diff options
80 files changed, 8141 insertions, 325 deletions
diff --git a/.bintray.json b/.bintray.json new file mode 100644 index 000000000..fb9e55368 --- /dev/null +++ b/.bintray.json @@ -0,0 +1,20 @@ +{ + "package": { + "name": "coq", + "repo": "coq", + "subject": "coq" + }, + + "version": { + "name": "8.8+alpha" + }, + + "files": + [ + {"includePattern": "_build/(.*\\.dmg)", "uploadPattern": "$1", + "matrixParams": { + "override": 1 } + } + ], + "publish": true +} diff --git a/.gitignore b/.gitignore index 71de7bb8d..36536ec96 100644 --- a/.gitignore +++ b/.gitignore @@ -84,6 +84,9 @@ test-suite/coq-makefile/*/subdir/done test-suite/coq-makefile/merlin1/.merlin test-suite/coq-makefile/plugin-reach-outside-API-and-fail/_CoqProject test-suite/coq-makefile/plugin-reach-outside-API-and-succeed-by-bypassing-the-API/_CoqProject +test-suite/coqdoc/Coqdoc.* +test-suite/coqdoc/index.html +test-suite/coqdoc/coqdoc.css # documentation @@ -9,6 +9,7 @@ ## If you're mentionned here and want to update your information, ## either amend this file and commit it, or contact the coqdev list +Abhishek Anand <abhishek.anand.iitg@gmail.com> Abhishek Anand (@brixpro-home) <abhishek.anand.iitg@gmail.com> Jim Apple <github.public@jbapple.com> jbapple <github.public@jbapple.com> Bruno Barras <bruno.barras@inria.fr> barras <barras@85f007b7-540e-0410-9357-904b9bb8a0f7> Bruno Barras <bruno.barras@inria.fr> barras-local <barras-local@85f007b7-540e-0410-9357-904b9bb8a0f7> @@ -27,7 +28,7 @@ Judicaël Courant <courant@gforge> courant <courant@85f007b7-54 Pierre Courtieu <Pierre.Courtieu@cnam.fr> courtieu <courtieu@85f007b7-540e-0410-9357-904b9bb8a0f7> David Delahaye <delahaye@gforge> delahaye <delahaye@85f007b7-540e-0410-9357-904b9bb8a0f7> Maxime Dénès <mail@maximedenes.fr> mdenes <mdenes@85f007b7-540e-0410-9357-904b9bb8a0f7> -Daniel de Rauglaudre <daniel.de_rauglaudre@inria.fr> ddr <ddr@85f007b7-540e-0410-9357-904b9bb8a0f7> +Maxime Dénès <mail@maximedenes.fr> Maxime Denes <maximedenes@gillespie.inria.fr> Olivier Desmettre <desmettr@gforge> desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> Damien Doligez <doligez@gforge> doligez <doligez@85f007b7-540e-0410-9357-904b9bb8a0f7> Jean-Christophe Filliâtre <Jean-Christophe.Filliatre@lri.fr> filliatr <filliatr@85f007b7-540e-0410-9357-904b9bb8a0f7> @@ -36,7 +37,9 @@ Julien Forest <julien.forest@ensiie.fr> jforest <jforest@85f007b7-540 Julien Forest <julien.forest@ensiie.fr> forest <jforest@mourvedre.ensiie.fr> Julien Forest <julien.forest@ensiie.fr> jforest <jforest@thune> Julien Forest <julien.forest@ensiie.fr> jforest <jforest@daneel.lan.home> +Julien Forest <julien.forest@ensiie.fr> Julien Forest <forest@ensiie.fr> Emilio Jesus Gallego Arias <e+git@x80.org> Emilio Jesús Gallego Arias <e+git@x80.org> +Gaëtan Gilbert <gaetan.gilbert@ens-lyon.fr> Gaetan Gilbert <gaetan.gilbert@ens-lyon.fr> Stéphane Glondu <steph@glondu.net> glondu <glondu@85f007b7-540e-0410-9357-904b9bb8a0f7> Stéphane Glondu <steph@glondu.net> Stephane Glondu <steph@glondu.net> Benjamin Grégoire <benjamin.gregoire@inria.fr> Benjamin Gregoire <Benjamin.Gregoire@inria.fr> @@ -51,9 +54,12 @@ Tom Hutchinson <thutchin@gforge> thutchin <thutchin@85f007b7-5 Cezary Kaliszyk <cek@gforge> cek <cek@85f007b7-540e-0410-9357-904b9bb8a0f7> Florent Kirchner <fkirchne@gforge> fkirchne <fkirchne@85f007b7-540e-0410-9357-904b9bb8a0f7> Florent Kirchner <fkirchne@gforge> kirchner <kirchner@85f007b7-540e-0410-9357-904b9bb8a0f7> -Matej Kosik <matej.kosik@inria.fr> Matej Kosik <m4tej.kosik@gmail.com> +Matej Košík <matej.kosik@inria.fr> Matej Kosik <m4tej.kosik@gmail.com> +Matej Košík <matej.kosik@inria.fr> Matej Kosik <matej.kosik@inria.fr> Marc Lasson <marc.lasson@gmail.com> mlasson <marc.lasson@gmail.com> +William Lawvere <mundungus.corleone@gmail.com> william-lawvere <mundungus.corleone@gmail.com> Pierre Letouzey <pierre.letouzey@inria.fr> letouzey <letouzey@85f007b7-540e-0410-9357-904b9bb8a0f7> +Pierre Letouzey <pierre.letouzey@inria.fr> letouzey <pierre.letouzey@inria.fr> Assia Mahboubi <assia.mahboubi@inria.fr> amahboub <amahboub@85f007b7-540e-0410-9357-904b9bb8a0f7> Evgeny Makarov <emakarov@gforge> emakarov <emakarov@85f007b7-540e-0410-9357-904b9bb8a0f7> Gregory Malecha <gmalecha@eecs.harvard.edu> Gregory Malecha <gmalecha@cs.harvard.edu> @@ -68,15 +74,19 @@ Julien Narboux <jnarboux@gforge> jnarboux <jnarboux@85f007b7-5 Julien Narboux <jnarboux@gforge> narboux <narboux@85f007b7-540e-0410-9357-904b9bb8a0f7> Jean-Marc Notin <notin@gforge> notin,no-port-forwarding,no-agent-forwarding,no-X11-forwarding,no-pty <notin,no-port-forwarding,no-agent-forwarding,no-X11-forwarding,no-pty@85f007b7-540e-0410-9357-904b9bb8a0f7> Jean-Marc Notin <notin@gforge> notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7> -Russel O'Connor <roconnor@gforge> roconnor <roconnor@85f007b7-540e-0410-9357-904b9bb8a0f7> +Russell O'Connor <roconnor@blockstream.io> roconnor <roconnor@85f007b7-540e-0410-9357-904b9bb8a0f7> +Russell O'Connor <roconnor@blockstream.io> roconnor-blockstream <roconnor@blockstream.com> Christine Paulin <cpaulin@gforge> cpaulin <cpaulin@85f007b7-540e-0410-9357-904b9bb8a0f7> Christine Paulin <cpaulin@gforge> mohring <mohring@85f007b7-540e-0410-9357-904b9bb8a0f7> Pierre-Marie Pédrot <pierre-marie.pedrot@inria.fr> ppedrot <ppedrot@85f007b7-540e-0410-9357-904b9bb8a0f7> Loïc Pottier <pottier@gforge> pottier <pottier@85f007b7-540e-0410-9357-904b9bb8a0f7> Matthias Puech <puech@gforge> puech <puech@85f007b7-540e-0410-9357-904b9bb8a0f7> -Yann Régis-Gianas <yrg@pps.univ-paris-diderot.fr> regisgia <regisgia@85f007b7-540e-0410-9357-904b9bb8a0f7> +Lars Rasmusson <lars.rasmusson@sics.se> larsr <Lars.Rasmusson@sics.se> +Daniel de Rauglaudre <daniel.de_rauglaudre@inria.fr> ddr <ddr@85f007b7-540e-0410-9357-904b9bb8a0f7> Daniel de Rauglaudre <daniel.de_rauglaudre@inria.fr> Daniel de Rauglaudre <daniel.de_rauglaudre@inria.fr> Daniel de Rauglaudre <daniel.de_rauglaudre@inria.fr> Daniel De Rauglaudre <ddr@gforge> +Yann Régis-Gianas <yrg@pps.univ-paris-diderot.fr> regisgia <regisgia@85f007b7-540e-0410-9357-904b9bb8a0f7> +Yann Régis-Gianas <yrg@pps.univ-paris-diderot.fr> Regis-Gianas <yrg@pps.univ-paris-diderot.fr> Clément Renard <clrenard@gforge> clrenard <clrenard@85f007b7-540e-0410-9357-904b9bb8a0f7> Claudio Sacerdoti Coen <sacerdot@gforge> sacerdot <sacerdot@85f007b7-540e-0410-9357-904b9bb8a0f7> Vincent Siles <vsiles@gforge> vsiles <vsiles@85f007b7-540e-0410-9357-904b9bb8a0f7> diff --git a/.travis.yml b/.travis.yml index 9c7ad553f..9300505f3 100644 --- a/.travis.yml +++ b/.travis.yml @@ -32,6 +32,7 @@ env: - COMPILER="system" - CAMLP5_VER="6.14" - NATIVE_COMP="yes" + - COQ_DEST="-local" # Main test suites matrix: - TEST_TARGET="test-suite" COMPILER="4.02.3+32bit" @@ -139,11 +140,46 @@ matrix: env: - TEST_TARGET="test-suite" - COMPILER="4.02.3" + - CAMLP5_VER="6.17" - NATIVE_COMP="no" + - COQ_DEST="-local" before_install: - brew update - - brew install opam - - brew install gnu-time + - brew install opam gnu-time + + - os: osx + env: + - TEST_TARGET="" + - COMPILER="4.02.3" + - CAMLP5_VER="6.17" + - NATIVE_COMP="no" + - COQ_DEST="-prefix ${PWD}/_install" + - EXTRA_CONF="-coqide opt -warn-error" + - EXTRA_OPAM="lablgtk-extras" + before_install: + - brew update + - brew install opam gnu-time gtk+ expat gtksourceview libxml2 gdk-pixbuf python3 + - pip3 install macpack + before_deploy: + - dev/build/osx/make-macos-dmg.sh + deploy: + provider: bintray + user: maximedenes + file: .bintray.json + key: + secure: "gUvXWwWR0gicDqsKOnBfe45taToSFied6gN8tCa5IOtl6E6gFoHoPZ83ZWXQsZP50oMDFS5eji0VQAFGEbOsGrTZaD9Y9Jnu34NND78SWL1tsJ6nHO3aCAoMpB0N3+oRuF6S+9HStU6KXWqgj+GeU4vZ4TOlG01RGctJa6U3vII=" + skip_cleanup: true + on: + all_branches: true + deploy: + provider: releases + api_key: + secure: "Z/ewvydCLXEhlBBtQGYm2nZ8o+2RP+MwA5uEDuu6mEpZttUZAYaoHivChxADLXz8LNKvUloIeBeIL/PrLk6QnhSur/s2iEYHssrnl99SkAPtoWggyfsdacuKLMkpLoZGOBIEYKPuXuEZyqvugSUO42rSya1zdjcnXc4l+E/bXMc=" + file: _build/*.dmg + skip_cleanup: true + on: + tags: true + repo: coq/coq before_install: - if [ "${TRAVIS_PULL_REQUEST}" != "false" ]; then echo "Tested commit (followed by parent commits):"; git log -1; for commit in `git log -1 --format="%P"`; do echo; git log -1 $commit; done; fi @@ -159,7 +195,7 @@ script: - set -e - echo 'Configuring Coq...' && echo -en 'travis_fold:start:coq.config\\r' -- ./configure -local -native-compiler ${NATIVE_COMP} ${EXTRA_CONF} +- ./configure ${COQ_DEST} -native-compiler ${NATIVE_COMP} ${EXTRA_CONF} - echo -en 'travis_fold:end:coq.config\\r' - echo 'Building Coq...' && echo -en 'travis_fold:start:coq.build\\r' diff --git a/API/API.ml b/API/API.ml index c952e123d..1d7a4a4f4 100644 --- a/API/API.ml +++ b/API/API.ml @@ -43,7 +43,7 @@ module Cbytecodes = Cbytecodes (* module Copcodes *) module Cemitcodes = Cemitcodes (* module Nativevalues *) -(* module Primitives *) +(* module CPrimitives *) module Opaqueproof = Opaqueproof module Declareops = Declareops module Retroknowledge = Retroknowledge diff --git a/API/API.mli b/API/API.mli index a0e77edd1..5804a82f6 100644 --- a/API/API.mli +++ b/API/API.mli @@ -3782,6 +3782,12 @@ sig | DefaultInline | InlineAt of int + type cumulative_inductive_parsing_flag = + | GlobalCumulativity + | GlobalNonCumulativity + | LocalCumulativity + | LocalNonCumulativity + type vernac_expr = | VernacLoad of verbose_flag * string | VernacTime of vernac_expr Loc.located @@ -3806,7 +3812,7 @@ sig | VernacExactProof of Constrexpr.constr_expr | VernacAssumption of (Decl_kinds.locality option * Decl_kinds.assumption_object_kind) * inline * (plident list * Constrexpr.constr_expr) with_coercion list - | VernacInductive of Decl_kinds.cumulative_inductive_flag * Decl_kinds.private_flag * inductive_flag * (inductive_expr * decl_notation list) list + | VernacInductive of cumulative_inductive_parsing_flag * Decl_kinds.private_flag * inductive_flag * (inductive_expr * decl_notation list) list | VernacFixpoint of Decl_kinds.locality option * (fixpoint_expr * decl_notation list) list | VernacCoFixpoint of @@ -4283,10 +4289,10 @@ module Constrextern : sig val extern_glob_constr : Names.Id.Set.t -> Glob_term.glob_constr -> Constrexpr.constr_expr val extern_glob_type : Names.Id.Set.t -> Glob_term.glob_constr -> Constrexpr.constr_expr - val extern_constr : ?lax:bool -> bool -> Environ.env -> Evd.evar_map -> Constr.t -> Constrexpr.constr_expr + val extern_constr : ?lax:bool -> bool -> Environ.env -> Evd.evar_map -> EConstr.t -> Constrexpr.constr_expr val without_symbols : ('a -> 'b) -> 'a -> 'b val print_universes : bool ref - val extern_type : bool -> Environ.env -> Evd.evar_map -> Term.types -> Constrexpr.constr_expr + val extern_type : bool -> Environ.env -> Evd.evar_map -> EConstr.t -> Constrexpr.constr_expr val with_universes : ('a -> 'b) -> 'a -> 'b val set_extern_reference : (?loc:Loc.t -> Names.Id.Set.t -> Globnames.global_reference -> Libnames.reference) -> unit @@ -1,12 +1,13 @@ -To be inserted at the proper place: +Changes beyond 8.7 +================== Notations - Recursive notations with the recursive pattern repeating on the right (e.g. "( x ; .. ; y ; z )") now supported. -Changes beyond V8.6 -=================== +Changes from 8.6.1 to 8.7+beta +============================== Tactics @@ -46,19 +47,46 @@ Tactics - In "Tactic Notation" or "TACTIC EXTEND", entry "constr_with_bindings" now uses type classes and rejects terms with unresolved holes, like entry "constr" does. To get the former behavior use - "open_constr_with_bindings" (possible source of incompatibility. + "open_constr_with_bindings" (possible source of incompatibility). - New e-variants eassert, eenough, epose proof, eset, eremember, epose which behave like the corresponding variants with no "e" but turn unresolved implicit arguments into existential variables, on the shelf, rather than failing. +- Tactic injection has become more powerful (closes BZ#4890) and its + documentation has been updated. +- New variants of the `first` and `solve` tacticals that do not rely + on parsing rules, meant to define tactic notations. +- Added support for side effects hooks in `cbv`, `cbn` and `simpl`. + The side effects are provided via a plugin: + https://github.com/herbelin/reduction-effects/ +- It is now possible to take hint database names as parameters in a + Ltac definition or a Tactic Notation. +- New option `Set Ltac Batch Debug` on top of `Set Ltac Debug` for + non-interactive Ltac debug output. -Vernacular Commands +Gallina -- Goals context can be printed in a more compact way when "Set - Printing Compact Contexts" is activated. +- Now supporting all kinds of binders, including 'pat, in syntax of record fields. +Vernacular Commands + +- Goals context can be printed in a more compact way when `Set + Printing Compact Contexts` is activated. +- Unfocused goals can be printed with the `Set Printing Unfocused` + option. +- `Print` now shows the types of let-bindings. +- The compatibility options for printing primitive projections + (`Set Printing Primitive Projection Parameters` and + `Set Printing Primitive Projection Compatibility`) are now off by default. +- Possibility to unset the printing of notations in a more fine grained + fashion than `Unset Printing Notations` is provided without any + user-syntax. The goal is that someone creates a plugin to experiment + such a user-syntax, to be later integrated in Coq when stabilized. +- `About` now tells if a reference is a coercion. - The deprecated `Save` vernacular and its form `Save Theorem id` to close proofs have been removed from the syntax. Please use `Qed`. +- `Search` now sorts results by relevance (the relevance metric is a + weighted sum of number of distinct symbols and size of the term). Standard Library @@ -68,7 +96,10 @@ Standard Library and, consequently, choice of representatives in equivalence classes. Various proof-theoretic characterizations of choice over setoids in file ChoiceFacts.v. -- The BigN, BigZ, BigZ libraries are not part anymore of Coq standard +- New lemmas about iff and about orders on positive and Z. +- New lemmas on powerRZ. +- Strengthened statement of JMeq_eq_dep (closes BZ#4912). +- The BigN, BigZ, BigZ libraries are no longer part of the Coq standard library, they are now provided by a separate repository https://github.com/coq/bignums The split has been done just after the Int31 library. @@ -81,6 +112,9 @@ Standard Library Plugins +- The Ssreflect plugin is now distributed with Coq. Its documentation has + been integrated as a chapter of the reference manual. This chapter is + work in progress so feedback is welcome. - The mathematical proof language (also known as declarative mode) was removed. - A new command Extraction TestCompile has been introduced, not meant for the general user but instead for Coq's test-suite. @@ -122,14 +156,77 @@ Build Infrastructure Universes - Cumulative inductive types. see prefixes "Cumulative", "NonCumulative" - for inductive definitions and the option "Set Inductive Cumulativity" + for inductive definitions and the option "Set Polymorphic Inductive Cumulativity" in the reference manual. +- New syntax `foo@{_}` to instantiate a polymorphic definition with + anonymous universes (can also be used with `Type`). + +XML Protocol and internal changes -XML Protocol +See dev/doc/changes.txt + +Many bugfixes including BZ#1859, BZ#2884, BZ#3613, BZ#3943, BZ#3994, +BZ#4250, BZ#4709, BZ#4720, BZ#4824, BZ#4844, BZ#4911, BZ#5026, BZ#5233, +BZ#5275, BZ#5315, BZ#5336, BZ#5360, BZ#5390, BZ#5414, BZ#5417, BZ#5420, +BZ#5439, BZ#5449, BZ#5475, BZ#5476, BZ#5482, BZ#5501, BZ#5507, BZ#5520, +BZ#5523, BZ#5524, BZ#5553, BZ#5577, BZ#5578, BZ#5589, BZ#5597, BZ#5598, +BZ#5607, BZ#5618, BZ#5619, BZ#5620, BZ#5641, BZ#5648, BZ#5651, BZ#5671. + +Many bugfixes on OS X and Windows (now the test-suite passes on these +platforms too). + +Many optimizations. + +Many documentation improvements. + +Changes from 8.6 to 8.6.1 +========================= -- The `query` call has been modified, now it carries a mandatory - "route_id" integer parameter, that associated the result of such - query with its generated feedback. +- Fix #5380: Default colors for CoqIDE are actually applied. +- Fix plugin warnings +- Document named evars (including Show ident) +- Fix Bug #5574, document function scope +- Adding a test case as requested in bug 5205. +- Fix Bug #5568, no dup notation warnings on repeated module imports +- Fix documentation of Typeclasses eauto := +- Refactor documentation of records. +- Protecting from warnings while compiling 8.6 +- Fixing an inconsistency between configure and configure.ml +- Add test-suite checks for coqchk with constraints +- Fix bug #5019 (looping zify on dependent types) +- Fix bug 5550: "typeclasses eauto with" does not work with section variables. +- Bug 5546, qualify datatype constructors when needed in Show Match +- Bug #5535, test for Show with -emacs +- Fix bug #5486, don't reverse ids in tuples +- Fixing #5522 (anomaly with free vars of pat) +- Fix bug #5526, don't check for nonlinearity in notation if printing only +- Fix bug #5255 +- Fix bug #3659: -time should understand multibyte encodings. +- FIx bug #5300: Anomaly: Uncaught exception Not_found" in "Print Assumptions". +- Fix outdated description in RefMan. +- Repairing `Set Rewriting Schemes` +- Fixing #5487 (v8.5 regression on ltac-matching expressions with evars). +- Fix description of command-line arguments for Add (Rec) LoadPath +- Fix bug #5377: @? patterns broken. +- add XML protocol doc +- Fix anomaly when doing [all:Check _.] during a proof. +- Correction of bug #4306 +- Fix #5435: [Eval native_compute in] raises anomaly. +- Instances should obey universe binders even when defined by tactics. +- Intern names bound in match patterns +- funind: Ignore missing info for current function +- Do not typecheck twice the type of opaque constants. +- show unused intro pattern warning +- [future] Be eager when "chaining" already resolved future values. +- Opaque side effects +- Fix #5132: coq_makefile generates incorrect install goal +- Run non-tactic comands without resilient_command +- Univs: fix bug #5365, generation of u+k <= v constraints +- make `emit' tail recursive +- Don't require printing-only notation to be productive +- Fix the way setoid_rewrite handles bindings. +- Fix for bug 5244 - set printing width ignored when given enough space +- Fix bug 4969, autoapply was not tagging shelved subgoals correctly Changes from V8.6beta1 to V8.6 ============================== @@ -54,6 +54,7 @@ FIND_SKIP_DIRS:='(' \ -name "$${GIT_DIR}" -o \ -name '_build' -o \ -name '_build_ci' -o \ + -name 'user-contrib' -o \ -name 'coq-makefile' -o \ -name '.opamcache' -o \ -name '.coq-native' \ @@ -137,6 +138,7 @@ endif # This should help preventing weird compilation failures caused by leftover # compiled files after deleting or moving some source files. +ifeq (,$(findstring clean,$(MAKECMDGOALS))) # Skip this for 'make clean' and alii ifndef ACCEPT_ALIEN_VO EXISTINGVO:=$(call find, '*.vo') KNOWNVO:=$(patsubst %.v,%.vo,$(call find, '*.v')) @@ -162,6 +164,7 @@ remove them first, for instance via 'make clean' \ (or skip this check via 'make ACCEPT_ALIEN_OBJ=1')) endif endif +endif # Apart from clean and tags, everything will be done in a sub-call to make # on Makefile.build. This way, we avoid doing here the -include of .d : diff --git a/Makefile.build b/Makefile.build index 1c31f6c81..92eaf7232 100644 --- a/Makefile.build +++ b/Makefile.build @@ -31,7 +31,7 @@ TIMED ?= # When $(TIMED) is set, the time command used by default is $(STDTIME) # (see below), unless the following variable is non-empty. For instance, -# it could be set to "'/usr/bin/time -p'". +# it could be set to "'/usr/bin/env time -p'". TIMECMD ?= # When non-empty, -time is passed to coqc and the output is recorded @@ -164,11 +164,11 @@ DEPENDENCIES := \ ########################################################################### # Default timing command -# Use /usr/bin/time on linux, gtime on Mac OS +# Use /usr/bin/env time on linux, gtime on Mac OS TIMEFMT?="$* (real: %e, user: %U, sys: %S, mem: %M ko)" ifneq (,$(TIMED)) -ifeq (0,$(shell /usr/bin/time -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) -STDTIME?=/usr/bin/time -f $(TIMEFMT) +ifeq (0,$(shell /usr/bin/env time -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) +STDTIME?=/usr/bin/env time -f $(TIMEFMT) else ifeq (0,$(shell gtime -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) STDTIME?=gtime -f $(TIMEFMT) @@ -177,7 +177,7 @@ STDTIME?=time endif endif else -STDTIME?=/usr/bin/time -f $(TIMEFMT) +STDTIME?=/usr/bin/env time -f $(TIMEFMT) endif TIMER=$(if $(TIMED), $(STDTIME), $(TIMECMD)) diff --git a/Makefile.doc b/Makefile.doc index 6a81b292e..dd7717359 100644 --- a/Makefile.doc +++ b/Makefile.doc @@ -36,7 +36,7 @@ HEVEA:=hevea HACHA:=hacha HEVEAOPTS:=-fix -exec xxdate.exe HEVEALIB:=/usr/local/lib/hevea:/usr/lib/hevea -HTMLSTYLE:=simple +HTMLSTYLE:=coqremote export TEXINPUTS:=$(HEVEALIB): ifdef COQDOC_NOBOOT COQTEXOPTS:=-n 72 -sl -small @@ -62,7 +62,7 @@ REFMANTEXFILES:=$(addprefix doc/refman/, \ headers.sty Reference-Manual.tex \ RefMan-pre.tex RefMan-int.tex RefMan-com.tex \ RefMan-uti.tex RefMan-ide.tex RefMan-add.tex RefMan-modr.tex \ - AsyncProofs.tex ) \ + AsyncProofs.tex RefMan-ssr.tex) \ $(REFMANCOQTEXFILES) \ REFMANEPSFILES:=doc/refman/coqide.eps doc/refman/coqide-queries.eps @@ -216,7 +216,15 @@ doc/refman/html/index.html: doc/refman/Reference-Manual.html $(REFMANPNGFILES) \ (cd doc/refman/html; $(HACHA) -nolinks -tocbis -o toc.html ../styles.hva ../Reference-Manual.html) $(INSTALLLIB) doc/refman/cover.html doc/refman/html/index.html @touch $(INDEXES) - -$(INSTALLLIB) doc/common/styles/html/$(HTMLSTYLE)/*.css doc/refman/html + (cd doc/common/styles/html/$(HTMLSTYLE);\ + for f in `find . -name \*.css`; do \ + install -m 644 -D $$f ../../../../refman/html/$$f;\ + done) + (cd doc/common/styles/html/$(HTMLSTYLE);\ + for f in `find . -name coqdoc.css -o -name style.css`; do \ + install -m 644 -D $$f ../../../../refman/html/;\ + done) + install -m 644 doc/common/styles/html/$(HTMLSTYLE)/*.css doc/refman/html refman-quick: (cd doc/refman;\ @@ -479,6 +487,12 @@ $(OCAMLDOCDIR)/%.pdf: $(OCAMLDOCDIR)/%.tex $(HIDE)(cd $(OCAMLDOCDIR) ; pdflatex -interaction=batchmode $*.tex && pdflatex -interaction=batchmode $*.tex) $(HIDE)(cd doc/tools/; show_latex_messages -no-overfull ../../$(OCAMLDOCDIR)/$*.log) +########################################################################### +# local web server +########################################################################### + +serve-refman-8080: refman + cd doc/refman/html; python3 -m http.server 8080 # For emacs: # Local Variables: diff --git a/Makefile.ide b/Makefile.ide index b534b385b..542d8c252 100644 --- a/Makefile.ide +++ b/Makefile.ide @@ -55,7 +55,8 @@ IDEFILES=$(wildcard ide/*.lang) ide/coq_style.xml ide/coq.png ide/MacOS/default_ GTKSHARE=$(shell pkg-config --variable=prefix gtk+-2.0)/share GTKBIN=$(shell pkg-config --variable=prefix gtk+-2.0)/bin GTKLIBS=$(shell pkg-config --variable=libdir gtk+-2.0) - +PIXBUFBIN=$(shell pkg-config --variable=prefix gdk-pixbuf-2.0)/bin +SOURCEVIEWSHARE=$(shell pkg-config --variable=prefix gtksourceview-2.0)/share ########################################################################### # CoqIde special targets @@ -127,21 +128,24 @@ ide/%.cmx: ide/%.ml ## Install targets #################### -.PHONY: install-coqide install-ide-bin install-ide-toploop install-ide-files install-ide-info install-ide-devfiles install-ide-byte +.PHONY: install-coqide install-ide-bin install-ide-toploop install-ide-files install-ide-info install-ide-devfiles install-ide-byte install-ide-toploop-byte install-coqide-byte ifeq ($(HASCOQIDE),no) install-coqide: install-ide-toploop else install-coqide: install-ide-bin install-ide-toploop install-ide-files install-ide-info install-ide-devfiles endif +ifeq ($(HASCOQIDE),no) +install-coqide-byte: install-ide-toploop-byte +else +install-coqide-byte: install-ide-toploop-byte install-ide-byte +endif # Apparently, coqide.byte is not meant to be installed install-ide-byte: $(MKDIR) $(FULLCOQLIB) $(INSTALLSH) $(FULLCOQLIB) $(IDECMA) - $(MKDIR) $(FULLCOQLIB)/toploop - $(INSTALLBIN) $(IDETOPLOOPCMA) $(FULLCOQLIB)/toploop/ install-ide-bin: $(MKDIR) $(FULLBINDIR) @@ -151,6 +155,10 @@ install-ide-toploop: ifeq ($(BEST),opt) $(INSTALLBIN) $(IDETOPLOOPCMA:.cma=.cmxs) $(FULLCOQLIB)/toploop/ endif +install-ide-toploop-byte: +ifneq ($(BEST),opt) + $(INSTALLBIN) $(IDETOPLOOPCMA) $(FULLCOQLIB)/toploop/ +endif install-ide-devfiles: $(MKDIR) $(FULLCOQLIB) @@ -193,15 +201,14 @@ $(COQIDEAPP)/Contents/Resources/share: $(COQIDEAPP)/Contents $(MKDIR) $@/coq/ $(INSTALLLIB) ide/coq.png ide/*.lang ide/coq_style.xml $@/coq/ $(MKDIR) $@/gtksourceview-2.0/{language-specs,styles} - $(INSTALLLIB) "$(GTKSHARE)/"gtksourceview-2.0/language-specs/{def.lang,language2.rng} $@/gtksourceview-2.0/language-specs/ - $(INSTALLLIB) "$(GTKSHARE)/"gtksourceview-2.0/styles/{styles.rng,classic.xml} $@/gtksourceview-2.0/styles/ + $(INSTALLLIB) "$(SOURCEVIEWSHARE)/"gtksourceview-2.0/language-specs/{def.lang,language2.rng} $@/gtksourceview-2.0/language-specs/ + $(INSTALLLIB) "$(SOURCEVIEWSHARE)/"gtksourceview-2.0/styles/{styles.rng,classic.xml} $@/gtksourceview-2.0/styles/ cp -R "$(GTKSHARE)/"locale $@ - cp -R "$(GTKSHARE)/"icons $@ cp -R "$(GTKSHARE)/"themes $@ $(COQIDEAPP)/Contents/Resources/loaders: $(COQIDEAPP)/Contents $(MKDIR) $@ - $(INSTALLLIB) $$("$(GTKBIN)/gdk-pixbuf-query-loaders" | sed -n -e '5 s!.*= \(.*\)$$!\1!p')/libpixbufloader-png.so $@ + $(INSTALLLIB) $$("$(PIXBUFBIN)/gdk-pixbuf-query-loaders" | sed -n -e '5 s!.*= \(.*\)$$!\1!p')/libpixbufloader-png.so $@ $(COQIDEAPP)/Contents/Resources/immodules: $(COQIDEAPP)/Contents $(MKDIR) $@ @@ -212,7 +219,7 @@ $(COQIDEAPP)/Contents/Resources/etc: $(COQIDEAPP)/Contents/Resources/lib $(MKDIR) $@/xdg/coq $(INSTALLLIB) ide/MacOS/default_accel_map $@/xdg/coq/coqide.keys $(MKDIR) $@/gtk-2.0 - { "$(GTKBIN)/gdk-pixbuf-query-loaders" $@/../loaders/*.so |\ + { "$(PIXBUFBIN)/gdk-pixbuf-query-loaders" $@/../loaders/*.so |\ sed -e "s!/.*\(/loaders/.*.so\)!@executable_path/../Resources/\1!"; } \ > $@/gtk-2.0/gdk-pixbuf.loaders { "$(GTKBIN)/gtk-query-immodules-2.0" $@/../immodules/*.so |\ @@ -224,32 +231,11 @@ $(COQIDEAPP)/Contents/Resources/etc: $(COQIDEAPP)/Contents/Resources/lib $(COQIDEAPP)/Contents/Resources/lib: $(COQIDEAPP)/Contents/Resources/immodules $(COQIDEAPP)/Contents/Resources/loaders $(COQIDEAPP)/Contents $(COQIDEINAPP) $(MKDIR) $@ - $(INSTALLLIB) $(GTKLIBS)/charset.alias $@/ - $(MKDIR) $@/pango/1.8.0/modules - $(INSTALLLIB) "$(GTKLIBS)/pango/1.8.0/modules/"*.so $@/pango/1.8.0/modules/ - { "$(GTKBIN)/pango-querymodules" $@/pango/1.8.0/modules/*.so |\ - sed -e "s!/.*\(/pango/1.8.0/modules/.*.so\)!@executable_path/../Resources/lib\1!"; } \ - > $@/pango/1.8.0/modules.cache - - for i in $$(otool -L $(COQIDEINAPP) |sed -n -e "\@$(GTKLIBS)@ s/[^/]*\(\/[^ ]*\) .*$$/\1/p"); \ - do cp $$i $@/; \ - ide/MacOS/relatify_with-respect-to_.sh $@/$$(basename $$i) $(GTKLIBS) $@; \ - done - for i in $@/../loaders/*.so $@/../immodules/*.so $@/pango/1.8.0/modules/*.so; \ - do \ - for j in $$(otool -L $$i | sed -n -e "\@$(GTKLIBS)@ s/[^/]*\(\/[^ ]*\) .*$$/\1/p"); \ - do cp $$j $@/; ide/MacOS/relatify_with-respect-to_.sh $@/$$(basename $$j) $(GTKLIBS) $@; done; \ - ide/MacOS/relatify_with-respect-to_.sh $$i $(GTKLIBS) $@; \ - done - EXTRAWORK=1; \ - while [ $${EXTRAWORK} -eq 1 ]; \ - do EXTRAWORK=0; \ - for i in $@/*.dylib; \ - do for j in $$(otool -L $$i | sed -n -e "\@$(GTKLIBS)@ s/[^/]*\(\/[^ ]*\) .*$$/\1/p"); \ - do EXTRAWORK=1; cp $$j $@/; ide/MacOS/relatify_with-respect-to_.sh $@/$$(basename $$j) $(GTKLIBS) $@; done; \ - done; \ + macpack -d ../Resources/lib $(COQIDEINAPP) + for i in $@/../loaders/*.so $@/../immodules/*.so; \ + do \ + macpack -d ../lib $$i; \ done - ide/MacOS/relatify_with-respect-to_.sh $(COQIDEINAPP) $(GTKLIBS) $@ $(COQIDEAPP)/Contents/Resources:$(COQIDEAPP)/Contents/Resources/etc $(COQIDEAPP)/Contents/Resources/share $(INSTALLLIB) ide/MacOS/*.icns $@ diff --git a/Makefile.install b/Makefile.install index 02ae724df..85ffc93d5 100644 --- a/Makefile.install +++ b/Makefile.install @@ -74,7 +74,7 @@ ifeq ($(BEST),opt) $(INSTALLBIN) $(TOPLOOPCMA:.cma=.cmxs) $(FULLCOQLIB)/toploop/ endif -install-byte: install-ide-byte +install-byte: install-coqide-byte $(MKDIR) $(FULLBINDIR) $(INSTALLBIN) $(COQTOPBYTE) $(FULLBINDIR) $(INSTALLBIN) $(TOPLOOPCMA) $(FULLCOQLIB)/toploop/ diff --git a/README.ci.md b/README.ci.md index 9e25390d7..cf9da5094 100644 --- a/README.ci.md +++ b/README.ci.md @@ -1,30 +1,42 @@ **WARNING:** This document is a work in progress and intended as a RFC. -If you are not a Coq Developer, don't follow this instructions yet. +If you are not a Coq Developer, don't follow these instructions yet. Introduction ============ -The Coq Travis CI infrastructure is meant to provide lightweight -automatics testing of pull requests. -If you are on GitLab, their integrated CI is also set up. +As of 2017, Coq's Git repository includes a `.travis.yml` file, a +`.gitlab-ci.yml` file, and supporting scripts, that enable lightweight +Continuous Integration (CI) tests to be run on clones of that repository stored +at Github or on a GitLab instance, respectively. This affords two benefits. -More comprehensive testing is the responsability of Coq's [Jenkins CI -server](https://ci.inria.fr/coq/) see, [XXX: add document] for -instructions on how to add your development to Jenkins. +First, it allows developers working on Coq itself to perform CI on their own +Git remotes, thereby enabling them to catch and fix problems with their +proposed changes before submitting pull requests to Coq itself. This in turn +reduces the risk of a faulty PR being opened against the official Coq +repository. -How to submit your development for Coq CI -========================================= +Secondly, it allows developers working on a library dependent on Coq to have +that library included in the Travis CI tests invoked by the official Coq +repository on GitHub. + +(More comprehensive testing than is provided by the Travis CI and GitLab CI +integration is the responsibility of Coq's [Jenkins CI +server](https://ci.inria.fr/coq/) see, [XXX: add document] for instructions on +how to add your development to Jenkins.) + +How to submit your library for inclusion in Coq's Travis CI builds +================================================================== CI provides a convenient way to perform testing of Coq changes versus a set of curated libraries. Are you an author of a Coq library who would be interested in having -the latest Coq changes validated against your development? +the latest Coq changes validated against it? -If so, keep reading! Getting Coq changes tested against your library -is easy, all that you need to do is: +If so, all you need to do is: -1. Put you development in a public repository tracking coq trunk. +1. Put your library in a public repository tracking the `master` + branch of Coq's Git repository. 2. Make sure that your development builds in less than 35 minutes. 3. Submit a PR adding your development. 4. ? diff --git a/dev/build/osx/make-macos-dmg.sh b/dev/build/osx/make-macos-dmg.sh index b43ada907..cbe2a5186 100755 --- a/dev/build/osx/make-macos-dmg.sh +++ b/dev/build/osx/make-macos-dmg.sh @@ -4,19 +4,13 @@ set -e # Configuration setup -eval `opam config env` -make distclean OUTDIR=$PWD/_install DMGDIR=$PWD/_dmg -./configure -debug -prefix $OUTDIR -native-compiler no VERSION=$(sed -n -e '/^let coq_version/ s/^[^"]*"\([^"]*\)"$/\1/p' configure.ml) APP=bin/CoqIDE_${VERSION}.app # Create a .app file with CoqIDE -~/.local/bin/jhbuild run make -j -l2 $APP - -# Build Coq and run test-suite -make && make check +make -j $NJOBS -l2 $APP # Add Coq to the .app file make OLDROOT=$OUTDIR COQINSTALLPREFIX=$APP/Contents/Resources/ install-coq install-ide-toploop @@ -29,7 +23,9 @@ mkdir -p $DMGDIR ln -sf /Applications $DMGDIR/Applications cp -r $APP $DMGDIR +mkdir -p _build + # Temporary countermeasure to hdiutil error 5341 -head -c9703424 /dev/urandom > $DMGDIR/.padding +# head -c9703424 /dev/urandom > $DMGDIR/.padding -hdiutil create -imagekey zlib-level=9 -volname CoqIDE_$VERSION -srcfolder $DMGDIR -ov -format UDZO CoqIDE_$VERSION.dmg +hdiutil create -imagekey zlib-level=9 -volname CoqIDE_$VERSION -srcfolder $DMGDIR -ov -format UDZO _build/CoqIDE_$VERSION.dmg diff --git a/dev/doc/changes.txt b/dev/doc/changes.txt index a48c491d3..0f1a28028 100644 --- a/dev/doc/changes.txt +++ b/dev/doc/changes.txt @@ -188,6 +188,9 @@ In Coqlib / reference location: - The tclWEAK_PROGRESS and tclNOTSAMEGOAL tacticals were removed. Their usecase was very specific. Use tclPROGRESS instead. +- New (internal) tactical `tclINDEPENDENTL` that combined with enter_one allows + to iterate a non-unit tactic on all goals and access their returned values. + - The unsafe flag of the Refine.refine function and its variants has been renamed and dualized into typecheck and has been made mandatory. diff --git a/doc/common/styles/html/coqremote/modules/node/node.css b/doc/common/styles/html/coqremote/modules/node/node.css new file mode 100644 index 000000000..60d01308e --- /dev/null +++ b/doc/common/styles/html/coqremote/modules/node/node.css @@ -0,0 +1,43 @@ + +.node-unpublished { + background-color: #fff4f4; +} +.preview .node { + background-color: #ffffea; +} +#node-admin-filter ul { + list-style-type: none; + padding: 0; + margin: 0; + width: 100%; +} +#node-admin-buttons { + float: left; /* LTR */ + margin-left: 0.5em; /* LTR */ + clear: right; /* LTR */ +} +td.revision-current { + background: #ffc; +} +.node-form .form-text { + display: block; + width: 95%; +} +.node-form .container-inline .form-text { + display: inline; + width: auto; +} +.node-form .standard { + clear: both; +} +.node-form textarea { + display: block; + width: 95%; +} +.node-form .attachments fieldset { + float: none; + display: block; +} +.terms-inline { + display: inline; +} diff --git a/doc/common/styles/html/coqremote/modules/system/defaults.css b/doc/common/styles/html/coqremote/modules/system/defaults.css new file mode 100644 index 000000000..eb983b7f8 --- /dev/null +++ b/doc/common/styles/html/coqremote/modules/system/defaults.css @@ -0,0 +1,52 @@ + +/* +** HTML elements +*/ +fieldset { + margin-bottom: 1em; + padding: .5em; +} +form { + margin: 0; + padding: 0; +} +hr { + height: 1px; + border: 1px solid gray; +} +img { + border: 0; +} +table { + border-collapse: collapse; +} +th { + text-align: left; /* LTR */ + padding-right: 1em; /* LTR */ + border-bottom: 3px solid #ccc; +} + +/* +** Markup free clearing +** Details: http://www.positioniseverything.net/easyclearing.html +*/ +.clear-block:after { + content: "."; + display: block; + height: 0; + clear: both; + visibility: hidden; +} + +.clear-block { + display: inline-block; +} + +/* Hides from IE-mac \*/ +* html .clear-block { + height: 1%; +} +.clear-block { + display: block; +} +/* End hide from IE-mac */ diff --git a/doc/common/styles/html/coqremote/modules/system/system.css b/doc/common/styles/html/coqremote/modules/system/system.css new file mode 100644 index 000000000..9371bb479 --- /dev/null +++ b/doc/common/styles/html/coqremote/modules/system/system.css @@ -0,0 +1,543 @@ + +/* +** HTML elements +*/ +body.drag { + cursor: move; +} +th.active img { + display: inline; +} +tr.even, tr.odd { + background-color: #eee; + border-bottom: 1px solid #ccc; + padding: 0.1em 0.6em; +} +tr.drag { + background-color: #fffff0; +} +tr.drag-previous { + background-color: #ffd; +} +td.active { + background-color: #ddd; +} +td.checkbox, th.checkbox { + text-align: center; +} +tbody { + border-top: 1px solid #ccc; +} +tbody th { + border-bottom: 1px solid #ccc; +} +thead th { + text-align: left; /* LTR */ + padding-right: 1em; /* LTR */ + border-bottom: 3px solid #ccc; +} + +/* +** Other common styles +*/ +.breadcrumb { + padding-bottom: .5em +} +div.indentation { + width: 20px; + height: 1.7em; + margin: -0.4em 0.2em -0.4em -0.4em; /* LTR */ + padding: 0.42em 0 0.42em 0.6em; /* LTR */ + float: left; /* LTR */ +} +div.tree-child { + background: url(../../misc/tree.png) no-repeat 11px center; /* LTR */ +} +div.tree-child-last { + background: url(../../misc/tree-bottom.png) no-repeat 11px center; /* LTR */ +} +div.tree-child-horizontal { + background: url(../../misc/tree.png) no-repeat -11px center; +} +.error { + color: #e55; +} +div.error { + border: 1px solid #d77; +} +div.error, tr.error { + background: #fcc; + color: #200; + padding: 2px; +} +.warning { + color: #e09010; +} +div.warning { + border: 1px solid #f0c020; +} +div.warning, tr.warning { + background: #ffd; + color: #220; + padding: 2px; +} +.ok { + color: #008000; +} +div.ok { + border: 1px solid #00aa00; +} +div.ok, tr.ok { + background: #dfd; + color: #020; + padding: 2px; +} +.item-list .icon { + color: #555; + float: right; /* LTR */ + padding-left: 0.25em; /* LTR */ + clear: right; /* LTR */ +} +.item-list .title { + font-weight: bold; +} +.item-list ul { + margin: 0 0 0.75em 0; + padding: 0; +} +.item-list ul li { + margin: 0 0 0.25em 1.5em; /* LTR */ + padding: 0; + list-style: disc; +} +ol.task-list li.active { + font-weight: bold; +} +.form-item { + margin-top: 1em; + margin-bottom: 1em; +} +tr.odd .form-item, tr.even .form-item { + margin-top: 0; + margin-bottom: 0; + white-space: nowrap; +} +tr.merge-down, tr.merge-down td, tr.merge-down th { + border-bottom-width: 0 !important; +} +tr.merge-up, tr.merge-up td, tr.merge-up th { + border-top-width: 0 !important; +} +.form-item input.error, .form-item textarea.error, .form-item select.error { + border: 2px solid red; +} +.form-item .description { + font-size: 0.85em; +} +.form-item label { + display: block; + font-weight: bold; +} +.form-item label.option { + display: inline; + font-weight: normal; +} +.form-checkboxes, .form-radios { + margin: 1em 0; +} +.form-checkboxes .form-item, .form-radios .form-item { + margin-top: 0.4em; + margin-bottom: 0.4em; +} +.marker, .form-required { + color: #f00; +} +.more-link { + text-align: right; /* LTR */ +} +.more-help-link { + font-size: 0.85em; + text-align: right; /* LTR */ +} +.nowrap { + white-space: nowrap; +} +.item-list .pager { + clear: both; + text-align: center; +} +.item-list .pager li { + background-image:none; + display:inline; + list-style-type:none; + padding: 0.5em; +} +.pager-current { + font-weight:bold; +} +.tips { + margin-top: 0; + margin-bottom: 0; + padding-top: 0; + padding-bottom: 0; + font-size: 0.9em; +} +dl.multiselect dd.b, dl.multiselect dd.b .form-item, dl.multiselect dd.b select { + font-family: inherit; + font-size: inherit; + width: 14em; +} +dl.multiselect dd.a, dl.multiselect dd.a .form-item { + width: 10em; +} +dl.multiselect dt, dl.multiselect dd { + float: left; /* LTR */ + line-height: 1.75em; + padding: 0; + margin: 0 1em 0 0; /* LTR */ +} +dl.multiselect .form-item { + height: 1.75em; + margin: 0; +} + +/* +** Inline items (need to override above) +*/ +.container-inline div, .container-inline label { + display: inline; +} + +/* +** Tab navigation +*/ +ul.primary { + border-collapse: collapse; + padding: 0 0 0 1em; /* LTR */ + white-space: nowrap; + list-style: none; + margin: 5px; + height: auto; + line-height: normal; + border-bottom: 1px solid #bbb; +} +ul.primary li { + display: inline; +} +ul.primary li a { + background-color: #ddd; + border-color: #bbb; + border-width: 1px; + border-style: solid solid none solid; + height: auto; + margin-right: 0.5em; /* LTR */ + padding: 0 1em; + text-decoration: none; +} +ul.primary li.active a { + background-color: #fff; + border: 1px solid #bbb; + border-bottom: #fff 1px solid; +} +ul.primary li a:hover { + background-color: #eee; + border-color: #ccc; + border-bottom-color: #eee; +} +ul.secondary { + border-bottom: 1px solid #bbb; + padding: 0.5em 1em; + margin: 5px; +} +ul.secondary li { + display: inline; + padding: 0 1em; + border-right: 1px solid #ccc; /* LTR */ +} +ul.secondary a { + padding: 0; + text-decoration: none; +} +ul.secondary a.active { + border-bottom: 4px solid #999; +} + +/* +** Autocomplete styles +*/ +/* Suggestion list */ +#autocomplete { + position: absolute; + border: 1px solid; + overflow: hidden; + z-index: 100; +} +#autocomplete ul { + margin: 0; + padding: 0; + list-style: none; +} +#autocomplete li { + background: #fff; + color: #000; + white-space: pre; + cursor: default; +} +#autocomplete li.selected { + background: #0072b9; + color: #fff; +} +/* Animated throbber */ +html.js input.form-autocomplete { + background-image: url(../../misc/throbber.gif); + background-repeat: no-repeat; + background-position: 100% 2px; /* LTR */ +} +html.js input.throbbing { + background-position: 100% -18px; /* LTR */ +} + +/* +** Collapsing fieldsets +*/ +html.js fieldset.collapsed { + border-bottom-width: 0; + border-left-width: 0; + border-right-width: 0; + margin-bottom: 0; + height: 1em; +} +html.js fieldset.collapsed * { + display: none; +} +html.js fieldset.collapsed legend { + display: block; +} +html.js fieldset.collapsible legend a { + padding-left: 15px; /* LTR */ + background: url(../../misc/menu-expanded.png) 5px 75% no-repeat; /* LTR */ +} +html.js fieldset.collapsed legend a { + background-image: url(../../misc/menu-collapsed.png); /* LTR */ + background-position: 5px 50%; /* LTR */ +} +/* Note: IE-only fix due to '* html' (breaks Konqueror otherwise). */ +* html.js fieldset.collapsed legend, +* html.js fieldset.collapsed legend *, +* html.js fieldset.collapsed table * { + display: inline; +} +/* For Safari 2 to prevent collapsible fieldsets containing tables from dissapearing due to tableheader.js. */ +html.js fieldset.collapsible { + position: relative; +} +html.js fieldset.collapsible legend a { + display: block; +} +/* Avoid jumping around due to margins collapsing into collapsible fieldset border */ +html.js fieldset.collapsible .fieldset-wrapper { + overflow: auto; +} + +/* +** Resizable text areas +*/ +.resizable-textarea { + width: 95%; +} +.resizable-textarea .grippie { + height: 9px; + overflow: hidden; + background: #eee url(../../misc/grippie.png) no-repeat center 2px; + border: 1px solid #ddd; + border-top-width: 0; + cursor: s-resize; +} +html.js .resizable-textarea textarea { + margin-bottom: 0; + width: 100%; + display: block; +} + +/* +** Table drag and drop. +*/ +.draggable a.tabledrag-handle { + cursor: move; + float: left; /* LTR */ + height: 1.7em; + margin: -0.4em 0 -0.4em -0.5em; /* LTR */ + padding: 0.42em 1.5em 0.42em 0.5em; /* LTR */ + text-decoration: none; +} +a.tabledrag-handle:hover { + text-decoration: none; +} +a.tabledrag-handle .handle { + margin-top: 4px; + height: 13px; + width: 13px; + background: url(../../misc/draggable.png) no-repeat 0 0; +} +a.tabledrag-handle-hover .handle { + background-position: 0 -20px; +} + +/* +** Teaser splitter +*/ +.joined + .grippie { + height: 5px; + background-position: center 1px; + margin-bottom: -2px; +} +/* Keeps inner content contained in Opera 9. */ +.teaser-checkbox { + padding-top: 1px; +} +div.teaser-button-wrapper { + float: right; /* LTR */ + padding-right: 5%; /* LTR */ + margin: 0; +} +.teaser-checkbox div.form-item { + float: right; /* LTR */ + margin: 0 5% 0 0; /* LTR */ + padding: 0; +} +textarea.teaser { + display: none; +} +html.js .no-js { + display: none; +} + +/* +** Progressbar styles +*/ +.progress { + font-weight: bold; +} +.progress .bar { + background: #fff url(../../misc/progress.gif); + border: 1px solid #00375a; + height: 1.5em; + margin: 0 0.2em; +} +.progress .filled { + background: #0072b9; + height: 1em; + border-bottom: 0.5em solid #004a73; + width: 0%; +} +.progress .percentage { + float: right; /* LTR */ +} +.progress-disabled { + float: left; /* LTR */ +} +.ahah-progress { + float: left; /* LTR */ +} +.ahah-progress .throbber { + width: 15px; + height: 15px; + margin: 2px; + background: transparent url(../../misc/throbber.gif) no-repeat 0px -18px; + float: left; /* LTR */ +} +tr .ahah-progress .throbber { + margin: 0 2px; +} +.ahah-progress-bar { + width: 16em; +} + +/* +** Formatting for welcome page +*/ +#first-time strong { + display: block; + padding: 1.5em 0 .5em; +} + +/* +** To be used with tableselect.js +*/ +tr.selected td { + background: #ffc; +} + +/* +** Floating header for tableheader.js +*/ +table.sticky-header { + margin-top: 0; + background: #fff; +} + +/* +** Installation clean URLs +*/ +#clean-url.install { + display: none; +} + +/* +** For anything you want to hide on page load when JS is enabled, so +** that you can use the JS to control visibility and avoid flicker. +*/ +html.js .js-hide { + display: none; +} + +/* +** Styles for the system modules page (admin/build/modules) +*/ +#system-modules div.incompatible { + font-weight: bold; +} + +/* +** Styles for the system themes page (admin/build/themes) +*/ +#system-themes-form div.incompatible { + font-weight: bold; +} + +/* +** Password strength indicator +*/ +span.password-strength { + visibility: hidden; +} +input.password-field { + margin-right: 10px; /* LTR */ +} +div.password-description { + padding: 0 2px; + margin: 4px 0 0 0; + font-size: 0.85em; + max-width: 500px; +} +div.password-description ul { + margin-bottom: 0; +} +.password-parent { + margin: 0 0 0 0; +} +/* +** Password confirmation checker +*/ +input.password-confirm { + margin-right: 10px; /* LTR */ +} +.confirm-parent { + margin: 5px 0 0 0; +} +span.password-confirm { + visibility: hidden; +} +span.password-confirm span { + font-weight: normal; +} diff --git a/doc/common/styles/html/coqremote/modules/user/user.css b/doc/common/styles/html/coqremote/modules/user/user.css new file mode 100644 index 000000000..7b2163e3d --- /dev/null +++ b/doc/common/styles/html/coqremote/modules/user/user.css @@ -0,0 +1,58 @@ + +#permissions td.module { + font-weight: bold; +} +#permissions td.permission { + padding-left: 1.5em; /* LTR */ +} +#access-rules .access-type, #access-rules .rule-type { + margin-right: 1em; /* LTR */ + float: left; /* LTR */ +} +#access-rules .access-type .form-item, #access-rules .rule-type .form-item { + margin-top: 0; +} +#access-rules .mask { + clear: both; +} +#user-login-form { + text-align: center; +} +#user-admin-filter ul { + list-style-type: none; + padding: 0; + margin: 0; + width: 100%; +} +#user-admin-buttons { + float: left; /* LTR */ + margin-left: 0.5em; /* LTR */ + clear: right; /* LTR */ +} +#user-admin-settings fieldset .description { + font-size: 0.85em; + padding-bottom: .5em; +} + +/* Generated by user.module but used by profile.module: */ +.profile { + clear: both; + margin: 1em 0; +} +.profile .picture { + float: right; /* LTR */ + margin: 0 1em 1em 0; /* LTR */ +} +.profile h3 { + border-bottom: 1px solid #ccc; +} +.profile dl { + margin: 0 0 1.5em 0; +} +.profile dt { + margin: 0 0 0.2em 0; + font-weight: bold; +} +.profile dd { + margin: 0 0 1em 0; +} diff --git a/doc/common/styles/html/coqremote/sites/all/themes/coq/coqdoc.css b/doc/common/styles/html/coqremote/sites/all/themes/coq/coqdoc.css new file mode 100644 index 000000000..d23ea8f36 --- /dev/null +++ b/doc/common/styles/html/coqremote/sites/all/themes/coq/coqdoc.css @@ -0,0 +1,329 @@ +body { padding: 0px 0px; + margin: 0px 0px; + background-color: white } + +#page { display: block; + padding: 0px; + margin: 0px; + padding-bottom: 10px; } + +#header { display: block; + position: relative; + padding: 0; + margin: 0; + vertical-align: middle; + border-bottom-style: solid; + border-width: thin } + +#header h1 { padding: 0; + margin: 0;} + + +/* Contents */ + +#main{ display: block; + padding: 10px; + font-family: sans-serif; + font-size: 100%; + line-height: 100% } + +#main h1 { line-height: 95% } /* allow for multi-line headers */ + +#main a.idref:visited {color : #416DFF; text-decoration : none; } +#main a.idref:link {color : #416DFF; text-decoration : none; } +#main a.idref:hover {text-decoration : none; } +#main a.idref:active {text-decoration : none; } + +#main a.modref:visited {color : #416DFF; text-decoration : none; } +#main a.modref:link {color : #416DFF; text-decoration : none; } +#main a.modref:hover {text-decoration : none; } +#main a.modref:active {text-decoration : none; } + +#main .keyword { color : #cf1d1d } +#main { color: black } + +.section { background-color: rgb(60%,60%,100%); + padding-top: 13px; + padding-bottom: 13px; + padding-left: 3px; + margin-top: 5px; + margin-bottom: 5px; + font-size : 175% } + +h2.section { background-color: rgb(80%,80%,100%); + padding-left: 3px; + padding-top: 12px; + padding-bottom: 10px; + font-size : 130% } + +h3.section { background-color: rgb(90%,90%,100%); + padding-left: 3px; + padding-top: 7px; + padding-bottom: 7px; + font-size : 115% } + +h4.section { +/* + background-color: rgb(80%,80%,80%); + max-width: 20em; + padding-left: 5px; + padding-top: 5px; + padding-bottom: 5px; +*/ + background-color: white; + padding-left: 0px; + padding-top: 0px; + padding-bottom: 0px; + font-size : 100%; + font-weight : bold; + text-decoration : underline; + } + +#main .doc { margin: 0px; + font-family: sans-serif; + font-size: 100%; + line-height: 125%; + max-width: 40em; + color: black; + padding: 10px; + background-color: #90bdff} + +.inlinecode { + display: inline; +/* font-size: 125%; */ + color: #666666; + font-family: monospace } + +.doc .inlinecode { + display: inline; + font-size: 120%; + color: rgb(30%,30%,70%); + font-family: monospace } + +.doc .inlinecode .id { + color: rgb(30%,30%,70%); +} + +.inlinecodenm { + display: inline; + color: #444444; +} + +.doc .code { + display: inline; + font-size: 120%; + color: rgb(30%,30%,70%); + font-family: monospace } + +.comment { + display: inline; + font-family: monospace; + color: rgb(50%,50%,80%); +} + +.code { + display: block; +/* padding-left: 15px; */ + font-size: 110%; + font-family: monospace; + } + +table.infrule { + border: 0px; + margin-left: 50px; + margin-top: 10px; + margin-bottom: 10px; +} + +td.infrule { + font-family: monospace; + text-align: center; +/* color: rgb(35%,35%,70%); */ + padding: 0px; + line-height: 100%; +} + +tr.infrulemiddle hr { + margin: 1px 0 1px 0; +} + +.infrulenamecol { + color: rgb(60%,60%,60%); + font-size: 80%; + padding-left: 1em; + padding-bottom: 0.1em +} + +/* Pied de page */ + +#footer { font-size: 65%; + font-family: sans-serif; } + +/* Identifiers: <span class="id" title="...">) */ + +.id { display: inline; } + +.id[title="constructor"] { + color: rgb(60%,0%,0%); +} + +.id[title="var"] { + color: rgb(40%,0%,40%); +} + +.id[title="variable"] { + color: rgb(40%,0%,40%); +} + +.id[title="definition"] { + color: rgb(0%,40%,0%); +} + +.id[title="abbreviation"] { + color: rgb(0%,40%,0%); +} + +.id[title="lemma"] { + color: rgb(0%,40%,0%); +} + +.id[title="instance"] { + color: rgb(0%,40%,0%); +} + +.id[title="projection"] { + color: rgb(0%,40%,0%); +} + +.id[title="method"] { + color: rgb(0%,40%,0%); +} + +.id[title="inductive"] { + color: rgb(0%,0%,80%); +} + +.id[title="record"] { + color: rgb(0%,0%,80%); +} + +.id[title="class"] { + color: rgb(0%,0%,80%); +} + +.id[title="keyword"] { + color : #cf1d1d; +/* color: black; */ +} + +/* Deprecated rules using the 'type' attribute of <span> (not xhtml valid) */ + +.id[type="constructor"] { + color: rgb(60%,0%,0%); +} + +.id[type="var"] { + color: rgb(40%,0%,40%); +} + +.id[type="variable"] { + color: rgb(40%,0%,40%); +} + +.id[type="definition"] { + color: rgb(0%,40%,0%); +} + +.id[type="abbreviation"] { + color: rgb(0%,40%,0%); +} + +.id[type="lemma"] { + color: rgb(0%,40%,0%); +} + +.id[type="instance"] { + color: rgb(0%,40%,0%); +} + +.id[type="projection"] { + color: rgb(0%,40%,0%); +} + +.id[type="method"] { + color: rgb(0%,40%,0%); +} + +.id[type="inductive"] { + color: rgb(0%,0%,80%); +} + +.id[type="record"] { + color: rgb(0%,0%,80%); +} + +.id[type="class"] { + color: rgb(0%,0%,80%); +} + +.id[type="keyword"] { + color : #cf1d1d; +/* color: black; */ +} + +.inlinecode .id { + color: rgb(0%,0%,0%); +} + + +/* TOC */ + +#toc h2 { + padding: 10px; + background-color: rgb(60%,60%,100%); +} + +#toc li { + padding-bottom: 8px; +} + +/* Index */ + +#index { + margin: 0; + padding: 0; + width: 100%; +} + +#index #frontispiece { + margin: 1em auto; + padding: 1em; + width: 60%; +} + +.booktitle { font-size : 140% } +.authors { font-size : 90%; + line-height: 115%; } +.moreauthors { font-size : 60% } + +#index #entrance { + text-align: center; +} + +#index #entrance .spacer { + margin: 0 30px 0 30px; +} + +#index #footer { + position: absolute; + bottom: 0; +} + +.paragraph { + height: 0.75em; +} + +ul.doclist { + margin-top: 0em; + margin-bottom: 0em; +} diff --git a/doc/common/styles/html/coqremote/sites/all/themes/coq/style.css b/doc/common/styles/html/coqremote/sites/all/themes/coq/style.css new file mode 100644 index 000000000..32c0b3316 --- /dev/null +++ b/doc/common/styles/html/coqremote/sites/all/themes/coq/style.css @@ -0,0 +1,801 @@ +body +{ + background: white; + color:#444; + font:normal normal normal small/1.5em "Lucida Grande", Verdana, sans-serif; + margin:0; + padding:0; +} + +h2 +{ + font-size:150%; + font-weight:normal; + margin:20px 0 0; +} + +h3 +{ + font-size:130%; + font-weight:normal; +} + +a:link,a:visited +{ + color:#660403; + font-weight:normal; + text-decoration:none; +} + +a:hover +{ + color: red; + text-decoration:none; +} + +#container +{ + margin: 0; + padding: 0; + } + + /*----------header, logo and site name styles----------*/ + #headertop + { + display: block; + /* position:absolute; */ + min-width: 700px; + top: 0; + width: 100%; + height:30px; + z-index: 1; + background: transparent url('images/header_top.png') repeat-x; + } + + #header + { + min-width: 700px; + width: 100%; height:70px; + position: relative; + left: 0; top: 0; + background: transparent url('images/header_bot.png') repeat-x; + } + + #logo + { + float:left; + z-index: 2; + position: absolute; + top: -15px; + left: 0px; + } + + #logo img + { + border:0; + float:left; + } + + #logoWrapper + { + line-height:4em; + } + + #siteName + { + position: relative; + top: 10px; left: 80px; + color:#fff; + float:left; + font-size:350%; + } + + #siteName a + { + color:#fff; + text-decoration:none; + } + + #siteName a:hover + { + color:#ddd; + text-decoration:none; + } + + #siteSlogan + { + color:#eee; + float:left; + font-size:170%; + margin:50px 0 0 10px; + text-transform:lowercase; + white-space:nowrap; + } + + /*----------nav styles -- primary links in header----------*/ + + #nav +{ + position:absolute; right:0; + margin: 0; + padding: 5px; + } + +#nav ul + { + list-style:none outside none; + list-style-image:none; + margin:0; + padding:0; + } + + #nav li + { + display: inline; + margin: 0; padding: 4px; + } + + #nav li a + { + border:medium none; + color:#ccc; + font-weight:normal; + padding-left:10px; + padding-right:10px; + text-decoration:none; + } + + #nav li a:hover + { + background:#7B0505 none repeat; + border:medium none; + border-left:1px solid #ddd; + border-right:1px solid #ddd; + color:#fff; + padding: 6px 9px 5px 9px; + } + + +/************** FOOTER *******************/ + + +#footer +{ + background:transparent url('images/footer.png') repeat-x; + width:100%; + clear:both; + font-size:85%; + text-align:center; + /* position:fixed; */ + margin: 0; + padding: 0; +} + + +#nav-footer +{ + display: inline; + color:#444; + margin: 0; + padding: 0; + text-align:right; + } + +#nav-footer ul + { + list-style:none outside none; + list-style-image:none; + margin:0; + padding:0px; padding-right: 5px; + } + +#nav-footer li +{ + display:inline; padding: 4px; +} + + #nav-footer li a + { + border:medium none; + color:#ccc; + font-size: 11px; + font-weight:normal; + padding-left: 10px; + padding-right: 10px; + text-decoration:none; + } + + #nav-footer li a:hover + { + background:#7B0505 none repeat; + border:medium none; + border-left:1px solid #ddd; + border-right:1px solid #ddd; + color:#fff; + margin:0; + padding: 3px 9px 0px 9px; + } + + + /*----------main content----------*/ + #content + { + display: block; + position: static; + +/* min-width: 640px; */ + max-width: 800px; + + margin-left:40px; + margin-right:300px; + padding: 2ex 2ex; + + z-index:1; + } + +.content { + display: block; + position: relative; + + margin: 0; + padding: 0; +} + + /*----------sidebar styles----------*/ + #sidebarWrapper + { + /* background:transparent url('images/sidebar_bottom.jpg') no-repeat scroll left bottom;*/ + display:block; + position:fixed; + /* avant : top: 100px; right:0px*/ + top: 15px; /* 180 */ + right:0px; + left: auto; + + margin-right: 0px; + + /* avant + width: 12%; + min-width:80px; */ + + /* width: 18%; */ + /* min-*/ + width:270px; + + z-index:0; + overflow:hidden; + +/* ajout precedent:*/ +/* min-height:320px; + padding:10px; + background-image:url('http://www.lix.polytechnique.fr/Labo/Denis.Cousineau/data/coq/rttr340bis.png'); + background-repeat : repeat-x ;*/ + +/* last ajout */ + /* min-height:510px; */ /* 360 */ + padding-left:0px; + padding-right:0px; + padding-top:105px; /* 40 */ + padding-bottom:/*105px*/115px; + /* background:transparent url('http://www.lix.polytechnique.fr/Labo/Denis.Cousineau/data/coq/trig6b.png') no-repeat scroll left top; */ + background:transparent url('images/sidebarbot.png') no-repeat scroll right bottom; + + } + +#sidebar { + padding-left: 40px; + padding-top: 105px; + overflow: visible; + background:transparent url('images/sidebartop.png') no-repeat scroll right top; +} + +#sidebar .title +{ + /* avant :border-bottom:1px solid #eee;*/ + /* avant : color:#660403;*/ + color:#2D0102; + font-size:120%; + font-weight:bold; + line-height:19px; + margin:10px 0; +} + +/*----------page styles----------*/ +.pageTitle +{ + color:#2D0102; + font-size:220%; + margin:10px 0 20px; +} + +.mission +{ + background-color:#efefef; + border:solid 1px #ccc; + margin:0 0 10px 0; + padding:10px; +} + +.messages +{ + color:#C80000; + font-size:110%; + margin:10px 0; +} + +/*----------node styles----------*/ +.nodeTitle +{ + background: url('images/nodeTitle.gif') no-repeat 0 100%; + color:#9a0000; + font-size: 100%; + margin:0; +} + +.nodeTitle a +{ + color:#660403; + text-decoration:none; +} + +.nodeTitle a:hover +{ + color:#d00000; + text-decoration:none; +} + +.node +{ + margin:0 0 20px; +} + +.content p +{ + margin:10px 0; +} + +.submitted +{ + color:#a3a3a3; + font-size:70%; +} + +.nodeLinks +{ + font-size:95%; + margin:0; + padding:0; +} + +.taxonomy +{ + background:url('icons/tag_red.png') no-repeat 0 7px; + font-size:80%; + padding:0 0 5px 16px; +} + +/*----------comment styles----------*/ +.commentTitle +{ + Border-bottom:1px solid #ddd; + color:#9a0000; + font-size:130%; + margin:20px 0 0; +} + +.commentTitle a +{ + color:#660403; + text-decoration:none; +} + +.commentTitle a:hover +{ + color:#d00000; + text-decoration:none; +} + +.commentLinks +{ + background:#f7f7f7; + border:1px solid #e1e1e1; + color:#444; + font-size:95%; + margin:20px 0 30px; + padding:4px 0 4px 4px; +} + + +/*----------img styles----------*/ +img +{ + padding:3px; +} + +/*----------icons for links----------*/ +.comment_comments a +{ + background:url('icons/comment.png') no-repeat 0 2px; + padding-bottom:5px; + padding-left:20px; +} + +.node_read_more a +{ + background:url('icons/page_white_go.png') no-repeat; + padding-bottom:5px; + padding-left:20px; +} + +.comment_add a,.comment_reply a +{ + background:url('icons/comment_add.png') no-repeat; + padding-bottom:5px; + padding-left:20px; +} +.comment_delete a +{ + background:url('icons/comment_delete.png') no-repeat; + padding-bottom:5px; + padding-left:20px; +} + +.comment_edit a +{ + background:url('icons/comment_edit.png') no-repeat; + padding-bottom:5px; + padding-left:20px; +} + +/*----------TinyMCE editor----------*/ +body.mceContentBody +{ + background:#fff; + color:#000; + font-size:12px; +} + +body.mceContentBody a:link +{ + color:#ff0000; +} + +/*----------table styles----------*/ +table +{ + margin:1em 0; + width:100%; +} + +thead th +{ + border-bottom:2px solid #AAA; + color:#494949; + font-weight:bold; +} + +td,th +{ + padding:.3em 0 .5em; +} + +tr.even,tr.odd,tbody th +{ + border:solid #D5D6D7; + border-width:1px 0; +} + +tr.even +{ + background:#fff; +} + +td.region,td.module,td.container +{ + background:#D5D6D7; + border-bottom:1px solid #AAA; + border-top:1.5em solid #fff; + color:#455067; + font-weight:bold; +} + +tr:first-child td.region,tr:first-child td.module,tr:first-child td.container +{ + border-top-width:0; +} + +td.menu-disabled,td.menu-disabled a +{ + background-color:#D5C2C2; + color:#000; +} + +/*----------other styles----------*/ + +.block +{ + margin:5px 0 20px; +} + +.thumbnail,.preview +{ + border:1px solid #ccc; +} + +.lstlisting { + display: block; + font-family: monospace; + white-space: pre; + margin: 1em 0; +} +.center { + text-align: center; +} +.centered { + display: block-inline; +} + +/*----------download table------------*/ + +table.downloadtable +{ + width:90%; + margin-left:auto; + margin-right:auto; +} + +table.downloadtable td.downloadheader +{ +padding: 2px 1em; +font-weight: bold; +font-size: 120%; +color: white; +background: transparent url('images/header_bot.png') repeat-x; +/*background-color: #660403; */ +border: solid 2px white; +border-left: none; +} + +table.downloadtable td.downloadcategory +{ +padding: 2px 1em; +background-color: #dfbfbe; +text-indent: 0; +} + +table.downloadtable td.downloadsize +{ +text-indent: 0; +white-space: nowrap; +height: 52px; +} + +table.downloadtable td +{ +padding: 2px 1em; +background-color: #dfbfbe; +border-right: solid white 2px; +} + + +table.downloadtable td.downloadtopline +{ +border-top: solid white 2px; +} + +table.downloadtable td.downloadtoprightline +{ +border-top: solid 2px white; 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+ left:0px; + + + margin: 0; + padding: .5ex 2em; + + text-indent: 2em; + text-align: justify; +} + + +.frameworklabel +{ + display: inline; + position:relative; + top:-1.3ex; + + margin-left:2ex; + padding-top:.4ex; + padding-bottom:.4ex; + padding-right:1ex; + padding-left:1ex; + + border: none; + background: white; + color: black; + + font-weight: bold; + font-size:115%; +} + +.frameworklinks { + display:block; + position:relative; + top:1.4ex; + + margin-right:2ex; + + text-align:right; + font-size:100% + } + +.frameworklinks ul +{ + display: inline; + padding: 0px 1ex; + + border: none; + background: white; +} + + +.frameworklinks li + { + display:inline; + padding: 1ex 0px; + } + + .frameworklinks li a +{ + border:medium none; + + margin: 0px 1ex; + padding-left:2px; + padding-right:3px; + + font-weight:normal; + text-decoration:none; + + color: #660003; +} + + .frameworklinks li a:hover + { + color: red; + + border: none; + } + +/* General flat lists */ +.flatlist li {display: inline} + +/* For sections in bycat.html */ +.bycatsection dt { + text-indent: 3em +} + +.bycatsection dt a +{ + font-weight: bold; + color:#444; +} + +/* footnote is used in the new contribution form */ +.footnote { + text-indent: 0pt; + font-size: 80%; + color: silver; + text-align: justify +} + +/****************** CoqIDE Screenshots *****************/ + + +.SCpager { + position:relative; + top:5px; + width:630px; + background: transparent url('images/header_bot.png') repeat-x; + padding:4px; +} + +.SCpagercontent { + width:390px; + position:relative; + margin-left:auto; + margin-right:auto; +} + +.SCthumb { + height:45px; + margin-left:2px; + margin-right:2px; +} + +.SCthumbselected { + height:55px; + margin-left:2px; + margin-right:2px; +} + +.SCcontent { + position:relative; + top:5px; + width:638px; + background-color: #dfbfbe; +} + +.SCscreenshot { + position:relative; + height:400px; + width:auto; + margin:15px auto 15px 19px; +} diff --git a/doc/refman/Extraction.tex b/doc/refman/Extraction.tex index 8cb049d50..499239b6f 100644 --- a/doc/refman/Extraction.tex +++ b/doc/refman/Extraction.tex @@ -381,6 +381,9 @@ some specific {\tt Extract Constant} when primitive counterparts exist. \Example Typical examples are the following: +\begin{coq_eval} +Require Extraction. +\end{coq_eval} \begin{coq_example} Extract Inductive unit => "unit" [ "()" ]. Extract Inductive bool => "bool" [ "true" "false" ]. diff --git a/doc/refman/RefMan-cic.tex b/doc/refman/RefMan-cic.tex index 96fb1eb75..ad795d406 100644 --- a/doc/refman/RefMan-cic.tex +++ b/doc/refman/RefMan-cic.tex @@ -558,7 +558,7 @@ $\Sort$ is called the sort of the inductive type $t$. \paragraph{Examples} \newcommand\ind[3]{$\mathsf{Ind}~[#1]\left(\hskip-.4em - \begin{array}{r @{\mathrm{~:=~}} l} + \begin{array}{r@{\mathrm{~:=~}}l} #2 & #3 \\ \end{array} \hskip-.4em @@ -569,7 +569,7 @@ The declaration for parameterized lists is: \begin{latexonly} \vskip.5em -\ind{1}{[\List:\Set\ra\Set]}{\left[\begin{array}{r \colon l} + \ind{1}{[\List:\Set\ra\Set]}{\left[\begin{array}{r@{:}l} \Nil & \forall A:\Set,\List~A \\ \cons & \forall A:\Set, A \ra \List~A \ra \List~A \end{array} @@ -613,8 +613,8 @@ Inductive list (A:Set) : Set := \noindent The declaration for a mutual inductive definition of {\tree} and {\forest} is: \begin{latexonly} \vskip.5em -\ind{~}{\left[\begin{array}{r \colon l}\tree&\Set\\\forest&\Set\end{array}\right]} - {\left[\begin{array}{r \colon l} +\ind{~}{\left[\begin{array}{r@{:}l}\tree&\Set\\\forest&\Set\end{array}\right]} + {\left[\begin{array}{r@{:}l} \node & \forest \ra \tree\\ \emptyf & \forest\\ \consf & \tree \ra \forest \ra \forest\\ @@ -680,15 +680,15 @@ with forest : Set := \noindent The declaration for a mutual inductive definition of {\even} and {\odd} is: \begin{latexonly} - \newcommand\GammaI{\left[\begin{array}{r \colon l} - \even & \nat\ra\Prop \\ - \odd & \nat\ra\Prop + \newcommand\GammaI{\left[\begin{array}{r@{:}l} + \even & \nat\ra\Prop \\ + \odd & \nat\ra\Prop \end{array} \right]} - \newcommand\GammaC{\left[\begin{array}{r \colon l} - \evenO & \even~\nO \\ - \evenS & \forall n : \nat, \odd~n \ra \even~(\nS~n)\\ - \oddS & \forall n : \nat, \even~n \ra \odd~(\nS~n) + \newcommand\GammaC{\left[\begin{array}{r@{:}l} + \evenO & \even~\nO \\ + \evenS & \forall n : \nat, \odd~n \ra \even~(\nS~n)\\ + \oddS & \forall n : \nat, \even~n \ra \odd~(\nS~n) \end{array} \right]} \vskip.5em @@ -769,7 +769,7 @@ Provided that our environment $E$ contains inductive definitions we showed befor these two inference rules above enable us to conclude that: \vskip.5em \newcommand\prefix{E[\Gamma]\vdash\hskip.25em} -$\begin{array}{@{} l} +$\begin{array}{@{}l} \prefix\even : \nat\ra\Prop\\ \prefix\odd : \nat\ra\Prop\\ \prefix\evenO : \even~\nO\\ @@ -1425,6 +1425,9 @@ If there is an hypothesis $h:a=b$ in the local context, it can be used for rewriting not only in logical propositions but also in any type. % In that case, the term \verb!eq_rec! which was defined as an axiom, is % now a term of the calculus. +\begin{coq_eval} +Require Extraction. +\end{coq_eval} \begin{coq_example} Print eq_rec. Extraction eq_rec. diff --git a/doc/refman/RefMan-gal.tex b/doc/refman/RefMan-gal.tex index 71977d3e9..ef12fe416 100644 --- a/doc/refman/RefMan-gal.tex +++ b/doc/refman/RefMan-gal.tex @@ -37,7 +37,7 @@ Similarly, the notation ``\nelist{\entry}{}'' stands for a non empty sequence of expressions parsed by the ``{\entry}'' entry, without any separator between. -At the end, the notation ``\sequence{\entry}{\tt sep}'' stands for a +Finally, the notation ``\sequence{\entry}{\tt sep}'' stands for a possibly empty sequence of expressions parsed by the ``{\entry}'' entry, separated by the literal ``{\tt sep}''. diff --git a/doc/refman/RefMan-int.tex b/doc/refman/RefMan-int.tex index eca3efcdd..2b9e4e605 100644 --- a/doc/refman/RefMan-int.tex +++ b/doc/refman/RefMan-int.tex @@ -58,7 +58,7 @@ Chapter~\ref{Addoc-coqide}. \section*{How to read this book} -This is a Reference Manual, not a User Manual, then it is not made for a +This is a Reference Manual, not a User Manual, so it is not made for a continuous reading. However, it has some structure that is explained below. diff --git a/doc/refman/RefMan-oth.tex b/doc/refman/RefMan-oth.tex index bf48057cd..8f43ebcfb 100644 --- a/doc/refman/RefMan-oth.tex +++ b/doc/refman/RefMan-oth.tex @@ -974,7 +974,20 @@ line provided it does not exceed the printing width (See {\tt Set Printing Width} above). \subsection[\tt Test Printing Compact Contexts.]{\tt Test Printing Compact Contexts.\optindex{Printing Compact Contexts}} -This command displays the current state of compaction of goal d'isolat. +This command displays the current state of compaction of goal. + + +\subsection[\tt Unset Printing Unfocused.]{\tt Unset Printing Unfocused.\optindex{Printing Unfocused}} +This command resets the displaying of goals to focused goals only +(default). Unfocused goals are created by focusing other goals with +bullets(see~\ref{bullets}) or curly braces (see~\ref{curlybacket}). + +\subsection[\tt Set Printing Unfocused.]{\tt Set Printing Unfocused.\optindex{Printing Unfocused}} +This command enables the displaying of unfocused goals. The goals are +displayed after the focused ones and are distinguished by a separator. + +\subsection[\tt Test Printing Unfocused.]{\tt Test Printing Unfocused.\optindex{Printing Unfocused}} +This command displays the current state of unfocused goals display. \subsection[\tt Set Printing Dependent Evars Line.]{\tt Set Printing Dependent Evars Line.\optindex{Printing Dependent Evars Line}} This command enables the printing of the ``{\tt (dependent evars: \ldots)}'' diff --git a/doc/refman/RefMan-pro.tex b/doc/refman/RefMan-pro.tex index 95fee3241..eb59ca584 100644 --- a/doc/refman/RefMan-pro.tex +++ b/doc/refman/RefMan-pro.tex @@ -308,7 +308,7 @@ last {\tt Focus} command. Succeeds in the proof is fully unfocused, fails is there are some goals out of focus. -\subsection[\tt \{ \textrm{and} \}]{\tt \{ \textrm{and} \}\comindex{\{}\comindex{\}}} +\subsection[\tt \{ \textrm{and} \}]{\tt \{ \textrm{and} \}\comindex{\{}\comindex{\}}}\label{curlybacket} The command {\tt \{} (without a terminating period) focuses on the first goal, much like {\tt Focus.} does, however, the subproof can only be unfocused when it has been fully solved (\emph{i.e.} when @@ -327,7 +327,7 @@ unfocus it or focus the next one. \end{ErrMsgs} \subsection[Bullets]{Bullets\comindex{+ (command)} - \comindex{- (command)}\comindex{* (command)}\index{Bullets}} + \comindex{- (command)}\comindex{* (command)}\index{Bullets}}\label{bullets} Alternatively to {\tt \{} and {\tt \}}, proofs can be structured with bullets. The use of a bullet $b$ for the first time focuses on the first goal $g$, the same bullet cannot be used again until the proof diff --git a/doc/refman/RefMan-sch.tex b/doc/refman/RefMan-sch.tex index d3719bed4..23a1c9b02 100644 --- a/doc/refman/RefMan-sch.tex +++ b/doc/refman/RefMan-sch.tex @@ -227,6 +227,7 @@ We define the function \texttt{div2} as follows: \begin{coq_eval} Reset Initial. +Require Import FunInd. \end{coq_eval} \begin{coq_example*} diff --git a/doc/refman/RefMan-ssr.tex b/doc/refman/RefMan-ssr.tex new file mode 100644 index 000000000..61f7421c4 --- /dev/null +++ b/doc/refman/RefMan-ssr.tex @@ -0,0 +1,4932 @@ +\achapter{The SSReflect proof language} +\aauthor{Georges Gonthier, Assia Mahboubi, Enrico Tassi} + +\newcommand{\ssr}{{\sc SSReflect}} + +% listing +\ifhevea\newcommand{\ssrC}[1]{\texttt{#1}}\else\newcommand{\ssrC}[1]{\text{\lstinline!#1!}}\fi +\ifhevea\renewenvironment{center}{\@open{div}{class="center"}\@open{div}{class="centered"}}{\@close{div}\@close{div}}\fi +% non-terminal +%\newcommand\ssrN[2][]{\ensuremath{\langle\mbox{\itshape\rmfamily\small #2}\rangle_{#1}}} +\newcommand\ssrN[2][]{{\textsl {#2}}\ensuremath{_{#1}}} +\ifhevea\newcommand{\underbar}[1]{\underline{#1}}\fi + +% TODO: only use \ssrC +\let\ssrL=\lstinline + +\newcommand{\iitem}{{\it i-item}} +\newcommand{\ditem}{{\it d-item}} +\newcommand{\optional}[1]{{\it[}#1{\it]}} +\newcommand{\optsep}{{\it|}} +\newcommand{\idx}[1]{\tacindex{#1 (ssreflect)}} +\newcommand{\idxC}[1]{\comindex{#1 (ssreflect)}} + +\newenvironment{new}% + {\begin{Sbox}\begin{minipage}{0.97\textwidth}% + \begin{flushright}\textcolor{red}{\fbox{Version 1.3}}% + \end{flushright}\noindent}% + {\end{minipage}\end{Sbox}\noindent\doublebox{\TheSbox}} +\section{Introduction}\label{sec:intro} + +This chapter describes a set of tactics known as \ssr{} +originally designed to provide support for the so-called \emph{small scale +reflection} proof methodology. Despite the original purpose this set of tactic +is of general interest and is available in Coq starting from version 8.7. + +\ssr{} was developed independently of the tactics described in +Chapter~\ref{Tactics}. Indeed the scope of the tactics part of +\ssr{} largely overlaps with the standard set of tactics. Eventually +the overlap will be reduced in future releases of Coq. + +Proofs written in \ssr{} typically look quite different from the +ones written using only tactics as per Chapter~\ref{Tactics}. +We try to summarise here the most ``visible'' ones in order to +help the reader already accustomed to the tactics described in +Chapter~\ref{Tactics}to read this chapter. + +The first difference between the tactics described in this +chapter and the tactics described in Chapter~\ref{Tactics} is the way +hypotheses are managed (we call this \emph{bookkeeping}). +In Chapter~\ref{Tactics} the most common +approach is to avoid moving explicitly hypotheses back and forth +between the context and the conclusion of the goal. On the contrary +in \ssr{} +all bookkeeping is performed on the conclusion of the goal, using for +that purpose a couple of syntactic constructions behaving similar to +tacticals (and often named as such in this chapter). +The \ssrC{:} tactical moves hypotheses from the context to the +conclusion, while \ssrC{=>} moves hypotheses from the +conclusion to the context, and \ssrC{in} moves back +and forth an hypothesis from the context to the conclusion for the +time of applying an action to it. + +While naming hypotheses is commonly done by means of an \ssrC{as} +clause in the basic model of Chapter~\ref{Tactics}, it is here to +\ssrC{=>} that this task is devoted. As tactics leave +new assumptions in the conclusion, and are often followed by +\ssrC{=>} to explicitly name them. +While generalizing the goal is normally +not explicitly needed in Chapter~\ref{Tactics}, it is an explicit +operation performed by \ssrC{:}. + +Beside the difference of bookkeeping model, this chapter includes +specific tactics which have no explicit counterpart in +Chapter~\ref{Tactics} such as tactics to mix forward steps and +generalizations as \ssrC{generally have} or \ssrC{without loss}. + +\ssr{} adopts the point of view that rewriting, definition +expansion and partial evaluation participate all to a same concept of +rewriting a goal in a larger sense. As such, all these functionalities are +provided by the \ssrC{rewrite} tactic. + +\ssrC{} includes a little language of patterns to select subterms in tactics +or tacticals where it matters. Its most notable application +is in the \ssrC{rewrite} tactic, where patterns are used to specify +where the rewriting step has to take place. + +Finally, \ssr{} supports the so-called reflection steps, typically +allowing to switch back and forth between the computational view and +logical view of a concept. + +To conclude it is worth mentioning that \ssr{} tactics +can be mixed with non \ssr{} tactics in the same proof, +or in the same LTac expression. The few exceptions +to this statement are described in section~\label{sec:compat}. + +\iffalse +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{How to read this documentation} + +The syntax of the tactics is presented as follows: +\begin{itemize} +\item \ssrC{terminals} are in typewriter font and \ssrN{non terminals} are + between angle brackets. +\item Optional parts of the grammar are surrounded by \optional{ } + brackets. These should not be confused with verbatim brackets + \ssrC{[ ]}, which are delimiters in the \ssr{} syntax. +\item A vertical rule {\optsep} indicates an alternative in the syntax, and + should not be confused with a + verbatim vertical rule between verbatim brackets \ssrC{[ | ]}. +\item A non empty list of non terminals (at least one item should be + present) is represented by \ssrN{non terminals}$^+$. A possibly empty + one is represented by \ssrN{non terminals}$^*$. +\item In a non empty list of non terminals, items are separated by blanks. +\end{itemize} +\fi + +% Hevea has no colors +\ifhevea \else +\noindent We follow the default color scheme of the \ssr{} mode for +ProofGeneral provided in the distribution: + +\centerline{ +\textcolor{dkblue}{\texttt{tactic}} or \textcolor{dkviolet}{\tt + Command} or \textcolor{dkgreen}{\tt keyword} or +\textcolor{dkpink}{\tt tactical}} + +\noindent Closing tactics/tacticals like \ssrC{exact} or \ssrC{by} (see section +\ref{ssec:termin}) are in red. +\fi + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Acknowledgments} +The authors would like to thank Fr\'ed\'eric Blanqui, Fran\,cois Pottier +and Laurence Rideau for their comments and suggestions. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\newpage\section{Usage} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Getting started}\label{sec:files} +To be available, the tactics presented in this manual need the +following minimal set of libraries to loaded: {\tt ssreflect.v}, {\tt +ssrfun.v} and {\tt ssrbool.v}. Moreover, these tactics come with a +methodology specific to the authors of Ssreflect and which requires a +few options to be set in a different way than in their default +way. All in all, this corresponds to working in the following context: + +\begin{lstlisting} + From Coq Require Import ssreflect ssrfun ssrbool. + Set Implicit Arguments. + Unset Strict Implicit. + Unset Printing Implicit Defensive. +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Compatibility issues}\label{sec:compat} +Requiring the above modules creates an environment which +is mostly compatible with the rest of \Coq{}, up to a few discrepancies: +\begin{itemize} +\item New keywords (\ssrC{is}) might clash with variable, constant, +tactic or tactical names, or with quasi-keywords in tactic or +vernacular notations. +\item New tactic(al)s names (\ssrC{last}, \ssrC{done}, \ssrC{have}, + \ssrC{suffices}, \ssrC{suff}, + \ssrC{without loss}, \ssrC{wlog}, \ssrC{congr}, \ssrC{unlock}) might clash + with user tactic names. +\item Identifiers with both leading and trailing \ssrC{_}, such as \ssrC{_x_}, +are reserved by \ssr{} and cannot appear in scripts. +\item The extensions to the \ssrC{rewrite} tactic are partly +incompatible with those available in current versions of \Coq{}; +in particular: +\ssrC{rewrite .. in (type of k)} or \\ \ssrC{rewrite .. in *} or any other +variant of \ssrC{rewrite} will not work, and the \ssr{} syntax and semantics for occurrence selection and +rule chaining is different. + +Use an explicit rewrite direction (\ssrC{rewrite <-} $\dots$ or \ssrC{rewrite ->} $\dots$) +to access the \Coq{} \ssrC{rewrite} tactic. +\item New symbols (\ssrC{//, /=, //=}) might clash with adjacent existing + symbols (e.g., '\ssrC{//}') instead of '\ssrC{/}''\ssrC{/}'). This can be avoided + by inserting white spaces. +\item New constant and theorem names might clash with the user +theory. This can be avoided by not importing all of \ssr{}: +\begin{lstlisting} + From Coq Require ssreflect. + Import ssreflect.SsrSyntax. +\end{lstlisting} +Note that the full syntax of \ssr{}'s {\tt rewrite} and reserved identifiers are +enabled only if the \ssrC{ssreflect} module has been required and if +\ssrC{SsrSyntax} has been imported. Thus a file that requires (without importing) + \ssrC{ssreflect} and imports \ssrC{SsrSyntax}, can be +required and imported without automatically enabling \ssr{}'s +extended rewrite syntax and reserved identifiers. +\item Some user notations (in particular, defining an infix ';') might +interfere with the "open term", parenthesis free, syntax of tactics +such as \ssrC{have}, \ssrC{set} and \ssrC{pose}. +\item The generalization of \ssrC{if} statements to non-Boolean +conditions is turned off by \ssr{}, because it is mostly subsumed by +\ssrC{Coercion} to \ssrC{bool} of the \ssrC{sum}XXX types (declared in +\ssrC{ssrfun.v}) +and the \ssrC{if} {\term} \ssrC{is} \ssrN{pattern} \ssrC{then} {\term} \ssrC{else} {\term} construct (see +\ref{ssec:patcond}). To use the generalized form, turn off the \ssr{} +Boolean \ssrC{if} notation using the command: +\begin{lstlisting} + Close Scope boolean_if_scope. +\end{lstlisting} +\item The following two options can be unset to disable the + incompatible \ssrC{rewrite} syntax and allow + reserved identifiers to appear in scripts. +\begin{lstlisting} + Unset SsrRewrite. + Unset SsrIdents. +\end{lstlisting} +\end{itemize} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Gallina extensions} + +Small-scale reflection makes an extensive use of the programming +subset of Gallina, \Coq{}'s logical specification language. This subset +is quite suited to the description of functions on representations, +because it closely follows the well-established design of the ML +programming language. The \ssr{} extension provides three additions +to Gallina, for pattern assignment, pattern testing, and polymorphism; +these mitigate minor but annoying discrepancies between Gallina and ML. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Pattern assignment}\label{ssec:patass} +The \ssr{} extension provides the following construct for +irrefutable pattern matching, that is, destructuring assignment: + +\ssrC{let: } \ssrN{pattern} \ssrC{:=} \ssrN[1]{term} \ssrC{in} \ssrN[2]{term} + +Note the colon `\ssrC{:}' after the \ssrC{let} keyword, which avoids any +ambiguity with a function +definition or \Coq{}'s basic destructuring \ssrC{let}. The \ssrC{let:} +construct differs from the latter in that +\begin{itemize} +\item The pattern can be nested (deep pattern matching), in + particular, this allows expression of the form: +\begin{lstlisting} + let: exist (x, y) p_xy := Hp in ... +\end{lstlisting} +\item The destructured constructor is explicitly given in the + pattern, and is used for type inference, e.g., +\begin{lstlisting} + Let f u := let: (m, n) := u in m + n. +\end{lstlisting} +using a colon \ssrC{let:}, infers \ssrC{f : nat * nat -> nat}, whereas +\begin{lstlisting} + Let f u := let (m, n) := u in m + n. +\end{lstlisting} +with a usual \ssrC{let}, requires an extra type annotation. +\end{itemize} +The \ssrC{let:} construct is just (more legible) notation for the primitive Gallina expression + +\begin{center} +\ssrC{match} \ssrN[1]{term} \ssrC{with} \ssrN{pattern} \ssrC{=>} \ssrN[2]{term} \ssrC{end} +\end{center} + +The \ssr{} destructuring assignment supports all the dependent match +annotations; the full syntax is + +\begin{center} +\ssrC{let:} \ssrN[1]{pattern} \ssrC{as} \ssrN{ident} \ssrC{in} \ssrN[2]{pattern} \ssrC{:=} \ssrN[1]{term} \ssrC{return} \ssrN[2]{term} \ssrC{in} \ssrN[3]{term} +\end{center} + +where \ssrN[2]{pattern} is a \emph{type} pattern and \ssrN[1]{term} and +\ssrN[2]{term} are types. + +When the \ssrC{as} and \ssrC{return} are both present, then \ssrN{ident} is bound +in both the type \ssrN[2]{term} and the expression \ssrN[3]{term}; +variables in the optional type pattern \ssrN[2]{pattern} are +bound only in the type \ssrN[2]{term}, and other variables in \ssrN[1]{pattern} are +bound only in the expression \ssrN[3]{term}, however. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Pattern conditional}\label{ssec:patcond} +The following construct can be used for a refutable pattern matching, +that is, pattern testing: + +\begin{center} +\ssrC{if}\ \ssrN[1]{term} \ssrC{is} \ssrN[1]{pattern} \ssrC{then} \ssrN[2]{term} \ssrC{else} \ssrN[3]{term} +\end{center} + +Although this construct is not strictly ML (it does exits in variants +such as the pattern calculus or the $\rho$-calculus), it turns out to be +very convenient for writing functions on representations, +because most such functions manipulate simple datatypes such as Peano +integers, options, +lists, or binary trees, and the pattern conditional above is almost +always the right construct +for analyzing such simple types. For example, the \ssrC{null} and +\ssrC{all} list function(al)s can be defined as follows: +\begin{lstlisting} + Variable d: Set. + Fixpoint |*null*| (s : list d) := if s is nil then true else false. + Variable a : d -> bool. + Fixpoint |*all*| (s : list d) : bool := + if s is cons x s' then a x && all s' else true. +\end{lstlisting} + +The pattern conditional also provides a notation for destructuring +assignment with a refutable pattern, adapted to the pure functional +setting of Gallina, which lacks a \\\texttt{Match\_Failure} exception. + +Like \ssrC{let:} above, the \ssrC{if}$\dots$\ssrC{is} construct is just (more legible) +notation for the primitive Gallina expression: + +\begin{center} +\ssrC{match} \ssrN[1]{term} \ssrC{with} \ssrN{pattern} \ssrC{=>} \ssrN[2]{term} \ssrC{| _ =>} \ssrN[2]{term} \ssrC{end} +\end{center} + +Similarly, it will always be displayed as the expansion of this form +in terms of primitive \ssrC{match} expressions (where the default +expression $\ssrN[3]{term}$ may be replicated). + + +Explicit pattern testing also largely subsumes the generalization of +the \ssrC{if} construct to all binary datatypes; compare: + +\begin{center} +\ssrC{if} {\term} \ssrC{is inl _ then} \ssrN[l]{term} \ssrC{else} \ssrN[r]{term} +\end{center} + +and: + +\begin{center} +\ssrC{if} {\term} \ssrC{then} \ssrN[l]{term} \ssrC{else} \ssrN[r]{term} +\end{center} + +The latter appears to be marginally shorter, but it is quite +ambiguous, and indeed often +requires an explicit annotation term : \ssrC{\{_\}+\{_\}} to type-check, +which evens the character count. + +Therefore, \ssr{} restricts by default the condition of a plain \ssrC{if} +construct to the standard \ssrC{bool} type; this avoids spurious type +annotations, e.g., in: +\begin{lstlisting} + Definition |*orb*| b1 b2 := if b1 then true else b2. +\end{lstlisting} +As pointed out in section~\ref{sec:compat}, this restriction can be removed with +the command: +\begin{lstlisting} + Close Scope boolean_if_scope. +\end{lstlisting} +Like \ssrC{let:} above, the \ssrC{if} {\term} \ssrC{is} \ssrN{pattern} +\ssrC{else} {\term} construct +supports the dependent \ssrC{match} annotations: + +\begin{center} +\ssrC{if} \ssrN[1]{term} \ssrC{is} \ssrN[1]{pattern} \ssrC{as} \ssrN{ident} \ssrC{in} \ssrN[2]{pattern} \ssrC{return} \ssrN[2]{term} \ssrC{then} \ssrN[3]{term} \ssrC{else} \ssrN[4]{term} +\end{center} + +As in \ssrC{let:} the variable \ssrN{ident} (and those in +the type pattern \ssrN[2]{pattern}) are bound in \ssrN[2]{term}; \ssrN{ident} is +also bound in \ssrN[3]{term} (but not in \ssrN[4]{term}), while the +variables in \ssrN[1]{pattern} are bound only in \ssrN[3]{term}. + +\noindent +Another variant allows to treat the else case first: + +\begin{center} +\ssrC{if} \ssrN[1]{term} \ssrC{isn't} \ssrN[1]{pattern} \ssrC{then} \ssrN[2]{term} \ssrC{else} \ssrN[3]{term} +\end{center} + +Note that \ssrN[1]{pattern} eventually binds variables in \ssrN[3]{term} +and not \ssrN[2]{term}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Parametric polymorphism}\label{ssec:parampoly} + +Unlike ML, polymorphism in core Gallina is explicit: the type +parameters of polymorphic functions must be declared explicitly, and +supplied at each point of use. However, \Coq{} provides two features +to suppress redundant parameters: +\begin{itemize} +\item Sections are used to provide (possibly implicit) parameters for + a set of definitions. +\item Implicit arguments declarations are used to tell \Coq{} to use + type inference to deduce some parameters from the context at each + point of call. +\end{itemize} +The combination of these features provides a fairly good emulation of ML-style +polymorphism, but unfortunately this emulation breaks down for +higher-order programming. Implicit arguments are indeed not inferred +at all points of use, but only at +points of call, leading to expressions such as +\begin{lstlisting} + Definition |*all_null*| (s : list T) := all (@null T) s. +\end{lstlisting} +Unfortunately, such higher-order expressions are quite frequent in +representation functions, especially those which use \Coq{}'s +\ssrC{Structure}s to emulate Haskell type classes. + +Therefore, \ssr{} provides a variant of \Coq{}'s implicit argument +declaration, which causes \Coq{} to fill in some implicit parameters +at each point of use, e.g., the above definition can be written: +\begin{lstlisting} + Definition |*all_null*| (s : list d) := all null s. +\end{lstlisting} +Better yet, it can be omitted entirely, since \ssrC{all_null s} isn't +much of an improvement over \ssrC{all null s}. + +The syntax of the new declaration is + +\begin{center} +\ssrC{Prenex Implicits} \ssrN{ident}$^+$. +\end{center} + +Let us denote $_1 \dots c_n$ the list of identifiers given to a +\ssrC{Prenex Implicits} command. +The command checks that each $c_i$ is the name of a functional +constant, whose implicit arguments are prenex, i.e., the first $n_i > +0$ arguments of $c_i$ are implicit; then it assigns +\ssrC{Maximal Implicit} status to these arguments. + +As these prenex implicit arguments are ubiquitous and have often large +display strings, it is strongly recommended to change the default +display settings of \Coq{} so that they are not printed (except after a +\ssrC{Set Printing All} command). +All \ssr{} library files thus start with the incantation +\begin{lstlisting} + Set Implicit Arguments. + Unset Strict Implicit. + Unset Printing Implicit Defensive. +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Anonymous arguments} + +When in a definition, the type of a certain argument is mandatory, but +not its name, one usually use ``arrow'' abstractions for prenex +arguments, or the \ssrC{(_ : }{\term}\ssrC{)} syntax for inner arguments. +In \ssr{}, the latter can be replaced by the open syntax `\ssrC{of\ }{\term}' +or (equivalently) `\ssrC{& }{\term}', which are both syntactically +equivalent to a \ssrC{(_ : }{\term}\ssrC{)} expression. + +For instance, the usual two-contrsuctor polymorphic type \ssrC{list}, +i.e. the one of the +standard {\tt List} library, can be defined by the following +declaration: +\begin{lstlisting} + Inductive list (A : Type) : Type := nil | cons of A & list A. +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Wildcards}\label{ssec:wild} + +The terms passed as arguments +to \ssr{} tactics can contain \emph{holes}, materialized by wildcards +\ssrC{_}. +Since \ssr{} allows a more powerful form of type inference for these +arguments, it enhances the possibilities of using such wildcards. +These holes are in particular used as a convenient shorthand for +abstractions, especially in local definitions or type expressions. + +Wildcards may be interpreted as abstractions (see for example sections +\ref{ssec:pose} and \ref{ssec:struct}), or their content can be +inferred from the whole +context of the goal (see for example section \ref{ssec:set}). +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Definitions} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Definitions}\label{ssec:pose} +\idx{pose \dots{} := \dots{}} +\idx{pose fix \dots{} := \dots{}} +\idx{pose cofix \dots{} := \dots{}} + +The \ssrC{pose} tactic allows to add a defined constant to a +proof context. \ssr{} generalizes this tactic in several ways. +In particular, the \ssr{} \ssrC{pose} tactic supports \emph{open syntax}: +the body of +the definition does not need surrounding parentheses. For instance: +\begin{lstlisting} + pose t := x + y. +\end{lstlisting} +is a valid tactic expression. + +The \ssrC{pose} tactic is also improved for the +local definition of higher order terms. +Local definitions of functions can use the same syntax as +global ones. The tactic: +\begin{lstlisting} + pose f x y := x + y. +\end{lstlisting} +adds to the context the defined constant: +\begin{lstlisting} + f := fun x y : nat => x + y : nat -> nat -> nat +\end{lstlisting} + +The \ssr{} \ssrC{pose} tactic also supports (co)fixpoints, +by providing the local counterpart of the +\ssrC{Fixpoint f := $\dots$ } and \ssrC{CoFixpoint f := $\dots$ } constructs. +For instance, the following tactic: +\begin{lstlisting} + pose fix f (x y : nat) {struct x} : nat := + if x is S p then S (f p y) else 0. +\end{lstlisting} +defines a local fixpoint \ssrC{f}, which mimics the standard \ssrC{plus} +operation on natural numbers. + +Similarly, local cofixpoints can be defined by a tactic of the form: +\begin{lstlisting} + pose cofix f (arg : T) ... +\end{lstlisting} + +The possibility to include wildcards in the body of the definitions + offers a smooth +way of defining local abstractions. The type of ``holes'' is +guessed by type inference, and the holes are abstracted. +For instance the tactic: +\begin{lstlisting} + pose f := _ + 1. +\end{lstlisting} +is shorthand for: +\begin{lstlisting} + pose f n := n + 1. +\end{lstlisting} + +When the local definition of a function involves both arguments and +holes, hole abstractions appear first. For instance, the +tactic: +\begin{lstlisting} + pose f x := x + _. +\end{lstlisting} +is shorthand for: +\begin{lstlisting} + pose f n x := x + n. +\end{lstlisting} + + +The interaction of the \ssrC{pose} tactic with the interpretation of +implicit arguments results in a powerful and concise syntax for local +definitions involving dependent types. +For instance, the tactic: +\begin{lstlisting} + pose f x y := (x, y). +\end{lstlisting} +adds to the context the local definition: +\begin{lstlisting} + pose f (Tx Ty : Type) (x : Tx) (y : Ty) := (x, y). +\end{lstlisting} +The generalization of wildcards makes the use of the \ssrC{pose} tactic +resemble ML-like definitions of polymorphic functions. + +% The use of \ssrC{Prenex Implicits} declarations (see section +% \ref{ssec:parampoly}), makes this feature specially convenient. +% Note that this combines with the interpretation of wildcards, and that +% it is possible to define: +% \begin{lstlisting} +% pose g x y : prod _ nat := (x, y). +% \end{lstlisting} +% which is equivalent to: +% \begin{lstlisting} +% pose g x (y : nat) := (x, y). +% \end{lstlisting} + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Abbreviations}\label{ssec:set} +\idx{set \dots{} := \dots{}} + + +The \ssr{} \ssrC{set} tactic performs abbreviations: it introduces a +defined constant for a subterm appearing in the goal and/or in the +context. + +\ssr{} extends the \ssrC{set} tactic by supplying: +\begin{itemize} +\item an open syntax, similarly to the \ssrC{pose} tactic; +\item a more aggressive matching algorithm; +\item an improved interpretation of wildcards, taking advantage of the + matching algorithm; +\item an improved occurrence selection mechanism allowing to abstract only + selected occurrences of a term. +\end{itemize} + +The general syntax of this tactic is +\begin{center} +\ssrC{set} \ssrN{ident} \optional{\ssrC{:} \ssrN[1]{term}} \ssrC{:=} \optional{\ssrN{occ-switch}} \ssrN[2]{term} +\end{center} +\begin{center} +\ssrN{occ-switch} ::= \ssrC{\{}[\ssrC{+}|\ssrC{-}] {\naturalnumber}$^*$ \ssrC{\}} +\end{center} + + +where: + +\begin{itemize} +\item \ssrN{ident} is a fresh identifier chosen by the user. +\item \ssrN[1]{term} is +an optional type annotation. The type annotation \ssrN[1]{term} can be +given in open syntax (no surrounding parentheses). If no \ssrN{occ-switch} +(described hereafter) is present, it is also +the case for \ssrN[2]{term}. +On the other hand, in presence of \ssrN{occ-switch}, parentheses +surrounding \ssrN[2]{term} are mandatory. +\item In the occurrence switch \ssrN{occ-switch}, if the first element + of the list is a {\naturalnumber}, this element should be a number, and not + an Ltac variable. The empty list \ssrC{\{\}} is not interpreted as a + valid occurrence switch. +\end{itemize} +% For example, the script: +% \begin{lstlisting} +% Goal forall (f : nat -> nat)(x y : nat), f x + f x = f x. +% move=> f x y. +% \end{lstlisting} + +The tactic: +\begin{lstlisting} + set t := f _. +\end{lstlisting} +transforms the goal \ssrC{f x + f x = f x} into \ssrC{t + t = t}, adding +\ssrC{t := f x} to the context, and the tactic: +\begin{lstlisting} + set t := {2}(f _). +\end{lstlisting} +transforms it into \ssrC{f x + t = f x}, adding \ssrC{t := f x} to the context. + +The type annotation \ssrN[1]{term} may +contain wildcards, which will be filled with the appropriate value by +the matching process. + +The tactic first tries to find a subterm of the goal matching +\ssrN[2]{term} (and its type \ssrN[1]{term}), +and stops at the first subterm it finds. Then the occurrences +of this subterm selected by the optional \ssrN{occ-switch} are replaced +by \ssrN{ident} and a definition \ssrN{ident} \ssrC{:=} {\term} is added to +the context. If no \ssrN{occ-switch} is present, then all the +occurrences are abstracted. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Matching} + +The matching algorithm compares a pattern \textit{term} + with a subterm of the goal by comparing their heads +and then pairwise unifying their arguments (modulo conversion). Head +symbols match under the following conditions: + +\begin{itemize} +\item If the head of \textit{term} is a constant, then it + should be syntactically equal to the head symbol of the subterm. +\item If this head is a projection of a canonical structure, + then canonical structure equations are used for the matching. +\item If the head of \textit{term} is \emph{not} a constant, the + subterm should have the same structure ($\lambda$ abstraction, + \ssrC{let}$\dots$\ssrC{in} structure \dots). +\item If the head of \textit{term} is a hole, the subterm should have + at least as many arguments as \textit{term}. For instance the tactic: +\begin{lstlisting} + set t := _ x. +\end{lstlisting} +transforms the goal \ssrL-x + y = z- into \ssrC{t y = z} and adds +\ssrC{t := plus x : nat -> nat} to the context. + +\item In the special case where \textit{term} is of the form + \ssrC{(let f := }$t_0$ \ssrC{in f) }$t_1\dots t_n$, + then the pattern \textit{term} is treated +as \ssrC{(_ }$t_1\dots t_n$\ssrC{)}. For each subterm in +the goal having the form $(A\ u_1\dots u_{n'})$ with $n' \geq n$, the +matching algorithm successively tries to find the largest +partial application $(A\ u_1\dots u_{i'})$ convertible to the head +$t_0$ of \textit{term}. For instance the following tactic: +\begin{lstlisting} + set t := (let g y z := y.+1 + z in g) 2. +\end{lstlisting} +transforms the goal +\begin{lstlisting} + (let f x y z := x + y + z in f 1) 2 3 = 6. +\end{lstlisting} +into \ssrC{t 3 = 6} and adds the local definition of \ssrC{t} to the +context. +\end{itemize} + +Moreover: +\begin{itemize} +\item Multiple holes in \textit{term} are treated as independent + placeholders. For instance, the tactic: +\begin{lstlisting} + set t := _ + _. +\end{lstlisting} +transforms the goal \ssrC{x + y = z} into \ssrC{t = z} and pushes +\ssrC{t := x + y : nat} in the context. +\item The type of the subterm matched should fit the type + (possibly casted by some type annotations) of the pattern + \textit{term}. +\item The replacement of the subterm found by the instantiated pattern + should not capture variables, hence the following script: +\begin{lstlisting} + Goal forall x : nat, x + 1 = 0. + set u := _ + 1. +\end{lstlisting} +raises an error message, since \ssrC{x} is bound in the goal. +\item Typeclass inference should fill in any residual hole, but +matching should never assign a value to a global existential variable. + +\end{itemize} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Occurrence selection}\label{sssec:occselect} + +\ssr{} provides a generic syntax for the selection of occurrences by +their position indexes. These \emph{occurrence switches} are shared by +all +\ssr{} tactics which require control on subterm selection like rewriting, +generalization, \dots + +An \emph{occurrence switch} can be: +\begin{itemize} +\item A list \ssrC{\{} {\naturalnumber}$^*$ \ssrC{\}} of occurrences affected by the + tactic. +For instance, the tactic: +\begin{lstlisting} + set x := {1 3}(f 2). +\end{lstlisting} +transforms the goal \ssrC{f 2 + f 8 = f 2 + f 2} into +\ssrC{x + f 8 = f 2 + x}, and adds the abbreviation +\ssrC{x := f 2} in the +context. Notice that some occurrences of a +given term may be hidden to the user, for example because of a +notation. The vernacular \ssrC{$\texttt{\textcolor{dkviolet}{Set }}$ + Printing All} command displays all +these hidden occurrences and should be used to find the correct +coding of the occurrences to be selected\footnote{Unfortunately, +even after a call to the Set Printing All command, some occurrences are +still not displayed to the user, essentially the ones possibly hidden +in the predicate of a dependent match structure.}. For instance, the +following script: +\begin{lstlisting} + Notation "a < b":= (le (S a) b). + Goal forall x y, x < y -> S x < S y. + intros x y; set t := S x. +\end{lstlisting} +generates the goal +\ssrC{t <= y -> t < S y} since \ssrC{x < y} is now a notation for +\ssrC{S x <= y}. +\item A list \ssrC{\{}{\naturalnumber}$^+$\ssrC{\}}. This is equivalent to + \ssrC{\{} {\naturalnumber}$^+$ \ssrC{\}} but the list should start with a number, and + not with an Ltac variable. +\item A list \ssrC{\{}{\naturalnumber}$^*$\ssrC{\}} of occurrences \emph{not} to be + affected by the tactic. For instance, the tactic: +\begin{lstlisting} + set x := {-2}(f 2). +\end{lstlisting} +behaves like +\begin{lstlisting} + set x := {1 3}(f 2). +\end{lstlisting} +on the goal \ssrL-f 2 + f 8 = f 2 + f 2- which has three occurrences of +the the term \ssrC{f 2} +\item In particular, the switch \ssrC{\{+\}} selects \emph{all} the + occurrences. This switch is useful to turn + off the default behavior of a tactic which automatically clears + some assumptions (see section \ref{ssec:discharge} for instance). +\item The switch \ssrC{\{-\}} imposes that \emph{no} occurrences of the + term should be affected by the tactic. The tactic: +\begin{lstlisting} + set x := {-}(f 2). +\end{lstlisting} +leaves the goal unchanged and adds the definition \ssrC{x := f 2} to the +context. This kind of tactic may be used to take advantage of the +power of the matching algorithm in a local definition, instead of +copying large terms by hand. +\end{itemize} + + +It is important to remember that matching \emph{precedes} occurrence +selection, hence the tactic: +\begin{lstlisting} + set a := {2}(_ + _). +\end{lstlisting} +transforms the goal \ssrC{x + y = x + y + z} into \ssrC{x + y = a + z} +and fails on the goal \\ +\ssrC{(x + y) + (z + z) = z + z} with the error message: +\begin{lstlisting} + User error: only 1 < 2 occurrence of (x + y + (z + z)) +\end{lstlisting} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Localization}\label{ssec:loc} + + +It is possible to define an abbreviation for a term appearing in the +context of a goal thanks to the \ssrC{in} tactical. + +A tactic of the form: + +\begin{center} + \ssrC{set x :=} {\term} \ssrC{in} \ssrN[1]{fact}\ssrC{...}\ssrN[n]{fact}. +\end{center} + +introduces a defined constant called \ssrC{x} in the context, and folds +it in the facts \textit{fact$_1 \dots$ fact$_n$} +The body of \ssrC{x} is the first subterm matching \textit{term} in +\textit{fact$_1 \dots$ fact$_n$}. + +A tactic of the form: + +\begin{center} + \ssrC{set x :=} {\term} \ssrC{in} \ssrN[1]{fact}\ssrC{...}\ssrN[n]{fact} \ssrC{*.} +\end{center} + +matches {\term} and then folds \ssrC{x} similarly in +\textit{fact$_1 \dots$ fact$_n$}, but also folds \ssrC{x} in the goal. + +A goal \ssrL-x + t = 4-, whose context contains \ssrC{Hx : x = 3}, is left +unchanged by the tactic: +\begin{lstlisting} + set z := 3 in Hx. +\end{lstlisting} +but the context is extended with the definition \ssrC{z := 3} and \ssrC{Hx} becomes +\ssrC{Hx : x = z}. +On the same goal and context, the tactic: +\begin{lstlisting} + set z := 3 in Hx *. +\end{lstlisting} +will moreover change the goal into \ssrL-x + t = S z-. Indeed, remember +that \ssrC{4} is just a notation for \ssrC{(S 3)}. + +The use of the \ssrC{in} tactical is not limited to the localization of +abbreviations: for a complete description of the \ssrC{in} tactical, see +section \ref{ssec:profstack}. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Basic tactics}\label{sec:book} + + + +A sizable fraction of proof scripts consists of steps that do not +"prove" anything new, but instead perform menial bookkeeping tasks +such as selecting the names of constants and assumptions or splitting +conjuncts. Although they are logically trivial, bookkeeping steps are +extremely important because they define the structure of the data-flow +of a proof script. This is especially true for reflection-based +proofs, which often involve large numbers of constants and +assumptions. Good bookkeeping consists in always explicitly declaring +(i.e., naming) all new constants and assumptions in the script, and +systematically pruning irrelevant constants and assumptions in the +context. This is essential in the context of an interactive +development environment (IDE), because it facilitates navigating the +proof, allowing to instantly "jump back" to the point at which a +questionable assumption was added, and to find relevant assumptions by +browsing the pruned context. While novice or casual \Coq{} users may +find the automatic name selection feature convenient, the usage of +such a feature severely undermines the readability and maintainability +of proof scripts, much like automatic variable declaration in programming +languages. The \ssr{} tactics are therefore designed to support +precise bookkeeping and to eliminate name generation heuristics. +The bookkeeping features of \ssr{} are implemented as tacticals (or +pseudo-tacticals), shared across most \ssr{} tactics, and thus form +the foundation of the \ssr{} proof language. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Bookkeeping}\label{ssec:profstack} +\idx{move: \dots{}} +\idx{move=> \dots{}} +\idx{move: \dots{} => \dots{}} +\idx{\dots{} in \dots{}} + +During the course of a proof \Coq{} always present the user with +a \emph{sequent} whose general form is +\begin{displaymath}\begin{array}{l} +%\arrayrulecolor{dkviolet} +c_i\ \ssrC{:}\ T_i \\ +\dots\\ +d_j\ \ssrC{:=}\ e_j\ \ssrC{:}\ T_j \\ +\dots\\ +F_k\ \ssrC{:}\ P_k \\ +\dots \\[3pt] +\hline\hline\\[-8pt] +\ssrC{forall}\ \ssrC{(}x_\ell\ \ssrC{:}\ T_\ell\ssrC{)}\ \dots,\\ +\ssrC{let}\ y_m\ \ssrC{:=}\ b_m\ \ssrC{in}\ \dots\ \ssrC{in}\\ +P_n\ \ssrC{->}\ \dots\ \ssrC{->}\ C +\end{array}\end{displaymath} +The \emph{goal} to be proved appears below the double line; above the line is +the \emph{context} of the sequent, a set of declarations of +\emph{constants}~$c_i$, \emph{defined constants}~$d_i$, and +\emph{facts}~$F_k$ that can be used to prove the goal (usually, $T_i, +T_j\;:\;\ssrC{Type}$ and $P_k\;:\;\ssrC{Prop}$). The various kinds of +declarations can come in any order. The top part of the context +consists of declarations produced by the \ssrC{Section} commands +\ssrC{Variable}, \ssrC{Let}, and \ssrC{Hypothesis}. This \emph{section context} +is never affected by the \ssr{} tactics: they only operate on +the lower part --- the \emph{proof context}. +As in the figure above, the goal often decomposes into a series of +(universally) quantified \emph{variables} +$\ssrC{(}x_\ell\;\ssrC{:}\;T_\ell\ssrC{)}$, local \emph{definitions} +$\ssrC{let}\;y_m\:\ssrC{:=}\;b_m\;\ssrC{in}$, and \emph{assumptions} +$P_n\;\ssrC{->}$, and a \emph{conclusion}~$C$ (as in the context, variables, +definitions, and assumptions can appear in any order). The conclusion +is what actually needs to be proved --- the rest of the goal can be +seen as a part of the proof context that happens to be ``below the line''. + +However, although they are logically equivalent, there are fundamental +differences between constants and facts on the one hand, and variables +and assumptions on the others. Constants and facts are +\emph{unordered}, but \emph{named} explicitly in the proof text; +variables and assumptions are \emph{ordered}, but \emph{unnamed}: the +display names of variables may change at any time because of +$\alpha$-conversion. + +Similarly, basic deductive steps such as \ssrC{apply} can only operate on +the goal because the Gallina terms that control their action (e.g., +the type of the lemma used by \ssrC{apply}) only provide unnamed bound +variables.\footnote{Thus scripts that depend on bound variable names, e.g., +via \ssrC{intros} or \ssrC{with}, are inherently fragile.} Since the proof +script can only refer directly to the context, it must constantly +shift declarations from the goal to the context and conversely in +between deductive steps. + +In \ssr{} these moves are performed by two \emph{tacticals} `\ssrC{=>}' +and `\ssrC{:}', so that the bookkeeping required by a deductive step can +be directly associated to that step, and that tactics in an \ssr{} +script correspond to actual logical steps in the proof rather than +merely shuffle facts. Still, some isolated bookkeeping is unavoidable, +such as naming variables and assumptions at the beginning of a proof. +\ssr{} provides a specific \ssrC{move} tactic for this purpose. + +Now \ssrC{move} does essentially nothing: it is mostly a placeholder for +`\ssrC{=>}' and `\ssrC{:}'. The `\ssrC{=>}' tactical moves variables, local +definitions, and assumptions to the context, while the `\ssrC{:}' +tactical moves facts and constants to the goal. For example, the proof +of\footnote{The name \ssrC{subnK} reads as +``right cancellation rule for \ssrC{nat} subtraction''.} +\begin{lstlisting} + Lemma |*subnK*| : forall m n, n <= m -> m - n + n = m. +\end{lstlisting}\noindent +might start with +\begin{lstlisting} + move=> m n le_n_m. +\end{lstlisting} +where \ssrC{move} does nothing, but \ssrL|=> m n le_m_n| changes the +variables and assumption of the goal in the constants \ssrC{m n : nat} +and the fact \ssrL|le_n_m : n <= m|, thus exposing the conclusion\\ + \ssrC{m - n + n = m}. + +The `\ssrC{:}' tactical is the converse of `\ssrC{=>}': it removes facts +and constants from the context by turning them into variables and assumptions. +Thus +\begin{lstlisting} + move: m le_n_m. +\end{lstlisting} +turns back \ssrC{m} and \ssrL|le_m_n| into a variable and an assumption, removing +them from the proof context, and changing the goal to +\begin{lstlisting} + forall m, n <= m -> m - n + n = m. +\end{lstlisting} +which can be proved by induction on \ssrC{n} using \ssrC{elim: n}. + +\noindent +Because they are tacticals, `\ssrC{:}' and `\ssrC{=>}' can be combined, as in +\begin{lstlisting} + move: m le_n_m => p le_n_p. +\end{lstlisting} +simultaneously renames \ssrL|m| and \ssrL|le_m_n| into \ssrL|p| and \ssrL|le_n_p|, +respectively, by first turning them into unnamed variables, then +turning these variables back into constants and facts. + +Furthermore, \ssr{} redefines the basic \Coq{} tactics \ssrC{case}, +\ssrC{elim}, and \ssrC{apply} so that they can take better advantage of +'\ssrC{:}' and `\ssrC{=>}'. In there \ssr{} variants, these tactic operate +on the first variable or constant of the goal and they do not use or +change the proof context. The `\ssrC{:}' tactical is used to operate on +an element in the context. For instance the proof of \ssrC{subnK} could +continue with +\begin{lstlisting} + elim: n. +\end{lstlisting} +instead of \ssrC{elim n}; this has the advantage of +removing \ssrC{n} from the context. Better yet, this \ssrC{elim} can be combined +with previous \ssrC{move} and with the branching version of the \ssrC{=>} tactical +(described in~\ref{ssec:intro}), +to encapsulate the inductive step in a single command: +\begin{lstlisting} + elim: n m le_n_m => [|n IHn] m => [_ | lt_n_m]. +\end{lstlisting} +which breaks down the proof into two subgoals, +\begin{lstlisting} + m - 0 + 0 = m +\end{lstlisting} +given \ssrC{m : nat}, and +\begin{lstlisting} + m - S n + S n = m +\end{lstlisting} +given \ssrC{m n : nat}, \ssrL|lt_n_m : S n <= m|, and +\begin{lstlisting} + IHn : forall m, n <= m -> m - n + n = m. +\end{lstlisting} +The '\ssrC{:}' and `\ssrC{=>}' tacticals can be explained very simply +if one views the goal as a stack of variables and assumptions piled +on a conclusion: +\begin{itemize} +\item {\tac} \ssrC{:} $a$ $b$ $c$ pushes the context constants $a$, $b$, $c$ +as goal variables \emph{before} performing {\tac}. +\item {\tac} \ssrC{=>} $a$ $b$ $c$ pops the top three goal variables as +context constants $a$, $b$, $c$, \emph{after} {\tac} +has been performed. +\end{itemize} +These pushes and pops do not need to balance out as in the examples above, +so +\begin{lstlisting} + move: m le_n_m => p. +\end{lstlisting} +would rename \ssrC{m} into \ssrC{p}, but leave an extra assumption \ssrC{n <= p} +in the goal. + +Basic tactics like \ssrC{apply} and \ssrC{elim} can also be used without the +'\ssrC{:}' tactical: for example we can directly start a proof of \ssrC{subnK} +by induction on the top variable \ssrC{m} with +\begin{lstlisting} + elim=> [|m IHm] n le_n. +\end{lstlisting} + +\noindent +The general form of the localization tactical \ssrC{in} is also best +explained in terms of the goal stack: + +\begin{center} + {\tac} \ssrC{in a H1 H2 *.} +\end{center} + +is basically equivalent to + +\begin{center} + \ssrC{move: a H1 H2;} {\tac} \ssrC{=> a H1 H2.} +\end{center} + +with two differences: the \ssrC{in} tactical will preserve the body of \ssrC{a} if +\ssrC{a} is a defined constant, and if the `\ssrC{*}' is omitted it +will use a temporary abbreviation to hide the statement of the goal +from \ssrC{/*tactic*/}. + +The general form of the \ssrC{in} tactical can be used directly with +the \ssrC{move}, \ssrC{case} and \ssrC{elim} tactics, so that one can write +\begin{lstlisting} + elim: n => [|n IHn] in m le_n_m *. +\end{lstlisting} +instead of +\begin{lstlisting} + elim: n m le_n_m => [|n IHn] m le_n_m. +\end{lstlisting} +This is quite useful for inductive proofs that involve many facts. + +\noindent See section \ref{ssec:gloc} for the general syntax and presentation +of the \ssrC{in} tactical. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{The defective tactics}\label{ssec:basictac} + +In this section we briefly present the three basic tactics performing +context manipulations and the main backward chaining tool. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{move} tactic.}\label{sssec:move} +\idx{move} + +The \ssrC{move} tactic, in its +defective form, behaves like the primitive \ssrC{hnf} \Coq{} tactic. For +example, such a defective: +\begin{lstlisting} + move. +\end{lstlisting} +exposes the first assumption in the goal, i.e. its changes the goal +\ssrC{\~ False} into \ssrC{False -> False}. + +More precisely, the \ssrC{move} tactic inspects the goal and does nothing +(\ssrC{idtac}) if an introduction step is possible, i.e. if the +goal is a product or a \ssrC{let}$\dots$\ssrC{in}, and performs \ssrC{hnf} +otherwise. + +Of course this tactic is most often used in combination with the +bookkeeping tacticals (see section \ref{ssec:intro} and +\ref{ssec:discharge}). These combinations mostly subsume the \ssrC{intros}, +\ssrC{generalize}, \ssrC{revert}, \ssrC{rename}, \ssrC{clear} and +\textcolor{dkblue}{\texttt{pattern}} tactics. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{case} tactic.} +\idx{case: \dots{}} + +The \ssrC{case} tactic performs +\emph{primitive case analysis} on (co)inductive types; specifically, +it destructs the top variable or assumption of the goal, +exposing its constructor(s) and its arguments, as well as setting the value +of its type family indices if it belongs to a type family +(see section \ref{ssec:typefam}). + +The \ssr{} \ssrC{case} tactic has a special behavior on +equalities. +If the top assumption of the goal is an equality, the \ssrC{case} tactic +``destructs'' it as a set of equalities between the constructor +arguments of its left and right hand sides, as per the +tactic \ssrC{injection}. +For example, \ssrC{case} changes the goal +\begin{lstlisting} + (x, y) = (1, 2) -> G. +\end{lstlisting} +into +\begin{lstlisting} + x = 1 -> y = 2 -> G. +\end{lstlisting} + +Note also that the case of \ssr{} performs \ssrC{False} +elimination, even if no branch is generated by this case operation. +Hence the command: +\begin{lstlisting} + case. +\end{lstlisting} +on a goal of the form \ssrC{False -> G} will succeed and prove the goal. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{elim} tactic.} +\idx{elim: \dots{}} + +The \ssrC{elim} tactic performs +inductive elimination on inductive types. +The defective: +\begin{lstlisting} + elim. +\end{lstlisting} +tactic performs inductive elimination on a goal whose top assumption +has an inductive type. For example on goal of the form: +\begin{lstlisting} + forall n : nat, m <= n +\end{lstlisting} + in a context containing \ssrC{m : nat}, the +\begin{lstlisting} + elim. +\end{lstlisting} +tactic produces two goals, +\begin{lstlisting} + m <= 0 +\end{lstlisting} +on one hand and +\begin{lstlisting} + forall n : nat, m <= n -> m <= S n +\end{lstlisting} +on the other hand. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{apply} tactic.}\label{sssec:apply} +\idx{apply: \dots{}} + +The \ssrC{apply} tactic is the main +backward chaining tactic of the proof system. It takes as argument any +\ssrC{/*term*/} and applies it to the goal. +Assumptions in the type of \ssrC{/*term*/} that don't directly match the +goal may generate one or more subgoals. + +In fact the \ssr{} tactic: +\begin{lstlisting} + apply. +\end{lstlisting} +is a synonym for: +\begin{lstlisting} + intro top; first [refine top | refine (top _) | refine (top _ _) | ...]; clear top. +\end{lstlisting} +where \ssrC{top} is fresh name, and the sequence of \ssrC{refine} tactics +tries to catch the appropriate number of wildcards to be inserted. +Note that this use of the \ssrC{refine} tactic implies that the tactic +tries to match the goal up to expansion of +constants and evaluation of subterms. + +\ssr{}'s \ssrC{apply} has a special behaviour on goals containing +existential metavariables of sort \ssrC{Prop}. Consider the +following example: +\begin{lstlisting} +Goal (forall y, 1 < y -> y < 2 -> exists x : { n | n < 3 }, proj1_sig x > 0). +move=> y y_gt1 y_lt2; apply: (ex_intro _ (exist _ y _)). + by apply: gt_trans _ y_lt2. +by move=> y_lt3; apply: lt_trans y_gt1. +\end{lstlisting} +Note that the last \ssrC{_} of the tactic \ssrC{apply: (ex_intro _ (exist _ y _))} +represents a proof that \ssrC{y < 3}. Instead of generating the following +goal +\begin{lstlisting} + 0 < (n:=3) (m:=y) ?54 +\end{lstlisting} +\noindent the system tries to prove \ssrC{y < 3} calling the \ssrC{trivial} +tactic. If it succeeds, let's say because the context contains +\ssrC{H : y < 3}, then the system generates the following goal: +\begin{lstlisting} + 0 < proj1_sig (exist (fun n => n < 3) y H +\end{lstlisting} +\noindent Otherwise the missing proof is considered to be irrelevant, and +is thus discharged generating the following goals: +\begin{lstlisting} + y < 3 + forall H : y < 3, proj1_sig (exist (fun n => n < 3) y H) +\end{lstlisting} +Last, the user can replace the \ssrC{trivial} tactic by defining +an Ltac expression named \ssrC{ssrautoprop}. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Discharge}\label{ssec:discharge} +\idx{\dots{} : \dots{}} + +The general syntax of the discharging tactical `\ssrC{:}' is: +\begin{center} + {\tac} \optional{\ssrN{ident}} \ssrC{:} \ssrN[1]{d-item} $\dots$ \ssrN[n]{d-item} \optional{\ssrN{clear-switch}} +\end{center} +where $n > 0$, and \ssrN{d-item} and \ssrN{clear-switch} are defined as +\begin{longtable}{rcl} +\ssrN{d-item} & ::= & \optional{\ssrN{occ-switch} {\optsep} \ssrN{clear-switch}} {\term} \\ +\ssrN{clear-switch}& ::=& \ssrC{\{} \ssrN[1]{ident}\, \ldots\, \ssrN[m]{ident} \ssrC{\}} +\end{longtable} +with the following requirements: +\begin{itemize} +\item {\tac} must be one of the four basic tactics described + in~\ref{ssec:basictac}, i.e., \ssrC{move}, \ssrC{case}, \ssrC{elim} or \ssrC{apply}, + the \ssrC{exact} tactic (section \ref{ssec:termin}), + the \ssrC{congr} tactic (section \ref{ssec:congr}), or the application + of the \emph{view} tactical `\ssrC{/}' (section \ref{ssec:assumpinterp}) + to one of \ssrC{move}, \ssrC{case}, or \ssrC{elim}. +\item The optional \ssrN{ident} specifies \emph{equation generation} + (section \ref{ssec:equations}), and is only allowed if {\tac} + is \ssrC{move}, \ssrC{case} or \ssrC{elim}, or the application of the + view tactical `\ssrC{/}' (section \ref{ssec:assumpinterp}) + to \ssrC{case} or \ssrC{elim}. +\item An \ssrN{occ-switch} selects occurrences of {\term}, + as in \ref{sssec:occselect}; \ssrN{occ-switch} is not allowed if + {\tac} is \ssrC{apply} or \ssrC{exact}. +\item A clear item \ssrN{clear-switch} specifies facts and constants to be + deleted from the proof context (as per the \ssrC{clear} tactic). +\end{itemize} +The `\ssrC{:}' tactical first \emph{discharges} all the \ssrN{d-item}s, +right to left, and then performs {\tac}, i.e., for each \ssrN{d-item}, +starting with $\ssrN[n]{d-item}$: +\begin{enumerate} +\item The \ssr{} matching algorithm described in section~\ref{ssec:set} + is used to find occurrences of {\term} in the goal, + after filling any holes `\ssrC{_}' in {\term}; however if {\tac} + is \ssrC{apply} or \ssrC{exact} a different matching algorithm, + described below, is used + \footnote{Also, a slightly different variant may be used for the first + \ssrN{d-item} of \ssrC{case} and \ssrC{elim}; see section~\ref{ssec:typefam}.}. +\item~\label{enum:gen} These occurrences are replaced by a new + variable; in particular, + if {\term} is a fact, this adds an assumption to the goal. +\item~\label{enum:clr} If {\term} is \emph{exactly} the name of a constant + or fact in the proof context, it is deleted from the context, + unless there is an \ssrN{occ-switch}. +\end{enumerate} +Finally, {\tac} is performed just after $\ssrN[1]{d-item}$ has been +generalized --- +that is, between steps \ref{enum:gen} and \ref{enum:clr} for $\ssrN[1]{d-item}$. +The names listed in the final \ssrN{clear-switch} (if it is present) +are cleared first, before $\ssrN[n]{d-item}$ is discharged. + +\noindent +Switches affect the discharging of a \ssrN{d-item} as follows: +\begin{itemize} +\item An \ssrN{occ-switch} restricts generalization (step~\ref{enum:gen}) + to a specific subset of the occurrences of {\term}, as per + \ref{sssec:occselect}, and prevents clearing (step~\ref{enum:clr}). +\item All the names specified by a \ssrN{clear-switch} are deleted from the + context in step~\ref{enum:clr}, possibly in addition to {\term}. +\end{itemize} +For example, the tactic: +\begin{lstlisting} + move: n {2}n (refl_equal n). +\end{lstlisting} +\begin{itemize} +\item first generalizes \ssrC{(refl_equal n : n = n)}; +\item then generalizes the second occurrence of \ssrC{n}. +\item finally generalizes all the other occurrences of \ssrC{n}, + and clears \ssrC{n} from the proof context + (assuming \ssrC{n} is a proof constant). +\end{itemize} +Therefore this tactic changes any goal \ssrC{G} into +\begin{lstlisting} + forall n n0 : nat, n = n0 -> G. +\end{lstlisting} +where the name \ssrC{n0} is picked by the \Coq{} display function, +and assuming \ssrC{n} appeared only in~\ssrC{G}. + +Finally, note that a discharge operation generalizes defined constants +as variables, and not as local definitions. To override this behavior, +prefix the name of the local definition with a \ssrC{@}, +like in \ssrC{move: @n}. + +This is in contrast with the behavior of the \ssrC{in} tactical (see section +\ref{ssec:gloc}), which preserves local definitions by default. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Clear rules} + +The clear step will fail if {\term} is a proof constant that +appears in other facts; in that case either the facts should be +cleared explicitly with a \ssrN{clear-switch}, or the clear step should be +disabled. The latter can be done by adding an \ssrN{occ-switch} or simply by +putting parentheses around {\term}: both +\begin{lstlisting} + move: (n). +\end{lstlisting} +and +\begin{lstlisting} + move: {+}n. +\end{lstlisting} +generalize \ssrC{n} without clearing \ssrC{n} from the proof context. + +The clear step will also fail if the \ssrN{clear-switch} contains a +\ssrN{ident} that is not in the \emph{proof} context. +Note that \ssr{} never clears a section constant. + +If {\tac} is \ssrC{move} or \ssrC{case} and an equation \ssrN{ident} is given, +then clear (step~\ref{enum:clr}) for $\ssrN[1]{d-item}$ is suppressed +(see section \ref{ssec:equations}). + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Matching for \ssrC{apply} and \ssrC{exact}}\label{sss:strongapply} + +The matching algorithm for \ssrN{d-item}s of the \ssr{} \ssrC{apply} and +\ssrC{exact} tactics +exploits the type of $\ssrN[1]{d-item}$ to interpret +wildcards in the other \ssrN{d-item} and to determine which occurrences of +these should be generalized. +Therefore, \ssrN{occur switch}es are not needed for \ssrC{apply} and \ssrC{exact}. + +Indeed, the \ssr{} tactic \ssrC{apply: H x} is equivalent to +\begin{lstlisting} + refine (@H _ ... _ x); clear H x +\end{lstlisting} +with an appropriate number of wildcards between \ssrC{H} and~\ssrC{x}. + +Note that this means that matching for \ssrC{apply} and \ssrC{exact} has +much more context to interpret wildcards; in particular it can accommodate +the `\ssrC{_}' \ssrN{d-item}, which would always be rejected after `\ssrC{move:}'. +For example, the tactic +\begin{lstlisting} + apply: trans_equal (Hfg _) _. +\end{lstlisting} +transforms the goal \ssrC{f a = g b}, whose context contains +\ssrC{(Hfg : forall x, f x = g x)}, into \ssrC{g a = g b}. +This tactic is equivalent (see section \ref{ssec:profstack}) to: +\begin{lstlisting} + refine (trans_equal (Hfg _) _). +\end{lstlisting} +and this is a common idiom for applying transitivity on the left hand side +of an equation. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{abstract} tactic}\label{ssec:abstract} +\idx{abstract: \dots{}} + +The \ssrC{abstract} tactic assigns an abstract constant previously introduced with +the \ssrC{[: name ]} intro pattern (see section~\ref{ssec:intro}, +page~\pageref{ssec:introabstract}). +In a goal like the following: +\begin{lstlisting} + m : nat + abs : <hidden> + n : nat + ============= + m < 5 + n +\end{lstlisting} +The tactic \ssrC{abstract: abs n} first generalizes the goal with respect to +\ssrC{n} (that is not visible to the abstract constant \ssrC{abs}) and then +assigns \ssrC{abs}. The resulting goal is: +\begin{lstlisting} + m : nat + n : nat + ============= + m < 5 + n +\end{lstlisting} +Once this subgoal is closed, all other goals having \ssrC{abs} in their context +see the type assigned to \ssrC{abs}. In this case: +\begin{lstlisting} + m : nat + abs : forall n, m < 5 + n +\end{lstlisting} + +For a more detailed example the user should refer to section~\ref{sssec:have}, +page~\pageref{sec:havetransparent}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Introduction}\label{ssec:intro} +\idx{\dots{} => \dots{}} + +The application of a tactic to a given goal can generate +(quantified) variables, assumptions, or definitions, which the user may want to +\emph{introduce} as new facts, constants or defined constants, respectively. +If the tactic splits the goal into several subgoals, +each of them may require the introduction of different constants and facts. +Furthermore it is very common to immediately decompose +or rewrite with an assumption instead of adding it to the context, +as the goal can often be simplified and even +proved after this. + +All these operations are performed by the introduction tactical +`\ssrC{=>}', whose general syntax is +\begin{center} + {\tac} \ssrC{=>} \ssrN[1]{i-item} $\dots$ \ssrN[n]{i-item} +\end{center} +where {\tac} can be any tactic, $n > 0$ and +\begin{longtable}{rcl} + \ssrN{i-item}& ::=& \ssrN{i-pattern} {\optsep} \ssrN{s-item} {\optsep} \ssrN{clear-switch} {\optsep} \ssrC{/}{\term} \\ + \ssrN{s-item}& ::=& \ssrC{/=} {\optsep} \ssrC{//} {\optsep} \ssrC{//=} \\ + \ssrN{i-pattern}& ::=& \ssrN{ident} {\optsep} \ssrC{_} {\optsep} \ssrC{?} {\optsep} \ssrC{*} {\optsep} \optional{\ssrN{occ-switch}}\ssrC{->} {\optsep} \optional{\ssrN{occ-switch}}\ssrC{<-} {\optsep} \\ + && \ssrC{[} \ssrN[1]{i-item}$^*$ \ssrC{|} $\dots$ \ssrC{|} \ssrN[m]{i-item}$^*$ \ssrC{]} {\optsep} \ssrC{-} {\optsep} \ssrC{[:} \ssrN{ident}$^+$ \ssrC{]} +\end{longtable} + +The `\ssrC{=>}' tactical first executes {\tac}, then the +\ssrN{i-item}s, left to right, i.e., starting from $\ssrN[1]{i-item}$. An +\ssrN{s-item} specifies a simplification operation; a $\ssrN{clear +switch}$ specifies context pruning as in~\ref{ssec:discharge}. The +\ssrN{i-pattern}s can be seen as a variant of \emph{intro patterns}~\ref{intros-pattern}: +each performs an introduction operation, i.e., pops some variables or +assumptions from the goal. + +An \ssrN{s-item} can simplify the set of subgoals or the subgoal themselves: +\begin{itemize} +\item \ssrC{//} removes all the ``trivial'' subgoals that can be resolved by + the \ssr{} tactic \ssrC{done} described in~\ref{ssec:termin}, i.e., it + executes \ssrC{try done}. +\item \ssrC{/=} simplifies the goal by performing partial evaluation, as + per the tactic \ssrC{simpl}.\footnote{Except \ssrC{/=} does not + expand the local definitions created by the \ssr{} \ssrC{in} tactical.} +\item \ssrC{//=} combines both kinds of simplification; it is equivalent + to \ssrC{/= //}, i.e., \ssrC{simpl; try done}. +\end{itemize} +When an \ssrN{s-item} bears a \ssrN{clear-switch}, then the \ssrN{clear-switch} is +executed \emph{after} the \ssrN{s-item}, e.g., \ssrL|{IHn}//| will solve +some subgoals, possibly using the fact \ssrL|IHn|, and will erase \ssrL|IHn| +from the context of the remaining subgoals. + +The last entry in the \ssrN{i-item} grammar rule, \ssrC{/}{\term}, +represents a view (see section~\ref{sec:views}). If $\ssrN[k+1]{i-item}$ +is a view \ssrN{i-item}, the view is applied to the assumption in top +position once $\ssrN[1]{i-item} \dots \ssrN[k]{i-item}$ have been performed. + +The view is applied to the top assumption. + +\ssr{} supports the following \ssrN{i-pattern}s: +\begin{itemize} +\item \ssrN{ident} pops the top variable, assumption, or local definition into + a new constant, fact, or defined constant \ssrN{ident}, respectively. + Note that defined constants cannot be introduced when + $\delta$-expansion is required to expose the top variable or assumption. +\item \ssrC{?} pops the top variable into an anonymous constant or fact, + whose name is picked by the tactic interpreter. + \ssr{} only generates names that + cannot appear later in the user script.\footnote{\ssr{} reserves + all identifiers of the form ``\ssrC{_x_}'', which is used for such + generated names.} +\item \ssrC{_} pops the top variable into an anonymous constant that will be + deleted from + the proof context of all the subgoals produced by the \ssrC{=>} tactical. + They should thus never be displayed, except in an error message + if the constant is still actually used in the goal or context after + the last \ssrN{i-item} has been executed (\ssrN{s-item}s can erase goals + or terms where the constant appears). +\item \ssrC{*} pops all the remaining apparent variables/assumptions + as anonymous constants/facts. Unlike \ssrC{?} and \ssrC{move} the \ssrC{*} + \ssrN{i-item} does not expand definitions in the goal to expose + quantifiers, so it may be useful to repeat a \ssrC{move=> *} tactic, + e.g., on the goal +\begin{lstlisting} + forall a b : bool, a <> b +\end{lstlisting} +a first \ssrC{move=> *} adds only \ssrC{_a_ : bool} and \ssrC{_b_ : bool} to +the context; it takes a second \ssrC{move=> *} to add +\ssrC{_Hyp_ : _a_ = _b_}. +\item $[\ssrN{occ-switch}]$\ssrC{->} (resp. $[\ssrN{occ-switch}]$\ssrC{<-}) + pops the top assumption + (which should be a rewritable proposition) into an anonymous fact, + rewrites (resp. rewrites right to left) the goal with this fact + (using the \ssr{} \ssrC{rewrite} tactic described in section~\ref{sec:rw}, + and honoring the optional occurrence selector), + and finally deletes the anonymous fact from the context. +\item\ssrC{[ $\ssrN[1]{i-item}^*$ | $\dots$ | $\ssrN[m]{i-item}^*$ ]}, + when it is the very \emph{first} \ssrN{i-pattern} after ${\tac}\;\ssrC{=>}$ + tactical \emph{and} {\tac} is not a \ssrC{move}, is a \emph{branching} + \ssrN{i-pattern}. It executes + the sequence $\ssrN[i]{i-item}^*$ on the $i^{\rm th}$ + subgoal produced by {\tac}. The execution of {\tac} + should thus generate exactly $m$ + subgoals, unless the \ssrC{[$\dots$]} \ssrN{i-pattern} comes after an initial + \ssrC{//} or \ssrC{//=} \ssrN{s-item} that closes some of the goals produced by + {\tac}, in which case exactly $m$ subgoals should remain after the + \ssrN{s-item}, or we have the trivial branching \ssrN{i-pattern} \ssrC{[]}, + which always does nothing, regardless of the number of remaining subgoals. +\item\ssrC{[ $\ssrN[1]{i-item}^*$ | $\dots$ | $\ssrN[m]{i-item}^*$ ]}, when it is + \emph{not} the first \ssrN{i-pattern} or when {\tac} is a + \ssrC{move}, is a \emph{destructing} \ssrN{i-pattern}. It starts by + destructing the top variable, using the \ssr{} \ssrC{case} tactic + described in~\ref{ssec:basictac}. It then behaves as the + corresponding branching \ssrN{i-pattern}, executing the sequence + $\ssrN[i]{i-item}^*$ in the $i^{\rm th}$ subgoal generated by the case + analysis; unless we have the trivial destructing \ssrN{i-pattern} + \ssrC{[]}, the latter should generate exactly $m$ subgoals, i.e., the + top variable should have an inductive type with exactly $m$ + constructors.\footnote{More precisely, it should have a quantified + inductive type with $a$ assumptions and $m - a$ constructors.} + While it is good style to use the $\ssrN[i]{i-item}^*$ + to pop the variables and assumptions corresponding to each constructor, + this is not enforced by \ssr{}. +\item\ssrC{-} does nothing, but counts as an intro pattern. It can also + be used to force the interpretation of + \ssrC{[ $\ssrN[1]{i-item}^*$ | $\dots$ | $\ssrN[m]{i-item}^*$ ]} + as a case analysis like in \ssrC{move=> -[H1 H2]}. It can also be used + to indicate explicitly the link between a view and a name like in + \ssrC{move=> /eqP-H1}. Last, it can serve as a separator between + views. Section~\ref{ssec:multiview} explains in which respect + the tactic \ssrC{move=> /v1/v2} differs from the tactic + \ssrC{move=> /v1-/v2}. +\item\ssrC{[: $\ssrN{ident}^+$ ]} introduces in the context an abstract constant + for each \ssrN{ident}. Its type has to be fixed later on by using + the \ssrC{abstract} tactic (see page~\pageref{ssec:abstract}). Before then + the type displayed is \ssrC{<hidden>}.\label{ssec:introabstract} +\end{itemize} +Note that \ssr{} does not support the syntax +$\ssrC{(}\ssrN{ipat}\ssrC{,}\dots\ssrC{,}\ssrN{ipat}\ssrC{)}$ for destructing +intro-patterns. + +Clears are deferred until the end of the intro pattern. For +example, given the goal: +\begin{lstlisting} +x, y : nat +================== +0 < x = true -> (0 < x) && (y < 2) = true +\end{lstlisting} +the tactic \ssrC{move=> \{x\} ->} successfully rewrites the goal and +deletes \ssrC{x} and the anonymous equation. The goal is thus turned into: +\begin{lstlisting} +y : nat +================== +true && (y < 2) = true +\end{lstlisting} +If the cleared names are reused in the same intro pattern, a renaming +is performed behind the scenes. + +Facts mentioned in a clear switch must be valid +names in the proof context (excluding the section context). + +The rules for interpreting branching and destructing \ssrN{i-pattern} +are motivated by the fact that it would be pointless to have a branching +pattern if {\tac} is a \ssrC{move}, and in most of the remaining cases +{\tac} is \ssrC{case} or \ssrC{elim}, which implies destruction. +The rules above imply that +\begin{lstlisting} + move=> [a b]. + case=> [a b]. + case=> a b. +\end{lstlisting} +are all equivalent, so which one to use is a matter of style; +\ssrC{move} should be used for casual decomposition, +such as splitting a pair, and \ssrC{case} should be used for actual decompositions, +in particular for type families (see~\ref{ssec:typefam}) +and proof by contradiction. + +The trivial branching \ssrN{i-pattern} can be used to force the branching +interpretation, e.g., +\begin{lstlisting} + case=> [] [a b] c. + move=> [[a b] c]. + case; case=> a b c. +\end{lstlisting} +are all equivalent. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Generation of equations}\label{ssec:equations} +\idx{move eq : \dots{}} + +The generation of named equations option stores the definition of a +new constant as an equation. The tactic: +\begin{lstlisting} + move En: (size l) => n. +\end{lstlisting} +where \ssrC{l} is a list, replaces \ssrC{size l} by \ssrC{n} in the goal and +adds the fact \ssrC{En : size l = n} to the context. + This is quite different from: +\begin{lstlisting} + pose n := (size l). +\end{lstlisting} +which generates a definition \ssrC{n := (size l)}. It is not possible to +generalize or +rewrite such a definition; on the other hand, it is automatically +expanded during +computation, whereas expanding the equation \ssrC{En} requires explicit +rewriting. + +The use of this equation name generation option with a \ssrC{case} or an +\ssrC{elim} tactic changes the status of the first \iitem{}, in order to +deal with the possible parameters of the constants introduced. + +On the +goal \ssrC{a <> b} where \ssrC{a, b} are natural numbers, the tactic: +\begin{lstlisting} + case E : a => [|n]. +\end{lstlisting} +generates two subgoals. The equation \ssrC{E : a = 0} (resp. \ssrC{E : a = + S n}, and the constant \ssrC{n : nat}) has been added to +the context of the goal \ssrC{0 <> b} (resp. \ssrC{S n <> b}). + +If the user does not provide a branching \iitem{} as first \iitem{}, +or if the \iitem{} does not provide enough names for the arguments of +a constructor, +then the constants generated are introduced under fresh \ssr{} names. +For instance, on the goal \ssrC{a <> b}, the tactic: +\begin{lstlisting} + case E : a => H. +\end{lstlisting} +also generates two subgoals, both requiring a proof of \ssrC{False}. + The hypotheses \ssrC{E : a = 0} and +\ssrC{H : 0 = b} (resp. \ssrC{E : a = S _n_} and +\ssrC{H : S _n_ = b}) have been added to the context of the first +subgoal (resp. the second subgoal). + +Combining the generation of named equations mechanism with the +\ssrC{case} tactic strengthens the power of a case analysis. On the other +hand, when combined with the \ssrC{elim} tactic, this feature is mostly +useful for +debug purposes, to trace the values of decomposed parameters and +pinpoint failing branches. + +% This feature is also useful +% to analyse and debug generate-and-test style scripts that prove program +% properties by generating a large set of input patterns and uniformly +% solving the corresponding subgoals by computation and rewriting, e.g, + +% \begin{lstlisting} +% case: et => [|e' et]; first by case: s. +% case: e => //; case: b; case: w. +% \end{lstlisting} +% If the above sequence fails, then it's easy enough to replace the line +% above with +% \begin{lstlisting} +% case: et => [|e' et]. +% case Ds: s; case De: e => //; case Db: b; case Dw: w=> [|s' w'] //=. +% \end{lstlisting} +% Then the first subgoal that appears will be the failing one, and the +% equations \ssrC{Ds}, \ssrC{De}, \ssrC{Db} +% and \ssrC{Dw} will pinpoint its branch. When the constructors of +% the decomposed type have arguments (like \ssrC{w : (seq nat)} +% above) these need to be +% introduced in order to generate the equation, so there should +% always be an explicit \iitem{} (\ssrC{\[|s' w'\]} above) that +% assigns names to these arguments. If this \iitem{} +% is omitted the arguments are introduced with default +% name; this +% feature should be +% avoided except for quick debugging runs (it has some uses in complex tactic +% sequences, however). + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Type families}\label{ssec:typefam} +\idx{case: \dots{} / \dots{}} + +When the top assumption of a goal has an inductive type, two +specific operations are possible: the case analysis performed by the +\ssrC{case} tactic, and the application of an induction principle, +performed by the \ssrC{elim} tactic. When this top assumption has an +inductive type, which is moreover an instance of a type family, \Coq{} +may need help from the user to specify which occurrences of the parameters +of the type should be substituted. + +A specific \ssrC{/} switch indicates the type family parameters of the +type of a \ditem{} immediately following this \ssrC{/} switch, using the +syntax: + +\begin{center} + \ssrC{[} \ssrC{case} {\optsep} \ssrC{elim} \ssrC{]:} \ssrN{d-item}$^+$ \ssrC{/} \ssrN{d-item}$^*$ +\end{center} + +The \ssrN{d-item}s on the right side of the \ssrC{/} switch are discharged +as described in section \ref{ssec:discharge}. The case analysis or +elimination will be done on the type of the top assumption after these +discharge operations. + +Every \ssrN{d-item} preceding the \ssrC{/} is interpreted as arguments of this +type, which should be an instance of an inductive type family. These terms are +not actually generalized, but rather selected for substitution. Occurrence +switches can be used to restrict the substitution. If a {\term} is left +completely implicit (e.g. writing just $\ssrC{\_}$), then a pattern is inferred +looking at the type of the top assumption. This allows for the compact syntax +\ssrC{case: \{2\}\_ / eqP}, were \ssrC{\_} is interpreted as \ssrC{(\_ == \_)}. Moreover +if the \ssrN{d-item}s list is too short, it is padded with an initial +sequence of $\ssrC{\_}$ of the right length. + +Here is a small example on lists. We define first a function which +adds an element at the end of a given list. +\begin{lstlisting} + Require Import List. + + Section LastCases. + Variable A : Type. + + Fixpoint |*add_last*|(a : A)(l : list A): list A := + match l with + |nil => a :: nil + |hd :: tl => hd :: (add_last a tl) + end. +\end{lstlisting} +Then we define an inductive predicate for +case analysis on lists according to their last element: +\begin{lstlisting} + Inductive |*last_spec*| : list A -> Type := + | LastSeq0 : last_spec nil + | LastAdd s x : last_spec (add_last x s). + + Theorem |*lastP*| : forall l : list A, last_spec l. +\end{lstlisting} +Applied to the goal: +\begin{lstlisting} + Goal forall l : list A, (length l) * 2 = length (app l l). +\end{lstlisting} +the command: +\begin{lstlisting} + move=> l; case: (lastP l). +\end{lstlisting} +generates two subgoals: +\begin{lstlisting} + length nil * 2 = length (nil ++ nil) +\end{lstlisting} +and +\begin{lstlisting} + forall (s : list A) (x : A), + length (add_last x s) * 2 = length (add_last x s ++ add_last x s) +\end{lstlisting} +both having \ssrC{l : list A} in their context. + +Applied to the same goal, the command: +\begin{lstlisting} + move=> l; case: l / (lastP l). +\end{lstlisting} +generates the same subgoals but \ssrC{l} has been cleared from both +contexts. + +Again applied to the same goal, the command: +\begin{lstlisting} + move=> l; case: {1 3}l / (lastP l). +\end{lstlisting} +generates the subgoals \ssrL-length l * 2 = length (nil ++ l)- and +\ssrL-forall (s : list A) (x : A), length l * 2 = length (add_last x s++l)- +where the selected occurrences on the left of the \ssrC{/} switch have +been substituted with \ssrC{l} instead of being affected by the case +analysis. + +The equation name generation feature combined with a type family \ssrC{/} + switch generates an equation for the \emph{first} dependent d-item +specified by the user. +Again starting with the above goal, the command: +\begin{lstlisting} + move=> l; case E: {1 3}l / (lastP l)=>[|s x]. +\end{lstlisting} +adds \ssrC{E : l = nil} and \ssrC{E : l = add_last x s}, +respectively, to the context of the two subgoals it generates. + +There must be at least one \emph{d-item} to the left of the \ssrC{/} +switch; this prevents any +confusion with the view feature. However, the \ditem{}s to the right of +the \ssrC{/} are optional, and if they are omitted the first assumption +provides the instance of the type family. + +The equation always refers to the first \emph{d-item} in the actual +tactic call, before any padding with initial $\ssrC{\_}$s. Thus, if an +inductive type has two family parameters, it is possible to have +\ssr{} generate an equation for the second one by omitting the pattern +for the first; note however that this will fail if the type of the +second parameter depends on the value of the first parameter. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Control flow} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Indentation and bullets}\label{ssec:indent} + +A linear development of \Coq{} scripts gives little information on +the structure of the proof. In addition, replaying a proof after some +changes in the statement to be proved will usually not display information to +distinguish between the various branches of case analysis for instance. + +To help the user in this organization of the proof script at +development time, \ssr{} provides some bullets to highlight the +structure of branching proofs. The available bullets are \ssrC{-}, +\ssrC{+} and \ssrC{*}. Combined with tabulation, this lets us highlight four +nested levels of branching; the most we have ever +needed is three. Indeed, the use of ``simpl and closing'' switches, of +terminators (see above section \ref{ssec:termin}) and selectors (see + section \ref{ssec:select}) is powerful enough +to avoid most of the time more than two levels of indentation. + +Here is a fragment of such a structured script: + +\begin{lstlisting} +case E1: (abezoutn _ _) => [[| k1] [| k2]]. +- rewrite !muln0 !gexpn0 mulg1 => H1. + move/eqP: (sym_equal F0); rewrite -H1 orderg1 eqn_mul1. + by case/andP; move/eqP. +- rewrite muln0 gexpn0 mulg1 => H1. + have F1: t %| t * S k2.+1 - 1. + apply: (@dvdn_trans (orderg x)); first by rewrite F0; exact: dvdn_mull. + rewrite orderg_dvd; apply/eqP; apply: (mulgI x). + rewrite -{1}(gexpn1 x) mulg1 gexpn_add leq_add_sub //. + by move: P1; case t. + rewrite dvdn_subr in F1; last by exact: dvdn_mulr. + + rewrite H1 F0 -{2}(muln1 (p ^ l)); congr (_ * _). + by apply/eqP; rewrite -dvdn1. + + by move: P1; case: (t) => [| [| s1]]. +- rewrite muln0 gexpn0 mul1g => H1. +... +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Terminators}\label{ssec:termin} +\idx{by \dots{}} + +To further structure scripts, \ssr{} +supplies \emph{terminating} tacticals to explicitly close off tactics. +When replaying scripts, we then have the nice property that +an error immediately occurs when a closed tactic fails to prove its +subgoal. + +It is hence recommended practice that the proof of any subgoal should +end with a tactic which \emph{fails if it does not solve the current + goal}, like \ssrC{discriminate}, \ssrC{contradiction} or \ssrC{assumption}. + +In fact, \ssr{} provides a generic tactical which turns any tactic into +a closing one (similar to \ssrC{now}). Its general syntax is: + +\begin{center} + \ssrC{by} {\tac}\ssrC{.} +\end{center} + +The Ltac expression: + +\begin{center} + \ssrC{by [}\ssrN[1]{tactic} \ssrC{| [}\ssrN[2]{tactic} \ssrC{| ...].} +\end{center} + +is equivalent to: + +\begin{center} + \ssrC{[by} \ssrN[1]{tactic} \ssrC{| by} \ssrN[2]{tactic} \ssrC{| ...].} +\end{center} + +and this form should be preferred to the former. + +In the script provided as example in section \ref{ssec:indent}, the +paragraph corresponding to each sub-case ends with a tactic line prefixed +with a \ssrC{by}, like in: + +\begin{center} + \ssrC{by apply/eqP; rewrite -dvdn1.} +\end{center} + + +The \ssrC{by} tactical is implemented using the user-defined, +and extensible \ssrC{done} tactic. This \ssrC{done} tactic tries to solve +the current goal by some trivial means and fails if it doesn't succeed. +Indeed, the tactic expression: + +\begin{center} + \ssrC{by} {\tac}\ssrC{.} +\end{center} + +is equivalent to: + +\begin{center} + {\tac}\ssrC{; done.} +\end{center} + +Conversely, the tactic + +\begin{center} + \ssrC{by [ ].} +\end{center} + +is equivalent to: + +\begin{center} + \ssrC{done.} +\end{center} + +The default implementation of the \ssrC{done} tactic, in the {\tt + ssreflect.v} file, is: + +\begin{lstlisting} +Ltac done := + trivial; hnf; intros; solve + [ do ![solve [trivial | apply: sym_equal; trivial] + | discriminate | contradiction | split] + | case not_locked_false_eq_true; assumption + | match goal with H : ~ _ |- _ => solve [case H; trivial] end ]. +\end{lstlisting} + +The lemma \ssrC{|*not_locked_false_eq_true*|} is needed to discriminate +\emph{locked} boolean predicates (see section \ref{ssec:lock}). +The iterator tactical \ssrC{do} is presented in section +\ref{ssec:iter}. +This tactic can be customized by the user, for instance to include an +\ssrC{auto} tactic. + +A natural and common way of closing a goal is to apply a lemma which +is the \ssrC{exact} one needed for the goal to be solved. The defective +form of the tactic: +\begin{lstlisting} + exact. +\end{lstlisting} +is equivalent to: +\begin{lstlisting} + do [done | by move=> top; apply top]. +\end{lstlisting} +where \ssrC{top} is a fresh name affected to the top assumption of the goal. +This applied form is supported by the \ssrC{:} discharge tactical, and +the tactic: +\begin{lstlisting} + exact: MyLemma. +\end{lstlisting} +is equivalent to: +\begin{lstlisting} + by apply: MyLemma. +\end{lstlisting} +(see section \ref{sss:strongapply} for the documentation of the \ssrC{apply:} +combination). + +\textit{Warning} The list of tactics, possibly chained by +semi-columns, that follows a \ssrC{by} keyword is considered as a +parenthesized block +applied to the current goal. Hence for example if the tactic: +\begin{lstlisting} + by rewrite my_lemma1. +\end{lstlisting} +succeeds, then the tactic: +\begin{lstlisting} + by rewrite my_lemma1; apply my_lemma2. +\end{lstlisting} +usually fails since it is equivalent to: +\begin{lstlisting} + by (rewrite my_lemma1; apply my_lemma2). +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Selectors}\label{ssec:select} +\idx{last \dots{} first} +\idx{first \dots{} last} + +When composing tactics, the two tacticals \ssrC{first} and +\ssrC{last} let the user restrict the application of a tactic to only one +of the subgoals generated by the previous tactic. This +covers the frequent cases where a tactic generates two subgoals one of +which can be easily disposed of. + +This is an other powerful way of linearization of scripts, since it +happens very often that a trivial subgoal can be solved in a less than +one line tactic. For instance, the tactic: + +\begin{center} + \ssrN[1]{tactic}\ssrC{; last by} \ssrN[2]{tactic}\ssrC{.} +\end{center} + +tries to solve the last subgoal generated by \ssrN[1]{tactic} using the +\ssrN[2]{tactic}, and fails if it does not succeeds. Its analogous + +\begin{center} + \ssrN[1]{tactic}\ssrC{; first by} \ssrN[2]{tactic}. +\end{center} + +tries to solve the first subgoal generated by \ssrN[1]{tactic} using the +tactic \ssrN[2]{tactic}, and fails if it does not succeeds. + + +\ssr{} also offers an extension of this facility, by supplying +tactics to \emph{permute} the subgoals generated by a tactic. +The tactic: + +\begin{center} + {\tac}\ssrC{; last first.} +\end{center} + +inverts the order of the subgoals generated by {\tac}. It is +equivalent to: + +\begin{center} + {\tac}\ssrC{; first last.} +\end{center} + + +More generally, the tactic: + +\begin{center} + {\tac}\ssrC{; last }${\naturalnumber}$ \ssrC{first.} +\end{center} + +where ${\naturalnumber}$ is +a \Coq{} numeral, or and Ltac variable denoting +a \Coq{} numeral, having the value $k$. It +rotates the $n$ subgoals $G_1, +\dots, G_n$ generated by {\tac}. The first subgoal becomes +$G_{n + 1 - k}$ and the circular order of subgoals remains unchanged. + +Conversely, the tactic: + + {\tac}\ssrC{; first }${\naturalnumber}$ \ssrC{last.} + +rotates the $n$ subgoals $G_1, +\dots, G_n$ generated by \ssrC{tactic} in order that the first subgoal +becomes $G_{k}$. + +Finally, the tactics \ssrC{last} and \ssrC{first} combine with the +branching syntax of Ltac: +if the tactic $\ssrN[0]{tactic}$ generates $n$ +subgoals on a given goal, then the tactic + + $tactic_0$\ssrC{; last }${\naturalnumber}$ \ssrC{[}$tactic_1$\ssrC{|}$\dots$\ssrC{|}$tactic_m$\ssrC{] || }$tactic_{m+1}$\ssrC{.} + +where ${\naturalnumber}$ denotes the integer $k$ as above, applies $tactic_1$ to the +$n -k + 1$-th goal, $\dots tactic_m$ to the $n -k + 2 - m$-th +goal and $tactic_{m+1}$ to the others. + +For instance, the script: +\begin{lstlisting} + Inductive test : nat -> Prop := + C1 : forall n, test n | C2 : forall n, test n | + C3 : forall n, test n | C4 : forall n, test n. + + Goal forall n, test n -> True. + move=> n t; case: t; last 2 [move=> k| move=> l]; idtac. +\end{lstlisting} + +creates a goal with four subgoals, the first and the last being +\ssrC{nat -> True}, the second and the third being \ssrC{True} with +respectively \ssrC{k : nat} and \ssrC{l : nat} in their context. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Iteration}\label{ssec:iter} +\idx{do \dots{} [ \dots{} ]} + +\ssr{} offers an accurate control on the repetition of +tactics, thanks to the \ssrC{do} tactical, whose general syntax is: + +\begin{center} + \ssrC{do} \optional{\ssrN{mult}} \ssrC{[} \ssrN[1]{tactic} \ssrC{|} $\dots$ \ssrC{|} \ssrN[n]{tactic} \ssrC{]} +\end{center} +where \ssrN{mult} is a \emph{multiplier}. + +Brackets can only be omitted if a single tactic is given \emph{and} a +multiplier is present. + +A tactic of the form: + +\begin{center} + \ssrC{do [} \tac$_1$ \ssrC{|} $\dots$ \ssrC{|} \tac$_n$\ssrC{].} +\end{center} + +is equivalent to the standard Ltac expression: + +\begin{center} + \ssrC{first [} \tac$_1$ \ssrC{|} $\dots$ \ssrC{|} \tac$_n$\ssrC{].} +\end{center} + + +The optional multiplier \ssrN{mult} specifies how many times +the action of {\tac} should be repeated on the current subgoal. + +There are four kinds of multipliers: + \begin{itemize} + \item \ssrC{n!}: the step {\tac} is repeated exactly $n$ times + (where $n$ is a positive integer argument). + \item \ssrC{!}: the step {\tac} is repeated as many times as possible, + and done at least once. + \item \ssrC{?}: the step {\tac} is repeated as many times as possible, + optionally. + \item \ssrC{n?}: the step {\tac} is repeated up to $n$ times, + optionally. + \end{itemize} + +For instance, the tactic: + +\begin{center} + {\tac} \ssrL+; do 1?rewrite mult_comm.+ +\end{center} + +rewrites at most one time the lemma \ssrC{mult_com} in all the subgoals +generated by {\tac} , whereas the tactic: + +\begin{center} + {\tac} \ssrL+; do 2!rewrite mult_comm.+ +\end{center} + +rewrites exactly two times the lemma \ssrC{mult_com} in all the subgoals +generated by {\tac}, and fails if this rewrite is not possible +in some subgoal. + +Note that the combination of multipliers and \ssrC{rewrite} is so often +used that multipliers are in fact integrated to the syntax of the \ssr{} +\ssrC{rewrite} tactic, see section \ref{sec:rw}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Localization}\label{ssec:gloc} +\idx{\dots{} in \dots{}} + +In sections \ref{ssec:loc} and \ref{ssec:profstack}, we have already +presented the \emph{localization} tactical \ssrC{in}, whose general +syntax is: +\begin{center} + {\tac} \ssrC{in} \ssrN{ident}$^+$ \optional{\ssrC{*}} +\end{center} + +where \ssrN{ident}$^+$ is a non empty list of fact +names in the context. On the left side of \ssrC{in}, {\tac} can be +\ssrC{move}, \ssrC{case}, \ssrC{elim}, \ssrC{rewrite}, \ssrC{set}, + or any tactic formed with the general iteration tactical \ssrC{do} (see + section \ref{ssec:iter}). + +The operation described by {\tac} is performed in the facts +listed in \ssrN{ident}$^+$ and in the goal if a \ssrC{*} ends +the list. + +The \ssrC{in} tactical successively: +\begin{itemize} +\item generalizes the selected hypotheses, possibly ``protecting'' the + goal if \ssrC{*} is not present, +\item performs {\tac}, on the obtained goal, +\item reintroduces the generalized facts, under the same names. +\end{itemize} + +This defective form of the \ssrC{do} tactical is useful to avoid clashes +between standard Ltac \ssrC{in} and the \ssr{} tactical \ssrC{in}. +For example, in the following script: +\begin{lstlisting} + Ltac |*mytac*| H := rewrite H. + + Goal forall x y, x = y -> y = 3 -> x + y = 6. + move=> x y H1 H2. + do [mytac H2] in H1 *. +\end{lstlisting} +the last tactic rewrites the hypothesis \ssrC{H2 : y = 3} both in +\ssrC{H1 : x = y} and in the goal \ssrC{x + y = 6}. + +By default \ssrC{in} keeps the body of local definitions. To erase +the body of a local definition during the generalization phase, +the name of the local definition must be written between parentheses, +like in \ssrC{rewrite H in H1 (def_n) $\;\;$H2}. + +From \ssr{} 1.5 the grammar for the \ssrC{in} tactical has been extended +to the following one: + +\begin{center} + {\tac} \ssrC{in} \optional{ + \ssrN{clear-switch} {\optsep} + \optional{\ssrC{@}}\ssrN{ident} {\optsep} + \ssrC{(}\ssrN{ident}\ssrC{)} {\optsep} + \ssrC{(}\optional{\ssrC{@}}\ssrN{ident} \ssrC{:=} \ssrN{c-pattern}\ssrC{)} + }$^+$ \optional{\ssrC{*}} +\end{center} + +In its simplest form the last option lets one rename hypotheses that can't be +cleared (like section variables). For example \ssrC{(y := x)} generalizes +over \ssrC{x} and reintroduces the generalized +variable under the name \ssrC{y} (and does not clear \ssrC{x}).\\ +For a more precise description the $\ssrC{(}[\ssrC{@}]\ssrN{ident}\ \ssrC{:=}\ \ssrN{c-pattern}\ssrC{)}$ +item refer to the ``Advanced generalization'' paragraph at page~\pageref{par:advancedgen}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Structure}\label{ssec:struct} + +Forward reasoning structures the script by explicitly specifying some +assumptions to be added to the proof context. It is closely associated +with the declarative style of proof, since an extensive use of these +highlighted statements +make the script closer to a (very detailed) text book proof. + +Forward chaining tactics allow to state an intermediate lemma and start a +piece of script dedicated to the proof of this statement. The use of +closing tactics (see section \ref{ssec:termin}) and of +indentation makes syntactically explicit the portion of the script +building the proof of the intermediate statement. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{have} tactic.} +\label{sssec:have} +\idx{have: \dots{}} +\idx{have: \dots{} := \dots{}} + +The main \ssr{} forward reasoning tactic is the \ssrC{have} tactic. It +can be use in two modes: one starts a new (sub)proof for an +intermediate result in the main proof, and the other +provides explicitly a proof term for this intermediate step. + +In the first mode, the syntax of \ssrC{have} in its defective form is: + + \ssrC{have: }{\term}\ssrC{.} + +This tactic supports open syntax for {\term}. +Applied to a goal \ssrC{G}, it generates a first subgoal requiring a +proof of {\term} in the context of \ssrC{G}. The second generated +subgoal is of the form {\term} \ssrC{-> G}, where {\term} becomes +the new top assumption, instead of being introduced with a fresh +name. At the proof-term level, the \ssrC{have} tactic creates a $\beta$ +redex, and introduces the lemma under a fresh name, automatically +chosen. + + +Like in the case of the \ssrC{pose} tactic (see section \ref{ssec:pose}), +the types of the holes are abstracted in {\term}. +For instance, the tactic: +\begin{lstlisting} + have: _ * 0 = 0. +\end{lstlisting} +is equivalent to: +\begin{lstlisting} + have: forall n : nat, n * 0 = 0. +\end{lstlisting} +The \ssrC{have} tactic also enjoys the same abstraction mechanism as the +\ssrC{pose} tactic for the non-inferred implicit arguments. For instance, +the tactic: +\begin{lstlisting} + have: forall x y, (x, y) = (x, y + 0). +\end{lstlisting} +opens a new subgoal to prove that: + +\noindent\ssrC{forall (T : Type) (x : T) (y : nat), (x, y) = (x, y + 0)} + + +The behavior of the defective \ssrC{have} tactic makes it possible to +generalize it in the +following general construction: +\begin{center} + \ssrC{have} \ssrN{i-item}$^*$ \optional{\ssrN{i-pattern}} + \optional{\ssrN{s-item} {\optsep} \ssrN{binder}$^+$} + \optional{\ssrC{:} \ssrN[1]{term}} + \optional{\ssrC{:=} \ssrN[2]{term} {\optsep} \ssrC{by} {\tac}} +\end{center} + +Open syntax is supported for $\ssrN[1]{term}$ and $\ssrN[2]{term}$. For the +description of +\iitem{}s and clear switches see section \ref{ssec:intro}. +The first mode of the \ssrC{have} tactic, which opens a sub-proof for an +intermediate result, uses tactics of the form: + +\begin{center} + \ssrC{have} \ssrN{clear-switch} \ssrN{i-item} \ssrC{:} {\term} \ssrC{by} {\tac}. +\end{center} + +which behave like:\\ + +\begin{center} + \ssrC{have:} {\term} \ssrC{; first by } {\tac}. +\end{center} +\begin{center} + \ssrC{ move=>} \ssrN{clear-switch} \ssrN{i-item}. +\end{center} + + +Note that the \ssrN{clear-switch} \emph{precedes} the +\ssrN{i-item}, which allows to reuse a name of the context, possibly used +by the proof of the assumption, to introduce the new assumption +itself. + +The \ssrC{by} feature is especially convenient when the proof script of the +statement is very short, basically when it fits in one line like in: +\begin{lstlisting} + have H : forall x y, x + y = y + x by move=> x y; rewrite addnC. +\end{lstlisting} + +The possibility of using \iitem{}s supplies a very concise +syntax for the further use of the intermediate step. For instance, +\begin{lstlisting} + have -> : forall x, x * a = a. +\end{lstlisting} +on a goal \ssrC{G}, opens a new subgoal asking for a proof of +\ssrC{forall x, x * a = a}, and a second subgoal in which the lemma + \ssrC{forall x, x * a = a} has been rewritten in the goal \ssrC{G}. Note + that in this last subgoal, the intermediate result does not appear in + the context. +Note that, thanks to the deferred execution of clears, the following +idiom is supported (assuming \ssrC{x} occurs in the goal only): +\begin{lstlisting} + have {x} -> : x = y +\end{lstlisting} + +An other frequent use of the intro patterns combined with \ssrC{have} is the +destruction of existential assumptions like in the tactic: +\begin{lstlisting} + have [x Px]: exists x : nat, x > 0. +\end{lstlisting} +which opens a new subgoal asking for a proof of \ssrC{exists x : nat, x > + 0} and a second subgoal in which the witness is introduced under +the name \ssrC{x : nat}, and its property under the name \ssrC{Px : x > 0}. + +An alternative use of the \ssrC{have} tactic is to provide the explicit proof +term for the intermediate lemma, using tactics of the form: + +\begin{center} + \ssrC{have} \optional{\ssrN{ident}} \ssrC{:=} {\term}. +\end{center} + +This tactic creates a new assumption of type the type of +{\term}. If the +optional \ssrN{ident} is present, this assumption is introduced under +the name \ssrN{ident}. Note that the body of the constant is lost for +the user. + +Again, non inferred implicit arguments and explicit holes are abstracted. For +instance, the tactic: +\begin{lstlisting} + have H := forall x, (x, x) = (x, x). +\end{lstlisting} +adds to the context \ssrC{H : Type -> Prop}. This is a schematic example but +the feature is specially useful when the proof term to give involves +for instance a lemma with some hidden implicit arguments. + +After the \ssrN{i-pattern}, a list of binders is allowed. +For example, if \ssrC{Pos_to_P} is a lemma that proves that +\ssrC{P} holds for any positive, the following command: +\begin{lstlisting} + have H x (y : nat) : 2 * x + y = x + x + y by auto. +\end{lstlisting} +will put in the context \ssrC{H : forall x, 2 * x = x + x}. A proof term +provided after \ssrC{:=} can mention these bound variables (that are +automatically introduced with the given names). +Since the \ssrN{i-pattern} can be omitted, to avoid ambiguity, bound variables +can be surrounded with parentheses even if no type is specified: +\begin{lstlisting} + have (x) : 2 * x = x + x by auto. +\end{lstlisting} + +The \ssrN{i-item}s and \ssrN{s-item} can be used to interpret the +asserted hypothesis with views (see section~\ref{sec:views}) or +simplify the resulting goals. + +The \ssrC{have} tactic also supports a \ssrC{suff} modifier which allows for +asserting that a given statement implies the current goal without +copying the goal itself. For example, given a goal \ssrC{G} the tactic +\ssrC{have suff H : P} results in the following two goals: +\begin{lstlisting} + |- P -> G + H : P -> G |- G +\end{lstlisting} +Note that \ssrC{H} is introduced in the second goal. The \ssrC{suff} +modifier is not compatible with the presence of a list of binders. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Generating \ssrC{let in} context entries with \ssrC{have}} +\label{sec:havetransparent} + +Since \ssr{} 1.5 the \ssrC{have} tactic supports a ``transparent'' modifier to +generate \ssrC{let in} context entries: the \ssrC{@} symbol in front of the context +entry name. For example: + +\begin{lstlisting} +have @i : 'I_n by apply: (Sub m); auto. +\end{lstlisting} +generates the following two context entry: +\begin{lstlisting} +i := Sub m proof_produced_by_auto : 'I_n +\end{lstlisting} + +Note that the sub-term produced by \ssrC{auto} is in general huge and +uninteresting, and hence one may want to hide it. + +For this purpose the \ssrC{[: name ]} intro pattern and the tactic +\ssrC{abstract} (see page~\pageref{ssec:abstract}) are provided. +Example: +\begin{lstlisting} +have [:blurb] @i : 'I_n by apply: (Sub m); abstract: blurb; auto. +\end{lstlisting} +generates the following two context entries: +\begin{lstlisting} +blurb : (m < n) (*1*) +i := Sub m blurb : 'I_n +\end{lstlisting} +The type of \ssrC{blurb} can be cleaned up by its annotations by just simplifying +it. The annotations are there for technical reasons only. + +When intro patterns for abstract constants are used in conjunction +with \ssrC{have} and an explicit term, they must be used as follows: + +\begin{lstlisting} +have [:blurb] @i : 'I_n := Sub m blurb. + by auto. +\end{lstlisting} + +In this case the abstract constant \ssrC{blurb} is assigned by using it +in the term that follows \ssrC{:=} and its corresponding goal is left to +be solved. Goals corresponding to intro patterns for abstract constants +are opened in the order in which the abstract constants are declared (not +in the ``order'' in which they are used in the term). + +Note that abstract constants do respect scopes. Hence, if a variable +is declared after their introduction, it has to be properly generalized (i.e. +explicitly passed to the abstract constant when one makes use of it). +For example any of the following two lines: +\begin{lstlisting} +have [:blurb] @i k : 'I_(n+k) by apply: (Sub m); abstract: blurb k; auto. +have [:blurb] @i k : 'I_(n+k) := apply: Sub m (blurb k); first by auto. +\end{lstlisting} +generates the following context: +\begin{lstlisting} +blurb : (forall k, m < n+k) (*1*) +i := fun k => Sub m (blurb k) : forall k, 'I_(n+k) +\end{lstlisting} + +Last, notice that the use of intro patterns for abstract constants is +orthogonal to the transparent flag \ssrC{@} for \ssrC{have}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{The \ssrC{have} tactic and type classes resolution} +\label{ssec:havetcresolution} + +Since \ssr{} 1.5 the \ssrC{have} tactic behaves as follows with respect to type +classes inference. + +\begin{itemize} +\item \ssrC{have foo : ty.} + Full inference for \ssrC{ty}. + The first subgoal demands a proof of such instantiated statement. +\item \ssrC{have foo : ty := .} + No inference for \ssrC{ty}. Unresolved instances are quantified in + \ssrC{ty}. The first subgoal demands a proof of such quantified + statement. Note that no proof term follows \ssrC{:=}, hence two + subgoals are generated. +\item \ssrC{have foo : ty := t.} + No inference for \ssrC{ty} and \ssrC{t}. +\item \ssrC{have foo := t.} + No inference for \ssrC{t}. Unresolved instances are quantified in the + (inferred) type of \ssrC{t} and abstracted in \ssrC{t}. +\end{itemize} + +The behavior of \ssr{} 1.4 and below (never resolve type classes) +can be restored with the option \ssrC{Set SsrHave NoTCResolution}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Variants: the \ssrC{suff} and \ssrC{wlog} tactics.} +\label{ssec:wlog} +\idx{suff: \dots{}} +\idx{suffices: \dots{}} +\idx{wlog: \dots{} / \dots{}} +\idx{without loss: \dots{} / \dots{}} + +As it is often the case in mathematical textbooks, forward +reasoning may be used in slightly different variants. +One of these variants is to show that the intermediate step $L$ +easily implies the initial goal $G$. By easily we mean here that +the proof of $L \Rightarrow G$ is shorter than the one of $L$ +itself. This kind of reasoning step usually starts with: +``It suffices to show that \dots''. + +This is such a frequent way of reasoning that \ssr{} has a variant of the +\ssrC{have} tactic called \ssrC{suffices} (whose abridged name is +\ssrC{suff}). The \ssrC{have} and \ssrC{suff} tactics are equivalent and +have the same syntax but: +\begin{itemize} +\item the order of the generated subgoals is inversed +\item but the optional clear item is still performed in the + \emph{second} branch. This means that the tactic: +\begin{lstlisting} + suff {H} H : forall x : nat, x >= 0. +\end{lstlisting} +fails if the context of the current goal indeed contains an +assumption named \ssrC{H}. +\end{itemize} +The rationale of this clearing policy is to make possible ``trivial'' +refinements of an assumption, without changing its name in the main +branch of the reasoning. + +The \ssrC{have} modifier can follow the \ssrC{suff} tactic. +For example, given a goal \ssrC{G} the tactic +\ssrC{suff have H : P} results in the following two goals: +\begin{lstlisting} + H : P |- G + |- (P -> G) -> G +\end{lstlisting} +Note that, in contrast with \ssrC{have suff}, the name \ssrC{H} has been introduced +in the first goal. + +Another useful construct is reduction, +showing that a particular case is in fact general enough to prove +a general property. This kind of reasoning step usually starts with: +``Without loss of generality, we can suppose that \dots''. +Formally, this corresponds to the proof of a goal \ssrC{G} by introducing +a cut \ssrN{wlog\_statement} \ssrC{-> G}. Hence the user shall provide a +proof for both \ssrC{(}\ssrN{wlog\_statement} \ssrC{-> G) -> G} and +\ssrN{wlog\_statement} \ssrC{-> G}. However, such cuts are usually rather +painful to perform by hand, because the statement +\ssrN{wlog\_statement} is tedious to write by hand, and somtimes even +to read. + +\ssr{} implements this kind of reasoning step through the \ssrC{without loss} +tactic, whose short name is \ssrC{wlog}. It offers support to describe +the shape of the cut statements, by providing the simplifying +hypothesis and by pointing at the elements of the initial goals which +should be generalized. The general syntax of \ssrC{without loss} is: + +\begin{center} + \ssrC{wlog} \optional{\ssrC{suff}} \optional{\ssrN{clear-switch}} \optional{\ssrN{i-item}} \ssrC{:} \optional{\ssrN[1]{ident} $\dots$ \ssrN[n]{ident}} \ssrC{/} {\term} +\end{center} + +where \ssrN[1]{ident} $\dots$ \ssrN[n]{ident} are identifiers for constants +in the context of the goal. Open syntax is supported for {\term}. + +In its defective form: + +\begin{center} + \ssrC{wlog: /} {\term}. +\end{center} + +on a goal \ssrC{G}, it creates two subgoals: a first one to prove the formula +\ssrC{(}{\term} \ssrC{-> G) -> G} and a second one to prove the formula +{\term} \ssrC{-> G}. + +:browse confirm wa +If the optional list \ssrN[1]{ident} $\dots$ \ssrN[n]{ident} is present on the left +side of \ssrC{/}, these constants are generalized in the premise +\ssrC{(}{\term} \ssrC{-> G)} of the first subgoal. By default the body of +local definitions is erased. This behavior can be inhibited +prefixing the name of the local definition with the \ssrC{@} character. + +In the second subgoal, the tactic: + +\begin{center} + \ssrC{move=>} \ssrN{clear-switch}\ssrC{} \ssrN{i-item}\ssrC{.} +\end{center} + +is performed if at least one of these optional switches is present in +the \ssrC{wlog} tactic. + +The \ssrC{wlog} tactic is specially useful when a symmetry argument +simplifies a proof. Here is an example showing the beginning of the +proof that quotient and reminder of natural number euclidean division +are unique. +\begin{lstlisting} + Lemma quo_rem_unicity: forall d q1 q2 r1 r2, + q1*d + r1 = q2*d + r2 -> r1 < d -> r2 < d -> (q1, r1) = (q2, r2). + move=> d q1 q2 r1 r2. + wlog: q1 q2 r1 r2 / q1 <= q2. + by case (le_gt_dec q1 q2)=> H; last symmetry; eauto with arith. +\end{lstlisting} + +The \ssrC{wlog suff} variant is simpler, since it cuts +\ssrN{wlog\_statement} instead of \ssrN{wlog\_statement} \ssrC{-> G}. It thus +opens the goals \ssrN{wlog\_statement} \ssrC{-> G} and \ssrN{wlog\_statement}. + +In its simplest form +the \ssrC{generally have :...} tactic +is equivalent to \ssrC{wlog suff :...} followed by \ssrC{last first}. +When the \ssrC{have} tactic +is used with the \ssrC{generally} (or \ssrC{gen}) modifier it accepts an +extra identifier followed by a comma before the usual intro pattern. +The identifier will name the new hypothesis in its more general form, +while the intro pattern will be used to process its instance. For example: +\begin{lstlisting} + Lemma simple n (ngt0 : 0 < n ) : P n. + gen have ltnV, /andP[nge0 neq0] : n ngt0 / (0 <= n) && (n != 0). +\end{lstlisting} +The first subgoal will be +\begin{lstlisting} + n : nat + ngt0 : 0 < n + ==================== + (0 <= n) && (n != 0) +\end{lstlisting} +while the second one will be +\begin{lstlisting} + n : nat + ltnV : forall n, 0 < n -> (0 <= n) && (n != 0) + nge0 : 0 <= n + neqn0 : n != 0 + ==================== + P n +\end{lstlisting} + +\paragraph{Advanced generalization}\label{par:advancedgen} +The complete syntax for the items on the left hand side of the \ssrC{/} +separator is the following one: +\begin{center} +\ssrN{clear-switch} {\optsep} \optional{\ssrC{@}} \ssrN{ident} {\optsep} \ssrC{(}\optional{\ssrC{@}}\ssrN{ident} \ssrC{:=} \ssrN{c-pattern}\ssrC{)} +\end{center} +Clear operations are intertwined with generalization operations. This +helps in particular avoiding dependency issues while generalizing some facts. + +\noindent +If an \ssrN{ident} is prefixed with the \ssrC{@} prefix mark, then a +let-in redex is created, which keeps track if its body (if any). The +syntax \ssrC{(}\ssrN{ident}\ssrC{:=}\ssrN{c-pattern}\ssrC{)} allows to +generalize an arbitrary term using a given name. Note that its simplest +form \ssrC{(x := y)} is just a renaming of \ssrC{y} into \ssrC{x}. In +particular, this can be useful in order to simulate the generalization +of a section variable, otherwise not allowed. Indeed renaming does not +require the original variable to be cleared. + + +\noindent +The syntax \ssrC{(@x := y)} generates a let-in abstraction but with the following +caveat: \ssrC{x} will not bind \ssrC{y}, but its body, whenever \ssrC{y} can be +unfolded. This cover the case of both local and global definitions, as +illustrated in the following example: + +\begin{lstlisting} +Section Test. +Variable x : nat. +Definition addx z := z + x. +Lemma test : x <= addx x. +wlog H : (y := x) (@twoy := addx x) / twoy = 2 * y. +\end{lstlisting} +\noindent +The first subgoal is: +\begin{lstlisting} + (forall y : nat, let twoy := y + y in twoy = 2 * y -> y <= twoy) -> + x <= addx x +\end{lstlisting} +\noindent +To avoid unfolding the term captured by the pattern \ssrC{add x} one +can use the pattern \ssrC{id (addx x)}, that would produce the following first +subgoal: +\begin{lstlisting} + (forall y : nat, let twoy := addx y in twoy = 2 * y -> y <= twoy) -> + x <= addx x +\end{lstlisting} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Rewriting}\label{sec:rw} +\idx{rewrite \dots{}} + +The generalized use of reflection implies that most of the +intermediate results handled are properties of effectively computable +functions. The most efficient mean of establishing such results are +computation and simplification of expressions involving such +functions, i.e., rewriting. \ssr{} therefore includes an extended +\ssrC{rewrite} tactic, that unifies and combines most of the rewriting +functionalities. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{An extended \ssrC{rewrite} tactic}\label{ssec:extrw} +The main features of the \ssrC{rewrite} tactic are: +\begin{itemize} +\item It can perform an entire series of such operations in any + subset of the goal and/or context; +\item It allows to perform rewriting, + simplifications, folding/unfolding of definitions, closing of goals; +\item Several rewriting operations can be chained in a single tactic; +\item Control over the occurrence at which rewriting is to be performed is + significantly enhanced. +\end{itemize} + + +The general form of an \ssr{} rewrite tactic is: + +\begin{center} + \ssrC{rewrite} \ssrN{rstep}$^+$\ssrC{.} +\end{center} + +The combination of a rewrite tactic with the \ssrC{in} tactical (see +section \ref{ssec:loc}) performs rewriting in both the context and the +goal. + +A rewrite step \ssrN{rstep} has the general form: + +\begin{center} + \optional{\ssrN{r-prefix}}\ssrN{r-item} +\end{center} + +where: + +\begin{longtable}{rcl} +\ssrN{r-prefix} & ::= & + \optional{\ssrC{-}} \optional{\ssrN{mult}} \optional{\ssrN{occ-switch} {\optsep} \ssrN{clear-switch}} \optional{\ssrC{[}\ssrN{r-pattern}\ssrC{]}}\\ +\ssrN{r-pattern} & ::= & +{\term} {\optsep} \ssrC{in} \optional{\ssrN{ident} \ssrC{in}} {\term} {\optsep} \optional{{\term} \ssrC{in} {\optsep} {\term} \ssrC{as} } \ssrN{ident} \ssrC{in} {\term}\\ +\ssrN{r-item} & ::= & +\optional{\ssrC{/}}{\term} {\optsep} \ssrN{s-item} \\ +\end{longtable} + + +% \begin{eqnarray*} +% \ssrN{r-prefix} & ::= & +% [\ssrC{-}]\ [\ssrN{mult}][\ssrN{occ-switch} | \ssrN{cl-item}][{\term}]\\ +% \ssrN{r-item} & ::= & +% [\ssrC{-}]{\term}\ |\ [\ssrC{-}]\ssrC{[}\ssrN[1]{term}\ssrC{]}\ssrC{/(}\ssrN[2]{term}\ssrC{)} \ |\ +% \ssrN{simpl switch} \ |\ \\ +% && \ssrN{eq-term} \ |\ \ssrC{(} \ssrN[1]{eq-term}\ssrC{,}\dots +% \ssrC{,}\ssrN[n]{eq-term} \ssrC{)} \ |\ \ssrC{(_ :}\ssrN{eq-term} \ssrC{)} +% \end{eqnarray*} + + +An \ssrN{r-prefix} contains annotations to qualify where and how the +rewrite operation should be performed: +\begin{itemize} +\item The optional initial \ssrC{-} indicates the direction of the rewriting + of \ssrN{r-item}: if present the direction is right-to-left and it is + left-to-right otherwise. +\item The multiplier \ssrN{mult} (see section \ref{ssec:iter}) + specifies if and how the rewrite operation should be repeated. +\item A rewrite operation matches the occurrences of a \emph{rewrite + pattern}, and replaces these occurrences by an other term, according + to the given \ssrN{r-item}. + The optional \emph{redex switch} $\ssrC{[}\ssrN{r-pattern}\ssrC{]}$, which + should always be surrounded by brackets, gives explicitly this + rewrite pattern. In its simplest form, it is a regular term. + If no explicit redex switch + is present the rewrite pattern to be matched is inferred from the + \ssrN{r-item}. +\item This optional {\term}, or + the \ssrN{r-item}, may be preceded by an + occurrence switch (see section \ref{ssec:select}) or a clear item + (see section \ref{ssec:discharge}), these two possibilities being + exclusive. An occurrence switch selects the occurrences of the + rewrite pattern which should be affected by the rewrite operation. +\end{itemize} + + +An \ssrN{r-item} can be: + + +\begin{itemize} +\item A \emph{simplification r-item}, represented by a + \ssrN{s-item} (see section \ref{ssec:intro}). +% In some cases, \ssrN{r-prefix}es are not supported. + Simplification operations are + intertwined with the possible other rewrite operations specified by + the list of r-items. +\item A \emph{folding/unfolding r-item}. The tactic: + + \ssrC{rewrite /}{\term} + +unfolds the head constant of \textit{term} in every occurrence of the +first matching of \textit{term} in the goal. In particular, if +\ssrC{my_def} is a (local or global) defined constant, the tactic: +\begin{lstlisting} + rewrite /my_def. +\end{lstlisting} +is analogous to: +\begin{lstlisting} + unfold my_def. +\end{lstlisting} +Conversely: +\begin{lstlisting} + rewrite -/my_def. +\end{lstlisting} +is equivalent to: +\begin{lstlisting} + fold my_def. +\end{lstlisting} +%\emph{Warning} The combination of redex switch with unfold +%\ssrN{r-item} is not yet implemented. + +When an unfold r-item is combined with a redex pattern, a conversion +operation is performed. A tactic of the form: + +\begin{center} + \ssrC{rewrite -[}\ssrN[1]{term}\ssrC{]/}\ssrN[2]{term}\ssrC{.} +\end{center} + +is equivalent to: + + +\begin{center} + \ssrC{change} \ssrN[1]{term} \ssrC{with} \ssrN[2]{term}\ssrC{.} +\end{center} + + +If \ssrN[2]{term} is a single constant and \ssrN[1]{term} head symbol +is not \ssrN[2]{term}, then the head symbol of \ssrN[1]{term} is +repeatedly unfolded until \ssrN[2]{term} appears. + +\begin{lstlisting} + Definition double x := x + x. + Definition ddouble x := double (double x). + Lemma ex1 x : ddouble x = 4 * x. + rewrite [ddouble _]/double. +\end{lstlisting} + +The resulting goal is: + +\begin{lstlisting} + double x + double x = 4 * x +\end{lstlisting} + +\emph{Warning} The \ssr{} terms containing holes are \emph{not} +typed as abstractions in this context. Hence the following script: +\begin{lstlisting} + Definition f := fun x y => x + y. + Goal forall x y, x + y = f y x. + move=> x y. + rewrite -[f y]/(y + _). +\end{lstlisting} +raises the error message +\begin{verbatim} + User error: fold pattern (y + _) does not match redex (f y) +\end{verbatim} +but the script obtained by replacing the last line with: +\begin{lstlisting} + rewrite -[f y x]/(y + _). +\end{lstlisting} +is valid. + + +\item A term, which can be: + \begin{itemize} + \item A term whose type has the form: + $$\ssrC{forall}\ (x_1\ :\ A_1)\dots(x_n\ :\ A_n),\ eq\ term_1\ term_2$$ + where $eq$ is the Leibniz equality or a registered setoid + equality. %In the case of setoid relations, the only supported + %r-prefix is the directional \ssrC{-}. + \item A list of terms $(t_1,\dots,t_n)$, each $t_i$ having a type of the + form: $$\ssrC{forall}\ (x_1\ :\ A_1)\dots(x_n\ :\ A_n),\ eq\ term_1\ term_2$$ where + $eq$ is the Leibniz equality or a registered setoid + equality. The tactic: + + \centerline{\ssrC{rewrite} \ssrN{r-prefix}\ssrC{(}$t_1$\ssrC{,}$\dots$\ssrC{,}$t_n$\ssrC{).}} + + is equivalent to: + + \centerline{\ssrC{do [rewrite} \ssrN{r-prefix} $t_1$ \ssrC{|} $\dots$ \ssrC| rewrite} \ssrN{r-prefix} $t_n$\ssrC{].} + + \item An anonymous rewrite lemma + \ssrC{(_ :} {\term}), where \textit{term} has again the form: + $$\ssrC{forall}\ (x_1\ :\ A_1)\dots(x_n\ :\ A_n),\ eq\ term_1\ term_2$$ + The tactic: + + \centerline{\ssrC{rewrite (_ :} {\term}\ssrC{)}} + + is in fact synonym of: + + \centerline{\ssrC{cutrewrite (}{\term}\ssrC{).}} + + + \end{itemize} + +\end{itemize} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Remarks and examples}\label{ssec:rwex} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Rewrite redex selection} +The general strategy of \ssr{} +is to grasp as many redexes as possible and to let the user select the +ones to be rewritten thanks to the improved syntax for the control of +rewriting. + +This may be a source of incompatibilities between the two \ssrC{rewrite} +tactics. + +In a rewrite tactic of the form: + + \ssrC{rewrite} \ssrN{occ-switch}\ssrC{[}\ssrN[1]{term}\ssrC{]}\ssrN[2]{term}. + +\ssrN[1]{term} is the explicit rewrite redex and +\ssrN[2]{term} is the +rewrite rule. This execution of this tactic unfolds as follows: + +\begin{itemize} +\item First \ssrN[1]{term} and \ssrN[2]{term} are $\beta\iota$ normalized. Then + \ssrN[2]{term} is put in head normal form if the Leibniz equality + constructor \ssrC{eq} is not the head symbol. This may involve $\zeta$ + reductions. +\item Then, the matching algorithm (see section \ref{ssec:set}) + determines the first subterm of the goal matching the rewrite pattern. + The rewrite pattern is + given by \ssrN[1]{term}, if an explicit redex pattern switch is provided, or by + the type of \ssrN[2]{term} otherwise. However, matching skips over + matches that would lead to trivial rewrites. All the + occurrences of this subterm in the goal are candidates for rewriting. +\item Then only the occurrences coded by \ssrN{occ-switch} (see again + section \ref{ssec:set}) are finally selected for rewriting. +\item The left hand side of $\ssrN[2]{term}$ is unified with the subterm found + by the matching algorithm, and if this succeeds, all the selected + occurrences in the goal are replaced by the right hand side of + $\ssrN[2]{term}$. +\item Finally the goal is $\beta\iota$ normalized. +\end{itemize} + +In the case $\ssrN[2]{term}$ is a list of terms, the first top-down (in +the goal) left-to-right (in the list) matching rule gets selected. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Chained rewrite steps} + + +The possibility to chain rewrite operations in a single tactic makes +scripts more compact and gathers in a single command line a bunch +of surgical +operations which would be described by a one sentence in a pen and +paper proof. + +Performing rewrite and simplification operations in a single tactic +enhances significantly the concision of scripts. For instance the +tactic: +\begin{lstlisting} + rewrite /my_def {2}[f _]/= my_eq //=. +\end{lstlisting} +unfolds \ssrC{my_def} in the goal, simplifies the second occurrence of the +first subterm matching pattern \ssrC{[f _]}, rewrites \ssrC{my_eq}, +simplifies the whole goal and closes trivial goals. + +Here are some concrete examples of chained rewrite operations, in the +proof of basic results on natural numbers arithmetic: + +\begin{lstlisting} + Lemma |*addnS*| : forall m n, m + n.+1 = (m + n).+1. + Proof. by move=> m n; elim: m. Qed. + + Lemma |*addSnnS*| : forall m n, m.+1 + n = m + n.+1. + Proof. move=> *; rewrite addnS; apply addSn. Qed. + + Lemma |*addnCA*| : forall m n p, m + (n + p) = n + (m + p). + Proof. by move=> m n; elim: m => [|m Hrec] p; rewrite ?addSnnS -?addnS. Qed. + + Lemma |*addnC*| : forall m n, m + n = n + m. + Proof. by move=> m n; rewrite -{1}[n]addn0 addnCA addn0. Qed. +\end{lstlisting} + +Note the use of the \ssrC{?} switch for parallel rewrite operations in +the proof of \ssrC{|*addnCA*|}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Explicit redex switches are matched first} +If an \ssrN{r-prefix} involves a \emph{redex switch}, the first step is to +find a subterm matching this redex pattern, independently from the left hand +side \ssrC{t1} of the equality the user wants to rewrite. + +For instance, if \ssrL-H : forall t u, t + u = u + t- is in the context of a +goal \ssrL-x + y = y + x-, the tactic: +\begin{lstlisting} + rewrite [y + _]H. +\end{lstlisting} +transforms the goal into \ssrL-x + y = x + y-. + +Note that if this first pattern matching is not compatible with the +\emph{r-item}, the rewrite fails, even if the goal contains a correct +redex matching both the redex switch and the left hand side of the +equality. For instance, if \ssrL-H : forall t u, t + u * 0 = t- is +in the context of a goal \ssrL-x + y * 4 + 2 * 0 = x + 2 * 0-, then tactic: +\begin{lstlisting} + rewrite [x + _]H. +\end{lstlisting} +raises the error message: +\begin{verbatim} + User error: rewrite rule H doesn't match redex (x + y * 4) +\end{verbatim} +while the tactic: +\begin{lstlisting} + rewrite (H _ 2). +\end{lstlisting} +transforms the goal into \ssrL-x + y * 4 = x + 2 * 0-. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Occurrence switches and redex switches} +The tactic: +\begin{lstlisting} + rewrite {2}[_ + y + 0](_: forall z, z + 0 = z). +\end{lstlisting} +transforms the goal: +\begin{lstlisting} + x + y + 0 = x + y + y + 0 + 0 + (x + y + 0) +\end{lstlisting} +into: +\begin{lstlisting} + x + y + 0 = x + y + y + 0 + 0 + (x + y) +\end{lstlisting} +and generates a second subgoal: +\begin{lstlisting} + forall z : nat, z + 0 = z +\end{lstlisting} +The second subgoal is generated by the use of an anonymous lemma in +the rewrite tactic. The effect of the tactic on the initial goal is to +rewrite this lemma at the second occurrence of the first matching +\ssrL-x + y + 0- of the explicit rewrite redex \ssrL-_ + y + 0-. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Occurrence selection and repetition} +Occurrence selection has priority over repetition switches. This means +the repetition of a rewrite tactic specified by a multiplier +will perform matching each time an elementary rewrite operation is +performed. Repeated rewrite tactics apply to every subgoal generated +by the previous tactic, including the previous instances of the +repetition. For example: +\begin{lstlisting} + Goal forall x y z : nat, x + 1 = x + y + 1. + move=> x y z. +\end{lstlisting} +creates a goal \ssrC{ x + 1 = x + y + 1}, which is turned into \ssrC{z = z} +by the additional tactic: +\begin{lstlisting} + rewrite 2!(_ : _ + 1 = z). +\end{lstlisting} +In fact, this last tactic generates \emph{three} subgoals, +respectively +\ssrC{ x + y + 1 = z}, \ssrC{ z = z} and \ssrC{x + 1 = z}. Indeed, the second +rewrite operation specified with the \ssrC{2!} multiplier applies to +the two subgoals generated by the first rewrite. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Multi-rule rewriting} +The \ssrC{rewrite} tactic can be provided a \emph{tuple} of rewrite rules, +or more generally a tree of such rules, since this tuple can feature +arbitrary inner parentheses. We call \emph{multirule} such a +generalized rewrite rule. This feature is of special interest when it +is combined with multiplier switches, which makes the \ssrC{rewrite} +tactic iterates the rewrite operations prescribed by the rules on the +current goal. For instance, let us define two triples \ssrC{multi1} and +\ssrC{multi2} as: +\begin{lstlisting} + Variables (a b c : nat). + + Hypothesis eqab : a = b. + + Hypothesis eqac : a = c. +\end{lstlisting} + +Executing the tactic: +\begin{lstlisting} + rewrite (eqab, eqac) +\end{lstlisting} +on the goal: +\begin{lstlisting} + ========= + a = a +\end{lstlisting} +turns it into \ssrC{b = b}, as rule \ssrC{eqab} is the first to apply among +the ones gathered in the tuple passed to the \ssrC{rewrite} +tactic. This multirule \ssrC{(eqab, eqac)} is actually a \Coq{} term and we +can name it with a definition: +\begin{lstlisting} +Definition |*multi1*| := (eqab, eqac). +\end{lstlisting} +In this case, the tactic \ssrC{rewrite multi1} is a synonym for +\ssrC{(eqab, eqac)}. More precisely, a multirule rewrites +the first subterm to which one of the rules applies in a left-to-right +traversal of the goal, with the first rule from the multirule tree in +left-to-right order. Matching is performed according to the algorithm +described in Section~\ref{ssec:set}, but literal matches have +priority. For instance if we add a definition and a new multirule to +our context: + +\begin{lstlisting} + Definition |*d*| := a. + + Hypotheses eqd0 : d = 0. + + Definition |*multi2*| := (eqab, eqd0). +\end{lstlisting} +then executing the tactic: +\begin{lstlisting} + rewrite multi2. +\end{lstlisting} +on the goal: +\begin{lstlisting} + ========= + d = b +\end{lstlisting} +turns it into \ssrC{0 = b}, as rule \ssrC{eqd0} applies without unfolding +the definition of \ssrC{d}. For repeated rewrites the selection process +is repeated anew. For instance, if we define: + +\begin{lstlisting} + Hypothesis eq_adda_b : forall x, x + a = b. + + Hypothesis eq_adda_c : forall x, x + a = c. + + Hypothesis eqb0 : b = 0. + + Definition |*multi3*| := (eq_adda_b, eq_adda_c, eqb0). +\end{lstlisting} +then executing the tactic: +\begin{lstlisting} + rewrite 2!multi3. +\end{lstlisting} +on the goal: +\begin{lstlisting} + ========= + 1 + a = 12 + a +\end{lstlisting} +turns it into \ssrC{0 = 12 + a}: it uses \ssrC{eq_adda_b} then \ssrC{eqb0} on the +left-hand side only. Now executing the tactic \ssrC{rewrite !multi3} +turns the same goal into \ssrC{0 = 0}. + +The grouping of rules inside a multirule does not affect the selection +strategy but can make it easier to include one rule set in another or +to (universally) quantify over the parameters of a subset of rules (as +there is special code that will omit unnecessary quantifiers for rules that +can be syntactically extracted). It is also possible to +reverse the direction of a rule subset, using a special dedicated syntax: +the tactic \ssrC{rewrite (=~ multi1)} is equivalent to +\ssrC{rewrite multi1_rev} with: +\begin{lstlisting} + Hypothesis eqba : b = a. + + Hypothesis eqca : c = a. + + Definition |*multi1_rev*| := (eqba, eqca). +\end{lstlisting} +except that the constants \ssrC{eqba, eqab, mult1_rev} have not been created. + +Rewriting with multirules +is useful to implement simplification or transformation +procedures, to be applied on terms of small to medium size. For +instance the library \ssrL{ssrnat} provides two implementations for +arithmetic operations on natural numbers: an elementary one and a tail +recursive version, less inefficient but also less convenient for +reasoning purposes. The library also provides one lemma per such +operation, stating that both versions return the same values when +applied to the same arguments: + +\begin{lstlisting} + Lemma |*addE*| : add =2 addn. + Lemma |*doubleE*| : double =1 doublen. + Lemma |*add_mulE*| n m s : add_mul n m s = addn (muln n m) s. + Lemma |*mulE*| : mul =2 muln. + Lemma |*mul_expE*| m n p : mul_exp m n p = muln (expn m n) p. + Lemma |*expE*| : exp =2 expn. + Lemma |*oddE*| : odd =1 oddn. +\end{lstlisting} + +The operation on the left hand side of each lemma is the efficient +version, and the corresponding naive implementation is on the right +hand side. In order to reason conveniently on expressions involving +the efficient operations, we gather all these rules in the +definition \ssrC{|*trecE*|}: +\begin{lstlisting} + Definition |*trecE*| := (addE, (doubleE, oddE), (mulE, add_mulE, (expE, mul_expE))). +\end{lstlisting} +The tactic: +\begin{lstlisting} + rewrite !trecE. +\end{lstlisting} +restores the naive versions of each operation in a goal involving the +efficient ones, e.g. for the purpose of a correctness proof. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Wildcards vs abstractions} + The \ssrC{rewrite} tactic supports r-items containing holes. For example + in the tactic $(1)$: +\begin{lstlisting} + rewrite (_ : _ * 0 = 0). +\end{lstlisting} + the term \ssrC{_ * 0 = 0} is interpreted as \ssrC{forall n : nat, n * 0 = 0}. + Anyway this tactic is \emph{not} equivalent to the tactic $(2)$: +\begin{lstlisting} + rewrite (_ : forall x, x * 0 = 0). +\end{lstlisting} + The tactic $(1)$ transforms the goal + \ssrL-(y * 0) + y * (z * 0) = 0- into \ssrC{y * (z * 0) = 0} + and generates a new subgoal to prove the statement \ssrC{y * 0 = 0}, + which is the \emph{instance} of the\\ \ssrC{forall x, x * 0 = 0} + rewrite rule that + has been used to perform the rewriting. On the other hand, tactic + $(2)$ performs the same rewriting on the current goal but generates a + subgoal to prove \ssrC{forall x, x * 0 = 0}. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{When \ssr{} \ssrC{rewrite} fails on standard \Coq{} licit rewrite} +In a few cases, the \ssr{} \ssrC{rewrite} tactic fails +rewriting some redexes which standard \Coq{} successfully rewrites. +There are two main cases: + +\begin{itemize} +\item \ssr{} never accepts to rewrite indeterminate patterns like: +\begin{lstlisting} + Lemma |*foo*| : forall x : unit, x = tt. +\end{lstlisting} +\ssr{} will however accept the $\eta\zeta$ expansion of this rule: +\begin{lstlisting} + Lemma |*fubar*| : forall x : unit, (let u := x in u) = tt. +\end{lstlisting} +\item In standard \Coq{}, suppose that we work in the following context: +\begin{lstlisting} + Variable g : nat -> nat. + Definition |*f*| := g. +\end{lstlisting} +then rewriting \ssrC{H : forall x, f x = 0} in the goal +\ssrC{g 3 + g 3 = g 6} succeeds +and transforms the goal into \ssrC{0 + 0 = g 6}. + +This rewriting is not possible in \ssr{} because there is no +occurrence of the head symbol \ssrC{f} of the rewrite rule in the +goal. Rewriting with \ssrC{H} first requires unfolding the occurrences of +\ssrC{f} where the substitution is to be performed (here there is a single +such occurrence), using tactic \ssrC{rewrite /f} (for a global +replacement of \ssrC{f} by \ssrC{g}) or \ssrC{rewrite $\ \ssrN{pattern}$/f}, for a +finer selection. +\end{itemize} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Existential metavariables and rewriting} +\label{ssec:rewcaveats} +The \ssrC{rewrite} tactic will not instantiate existing existential +metavariables when matching a redex pattern. + +If a rewrite rule generates a goal +with new existential metavariables, these will be generalized as for \ssrC{apply} +(see page~\pageref{sssec:apply}) and corresponding new goals will be generated. +For example, consider the following script: + +\begin{lstlisting} + Lemma |*ex3*| (x : 'I_2) y (le_1 : y < 1) (E : val x = y) : Some x = insub y. + rewrite insubT ?(leq_trans le_1)// => le_2. +\end{lstlisting} + +Since \ssrC{insubT} has the following type: + +\begin{lstlisting} + forall T P (sT : subType P) (x : T) (Px : P x), insub x = Some (Sub x Px) +\end{lstlisting} + +and since the implicit argument corresponding to the \ssrC{Px} abstraction is not +supplied by the user, the resulting goal should be \ssrC{Some x = Some (Sub y +$\;\;?_{Px}$)}. Instead, \ssr{} \ssrC{rewrite} tactic generates the two following +goals: +\begin{lstlisting} + y < 2 + forall Hyp0 : y < 2, Some x = Some (Sub y Hyp0) +\end{lstlisting} +The script closes the former with \ssrC{?(leq_trans le_1)//}, then it introduces +the new generalization naming it \ssrC{le_2}. + +\begin{lstlisting} + x : 'I_2 + y : nat + le_1 : y < 1 + E : val x = y + le_2 : y < 2 + ============================ + Some x = Some (Sub y le_2) +\end{lstlisting} + +As a temporary limitation, this behavior is available only if the rewriting +rule is stated using Leibniz equality (as opposed to setoid relations). +It will be extended to other rewriting relations in the future. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Locking, unlocking} \label{ssec:lock} + +As program proofs tend to generate large goals, it is important to be +able to control the partial evaluation performed by the simplification +operations that are performed by the tactics. These evaluations can +for example come from a \ssrC{/=} simplification switch, or from rewrite steps +which may expand large terms while performing conversion. We definitely +want to avoid repeating large subterms of the goal in +the proof script. We do this by +``clamping down'' selected function symbols in the goal, which +prevents them from +being considered in simplification or rewriting steps. This clamping +is accomplished by using the occurrence switches (see section +\ref{sssec:occselect}) together with ``term tagging'' operations. + +\ssr{} provides two levels of tagging. + +The first one uses auxiliary definitions to introduce a provably equal +copy of any term \ssrC{t}. However this copy is (on purpose) +\emph{not convertible} to \ssrC{t} in the \Coq{} system\footnote{This is + an implementation feature: there is not such obstruction in the + metatheory}. The job is done by the following construction: + +\begin{lstlisting} + Lemma |*master_key*| : unit. Proof. exact tt. Qed. + Definition |*locked*| A := let: tt := master_key in fun x : A => x. + Lemma |*lock*| : forall A x, x = locked x :> A. +\end{lstlisting} +Note that the definition of \ssrC{|*master_key*|} is explicitly opaque. +The equation \ssrC{t = locked t} given by the \ssrC{lock} lemma can be used +for selective rewriting, blocking on the fly the reduction in the +term \ssrC{t}. +For example the script: +\begin{lstlisting} + Require Import List. + Variable A : Type. + + Fixpoint |*my_has*| (p : A -> bool)(l : list A){struct l} : bool:= + match l with + |nil => false + |cons x l => p x || (my_has p l) + end. + + Goal forall a x y l, a x = true -> my_has a ( x :: y :: l) = true. + move=> a x y l Hax. +\end{lstlisting} +where \ssrL{||} denotes the boolean disjunction, results in a goal +\ssrC{my_has a ( x :: y :: l) = true}. The tactic: +\begin{lstlisting} + rewrite {2}[cons]lock /= -lock. +\end{lstlisting} +turns it into \ssrC{a x || my_has a (y :: l) = true}. +Let us now start by reducing the initial goal without blocking reduction. +The script: +\begin{lstlisting} + Goal forall a x y l, a x = true -> my_has a ( x :: y :: l) = true. + move=> a x y l Hax /=. +\end{lstlisting} +creates a goal \ssrC{(a x) || (a y) || (my_has a l) = true}. Now the +tactic: +\begin{lstlisting} + rewrite {1}[orb]lock orbC -lock. +\end{lstlisting} +where \ssrC{orbC} states the commutativity of \ssrC{orb}, changes the +goal into\\ \ssrC{(a x) || (my_has a l) || (a y) = true}: only the +arguments of the second disjunction where permuted. + + +It is sometimes desirable to globally prevent a definition from being +expanded by simplification; this is done by adding \ssrC{locked} in the +definition. + +For instance, the function \ssrC{|*fgraph_of_fun*|} maps a function whose +domain and codomain are finite types to a concrete representation of +its (finite) graph. Whatever implementation of this transformation we +may use, we want it to be hidden to simplifications and tactics, to +avoid the collapse of the graph object: +\begin{lstlisting} + Definition |*fgraph_of_fun*| := + locked + (fun (d1 :finType) (d2 :eqType) (f : d1 -> d2) => Fgraph (size_maps f _)). +\end{lstlisting} + +We provide a special tactic \ssrC{unlock} for unfolding such definitions +while removing ``locks'', e.g., the tactic: + + \ssrC{unlock} \ssrN{occ-switch}\ssrC{fgraph_of_fun}. + +replaces the occurrence(s) of \ssrC{fgraph_of_fun} coded by the \ssrN{occ-switch} +with \ssrC{(Fgraph (size_maps _ _))} in the goal. + +We found that it was usually preferable to prevent the expansion of +some functions by the partial evaluation switch ``/='', unless +this allowed the evaluation of a condition. This is possible thanks to +an other mechanism of term tagging, resting on the following +\emph{Notation}: +\begin{lstlisting} + Notation "'nosimpl' t" := (let: tt := tt in t). +\end{lstlisting} + +The term \ssrC{(nosimpl t)} simplifies to t \emph{except} in a +definition. More precisely, +given: +\begin{lstlisting} + Definition |*foo*| := (nosimpl bar). +\end{lstlisting} +the term \ssrC{foo (or (foo t'))} will \emph{not} be expanded by the +\emph{simpl} tactic unless it is in a forcing context (e.g., in +\ssrC{match foo t' with $\dots$ end}, \ssrC{foo t'} will be reduced if this allows +\ssrC{match} to be reduced). Note that \ssrC{nosimpl bar} is simply notation +for a term that reduces to \ssrC{bar}; hence \ssrC{unfold foo} will replace + \ssrC{foo} by \ssrC{bar}, and \ssrC{fold foo} will replace \ssrC{bar} by + \ssrC{foo}. + +\emph{Warning} The \ssrC{nosimpl} trick only works if no reduction is +apparent in \ssrC{t}; in particular, the declaration: +\begin{lstlisting} + Definition |*foo*| x := nosimpl (bar x). +\end{lstlisting} +will usually not work. Anyway, the common practice is to tag only the +function, and to use the following definition, which blocks the +reduction as expected: +\begin{lstlisting} + Definition |*foo*| x := nosimpl bar x. +\end{lstlisting} + + +A standard example making this technique shine is the case of +arithmetic operations. We define for instance: +\begin{lstlisting} + Definition |*addn*| := nosimpl plus. +\end{lstlisting} +The operation \ssrC{addn} behaves exactly like plus, except that +\ssrC{(addn (S n) m)} will not +simplify spontaneously to \ssrC{(S (addn n m))} (the two terms, however, are +inter-convertible). In addition, the unfolding step: +\begin{lstlisting} +rewrite /addn +\end{lstlisting} +will replace \ssrC{addn} directly with \ssrC{plus}, so the \ssrC{nosimpl} form +is essentially invisible. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Congruence}\label{ssec:congr} + +Because of the way matching interferes with type families parameters, +the tactic: +\begin{lstlisting} + apply: my_congr_property. +\end{lstlisting} +will generally fail to perform congruence simplification, even on +rather simple cases. We therefore provide a +more robust alternative in which the function is supplied: +$$\ssrC{congr}\ [\ssrN{int}]\ {\term}$$ + +This tactic: +\begin{itemize} +\item checks that the goal is a Leibniz equality +\item matches both sides of this equality with ``{\term} applied to + some arguments'', inferring the right number of arguments from the goal + and the type of {\term}. This may + expand some definitions or fixpoints. +\item generates the subgoals corresponding to pairwise equalities of + the arguments present in the goal. +\end{itemize} + +The goal can be a non dependent product \ssrC{P -> Q}. +In that case, the system asserts the equation \ssrC{P = Q}, uses it to solve +the goal, and calls the \ssrC{congr} tactic on the remaining goal +\ssrC{P = Q}. This can be useful for instance to perform a transitivity +step, like in the following situation: +\begin{lstlisting} + x, y, z : nat + =============== + x = y -> x = z +\end{lstlisting} +the tactic \ssrC{congr (_ = _)} turns this goal into: + +\begin{lstlisting} + x, y, z : nat + =============== + y = z +\end{lstlisting} +which can also be obtained starting from: +\begin{lstlisting} + x, y, z : nat + h : x = y + =============== + x = z +\end{lstlisting} +and using the tactic \ssrC{congr (_ = _): h}. + +The optional \ssrN{int} forces the number of arguments for which the +tactic should generate equality proof obligations. + +This tactic supports equalities between applications with dependent +arguments. Yet dependent arguments should have exactly the same +parameters on both sides, and these parameters should appear as first +arguments. + +The following script: +\begin{lstlisting} + Definition f n := match n with 0 => plus | S _ => mult end. + Definition g (n m : nat) := plus. + + Goal forall x y, f 0 x y = g 1 1 x y. + by move=> x y; congr plus. + Qed. +\end{lstlisting} +shows that the \ssrC{congr} tactic matches \ssrC{plus} with \ssrC{f 0} on the +left hand side and \ssrC{g 1 1} on the right hand side, and solves the goal. + +The script: +\begin{lstlisting} + Goal forall n m, m <= n -> S m + (S n - S m) = S n. + move=> n m Hnm; congr S; rewrite -/plus. +\end{lstlisting} +generates the subgoal \ssrC{m + (S n - S m) = n}. The tactic +\ssrC{rewrite -/plus} folds back the expansion of \ssrC{plus} which was +necessary for matching both sides of the equality with an application +of \ssrC{S}. + +Like most \ssr{} arguments, {\term} can contain wildcards. +The script: +\begin{lstlisting} + Goal forall x y, x + (y * (y + x - x)) = x * 1 + (y + 0) * y. + move=> x y; congr ( _ + (_ * _)). +\end{lstlisting} +generates three subgoals, respectively \ssrC{x = x * 1}, \ssrC{y = y + 0} +and \ssrC{ y + x - x = y}. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Contextual patterns} +\label{ssec:rewp} + +The simple form of patterns used so far, ${\term}s$ possibly containing +wild cards, often require an additional \ssrN{occ-switch} to be specified. +While this may work pretty fine for small goals, the use of polymorphic +functions and dependent types may lead to an invisible duplication of functions +arguments. These copies usually end up in types hidden by the implicit +arguments machinery or by user defined notations. In these situations +computing the right occurrence numbers is very tedious because they must be +counted on the goal as printed after setting the \ssrC{Printing All} flag. +Moreover the resulting script is not really informative for the reader, since +it refers to occurrence numbers he cannot easily see. + +Contextual patterns mitigate these issues allowing to specify occurrences +according to the context they occur in. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Syntax} + +The following table summarizes the full syntax of +\ssrN{c-pattern} and the corresponding subterm(s) identified +by the pattern. +In the third column we use s.m.r. for +``the subterms matching the redex'' specified in the second column. + +\begin{center} +%\begin{tabularx}{\textwidth}{>{\arraybackslash}m{0.30\textwidth}|>{\arraybackslash}m{0.21\textwidth}|>{\arraybackslash}m{0.39\textwidth}} +\begin{tabular}{llp{10em}} +\ssrN{c-pattern} & redex & subterms affected \\ +\hline +{\term} & {\term} & all occurrences of {\term}\\ +\hline +$\ssrN{ident}\ \ssrC{in}\ {\term}$ & + subterm of {\term} selected by \ssrN{ident} & + all the subterms identified by \ssrN{ident} in all + the occurrences of {\term} \\ +\hline +$\ssrN[1]{term}\ \ssrC{in}\ \ssrN{ident}\ \ssrC{in}\ \ssrN[2]{term}$ & $\ssrN[1]{term}$ & + in all s.m.r. in all the subterms identified by \ssrN{ident} in all + the occurrences of $\ssrN[2]{term}$ \\ +\hline +$\ssrN[1]{term}\ \ssrC{as}\ \ssrN{ident}\ \ssrC{in}\ \ssrN[2]{term}$ & $\ssrN[1]{term}$ & + in all the subterms identified by \ssrN{ident} in all + the occurrences of $\ssrN[2]{term}[\ssrN[1]{term}/\ssrN{ident}]$\\ +\hline +%\end{tabularx} +\end{tabular} +\end{center} + +The \ssrC{rewrite} tactic supports two more patterns obtained +prefixing the first two with \ssrC{in}. The intended meaning is that the +pattern identifies all subterms of the specified context. The +\ssrC{rewrite} tactic will infer a pattern for the redex looking at the +rule used for rewriting. + +\begin{center} +\begin{tabularx}{\textwidth}{>{\arraybackslash}m{0.30\textwidth}|>{\arraybackslash}m{0.21\textwidth}|>{\arraybackslash}m{0.39\textwidth}} +\ssrN{r-pattern} & redex & subterms affected \\ +\hline +$\ssrC{in}\ {\term}$ & inferred from rule & + in all s.m.r. in all occurrences of {\term}\\ +\hline +$\ssrC{in}\ \ssrN{ident}\ \ssrC{in}\ {\term}$ & inferred from rule & + in all s.m.r. in all the subterms identified by \ssrN{ident} in all + the occurrences of {\term} \\ +\hline +\end{tabularx} +\end{center} + +The first \ssrN{c-pattern} is the simplest form matching any +context but selecting a specific redex and has been described in the +previous sections. We have seen so far that the possibility of +selecting a redex using a term with holes is already a powerful mean of redex +selection. Similarly, any {\term}s provided by the +user in the more complex forms of \ssrN{c-pattern}s presented in the +tables above can contain holes. + +For a quick glance at what can be expressed with the last +\ssrN{r-pattern} consider the goal \ssrC{a = b} and the tactic +\begin{lstlisting} + rewrite [in X in _ = X]rule. +\end{lstlisting} +It rewrites all occurrences of the left hand side of \ssrC{rule} inside +\ssrC{b} only (\ssrC{a}, and the hidden type of the equality, are ignored). +Note that the variant \ssrC{rewrite [X in _ = X]rule} would have +rewritten \ssrC{b} exactly (i.e., it would only work if \ssrC{b} and the +left hand side of \ssrC{rule} can be unified). + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Matching contextual patterns} + +The \ssrN{c-pattern}s and \ssrN{r-pattern}s involving +{\term}s with holes are matched +against the goal in order to find a closed instantiation. This +matching proceeds as follows: + +\begin{center} +\begin{tabularx}{\textwidth}{>{\arraybackslash}m{0.30\textwidth}|>{\arraybackslash}m{0.65\textwidth}} +\ssrN{c-pattern} & instantiation order and place for $\ssrN[i]{term}$ and redex\\ +\hline +{\term} & {\term} is matched against the goal, redex is unified with + the instantiation of {\term}\\ +\hline +$\ssrN{ident}\ \ssrC{in}\ {\term}$ & + {\term} is matched against the goal, redex is + unified with the subterm of the + instantiation of {\term} identified by \ssrN{ident}\\ +\hline +$\ssrN[1]{term}\ \ssrC{in}\ \ssrN{ident}\ \ssrC{in}\ \ssrN[2]{term}$ & + $\ssrN[2]{term}$ is matched against the goal, $\ssrN[1]{term}$ is + matched against the subterm of the + instantiation of $\ssrN[1]{term}$ identified by \ssrN{ident}, + redex is unified with the instantiation of $\ssrN[1]{term}$\\ +\hline +$\ssrN[1]{term}\ \ssrC{as}\ \ssrN{ident}\ \ssrC{in}\ \ssrN[2]{term}$ & + $\ssrN[2]{term}[\ssrN[1]{term}/\ssrN{ident}]$ + is matched against the goal, + redex is unified with the instantiation of $\ssrN[1]{term}$\\ +\hline +\end{tabularx} +\end{center} + +In the following patterns, the redex is intended to be inferred from the +rewrite rule. + +\begin{center} +\begin{tabularx}{\textwidth}{>{\arraybackslash}m{0.30\textwidth}|>{\arraybackslash}m{0.65\textwidth}} +\ssrN{r-pattern} & instantiation order and place for $\ssrN[i]{term}$ and redex\\ +\hline +$\ssrC{in}\ \ssrN{ident}\ \ssrC{in}\ {\term}$ & + {\term} is matched against the goal, the redex is + matched against the subterm of the + instantiation of {\term} identified by \ssrN{ident}\\ +\hline +$\ssrC{in}\ {\term}$ & {\term} is matched against the goal, redex is + matched against the instantiation of {\term}\\ +\hline +\end{tabularx} +\end{center} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Examples} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection{Contextual pattern in \ssrC{set} and the \ssrC{:} tactical} + +As already mentioned in section~\ref{ssec:set} the \ssrC{set} tactic +takes as an argument a term in open syntax. This term is interpreted +as the simplest for of \ssrN{c-pattern}. To void confusion in the grammar, +open syntax is supported only for the simplest form of patterns, while + parentheses are required around more complex patterns. + +\begin{lstlisting} +set t := (X in _ = X). +set t := (a + _ in X in _ = X). +\end{lstlisting} + +Given the goal \ssrC{a + b + 1 = b + (a + 1)} the first tactic +captures \ssrC{b + (a + 1)}, while the latter \ssrC{a + 1}. + +Since the user may define an infix notation for \ssrC{in} the former +tactic may result ambiguous. The disambiguation rule implemented is +to prefer patterns over simple terms, but to interpret a pattern with +double parentheses as a simple term. For example +the following tactic would capture any occurrence of the term `\ssrC{a in A}'. + +\begin{lstlisting} +set t := ((a in A)). +\end{lstlisting} + +Contextual pattern can also be used as arguments of the \ssrC{:} tactical. +For example: +\begin{lstlisting} +elim: n (n in _ = n) (refl_equal n). +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection{Contextual patterns in \ssrC{rewrite}} +As a more comprehensive example consider the following goal: +\begin{lstlisting} + (x.+1 + y) + f (x.+1 + y) (z + (x + y).+1) = 0 +\end{lstlisting} +The tactic \ssrC{rewrite [in f _ _]addSn} turns it into: +\begin{lstlisting} + (x.+1 + y) + f (x + y).+1 (z + (x + y).+1) = 0 +\end{lstlisting} +since the simplification rule \ssrC{addSn} is applied only under the \ssrC{f} symbol. +Then we simplify also the first addition and expand \ssrC{0} into \ssrC{0+0}. +\begin{lstlisting} + rewrite addSn -[X in _ = X]addn0. +\end{lstlisting} +obtaining: +\begin{lstlisting} + (x + y).+1 + f (x + y).+1 (z + (x + y).+1) = 0 + 0 +\end{lstlisting} +Note that the right hand side of \ssrC{addn0} is undetermined, but the +rewrite pattern specifies the redex explicitly. The right hand side of +\ssrC{addn0} is unified with the term identified by \ssrC{X}, \ssrC{0} here. + +The following pattern does not specify a redex, since it +identifies an entire region, hence the rewrite rule has to be instantiated +explicitly. Thus the tactic: +\begin{lstlisting} + rewrite -{2}[in X in _ = X](addn0 0). +\end{lstlisting} +changes the goal as follows: +\begin{lstlisting} + (x + y).+1 + f (x + y).+1 (z + (x + y).+1) = 0 + (0 + 0) +\end{lstlisting} +The following tactic is quite tricky: +\begin{lstlisting} + rewrite [_.+1 in X in f _ X](addnC x.+1). +\end{lstlisting} +and the resulting goals is: +\begin{lstlisting} + (x + y).+1 + f (x + y).+1 (z + (y + x.+1)) = 0 + (0 + 0) +\end{lstlisting} +The explicit redex \ssrC{_.+1} is important since its head +constant \ssrC{S} differs from the head constant inferred from +\ssrC{(addnC x.+1)} (that is \ssrC{addn}, denoted \ssrC{+} here). +Moreover, the pattern \ssrC{f _ X} is important to rule out the first occurrence +of \ssrC{(x + y).+1}. Last, only the subterms of \ssrC{f _ X} identified by \ssrC{X} are +rewritten, thus the first argument of \ssrC{f} is skipped too. +Also note the pattern \ssrC{_.+1} is interpreted in the context +identified by \ssrC{X}, thus it gets instantiated to \ssrC{(y + x).+1} and +not \ssrC{(x + y).+1}. + +The last rewrite pattern allows to specify exactly the shape of the term +identified by \ssrC{X}, that is thus unified with the left hand side of the +rewrite rule. +\begin{lstlisting} + rewrite [x.+1 + y as X in f X _]addnC. +\end{lstlisting} +The resulting goal is: +\begin{lstlisting} + (x + y).+1 + f (y + x.+1) (z + (y + x.+1)) = 0 + (0 + 0) +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Patterns for recurrent contexts} + +The user can define shortcuts for recurrent contexts corresponding to the +\ssrN{ident} \ssrC{in} {\term} part. The notation scope identified +with \ssrC{\%pattern} provides a special notation `\ssrC{(X in t)}' the user +must adopt to define context shortcuts. + +The following example is taken from \ssrC{ssreflect.v} where the +\ssrC{LHS} and \ssrC{RHS} shortcuts are defined. + +\begin{lstlisting} +Notation RHS := (X in _ = X)%pattern. +Notation LHS := (X in X = _)%pattern. +\end{lstlisting} + +Shortcuts defined this way can be freely used in place of the +trailing \ssrN{ident} \ssrC{in} {\term} part of any contextual +pattern. +Some examples follow: + +\begin{lstlisting} +set rhs := RHS. +rewrite [in RHS]rule. +case: (a + _ in RHS). +\end{lstlisting} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Views and reflection}\label{sec:views} + +The bookkeeping facilities presented in section \ref{sec:book} are +crafted to ease simultaneous introductions and generalizations of facts and +casing, +naming $\dots$ operations. It also a common practice to make a stack +operation immediately followed by an \emph{interpretation} of the fact +being pushed, +that is, to apply a lemma to this fact before passing it +to a tactic for decomposition, application and so on. + + +% possibly + +% Small scale reflection consists in using a two levels +% approach locally when developing formal proofs. This means that a +% fact, which may be an assumption, or the goal itself, will often be +% \emph{interpreted} before being passed to a tactic +% for decomposition, application and so on. + +\ssr{} provides a convenient, unified syntax to combine these +interpretation operations with the proof stack operations. This +\emph{view mechanism} relies on the combination of the \ssrC{/} view +switch with bookkeeping tactics and tacticals. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Interpreting eliminations} +\idx{elim/\dots{}} + +The view syntax combined with the \ssrC{elim} tactic specifies an +elimination scheme to +be used instead of the default, generated, one. Hence the \ssr{} tactic: +\begin{lstlisting} + elim/V. +\end{lstlisting} +is a synonym for: +\begin{lstlisting} + intro top; elim top using V; clear top. +\end{lstlisting} +where \ssrC{top} is a fresh name and \ssrC{V} any second-order lemma. + +Since an elimination view supports the two bookkeeping tacticals of +discharge and introduction (see section \ref{sec:book}), the \ssr{} tactic: +\begin{lstlisting} + elim/V: x => y. +\end{lstlisting} +is a synonym for: +\begin{lstlisting} + elim x using V; clear x; intro y. +\end{lstlisting} +where \ssrC{x} is a variable in the context, \ssrC{y} a fresh name and \ssrC{V} +any second order lemma; \ssr{} relaxes the syntactic restrictions of +the \Coq{} \ssrC{elim}. The first pattern following \ssrC{:} can be a \ssrC{_} +wildcard if the conclusion of the view \ssrC{V} specifies a pattern for +its last argument (e.g., if \ssrC{V} is a functional induction lemma +generated by the \ssrC{Function} command). + +The elimination view mechanism is compatible with the equation name +generation (see section \ref{ssec:equations}). + +The following script illustrate a toy example of this feature. Let us +define a function adding an element at the end of a list: +\begin{lstlisting} + Require Import List. + + Variable d : Type. + + Fixpoint |*add_last*|(s : list d) (z : d) {struct s} : list d := + match s with + | nil => z :: nil + | cons x s' => cons x (add_last s' z) + end. +\end{lstlisting} + +One can define an alternative, reversed, induction principle on inductively +defined \ssrC{list}s, by proving the following lemma: + +\begin{lstlisting} + Lemma |*last_ind_list*| : forall (P : list d -> Type), + P nil -> + (forall (s : list d) (x : d), P s -> P (add_last s x)) -> forall s : list d, P s. +\end{lstlisting} + +Then the combination of elimination views with equation names result +in a concise syntax for reasoning inductively using the user +defined elimination scheme. The script: +\begin{lstlisting} + Goal forall (x : d)(l : list d), l = l. + move=> x l. + elim/last_ind_list E : l=> [| u v]; last first. +\end{lstlisting} +generates two subgoals: the first one to prove \ssrC{nil = nil} in a +context featuring \ssrC{E : l = nil} and the second to prove +\ssrC{add_last u v = add_last u v}, in a context containing +\ssrC{E : l = add_last u v}. + +User provided eliminators (potentially generated with the +\ssrC{Function} \Coq{}'s command) can be combined with the type family switches +described in section~\ref{ssec:typefam}. Consider an eliminator +\ssrC{foo_ind} of type: + + \ssrC{foo_ind : forall $\dots$, forall x : T, P p$_1$ $\dots$ p$_m$} + +and consider the tactic + + \ssrC{elim/foo_ind: e$_1$ $\dots$ / e$_n$} + +The \ssrC{elim/} tactic distinguishes two cases: +\begin{description} +\item[truncated eliminator] when \ssrC{x} does not occur in \ssrC{P p$_1 \dots$ p$_m$} + and the type of \ssrC{e$_n$} unifies with \ssrC{T} and \ssrC{e$_n$} is not \ssrC{_}. + In that case, \ssrC{e$_n$} is passed to the eliminator as the last argument + (\ssrC{x} in \ssrC{foo_ind}) and \ssrC{e$_{n-1} \dots$ e$_1$} are used as patterns + to select in the goal the occurrences that will be bound by the + predicate \ssrC{P}, thus it must be possible to unify the sub-term of + the goal matched by \ssrC{e$_{n-1}$} with \ssrC{p$_m$}, the one matched by + \ssrC{e$_{n-2}$} with \ssrC{p$_{m-1}$} and so on. +\item[regular eliminator] in all the other cases. Here it must be + possible to unify the term matched by + \ssrC{e$_n$} with \ssrC{p$_m$}, the one matched by + \ssrC{e$_{n-1}$} with \ssrC{p$_{m-1}$} and so on. Note that + standard eliminators have the shape \ssrC{$\dots$forall x, P $\dots$ x}, thus + \ssrC{e$_n$} is the pattern identifying the eliminated term, as expected. +\end{description} +As explained in section~\ref{ssec:typefam}, the initial prefix of +\ssrC{e$_i$} can be omitted. + +Here an example of a regular, but non trivial, eliminator: +\begin{lstlisting} + Function |*plus*| (m n : nat) {struct n} : nat := + match n with 0 => m | S p => S (plus m p) end. +\end{lstlisting} +The type of \ssrC{plus_ind} is +\begin{lstlisting} +plus_ind : forall (m : nat) (P : nat -> nat -> Prop), + (forall n : nat, n = 0 -> P 0 m) -> + (forall n p : nat, n = p.+1 -> P p (plus m p) -> P p.+1 (plus m p).+1) -> + forall n : nat, P n (plus m n) +\end{lstlisting} +Consider the following goal +\begin{lstlisting} + Lemma |*exF*| x y z: plus (plus x y) z = plus x (plus y z). +\end{lstlisting} +The following tactics are all valid and perform the same elimination +on that goal. +\begin{lstlisting} + elim/plus_ind: z / (plus _ z). + elim/plus_ind: {z}(plus _ z). + elim/plus_ind: {z}_. + elim/plus_ind: z / _. +\end{lstlisting} +In the two latter examples, being the user provided pattern a wildcard, the +pattern inferred from the type of the eliminator is used instead. For both +cases it is \ssrC{(plus _ _)} and matches the subterm \ssrC{plus (plus x y)$\;$z} thus +instantiating the latter \ssrC{_} with \ssrC{z}. Note that the tactic +\ssrC{elim/plus_ind: y / _} would have resulted in an error, since \ssrC{y} and \ssrC{z} +do no unify but the type of the eliminator requires the second argument of +\ssrC{P} to be the same as the second argument of \ssrC{plus} in the second +argument of \ssrC{P}. + +Here an example of a truncated eliminator. Consider the goal +\begin{lstlisting} + p : nat_eqType + n : nat + n_gt0 : 0 < n + pr_p : prime p + ================= + p %| \prod_(i <- prime_decomp n | i \in prime_decomp n) i.1 ^ i.2 -> + exists2 x : nat * nat, x \in prime_decomp n & p = x.1 +\end{lstlisting} +and the tactic +\begin{lstlisting} +elim/big_prop: _ => [| u v IHu IHv | [q e] /=]. +\end{lstlisting} +where the type of the eliminator is +\begin{lstlisting} +big_prop: forall (R : Type) (Pb : R -> Type) (idx : R) (op1 : R -> R -> R), + Pb idx -> + (forall x y : R, Pb x -> Pb y -> Pb (op1 x y)) -> + forall (I : Type) (r : seq I) (P : pred I) (F : I -> R), + (forall i : I, P i -> Pb (F i)) -> + Pb (\big[op1/idx]_(i <- r | P i) F i) +\end{lstlisting} +Since the pattern for the argument of \ssrC{Pb} is not specified, the inferred one +is used instead: \ssrC{(\\big[_/_]_(i <- _ | _ i) _ i)}, and after the +introductions, the following goals are generated. +\begin{lstlisting} +subgoal 1 is: + p %| 1 -> exists2 x : nat * nat, x \in prime_decomp n & p = x.1 +subgoal 2 is: + p %| u * v -> exists2 x : nat * nat, x \in prime_decomp n & p = x.1 +subgoal 3 is: + (q, e) \in prime_decomp n -> p %| q ^ e -> + exists2 x : nat * nat, x \in prime_decomp n & p = x.1 +\end{lstlisting} +Note that the pattern matching algorithm instantiated all the variables +occurring in the pattern. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Interpreting assumptions}\label{ssec:assumpinterp} +\idx{move/\dots{}} + +Interpreting an assumption in the context of a proof is applying it a +correspondence lemma before generalizing, and/or decomposing it. +For instance, with the extensive use of boolean reflection (see +section \ref{ssec:boolrefl}), it is +quite frequent to need to decompose the logical interpretation of (the +boolean expression of) a +fact, rather than the fact itself. +This can be achieved by a combination of \ssrC{move : _ => _} +switches, like in the following script, where \ssrC{||} is a notation for +the boolean disjunction: +\begin{lstlisting} + Variables P Q : bool -> Prop. + Hypothesis |*P2Q*| : forall a b, P (a || b) -> Q a. + + Goal forall a, P (a || a) -> True. + move=> a HPa; move: {HPa}(P2Q _ _ HPa) => HQa. +\end{lstlisting} +which transforms the hypothesis \ssrC{HPn : P n} which has been +introduced from the initial statement into \ssrC{HQn : Q n}. +This operation is so common that the tactic shell has +specific syntax for it. +The following scripts: +\begin{lstlisting} + Goal forall a, P (a || a) -> True. + move=> a HPa; move/P2Q: HPa => HQa. +\end{lstlisting} +or more directly: +\begin{lstlisting} + Goal forall a, P (a || a) -> True. + move=> a; move/P2Q=> HQa. +\end{lstlisting} +are equivalent to the former one. The former script shows how to +interpret a fact (already in the context), thanks to the discharge +tactical (see section \ref{ssec:discharge}) and the latter, how to +interpret the top assumption of a goal. Note +that the number of wildcards to be inserted to find the correct +application of the view lemma to the hypothesis has been automatically +inferred. + +The view mechanism is compatible with the \ssrC{case} tactic and with the +equation name generation mechanism (see section \ref{ssec:equations}): +\begin{lstlisting} + Variables P Q: bool -> Prop. + Hypothesis |*Q2P*| : forall a b, Q (a || b) -> P a \/ P b. + + Goal forall a b, Q (a || b) -> True. + move=> a b; case/Q2P=> [HPa | HPb]. +\end{lstlisting} +creates two new subgoals whose contexts no more contain +\ssrC{HQ : Q (a || b)} but respectively \ssrC{HPa : P a} and +\ssrC{HPb : P b}. This view tactic +performs: +\begin{lstlisting} + move=> a b HQ; case: {HQ}(Q2P _ _ HQ) => [HPa | HPb]. +\end{lstlisting} + +The term on the right of the \ssrC{/} view switch is called a \emph{view + lemma}. Any \ssr{} term coercing to a product type can be used as a +view lemma. + + +The examples we have given so far explicitly provide the direction of the +translation to be performed. In fact, view lemmas need not to be +oriented. The view mechanism is able to detect which +application is relevant for the current goal. For instance, the +script: +\begin{lstlisting} + Variables P Q: bool -> Prop. + Hypothesis |*PQequiv*| : forall a b, P (a || b) <-> Q a. + + Goal forall a b, P (a || b) -> True. + move=> a b; move/PQequiv=> HQab. +\end{lstlisting} +has the same behavior as the first example above. + +The view mechanism can insert automatically a \emph{view hint} to +transform the double implication into the expected simple implication. +The last script is in fact equivalent to: +\begin{lstlisting} + Goal forall a b, P (a || b) -> True. + move=> a b; move/(iffLR (PQequiv _ _)). +\end{lstlisting} +where: +\begin{lstlisting} + Lemma |*iffLR*| : forall P Q, (P <-> Q) -> P -> Q. +\end{lstlisting} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Specializing assumptions} +\idx{move/\dots{}} + +The special case when the \emph{head symbol} of the view lemma is a +wildcard is used to interpret an assumption by \emph{specializing} +it. The view mechanism hence offers the possibility to +apply a higher-order assumption to some given arguments. + +For example, the script: +\begin{lstlisting} + Goal forall z, (forall x y, x + y = z -> z = x) -> z = 0. + move=> z; move/(_ 0 z). +\end{lstlisting} +changes the goal into: +\begin{lstlisting} + (0 + z = z -> z = 0) -> z = 0 +\end{lstlisting} + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Interpreting goals}\label{ssec:goalinterp} + +In a similar way, it is also often convenient to interpret a goal by changing +it into an equivalent proposition. The view mechanism of \ssr{} has a +special syntax \ssrC{apply/} for combining simultaneous goal +interpretation operations and +bookkeeping steps in a single tactic. + +With the hypotheses of section \ref{ssec:assumpinterp}, the following +script, where \ssrL+~~+ denotes the boolean negation: +\begin{lstlisting} + Goal forall a, P ((~~ a) || a). + move=> a; apply/PQequiv. +\end{lstlisting} +transforms the goal into \ssrC{Q (~~ a)}, and is equivalent to: +\begin{lstlisting} + Goal forall a, P ((~~ a) || a). + move=> a; apply: (iffRL (PQequiv _ _)). +\end{lstlisting} +where \ssrC{iffLR} is the analogous of \ssrC{iffRL} for the converse +implication. + +Any \ssr{} term whose type coerces to a double implication can be used +as a view for goal interpretation. + +Note that the goal interpretation view mechanism supports both +\ssrC{apply} and \ssrC{exact} tactics. As expected, a goal interpretation +view command \ssrC{exact/$term$} should solve the current goal or it will +fail. + + +\emph{Warning} Goal interpretation view tactics are \emph{not} compatible +with the bookkeeping tactical \ssrC{=>} since this would be redundant with +the \ssrC{apply:} {\term} \ssrC{=> _} construction. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Boolean reflection}\label{ssec:boolrefl} +In the Calculus of Inductive Construction, there is +an obvious distinction between logical propositions and boolean values. +On the one hand, logical propositions are objects +of \emph{sort} \ssrC{Prop} which is the carrier of intuitionistic +reasoning. Logical connectives in \ssrC{Prop} are \emph{types}, which give precise +information on the structure of their proofs; this information is +automatically exploited by \Coq{} tactics. For example, \Coq{} knows that a +proof of \ssrL+A \/ B+ is either a proof of \ssrC{A} or a proof of \ssrC{B}. +The tactics \ssrC{left} and \ssrC{right} change the goal \ssrL+A \/ B+ +to \ssrC{A} and \ssrC{B}, respectively; dualy, the tactic \ssrC{case} reduces the goal +\ssrL+A \/ B => G+ to two subgoals \ssrC{A => G} and \ssrC{B => G}. + +On the other hand, \ssrC{bool} is an inductive \emph{datatype} +with two constructors \ssrC{true} and \ssrC{false}. +Logical connectives on \ssrC{bool} are \emph{computable functions}, defined by +their truth tables, using case analysis: +\begin{lstlisting} + Definition (b1 || b2) := if b1 then true else b2. +\end{lstlisting} +Properties of such connectives are also established using case +analysis: the tactic \ssrC{by case: b} solves the goal +\begin{lstlisting} + b || ~~ b = true +\end{lstlisting} +by replacing \ssrC{b} first by \ssrC{true} and then by \ssrC{false}; in either case, +the resulting subgoal reduces by computation to the trivial +\ssrC{true = true}. + +Thus, \ssrC{Prop} and \ssrC{bool} are truly complementary: the former +supports robust natural deduction, the latter allows brute-force +evaluation. +\ssr{} supplies +a generic mechanism to have the best of the two worlds and move freely +from a propositional version of a +decidable predicate to its boolean version. + +First, booleans are injected into propositions +using the coercion mechanism: +\begin{lstlisting} + Coercion |*is_true*| (b : bool) := b = true. +\end{lstlisting} +This allows any boolean formula~\ssrC{b} to be used in a context +where \Coq{} would expect a proposition, e.g., after \ssrC{Lemma $\dots$ : }. +It is then interpreted as \ssrC{(is_true b)}, i.e., +the proposition \ssrC{b = true}. Coercions are elided by the pretty-printer, +so they are essentially transparent to the user. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{The \ssrC{reflect} predicate}\label{ssec:reflpred} + +To get all the benefits of the boolean reflection, it is in fact +convenient to introduce the following inductive predicate +\ssrC{reflect} to relate propositions and booleans: + +\begin{lstlisting} + Inductive |*reflect*| (P: Prop): bool -> Type := + | Reflect_true: P => reflect P true + | Reflect_false: ~P => reflect P false. +\end{lstlisting} + +The statement \ssrC{(reflect P b)} asserts that \ssrC{(is_true b)} +and \ssrC{P} are logically equivalent propositions. + +For instance, the following lemma: +\begin{lstlisting} + Lemma |*andP*|: forall b1 b2, reflect (b1 /\ b2) (b1 && b2). +\end{lstlisting} +relates the boolean conjunction \ssrC{&&} to +the logical one \ssrL+/\+. +Note that in \ssrC{andP}, \ssrC{b1} and \ssrC{b2} are two boolean variables and +the proposition \ssrL+b1 /\ b2+ hides two coercions. +The conjunction of \ssrC{b1} and \ssrC{b2} can then be viewed +as \ssrL+b1 /\ b2+ or as \ssrC{b1 && b2}. + + +Expressing logical equivalences through this family of inductive types +makes possible to take benefit from \emph{rewritable equations} +associated to the case analysis of \Coq{}'s inductive types. + +Since the equivalence predicate is defined in \Coq{} as: +\begin{lstlisting} + Definition |*iff*| (A B:Prop) := (A -> B) /\ (B -> A). +\end{lstlisting} +where \ssrC{/\\} is a notation for \ssrC{and}: +\begin{lstlisting} + Inductive |*and*| (A B:Prop) : Prop := + conj : A -> B -> and A B +\end{lstlisting} + +This make case analysis very different according to the way an +equivalence property has been defined. + + +For instance, if we have proved the lemma: +\begin{lstlisting} + Lemma |*andE*|: forall b1 b2, (b1 /\ b2) <-> (b1 && b2). +\end{lstlisting} +let us compare the respective behaviours of \ssrC{andE} and \ssrC{andP} on a +goal: +\begin{lstlisting} + Goal forall b1 b2, if (b1 && b2) then b1 else ~~(b1||b2). +\end{lstlisting} + +The command: +\begin{lstlisting} + move=> b1 b2; case (@andE b1 b2). +\end{lstlisting} +generates a single subgoal: +\begin{lstlisting} + (b1 && b2 -> b1 /\ b2) -> (b1 /\ b2 -> b1 && b2) -> + if b1 && b2 then b1 else ~~ (b1 || b2) +\end{lstlisting} + +while the command: +\begin{lstlisting} + move=> b1 b2; case (@andP b1 b2). +\end{lstlisting} +generates two subgoals, respectively \ssrL+b1 /\ b2 -> b1+ and +\ssrL+~ (b1 /\ b2) -> ~~ (b1 || b2)+. + + + +Expressing reflection relation through the \ssrC{reflect} predicate +is hence a very convenient way to deal with classical reasoning, by +case analysis. Using the \ssrC{reflect} predicate allows moreover to +program rich specifications inside +its two constructors, which will be automatically taken into account +during destruction. This formalisation style gives far more +efficient specifications than quantified (double) implications. + + +A naming convention in \ssr{} is to postfix the name of view lemmas with \ssrC{P}. +For example, \ssrC{orP} relates \ssrC{||} and \ssrL+\/+, \ssrC{negP} relates +\ssrL+~~+ and \ssrL+~+. + +The view mechanism is compatible with \ssrC{reflect} predicates. + +For example, the script +\begin{lstlisting} + Goal forall a b : bool, a -> b -> a /\\ b. + move=> a b Ha Hb; apply/andP. +\end{lstlisting} +changes the goal \ssrL+a /\ b+ to \ssrC{a && b} (see section \ref{ssec:goalinterp}). + +Conversely, the script +\begin{lstlisting} + Goal forall a b : bool, a /\ b -> a. + move=> a b; move/andP. +\end{lstlisting} +changes the goal \ssrL+a /\ b -> a+ into \ssrC{a && b -> a} (see section +\ref{ssec:assumpinterp}). + + +The same tactics can also be used to perform the converse +operation, changing a boolean conjunction into a logical one. The view +mechanism guesses the direction of the +transformation to be used i.e., the constructor of the \ssrC{reflect} +predicate which should be chosen. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{General mechanism for interpreting goals and assumptions} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Specializing assumptions} +\idx{move/\dots{}} + +The \ssr{} +tactic: + + \ssrC{move/(_} \ssrN[1]{term} $\dots$ \ssrN[n]{term}\ssrC{)} + +\noindent +is equivalent to the tactic: + + \ssrC{intro top; generalize (top} \ssrN[1]{term} $\dots$ \ssrN[n]{term}\ssrC{); clear top.} + +\noindent +where \ssrC{top} is a fresh name for introducing the top assumption of +the current goal. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Interpreting assumptions} +\label{sssec:hypview} +The general form of an assumption view tactic is: + +\begin{center} + \optional{\ssrC{move} {\optsep} \ssrC{case}} \ssrC{/} \ssrN[0]{term} +\end{center} + +The term \ssrN[0]{term}, called the \emph{view lemma} can be: +\begin{itemize} +\item a (term coercible to a) function; +\item a (possibly quantified) implication; +\item a (possibly quantified) double implication; +\item a (possibly quantified) instance of the \ssrC{reflect} predicate + (see section \ref{ssec:reflpred}). +\end{itemize} + +Let \ssrC{top} be the top assumption in the goal. + +There are three steps in the behaviour of an assumption view tactic: +\begin{itemize} +\item It first introduces \ssrL+top+. +\item If the type of \ssrN[0]{term} is neither a double implication nor + an instance of the \ssrC{reflect} predicate, then the tactic + automatically generalises a term of the form: + +\begin{center} + \ssrC{(}\ssrN[0]{term} \ssrN[1]{term} $\dots$ \ssrN[n]{term}\ssrC{)} +\end{center} + + where the terms \ssrN[1]{term} $\dots$ \ssrN[n]{term} instantiate the + possible quantified variables of \ssrN[0]{term}, in order for + \ssrC{(}\ssrN[0]{term} \ssrN[1]{term} $\dots$ \ssrN[n]{term} \ssrC{top)} to be well typed. +\item If the type of $\ssrN[0]{term}$ is an equivalence, or + an instance of the \ssrC{reflect} predicate, it generalises a term of + the form: + \begin{center} + (\ssrN[vh]{term} (\ssrN[0]{term} \ssrN[1]{term} $\dots$ \ssrN[n]{term})) + \end{center} + where the term \ssrN[vh]{term} inserted is called an + \emph{assumption interpretation view hint}. +\item It finally clears \ssrC{top}. +\end{itemize} +For a \ssrC{case/}\ssrN[0]{term} tactic, the generalisation step is +replaced by a case analysis step. + +\emph{View hints} are declared by the user (see section +\ref{ssec:vhints}) and are stored in the \ssrC{Hint View} database. +The proof engine automatically +detects from the shape of the top assumption \ssrC{top} and of the view +lemma $\ssrN[0]{term}$ provided to the tactic the appropriate view hint in +the database to be inserted. + +If $\ssrN[0]{term}$ is a double implication, then the view hint \ssrC{A} will +be one of the defined view hints for implication. These hints are by +default the ones present in the file {\tt ssreflect.v}: +\begin{lstlisting} + Lemma |*iffLR*| : forall P Q, (P <-> Q) -> P -> Q. +\end{lstlisting} +which transforms a double implication into the left-to-right one, or: +\begin{lstlisting} + Lemma |*iffRL*| : forall P Q, (P <-> Q) -> Q -> P. +\end{lstlisting} +which produces the converse implication. In both cases, the two first +\ssrC{Prop} arguments are implicit. + +If $\ssrN[0]{term}$ is an instance of the \ssrC{reflect} predicate, then \ssrC{A} +will be one of the defined view hints for the \ssrC{reflect} +predicate, which are by +default the ones present in the file {\tt ssrbool.v}. +These hints are not only used for choosing the appropriate direction of +the translation, but they also allow complex transformation, involving +negations. + For instance the hint: +\begin{lstlisting} + Lemma |*introN*| : forall (P : Prop) (b : bool), reflect P b -> ~ P -> ~~ b. +\end{lstlisting} +makes the following script: +\begin{lstlisting} + Goal forall a b : bool, a -> b -> ~~ (a && b). + move=> a b Ha Hb. apply/andP. +\end{lstlisting} +transforms the goal into \ssrC{ \~ (a /\ b)}. +In fact\footnote{The current state of the proof shall be displayed by + the \ssrC{Show Proof} command of \Coq{} proof mode.} +this last script does not exactly use the hint \ssrC{introN}, but the +more general hint: +\begin{lstlisting} + Lemma |*introNTF*| : forall (P : Prop) (b c : bool), + reflect P b -> (if c then ~ P else P) -> ~~ b = c +\end{lstlisting} +The lemma \ssrL+|*introN*|+ is an instantiation of \ssrC{introNF} using + \ssrC{c := true}. + +Note that views, being part of \ssrN{i-pattern}, can be used to interpret +assertions too. For example the following script asserts \ssrC{a \&\& b} +but actually used its propositional interpretation. +\begin{lstlisting} + Lemma |*test*| (a b : bool) (pab : b && a) : b. + have /andP [pa ->] : (a && b) by rewrite andbC. +\end{lstlisting} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsubsection*{Interpreting goals} +\idx{apply/\dots{}} + +A goal interpretation view tactic of the form: + +\begin{center} + \ssrC{apply/} \ssrN[0]{term} +\end{center} +applied to a goal \ssrC{top} is interpreted in the following way: +\begin{itemize} +\item If the type of $\ssrN[0]{term}$ is not an instance of the + \ssrC{reflect} predicate, nor an equivalence, + then the term $\ssrN[0]{term}$ is applied to the current goal \ssrC{top}, + possibly inserting implicit arguments. +\item If the type of $\ssrN[0]{term}$ is an instance of the \ssrC{reflect} + predicate or an equivalence, then +a \emph{goal interpretation view hint} can possibly be inserted, which +corresponds to the application of a term +\ssrC{($\ssrN[vh]{term}$ ($\ssrN[0]{term}$ _ $\dots$ _))} to the current +goal, possibly inserting implicit arguments. +\end{itemize} + +Like assumption interpretation view hints, goal interpretation ones +are user defined lemmas stored (see section \ref{ssec:vhints}) in the +\ssrC{Hint View} database bridging +the possible gap between the type of $\ssrN[0]{term}$ and the type of the +goal. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Interpreting equivalences} +\idx{apply/\dots{}/\dots{}} + +Equivalent boolean propositions are simply \emph{equal} boolean terms. +A special construction helps the user to prove boolean equalities by +considering them as logical double implications (between their coerced +versions), while +performing at the same time logical operations on both sides. + +The syntax of double views is: +\begin{center} + \ssrC{apply/} \ssrN[l]{term} \ssrC{/} \ssrN[r]{term} +\end{center} + +The term \ssrN[l]{term} is the view lemma applied to the left hand side of the +equality, \ssrN[r]{term} is the one applied to the right hand side. + +In this context, the identity view: +\begin{lstlisting} +Lemma |*idP*| : reflect b1 b1. +\end{lstlisting} +is useful, for example the tactic: +\begin{lstlisting} + apply/idP/idP. +\end{lstlisting} +transforms the goal +\ssrL+~~ (b1 || b2)= b3+ + into two subgoals, respectively + \ssrL+~~ (b1 || b2) -> b3+ and \\ +\ssrL+b3 -> ~~ (b1 || b2).+ + +The same goal can be decomposed in several ways, and the user may +choose the most convenient interpretation. For instance, the tactic: +\begin{lstlisting} + apply/norP/idP. +\end{lstlisting} +applied on the same goal \ssrL+~~ (b1 || b2) = b3+ generates the subgoals +\ssrL+~~ b1 /\ ~~ b2 -> b3+ and\\ +\ssrL+b3 -> ~~ b1 /\ ~~ b2+. + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Declaring new \ssrC{Hint View}s}\label{ssec:vhints} +\idxC{Hint View} + +The database of hints for the view mechanism is extensible via a +dedicated vernacular command. As library {\tt ssrbool.v} already +declares a corpus of hints, this feature is probably useful only for +users who define their own logical connectives. Users can declare +their own hints following the syntax used in {\tt ssrbool.v}: + +\begin{center} + \ssrC{Hint View for} {\tac} \ssrC{/} \ssrN{ident} \optional{\ssrC{|}{\naturalnumber}} +\end{center} + + where {\tac}$\in \{$\ssrC{move, apply}$\}$, \ssrN{ident} is the +name of the lemma to be declared as a hint, and ${\naturalnumber}$ a natural +number. If \ssrL+move+ is used as {\tac}, the hint is declared for +assumption interpretation tactics, \ssrL+apply+ declares hints for goal +interpretations. +Goal interpretation view hints are declared for both simple views and +left hand side views. The optional natural number ${\naturalnumber}$ is the +number of implicit arguments to be considered for the declared hint +view lemma \ssrC{name_of_the_lemma}. + +The command: + +\begin{center} + \ssrC{Hint View for apply//} \ssrN{ident}\optional{\ssrC{|}{\naturalnumber}}. +\end{center} + +with a double slash \ssrL+//+, declares hint views for right hand sides of +double views. + + +\noindent See the files {\tt ssreflect.v} and {\tt ssrbool.v} for examples. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection{Multiple views}\label{ssec:multiview} + +The hypotheses and the goal can be interpreted applying multiple views in +sequence. Both \ssrC{move} and \ssrC{apply} can be followed by an arbitrary number +of \ssrC{/}$\ssrN[i]{term}$. The main difference between the following two tactics +\begin{lstlisting} + apply/v1/v2/v3. + apply/v1; apply/v2; apply/v3. +\end{lstlisting} +is that the former applies all the views to the principal goal. +Applying a view with hypotheses generates new goals, and the second line +would apply the view \ssrC{v2} to all the goals generated by \ssrC{apply/v1}. +Note that the NO-OP intro pattern \ssrC{-} can be used to separate two +views, making the two following examples equivalent: +\begin{lstlisting} + move=> /v1; move=> /v2. + move=> /v1-/v2. +\end{lstlisting} + +The tactic \ssrC{move} can be used together with the \ssrC{in} +tactical to pass a given hypothesis to a lemma. For example, if +\ssrC{P2Q : P -> Q } and \ssrC{Q2R : Q -> R}, the following +tactic turns the hypothesis \ssrC{p : P} into \ssrC{P : R}. +\begin{lstlisting} + move/P2Q/Q2R in p. +\end{lstlisting} + +If the list of views is of length two, \ssrC{Hint View}s for interpreting +equivalences are indeed taken into account, otherwise only single +\ssrC{Hint View}s are used. +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{\ssr{} searching tool} +\idxC{Search \dots{}} + +\ssr{} proposes an extension of the \ssrC{Search} command. Its syntax is: + +\begin{center} + \ssrC{Search} \optional{\ssrN{pattern}} \optional{\optional{\ssrC{\-}} \optional{\ssrN{string}\optional{\ssrC{\%}\ssrN{key}} {\optsep} \ssrN{pattern}}}$^*$ \optional{\ssrC{in} \optional{\optional{\ssrC{\-}} \ssrN{name} }$^+$} +\end{center} + +% \begin{lstlisting} +% Search [[\~]\ssrN{string}]$^*$ [\ssrN{pattern}] [[$\ssrN[1]{pattern} \dots $ $\ssrN[n]{pattern}$]] $[[$inside$|$outside$]$ $M_1 \dots M_n$]. +% \end{lstlisting} + +% This tactic returns the list of defined constants matching the +% given criteria: +% \begin{itemize} +% \item \ssrL+[[-]\ssrN{string}]$^*$+ is an open sequence of strings, which sould +% all appear in the name of the returned constants. The optional \ssrL+-+ +% prefixes strings that are required \emph{not} to appear. +% % \item \ssrN{pattern} should be a subterm of the +% % \emph{conclusion} of the lemmas found by the command. If a lemma features +% % an occurrence +% % of this pattern only in one or several of its assumptions, it will not be +% % selected by the searching tool. +% \item +% \ssrL=[$\ssrN{pattern}^+$]= +% is a list of \ssr{} terms, which may +% include types, that are required to appear in the returned constants. +% Terms with holes should be surrounded by parentheses. +% \item $\ssrC{in}\ [[\ssrC{\-}]M]^+$ limits the search to the signature +% of open modules given in the list, but the ones preceeded by the +% $\ssrC{\-}$ flag. The +% command: +% \begin{lstlisting} +% Search in M. +% \end{lstlisting} +% is hence a way of obtaining the complete signature of the module \ssrL{M}. +% \end{itemize} +where \ssrN{name} is the name of an open module. +This command search returns the list of lemmas: +\begin{itemize} +\item whose \emph{conclusion} contains a subterm matching the optional + first \ssrN{pattern}. A $\ssrC{-}$ reverses the test, producing the list + of lemmas whose conclusion does not contain any subterm matching + the pattern; +\item whose name contains the given string. A $\ssrC{-}$ prefix reverses + the test, producing the list of lemmas whose name does not contain the + string. A string that contains symbols or +is followed by a scope \ssrN{key}, is interpreted as the constant whose +notation involves that string (e.g., \ssrL=+= for \ssrL+addn+), if this is +unambiguous; otherwise the diagnostic includes the output of the +\ssrC{Locate} vernacular command. + +\item whose statement, including assumptions and types, contains a + subterm matching the next patterns. If a pattern is prefixed by + $\ssrC{-}$, the test is reversed; +\item contained in the given list of modules, except the ones in the + modules prefixed by a $\ssrC{-}$. +\end{itemize} + +Note that: +\begin{itemize} +\item As for regular terms, patterns can feature scope + indications. For instance, the command: +\begin{lstlisting} + Search _ (_ + _)%N. +\end{lstlisting} +lists all the lemmas whose statement (conclusion or hypotheses) +involve an application of the binary operation denoted by the infix +\ssrC{+} symbol in the \ssrC{N} scope (which is \ssr{} scope for natural numbers). +\item Patterns with holes should be surrounded by parentheses. +\item Search always volunteers the expansion of the notation, avoiding the + need to execute Locate independently. Moreover, a string fragment + looks for any notation that contains fragment as + a substring. If the \ssrL+ssrbool+ library is imported, the command: +\begin{lstlisting} + Search "~~". +\end{lstlisting} +answers : +\begin{lstlisting} +"~~" is part of notation (~~ _) +In bool_scope, (~~ b) denotes negb b +negbT forall b : bool, b = false -> ~~ b +contra forall c b : bool, (c -> b) -> ~~ b -> ~~ c +introN forall (P : Prop) (b : bool), reflect P b -> ~ P -> ~~ b +\end{lstlisting} + \item A diagnostic is issued if there are different matching notations; + it is an error if all matches are partial. +\item Similarly, a diagnostic warns about multiple interpretations, and + signals an error if there is no default one. +\item The command \ssrC{Search in M.} +is a way of obtaining the complete signature of the module \ssrL{M}. +\item Strings and pattern indications can be interleaved, but the + first indication has a special status if it is a pattern, and only + filters the conclusion of lemmas: +\begin{itemize} + \item The command : + \begin{lstlisting} + Search (_ =1 _) "bij". + \end{lstlisting} +lists all the lemmas whose conclusion features a '$\ssrC{=1}$' and whose +name contains the string \verb+bij+. +\item The command : + \begin{lstlisting} + Search "bij" (_ =1 _). + \end{lstlisting} +lists all the lemmas whose statement, including hypotheses, features a +'$\ssrC{=1}$' and whose name contains the string \verb+bij+. + +\end{itemize} + +\end{itemize} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Synopsis and Index} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Parameters} + +\begin{minipage}[c]{\textwidth}\renewcommand{\footnoterule}{} +\begin{longtable}{lcl} +\ssrN{d-tactic} && one of the + \ssrC{elim}, \ssrC{case}, \ssrC{congr}, \ssrC{apply}, \ssrC{exact} + and \ssrC{move} \ssr{} tactics \\ +\ssrN{fix-body} && standard \Coq{} \textit{fix\_body}\\ +\ssrN{ident} && standard \Coq{} identifier\\ +\ssrN{int} && integer literal \\ +\ssrN{key} && notation scope\\ +\ssrN{name} && module name\\ +${\naturalnumber}$ && \ssrN{int} or Ltac variable denoting a standard \Coq{} numeral\footnote{The name of this Ltac variable should not be the name of a tactic which can be followed by a bracket + \ssrL+[+, like \ssrL+do+, \ssrL+ have+,\dots}\\ +\ssrN{pattern} && synonym for {\term}\\ +\ssrN{string} && standard \Coq{} string\\ +{\tac} && standard \Coq{} tactic or \ssr{} tactic\\ +{\term} & \hspace{1cm} & Gallina term, possibly containing wildcards\\ +%\ssrN{view} && global constant\\ +\end{longtable} +\end{minipage} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Items and switches} + +\begin{longtable}{lclr} +\ssrN{binder} & {\ident} {\optsep} \ssrC{(} {\ident} \optional{\ssrC{:} {\term} } \ssrC{)} & binder& p. \pageref{ssec:pose}\\ +\\ +\ssrN{clear-switch} & \ssrC{\{} {\ident}$^+$ \ssrC{\}} & clear switch & p. \pageref{ssec:discharge}\\ +\\ +\ssrN{c-pattern} & \optional{{\term} \ssrC{in} {\optsep} {\term} \ssrC{as}} {\ident} \ssrC{in} {\term} & context pattern & p. \pageref{ssec:rewp} \\ +\\ +\ssrN{d-item} & \optional{\ssrN{occ-switch} {\optsep} \ssrN{clear-switch}} \optional{{\term} {\optsep} \ssrC{(}\ssrN{c-pattern}\ssrC{)}} & discharge item & p. \pageref{ssec:discharge}\\ +\\ +\ssrN{gen-item} & \optional{\ssrC{@}}{\ident} {\optsep} \ssrC{(}{\ident}\ssrC{)} {\optsep} \ssrC{(}\optional{\ssrC{@}}{\ident} \ssrC{:=} \ssrN{c-pattern}\ssrC{)} & generalization item & p. \pageref{ssec:struct}\\ +\\ +\ssrN{i-pattern} & {\ident} {\optsep} \ssrC{_} {\optsep} \ssrC{?} {\optsep} \ssrC{*} {\optsep} \optional{\ssrN{occ-switch}}\ssrC{->} {\optsep} \optional{\ssrN{occ-switch}}\ssrC{<-} {\optsep} & intro pattern & p. \pageref{ssec:intro}\\ +& \ssrC{[} \ssrN{i-item}$^*$ \ssrC{|} $\dots$ \ssrC{|} \ssrN{i-item}$^*$ \ssrC{]} {\optsep} \ssrC{-} {\optsep} \ssrC{[:} {\ident}$^+$\ssrC{]} &\\ +\\ +\ssrN{i-item} & \ssrN{clear-switch} {\optsep} \ssrN{s-item} {\optsep} \ssrN{i-pattern} {\optsep} \ssrC{/}{\term} & intro item & p. \pageref{ssec:intro}\\ +\\ +\ssrN{int-mult} & \optional{{\naturalnumber}} \ssrN{mult-mark} & multiplier & p. \pageref{ssec:iter}\\ +\\ +\ssrN{occ-switch} & \ssrC{\{} \optional{\ssrC{+} {\optsep} \ssrC{-}} {\naturalnumber}$^*$\ssrC{\}} & occur. switch & p. \pageref{sssec:occselect}\\ +\\ +\ssrN{mult} & \optional{{\naturalnumber}} \ssrN{mult-mark} & multiplier & p. \pageref{ssec:iter}\\ +\\ +\ssrN{mult-mark} & \ssrC{?} {\optsep} \ssrC{!} & multiplier mark & p. \pageref{ssec:iter}\\ +\\ +\ssrN{r-item} & \optional{\ssrC{/}} {\term} {\optsep} \ssrN{s-item} & rewrite item & p. \pageref{ssec:extrw}\\ +\\ +\ssrN{r-prefix} & \optional{\ssrC{-}} \optional{\ssrN{int-mult}} \optional{\ssrN{occ-switch} {\optsep} \ssrN{clear-switch}} \optional{\ssrC{[}\ssrN{r-pattern}\ssrC{]}} & rewrite prefix & p. \pageref{ssec:extrw}\\ +\\ +\ssrN{r-pattern} & {\term} {\optsep} \ssrN{c-pattern} {\optsep} \ssrC{in} \optional{{\ident} \ssrC{in}} {\term} & rewrite pattern & p. \pageref{ssec:extrw}\\ +\\ +\ssrN{r-step} & \optional{\ssrN{r-prefix}}\ssrN{r-item} & rewrite step & p. \pageref{ssec:extrw}\\ +\\ +\ssrN{s-item} & \ssrC{/=} {\optsep} \ssrC{//} {\optsep} \ssrC{//=} & simplify switch & p. \pageref{ssec:intro}\\ +\\ +\end{longtable} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Tactics} +\emph{Note}: \ssrC{without loss} and \ssrC{suffices} are synonyms for \ssrC{wlog} and +\ssrC{suff} respectively. + +\begin{longtable}{llr} +\ssrC{move} & \textcolor{dkblue}{\texttt{idtac}} or \ssrC{hnf}& p. \pageref{ssec:profstack} \\ +\ssrC{apply} & application & p. \pageref{ssec:basictac}\\ +\ssrC{exact} &&\\ +\ssrC{abstract} && p. \pageref{ssec:abstract}, \pageref{sec:havetransparent}\\ +\\ +\ssrC{elim} & induction & p. \pageref{ssec:basictac}\\ +\ssrC{case} & case analysis & p. \pageref{ssec:basictac}\\ +\\ +\ssrC{rewrite} \ssrN{rstep}$^+$ & rewrite& p. \pageref{ssec:extrw}\\ +\\ +\ssrC{have} \ssrN{i-item}$^*$ \optional{\ssrN{i-pattern}} \optional{\ssrN{s-item} {\optsep} \ssrN{binder}$^+$} \optional{\ssrC{:} {\term}} \ssrC{:=} {\term} & forward & p. \pageref{ssec:struct}\\ +\ssrC{have} \ssrN{i-item}$^*$ \optional{\ssrN{i-pattern}} \optional{\ssrN{s-item}{\optsep} \ssrN{binder}$^+$} \ssrC{:} {\term} \optional{\ssrC{by} {\tac}} & chaining & \\ +\ssrC{have suff} \optional{\ssrN{clear-switch}} \optional{\ssrN{i-pattern}} \optional{\ssrC{:} {\term}} \ssrC{:=} {\term} & & \\ +\ssrC{have suff} \optional{\ssrN{clear-switch}} \optional{\ssrN{i-pattern}} \ssrC{:} {\term} \optional{\ssrC{by} {\tac}} & & \\ +\ssrC{gen have} \optional{{\ident}\ssrC{,}} \optional{\ssrN{i-pattern}} \ssrC{:} \ssrN{gen-item}$^+$ \ssrC{/} {\term} \optional{\ssrC{by} {\tac}} & & \\ +\\ +\ssrC{wlog} \optional{\ssrC{suff}} \optional{\ssrN{i-item}} \ssrC{:} \optional{\ssrN{gen-item}{\optsep} \ssrN{clear-switch}}$^*$ \ssrC{/} {\term} & specializing & p. \pageref{ssec:struct} \\ +\\ +\ssrC{suff} \ssrN{i-item}$^*$ \optional{\ssrN{i-pattern}} \optional{\ssrN{binder}$^+$} \ssrC{:} {\term} \optional{\ssrC{by} {\tac}} & backchaining & p. \pageref{ssec:struct}\\ +\ssrC{suff} \optional{\ssrC{have}} \optional{\ssrN{clear-switch}} \optional{\ssrN{i-pattern}} \ssrC{:} {\term} \optional{\ssrC{by} {\tac}} & & \\ +\\ +\ssrC{pose} {\ident} \ssrC{:=} {\term} & local definition& p. \pageref{ssec:pose}\\ +\ssrC{pose} {\ident} \ssrN{binder}$^+$ \ssrC{:=} {\term} & \rlap{local function definition}& \\ +\ssrC{pose fix} \ssrN{fix-body} & \rlap{local fix definition} & \\ +\ssrC{pose cofix} \ssrN{fix-body} & \rlap{local cofix definition} & \\ +\\ +\ssrC{set} {\ident} \optional{\ssrC{:} {\term}} \ssrC{:=} \optional{\ssrN{occ-switch}} \optional{{\term}{\optsep} \ssrC{(}\ssrN{c-pattern}\ssrC{)}} & abbreviation&p. \pageref{ssec:set}\\ +\\ +\ssrC{unlock} \optional{\ssrN{r-prefix}]{\ident}}$^*$ & unlock & p. \pageref{ssec:lock}\\ +\\ +\ssrC{congr} \optional{\naturalnumber} {\term} & congruence& p. \pageref{ssec:congr}\\ +\end{longtable} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Tacticals} + +\begin{longtable}{lclr} +\ssrN{d-tactic} \optional{\ident} \ssrC{:} \ssrN{d-item}$^{+}$ \optional{\ssrN{clear-switch}} & & discharge & p. \pageref{ssec:discharge}\\ +\\ +{\tac} \ssrC{=>} \ssrN{i-item}$^+$ && introduction & p. \pageref{ssec:intro}\\ +\\ +{\tac} \ssrC{in} \optional{\ssrN{gen-item} {\optsep} \ssrN{clear-switch}}$^+$ \optional{\ssrC{*}} && localization & p. \pageref{ssec:gloc}\\ +\\ +\ssrC{do} \optional{\ssrN{mult}} \ssrC{[} \nelist{\tac}{|} \ssrC{]}&& iteration & p. \pageref{ssec:iter}\\ +\ssrC{do} \ssrN{mult} {\tac} &&& \\ +\\ +{\tac} \ssrC{ ; first} \optional{\naturalnumber} \ssrC{[}\nelist{\tac}{|}\ssrC{]} && selector & p. \pageref{ssec:select}\\ +{\tac} \ssrC{ ; last} \optional{\naturalnumber} \ssrC{[}\nelist{\tac}{|}\ssrC{]} \\ +{\tac} \ssrC{ ; first} \optional{\naturalnumber} \ssrC{last} && subgoals & p. \pageref{ssec:select}\\ +{\tac} \ssrC{; last} \optional{\naturalnumber} \ssrC{first} && rotation & \\ +\\ +\ssrC{by [} \nelist{\tac}{|} \ssrC{]} && closing & p. \pageref{ssec:termin}\\ +\ssrC{by []} \\ +\ssrC{by} {\tac} \\ +\end{longtable} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\subsection*{Commands} +\begin{longtable}{lclr} +\ssrL+Hint View for+ \optional{\ssrL+move+ {\it |} \ssrL+apply+} {\tt /} {\ident} \optional{{\tt|} {\naturalnumber}} && view hint +declaration & p. \pageref{ssec:vhints}\\ +\\ +\ssrL+Hint View for apply//+ {\ident} \optional{{\tt|}{\naturalnumber}} && right hand side double + & p. \pageref{ssec:vhints}\\ +&& view hint declaration &\\ +\\ +%\ssrL+Import Prenex Implicits+ && enable prenex implicits & +%p. \pageref{ssec:parampoly}\\ +%\\ +\ssrL+Prenex Implicits+ {\ident}$^+$ & \hspace{.6cm} & prenex implicits decl. + & p. \pageref{ssec:parampoly}\\ + +\end{longtable} + +\iffalse + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Changes} + +\subsection{\ssr{} version 1.3} +All changes are retrocompatible extensions but for: +\begin{itemize} +\item Occurrences in the type family switch now refer only to the goal, while + before they used to refer also to the types in the abstractions of the + predicate used by the eliminator. This bug used to affect lemmas like + \ssrC{boolP}. See the relative comments in \ssrC{ssrbool.v}. +\item Clear switches can only mention existing hypothesis and + otherwise fail. This can in particular affect intro patterns + simultaneously applied to several goals. + % commit: 2686 +\item A bug in the \ssrC{rewrite} tactic allowed to + instantiate existential metavariables occurring in the goal. + This is not the case any longer (see section~\ref{ssec:rewcaveats}). +\item The \ssrC{fold} and \ssrC{unfold} \ssrN{r-items} for \ssrC{rewrite} used to + fail silently when used in combination with a \ssrN{r-pattern} matching no + goal subterm. They now fail. The old behavior can be obtained using + the \ssrC{?} multiplier (see section~\ref{ssec:extrw}). +\item \Coq{} 8.2 users with a statically linked toplevel must comment out the\\ + \ssrC{Declare ML Module "ssreflect".}\\ + line at the beginning of \ssrC{ssreflect.v} to compile the 1.3 library. +\end{itemize} +New features: +\begin{itemize} +\item Contextual \ssrC{rewrite} patterns. + The context surrounding the redex can now be used to specify which + redex occurrences should be rewritten (see section~\ref{ssec:rewp}).\\ + \ssrC{rewrite [in X in _ = X]addnC.} + % commit: 2690, 2689, 2718, 2733 +\item Proof irrelevant interpretation of goals with existential metavariables. + Goals containing an existential metavariable of sort \ssrC{Prop} are + generalized over it, and a new goal for the missing subproof is + generated (see page~\pageref{sssec:apply} and + section~\ref{ssec:rewcaveats}).\\ + \ssrC{apply: (ex_intro _ (@Ordinal _ y _)).}\\ + \ssrC{rewrite insubT.} + % commit: 2553, 2544, 2543, 2733 +\item Views are now part of \ssrN{i-pattern} and can thus be used + inside intro patterns (see section~\ref{ssec:intro}).\\ + \ssrC{move=> a b /andP [Ha Hb].} + % commit: 2720 +\item Multiple views for \ssrC{move}, \ssrC{move $\dots$ in} and \ssrC{apply} + (see section~\ref{ssec:multiview}).\\ + \ssrC{move/v1/v2/v3.}\\ + \ssrC{move/v1/v2/v3 in H.}\\ + \ssrC{apply/v1/v2/v3.} + % commit: 2720 +\item \ssrC{have} and \ssrC{suff} idiom with view (see section~\ref{sssec:hypview}). +\begin{lstlisting} + Lemma |*test*| (a b : bool) (pab : a && b) : b. + have {pab} /= /andP [pa ->] // : true && (a && b) := pab. +\end{lstlisting} + % commit: 2726 +\item \ssrC{have suff}, \ssrC{suff have} and \ssrC{wlog suff} forward reasoning + tactics (see section~\ref{ssec:struct}).\\ + \ssrC{have suff H : P.} + % commit: 2633 +\item Binders support in \ssrC{have} (see section~\ref{sssec:have}).\\ + \ssrC{have H x y (r : R x y) : P x -> Q y.} + % commit: 2633 +\item Deferred clear switches. Clears are deferred to the end of the + intro pattern. In the meanwhile, cleared variables are still + part of the context, thus the goal can mention them, but are + renamed to non accessible dummy names (see section~\ref{ssec:intro}).\\ + \ssrC{suff: G \\x H = K; first case/dprodP=> \{G H\} [[G H -> -> defK]].} + % commit: 2660 +\item Relaxed alternation condition in intro patterns. The + \ssrN{i-item} grammar rule is simplified (see section~\ref{ssec:intro}).\\ + \ssrC{move=> a \{H\} /= \{H1\} // b c /= \{H2\}.} + % commit: 2713 +\item Occurrence selection for \ssrC{->} and \ssrC{<-} intro pattern + (see section~\ref{ssec:intro}).\\ + \ssrC{move=> a b H \{2\}->.} + % commit: 2714 +\item Modifiers for the discharging '\ssrC{:}' and \ssrC{in} tactical to override + the default behavior when dealing with local definitions (let-in): + \ssrC{@f} forces the body of \ssrC{f} to be kept, \ssrC{(f)} forces the body of + \ssrC{f} to be dropped (see sections~\ref{ssec:discharge} + and~\ref{ssec:gloc}).\\ + \ssrC{move: x y @f z.}\\ + \ssrC{rewrite rule in (f) $\;\;$H.} + %commit: 2659, 2710 +\item Type family switch in \ssrC{elim} and \ssrC{case} + can contain patterns with occurrence switch + (see section~\ref{ssec:typefam}).\\ + \ssrC{case: \{2\}(_ == x) / eqP.} + % commit: 2593, 2598, 2539, 2538, 2527, 2529 +\item Generic second order predicate support for \ssrC{elim} + (see section~\ref{sec:views}).\\ + \ssrC{elim/big\_prop: _} + % commit: 2767 +\item The \ssrC{congr} tactic now also works on products (see + section~\ref{ssec:congr}). +\begin{lstlisting} + Lemma |*test*| x (H : P x) : P y. + congr (P _): H. +\end{lstlisting} + % commit: 2608 +\item Selectors now support Ltac variables + (see section~\ref{ssec:select}).\\ + \ssrC{let n := 3 in tac; first n last.} + % commit: 2725 +\item Deprecated use of \ssrC{Import Prenex Implicits} directive. + It must be replaced with the \Coq{} \ssrC{Unset Printing + Implicit Defensive} vernacular command. +\item New synonym \ssrC{Canonical} for \ssrC{Canonical Structure}. +\end{itemize} +\subsection{\ssr{} version 1.4} +New features: +\begin{itemize} +\item User definable recurrent contexts (see section~\ref{ssec:rewp}).\\ + \ssrC{Notation RHS := (X in _ = X)\%pattern} +\item Contextual patterns in + \ssrC{set} and `\ssrC{:}' (see section~\ref{ssec:rewp}).\\ + \ssrC{set t := (a + _ in RHS)} +\item NO-OP intro pattern (see section~\ref{ssec:intro}).\\ + \ssrC{move=> /eqP-H /fooP-/barP} +\item \ssrC{if $\ {\term}\ $ isn't $\ \ssrN{pattern}\ $ then $\ {\term}\ $ + else $\ {\term}\ $} notation (see section~\ref{ssec:patcond}).\\ + \ssrC{if x isn't Some y then simple else complex y} +\end{itemize} +\subsection{\ssr{} version 1.5} +Incompatibilities: +\begin{itemize} +\item The \ssrC{have} tactic now performs type classes resolution. The old + behavior can be restored with \ssrC{Set SsrHave NoTCResolution} +\end{itemize} +Fixes: +\begin{itemize} +\item The \ssrC{let foo := type of t in} syntax of standard \ssrC{Ltac} has + been made compatible with \ssr{} and can be freely used even if + the \ssr{} plugin is loaded +\end{itemize} +New features: +\begin{itemize} +\item Generalizations supported in have (see section~\ref{ssec:struct}).\\ + \ssrC{generally have hx2px, pa : a ha / P a.} +\item Renaming and patterns in wlog (see section~\ref{ssec:struct} and + page \pageref{par:advancedgen}).\\ + \ssrC{wlog H : (n := m)$\;$ (x := m + _)$\;$ / T x}.\\ + \ssrC{wlog H : (n := m)$\;$ (@ldef := secdef m)$\;$ / T x}. +\item Renaming, patterns and clear switches in \ssrC{in} + tactical (see section~\ref{ssec:gloc}).\\ + \ssrC{$\dots$ in H1 \{H2\} (n := m).} +\item Handling of type classes in \ssrC{have} + (see page~\pageref{ssec:havetcresolution}).\\ + \ssrC{have foo : ty. (* TC inference for ty *)}\\ + \ssrC{have foo : ty := . (* no TC inference for ty *)}\\ + \ssrC{have foo : ty := t. (* no TC inference for ty and t *)}\\ + \ssrC{have foo := t. (* no TC inference for t *)} +\item Transparent flag for \ssrC{have} to generate a \ssrC{let in} context entry + (see page~\pageref{sec:havetransparent}).\\ + \ssrC{have @i : 'I\_n by apply: (Sub m); auto.} +\item Intro pattern \ssrC{[: foo bar ]} to create abstract variables + (see page~\pageref{ssec:introabstract}). +\item Tactic \ssrC{abstract:} to assign an abstract variable + (see page~\pageref{ssec:abstract}).\\ + \ssrC{have [: blurb ] @i : 'I\_n by apply: (Sub m); abstract: blurb; auto.}\\ + \ssrC{have [: blurb ] i : 'I\_n := Sub m blurb; first by auto.} + +\end{itemize} + +\fi diff --git a/doc/refman/RefMan-tac.tex b/doc/refman/RefMan-tac.tex index b13ae9b7b..b3b0df5c8 100644 --- a/doc/refman/RefMan-tac.tex +++ b/doc/refman/RefMan-tac.tex @@ -4671,50 +4671,15 @@ congruence. \end{ErrMsgs} +\section{Checking properties of terms} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -\section{Everything after this point has yet to be sorted} - +Each of the following tactics acts as the identity if the check succeeds, and results in an error otherwise. \subsection{\tt constr\_eq \term$_1$ \term$_2$} \tacindex{constr\_eq} \label{constreq} -This tactic applies to any goal. It checks whether its arguments are -equal modulo alpha conversion and casts. +This tactic checks whether its arguments are equal modulo alpha conversion and casts. \ErrMsg \errindex{Not equal} @@ -4722,8 +4687,8 @@ equal modulo alpha conversion and casts. \tacindex{unify} \label{unify} -This tactic applies to any goal. It checks whether its arguments are -unifiable, potentially instantiating existential variables. +This tactic checks whether its arguments are unifiable, potentially +instantiating existential variables. \ErrMsg \errindex{Not unifiable} @@ -4738,9 +4703,9 @@ unifiable, potentially instantiating existential variables. \tacindex{is\_evar} \label{isevar} -This tactic applies to any goal. It checks whether its argument is an -existential variable. Existential variables are uninstantiated -variables generated by e.g. {\tt eapply} (see Section~\ref{apply}). +This tactic checks whether its argument is a current existential +variable. Existential variables are uninstantiated variables generated +by {\tt eapply} (see Section~\ref{apply}) and some other tactics. \ErrMsg \errindex{Not an evar} @@ -4748,10 +4713,9 @@ variables generated by e.g. {\tt eapply} (see Section~\ref{apply}). \tacindex{has\_evar} \label{hasevar} -This tactic applies to any goal. It checks whether its argument has an -existential variable as a subterm. Unlike {\tt context} patterns -combined with {\tt is\_evar}, this tactic scans all subterms, -including those under binders. +This tactic checks whether its argument has an existential variable as +a subterm. Unlike {\tt context} patterns combined with {\tt is\_evar}, +this tactic scans all subterms, including those under binders. \ErrMsg \errindex{No evars} @@ -4759,8 +4723,8 @@ including those under binders. \tacindex{is\_var} \label{isvar} -This tactic applies to any goal. It checks whether its argument is a -variable or hypothesis in the current goal context or in the opened sections. +This tactic checks whether its argument is a variable or hypothesis in the +current goal context or in the opened sections. \ErrMsg \errindex{Not a variable or hypothesis} diff --git a/doc/refman/RefMan-tacex.tex b/doc/refman/RefMan-tacex.tex index 9f4ddc804..cb8f916f1 100644 --- a/doc/refman/RefMan-tacex.tex +++ b/doc/refman/RefMan-tacex.tex @@ -849,7 +849,7 @@ Ltac DSimplif trm := Ltac Length trm := match trm with | (_ * ?B) => let succ := Length B in constr:(S succ) - | _ => constr:1 + | _ => constr:(1) end. Ltac assoc := repeat rewrite <- Ass. \end{coq_example} diff --git a/doc/refman/Reference-Manual.tex b/doc/refman/Reference-Manual.tex index 291c07de4..fc1c01cf2 100644 --- a/doc/refman/Reference-Manual.tex +++ b/doc/refman/Reference-Manual.tex @@ -22,6 +22,17 @@ \usepackage{xspace} \usepackage{pmboxdraw} \usepackage{float} +\usepackage{color} + \definecolor{dkblue}{rgb}{0,0.1,0.5} + \definecolor{lightblue}{rgb}{0,0.5,0.5} + \definecolor{dkgreen}{rgb}{0,0.4,0} + \definecolor{dk2green}{rgb}{0.4,0,0} + \definecolor{dkviolet}{rgb}{0.6,0,0.8} + \definecolor{dkpink}{rgb}{0.2,0,0.6} +\usepackage{listings} + \def\lstlanguagefiles{coq-listing.tex} +\usepackage{tabularx} +\usepackage{array,longtable} \floatstyle{boxed} \restylefloat{figure} @@ -99,6 +110,11 @@ Options A and B of the licence are {\em not} elected.} \include{RefMan-ltac.v}% Writing tactics \include{RefMan-tacex.v}% Detailed Examples of tactics +\lstset{language=SSR} +\lstset{moredelim=[is][]{|*}{*|}} +\lstset{moredelim=*[is][\itshape\rmfamily]{/*}{*/}} +\include{RefMan-ssr} + \part{User extensions} \include{RefMan-syn.v}% The Syntax and the Grammar commands %%SUPPRIME \include{RefMan-tus.v}% Writing tactics diff --git a/doc/refman/Setoid.tex b/doc/refman/Setoid.tex index 2c9602a22..6c7928438 100644 --- a/doc/refman/Setoid.tex +++ b/doc/refman/Setoid.tex @@ -156,9 +156,9 @@ compatibility constraints. \begin{cscexample}[Rewriting] Continuing the previous examples, suppose that the user must prove \texttt{set\_eq int (union int (union int S1 S2) S2) (f S1 S2)} under the -hypothesis \texttt{H: set\_eq int S2 (nil int)}. It is possible to +hypothesis \texttt{H: set\_eq int S2 (@nil int)}. It is possible to use the \texttt{rewrite} tactic to replace the first two occurrences of -\texttt{S2} with \texttt{nil int} in the goal since the context +\texttt{S2} with \texttt{@nil int} in the goal since the context \texttt{set\_eq int (union int (union int S1 nil) nil) (f S1 S2)}, being a composition of morphisms instances, is a morphism. However the tactic will fail replacing the third occurrence of \texttt{S2} unless \texttt{f} diff --git a/doc/refman/Universes.tex b/doc/refman/Universes.tex index 2bb1301c7..6ea253739 100644 --- a/doc/refman/Universes.tex +++ b/doc/refman/Universes.tex @@ -134,12 +134,14 @@ producing global universe constraints, one can use the \asection{{\tt Cumulative, NonCumulative}} \comindex{Cumulative} \comindex{NonCumulative} -\optindex{Inductive Cumulativity} +\optindex{Polymorphic Inductive Cumulativity} -Inductive types, coinductive types, variants and records can be +Polymorphic inductive types, coinductive types, variants and records can be declared cumulative using the \texttt{Cumulative}. Alternatively, -there is an option \texttt{Set Inductive Cumulativity} which when set, -makes all subsequent inductive definitions cumulative. Consider the examples below. +there is an option \texttt{Set Polymorphic Inductive Cumulativity} which when set, +makes all subsequent \emph{polymorphic} inductive definitions cumulative. When set, +inductive types and the like can be enforced to be +\emph{non-cumulative} using the \texttt{NonCumulative} prefix. Consider the examples below. \begin{coq_example*} Polymorphic Cumulative Inductive list {A : Type} := | nil : list @@ -158,24 +160,61 @@ This also means that any two instances of \texttt{list} are convertible: $\WTEGCONV{\mathtt{list@\{i\}} A}{\mathtt{list@\{j\}} B}$ whenever $\WTEGCONV{A}{B}$ and furthermore their corresponding (when fully applied to convertible arguments) constructors. See Chapter~\ref{Cic} for more details on convertibility and subtyping. -Also notice the subtyping constraints for the \emph{non-cumulative} version of list: +The following is an example of a record with non-trivial subtyping relation: \begin{coq_example*} -Polymorphic NonCumulative Inductive list' {A : Type} := -| nil' : list' -| cons' : A -> list' -> list'. +Polymorphic Cumulative Record packType := {pk : Type}. \end{coq_example*} \begin{coq_example} -Print list'. +Print packType. +\end{coq_example} +Notice that as expected, \texttt{packType@\{i\}} and \texttt{packType@\{j\}} are +convertible if and only if \texttt{i $=$ j}. + +Cumulative inductive types, coninductive types, variants and records +only make sense when they are universe polymorphic. Therefore, an +error is issued whenever the user uses the \texttt{Cumulative} or +\texttt{NonCumulative} prefix in a monomorphic context. +Notice that this is not the case for the option \texttt{Set Polymorphic Inductive Cumulativity}. +That is, this option, when set, makes all subsequent \emph{polymorphic} +inductive declarations cumulative (unless, of course the \texttt{NonCumulative} prefix is used) +but has no effect on \emph{monomorphic} inductive declarations. +Consider the following examples. +\begin{coq_example} +Monomorphic Cumulative Inductive Unit := unit. +\end{coq_example} +\begin{coq_example} +Monomorphic NonCumulative Inductive Unit := unit. \end{coq_example} -The following is an example of a record with non-trivial subtyping relation: \begin{coq_example*} -Polymorphic Cumulative Record packType := {pk : Type}. +Set Polymorphic Inductive Cumulativity. +Inductive Unit := unit. \end{coq_example*} \begin{coq_example} -Print packType. +Print Unit. \end{coq_example} -Notice that as expected, \texttt{packType@\{i\}} and \texttt{packType@\{j\}} are convertible if and only if \texttt{i $=$ j}. +\subsection*{An example of a proof using cumulativity} + +\begin{coq_example} +Set Universe Polymorphism. +Set Polymorphic Inductive Cumulativity. + +Inductive eq@{i} {A : Type@{i}} (x : A) : A -> Type@{i} := eq_refl : eq x x. + +Definition funext_type@{a b e} (A : Type@{a}) (B : A -> Type@{b}) + := forall f g : (forall a, B a), + (forall x, eq@{e} (f x) (g x)) + -> eq@{e} f g. + +Section down. + Universes a b e e'. + Constraint e' < e. + Lemma funext_down {A B} + (H : @funext_type@{a b e} A B) : @funext_type@{a b e'} A B. + Proof. + exact H. + Defined. +\end{coq_example} \asection{Global and local universes} @@ -293,8 +332,18 @@ Universes k l. Check (le@{k l}). \end{coq_example} -User-named universes are considered rigid for unification and are never -minimized. +User-named universes and the anonymous universe implicitly attached to +an explicit $Type$ are considered rigid for unification and are never +minimized. Flexible anonymous universes can be produced with an +underscore or by omitting the annotation to a polymorphic definition. + +\begin{coq_example} + Check (fun x => x) : Type -> Type. + Check (fun x => x) : Type -> Type@{_}. + + Check le@{k _}. + Check le. +\end{coq_example} \subsection{\tt Unset Strict Universe Declaration. \optindex{Strict Universe Declaration} diff --git a/doc/refman/coq-listing.tex b/doc/refman/coq-listing.tex new file mode 100644 index 000000000..c69c3b1b8 --- /dev/null +++ b/doc/refman/coq-listing.tex @@ -0,0 +1,152 @@ +%======================================================================= +% Listings LaTeX package style for Gallina + SSReflect (Assia Mahboubi 2007) + +\lstdefinelanguage{SSR} { + +% Anything betweeen $ becomes LaTeX math mode +mathescape=true, +% Comments may or not include Latex commands +texcl=false, + + +% Vernacular commands +morekeywords=[1]{ +From, Section, Module, End, Require, Import, Export, Defensive, Function, +Variable, Variables, Parameter, Parameters, Axiom, Hypothesis, Hypotheses, +Notation, Local, Tactic, Reserved, Scope, Open, Close, Bind, Delimit, +Definition, Let, Ltac, Fixpoint, CoFixpoint, Add, Morphism, Relation, +Implicit, Arguments, Set, Unset, Contextual, Strict, Prenex, Implicits, +Inductive, CoInductive, Record, Structure, Canonical, Coercion, +Theorem, Lemma, Corollary, Proposition, Fact, Remark, Example, +Proof, Goal, Save, Qed, Defined, Hint, Resolve, Rewrite, View, +Search, Show, Print, Printing, All, Graph, Projections, inside, +outside, Locate, Maximal}, + +% Gallina +morekeywords=[2]{forall, exists, exists2, fun, fix, cofix, struct, + match, with, end, as, in, return, let, if, is, then, else, + for, of, nosimpl}, + +% Sorts +morekeywords=[3]{Type, Prop}, + +% Various tactics, some are std Coq subsumed by ssr, for the manual purpose +morekeywords=[4]{ + pose, set, move, case, elim, apply, clear, + hnf, intro, intros, generalize, rename, pattern, after, + destruct, induction, using, refine, inversion, injection, + rewrite, congr, unlock, compute, ring, field, + replace, fold, unfold, change, cutrewrite, simpl, + have, gen, generally, suff, wlog, suffices, without, loss, nat_norm, + assert, cut, trivial, revert, bool_congr, nat_congr, abstract, + symmetry, transitivity, auto, split, left, right, autorewrite}, + +% Terminators +morekeywords=[5]{ + by, done, exact, reflexivity, tauto, romega, omega, + assumption, solve, contradiction, discriminate}, + + +% Control +morekeywords=[6]{do, last, first, try, idtac, repeat}, + +% Various symbols +% For the ssr manual we turn off the prettyprint of formulas +% literate= +% {->}{{$\rightarrow\,$}}2 +% {->}{{\tt ->}}3 +% {<-}{{$\leftarrow\,$}}2 +% {<-}{{\tt <-}}2 +% {>->}{{$\mapsto$}}3 +% {<=}{{$\leq$}}1 +% {>=}{{$\geq$}}1 +% {<>}{{$\neq$}}1 +% {/\\}{{$\wedge$}}2 +% {\\/}{{$\vee$}}2 +% {<->}{{$\leftrightarrow\;$}}3 +% {<=>}{{$\Leftrightarrow\;$}}3 +% {:nat}{{$~\in\mathbb{N}$}}3 +% {fforall\ }{{$\forall_f\,$}}1 +% {forall\ }{{$\forall\,$}}1 +% {exists\ }{{$\exists\,$}}1 +% {negb}{{$\neg$}}1 +% {spp}{{:*:\,}}1 +% {~}{{$\sim$}}1 +% {\\in}{{$\in\;$}}1 +% {/\\}{$\land\,$}1 +% {:*:}{{$*$}}2 +% {=>}{{$\,\Rightarrow\ $}}1 +% {=>}{{\tt =>}}2 +% {:=}{{{\tt:=}\,\,}}2 +% {==}{{$\equiv$}\,}2 +% {!=}{{$\neq$}\,}2 +% {^-1}{{$^{-1}$}}1 +% {elt'}{elt'}1 +% {=}{{\tt=}\,\,}2 +% {+}{{\tt+}\,\,}2, +literate= + {isn't }{{{\ttfamily\color{dkgreen} isn't }}}1, + +% Comments delimiters, we do turn this off for the manual +%comment=[s]{(*}{*)}, + +% Spaces are not displayed as a special character +showstringspaces=false, + +% String delimiters +morestring=[b]", +morestring=[d]", + +% Size of tabulations +tabsize=3, + +% Enables ASCII chars 128 to 255 +extendedchars=true, + +% Case sensitivity +sensitive=true, + +% Automatic breaking of long lines +breaklines=true, + +% Default style fors listings +basicstyle=\ttfamily, + +% Position of captions is bottom +captionpos=b, + +% Full flexible columns +columns=[l]fullflexible, + +% Style for (listings') identifiers +identifierstyle={\ttfamily\color{black}}, +% Note : highlighting of Coq identifiers is done through a new +% delimiter definition through an lstset at the begining of the +% document. Don't know how to do better. + +% Style for declaration keywords +keywordstyle=[1]{\ttfamily\color{dkviolet}}, + +% Style for gallina keywords +keywordstyle=[2]{\ttfamily\color{dkgreen}}, + +% Style for sorts keywords +keywordstyle=[3]{\ttfamily\color{lightblue}}, + +% Style for tactics keywords +keywordstyle=[4]{\ttfamily\color{dkblue}}, + +% Style for terminators keywords +keywordstyle=[5]{\ttfamily\color{red}}, + + +%Style for iterators +keywordstyle=[6]{\ttfamily\color{dkpink}}, + +% Style for strings +stringstyle=\ttfamily, + +% Style for comments +commentstyle=\rmfamily, + +} diff --git a/doc/tutorial/Tutorial.tex b/doc/tutorial/Tutorial.tex index 8337b1c48..77ce8574f 100644 --- a/doc/tutorial/Tutorial.tex +++ b/doc/tutorial/Tutorial.tex @@ -241,7 +241,7 @@ Variables A B C : Prop. \end{coq_example} We shall consider simple implications, such as $A\ra B$, read as -``$A$ implies $B$''. Remark that we overload the arrow symbol, which +``$A$ implies $B$''. Note that we overload the arrow symbol, which has been used above as the functionality type constructor, and which may be used as well as propositional connective: \begin{coq_example} @@ -289,7 +289,7 @@ apply H. We are now in the situation where we have two judgments as conjectures that remain to be proved. Only the first is listed in full, for the others the system displays only the corresponding subgoal, without its -local hypotheses list. Remark that \verb:apply: has kept the local +local hypotheses list. Note that \verb:apply: has kept the local hypotheses of its father judgment, which are still available for the judgments it generated. @@ -654,7 +654,7 @@ Hypothesis R_transitive : forall x y z : D, R x y -> R y z -> R x z. \end{coq_example} -Remark the syntax \verb+forall x : D,+ which stands for universal quantification +Note the syntax \verb+forall x : D,+ which stands for universal quantification $\forall x : D$. \subsection{Existential quantification} @@ -664,10 +664,10 @@ We now state our lemma, and enter proof mode. Lemma refl_if : forall x : D, (exists y, R x y) -> R x x. \end{coq_example} -Remark that the hypotheses which are local to the currently opened sections +The hypotheses that are local to the currently opened sections are listed as local hypotheses to the current goals. -The rationale is that these hypotheses are going to be discharged, as we -shall see, when we shall close the corresponding sections. +That is because these hypotheses are going to be discharged, as +we shall see, when we shall close the corresponding sections. Note the functional syntax for existential quantification. The existential quantifier is built from the operator \verb:ex:, which expects a @@ -687,7 +687,7 @@ verifies \verb:P:. Let us see how this works on this simple example. intros x x_Rlinked. \end{coq_example} -Remark that \verb:intros: treats universal quantification in the same way +Note that \verb:intros: treats universal quantification in the same way as the premises of implications. Renaming of bound variables occurs when it is needed; for instance, had we started with \verb:intro y:, we would have obtained the goal: @@ -859,7 +859,7 @@ Check weird. Check drinker. \end{coq_example} -Remark how the three theorems are completely generic in the most general +Note how the three theorems are completely generic in the most general fashion; the domain \verb:D: is discharged in all of them, \verb:R: is discharged in \verb:refl_if: only, \verb:P: is discharged only in \verb:weird: and @@ -867,7 +867,7 @@ the domain \verb:D: is discharged in all of them, \verb:R: is discharged in Finally, the excluded middle hypothesis is discharged only in \verb:drinker:. -Note that the name \verb:d: has vanished as well from +Note, too, that the name \verb:d: has vanished from the statements of \verb:weird: and \verb:drinker:, since \Coq's pretty-printer replaces systematically a quantification such as \texttt{forall d : D, E}, diff --git a/ide/wg_Detachable.ml b/ide/wg_Detachable.ml index e5b436427..3d3a5ccb2 100644 --- a/ide/wg_Detachable.ml +++ b/ide/wg_Detachable.ml @@ -19,7 +19,7 @@ class detachable (obj : ([> Gtk.box] as 'a) Gobject.obj) = inherit GPack.box_skel (obj :> Gtk.box Gobject.obj) as super val but = GButton.button () - val win = GWindow.window () + val win = GWindow.window ~type_hint:`DIALOG () val frame = GBin.frame ~shadow_type:`NONE () val mutable detached = false val mutable detached_cb = (fun _ -> ()) diff --git a/interp/constrextern.ml b/interp/constrextern.ml index fcaee5c93..54861ae4c 100644 --- a/interp/constrextern.ml +++ b/interp/constrextern.ml @@ -1098,7 +1098,6 @@ let extern_constr_gen lax goal_concl_style scopt env sigma t = (* Not "goal_concl_style" means do alpha-conversion avoiding only *) (* those goal/section/rel variables that occurs in the subterm under *) (* consideration; see namegen.ml for further details *) - let t = EConstr.of_constr t in let avoid = if goal_concl_style then ids_of_context env else [] in let r = Detyping.detype ~lax:lax goal_concl_style avoid env sigma t in let vars = vars_of_env env in @@ -1111,7 +1110,6 @@ let extern_constr ?(lax=false) goal_concl_style env sigma t = extern_constr_gen lax goal_concl_style None env sigma t let extern_type goal_concl_style env sigma t = - let t = EConstr.of_constr t in let avoid = if goal_concl_style then ids_of_context env else [] in let r = Detyping.detype goal_concl_style avoid env sigma t in extern_glob_type (vars_of_env env) r @@ -1198,8 +1196,6 @@ let extern_constr_pattern env sigma pat = extern true (None,[]) Id.Set.empty (glob_of_pat env sigma pat) let extern_rel_context where env sigma sign = - let sign = List.map (fun d -> Termops.map_rel_decl EConstr.of_constr d) sign in - let where = Option.map EConstr.of_constr where in let a = detype_rel_context where [] (names_of_rel_context env,env) sigma sign in let vars = vars_of_env env in let a = List.map (extended_glob_local_binder_of_decl) a in diff --git a/interp/constrextern.mli b/interp/constrextern.mli index b5242b347..ffa891c50 100644 --- a/interp/constrextern.mli +++ b/interp/constrextern.mli @@ -9,6 +9,7 @@ open Names open Term open Termops +open EConstr open Environ open Libnames open Globnames @@ -41,7 +42,7 @@ val extern_reference : ?loc:Loc.t -> Id.Set.t -> global_reference -> reference val extern_type : bool -> env -> Evd.evar_map -> types -> constr_expr val extern_sort : Evd.evar_map -> sorts -> glob_sort val extern_rel_context : constr option -> env -> Evd.evar_map -> - Context.Rel.t -> local_binder_expr list + rel_context -> local_binder_expr list (** Printing options *) val print_implicits : bool ref diff --git a/intf/vernacexpr.ml b/intf/vernacexpr.ml index 6ef9532ad..2adf522b7 100644 --- a/intf/vernacexpr.ml +++ b/intf/vernacexpr.ml @@ -305,6 +305,14 @@ type inline = type module_ast_inl = module_ast * inline type module_binder = bool option * lident list * module_ast_inl +(** Cumulativity can be set globally, locally or unset locally and it + can not enabled at all. *) +type cumulative_inductive_parsing_flag = + | GlobalCumulativity + | GlobalNonCumulativity + | LocalCumulativity + | LocalNonCumulativity + (** {6 The type of vernacular expressions} *) type vernac_expr = @@ -336,7 +344,7 @@ type vernac_expr = | VernacExactProof of constr_expr | VernacAssumption of (locality option * assumption_object_kind) * inline * (plident list * constr_expr) with_coercion list - | VernacInductive of cumulative_inductive_flag * private_flag * inductive_flag * (inductive_expr * decl_notation list) list + | VernacInductive of cumulative_inductive_parsing_flag * private_flag * inductive_flag * (inductive_expr * decl_notation list) list | VernacFixpoint of locality option * (fixpoint_expr * decl_notation list) list | VernacCoFixpoint of diff --git a/kernel/primitives.ml b/kernel/cPrimitives.ml index 14c11bf10..14c11bf10 100644 --- a/kernel/primitives.ml +++ b/kernel/cPrimitives.ml diff --git a/kernel/primitives.mli b/kernel/cPrimitives.mli index 8cdffb670..8cdffb670 100644 --- a/kernel/primitives.mli +++ b/kernel/cPrimitives.mli diff --git a/kernel/environ.ml b/kernel/environ.ml index d2c737ab0..621a9931d 100644 --- a/kernel/environ.ml +++ b/kernel/environ.ml @@ -624,39 +624,39 @@ fun rk value field -> native_constant_dynamic = Some Nativelambda.compile_dynamic_int31; } | KInt31 (_, Int31Plus) -> int31_binop_from_const Cbytecodes.Kaddint31 - Primitives.Int31add + CPrimitives.Int31add | KInt31 (_, Int31PlusC) -> int31_binop_from_const Cbytecodes.Kaddcint31 - Primitives.Int31addc + CPrimitives.Int31addc | KInt31 (_, Int31PlusCarryC) -> int31_binop_from_const Cbytecodes.Kaddcarrycint31 - Primitives.Int31addcarryc + CPrimitives.Int31addcarryc | KInt31 (_, Int31Minus) -> int31_binop_from_const Cbytecodes.Ksubint31 - Primitives.Int31sub + CPrimitives.Int31sub | KInt31 (_, Int31MinusC) -> int31_binop_from_const Cbytecodes.Ksubcint31 - Primitives.Int31subc + CPrimitives.Int31subc | KInt31 (_, Int31MinusCarryC) -> int31_binop_from_const - Cbytecodes.Ksubcarrycint31 Primitives.Int31subcarryc + Cbytecodes.Ksubcarrycint31 CPrimitives.Int31subcarryc | KInt31 (_, Int31Times) -> int31_binop_from_const Cbytecodes.Kmulint31 - Primitives.Int31mul + CPrimitives.Int31mul | KInt31 (_, Int31TimesC) -> int31_binop_from_const Cbytecodes.Kmulcint31 - Primitives.Int31mulc + CPrimitives.Int31mulc | KInt31 (_, Int31Div21) -> int31_op_from_const 3 Cbytecodes.Kdiv21int31 - Primitives.Int31div21 + CPrimitives.Int31div21 | KInt31 (_, Int31Diveucl) -> int31_binop_from_const Cbytecodes.Kdivint31 - Primitives.Int31diveucl + CPrimitives.Int31diveucl | KInt31 (_, Int31AddMulDiv) -> int31_op_from_const 3 Cbytecodes.Kaddmuldivint31 - Primitives.Int31addmuldiv + CPrimitives.Int31addmuldiv | KInt31 (_, Int31Compare) -> int31_binop_from_const Cbytecodes.Kcompareint31 - Primitives.Int31compare + CPrimitives.Int31compare | KInt31 (_, Int31Head0) -> int31_unop_from_const Cbytecodes.Khead0int31 - Primitives.Int31head0 + CPrimitives.Int31head0 | KInt31 (_, Int31Tail0) -> int31_unop_from_const Cbytecodes.Ktail0int31 - Primitives.Int31tail0 + CPrimitives.Int31tail0 | KInt31 (_, Int31Lor) -> int31_binop_from_const Cbytecodes.Klorint31 - Primitives.Int31lor + CPrimitives.Int31lor | KInt31 (_, Int31Land) -> int31_binop_from_const Cbytecodes.Klandint31 - Primitives.Int31land + CPrimitives.Int31land | KInt31 (_, Int31Lxor) -> int31_binop_from_const Cbytecodes.Klxorint31 - Primitives.Int31lxor + CPrimitives.Int31lxor | _ -> empty_reactive_info let _ = Hook.set Retroknowledge.dispatch_hook dispatch diff --git a/kernel/kernel.mllib b/kernel/kernel.mllib index 994634854..917e4f6f1 100644 --- a/kernel/kernel.mllib +++ b/kernel/kernel.mllib @@ -17,7 +17,7 @@ Opaqueproof Declarations Entries Nativevalues -Primitives +CPrimitives Declareops Retroknowledge Conv_oracle diff --git a/kernel/nativecode.ml b/kernel/nativecode.ml index da7fcd6f2..e08d913bc 100644 --- a/kernel/nativecode.ml +++ b/kernel/nativecode.ml @@ -296,7 +296,7 @@ type primitive = | MLmagic | MLarrayget | Mk_empty_instance - | Coq_primitive of Primitives.t * (prefix * constant) option + | Coq_primitive of CPrimitives.t * (prefix * constant) option let eq_primitive p1 p2 = match p1, p2 with @@ -361,9 +361,9 @@ let primitive_hash = function | MLsub -> 33 | MLmul -> 34 | MLmagic -> 35 - | Coq_primitive (prim, None) -> combinesmall 36 (Primitives.hash prim) + | Coq_primitive (prim, None) -> combinesmall 36 (CPrimitives.hash prim) | Coq_primitive (prim, Some (prefix,kn)) -> - combinesmall 37 (combine3 (String.hash prefix) (Constant.hash kn) (Primitives.hash prim)) + combinesmall 37 (combine3 (String.hash prefix) (Constant.hash kn) (CPrimitives.hash prim)) | Mk_proj -> 38 | MLarrayget -> 39 | Mk_empty_instance -> 40 @@ -921,7 +921,7 @@ let merge_branches t = type prim_aux = - | PAprim of string * constant * Primitives.t * prim_aux array + | PAprim of string * constant * CPrimitives.t * prim_aux array | PAml of mllambda let add_check cond args = @@ -988,11 +988,11 @@ let compile_prim decl cond paux = | Int31lt -> if Sys.word_size = 64 then app_prim Mk_bool [|(app_prim MLlt (args_to_int args))|] - else app_prim (Coq_primitive (Primitives.Int31lt,None)) args + else app_prim (Coq_primitive (CPrimitives.Int31lt,None)) args | Int31le -> if Sys.word_size = 64 then app_prim Mk_bool [|(app_prim MLle (args_to_int args))|] - else app_prim (Coq_primitive (Primitives.Int31le, None)) args + else app_prim (Coq_primitive (CPrimitives.Int31le, None)) args | Int31lsl -> of_int (mk_lsl (args_to_int args)) | Int31lsr -> of_int (mk_lsr (args_to_int args)) | Int31land -> of_int (mk_land (args_to_int args)) @@ -1752,9 +1752,9 @@ let pp_mllam fmt l = | MLarrayget -> Format.fprintf fmt "Array.get" | Mk_empty_instance -> Format.fprintf fmt "Univ.Instance.empty" | Coq_primitive (op,None) -> - Format.fprintf fmt "no_check_%s" (Primitives.to_string op) + Format.fprintf fmt "no_check_%s" (CPrimitives.to_string op) | Coq_primitive (op, Some (prefix,kn)) -> - Format.fprintf fmt "%s %a" (Primitives.to_string op) + Format.fprintf fmt "%s %a" (CPrimitives.to_string op) pp_mllam (MLglobal (Gconstant (prefix, kn))) in Format.fprintf fmt "@[%a@]" pp_mllam l diff --git a/kernel/nativeinstr.mli b/kernel/nativeinstr.mli index cb79877e8..2353470f0 100644 --- a/kernel/nativeinstr.mli +++ b/kernel/nativeinstr.mli @@ -30,7 +30,7 @@ and lambda = | Lapp of lambda * lambda array | Lconst of prefix * pconstant | Lproj of prefix * constant (* prefix, projection name *) - | Lprim of prefix * constant * Primitives.t * lambda array + | Lprim of prefix * constant * CPrimitives.t * lambda array | Lcase of annot_sw * lambda * lambda * lam_branches (* annotations, term being matched, accu, branches *) | Lif of lambda * lambda * lambda diff --git a/kernel/nativelambda.mli b/kernel/nativelambda.mli index bfa3bf941..156e4f834 100644 --- a/kernel/nativelambda.mli +++ b/kernel/nativelambda.mli @@ -38,5 +38,5 @@ val compile_dynamic_int31 : bool -> prefix -> constructor -> lambda array -> val before_match_int31 : inductive -> bool -> prefix -> constructor -> lambda -> lambda -val compile_prim : Primitives.t -> constant -> bool -> prefix -> lambda array -> +val compile_prim : CPrimitives.t -> constant -> bool -> prefix -> lambda array -> lambda diff --git a/lib/flags.ml b/lib/flags.ml index 40bad9035..d4be81c61 100644 --- a/lib/flags.ml +++ b/lib/flags.ml @@ -164,9 +164,9 @@ let use_polymorphic_flag () = let make_polymorphic_flag b = local_polymorphic_flag := Some b -let inductive_cumulativity = ref false -let make_inductive_cumulativity b = inductive_cumulativity := b -let is_inductive_cumulativity () = !inductive_cumulativity +let polymorphic_inductive_cumulativity = ref false +let make_polymorphic_inductive_cumulativity b = polymorphic_inductive_cumulativity := b +let is_polymorphic_inductive_cumulativity () = !polymorphic_inductive_cumulativity (** [program_mode] tells that Program mode has been activated, either globally via [Set Program] or locally via the Program command prefix. *) diff --git a/lib/flags.mli b/lib/flags.mli index 388a3ff55..3024c6039 100644 --- a/lib/flags.mli +++ b/lib/flags.mli @@ -114,9 +114,9 @@ val is_universe_polymorphism : unit -> bool val make_polymorphic_flag : bool -> unit val use_polymorphic_flag : unit -> bool -(** Global inductive cumulativity flag. *) -val make_inductive_cumulativity : bool -> unit -val is_inductive_cumulativity : unit -> bool +(** Global polymorphic inductive cumulativity flag. *) +val make_polymorphic_inductive_cumulativity : bool -> unit +val is_polymorphic_inductive_cumulativity : unit -> bool val warn : bool ref val make_warn : bool -> unit diff --git a/lib/minisys.ml b/lib/minisys.ml index 1ed017e48..706f0430c 100644 --- a/lib/minisys.ml +++ b/lib/minisys.ml @@ -44,11 +44,13 @@ let ok_dirname f = (* Check directory can be opened *) let exists_dir dir = + (* See BZ#5391 on windows failing on a trailing (back)slash *) let rec strip_trailing_slash dir = let len = String.length dir in if len > 0 && (dir.[len-1] = '/' || dir.[len-1] = '\\') then strip_trailing_slash (String.sub dir 0 (len-1)) else dir in - try Sys.is_directory (strip_trailing_slash dir) with Sys_error _ -> false + let dir = if Sys.os_type = "Win32" then strip_trailing_slash dir else dir in + try Sys.is_directory dir with Sys_error _ -> false let apply_subdir f path name = (* we avoid all files and subdirs starting by '.' (e.g. .svn) *) diff --git a/library/lib.ml b/library/lib.ml index c6a0253b3..5418003eb 100644 --- a/library/lib.ml +++ b/library/lib.ml @@ -162,6 +162,13 @@ let find_entry_p p = in find !lib_state.lib_stk +let find_entries_p p = + let rec find = function + | [] -> [] + | ent::l -> if p ent then ent::find l else find l + in + find !lib_state.lib_stk + let split_lib_gen test = let rec collect after equal = function | hd::before when test hd -> collect after (hd::equal) before @@ -328,16 +335,18 @@ let start_compilation s mp = lib_state := { !lib_state with comp_name = Some s; path_prefix = prefix } +let open_blocks_message es = + let open_block_name = function + | oname, OpenedSection _ -> str "section " ++ pr_id (basename (fst oname)) + | oname, OpenedModule (ty,_,_,_) -> str (module_kind ty) ++ spc () ++ pr_id (basename (fst oname)) + | _ -> assert false in + str "The " ++ pr_enum open_block_name es ++ spc () ++ + str "need" ++ str (if List.length es == 1 then "s" else "") ++ str " to be closed." + let end_compilation_checks dir = - let _ = - try match snd (find_entry_p is_opening_node) with - | OpenedSection _ -> user_err Pp.(str "There are some open sections.") - | OpenedModule (ty,_,_,_) -> - user_err ~hdr:"Lib.end_compilation_checks" - (str "There are some open " ++ str (module_kind ty) ++ str "s.") - | _ -> assert false - with Not_found -> () - in + let _ = match find_entries_p is_opening_node with + | [] -> () + | es -> user_err ~hdr:"Lib.end_compilation_checks" (open_blocks_message es) in let is_opening_lib = function _,CompilingLibrary _ -> true | _ -> false in let oname = diff --git a/parsing/g_vernac.ml4 b/parsing/g_vernac.ml4 index 3d29fca77..93a778274 100644 --- a/parsing/g_vernac.ml4 +++ b/parsing/g_vernac.ml4 @@ -168,8 +168,13 @@ GEXTEND Gram let indl=List.map (fun ((a,b,c,d),e) -> ((a,b,c,k,d),e)) indl in let cum = match cum with - Some b -> b - | None -> Flags.is_inductive_cumulativity () + Some true -> LocalCumulativity + | Some false -> LocalNonCumulativity + | None -> + if Flags.is_polymorphic_inductive_cumulativity () then + GlobalCumulativity + else + GlobalNonCumulativity in VernacInductive (cum, priv,f,indl) | "Fixpoint"; recs = LIST1 rec_definition SEP "with" -> diff --git a/plugins/firstorder/sequent.ml b/plugins/firstorder/sequent.ml index 5ba98fb58..05194164b 100644 --- a/plugins/firstorder/sequent.ml +++ b/plugins/firstorder/sequent.ml @@ -233,7 +233,7 @@ let extend_with_auto_hints env sigma l seq = let print_cmap map= let print_entry c l s= - let xc=Constrextern.extern_constr false (Global.env ()) Evd.empty c in + let xc=Constrextern.extern_constr false (Global.env ()) Evd.empty (EConstr.of_constr c) in str "| " ++ prlist Printer.pr_global l ++ str " : " ++ diff --git a/plugins/funind/glob_term_to_relation.ml b/plugins/funind/glob_term_to_relation.ml index 8555a0b22..8cf5e8442 100644 --- a/plugins/funind/glob_term_to_relation.ml +++ b/plugins/funind/glob_term_to_relation.ml @@ -1492,7 +1492,7 @@ let do_build_inductive in let msg = str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac (Vernacexpr.VernacInductive(false,false,Decl_kinds.Finite,repacked_rel_inds)) + Ppvernac.pr_vernac (Vernacexpr.VernacInductive(Vernacexpr.GlobalNonCumulativity,false,Decl_kinds.Finite,repacked_rel_inds)) ++ fnl () ++ msg in @@ -1507,7 +1507,7 @@ let do_build_inductive in let msg = str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac (Vernacexpr.VernacInductive(false,false,Decl_kinds.Finite,repacked_rel_inds)) + Ppvernac.pr_vernac (Vernacexpr.VernacInductive(Vernacexpr.GlobalNonCumulativity,false,Decl_kinds.Finite,repacked_rel_inds)) ++ fnl () ++ CErrors.print reraise in diff --git a/plugins/funind/indfun.ml b/plugins/funind/indfun.ml index 89537ad3f..8769f5668 100644 --- a/plugins/funind/indfun.ml +++ b/plugins/funind/indfun.ml @@ -618,7 +618,7 @@ let recompute_binder_list (fixpoint_exprl : (Vernacexpr.fixpoint_expr * Vernacex let fixl,ntns = Command.extract_fixpoint_components false fixpoint_exprl in let ((_,_,typel),_,ctx,_) = Command.interp_fixpoint fixl ntns in let constr_expr_typel = - with_full_print (List.map (Constrextern.extern_constr false (Global.env ()) (Evd.from_ctx ctx))) typel in + with_full_print (List.map (fun c -> Constrextern.extern_constr false (Global.env ()) (Evd.from_ctx ctx) (EConstr.of_constr c))) typel in let fixpoint_exprl_with_new_bl = List.map2 (fun ((lna,(rec_arg_opt,rec_order),bl,ret_typ,opt_body),notation_list) fix_typ -> @@ -855,9 +855,9 @@ let make_graph (f_ref:global_reference) = let sigma = Evd.from_env env in let extern_body,extern_type = with_full_print (fun () -> - (Constrextern.extern_constr false env sigma body, + (Constrextern.extern_constr false env sigma (EConstr.of_constr body), Constrextern.extern_type false env sigma - ((*FIXME*) c_body.const_type) + (EConstr.of_constr (*FIXME*) c_body.const_type) ) ) () diff --git a/plugins/funind/merge.ml b/plugins/funind/merge.ml index 52a82b0e5..3ae922190 100644 --- a/plugins/funind/merge.ml +++ b/plugins/funind/merge.ml @@ -812,13 +812,13 @@ let merge_rec_params_and_arity prms1 prms2 shift (concl:constr) = let typ = glob_constr_to_constr_expr tp in CLocalAssum ([(Loc.tag nme)], Constrexpr_ops.default_binder_kind, typ) :: acc) [] params in - let concl = Constrextern.extern_constr false (Global.env()) Evd.empty concl in + let concl = Constrextern.extern_constr false (Global.env()) Evd.empty (EConstr.of_constr concl) in let arity,_ = List.fold_left (fun (acc,env) decl -> let nm = Context.Rel.Declaration.get_name decl in let c = RelDecl.get_type decl in - let typ = Constrextern.extern_constr false env Evd.empty c in + let typ = Constrextern.extern_constr false env Evd.empty (EConstr.of_constr c) in let newenv = Environ.push_rel (LocalAssum (nm,c)) env in CAst.make @@ CProdN ([[(Loc.tag nm)],Constrexpr_ops.default_binder_kind,typ] , acc) , newenv) (concl,Global.env()) diff --git a/plugins/ltac/g_class.ml4 b/plugins/ltac/g_class.ml4 index dd24aa3db..104977aef 100644 --- a/plugins/ltac/g_class.ml4 +++ b/plugins/ltac/g_class.ml4 @@ -20,7 +20,7 @@ let set_transparency cl b = List.iter (fun r -> let gr = Smartlocate.global_with_alias r in let ev = Tacred.evaluable_of_global_reference (Global.env ()) gr in - Classes.set_typeclass_transparency ev false b) cl + Classes.set_typeclass_transparency ev (Locality.make_section_locality None) b) cl VERNAC COMMAND EXTEND Typeclasses_Unfold_Settings CLASSIFIED AS SIDEFF | [ "Typeclasses" "Transparent" reference_list(cl) ] -> [ diff --git a/plugins/setoid_ring/Ring_tac.v b/plugins/setoid_ring/Ring_tac.v index fc02cef10..329fa0ee8 100644 --- a/plugins/setoid_ring/Ring_tac.v +++ b/plugins/setoid_ring/Ring_tac.v @@ -427,19 +427,37 @@ Tactic Notation "ring_simplify" constr_list(rl) "in" hyp(H):= let t := type of H in let g := fresh "goal" in set (g:= G); - generalize H;clear H; + generalize H; ring_lookup (PackRing Ring_simplify) [] rl t; - intro H; + (* + Correction of bug 1859: + we want to leave H at its initial position + this is obtained by adding a copy of H (H'), + move it just after H, remove H and finally + rename H into H' + *) + let H' := fresh "H" in + intro H'; + move H' after H; + clear H;rename H' into H; unfold g;clear g. -Tactic Notation - "ring_simplify" "["constr_list(lH)"]" constr_list(rl) "in" hyp(H):= +Tactic Notation "ring_simplify" "["constr_list(lH)"]" constr_list(rl) "in" hyp(H):= let G := Get_goal in let t := type of H in let g := fresh "goal" in set (g:= G); - generalize H;clear H; + generalize H; ring_lookup (PackRing Ring_simplify) [lH] rl t; - intro H; - unfold g;clear g. - + (* + Correction of bug 1859: + we want to leave H at its initial position + this is obtained by adding a copy of H (H'), + move it just after H, remove H and finally + rename H into H' + *) + let H' := fresh "H" in + intro H'; + move H' after H; + clear H;rename H' into H; + unfold g;clear g.
\ No newline at end of file diff --git a/pretyping/typeclasses.ml b/pretyping/typeclasses.ml index d4fa266c0..375a8a983 100644 --- a/pretyping/typeclasses.ml +++ b/pretyping/typeclasses.ml @@ -84,8 +84,8 @@ type instance = { is_class: global_reference; is_info: Vernacexpr.hint_info_expr; (* Sections where the instance should be redeclared, - -1 for discard, 0 for none. *) - is_global: int; + None for discard, Some 0 for none. *) + is_global: int option; is_poly: bool; is_impl: global_reference; } @@ -98,9 +98,11 @@ let hint_priority is = is.is_info.Vernacexpr.hint_priority let new_instance cl info glob poly impl = let global = - if glob then Lib.sections_depth () - else -1 + if glob then Some (Lib.sections_depth ()) + else None in + if match global with Some n -> n>0 && isVarRef impl | _ -> false then + CErrors.user_err (Pp.str "Cannot set Global an instance referring to a section variable."); { is_class = cl.cl_impl; is_info = info ; is_global = global ; @@ -350,22 +352,34 @@ let subst_instance (subst, (action, inst)) = action, is_impl = fst (subst_global subst inst.is_impl) } let discharge_instance (_, (action, inst)) = - if inst.is_global <= 0 then None - else Some (action, + match inst.is_global with + | None -> None + | Some n -> + assert (not (isVarRef inst.is_impl)); + Some (action, { inst with - is_global = pred inst.is_global; + is_global = Some (pred n); is_class = Lib.discharge_global inst.is_class; is_impl = Lib.discharge_global inst.is_impl }) -let is_local i = Int.equal i.is_global (-1) +let is_local i = (i.is_global == None) + +let is_local_for_hint i = + match i.is_global with + | None -> true (* i.e. either no Global keyword not in section, or in section *) + | Some n -> n <> 0 (* i.e. in a section, declare the hint as local + since discharge is managed by rebuild_instance which calls again + add_instance_hint; don't ask hints to take discharge into account + itself *) let add_instance check inst = let poly = Global.is_polymorphic inst.is_impl in - add_instance_hint (IsGlobal inst.is_impl) [inst.is_impl] (is_local inst) + let local = is_local_for_hint inst in + add_instance_hint (IsGlobal inst.is_impl) [inst.is_impl] local inst.is_info poly; List.iter (fun (path, pri, c) -> add_instance_hint (IsConstr c) path - (is_local inst) pri poly) + local pri poly) (build_subclasses ~check:(check && not (isVarRef inst.is_impl)) (Global.env ()) (Evd.from_env (Global.env ())) inst.is_impl inst.is_info) @@ -404,6 +418,7 @@ let declare_instance info local glob = let info = Option.default {hint_priority = None; hint_pattern = None} info in match class_of_constr Evd.empty (EConstr.of_constr ty) with | Some (rels, ((tc,_), args) as _cl) -> + assert (not (isVarRef glob) || local); add_instance (new_instance tc info (not local) (Flags.use_polymorphic_flag ()) glob) | None -> () diff --git a/printing/ppvernac.ml b/printing/ppvernac.ml index a68b569cb..4c50c2f36 100644 --- a/printing/ppvernac.ml +++ b/printing/ppvernac.ml @@ -760,7 +760,11 @@ open Decl_kinds | Class _ -> "Class" | Variant -> "Variant" in if p then - let cm = if cum then "Cumulative" else "NonCumulative" in + let cm = + match cum with + | GlobalCumulativity | LocalCumulativity -> "Cumulative" + | GlobalNonCumulativity | LocalNonCumulativity -> "NonCumulative" + in cm ^ " " ^ kind else kind in diff --git a/printing/printer.ml b/printing/printer.ml index c6cf2254f..e9d104b49 100644 --- a/printing/printer.ml +++ b/printing/printer.ml @@ -79,23 +79,23 @@ let _ = and only names of goal/section variables and rel names that do _not_ occur in the scope of the binder to be printed are avoided. *) -let pr_constr_core goal_concl_style env sigma t = +let pr_econstr_core goal_concl_style env sigma t = pr_constr_expr (extern_constr goal_concl_style env sigma t) -let pr_lconstr_core goal_concl_style env sigma t = +let pr_leconstr_core goal_concl_style env sigma t = pr_lconstr_expr (extern_constr goal_concl_style env sigma t) -let pr_lconstr_env env = pr_lconstr_core false env -let pr_constr_env env = pr_constr_core false env +let pr_lconstr_env env sigma c = pr_leconstr_core false env sigma (EConstr.of_constr c) +let pr_constr_env env sigma c = pr_econstr_core false env sigma (EConstr.of_constr c) let _ = Hook.set Refine.pr_constr pr_constr_env -let pr_lconstr_goal_style_env env = pr_lconstr_core true env -let pr_constr_goal_style_env env = pr_constr_core true env +let pr_lconstr_goal_style_env env sigma c = pr_leconstr_core true env sigma (EConstr.of_constr c) +let pr_constr_goal_style_env env sigma c = pr_econstr_core true env sigma (EConstr.of_constr c) let pr_open_lconstr_env env sigma (_,c) = pr_lconstr_env env sigma c let pr_open_constr_env env sigma (_,c) = pr_constr_env env sigma c -let pr_leconstr_env env sigma c = pr_lconstr_env env sigma (EConstr.to_constr sigma c) -let pr_econstr_env env sigma c = pr_constr_env env sigma (EConstr.to_constr sigma c) +let pr_leconstr_env env sigma c = pr_leconstr_core false env sigma c +let pr_econstr_env env sigma c = pr_econstr_core false env sigma c (* NB do not remove the eta-redexes! Global.env() has side-effects... *) let pr_lconstr t = @@ -128,13 +128,13 @@ let pr_lconstr_under_binders c = let (sigma, env) = get_current_context () in pr_lconstr_under_binders_env env sigma c -let pr_type_core goal_concl_style env sigma t = +let pr_etype_core goal_concl_style env sigma t = pr_constr_expr (extern_type goal_concl_style env sigma t) -let pr_ltype_core goal_concl_style env sigma t = +let pr_letype_core goal_concl_style env sigma t = pr_lconstr_expr (extern_type goal_concl_style env sigma t) -let pr_ltype_env env = pr_ltype_core false env -let pr_type_env env = pr_type_core false env +let pr_ltype_env env sigma c = pr_letype_core false env sigma (EConstr.of_constr c) +let pr_type_env env sigma c = pr_etype_core false env sigma (EConstr.of_constr c) let pr_ltype t = let (sigma, env) = get_current_context () in @@ -143,10 +143,9 @@ let pr_type t = let (sigma, env) = get_current_context () in pr_type_env env sigma t -let pr_etype_env env sigma c = pr_type_env env sigma (EConstr.to_constr sigma c) -let pr_letype_env env sigma c = pr_ltype_env env sigma (EConstr.to_constr sigma c) -let pr_goal_concl_style_env env sigma c = - pr_ltype_core true env sigma (EConstr.to_constr sigma c) +let pr_etype_env env sigma c = pr_etype_core false env sigma c +let pr_letype_env env sigma c = pr_letype_core false env sigma c +let pr_goal_concl_style_env env sigma c = pr_letype_core true env sigma c let pr_ljudge_env env sigma j = (pr_leconstr_env env sigma j.uj_val, pr_leconstr_env env sigma j.uj_type) @@ -191,7 +190,7 @@ let pr_constr_pattern t = let pr_sort sigma s = pr_glob_sort (extern_sort sigma s) let _ = Termops.set_print_constr - (fun env sigma t -> pr_lconstr_expr (extern_constr ~lax:true false env sigma (EConstr.Unsafe.to_constr t))) + (fun env sigma t -> pr_lconstr_expr (extern_constr ~lax:true false env sigma t)) let pr_in_comment pr x = str "(* " ++ pr x ++ str " *)" @@ -364,6 +363,7 @@ let pr_named_context env sigma ne_context = ne_context ~init:(mt ())) let pr_rel_context env sigma rel_context = + let rel_context = List.map (fun d -> Termops.map_rel_decl EConstr.of_constr d) rel_context in pr_binders (extern_rel_context None env sigma rel_context) let pr_rel_context_of env sigma = @@ -479,7 +479,8 @@ let pr_transparent_state (ids, csts) = (* display complete goal *) let default_pr_goal gs = - let (g,sigma) = Goal.V82.nf_evar (project gs) (sig_it gs) in + let g = sig_it gs in + let sigma = project gs in let env = Goal.V82.env sigma g in let concl = Goal.V82.concl sigma g in let goal = diff --git a/test-suite/Makefile b/test-suite/Makefile index beb80a3df..78d90aad8 100644 --- a/test-suite/Makefile +++ b/test-suite/Makefile @@ -33,6 +33,7 @@ BIN := $(shell cd ..; pwd)/bin/ coqtop := $(BIN)coqtop -coqlib $(LIB) -boot -q -batch -test-mode -R prerequisite TestSuite coqc := $(BIN)coqc -coqlib $(LIB) -R prerequisite TestSuite coqchk := $(BIN)coqchk -coqlib $(LIB) -R prerequisite TestSuite +coqdoc := $(BIN)coqdoc coqtopbyte := $(BIN)coqtop.byte coqtopload := $(coqtop) -top Top -async-proofs-cache force -load-vernac-source @@ -85,7 +86,8 @@ COMPLEXITY := $(if $(bogomips),complexity) BUGS := bugs/opened bugs/closed VSUBSYSTEMS := prerequisite success failure $(BUGS) output \ - output-modulo-time interactive micromega $(COMPLEXITY) modules stm + output-modulo-time interactive micromega $(COMPLEXITY) modules stm \ + coqdoc # All subsystems SUBSYSTEMS := $(VSUBSYSTEMS) misc bugs ide vio coqchk coq-makefile @@ -153,6 +155,7 @@ summary: $(call summary_dir, "VI tests", vio); \ $(call summary_dir, "Coqchk tests", coqchk); \ $(call summary_dir, "Coq makefile", coq-makefile); \ + $(call summary_dir, "Coqdoc tests", coqdoc); \ nb_success=`find . -name '*.log' -exec tail -n2 '{}' \; | grep -e $(log_success) | wc -l`; \ nb_failure=`find . -name '*.log' -exec tail -n2 '{}' \; | grep -e $(log_failure) | wc -l`; \ nb_tests=`expr $$nb_success + $$nb_failure`; \ @@ -456,6 +459,8 @@ ide : $(patsubst %.fake,%.fake.log,$(wildcard ide/*.fake)) fi; \ } > "$@" +# vio compilation + vio: $(patsubst %.v,%.vio.log,$(wildcard vio/*.v)) %.vio.log:%.v @@ -473,6 +478,8 @@ vio: $(patsubst %.v,%.vio.log,$(wildcard vio/*.v)) fi; \ } > "$@" +# coqchk + coqchk: $(patsubst %.v,%.chk.log,$(wildcard coqchk/*.v)) %.chk.log:%.v @@ -489,6 +496,8 @@ coqchk: $(patsubst %.v,%.chk.log,$(wildcard coqchk/*.v)) fi; \ } > "$@" +# coq_makefile + coq-makefile: $(patsubst %/run.sh,%.log,$(wildcard coq-makefile/*/run.sh)) coq-makefile/%.log : coq-makefile/%/run.sh @@ -505,3 +514,27 @@ coq-makefile/%.log : coq-makefile/%/run.sh echo " $<...Error!"; \ fi; \ ) > "$@" + +# coqdoc + +coqdoc: $(patsubst %.sh,%.log,$(wildcard coqdoc/*.sh)) + +$(addsuffix .log,$(wildcard coqdoc/*.v)): %.v.log: %.v %.html.out %.tex.out $(PREREQUISITELOG) + @echo "TEST $< $(call get_coq_prog_args_in_parens,"$<")" + $(HIDE){ \ + echo $(call log_intro,$<); \ + $(coqc) -R coqdoc Coqdoc $* 2>&1; \ + cd coqdoc; \ + f=`basename $*`; \ + $(coqdoc) -R . Coqdoc -coqlib http://coq.inria.fr/stdlib --html $$f.v; \ + $(coqdoc) -R . Coqdoc -coqlib http://coq.inria.fr/stdlib --latex $$f.v; \ + diff -u --strip-trailing-cr $$f.html.out Coqdoc.$$f.html 2>&1; R=$$?; times; \ + grep -v "^%%" Coqdoc.$$f.tex | diff -u --strip-trailing-cr $$f.tex.out - 2>&1; S=$$?; times; \ + if [ $$R = 0 -a $$S = 0 ]; then \ + echo $(log_success); \ + echo " $<...Ok"; \ + else \ + echo $(log_failure); \ + echo " $<...Error! (unexpected output)"; \ + fi; \ + } > "$@" diff --git a/test-suite/bugs/closed/1859.v b/test-suite/bugs/closed/1859.v new file mode 100644 index 000000000..43acfe4ba --- /dev/null +++ b/test-suite/bugs/closed/1859.v @@ -0,0 +1,20 @@ +Require Import Ring. +Require Import ArithRing. + +Ltac ring_simplify_neq := + match goal with + | [ H: ?X <> ?Y |- _ ] => progress ring_simplify X Y in H + end. + +Lemma toto : forall x y, x*1 <> y*1 -> y*1 <> x*1 -> x<>y. +Proof. + intros. + ring_simplify_neq. + ring_simplify_neq. + (* make sure ring_simplify has simplified both hypotheses *) + match goal with + | [ H: context[_*1] |- _ ] => fail 1 + | _ => idtac + end. + auto. +Qed. diff --git a/test-suite/bugs/closed/5598.v b/test-suite/bugs/closed/5598.v new file mode 100644 index 000000000..55fef1a57 --- /dev/null +++ b/test-suite/bugs/closed/5598.v @@ -0,0 +1,8 @@ +(* Checking when discharge of an existing class is possible *) +Section foo. + Context {T} (a : T) (b : T). + Let k := eq_refl a. + Existing Class eq. + Fail Global Existing Instance k. + Existing Instance k. +End foo. diff --git a/test-suite/coqchk/cumulativity.v b/test-suite/coqchk/cumulativity.v index a978f6b90..7906a5b15 100644 --- a/test-suite/coqchk/cumulativity.v +++ b/test-suite/coqchk/cumulativity.v @@ -1,5 +1,5 @@ Set Universe Polymorphism. -Set Inductive Cumulativity. +Set Polymorphic Inductive Cumulativity. Set Printing Universes. Inductive List (A: Type) := nil | cons : A -> List A -> List A. diff --git a/test-suite/coqdoc/bug5648.html.out b/test-suite/coqdoc/bug5648.html.out new file mode 100644 index 000000000..06789c1c1 --- /dev/null +++ b/test-suite/coqdoc/bug5648.html.out @@ -0,0 +1,53 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> +<link href="coqdoc.css" rel="stylesheet" type="text/css" /> +<title>Coqdoc.bug5648</title> +</head> + +<body> + +<div id="page"> + +<div id="header"> +</div> + +<div id="main"> + +<h1 class="libtitle">Library Coqdoc.bug5648</h1> + +<div class="code"> +<span class="id" title="keyword">Lemma</span> <a name="a"><span class="id" title="lemma">a</span></a> : <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a>.<br/> +<span class="id" title="keyword">Proof</span>.<br/> +<span class="id" title="tactic">auto</span>.<br/> +<span class="id" title="keyword">Qed</span>.<br/> + +<br/> +<span class="id" title="keyword">Variant</span> <a name="t"><span class="id" title="inductive">t</span></a> :=<br/> +| <a name="A"><span class="id" title="constructor">A</span></a> | <a name="Add"><span class="id" title="constructor">Add</span></a> | <a name="G"><span class="id" title="constructor">G</span></a> | <a name="Goal"><span class="id" title="constructor">Goal</span></a> | <a name="L"><span class="id" title="constructor">L</span></a> | <a name="Lemma"><span class="id" title="constructor">Lemma</span></a> | <a name="P"><span class="id" title="constructor">P</span></a> | <a name="Proof"><span class="id" title="constructor">Proof</span></a> .<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="d"><span class="id" title="definition">d</span></a> <span class="id" title="var">x</span> :=<br/> + <span class="id" title="keyword">match</span> <a class="idref" href="Coqdoc.bug5648.html#x"><span class="id" title="variable">x</span></a> <span class="id" title="keyword">with</span><br/> + | <a class="idref" href="Coqdoc.bug5648.html#A"><span class="id" title="constructor">A</span></a> => 0<br/> + | <a class="idref" href="Coqdoc.bug5648.html#Add"><span class="id" title="constructor">Add</span></a> => 1<br/> + | <a class="idref" href="Coqdoc.bug5648.html#G"><span class="id" title="constructor">G</span></a> => 2<br/> + | <a class="idref" href="Coqdoc.bug5648.html#Goal"><span class="id" title="constructor">Goal</span></a> => 3<br/> + | <a class="idref" href="Coqdoc.bug5648.html#L"><span class="id" title="constructor">L</span></a> => 4<br/> + | <a class="idref" href="Coqdoc.bug5648.html#Lemma"><span class="id" title="constructor">Lemma</span></a> => 5<br/> + | <a class="idref" href="Coqdoc.bug5648.html#P"><span class="id" title="constructor">P</span></a> => 6<br/> + | <a class="idref" href="Coqdoc.bug5648.html#Proof"><span class="id" title="constructor">Proof</span></a> => 7<br/> + <span class="id" title="keyword">end</span>.<br/> +</div> +</div> + +<div id="footer"> +<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> +</div> + +</div> + +</body> +</html>
\ No newline at end of file diff --git a/test-suite/coqdoc/bug5648.tex.out b/test-suite/coqdoc/bug5648.tex.out new file mode 100644 index 000000000..b0b732eff --- /dev/null +++ b/test-suite/coqdoc/bug5648.tex.out @@ -0,0 +1,49 @@ +\documentclass[12pt]{report} +\usepackage[]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{fullpage} +\usepackage{coqdoc} +\usepackage{amsmath,amssymb} +\usepackage{url} +\begin{document} +\coqlibrary{Coqdoc.bug5648}{Library }{Coqdoc.bug5648} + +\begin{coqdoccode} +\coqdocnoindent +\coqdockw{Lemma} \coqdef{Coqdoc.bug5648.a}{a}{\coqdoclemma{a}} : \coqexternalref{True}{http://coq.inria.fr/stdlib/Coq.Init.Logic}{\coqdocinductive{True}}.\coqdoceol +\coqdocnoindent +\coqdockw{Proof}.\coqdoceol +\coqdocnoindent +\coqdoctac{auto}.\coqdoceol +\coqdocnoindent +\coqdockw{Qed}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Variant} \coqdef{Coqdoc.bug5648.t}{t}{\coqdocinductive{t}} :=\coqdoceol +\coqdocnoindent +\ensuremath{|} \coqdef{Coqdoc.bug5648.A}{A}{\coqdocconstructor{A}} \ensuremath{|} \coqdef{Coqdoc.bug5648.Add}{Add}{\coqdocconstructor{Add}} \ensuremath{|} \coqdef{Coqdoc.bug5648.G}{G}{\coqdocconstructor{G}} \ensuremath{|} \coqdef{Coqdoc.bug5648.Goal}{Goal}{\coqdocconstructor{Goal}} \ensuremath{|} \coqdef{Coqdoc.bug5648.L}{L}{\coqdocconstructor{L}} \ensuremath{|} \coqdef{Coqdoc.bug5648.Lemma}{Lemma}{\coqdocconstructor{Lemma}} \ensuremath{|} \coqdef{Coqdoc.bug5648.P}{P}{\coqdocconstructor{P}} \ensuremath{|} \coqdef{Coqdoc.bug5648.Proof}{Proof}{\coqdocconstructor{Proof}} .\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.bug5648.d}{d}{\coqdocdefinition{d}} \coqdocvar{x} :=\coqdoceol +\coqdocindent{1.00em} +\coqdockw{match} \coqdocvariable{x} \coqdockw{with}\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.A}{\coqdocconstructor{A}} \ensuremath{\Rightarrow} 0\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.Add}{\coqdocconstructor{Add}} \ensuremath{\Rightarrow} 1\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.G}{\coqdocconstructor{G}} \ensuremath{\Rightarrow} 2\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.Goal}{\coqdocconstructor{Goal}} \ensuremath{\Rightarrow} 3\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.L}{\coqdocconstructor{L}} \ensuremath{\Rightarrow} 4\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.Lemma}{\coqdocconstructor{Lemma}} \ensuremath{\Rightarrow} 5\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.P}{\coqdocconstructor{P}} \ensuremath{\Rightarrow} 6\coqdoceol +\coqdocindent{1.00em} +\ensuremath{|} \coqref{Coqdoc.bug5648.Proof}{\coqdocconstructor{Proof}} \ensuremath{\Rightarrow} 7\coqdoceol +\coqdocindent{1.00em} +\coqdockw{end}.\coqdoceol +\end{coqdoccode} +\end{document} diff --git a/test-suite/coqdoc/bug5648.v b/test-suite/coqdoc/bug5648.v new file mode 100644 index 000000000..9b62dd1e1 --- /dev/null +++ b/test-suite/coqdoc/bug5648.v @@ -0,0 +1,19 @@ +Lemma a : True. +Proof. +auto. +Qed. + +Variant t := +| A | Add | G | Goal | L | Lemma | P | Proof . + +Definition d x := + match x with + | A => 0 + | Add => 1 + | G => 2 + | Goal => 3 + | L => 4 + | Lemma => 5 + | P => 6 + | Proof => 7 + end. diff --git a/test-suite/coqdoc/links.html.out b/test-suite/coqdoc/links.html.out new file mode 100644 index 000000000..7d7d01c1b --- /dev/null +++ b/test-suite/coqdoc/links.html.out @@ -0,0 +1,206 @@ +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" +"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1" /> +<link href="coqdoc.css" rel="stylesheet" type="text/css" /> +<title>Coqdoc.links</title> +</head> + +<body> + +<div id="page"> + +<div id="header"> +</div> + +<div id="main"> + +<h1 class="libtitle">Library Coqdoc.links</h1> + +<div class="code"> +</div> + +<div class="doc"> +Various checks for coqdoc + +<div class="paragraph"> </div> + +<ul class="doclist"> +<li> symbols should not be inlined in string g + +</li> +<li> links to both kinds of notations in a' should work to the right notation + +</li> +<li> with utf8 option, forall must be unicode + +</li> +<li> splitting between symbols and ident should be correct in a' and c + +</li> +<li> ".." should be rendered correctly + +</li> +</ul> + +</div> +<div class="code"> + +<br/> +<span class="id" title="keyword">Require</span> <span class="id" title="keyword">Import</span> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Strings.String.html#"><span class="id" title="library">String</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="g"><span class="id" title="definition">g</span></a> := "dfjkh""sdfhj forall <> * ~"%<span class="id" title="var">string</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="a"><span class="id" title="definition">a</span></a> (<span class="id" title="var">b</span>: <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>) := <a class="idref" href="Coqdoc.links.html#b"><span class="id" title="variable">b</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="f"><span class="id" title="definition">f</span></a> := <span class="id" title="keyword">forall</span> <span class="id" title="var">C</span>:<span class="id" title="keyword">Prop</span>, <a class="idref" href="Coqdoc.links.html#C"><span class="id" title="variable">C</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">"</span></a>n ++ m" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#plus"><span class="id" title="abbreviation">plus</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span>).<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">"</span></a>n ++ m" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#mult"><span class="id" title="abbreviation">mult</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span>). +<br/> +<span class="id" title="keyword">Notation</span> <a name="6b97e27793a3d22f5c0d1dd63170fd68"><span class="id" title="notation">"</span></a>n ** m" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#plus"><span class="id" title="abbreviation">plus</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 60).<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="3e01fbae4590c7b7699ff99ce61580e1"><span class="id" title="notation">"</span></a>n ▵ m" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#plus"><span class="id" title="abbreviation">plus</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 60).<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">"</span></a>n '_' ++ 'x' m" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#plus"><span class="id" title="abbreviation">plus</span></a> <span class="id" title="var">n</span> <span class="id" title="var">m</span>) (<span class="id" title="tactic">at</span> <span class="id" title="keyword">level</span> 3).<br/> + +<br/> +<span class="id" title="keyword">Inductive</span> <a name="eq"><span class="id" title="inductive">eq</span></a> (<span class="id" title="var">A</span>:<span class="id" title="keyword">Type</span>) (<span class="id" title="var">x</span>:<a class="idref" href="Coqdoc.links.html#A"><span class="id" title="variable">A</span></a>) : <span class="id" title="var">A</span> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Logic.html#d43e996736952df71ebeeae74d10a287"><span class="id" title="notation">-></span></a> <span class="id" title="keyword">Prop</span> := <a name="eq_refl"><span class="id" title="constructor">eq_refl</span></a> : <a class="idref" href="Coqdoc.links.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="Coqdoc.links.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> <a class="idref" href="Coqdoc.links.html#x"><span class="id" title="variable">x</span></a> <a class="idref" href="Coqdoc.links.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:></span></a><a class="idref" href="Coqdoc.links.html#A"><span class="id" title="variable">A</span></a><br/> +<br/> +<span class="id" title="keyword">where</span> <a name="8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">"</span></a>x = y :> A" := (@<a class="idref" href="Coqdoc.links.html#eq"><span class="id" title="variable">eq</span></a> <span class="id" title="var">A</span> <span class="id" title="var">x</span> <span class="id" title="var">y</span>) : <span class="id" title="var">type_scope</span>.<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="eq0"><span class="id" title="definition">eq0</span></a> := 0 <a class="idref" href="Coqdoc.links.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">=</span></a> 0 <a class="idref" href="Coqdoc.links.html#8f9364556521ebb498093f28eea2240f"><span class="id" title="notation">:></span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="548d1059c499c9b2a9b95b07e68c2090"><span class="id" title="notation">"</span></a>( x # y ; .. ; z )" := (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#pair"><span class="id" title="constructor">pair</span></a> .. (<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#pair"><span class="id" title="constructor">pair</span></a> <span class="id" title="var">x</span> <span class="id" title="var">y</span>) .. <span class="id" title="var">z</span>).<br/> + +<br/> +<span class="id" title="keyword">Definition</span> <a name="9f5a1d89cbd4d38f5e289576db7123d1"><span class="id" title="definition">b_α</span></a> := <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a><a class="idref" href="Coqdoc.links.html#548d1059c499c9b2a9b95b07e68c2090"><span class="id" title="notation">(</span></a>0<a class="idref" href="Coqdoc.links.html#548d1059c499c9b2a9b95b07e68c2090"><span class="id" title="notation">#</span></a>0<a class="idref" href="Coqdoc.links.html#548d1059c499c9b2a9b95b07e68c2090"><span class="id" title="notation">;</span></a>0<a class="idref" href="Coqdoc.links.html#548d1059c499c9b2a9b95b07e68c2090"><span class="id" title="notation">)</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">,</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">(</span></a>0 <a class="idref" href="Coqdoc.links.html#6b97e27793a3d22f5c0d1dd63170fd68"><span class="id" title="notation">**</span></a> 0<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#44400027531d4bc3f586a1997dc874c0"><span class="id" title="notation">))</span></a>.<br/> + +<br/> +<span class="id" title="keyword">Notation</span> <a name="h"><span class="id" title="abbreviation">h</span></a> := <a class="idref" href="Coqdoc.links.html#a"><span class="id" title="definition">a</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Section</span> <a name="test"><span class="id" title="section">test</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Variables</span> <a name="test.b'"><span class="id" title="variable">b'</span></a> <a name="test.b2"><span class="id" title="variable">b2</span></a>: <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Notation</span> <a name="4ab0449b36c75cf94e08c5822ea83e3d"><span class="id" title="notation">"</span></a>n + m" := (<span class="id" title="var">n</span> <a class="idref" href="Coqdoc.links.html#3e01fbae4590c7b7699ff99ce61580e1"><span class="id" title="notation">▵</span></a> <span class="id" title="var">m</span>) : <span class="id" title="var">my_scope</span>.<br/> + +<br/> + <span class="id" title="keyword">Delimit</span> <span class="id" title="keyword">Scope</span> <span class="id" title="var">my_scope</span> <span class="id" title="keyword">with</span> <span class="id" title="var">my</span>.<br/> + +<br/> + <span class="id" title="keyword">Notation</span> <a name="l"><span class="id" title="abbreviation">l</span></a> := 0.<br/> + +<br/> + <span class="id" title="keyword">Definition</span> <a name="ab410a966ac148e9b78c65c6cdf301fd"><span class="id" title="definition">α</span></a> := (0 <a class="idref" href="Coqdoc.links.html#4ab0449b36c75cf94e08c5822ea83e3d"><span class="id" title="notation">+</span></a> <a class="idref" href="Coqdoc.links.html#l"><span class="id" title="abbreviation">l</span></a>)%<span class="id" title="var">my</span>.<br/> + +<br/> + <span class="id" title="keyword">Definition</span> <a name="a'"><span class="id" title="definition">a'</span></a> <span class="id" title="var">b</span> := <a class="idref" href="Coqdoc.links.html#test.b'"><span class="id" title="variable">b'</span></a><a class="idref" href="Coqdoc.links.html#1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">++</span></a>0<a class="idref" href="Coqdoc.links.html#1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">++</span></a><a class="idref" href="Coqdoc.links.html#test.b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">_</span></a> <a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">++</span></a><a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">x</span></a> <a class="idref" href="Coqdoc.links.html#b"><span class="id" title="variable">b</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Definition</span> <a name="c"><span class="id" title="definition">c</span></a> := <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">{</span></a><a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">}+{</span></a><a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Logic.html#True"><span class="id" title="inductive">True</span></a><a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Specif.html#5bf2050e90b21ebc82dc5463d1ba338e"><span class="id" title="notation">}</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Definition</span> <a name="d"><span class="id" title="definition">d</span></a> := (1<a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a>2)%<span class="id" title="var">nat</span>.<br/> + +<br/> + <span class="id" title="keyword">Lemma</span> <a name="e"><span class="id" title="lemma">e</span></a> : <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#3dcaec3b772747610227247939f96b01"><span class="id" title="notation">+</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> + <span class="id" title="var">Admitted</span>.<br/> + +<br/> + <span class="id" title="keyword">End</span> <a class="idref" href="Coqdoc.links.html#test"><span class="id" title="section">test</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Section</span> <a name="test2"><span class="id" title="section">test2</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Variables</span> <a name="test2.b'"><span class="id" title="variable">b'</span></a>: <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Section</span> <a name="test2.test"><span class="id" title="section">test</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Variables</span> <a name="test2.test.b2"><span class="id" title="variable">b2</span></a>: <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#nat"><span class="id" title="inductive">nat</span></a>.<br/> + +<br/> + <span class="id" title="keyword">Definition</span> <a name="a''"><span class="id" title="definition">a''</span></a> <span class="id" title="var">b</span> := <a class="idref" href="Coqdoc.links.html#test2.b'"><span class="id" title="variable">b'</span></a> <a class="idref" href="Coqdoc.links.html#1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">++</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Datatypes.html#O"><span class="id" title="constructor">O</span></a> <a class="idref" href="Coqdoc.links.html#1a1c7f13320341c3638e9edcc3e6389d"><span class="id" title="notation">++</span></a> <a class="idref" href="Coqdoc.links.html#test2.test.b2"><span class="id" title="variable">b2</span></a> <a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">_</span></a> <a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">++</span></a> <a class="idref" href="Coqdoc.links.html#347f39a83bf7d45676cff54fd7e8966f"><span class="id" title="notation">x</span></a> <a class="idref" href="Coqdoc.links.html#b"><span class="id" title="variable">b</span></a> <a class="idref" href="http://coq.inria.fr/stdlib/Coq.Init.Peano.html#b3eea360671e1b32b18a26e15b3aace3"><span class="id" title="notation">+</span></a> <a class="idref" href="Coqdoc.links.html#h"><span class="id" title="abbreviation">h</span></a> 0.<br/> + +<br/> + <span class="id" title="keyword">End</span> <a class="idref" href="Coqdoc.links.html#test2.test"><span class="id" title="section">test</span></a>.<br/> + +<br/> + <span class="id" title="keyword">End</span> <a class="idref" href="Coqdoc.links.html#test2"><span class="id" title="section">test2</span></a>.<br/> + +<br/> +</div> + +<div class="doc"> +skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +<div class="paragraph"> </div> + + skip +</div> +<div class="code"> + +<br/> +</div> +</div> + +<div id="footer"> +<hr/><a href="index.html">Index</a><hr/>This page has been generated by <a href="http://coq.inria.fr/">coqdoc</a> +</div> + +</div> + +</body> +</html>
\ No newline at end of file diff --git a/test-suite/coqdoc/links.tex.out b/test-suite/coqdoc/links.tex.out new file mode 100644 index 000000000..844fb3031 --- /dev/null +++ b/test-suite/coqdoc/links.tex.out @@ -0,0 +1,162 @@ +\documentclass[12pt]{report} +\usepackage[]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{fullpage} +\usepackage{coqdoc} +\usepackage{amsmath,amssymb} +\usepackage{url} +\begin{document} +\coqlibrary{Coqdoc.links}{Library }{Coqdoc.links} + +\begin{coqdoccode} +\end{coqdoccode} +Various checks for coqdoc + + + +\begin{itemize} +\item symbols should not be inlined in string g + +\item links to both kinds of notations in a' should work to the right notation + +\item with utf8 option, forall must be unicode + +\item splitting between symbols and ident should be correct in a' and c + +\item ``..'' should be rendered correctly + +\end{itemize} +\begin{coqdoccode} +\coqdocemptyline +\coqdocnoindent +\coqdockw{Require} \coqdockw{Import} \coqexternalref{}{http://coq.inria.fr/stdlib/Coq.Strings.String}{\coqdoclibrary{String}}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.links.g}{g}{\coqdocdefinition{g}} := "dfjkh""sdfhj forall <> * \~{}"\%\coqdocvar{string}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.links.a}{a}{\coqdocdefinition{a}} (\coqdocvar{b}: \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}) := \coqdocvariable{b}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.links.f}{f}{\coqdocdefinition{f}} := \coqdockw{\ensuremath{\forall}} \coqdocvar{C}:\coqdockw{Prop}, \coqdocvariable{C}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::x '++' x}{"}{"}n ++ m" := (\coqexternalref{plus}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocabbreviation{plus}} \coqdocvar{n} \coqdocvar{m}).\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::x '++' x}{"}{"}n ++ m" := (\coqexternalref{mult}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocabbreviation{mult}} \coqdocvar{n} \coqdocvar{m}). \coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::x '**' x}{"}{"}n ** m" := (\coqexternalref{plus}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocabbreviation{plus}} \coqdocvar{n} \coqdocvar{m}) (\coqdoctac{at} \coqdockw{level} 60).\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::x 'xE2x96xB5' x}{"}{"}n ▵ m" := (\coqexternalref{plus}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocabbreviation{plus}} \coqdocvar{n} \coqdocvar{m}) (\coqdoctac{at} \coqdockw{level} 60).\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::x ''' ''' '++' 'x' x}{"}{"}n '\_' ++ 'x' m" := (\coqexternalref{plus}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocabbreviation{plus}} \coqdocvar{n} \coqdocvar{m}) (\coqdoctac{at} \coqdockw{level} 3).\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Inductive} \coqdef{Coqdoc.links.eq}{eq}{\coqdocinductive{eq}} (\coqdocvar{A}:\coqdockw{Type}) (\coqdocvar{x}:\coqdocvariable{A}) : \coqdocvar{A} \coqexternalref{:type scope:x '->' x}{http://coq.inria.fr/stdlib/Coq.Init.Logic}{\coqdocnotation{\ensuremath{\rightarrow}}} \coqdockw{Prop} := \coqdef{Coqdoc.links.eq refl}{eq\_refl}{\coqdocconstructor{eq\_refl}} : \coqdocvariable{x} \coqref{Coqdoc.links.:type scope:x '=' x ':>' x}{\coqdocnotation{=}} \coqdocvariable{x} \coqref{Coqdoc.links.:type scope:x '=' x ':>' x}{\coqdocnotation{:>}}\coqdocvariable{A}\coqdoceol +\coqdocnoindent +\coqdoceol +\coqdocnoindent +\coqdockw{where} \coqdef{Coqdoc.links.:type scope:x '=' x ':>' x}{"}{"}x = y :> A" := (@\coqdocvariable{eq} \coqdocvar{A} \coqdocvar{x} \coqdocvar{y}) : \coqdocvar{type\_scope}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.links.eq0}{eq0}{\coqdocdefinition{eq0}} := 0 \coqref{Coqdoc.links.:type scope:x '=' x ':>' x}{\coqdocnotation{=}} 0 \coqref{Coqdoc.links.:type scope:x '=' x ':>' x}{\coqdocnotation{:>}} \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.::'(' x 'x23' x ';' '..' ';' x ')'}{"}{"}( x \# y ; .. ; z )" := (\coqexternalref{pair}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocconstructor{pair}} .. (\coqexternalref{pair}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocconstructor{pair}} \coqdocvar{x} \coqdocvar{y}) .. \coqdocvar{z}).\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Definition} \coqdef{Coqdoc.links.b xCExB1}{b\_α}{\coqdocdefinition{b\_α}} := \coqexternalref{:core scope:'(' x ',' x ',' '..' ',' x ')'}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocnotation{(}}\coqref{Coqdoc.links.::'(' x 'x23' x ';' '..' ';' x ')'}{\coqdocnotation{(}}0\coqref{Coqdoc.links.::'(' x 'x23' x ';' '..' ';' x ')'}{\coqdocnotation{\#}}0\coqref{Coqdoc.links.::'(' x 'x23' x ';' '..' ';' x ')'}{\coqdocnotation{;}}0\coqref{Coqdoc.links.::'(' x 'x23' x ';' '..' ';' x ')'}{\coqdocnotation{)}} \coqexternalref{:core scope:'(' x ',' x ',' '..' ',' x ')'}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocnotation{,}} \coqexternalref{:core scope:'(' x ',' x ',' '..' ',' x ')'}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocnotation{(}}0 \coqref{Coqdoc.links.::x '**' x}{\coqdocnotation{**}} 0\coqexternalref{:core scope:'(' x ',' x ',' '..' ',' x ')'}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocnotation{))}}.\coqdoceol +\coqdocemptyline +\coqdocnoindent +\coqdockw{Notation} \coqdef{Coqdoc.links.h}{h}{\coqdocabbreviation{h}} := \coqref{Coqdoc.links.a}{\coqdocdefinition{a}}.\coqdoceol +\coqdocemptyline +\coqdocindent{1.00em} +\coqdockw{Section} \coqdef{Coqdoc.links.test}{test}{\coqdocsection{test}}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Variables} \coqdef{Coqdoc.links.test.b'}{b'}{\coqdocvariable{b'}} \coqdef{Coqdoc.links.test.b2}{b2}{\coqdocvariable{b2}}: \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Notation} \coqdef{Coqdoc.links.test.:my scope:x '+' x}{"}{"}n + m" := (\coqdocvar{n} \coqref{Coqdoc.links.::x 'xE2x96xB5' x}{\coqdocnotation{▵}} \coqdocvar{m}) : \coqdocvar{my\_scope}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Delimit} \coqdockw{Scope} \coqdocvar{my\_scope} \coqdockw{with} \coqdocvar{my}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Notation} \coqdef{Coqdoc.links.l}{l}{\coqdocabbreviation{l}} := 0.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Definition} \coqdef{Coqdoc.links.xCExB1}{α}{\coqdocdefinition{α}} := (0 \coqref{Coqdoc.links.test.:my scope:x '+' x}{\coqdocnotation{+}} \coqref{Coqdoc.links.l}{\coqdocabbreviation{l}})\%\coqdocvar{my}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Definition} \coqdef{Coqdoc.links.a'}{a'}{\coqdocdefinition{a'}} \coqdocvar{b} := \coqdocvariable{b'}\coqref{Coqdoc.links.::x '++' x}{\coqdocnotation{++}}0\coqref{Coqdoc.links.::x '++' x}{\coqdocnotation{++}}\coqdocvariable{b2} \coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{\_}} \coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{++}}\coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{x}} \coqdocvariable{b}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Definition} \coqdef{Coqdoc.links.c}{c}{\coqdocdefinition{c}} := \coqexternalref{:type scope:'x7B' x 'x7D' '+' 'x7B' x 'x7D'}{http://coq.inria.fr/stdlib/Coq.Init.Specif}{\coqdocnotation{\{}}\coqexternalref{True}{http://coq.inria.fr/stdlib/Coq.Init.Logic}{\coqdocinductive{True}}\coqexternalref{:type scope:'x7B' x 'x7D' '+' 'x7B' x 'x7D'}{http://coq.inria.fr/stdlib/Coq.Init.Specif}{\coqdocnotation{\}+\{}}\coqexternalref{True}{http://coq.inria.fr/stdlib/Coq.Init.Logic}{\coqdocinductive{True}}\coqexternalref{:type scope:'x7B' x 'x7D' '+' 'x7B' x 'x7D'}{http://coq.inria.fr/stdlib/Coq.Init.Specif}{\coqdocnotation{\}}}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Definition} \coqdef{Coqdoc.links.d}{d}{\coqdocdefinition{d}} := (1\coqexternalref{:nat scope:x '+' x}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocnotation{+}}2)\%\coqdocvar{nat}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Lemma} \coqdef{Coqdoc.links.e}{e}{\coqdoclemma{e}} : \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}} \coqexternalref{:type scope:x '+' x}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocnotation{+}} \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}.\coqdoceol +\coqdocindent{2.00em} +\coqdocvar{Admitted}.\coqdoceol +\coqdocemptyline +\coqdocindent{1.00em} +\coqdockw{End} \coqref{Coqdoc.links.test}{\coqdocsection{test}}.\coqdoceol +\coqdocemptyline +\coqdocindent{1.00em} +\coqdockw{Section} \coqdef{Coqdoc.links.test2}{test2}{\coqdocsection{test2}}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Variables} \coqdef{Coqdoc.links.test2.b'}{b'}{\coqdocvariable{b'}}: \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{Section} \coqdef{Coqdoc.links.test2.test}{test}{\coqdocsection{test}}.\coqdoceol +\coqdocemptyline +\coqdocindent{3.00em} +\coqdockw{Variables} \coqdef{Coqdoc.links.test2.test.b2}{b2}{\coqdocvariable{b2}}: \coqexternalref{nat}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocinductive{nat}}.\coqdoceol +\coqdocemptyline +\coqdocindent{3.00em} +\coqdockw{Definition} \coqdef{Coqdoc.links.a''}{a'{}'}{\coqdocdefinition{a'{}'}} \coqdocvar{b} := \coqdocvariable{b'} \coqref{Coqdoc.links.::x '++' x}{\coqdocnotation{++}} \coqexternalref{O}{http://coq.inria.fr/stdlib/Coq.Init.Datatypes}{\coqdocconstructor{O}} \coqref{Coqdoc.links.::x '++' x}{\coqdocnotation{++}} \coqdocvariable{b2} \coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{\_}} \coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{++}} \coqref{Coqdoc.links.::x ''' ''' '++' 'x' x}{\coqdocnotation{x}} \coqdocvariable{b} \coqexternalref{:nat scope:x '+' x}{http://coq.inria.fr/stdlib/Coq.Init.Peano}{\coqdocnotation{+}} \coqref{Coqdoc.links.h}{\coqdocabbreviation{h}} 0.\coqdoceol +\coqdocemptyline +\coqdocindent{2.00em} +\coqdockw{End} \coqref{Coqdoc.links.test2.test}{\coqdocsection{test}}.\coqdoceol +\coqdocemptyline +\coqdocindent{1.00em} +\coqdockw{End} \coqref{Coqdoc.links.test2}{\coqdocsection{test2}}.\coqdoceol +\coqdocemptyline +\end{coqdoccode} +skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip + + skip \begin{coqdoccode} +\coqdocemptyline +\end{coqdoccode} +\end{document} diff --git a/test-suite/output/UnclosedBlocks.out b/test-suite/output/UnclosedBlocks.out new file mode 100644 index 000000000..b83e94ad4 --- /dev/null +++ b/test-suite/output/UnclosedBlocks.out @@ -0,0 +1,3 @@ + +Error: The section Baz, module type Bar and module Foo need to be closed. + diff --git a/test-suite/output/UnclosedBlocks.v b/test-suite/output/UnclosedBlocks.v new file mode 100644 index 000000000..854bd6a6d --- /dev/null +++ b/test-suite/output/UnclosedBlocks.v @@ -0,0 +1,8 @@ +(* -*- mode: coq; coq-prog-args: ("-compile" "UnclosedBlocks.v") *) +Module Foo. + Module Closed. + End Closed. + Module Type Bar. + Section Baz. + (* end-of-compilation error message reports unclosed sections, blocks, and + module types *) diff --git a/test-suite/success/cumulativity.v b/test-suite/success/cumulativity.v index ebf817cfc..0ee85712e 100644 --- a/test-suite/success/cumulativity.v +++ b/test-suite/success/cumulativity.v @@ -1,5 +1,11 @@ +Polymorphic Cumulative Inductive T1 := t1 : T1. +Fail Monomorphic Cumulative Inductive T2 := t2 : T2. + +Polymorphic Cumulative Record R1 := { r1 : T1 }. +Fail Monomorphic Cumulative Inductive R2 := {r2 : T1}. + Set Universe Polymorphism. -Set Inductive Cumulativity. +Set Polymorphic Inductive Cumulativity. Set Printing Universes. Inductive List (A: Type) := nil | cons : A -> List A -> List A. @@ -62,4 +68,33 @@ End subtyping_test. Record A : Type := { a :> Type; }. -Record B (X : A) : Type := { b : X; }.
\ No newline at end of file +Record B (X : A) : Type := { b : X; }. + +NonCumulative Inductive NCList (A: Type) + := ncnil | nccons : A -> NCList A -> NCList A. + +Section NCListLift. + Universe i j. + + Constraint i < j. + + Fail Definition LiftNCL {A} : NCList@{i} A -> NCList@{j} A := fun x => x. + +End NCListLift. + +Inductive eq@{i} {A : Type@{i}} (x : A) : A -> Type@{i} := eq_refl : eq x x. + +Definition funext_type@{a b e} (A : Type@{a}) (B : A -> Type@{b}) + := forall f g : (forall a, B a), + (forall x, eq@{e} (f x) (g x)) + -> eq@{e} f g. + +Section down. + Universes a b e e'. + Constraint e' < e. + Lemma funext_down {A B} + : @funext_type@{a b e} A B -> @funext_type@{a b e'} A B. + Proof. + intros H f g Hfg. exact (H f g Hfg). + Defined. +End down. diff --git a/tools/CoqMakefile.in b/tools/CoqMakefile.in index e54ea45d4..9f891afe5 100644 --- a/tools/CoqMakefile.in +++ b/tools/CoqMakefile.in @@ -63,11 +63,11 @@ VERBOSE ?= # Time the Coq process (set to non empty), and how (see default value) TIMED?= TIMECMD?= -# Use /usr/bin/time on linux, gtime on Mac OS +# Use /usr/bin/env time on linux, gtime on Mac OS TIMEFMT?="$* (real: %e, user: %U, sys: %S, mem: %M ko)" ifneq (,$(TIMED)) -ifeq (0,$(shell /usr/bin/time -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) -STDTIME?=/usr/bin/time -f $(TIMEFMT) +ifeq (0,$(shell /usr/bin/env time -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) +STDTIME?=/usr/bin/env time -f $(TIMEFMT) else ifeq (0,$(shell gtime -f $(TIMEFMT) true >/dev/null 2>/dev/null; echo $$?)) STDTIME?=gtime -f $(TIMEFMT) @@ -76,7 +76,7 @@ STDTIME?=time endif endif else -STDTIME?=/usr/bin/time -f $(TIMEFMT) +STDTIME?=/usr/bin/env time -f $(TIMEFMT) endif # Coq binaries @@ -170,7 +170,7 @@ COQMAKEFILE_VERSION:=@COQ_VERSION@ COQSRCLIBS?= $(foreach d,$(COQ_SRC_SUBDIRS), -I "$(COQLIB)$(d)") -CAMLFLAGS=$(OCAMLLIBS) $(COQSRCLIBS) -I $(CAMLP4LIB) +CAMLFLAGS=$(OCAMLLIBS) $(COQSRCLIBS) -I $(CAMLP4LIB) $(OCAML_API_FLAGS) CAMLLIB:=$(shell "$(OCAMLFIND)" printconf stdlib) diff --git a/tools/coq_makefile.ml b/tools/coq_makefile.ml index 327f53520..0f38d1938 100644 --- a/tools/coq_makefile.ml +++ b/tools/coq_makefile.ml @@ -203,8 +203,12 @@ let generate_conf_coq_config oc args bypass_API = section oc "Coq configuration."; let src_dirs = if bypass_API then Coq_config.all_src_dirs - else Coq_config.api_dirs @ Coq_config.plugins_dirs @ ["-open API"] in + else Coq_config.api_dirs @ Coq_config.plugins_dirs in Envars.print_config ~prefix_var_name:"COQMF_" oc src_dirs; + if bypass_API then + Printf.fprintf oc "OCAML_API_FLAGS=\n" + else + Printf.fprintf oc "OCAML_API_FLAGS=-open API\n"; fprintf oc "COQMF_WINDRIVE=%s\n" (windrive Coq_config.coqlib) ;; diff --git a/tools/coqdoc/index.ml b/tools/coqdoc/index.ml index 8ba615670..1bbf76490 100644 --- a/tools/coqdoc/index.ml +++ b/tools/coqdoc/index.ml @@ -117,7 +117,7 @@ let find_module m = if Hashtbl.mem local_modules m then Local else - try External (Filename.concat (find_external_library m) m) + try External (find_external_library m ^ "/" ^ m) with Not_found -> Unknown diff --git a/tools/coqdoc/output.ml b/tools/coqdoc/output.ml index 5c0d2a39b..d043c4a58 100644 --- a/tools/coqdoc/output.ml +++ b/tools/coqdoc/output.ml @@ -693,25 +693,21 @@ module Html = struct printf "<span class=\"id\" title=\"keyword\">%s</span>" (translate s) let ident s loc = - if is_keyword s then begin - printf "<span class=\"id\" title=\"keyword\">%s</span>" (translate s) - end else begin - try - match loc with - | None -> raise Not_found - | Some loc -> - reference (translate s) (Index.find (get_module false) loc) - with Not_found -> - if is_tactic s then - printf "<span class=\"id\" title=\"tactic\">%s</span>" (translate s) - else - if !Cdglobals.interpolate && !in_doc (* always a var otherwise *) - then - try reference (translate s) (Index.find_string (get_module false) s) - with _ -> Tokens.output_tagged_ident_string s - else - Tokens.output_tagged_ident_string s - end + try + match loc with + | None -> raise Not_found + | Some loc -> + reference (translate s) (Index.find (get_module false) loc) + with Not_found -> + if is_tactic s then + printf "<span class=\"id\" title=\"tactic\">%s</span>" (translate s) + else if is_keyword s then + printf "<span class=\"id\" title=\"keyword\">%s</span>" (translate s) + else if !Cdglobals.interpolate && !in_doc (* always a var otherwise *) then + try reference (translate s) (Index.find_string (get_module false) s) + with Not_found -> Tokens.output_tagged_ident_string s + else + Tokens.output_tagged_ident_string s let proofbox () = printf "<font size=-2>☐</font>" diff --git a/vernac/himsg.ml b/vernac/himsg.ml index 0e5184905..2be10a039 100644 --- a/vernac/himsg.ml +++ b/vernac/himsg.ml @@ -100,17 +100,18 @@ let pr_ljudge_env e s c = let v,t = pr_ljudge_env e s c in (quote v,quote t) (** A canonisation procedure for constr such that comparing there externalisation catches more equalities *) -let canonize_constr c = +let canonize_constr sigma c = (* replaces all the names in binders by [dn] ("default name"), ensures that [alpha]-equivalent terms will have the same externalisation. *) + let open EConstr in let dn = Name.Anonymous in let rec canonize_binders c = - match Term.kind_of_term c with + match EConstr.kind sigma c with | Prod (_,t,b) -> mkProd(dn,t,b) | Lambda (_,t,b) -> mkLambda(dn,t,b) | LetIn (_,u,t,b) -> mkLetIn(dn,u,t,b) - | _ -> Term.map_constr canonize_binders c + | _ -> EConstr.map sigma canonize_binders c in canonize_binders c @@ -118,8 +119,8 @@ let canonize_constr c = let display_eq ~flags env sigma t1 t2 = (* terms are canonized, then their externalisation is compared syntactically *) let open Constrextern in - let t1 = canonize_constr t1 in - let t2 = canonize_constr t2 in + let t1 = canonize_constr sigma t1 in + let t2 = canonize_constr sigma t2 in let ct1 = Flags.with_options flags (fun () -> extern_constr false env sigma t1) () in let ct2 = Flags.with_options flags (fun () -> extern_constr false env sigma t2) () in Constrexpr_ops.constr_expr_eq ct1 ct2 @@ -129,7 +130,7 @@ let display_eq ~flags env sigma t1 t2 = let rec pr_explicit_aux env sigma t1 t2 = function | [] -> (** no specified flags: default. *) - (quote (Printer.pr_lconstr_env env sigma t1), quote (Printer.pr_lconstr_env env sigma t2)) + (quote (Printer.pr_leconstr_env env sigma t1), quote (Printer.pr_leconstr_env env sigma t2)) | flags :: rem -> let equal = display_eq ~flags env sigma t1 t2 in if equal then @@ -153,7 +154,7 @@ let explicit_flags = [print_universes; print_implicits; print_coercions; print_no_symbol] (** and more! *) ] let pr_explicit env sigma t1 t2 = - pr_explicit_aux env sigma (EConstr.to_constr sigma t1) (EConstr.to_constr sigma t2) explicit_flags + pr_explicit_aux env sigma t1 t2 explicit_flags let pr_db env i = try diff --git a/vernac/obligations.ml b/vernac/obligations.ml index 28aeaa725..a4fe49020 100644 --- a/vernac/obligations.ml +++ b/vernac/obligations.ml @@ -650,7 +650,7 @@ let declare_obligation prg obl body ty uctx = let constant = Declare.declare_constant obl.obl_name ~local:true (DefinitionEntry ce,IsProof Property) in - if not opaque then add_hint false prg constant; + if not opaque then add_hint (Locality.make_section_locality None) prg constant; definition_message obl.obl_name; true, { obl with obl_body = if poly then diff --git a/vernac/vernacentries.ml b/vernac/vernacentries.ml index adf24d23b..4f63ed6f4 100644 --- a/vernac/vernacentries.ml +++ b/vernac/vernacentries.ml @@ -522,7 +522,21 @@ let vernac_assumption locality poly (local, kind) l nl = let status = do_assumptions kind nl l in if not status then Feedback.feedback Feedback.AddedAxiom +let should_treat_as_cumulative cum poly = + if poly then + match cum with + | GlobalCumulativity | LocalCumulativity -> true + | GlobalNonCumulativity | LocalNonCumulativity -> false + else + match cum with + | GlobalCumulativity | GlobalNonCumulativity -> false + | LocalCumulativity -> + user_err Pp.(str "The Cumulative prefix can only be used in a polymorphic context.") + | LocalNonCumulativity -> + user_err Pp.(str "The NonCumulative prefix can only be used in a polymorphic context.") + let vernac_record cum k poly finite struc binders sort nameopt cfs = + let is_cumulative = should_treat_as_cumulative cum poly in let const = match nameopt with | None -> add_prefix "Build_" (snd (fst (snd struc))) | Some (_,id as lid) -> @@ -533,13 +547,14 @@ let vernac_record cum k poly finite struc binders sort nameopt cfs = match x with | Vernacexpr.AssumExpr ((loc, Name id), _) -> Dumpglob.dump_definition (loc,id) false "proj" | _ -> ()) cfs); - ignore(Record.definition_structure (k,cum,poly,finite,struc,binders,cfs,const,sort)) + ignore(Record.definition_structure (k,is_cumulative,poly,finite,struc,binders,cfs,const,sort)) (** When [poly] is true the type is declared polymorphic. When [lo] is true, then the type is declared private (as per the [Private] keyword). [finite] indicates whether the type is inductive, co-inductive or neither. *) let vernac_inductive cum poly lo finite indl = + let is_cumulative = should_treat_as_cumulative cum poly in if Dumpglob.dump () then List.iter (fun (((coe,(lid,_)), _, _, _, cstrs), _) -> match cstrs with @@ -576,7 +591,7 @@ let vernac_inductive cum poly lo finite indl = | _ -> user_err Pp.(str "Cannot handle mutually (co)inductive records.") in let indl = List.map unpack indl in - do_mutual_inductive indl cum poly lo finite + do_mutual_inductive indl is_cumulative poly lo finite let vernac_fixpoint locality poly local l = let local = enforce_locality_exp locality local in @@ -1363,10 +1378,10 @@ let _ = let _ = declare_bool_option { optdepr = false; - optname = "inductive cumulativity"; - optkey = ["Inductive"; "Cumulativity"]; - optread = Flags.is_inductive_cumulativity; - optwrite = Flags.make_inductive_cumulativity } + optname = "Polymorphic inductive cumulativity"; + optkey = ["Polymorphic"; "Inductive"; "Cumulativity"]; + optread = Flags.is_polymorphic_inductive_cumulativity; + optwrite = Flags.make_polymorphic_inductive_cumulativity } let _ = declare_int_option |