; raise exn
-
-module Explain = Fhimsg.Make(struct let pr_term = pr_term end)
-
-let rec explain_exn = function
-  | TypeError (k,ctx,te) -> 
-      mSGNL (hov 0 (str "type error:" ++ spc () ++ 
-		      Explain.explain_type_error k ctx te ++ fnl ()))
-  | Stdpp.Exc_located (_,exn) -> 
-      explain_exn exn
-  | exn -> 
-      mSGNL (hov 0 (str"error: " ++ str (Printexc.to_string exn) ++ fnl ()))
-
-let top () =
-  let cs = Stream.of_channel stdin in
-  while true do
-    try
-      let c = Grammar.Entry.parse command cs in execute c
-    with 
-      | End_of_file | Stdpp.Exc_located (_, End_of_file) -> exit 0
-      | exn -> explain_exn exn
-  done
-
-let main () =
-  if Array.length Sys.argv = 1 then
-    parse_file "test"
-  else
-    if Sys.argv.(1) = "-top" then top () else parse_file (Sys.argv.(1))
-
-let _ = Printexc.print main ()
-
diff --git a/toplevel/mltop.ml4 b/toplevel/mltop.ml4
index 30cffa34..ac30f890 100644
--- a/toplevel/mltop.ml4
+++ b/toplevel/mltop.ml4
@@ -11,7 +11,7 @@
  * camlp4deps will not work for this file unless Makefile system enhanced.
  *)
 
-(* $Id: mltop.ml4 10348 2007-12-06 17:36:14Z aspiwack $ *)
+(* $Id: mltop.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Util
 open Pp
@@ -99,8 +99,8 @@ let dir_ml_load s =
       (try t.load_obj s
        with
        | (UserError _ | Failure _ | Anomaly _ | Not_found as u) -> raise u
-       | _ -> errorlabstrm "Mltop.load_object" [< str"Cannot link ml-object ";
-                str s; str" to Coq code." >])
+       | _ -> errorlabstrm "Mltop.load_object" (str"Cannot link ml-object " ++
+                str s ++ str" to Coq code."))
 (* TO DO: .cma loading without toplevel *)
     | WithoutTop ->
       IFDEF Byte THEN
@@ -108,7 +108,7 @@ let dir_ml_load s =
 	 * if this code section starts to use a module not used elsewhere
 	 * in this file, the Makefile dependency logic needs to be updated.
 	 *)
-        let _,gname = where_in_path !coq_mlpath_copy s in
+        let _,gname = where_in_path true !coq_mlpath_copy s in
         try
           Dynlink.loadfile gname;
 	  Dynlink.add_interfaces 
@@ -116,11 +116,11 @@ let dir_ml_load s =
 				(Filename.basename gname) ".cmo"))] 
 	    [Filename.dirname gname]
 	with | Dynlink.Error a ->
-          errorlabstrm "Mltop.load_object" [< str (Dynlink.error_message a) >]
+          errorlabstrm "Mltop.load_object" (str (Dynlink.error_message a))
       ELSE () END
     | Native ->
 	errorlabstrm "Mltop.no_load_object"
-          [< str"Loading of ML object file forbidden in a native Coq" >]
+          (str"Loading of ML object file forbidden in a native Coq.")
 
 (* Dynamic interpretation of .ml *)
 let dir_ml_use s =
@@ -145,10 +145,10 @@ let add_path ~unix_path:dir ~coq_root:coq_dirpath =
   if exists_dir dir then
     begin
       add_ml_dir dir;
-      Library.add_load_path (dir,coq_dirpath)
+      Library.add_load_path true (dir,coq_dirpath)
     end
   else
-    msg_warning [< str ("Cannot open " ^ dir) >]
+    msg_warning (str ("Cannot open " ^ dir))
 
 let convert_string d =
   try Names.id_of_string d
@@ -159,19 +159,18 @@ let convert_string d =
     failwith "caught"
 
 let add_rec_path ~unix_path:dir ~coq_root:coq_dirpath =
-  let dirs = all_subdirs dir in
-  let prefix = Names.repr_dirpath coq_dirpath in
-  if dirs <> [] then
+  if exists_dir dir then
+    let dirs = all_subdirs dir in
+    let prefix = Names.repr_dirpath coq_dirpath in
     let convert_dirs (lp,cp) =
-      (lp,Names.make_dirpath
-            ((List.map convert_string (List.rev cp))@prefix)) in
+      (lp,Names.make_dirpath (List.map convert_string (List.rev cp)@prefix)) in
     let dirs = map_succeed convert_dirs dirs in
-    begin
-      List.iter (fun lpe -> add_ml_dir (fst lpe)) dirs;
-      List.iter Library.add_load_path dirs
-    end
+    List.iter (fun lpe -> add_ml_dir (fst lpe)) dirs;
+    add_ml_dir dir;
+    List.iter (Library.add_load_path false) dirs;
+    Library.add_load_path true (dir,Names.make_dirpath prefix)
   else
-    msg_warning [< str ("Cannot open " ^ dir) >]
+    msg_warning (str ("Cannot open " ^ dir))
 
 (* convertit un nom quelconque en nom de fichier ou de module *) 
 let mod_of_name name =
@@ -191,7 +190,7 @@ let file_of_name name =
   if (is_in_path !coq_mlpath_copy fname) then fname
   else
     errorlabstrm "Mltop.load_object"
-      [< str"File not found on loadpath : "; str (bname^".cm[oa]") >]
+      (str"File not found on loadpath : " ++ str (bname^".cm[oa]"))
 
 (* TODO: supprimer ce hack, si possible *)
 (* Initialisation of ML modules that need the state (ex: tactics like
@@ -248,7 +247,7 @@ let unfreeze_ml_modules x =
            load_object mname fname
          else 
 	   errorlabstrm "Mltop.unfreeze_ml_modules"
-             [< str"Loading of ML object file forbidden in a native Coq" >];
+             (str"Loading of ML object file forbidden in a native Coq.");
        add_loaded_module mname)
     x
 
@@ -271,11 +270,11 @@ let cache_ml_module_object (_,{mnames=mnames}) =
          begin 
 	   try 
 	     if_verbose 
-	       msg [< str"[Loading ML file "; str fname; str" ..." >];
+	       msg (str"[Loading ML file " ++ str fname ++ str" ...");
              load_object mname fname;
-             if_verbose msgnl [< str"done]" >]
+             if_verbose msgnl (str"done]")
            with e -> 
-	     if_verbose msgnl [< str"failed]" >]; 
+	     if_verbose msgnl (str"failed]"); 
 	     raise e
 	 end;
          add_loaded_module mname)
@@ -294,11 +293,11 @@ let declare_ml_modules l =
     
 let print_ml_path () =
   let l = !coq_mlpath_copy in
-  ppnl [< str"ML Load Path:"; fnl (); str"  ";
-          hv 0 (prlist_with_sep pr_fnl pr_str l) >]
+  ppnl (str"ML Load Path:" ++ fnl () ++ str"  " ++
+          hv 0 (prlist_with_sep pr_fnl pr_str l))
 
 	  (* Printing of loaded ML modules *)
 	  
 let print_ml_modules () =
   let l = get_loaded_modules () in
-  pp [< str"Loaded ML Modules: " ; pr_vertical_list pr_str l >]
+  pp (str"Loaded ML Modules: " ++ pr_vertical_list pr_str l)
diff --git a/toplevel/record.ml b/toplevel/record.ml
index 5629bb71..306ab047 100644
--- a/toplevel/record.ml
+++ b/toplevel/record.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: record.ml 11024 2008-05-30 12:41:39Z msozeau $ *)
+(* $Id: record.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -31,29 +31,46 @@ open Topconstr
 
 (********** definition d'un record (structure) **************)
 
-let interp_decl sigma env = function
-  | Vernacexpr.AssumExpr((_,id),t) -> (id,None,interp_type Evd.empty env t)
-  | Vernacexpr.DefExpr((_,id),c,t) ->
-      let c = match t with
-	| None -> c
-	| Some t -> mkCastC (c, Rawterm.CastConv (DEFAULTcast,t))
-      in
-      let j = interp_constr_judgment Evd.empty env c in
-      (id,Some j.uj_val, refresh_universes j.uj_type)
+let interp_evars evdref env ?(impls=([],[])) k typ =
+  let typ' = intern_gen true ~impls (Evd.evars_of !evdref) env typ in
+  let imps = Implicit_quantifiers.implicits_of_rawterm typ' in
+    imps, Pretyping.Default.understand_tcc_evars evdref env k typ'
+
+let mk_interning_data env na impls typ =
+  let impl = Impargs.compute_implicits_with_manual env typ (Impargs.is_implicit_args()) impls
+  in (out_name na, ([], impl, Notation.compute_arguments_scope typ))
+    
+let interp_fields_evars isevars env l =
+  List.fold_left
+    (fun (env, uimpls, params, impls) ((loc, i), b, t) ->
+      let impl, t' = interp_evars isevars env ~impls Pretyping.IsType t in
+      let b' = Option.map (fun x -> snd (interp_evars isevars env ~impls (Pretyping.OfType (Some t')) x)) b in
+      let data = mk_interning_data env i impl t' in
+      let d = (i,b',t') in
+	(push_rel d env, impl :: uimpls, d::params, ([], data :: snd impls)))
+    (env, [], [], ([], [])) l    
+
+let binder_of_decl = function
+  | Vernacexpr.AssumExpr(n,t) -> (n,None,t)
+  | Vernacexpr.DefExpr(n,c,t) -> (n,Some c, match t with Some c -> c | None -> CHole (fst n, None))
+
+let binders_of_decls = List.map binder_of_decl
 
 let typecheck_params_and_fields id t ps fs =
   let env0 = Global.env () in
-  let (env1,newps), _ = interp_context Evd.empty env0 ps in
+  let (env1,newps), imps = interp_context Evd.empty env0 ps in
   let fullarity = it_mkProd_or_LetIn t newps in
   let env_ar = push_rel_context newps (push_rel (Name id,None,fullarity) env0) in
-  let env2,newfs =
-    List.fold_left
-      (fun (env,newfs) d ->
-         let decl = interp_decl Evd.empty env d in
-         (push_rel decl env, decl::newfs))
-      (env_ar,[]) fs
+  let evars = ref (Evd.create_evar_defs Evd.empty) in
+  let env2,impls,newfs,data =
+    interp_fields_evars evars env_ar (binders_of_decls fs)
   in
-  newps, newfs
+  let newps = Evarutil.nf_rel_context_evar (Evd.evars_of !evars) newps in
+  let newfs = Evarutil.nf_rel_context_evar (Evd.evars_of !evars) newfs in
+  let ce t = Evarutil.check_evars env0 Evd.empty !evars t in
+    List.iter (fun (n, b, t) -> Option.iter ce b; ce t) newps;
+    List.iter (fun (n, b, t) -> Option.iter ce b; ce t) newfs;
+    imps, newps, impls, newfs
 
 let degenerate_decl (na,b,t) =
   let id = match na with
@@ -70,24 +87,25 @@ type record_error =
 let warning_or_error coe indsp err =
   let st = match err with
     | MissingProj (fi,projs) ->
-	let s,have = if List.length projs > 1 then "s","have" else "","has" in
+	let s,have = if List.length projs > 1 then "s","were" else "","was" in
         (str(string_of_id fi) ++
-	   str" cannot be defined because the projection" ++ str s ++ spc () ++
-           prlist_with_sep pr_coma pr_id projs ++ spc () ++ str have ++ str "n't.")
+	   strbrk" cannot be defined because the projection" ++ str s ++ spc () ++
+           prlist_with_sep pr_coma pr_id projs ++ spc () ++ str have ++ 
+	   strbrk " not defined.")
     | BadTypedProj (fi,ctx,te) ->
 	match te with
 	  | ElimArity (_,_,_,_,Some (_,_,NonInformativeToInformative)) ->
               (pr_id fi ++ 
-		str" cannot be defined because it is informative and " ++
+		strbrk" cannot be defined because it is informative and " ++
 		Printer.pr_inductive (Global.env()) indsp ++
-		str " is not.")   
+		strbrk " is not.")   
 	  | ElimArity (_,_,_,_,Some (_,_,StrongEliminationOnNonSmallType)) ->
 	      (pr_id fi ++ 
-		str" cannot be defined because it is large and " ++
+		strbrk" cannot be defined because it is large and " ++
 		Printer.pr_inductive (Global.env()) indsp ++
-		str " is not.")
+		strbrk " is not.")
 	  | _ -> 
-              (pr_id fi ++ str " cannot be defined because it is not typable")
+              (pr_id fi ++ strbrk " cannot be defined because it is not typable.")
   in
   if coe then errorlabstrm "structure" st;
   Flags.if_verbose ppnl (hov 0 (str"Warning: " ++ st))
@@ -131,7 +149,7 @@ let instantiate_possibly_recursive_type indsp paramdecls fields =
   substl_rel_context (subst@[mkInd indsp]) fields
 
 (* We build projections *)
-let declare_projections indsp ?(kind=StructureComponent) ?name coers fields =
+let declare_projections indsp ?(kind=StructureComponent) ?name coers fieldimpls fields =
   let env = Global.env() in
   let (mib,mip) = Global.lookup_inductive indsp in
   let paramdecls = mib.mind_params_ctxt in
@@ -142,8 +160,8 @@ let declare_projections indsp ?(kind=StructureComponent) ?name coers fields =
   let fields = instantiate_possibly_recursive_type indsp paramdecls fields in
   let lifted_fields = lift_rel_context 1 fields in
   let (_,kinds,sp_projs,_) =
-    List.fold_left2
-      (fun (nfi,kinds,sp_projs,subst) coe (fi,optci,ti) ->
+    list_fold_left3
+      (fun (nfi,kinds,sp_projs,subst) coe (fi,optci,ti) impls ->
 	let (sp_projs,subst) =
 	  match fi with
 	  | Anonymous ->
@@ -180,6 +198,8 @@ let declare_projections indsp ?(kind=StructureComponent) ?name coers fields =
                   raise (NotDefinable (BadTypedProj (fid,ctx,te))) in
 	      let refi = ConstRef kn in
 	      let constr_fi = mkConst kn in
+	      Impargs.maybe_declare_manual_implicits 
+		false refi (Impargs.is_implicit_args()) impls;
 	      if coe then begin
 	        let cl = Class.class_of_global (IndRef indsp) in
 	        Class.try_add_new_coercion_with_source refi Global cl
@@ -191,28 +211,18 @@ let declare_projections indsp ?(kind=StructureComponent) ?name coers fields =
 	      warning_or_error coe indsp why;
 	      (None::sp_projs,NoProjection fi::subst) in
       (nfi-1,(optci=None)::kinds,sp_projs,subst))
-      (List.length fields,[],[],[]) coers (List.rev fields)
+      (List.length fields,[],[],[]) coers (List.rev fields) (List.rev fieldimpls)
   in (kinds,sp_projs)
 
-(* [fs] corresponds to fields and [ps] to parameters; [coers] is a boolean 
-   list telling if the corresponding fields must me declared as coercion *)
-let definition_structure ((is_coe,(_,idstruc)),ps,cfs,idbuild,s) =
-  let coers,fs = List.split cfs in
-  let extract_name acc = function
-      Vernacexpr.AssumExpr((_,Name id),_) -> id::acc
-    | Vernacexpr.DefExpr ((_,Name id),_,_) -> id::acc
-    | _ -> acc in
-  let allnames =  idstruc::(List.fold_left extract_name [] fs) in
-  if not (list_distinct allnames) then error "Two objects have the same name";
-  (* Now, younger decl in params and fields is on top *)
-  let params,fields = typecheck_params_and_fields idstruc (mkSort s) ps fs in
+let declare_structure id idbuild paramimpls params arity fieldimpls fields
+    ?(kind=StructureComponent) ?name is_coe coers =
   let nparams = List.length params and nfields = List.length fields in
   let args = extended_rel_list nfields params in
   let ind = applist (mkRel (1+nparams+nfields), args) in
   let type_constructor = it_mkProd_or_LetIn ind fields in
   let mie_ind =
-    { mind_entry_typename = idstruc;
-      mind_entry_arity = mkSort s;
+    { mind_entry_typename = id;
+      mind_entry_arity = arity;
       mind_entry_consnames = [idbuild];
       mind_entry_lc = [type_constructor] } in
   let declare_as_coind =
@@ -223,10 +233,27 @@ let definition_structure ((is_coe,(_,idstruc)),ps,cfs,idbuild,s) =
       mind_entry_record = true;
       mind_entry_finite = not declare_as_coind;
       mind_entry_inds = [mie_ind] } in
-  let kn = declare_mutual_with_eliminations true mie [] in
+  let kn = Command.declare_mutual_with_eliminations true mie [(paramimpls,[])] in
   let rsp = (kn,0) in (* This is ind path of idstruc *)
-  let kinds,sp_projs = declare_projections rsp coers fields in
-  let build = ConstructRef (rsp,1) in (* This is construct path of idbuild *)
-  if is_coe then Class.try_add_new_coercion build Global;
-  Recordops.declare_structure(rsp,idbuild,List.rev kinds,List.rev sp_projs);
-  kn
+  let kinds,sp_projs = declare_projections rsp ~kind ?name coers fieldimpls fields in
+  let build = ConstructRef (rsp,1) in
+    if is_coe then Class.try_add_new_coercion build Global;
+    Recordops.declare_structure(rsp,idbuild,List.rev kinds,List.rev sp_projs);
+    kn
+
+(* [fs] corresponds to fields and [ps] to parameters; [coers] is a boolean 
+   list telling if the corresponding fields must me declared as coercion *)
+let definition_structure ((is_coe,(_,idstruc)),ps,cfs,idbuild,s) =
+  let coers,fs = List.split cfs in
+  let extract_name acc = function
+      Vernacexpr.AssumExpr((_,Name id),_) -> id::acc
+    | Vernacexpr.DefExpr ((_,Name id),_,_) -> id::acc
+    | _ -> acc in
+  let allnames =  idstruc::(List.fold_left extract_name [] fs) in
+  if not (list_distinct allnames) then error "Two objects have the same name";
+  (* Now, younger decl in params and fields is on top *)
+  let implpars, params, implfs, fields = typecheck_params_and_fields idstruc (mkSort s) ps fs in
+  let implfs = List.map 
+    (fun impls -> implpars @ Impargs.lift_implicits (succ (List.length params)) impls) implfs in
+    declare_structure idstruc idbuild implpars params (mkSort s) implfs fields is_coe coers
+  
diff --git a/toplevel/record.mli b/toplevel/record.mli
index 9642b351..48181437 100644
--- a/toplevel/record.mli
+++ b/toplevel/record.mli
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: record.mli 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: record.mli 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 (*i*)
 open Names
@@ -14,6 +14,7 @@ open Term
 open Sign
 open Vernacexpr
 open Topconstr
+open Impargs
 (*i*)
 
 (* [declare_projections ref name coers params fields] declare projections of
@@ -21,7 +22,18 @@ open Topconstr
    as coercions accordingly to [coers]; it returns the absolute names of projections *)
 
 val declare_projections :
-  inductive -> ?kind:Decl_kinds.definition_object_kind -> ?name:identifier -> bool list -> rel_context -> bool list * constant option list
+  inductive -> ?kind:Decl_kinds.definition_object_kind -> ?name:identifier ->
+  bool list -> manual_explicitation list list -> rel_context -> 
+  bool list * constant option list
+
+val declare_structure : identifier -> identifier -> 
+  manual_explicitation list -> rel_context -> (* params *)
+  Term.constr -> (* arity *)
+  Impargs.manual_explicitation list list -> Sign.rel_context -> (* fields *)
+  ?kind:Decl_kinds.definition_object_kind -> ?name:identifier ->
+  bool -> (* coercion? *)
+  bool list -> (* field coercions *)
+  mutual_inductive
 
 val definition_structure :
   lident with_coercion * local_binder list *
diff --git a/toplevel/toplevel.ml b/toplevel/toplevel.ml
index 42f2883a..8a9ef501 100644
--- a/toplevel/toplevel.ml
+++ b/toplevel/toplevel.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: toplevel.ml 10916 2008-05-10 15:38:36Z herbelin $ *)
+(* $Id: toplevel.ml 11317 2008-08-07 15:52:38Z barras $ *)
 
 open Pp
 open Util
@@ -140,13 +140,15 @@ let print_highlight_location ib loc =
 (* Functions to report located errors in a file. *)
 
 let print_location_in_file s inlibrary fname loc =
-  let errstrm = (str"Error while reading " ++ str s ++ str":") in
-  if loc = dummy_loc then 
-    (errstrm ++ str", unknown location." ++ fnl ())
+  let errstrm = str"Error while reading " ++ str s in
+  if loc = dummy_loc then
+    hov 1 (errstrm ++ spc() ++ str" (unknown location):") ++ fnl ()
   else
+    let errstrm =
+      if s = fname then mt() else errstrm ++ str":" ++ fnl() in
     if inlibrary then
-      (errstrm ++ fnl () ++ str"Module " ++ str ("\""^fname^"\"") ++
-       str" characters " ++ Cerrors.print_loc loc ++ fnl ())
+      hov 0 (errstrm ++ str"Module " ++ str ("\""^fname^"\"") ++ spc() ++
+             str"characters " ++ Cerrors.print_loc loc) ++ fnl ()
     else
     let (bp,ep) = unloc loc in
     let ic = open_in fname in
@@ -160,10 +162,15 @@ let print_location_in_file s inlibrary fname loc =
     try
       let (line, bol) = line_of_pos 1 0 0 in
       close_in ic;
-      (errstrm  ++ str"File " ++ str ("\""^fname^"\"") ++
-         str", line " ++ int line ++
-         str", characters " ++ Cerrors.print_loc (make_loc (bp-bol,ep-bol)) ++ str":" ++ fnl ())
-    with e -> (close_in ic; (errstrm ++ str", invalid location." ++ fnl ()))
+      hov 0
+        (errstrm ++ str"File " ++ str ("\""^fname^"\"") ++ str"," ++ spc() ++
+         hov 0 (str"line " ++ int line ++ str"," ++ spc() ++
+                str"characters " ++
+                Cerrors.print_loc (make_loc (bp-bol,ep-bol))) ++ str":") ++
+      fnl ()
+    with e ->
+      (close_in ic;
+       hov 1 (errstrm ++ spc() ++ str"(invalid location):") ++ fnl ())
 	
 let print_command_location ib dloc =
   match dloc with
diff --git a/toplevel/usage.ml b/toplevel/usage.ml
index 782fdc80..b0b0f826 100644
--- a/toplevel/usage.ml
+++ b/toplevel/usage.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: usage.ml 8932 2006-06-09 09:29:03Z notin $ *)
+(* $Id: usage.ml 11209 2008-07-05 10:17:49Z herbelin $ *)
 
 let version () =
   Printf.printf "The Coq Proof Assistant, version %s (%s)\n"
@@ -20,10 +20,14 @@ let print_usage_channel co command =
   output_string co command;
   output_string co "Coq options are:\n";
   output_string co
-"  -I dir                 add directory dir in the include path
+"  -I dir -as coqdir      map physical dir to logical coqdir
+  -I dir                 map directory dir to the empty logical path
   -include dir           (idem)
-  -R dir coqdir          recursively map physical dir to logical coqdir 
+  -R dir -as coqdir      recursively map physical dir to logical coqdir 
+  -R dir coqdir          (idem)
   -top coqdir            set the toplevel name to be coqdir instead of Top
+  -notop    r            set the toplevel name to be the empty logical path
+  -exclude-dir f         exclude subdirectories named f for option -R
 
   -inputstate f          read state from file f.coq
   -is f                  (idem)
diff --git a/toplevel/vernacentries.ml b/toplevel/vernacentries.ml
index 402f3b34..3f474239 100644
--- a/toplevel/vernacentries.ml
+++ b/toplevel/vernacentries.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: vernacentries.ml 11065 2008-06-06 22:39:43Z msozeau $ i*)
+(*i $Id: vernacentries.ml 11313 2008-08-07 11:15:03Z barras $ i*)
 
 (* Concrete syntax of the mathematical vernacular MV V2.6 *)
 
@@ -95,7 +95,7 @@ let show_script () =
   let pts = get_pftreestate () in
   let pf = proof_of_pftreestate pts
   and evc = evc_of_pftreestate pts in
-  msgnl_with !Pp_control.deep_ft (print_treescript true evc pf)
+  msgnl_with !Pp_control.deep_ft (print_treescript evc pf)
 
 let show_thesis () =
      msgnl (anomaly "TODO" )
@@ -175,17 +175,17 @@ let show_match id =
 		^ " => \n" ^ acc)
 	"end" patterns in
     msg (str ("match # with\n" ^ cases))
-  with Not_found -> error "Unknown inductive type"
+  with Not_found -> error "Unknown inductive type."
 
 (* "Print" commands *)
 
 let print_path_entry (s,l) =
-  (str s ++ str " " ++ tbrk (0,2) ++ str (string_of_dirpath l))
+  (str (string_of_dirpath l) ++ str " " ++ tbrk (0,0) ++ str s)
 
 let print_loadpath () =
   let l = Library.get_full_load_paths () in
-  msgnl (Pp.t (str "Physical path:                                 " ++
-		 tab () ++ str "Logical Path:" ++ fnl () ++ 
+  msgnl (Pp.t (str "Logical Path:                 " ++
+		 tab () ++ str "Physical path:" ++ fnl () ++
 		 prlist_with_sep pr_fnl print_path_entry l))
 
 let print_modules () =
@@ -232,7 +232,7 @@ let dump_universes s =
 
 let locate_file f =
   try
-    let _,file = System.where_in_path (Library.get_load_paths ()) f in
+    let _,file = System.where_in_path false (Library.get_load_paths ()) f in
     msgnl (str file)
   with Not_found -> 
     msgnl (hov 0 (str"Can't find file" ++ spc () ++ str f ++ spc () ++
@@ -240,24 +240,26 @@ let locate_file f =
 
 let msg_found_library = function
   | Library.LibLoaded, fulldir, file ->
-      msgnl(pr_dirpath fulldir ++ str " has been loaded from file" ++ fnl () ++
-      str file)
+      msgnl (hov 0
+	(pr_dirpath fulldir ++ strbrk " has been loaded from file " ++
+	 str file))
   | Library.LibInPath, fulldir, file ->
-      msgnl(pr_dirpath fulldir ++ str " is bound to file " ++ str file)
+      msgnl (hov 0
+	(pr_dirpath fulldir ++ strbrk " is bound to file " ++ str file))
 let msg_notfound_library loc qid = function
   | Library.LibUnmappedDir ->
       let dir = fst (repr_qualid qid) in
       user_err_loc (loc,"locate_library",
-        str "Cannot find a physical path bound to logical path " ++
-           pr_dirpath dir ++ fnl ())
+        strbrk "Cannot find a physical path bound to logical path " ++
+           pr_dirpath dir ++ str".")
   | Library.LibNotFound ->
       msgnl (hov 0 
-	(str"Unable to locate library" ++ spc () ++ pr_qualid qid))
+	(strbrk "Unable to locate library " ++ pr_qualid qid ++ str"."))
   | e -> assert false
 
 let print_located_library r =
   let (loc,qid) = qualid_of_reference r in
-  try msg_found_library (Library.locate_qualified_library qid)
+  try msg_found_library (Library.locate_qualified_library false qid)
   with e -> msg_notfound_library loc qid e
 
 let print_located_module r = 
@@ -329,7 +331,7 @@ let vernac_definition (local,_,_ as k) (_,id as lid) def hook =
   | ProveBody (bl,t) ->   (* local binders, typ *)
       if Lib.is_modtype () then
 	errorlabstrm "Vernacentries.VernacDefinition"
-	  (str "Proof editing mode not supported in module types")
+	  (str "Proof editing mode not supported in module types.")
       else
 	let hook _ _ = () in
 	start_proof_and_print (local,DefinitionBody Definition)
@@ -351,10 +353,10 @@ let vernac_start_proof kind l lettop hook =
   if not(refining ()) then
     if lettop then
       errorlabstrm "Vernacentries.StartProof"
-	(str "Let declarations can only be used in proof editing mode");
+	(str "Let declarations can only be used in proof editing mode.");
   if Lib.is_modtype () then
     errorlabstrm "Vernacentries.StartProof"
-      (str "Proof editing mode not supported in module types");
+      (str "Proof editing mode not supported in module types.");
   start_proof_and_print (Global, Proof kind) l hook
 
 let vernac_end_proof = function
@@ -377,7 +379,7 @@ let vernac_exact_proof c =
       save_named true end
     else
       errorlabstrm "Vernacentries.ExactProof"
-	(str "Command 'Proof ...' can only be used at the beginning of the proof")
+	(strbrk "Command 'Proof ...' can only be used at the beginning of the proof.")
   	
 let vernac_assumption kind l nl=
   let global = fst kind = Global in
@@ -421,7 +423,7 @@ let vernac_declare_module export (loc, id) binders_ast mty_ast_o =
   (* We check the state of the system (in section, in module type)
      and what module information is supplied *)
   if Lib.sections_are_opened () then
-    error "Modules and Module Types are not allowed inside sections";
+    error "Modules and Module Types are not allowed inside sections.";
   let binders_ast = List.map
    (fun (export,idl,ty) ->
      if export <> None then
@@ -441,7 +443,7 @@ let vernac_define_module export (loc, id) binders_ast mty_ast_o mexpr_ast_o =
   (* We check the state of the system (in section, in module type)
      and what module information is supplied *)
   if Lib.sections_are_opened () then
-    error "Modules and Module Types are not allowed inside sections";
+    error "Modules and Module Types are not allowed inside sections.";
   match mexpr_ast_o with
     | None ->
        check_no_pending_proofs ();
@@ -488,7 +490,7 @@ let vernac_end_module export (loc,id) =
 
 let vernac_declare_module_type (loc,id) binders_ast mty_ast_o =
   if Lib.sections_are_opened () then
-    error "Modules and Module Types are not allowed inside sections";
+    error "Modules and Module Types are not allowed inside sections.";
   
   match mty_ast_o with
     | None ->
@@ -552,7 +554,7 @@ let vernac_record struc binders sort nameopt cfs =
   let s = match kind_of_term s with
     | Sort s -> s
     | _ -> user_err_loc
-        (constr_loc sort,"definition_structure", str "Sort expected") in
+        (constr_loc sort,"definition_structure", str "Sort expected.") in
     if !dump then (
       dump_definition (snd struc) false "rec";
       List.iter (fun (_, x) ->
@@ -615,7 +617,6 @@ let vernac_instance glob sup inst props pri =
   ignore(Classes.new_instance ~global:glob sup inst props pri)
 
 let vernac_context l =
-  if !dump then List.iter (fun x -> dump_constraint x true "var") l;
   Classes.context l
 
 let vernac_declare_instance id =
@@ -626,7 +627,7 @@ let vernac_declare_instance id =
 (* Solving *)
 let vernac_solve n tcom b =
   if not (refining ()) then
-    error "Unknown command of the non proof-editing mode";
+    error "Unknown command of the non proof-editing mode.";
   Decl_mode.check_not_proof_mode "Unknown proof instruction";
   begin
     if b then 
@@ -653,7 +654,7 @@ let vernac_solve_existential = instantiate_nth_evar_com
 
 let vernac_set_end_tac tac =
   if not (refining ()) then
-    error "Unknown command of the non proof-editing mode";
+    error "Unknown command of the non proof-editing mode.";
   if tac <> (Tacexpr.TacId []) then set_end_tac (Tacinterp.interp tac) else ()
     (* TO DO verifier s'il faut pas mettre exist s | TacId s ici*)
 
@@ -771,7 +772,7 @@ let vernac_reserve idl c =
 
 let make_silent_if_not_pcoq b =
   if !pcoq <> None then 
-    error "Turning on/off silent flag is not supported in Centaur mode"
+    error "Turning on/off silent flag is not supported in Pcoq mode."
   else make_silent b
 
 let _ =
@@ -790,6 +791,14 @@ let _ =
       optread  = Impargs.is_implicit_args;
       optwrite = Impargs.make_implicit_args }
 
+let _ =
+  declare_bool_option 
+    { optsync  = true;
+      optname  = "manual implicit arguments";
+      optkey   = (TertiaryTable ("Manual","Implicit","Arguments"));
+      optread  = Impargs.is_manual_implicit_args;
+      optwrite = Impargs.make_manual_implicit_args }
+
 let _ =
   declare_bool_option 
     { optsync  = true;
@@ -825,7 +834,7 @@ let _ =
 let _ =
   declare_bool_option 
     { optsync  = true;
-      optname  = "implicit arguments defensive printing";
+      optname  = "implicit status of reversible patterns";
       optkey   = (TertiaryTable ("Reversible","Pattern","Implicit"));
       optread  = Impargs.is_reversible_pattern_implicit_args;
       optwrite = Impargs.make_reversible_pattern_implicit_args }
@@ -1096,7 +1105,7 @@ let global_module r =
   try Nametab.full_name_module qid
   with Not_found -> 
     user_err_loc (loc, "global_module",
-      str "Module/section " ++ pr_qualid qid ++ str " not found")
+      str "Module/section " ++ pr_qualid qid ++ str " not found.")
 
 let interp_search_restriction = function
   | SearchOutside l -> (List.map global_module l, true)
@@ -1143,7 +1152,7 @@ let vernac_goal = function
         start_proof_com (Global, Proof unnamed_kind) [None,c] (fun _ _ ->());
 	print_subgoals ()
       end else 
-	error "repeated Goal not permitted in refining mode"
+	error "repeated Goal not permitted in refining mode."
 
 let vernac_abort = function
   | None ->
@@ -1161,7 +1170,7 @@ let vernac_abort_all () =
     delete_all_proofs ();
     message "Current goals aborted"
   end else
-    error "No proof-editing in progress"
+    error "No proof-editing in progress."
 
 let vernac_restart () = restart_proof(); print_subgoals ()
 
@@ -1217,7 +1226,7 @@ let apply_subproof f occ =
   f evc (Global.named_context()) pf
 
 let explain_proof occ =
-  msg (apply_subproof (fun evd _ -> print_treescript true evd) occ)
+  msg (apply_subproof (fun evd _ -> print_treescript evd) occ)
 
 let explain_tree occ =
   msg (apply_subproof print_proof occ)
@@ -1256,7 +1265,7 @@ let vernac_check_guard () =
 	pfterm; 
       (str "The condition holds up to here")
     with UserError(_,s) -> 
-      (str ("Condition violated : ") ++s)
+      (str ("Condition violated: ") ++s)
   in 
   msgnl message
 
diff --git a/toplevel/vernacexpr.ml b/toplevel/vernacexpr.ml
index 744c3a6f..663e2e3c 100644
--- a/toplevel/vernacexpr.ml
+++ b/toplevel/vernacexpr.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(*i $Id: vernacexpr.ml 11024 2008-05-30 12:41:39Z msozeau $ i*)
+(*i $Id: vernacexpr.ml 11282 2008-07-28 11:51:53Z msozeau $ i*)
 
 open Util
 open Names
@@ -239,7 +239,7 @@ type vernac_expr =
 	(lident * lident list * constr_expr) list * (* props *)
 	int option (* Priority *)
 
-  | VernacContext of typeclass_context
+  | VernacContext of local_binder list
 	
   | VernacDeclareInstance of
       lident (* instance name *)
diff --git a/toplevel/vernacinterp.ml b/toplevel/vernacinterp.ml
index f43c0c5e..41669c47 100644
--- a/toplevel/vernacinterp.ml
+++ b/toplevel/vernacinterp.ml
@@ -6,7 +6,7 @@
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
 
-(* $Id: vernacinterp.ml 10348 2007-12-06 17:36:14Z aspiwack $ *)
+(* $Id: vernacinterp.ml 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Pp
 open Util
@@ -31,7 +31,7 @@ let vinterp_add s f =
     Hashtbl.add vernac_tab s f
   with Failure _ ->
     errorlabstrm "vinterp_add"
-      (str"Cannot add the vernac command " ++ str s ++ str" twice")
+      (str"Cannot add the vernac command " ++ str s ++ str" twice.")
 
 let overwriting_vinterp_add s f =
   begin 
@@ -46,7 +46,7 @@ let vinterp_map s =
     Hashtbl.find vernac_tab s
   with Not_found -> 
     errorlabstrm "Vernac Interpreter"
-      (str"Cannot find vernac command " ++ str s)
+      (str"Cannot find vernac command " ++ str s ++ str".")
 
 let vinterp_init () = Hashtbl.clear vernac_tab
 
diff --git a/toplevel/whelp.ml4 b/toplevel/whelp.ml4
index 58703c8e..62aaa303 100644
--- a/toplevel/whelp.ml4
+++ b/toplevel/whelp.ml4
@@ -8,7 +8,7 @@
 
 (*i camlp4deps: "parsing/grammar.cma" i*)
 
-(* $Id: whelp.ml4 10904 2008-05-08 16:31:26Z herbelin $ *)
+(* $Id: whelp.ml4 11309 2008-08-06 10:30:35Z herbelin $ *)
 
 open Flags
 open Pp
@@ -80,7 +80,9 @@ let uri_of_dirpath dir =
 
 let error_whelp_unknown_reference ref =
   let qid = Nametab.shortest_qualid_of_global Idset.empty ref in
-  error ("Definitions of the current session not supported in Whelp: " ^ string_of_qualid qid)
+  errorlabstrm ""
+    (strbrk "Definitions of the current session, like " ++ pr_qualid qid ++ 
+     strbrk ", are not supported in Whelp.")
 
 let uri_of_repr_kn ref (mp,dir,l) = 
   match mp with
@@ -104,7 +106,7 @@ let uri_of_ind_pointer l =
 
 let uri_of_global ref =
   match ref with
-  | VarRef id -> error ("Unknown Whelp reference: "^(string_of_id id))
+  | VarRef id -> error ("Unknown Whelp reference: "^(string_of_id id)^".")
   | ConstRef cst ->
       uri_of_repr_kn ref (repr_con cst); url_string ".con"
   | IndRef (kn,i) -> 
@@ -165,7 +167,7 @@ let rec uri_of_constr c =
   | RCast (_,c, CastConv (_,t)) ->
       uri_of_constr c; url_string ":"; uri_of_constr t
   | RRec _ | RIf _ | RLetTuple _ | RCases _ ->
-      error "Whelp does not support pattern-matching and (co-)fixpoint"
+      error "Whelp does not support pattern-matching and (co-)fixpoint."
   | RVar _ | RRef _ | RHole _ | REvar _ | RSort _ | RCast (_,_, CastCoerce) ->
       anomaly "Written w/o parenthesis"
   | RPatVar _ | RDynamic _ -> 
-- 
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