Imported Upstream version 8.0pl3+8.1alphaupstream/8.0pl3+8.1alpha

21 files changed, 10916 insertions, 0 deletions

diff --git a/dev/doc/Makefile b/dev/doc/Makefile
new file mode 100644
index 00000000..a0bef897
--- /dev/null
+++ b/dev/doc/Makefile
@@ -0,0 +1,67 @@
+
+# Makefile for doc/
+
+all:: newparse 
+#newsyntax.dvi minicoq.dvi
+
+
+OBJS=lex.cmo ast.cmo parse.cmo syntax.cmo
+
+newparse: $(OBJS) syntax.mli lex.ml syntax.ml
+	ocamlc -o newparse $(OBJS)
+
+.ml.cmo:
+	ocamlc -c $<
+
+.mli.cmi:
+	ocamlc -c $<
+
+.mll.ml:
+	ocamllex $<
+
+.mly.ml:
+	ocamlyacc -v $<
+
+.mly.mli:
+	ocamlyacc -v $<
+
+clean::
+	rm -f *.cm* *.output syntax.ml syntax.mli lex.ml newparse
+
+parse.cmo: ast.cmo
+syntax.cmi: parse.cmo
+syntax.cmo: lex.cmo parse.cmo syntax.cmi
+lex.cmo: syntax.cmi
+ast.cmo: ast.ml
+
+newsyntax.dvi: newsyntax.tex
+	latex $<
+	latex $<
+
+coq.dvi: coq.tex
+	latex coq
+	latex coq
+
+coq.tex::
+	make -C .. doc/coq.tex
+
+depend:: kernel.dep.ps library.dep.ps pretyping.dep.ps parsing.dep.ps \
+         proofs.dep.ps tactics.dep.ps toplevel.dep.ps interp.dep.ps
+
+%.dot: ../%
+	(cd ../$*; ocamldep *.ml *.mli) | ocamldot -lr > $@
+
+%.dep.ps: %.dot
+	dot -Tps $< -o $@
+
+clean::
+	rm -f *~ *.log *.aux
+
+.SUFFIXES: .tex .dvi .ps .cmo .cmi .mli .ml .mll .mly
+
+.tex.dvi:
+	latex $< && latex $<
+
+.dvi.ps:
+	dvips $< -o $@
+
diff --git a/dev/doc/ast.ml b/dev/doc/ast.ml
new file mode 100644
index 00000000..2153ef47
--- /dev/null
+++ b/dev/doc/ast.ml
@@ -0,0 +1,47 @@
+
+type constr_ast =
+  Pair of constr_ast * constr_ast
+| Prod of binder list * constr_ast
+| Lambda of binder list * constr_ast
+| Let of string * constr_ast * constr_ast
+| LetCase of binder list * constr_ast * constr_ast
+| IfCase of constr_ast * constr_ast * constr_ast
+| Eval of red_fun * constr_ast
+| Infix of string * constr_ast * constr_ast
+| Prefix of string * constr_ast
+| Postfix of string * constr_ast
+| Appl of constr_ast * constr_arg list
+| ApplExpl of string list * constr_ast list
+| Scope of string * constr_ast
+| Qualid of string list
+| Prop | Set | Type
+| Int of string
+| Hole
+| Meta of string
+| Fixp of fix_kind *
+      (string * binder list * constr_ast * string option * constr_ast) list *
+      string
+| Match of case_item list * constr_ast option *
+           (pattern list * constr_ast) list 
+
+and red_fun = Simpl
+
+and binder = string * constr_ast
+
+and constr_arg = string option * constr_ast
+
+and fix_kind = Fix | CoFix
+
+and case_item = constr_ast * (string option * constr_ast option)
+
+and pattern = 
+  PatAs of pattern * string
+| PatType of pattern * constr_ast
+| PatConstr of string * pattern list
+| PatVar of string
+
+let mk_cast c t =
+  if t=Hole then c else Infix(":",c,t)
+
+let mk_lambda bl t =
+  if bl=[] then t else Lambda(bl,t)
diff --git a/dev/doc/check-grammar b/dev/doc/check-grammar
new file mode 100755
index 00000000..67da1bc5
--- /dev/null
+++ b/dev/doc/check-grammar
@@ -0,0 +1,50 @@
+#!/bin/bash
+# This scripts checks that the new grammar of Coq as defined in syntax-v8.tex
+# is consistent in the sense that all invoked non-terminals are defined
+
+defined-nt() {
+  grep "\\DEFNT{.*}" syntax-v8.tex | sed -e "s|.*DEFNT{\([^}]*\)}.*|\1|"|\
+    sort | sort -u
+}
+
+used-nt() {
+  cat syntax-v8.tex | tr \\\\ \\n | grep "^NT{.*}" |\
+    sed -e "s|^NT{\([^}]*\)}.*|\1|" | egrep -v ^\#1\|non-terminal | sort -u
+}
+
+used-term() {
+  cat syntax-v8.tex | tr \\\\ \\n | grep "^TERM{.*}" |\
+    sed -e "s|^TERM{\([^}]*\)}.*|\1|" -e "s|\\$||g" | egrep -v ^\#1\|terminal | sort -u
+}
+
+used-kwd() {
+  cat syntax-v8.tex | tr \\\\ \\n | grep "^KWD{.*}" |\
+    sed -e "s|^KWD{\([^}]*\)}.*|\1|" -e "s|\\$||g" | egrep -v ^\#1 | sort -u
+}
+
+defined-nt > def
+used-nt > use
+used-term > use-t
+used-kwd > use-k
+diff def use > df
+
+###############################
+echo
+if grep ^\> df > /dev/null 2>&1 ; then
+  echo Undefined non-terminals:
+  echo ========================
+  echo
+  grep ^\> df | sed -e "s|^> ||"
+  echo
+fi
+if grep ^\< df > /dev/null 2>&1 ; then
+  echo Unused non-terminals:
+  echo =====================
+  echo
+  grep ^\< df | sed -e "s|^< ||"
+  echo
+fi
+#echo Used terminals:
+#echo ===============
+#echo
+#cat use-t
\ No newline at end of file
diff --git a/dev/doc/interp.dep.ps b/dev/doc/interp.dep.ps
new file mode 100644
index 00000000..b0554481
--- /dev/null
+++ b/dev/doc/interp.dep.ps
@@ -0,0 +1,583 @@
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diff --git a/dev/doc/intro.tex b/dev/doc/intro.tex
new file mode 100644
index 00000000..4cec8673
--- /dev/null
+++ b/dev/doc/intro.tex
@@ -0,0 +1,25 @@
+
+\ocwsection This is \Coq, a proof assistant for the \CCI.
+This document describes the implementation of \Coq.
+It has been automatically generated from the source of
+\Coq\ using \textsf{ocamlweb}, a literate programming tool for
+\textsf{Objective Caml}\footnote{\Coq, \textsf{Objective Caml} and
+  \textsf{ocamlweb} are all freely available at
+  \textsf{http://coq.inria.fr/}, \textsf{http://caml.inria.fr/} and
+  \textsf{http://www.lri.fr/\~{}filliatr/ocamlweb}.}.
+The source files are organized in several directories, which are
+described here as separate chapters.
+
+\begin{center}
+  \begin{tabular}{p{10cm}rr}
+    Chapter & section & page \\[0.5em]
+    \hline\\[0.2em]
+    Utility libraries \dotfill & \refsec{lib}     & \pageref{lib}     \\[0.5em]
+    Kernel            \dotfill & \refsec{kernel}  & \pageref{kernel}  \\[0.5em]
+    Library           \dotfill & \refsec{library} & \pageref{library} \\[0.5em]
+    Pretyping     \dotfill & \refsec{pretyping} & \pageref{pretyping} \\[0.5em]
+    Proof engine      \dotfill & \refsec{proofs}  & \pageref{proofs}  \\[0.5em]
+    Tactics           \dotfill & \refsec{tactics} & \pageref{tactics} \\[0.5em]
+    Toplevel          \dotfill & \refsec{toplevel}& \pageref{toplevel}\\[0.5em]
+  \end{tabular}
+\end{center}
\ No newline at end of file
diff --git a/dev/doc/kernel.dep.ps b/dev/doc/kernel.dep.ps
new file mode 100644
index 00000000..3c00121e
--- /dev/null
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@@ -0,0 +1,1454 @@
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diff --git a/dev/doc/lex.mll b/dev/doc/lex.mll
new file mode 100644
index 00000000..617163e7
--- /dev/null
+++ b/dev/doc/lex.mll
@@ -0,0 +1,81 @@
+
+{
+ open Lexing
+ open Syntax
+
+ let chan_out = ref stdout
+
+ let comment_depth = ref 0
+ let print s = output_string !chan_out s
+ 
+ exception Fin_fichier
+
+}
+
+let space = [' ' '\t' '\n']
+let letter = ['a'-'z' 'A'-'Z']
+let digit = ['0'-'9']
+
+let identifier = letter (letter | digit | ['_' '\''])*
+let number = digit+
+let oper = ['-' '+' '/' '*' '|' '>' '<' '=' '%' '#' '$' ':' '\\' '?'
+            '.' '!' '@' ]+
+
+rule token = parse
+  | "let" {LET}
+  | "in" {IN}
+  | "match" {MATCH}
+  | "with" {WITH}
+  | "end" {END}
+  | "and" {AND}
+  | "fun" {FUN}
+  | "if" {IF}
+  | "then" {THEN}
+  | "else" {ELSE}
+  | "eval" {EVAL}
+  | "for" {FOR}
+  | "Prop" {PROP}
+  | "Set" {SET}
+  | "Type" {TYPE}
+  | "fix" {FIX}
+  | "cofix" {COFIX}
+  | "struct" {STRUCT}
+  | "as" {AS}
+
+  | "Simpl" {SIMPL}
+
+  | "_" {WILDCARD}
+  | "(" {LPAR}
+  | ")" {RPAR}
+  | "{" {LBRACE}
+  | "}" {RBRACE}
+  | "!" {BANG}
+  | "@" {AT}
+  | ":" {COLON}
+  | ":=" {COLONEQ}
+  | "." {DOT}
+  | "," {COMMA}
+  | "->" {OPER "->"}
+  | "=>" {RARROW}
+  | "|" {BAR}
+  | "%" {PERCENT}
+
+  | '?' { META(ident lexbuf)}
+  | number { INT(Lexing.lexeme lexbuf) }
+  | oper { OPER(Lexing.lexeme lexbuf) }
+  | identifier { IDENT (Lexing.lexeme lexbuf) }
+  | "(*" (*"*)"*)       { comment_depth := 1;
+                          comment lexbuf;
+		          token lexbuf }
+  | space+     { token lexbuf}
+  | eof        { EOF }
+
+and ident = parse
+  | identifier { Lexing.lexeme lexbuf }
+
+and comment = parse
+  | "(*" (*"*)"*)  { incr comment_depth; comment lexbuf }
+  | (*"(*"*) "*)"
+      { decr comment_depth; if !comment_depth > 0 then comment lexbuf }
+  | eof   { raise Fin_fichier } 
+  | _     { comment lexbuf }
diff --git a/dev/doc/library.dep.ps b/dev/doc/library.dep.ps
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index 00000000..1c68240e
--- /dev/null
+++ b/dev/doc/library.dep.ps
@@ -0,0 +1,836 @@
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+%%For: (herbelin) Hugo Herbelin
+%%Title: G
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+  dup 307 /Ccedilla
+  dup 311 /Eacute
+  dup 312 /Ecircumflex
+  dup 313 /Edieresis
+  dup 310 /Egrave
+  dup 315 /Iacute
+  dup 316 /Icircumflex
+  dup 317 /Idieresis
+  dup 314 /Igrave
+  dup 334 /Udieresis
+  dup 335 /Yacute
+  dup 376 /thorn
+  dup 337 /germandbls
+  dup 341 /aacute
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+  dup 344 /adieresis
+  dup 346 /ae
+  dup 340 /agrave
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+  dup 347 /ccedilla
+  dup 351 /eacute
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+  dup 356 /icircumflex
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+  dup 360 /dcroat
+  dup 361 /ntilde
+  dup 363 /oacute
+  dup 364 /ocircumflex
+  dup 366 /odieresis
+  dup 362 /ograve
+  dup 365 /otilde
+  dup 370 /oslash
+  dup 372 /uacute
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+  dup 374 /udieresis
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diff --git a/dev/doc/macros.tex b/dev/doc/macros.tex
new file mode 100644
index 00000000..6beacf7b
--- /dev/null
+++ b/dev/doc/macros.tex
@@ -0,0 +1,7 @@
+
+% macros for coq.tex
+
+\newcommand{\Coq}{\textsf{Coq}}
+\newcommand{\CCI}{Calculus of Inductive Constructions}
+
+\newcommand{\refsec}[1]{\textbf{\ref{#1}}}
\ No newline at end of file
diff --git a/dev/doc/memo-v8.tex b/dev/doc/memo-v8.tex
new file mode 100644
index 00000000..8d116de2
--- /dev/null
+++ b/dev/doc/memo-v8.tex
@@ -0,0 +1,286 @@
+
+\documentclass{article}
+
+\usepackage{verbatim}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{array}
+\usepackage{fullpage}
+
+\author{B.~Barras}
+\title{An introduction to syntax of Coq V8}
+
+%% Le _ est un caractère normal
+\catcode`\_=13
+\let\subscr=_
+\def_{\ifmmode\sb\else\subscr\fi}
+
+\def\NT#1{\langle\textit{#1}\rangle}
+\def\NTL#1#2{\langle\textit{#1}\rangle_{#2}}
+\def\TERM#1{\textsf{\bf #1}}
+
+\newenvironment{transbox}
+  {\begin{center}\tt\begin{tabular}{l|ll} \hfil\textrm{V7} & \hfil\textrm{V8} \\ \hline}
+  {\end{tabular}\end{center}}
+\def\TRANS#1#2
+  {\begin{tabular}[t]{@{}l@{}}#1\end{tabular} & 
+   \begin{tabular}[t]{@{}l@{}}#2\end{tabular} \\}
+\def\TRANSCOM#1#2#3
+  {\begin{tabular}[t]{@{}l@{}}#1\end{tabular} & 
+   \begin{tabular}[t]{@{}l@{}}#2\end{tabular} & #3 \\}
+
+\begin{document}
+
+\maketitle
+
+The goal of this document is to introduce by example to the new syntax of
+Coq. It is strongly recommended to read first the definition of the new
+syntax, but this document should also be useful for the eager user who wants
+to start with the new syntax quickly.
+
+
+\section{Changes in lexical conventions w.r.t. V7}
+
+\subsection{Identifiers}
+
+The lexical conventions changed: \TERM{_} is not a regular identifier
+anymore. It is used in terms as a placeholder for subterms to be inferred
+at type-checking, and in patterns as a non-binding variable.
+
+Furthermore, only letters (unicode letters), digits, single quotes and
+_ are allowed after the first character.
+
+\subsection{Quoted string}
+
+Quoted strings are used typically to give a filename (which may not
+be a regular identifier). As before they are written between double
+quotes ("). Unlike for V7, there is no escape character: characters
+are written normaly but the double quote which is doubled.
+
+\section{Main changes in terms w.r.t. V7}
+
+
+\subsection{Precedence of application}
+
+In the new syntax, parentheses are not really part of the syntax of
+application. The precedence of application (10) is tighter than all
+prefix and infix notations. It makes it possible to remove parentheses
+in many contexts.
+
+\begin{transbox}
+\TRANS{(A x)->(f x)=(g y)}{A x -> f x = g y}
+\TRANS{(f [x]x)}{f (fun x => x)}
+\end{transbox}
+
+
+\subsection{Arithmetics and scopes}
+
+The specialized notation for \TERM{Z} and \TERM{R} (introduced by
+symbols \TERM{`} and \TERM{``}) have disappeared. They have been
+replaced by the general notion of scope.
+
+\begin{center}
+\begin{tabular}{l|l|l}
+type & scope name & delimiter \\
+\hline
+types & type_scope & \TERM{T} \\
+\TERM{bool} & bool_scope & \\
+\TERM{nat} & nat_scope & \TERM{nat} \\
+\TERM{Z} & Z_scope & \TERM{Z} \\
+\TERM{R} & R_scope & \TERM{R} \\
+\TERM{positive} & positive_scope & \TERM{P}
+\end{tabular}
+\end{center}
+
+In order to use notations of arithmetics on \TERM{Z}, its scope must be opened with command \verb+Open Scope Z_scope.+ Another possibility is using the scope change notation (\TERM{\%}). The latter notation is to be used when notations of several scopes appear in the same expression.
+
+In examples below, scope changes are not needed if the appropriate scope
+has been opened. Scope nat_scope is opened in the initial state of Coq.
+\begin{transbox}
+\TRANSCOM{`0+x=x+0`}{0+x=x+0}{\textrm{Z_scope}}
+\TRANSCOM{``0 + [if b then ``1`` else ``2``]``}{0 + if b then 1 else 2}{\textrm{R_scope}}
+\TRANSCOM{(0)}{0}{\textrm{nat_scope}}
+\end{transbox}
+
+Below is a table that tells which notation is available in which
+scope. The relative precedences and associativity of operators is the
+same as in usual mathematics. See the reference manual for more
+details. However, it is important to remember that unlike V7, the type
+operators for product and sum are left associative, in order not to
+clash with arithmetic operators.
+
+\begin{center}
+\begin{tabular}{l|l}
+scope & notations \\
+\hline
+nat_scope & $+ ~- ~* ~< ~\leq ~> ~\geq$ \\
+Z_scope & $+ ~- ~* ~/ ~\TERM{mod} ~< ~\leq ~> ~\geq ~?=$ \\
+R_scope & $+ ~- ~* ~/ ~< ~\leq ~> ~\geq$ \\
+type_scope & $* ~+$ \\
+bool_scope & $\TERM{\&\&} ~\TERM{$||$} ~\TERM{-}$ \\
+list_scope & $\TERM{::} ~\TERM{++}$
+\end{tabular}
+\end{center}
+(Note: $\leq$ is written \TERM{$<=$})
+
+
+
+\subsection{Notation for implicit arguments}
+
+The explicitation of arguments is closer to the \emph{bindings} notation in
+tactics. Argument positions follow the argument names of the head constant.
+
+\begin{transbox}
+\TRANS{f 1!t1 2!t2}{f (x:=t1) (y:=t2)}
+\TRANS{!f t1 t2}{@f t1 t2}
+\end{transbox}
+
+
+\subsection{Universal quantification}
+
+The universal quantification and dependent product types are now
+materialized with the \TERM{forall} keyword before the binders and a
+comma after the binders.
+
+The syntax of binders also changed significantly. A binder can simply be
+a name when its type can be inferred. In other cases, the name and the type
+of the variable are put between parentheses. When several consecutive
+variables have the same type, they can be grouped. Finally, if all variables
+have the same type parentheses can be omitted.
+
+\begin{transbox}
+\TRANS{(x:A)B}{forall (x:~A), B ~~\textrm{or}~~ forall x:~A, B}
+\TRANS{(x,y:nat)P}{forall (x y :~nat), P ~~\textrm{or}~~ forall x y :~nat, P}
+\TRANS{(x,y:nat;z:A)P}{forall (x y :~nat) (z:A), P}
+\TRANS{(x,y,z,t:?)P}{forall x y z t, P}
+\TRANS{(x,y:nat;z:?)P}{forall (x y :~nat) z, P}
+\end{transbox}
+
+\subsection{Abstraction}
+
+The notation for $\lambda$-abstraction follows that of universal
+quantification. The binders are surrounded by keyword \TERM{fun}
+and $\Rightarrow$ (\verb+=>+ in ascii).
+
+\begin{transbox}
+\TRANS{[x,y:nat; z](f a b c)}{fun (x y:nat) z => f a b c}
+\end{transbox}
+
+
+\subsection{Pattern-matching}
+
+Beside the usage of the keyword pair \TERM{match}/\TERM{with} instead of
+\TERM{Cases}/\TERM{of}, the main change is the notation for the type of
+branches and return type. It is no longer written between \TERM{$<$ $>$} before
+the \TERM{Cases} keyword, but interleaved with the destructured objects.
+
+The idea is that for each destructured object, one may specify a variable
+name to tell how the branches types depend on this destructured objects (case
+of a dependent elimination), and also how they depend on the value of the
+arguments of the inductive type of the destructured objects. The type of
+branches is then given after the keyword \TERM{return}, unless it can be
+inferred.
+
+Moreover, when the destructured object is a variable, one may use this
+variable in the return type.
+
+\begin{transbox}
+\TRANS{Cases n of\\~~ O => O \\| (S k) => (1) end}{match n with\\~~ 0 => 0 \\| (S k) => 1 end}
+\TRANS{Cases m n of \\~~0 0 => t \\| ... end}{match m, n with \\~~0, 0 => t \\| .. end}
+\TRANS{<[n:nat](P n)>Cases T of ... end}{match T as n return P n with ... end}
+\TRANS{<[n:nat][p:(even n)]\~{}(odd n)>Cases p of\\~~ ... \\end}{match p in even n return \~{} odd n with\\~~ ...\\end}
+\end{transbox}
+
+
+\subsection{Fixpoints and cofixpoints}
+
+An easier syntax for non-mutual fixpoints is provided, making it very close
+to the usual notation for non-recursive functions. The decreasing argument
+is now indicated by an annotation between curly braces, regardless of the
+binders grouping. The annotation can be omitted if the binders introduce only
+one variable. The type of the result can be omitted if inferable.
+
+\begin{transbox}
+\TRANS{Fix plus\{plus [n:nat] : nat -> nat :=\\~~ [m]...\}}{fix plus (n m:nat) \{struct n\}: nat := ...}
+\TRANS{Fix fact\{fact [n:nat]: nat :=\\
+~~Cases n of\\~~~~ O => (1) \\~~| (S k) => (mult n (fact k)) end\}}{fix fact
+  (n:nat) :=\\
+~~match n with \\~~~~0 => 1 \\~~| (S k) => n * fact k end}
+\end{transbox}
+
+There is a syntactic sugar for mutual fixpoints associated to a local
+definition:
+
+\begin{transbox}
+\TRANS{let f := Fix f \{f [x:A] : T := M\} in\\(g (f y))}{let fix f (x:A) : T := M in\\g (f x)}
+\end{transbox}
+
+The same applies to cofixpoints, annotations are not allowed in that case.
+
+\subsection{Notation for type cast}
+
+\begin{transbox}
+\TRANS{O :: nat}{0 : nat}
+\end{transbox}
+
+\section{Main changes in tactics w.r.t. V7}
+
+The main change is that all tactic names are lowercase. This also holds for
+Ltac keywords.
+
+\subsection{Ltac}
+
+Definitions of macros are introduced by \TERM{Ltac} instead of
+\TERM{Tactic Definition}, \TERM{Meta Definition} or \TERM{Recursive
+Definition}.
+
+Rules of a match command are not between square brackets anymore.
+
+Context (understand a term with a placeholder) instantiation \TERM{inst}
+became \TERM{context}. Syntax is unified with subterm matching.
+
+\begin{transbox}
+\TRANS{match t with [C[x=y]] => inst C[y=x]}{match t with context C[x=y] => context C[y=x]}
+\end{transbox}
+
+\subsection{Named arguments of theorems}
+
+\begin{transbox}
+\TRANS{Apply thm with x:=t 1:=u}{apply thm with (x:=t) (1:=u)}
+\end{transbox}
+
+
+\subsection{Occurrences}
+
+To avoid ambiguity between a numeric literal and the optionnal
+occurence numbers of this term, the occurence numbers are put after
+the term itself. This applies to tactic \TERM{pattern} and also
+\TERM{unfold}
+\begin{transbox}
+\TRANS{Pattern 1 2 (f x) 3 4 d y z}{pattern (f x at 1 2) (d at 3 4) y z}
+\end{transbox}
+
+\section{Main changes in vernacular commands w.r.t. V7}
+
+
+\subsection{Binders}
+
+The binders of vernacular commands changed in the same way as those of
+fixpoints. This also holds for parameters of inductive definitions.
+
+
+\begin{transbox}
+\TRANS{Definition x [a:A] : T := M}{Definition x (a:A) : T := M}
+\TRANS{Inductive and [A,B:Prop]: Prop := \\~~conj : A->B->(and A B)}%
+      {Inductive and (A B:Prop): Prop := \\~~conj : A -> B -> and A B}
+\end{transbox}
+
+\subsection{Hints}
+
+The syntax of \emph{extern} hints changed: the pattern and the tactic
+to be applied are separated by a \TERM{$\Rightarrow$}.
+\begin{transbox}
+\TRANS{Hint Extern 4 (toto ?) Apply lemma}{Hint Extern 4 (toto _) => apply lemma}
+\end{transbox}
+
+\end{document}
diff --git a/dev/doc/minicoq.tex b/dev/doc/minicoq.tex
new file mode 100644
index 00000000..a34b03a4
--- /dev/null
+++ b/dev/doc/minicoq.tex
@@ -0,0 +1,98 @@
+\documentclass{article}
+
+\usepackage{fullpage}
+\input{./macros.tex}
+\newcommand{\minicoq}{\textsf{minicoq}}
+\newcommand{\nonterm}[1]{\textit{#1}}
+\newcommand{\terminal}[1]{\textsf{#1}}
+\newcommand{\listzero}{\textit{LIST$_0$}}
+\newcommand{\listun}{\textit{LIST$_1$}}
+\newcommand{\sep}{\textit{SEP}}
+
+\title{Minicoq: a type-checker for the pure \\ 
+       Calculus of Inductive Constructions}
+
+
+\begin{document}
+
+\maketitle
+
+\section{Introduction}
+
+\minicoq\ is a minimal toplevel for the \Coq\ kernel.
+
+
+\section{Grammar of terms}
+
+The grammar of \minicoq's terms is given in Figure~\ref{fig:terms}. 
+
+\begin{figure}[htbp]
+  \hrulefill
+  \begin{center}
+    \begin{tabular}{lrl}
+      term & ::= & identifier \\
+           & $|$ & \terminal{Rel} integer \\
+           & $|$ & \terminal{Set} \\
+           & $|$ & \terminal{Prop} \\
+           & $|$ & \terminal{Type} \\
+           & $|$ & \terminal{Const} identifier \\
+           & $|$ & \terminal{Ind} identifier integer \\
+           & $|$ & \terminal{Construct} identifier integer integer \\
+           & $|$ & \terminal{[} name \terminal{:} term
+                   \terminal{]} term \\
+           & $|$ & \terminal{(} name \terminal{:} term
+                   \terminal{)} term \\
+           & $|$ & term \verb!->! term \\
+           & $|$ & \terminal{(} \listun\ term \terminal{)} \\
+           & $|$ & \terminal{(} term \terminal{::} term \terminal{)} \\
+           & $|$ & \verb!<! term \verb!>! \terminal{Case}
+                   term \terminal{of} \listzero\ term \terminal{end} 
+      \\[1em]
+      name & ::= & \verb!_! \\
+           & $|$ & identifier 
+   \end{tabular}
+  \end{center}
+  \hrulefill
+  \caption{Grammar of terms}
+  \label{fig:terms}
+\end{figure}
+
+\section{Commands}
+The grammar of \minicoq's commands are given in
+Figure~\ref{fig:commands}. All commands end with a dot.
+
+\begin{figure}[htbp]
+  \hrulefill
+  \begin{center}
+    \begin{tabular}{lrl}
+      command & ::= & \terminal{Definition} identifier \terminal{:=} term. \\
+              & $|$ & \terminal{Definition} identifier \terminal{:} term
+                      \terminal{:=} term. \\
+              & $|$ & \terminal{Parameter} identifier \terminal{:} term. \\
+              & $|$ & \terminal{Variable} identifier \terminal{:} term. \\
+              & $|$ & \terminal{Inductive} \terminal{[} \listzero\ param 
+                      \terminal{]} \listun\ inductive \sep\ 
+                      \terminal{with}. \\
+              & $|$ & \terminal{Check} term. 
+      \\[1em]
+      param   & ::= & identifier 
+      \\[1em]
+      inductive & ::= & identifier \terminal{:} term \terminal{:=}
+                        \listzero\ constructor \sep\ \terminal{$|$}
+      \\[1em]
+      constructor & ::= & identifier \terminal{:} term
+    \end{tabular}
+  \end{center}
+  \hrulefill
+  \caption{Commands}
+  \label{fig:commands}
+\end{figure}
+
+
+\end{document}
+
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 
diff --git a/dev/doc/newsyntax.tex b/dev/doc/newsyntax.tex
new file mode 100644
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--- /dev/null
+++ b/dev/doc/newsyntax.tex
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+
+%% -*-french-tex-*-
+
+\documentclass{article}
+
+\usepackage{verbatim}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage[french]{babel}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{array}
+
+
+\author{B.~Barras}
+\title{Proposition de syntaxe pour Coq}
+
+%% Le _ est un caractère normal
+\catcode`\_=13
+\let\subscr=_
+\def_{\ifmmode\sb\else\subscr\fi}
+
+%% Macros pour les grammaires
+\def\NT#1{\langle\textit{#1}\rangle}
+\def\TERM#1{\textsf{#1}}
+\def\STAR#1{#1\!*}
+\def\PLUS#1{#1\!+}
+
+%% Tableaux de definition de non-terminaux
+\newenvironment{cadre}
+        {\begin{array}{|c|}\hline\\}
+        {\\\\\hline\end{array}}
+\newenvironment{rulebox}
+        {$$\begin{cadre}\begin{array}{r@{~}c@{~}l@{}r}}
+        {\end{array}\end{cadre}$$}
+\def\DEFNT#1{\NT{#1} & ::= &}
+\def\EXTNT#1{\NT{#1} & ::= & ... \\&|&}
+\def\RNAME#1{(\textsc{#1})}
+\def\SEPDEF{\\\\}
+\def\nlsep{\\&|&}
+
+
+\begin{document}
+
+\maketitle
+
+\section{Grammaire des tactiques}
+\label{tacticsyntax}
+
+La réflexion de la rénovation de la syntaxe des tactiques n'est pas
+encore aussi poussée que pour les termes (section~\ref{constrsyntax}),
+mais cette section vise à énoncer les quelques principes que l'on
+souhaite suivre. 
+
+\begin{itemize}
+\item Réutiliser les mots-clés de la syntaxe des termes (i.e. en
+  minuscules) pour les constructions similaires de tactiques (let_in,
+  match, and, etc.). Le connecteur logique \texttt{and} n'étant que
+  rarement utilisé autrement que sous la forme \texttt{$\wedge$} (sauf
+  dans le code ML), on pourrait dégager ce mot-clé.
+\item Les arguments passés aux tactiques sont principalement des
+  termes, on préconise l'utilisation d'un symbole spécial (par exemple
+  l'apostrophe) pour passer une tactique ou une expression
+  (AST). L'idée étant que l'on écrit plus souvent des tactiques
+  prenant des termes en argument que des tacticals.
+\end{itemize}
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{tactic}
+       \NT{tactic} ~\TERM{\&} ~\NT{tactic}            & \RNAME{then}
+\nlsep \TERM{[} ~\NT{tactic}~\TERM{|}~...
+      ~\TERM{|}~\NT{tactic}~\TERM{]}                  & \RNAME{par}
+\nlsep \NT{ident} ~\STAR{\NT{tactic-arg}}   ~~~       & \RNAME{apply}
+\nlsep \TERM{fun} ~....                               & \RNAME{function}
+\nlsep \NT{simple-tactic}
+\SEPDEF
+\DEFNT{tactic-arg}
+       \NT{constr}
+\nlsep \TERM{'} ~\NT{tactic}
+\SEPDEF
+\DEFNT{simple-tactic}
+       \TERM{Apply} ~\NT{binding-term}
+\nlsep \NT{elim-kw} ~\NT{binding-term}
+\nlsep \NT{elim-kw} ~\NT{binding-term} ~\TERM{using} ~\NT{binding-term}
+\nlsep \TERM{Intros} ~\NT{intro-pattern}
+\SEPDEF
+\DEFNT{elim-kw}
+       \TERM{Elim} ~\mid~ \TERM{Case} ~\mid~ \TERM{Induction}
+       ~\mid~ \TERM{Destruct}
+\end{rulebox}
+\caption{Grammaire des tactiques}
+\label{tactic}
+\end{figure}
+
+
+\subsection{Arguments de tactiques}
+
+La syntaxe actuelle des arguments de tactiques est que l'on parse par
+défaut une expression de tactique, ou bien l'on parse un terme si
+celui-ci est préfixé par \TERM{'} (sauf dans le cas des
+variables). Cela est gênant pour les utilisateurs qui doivent écrire
+des \TERM{'} pour leurs tactiques.
+
+À mon avis, il n'est pas souhaitable pour l'utilisateur de l'obliger à
+marquer une différence entre les tactiques ``primitives'' (en fait
+``système'') et les tactiques définies par Ltac. En effet, on se
+dirige inévitablement vers une situation où il existera des librairies
+de tactiques et il va devenir difficile de savoir facilement s'il faut
+ou non mettre des \TERM{'}.
+
+
+
+\subsection{Bindings}
+
+Dans un premier temps, les ``bindings'' sont toujours considérés comme
+une construction du langage des tactiques, mais il est intéressant de
+prévoir l'extension de ce procédé aux termes, puisqu'il s'agit
+simplement de construire un n{\oe}ud d'application dans lequel on
+donne les arguments par nom ou par position, les autres restant à
+inférer. Le principal point est de trouver comment combiner de manière
+uniforme ce procédé avec les arguments implicites.
+
+Il est toutefois important de réfléchir dès maintenant à une syntaxe
+pour éviter de rechanger encore la syntaxe.
+
+Intégrer la notation \TERM{with} aux termes peut poser des problèmes
+puisque ce mot-clé est utilisé pour le filtrage: comment parser (en
+LL(1)) l'expression:
+\begin{verbatim}
+Cases x with y ...
+\end{verbatim}
+
+Soit on trouve un autre mot-clé, soit on joue avec les niveaus de
+priorité en obligeant a parenthéser le \TERM{with} des ``bindings'':
+\begin{verbatim}
+Cases (x with y) with (C z) => ...
+\end{verbatim}
+ce qui introduit un constructeur moralement équivalent à une
+application situé à une priorité totalement différente (les
+``bindings'' seraient au plus haut niveau alors que l'application est
+à un niveau bas).
+
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{binding-term}
+       \NT{constr} ~\TERM{with} ~\STAR{\NT{binding}}
+\SEPDEF
+\DEFNT{binding}
+       \NT{constr}
+\end{rulebox}
+\caption{Grammaire des bindings}
+\label{bindings}
+\end{figure}
+
+\subsection{Enregistrements}
+
+Il faudrait aménager la syntaxe des enregistrements dans l'optique
+d'avoir des enregistrements anonymes (termes de première classe), même
+si pour l'instant, on ne dispose que d'enregistrements définis a
+toplevel.
+
+Exemple de syntaxe pour les types d'enregistrements:
+\begin{verbatim}
+{ x1 : A1;
+  x2 : A2(x1);
+  _ : T;   (* Pas de projection disponible *)
+  y;       (* Type infere *)
+  ...      (* ; optionnel pour le dernier champ *)
+}
+\end{verbatim}
+
+Exemple de syntaxe pour le constructeur:
+\begin{verbatim}
+{ x1 = O;
+  x2 : A2(x1) = v1;
+  _ = v2;
+  ...
+}
+\end{verbatim}
+Quant aux dépendences, une convention pourrait être de considérer les
+champs non annotés par le type comme non dépendants.
+
+Plusieurs interrogations:
+\begin{itemize}
+\item l'ordre des champs doit-il être respecté ?
+  sinon, que faire pour les champs sans projection ?
+\item autorise-t-on \texttt{v1} a mentionner \texttt{x1} (comme dans
+  la définition d'un module), ce qui se comporterait comme si on avait
+  écrit \texttt{v1} à la place. Cela pourrait être une autre manière
+  de déclarer les dépendences
+\end{itemize}
+
+La notation pointée pour les projections pose un problème de parsing,
+sauf si l'on a une convention lexicale qui discrimine les noms de
+modules des projections et identificateurs: \texttt{x.y.z} peut être
+compris comme \texttt{(x.y).z} ou texttt{x.(y.z)}.
+
+
+\section{Grammaire des termes}
+\label{constrsyntax}
+
+\subsection{Quelques principes}
+
+\begin{enumerate}
+\item Diminuer le nombre de niveaux de priorité en regroupant les
+  règles qui se ressemblent: infixes, préfixes, lieurs (constructions
+  ouvertes à droite), etc.
+\item Éviter de surcharger la signification d'un symbole (ex:
+  \verb+( )+ comme parenthésage et produit dans la V7).
+\item Faire en sorte que les membres gauches (motifs de Cases, lieurs
+  d'abstraction ou de produits) utilisent une syntaxe compatible avec
+  celle des membres droits (branches de Cases et corps de fonction).
+\end{enumerate}
+
+\subsection{Présentation de la grammaire}
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{paren-constr}
+       \NT{cast-constr}~\TERM{,}~\NT{paren-constr}     &\RNAME{pair}
+\nlsep \NT{cast-constr}
+\SEPDEF
+\DEFNT{cast-constr}
+       \NT{constr}~\TERM{\!\!:}~\NT{cast-constr}       &\RNAME{cast}
+\nlsep \NT{constr}
+\SEPDEF
+\DEFNT{constr}
+       \NT{appl-constr}~\NT{infix}~\NT{constr}      &\RNAME{infix}
+\nlsep \NT{prefix}~\NT{constr}                      &\RNAME{prefix}
+\nlsep \NT{constr}~\NT{postfix}                     &\RNAME{postfix}
+\nlsep \NT{appl-constr}
+\SEPDEF
+\DEFNT{appl-constr}
+       \NT{appl-constr}~\PLUS{\NT{appl-arg}}           &\RNAME{apply}
+\nlsep \TERM{@}~\NT{global}~\PLUS{\NT{simple-constr}}  &\RNAME{expl-apply}
+\nlsep \NT{simple-constr}
+\SEPDEF
+\DEFNT{appl-arg}
+       \TERM{@}~\NT{int}~\TERM{\!:=}~\NT{simple-constr}  &\RNAME{impl-arg}
+\nlsep \NT{simple-constr}
+\SEPDEF
+\DEFNT{simple-constr}
+       \NT{atomic-constr}
+\nlsep \TERM{(}~\NT{paren-constr}~\TERM{)}
+\nlsep \NT{match-constr}
+\nlsep \NT{fix-constr}
+%% \nlsep \TERM{<\!\!:ast\!\!:<}~\NT{ast}~\TERM{>\!>} &\RNAME{quotation}
+\end{rulebox}
+\caption{Grammaire des termes}
+\label{constr}
+\end{figure}
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{prefix}
+       \TERM{!}~\PLUS{\NT{binder}}~\TERM{.}~    &\RNAME{prod}
+\nlsep \TERM{fun} ~\PLUS{\NT{binder}} ~\TERM{$\Rightarrow$} &\RNAME{lambda}
+\nlsep \TERM{let}~\NT{ident}~\STAR{\NT{binder}} ~\TERM{=}~\NT{constr}
+        ~\TERM{in}  &\RNAME{let}
+%\nlsep \TERM{let (}~\NT{comma-ident-list}~\TERM{) =}~\NT{constr}
+%        ~\TERM{in}   &~~~\RNAME{let-case}
+\nlsep \TERM{if}~\NT{constr}~\TERM{then}~\NT{constr}~\TERM{else}
+      &\RNAME{if-case}
+\nlsep \TERM{eval}~\NT{red-fun}~\TERM{in}       &\RNAME{eval}
+\SEPDEF
+\DEFNT{infix}
+      \TERM{$\rightarrow$}                     & \RNAME{impl}
+\SEPDEF
+\DEFNT{atomic-constr}
+      \TERM{_}
+\nlsep \TERM{?}\NT{int}
+\nlsep \NT{sort}
+\nlsep \NT{global}
+\SEPDEF
+\DEFNT{binder}
+       \NT{ident}                              &\RNAME{infer}
+\nlsep \TERM{(}~\NT{ident}~\NT{type}~\TERM{)}  &\RNAME{binder}
+\SEPDEF
+\DEFNT{type}
+       \TERM{\!:}~\NT{constr}
+\nlsep \epsilon
+\end{rulebox}
+\caption{Grammaires annexes aux termes}
+\label{gram-annexes}
+\end{figure}
+
+La grammaire des termes (correspondant à l'état \texttt{barestate})
+est décrite figures~\ref{constr} et~\ref{gram-annexes}. On constate
+par rapport aux précédentes versions de Coq d'importants changements
+de priorité, le plus marquant étant celui de l'application qui se
+trouve désormais juste au dessus\footnote{La convention est de
+considérer les opérateurs moins lieurs comme ``au dessus'',
+c'est-à-dire ayant un niveau de priorité plus élévé (comme c'est le
+cas avec le niveau de la grammaire actuelle des termes).} des
+constructions fermées à gauche et à droite.
+
+La grammaire des noms globaux est la suivante:
+\begin{eqnarray*}
+\DEFNT{global}
+      \NT{ident}
+%% \nlsep \TERM{\$}\NT{ident}
+\nlsep \NT{ident}\TERM{.}\NT{global}
+\end{eqnarray*}
+
+Le $\TERM{_}$ dénote les termes à synthétiser. Les métavariables sont
+reconnues au niveau du lexer pour ne pas entrer en conflit avec le
+$\TERM{?}$ de l'existentielle.
+
+Les opérateurs infixes ou préfixes sont tous au même niveau de
+priorité du point de vue de Camlp4. La solution envisagée est de les
+gérer à la manière de Yacc, avec une pile (voir discussions plus
+bas). Ainsi, l'implication est un infixe normal; la quantification
+universelle et le let sont vus comme des opérateurs préfixes avec un
+niveau de priorité plus haut (i.e. moins lieur). Il subsiste des
+problèmes si l'on ne veut pas écrire de parenthèses dans:
+\begin{verbatim}
+ A -> (!x. B -> (let y = C in D))
+\end{verbatim}
+
+La solution proposée est d'analyser le membre droit d'un infixe de
+manière à autoriser les préfixes et les infixes de niveau inférieur,
+et d'exiger le parenthésage que pour les infixes de niveau supérieurs.
+
+En revanche, à l'affichage, certains membres droits seront plus
+lisibles s'ils n'utilisent pas cette astuce:
+\begin{verbatim}
+(fun x => x) = fun x => x
+\end{verbatim}
+
+La proposition est d'autoriser ce type d'écritures au parsing, mais
+l'afficheur écrit de manière standardisée en mettant quelques
+parenthèses superflues: $\TERM{=}$ serait symétrique alors que
+$\rightarrow$ appellerait l'afficheur de priorité élevée pour son
+sous-terme droit.
+
+Les priorités des opérateurs primitifs sont les suivantes (le signe
+$*$ signifie que pour le membre droit les opérateurs préfixes seront
+affichés sans parenthèses quel que soit leur priorité):
+$$
+\begin{array}{c|l}
+$symbole$ & $priorité$ \\
+\hline
+\TERM{!}      & 200\,R* \\
+\TERM{fun}    & 200\,R* \\
+\TERM{let}    & 200\,R* \\
+\TERM{if}     & 200\,R \\
+\TERM{eval}   & 200\,R \\
+\rightarrow   & 90\,R*
+\end{array}
+$$
+
+Il y a deux points d'entrée pour les termes: $\NT{constr}$ et
+$\NT{simple-constr}$. Le premier peut être utilisé lorsqu'il est suivi
+d'un séparateur particulier. Dans le cas où l'on veut une liste de
+termes séparés par un espace, il faut lire des $\NT{simple-constr}$.
+
+
+
+Les constructions $\TERM{fix}$ et $\TERM{cofix}$ (voir aussi
+figure~\ref{gram-fix}) sont fermées par end pour simplifier
+l'analyse. Sinon, une expression de point fixe peut être suivie par un
+\TERM{in} ou un \TERM{and}, ce qui pose les mêmes problèmes que le
+``dangling else'': dans
+\begin{verbatim}
+fix f1 x {x} = fix f2 y {y} = ... and ... in ...
+\end{verbatim}
+il faut définir une stratégie pour associer le \TERM{and} et le
+\TERM{in} au bon point fixe.
+
+Un autre avantage est de faire apparaitre que le \TERM{fix} est un
+constructeur de terme de première classe et pas un lieur:
+\begin{verbatim}
+fix f1 ... and f2 ...
+in f1 end x
+\end{verbatim}
+Les propositions précédentes laissaient \texttt{f1} et \texttt{x}
+accolés, ce qui est source de confusion lorsque l'on fait par exemple
+\texttt{Pattern (f1 x)}.
+
+Les corps de points fixes et co-points fixes sont identiques, bien que
+ces derniers n'aient pas d'information de décroissance. Cela
+fonctionne puisque l'annotation est optionnelle. Cela préfigure des
+cas où l'on arrive à inférer quel est l'argument qui décroit
+structurellement (en particulier dans le cas où il n'y a qu'un seul
+argument).
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{fix-expr}
+       \TERM{fix}~\NT{fix-decls}    ~\NT{fix-select} ~\TERM{end} &\RNAME{fix}
+\nlsep \TERM{cofix}~\NT{cofix-decls}~\NT{fix-select} ~\TERM{end} &\RNAME{cofix}
+\SEPDEF
+\DEFNT{fix-decls}
+       \NT{fix-decl}~\TERM{and}~\NT{fix-decls}
+\nlsep \NT{fix-decl}
+\SEPDEF
+\DEFNT{fix-decl}
+       \NT{ident}~\PLUS{\NT{binder}}~\NT{type}~\NT{annot}
+       ~\TERM{=}~\NT{constr}
+\SEPDEF
+\DEFNT{annot}
+       \TERM{\{}~\NT{ident}~\TERM{\}}
+\nlsep \epsilon
+\SEPDEF
+\DEFNT{fix-select}
+       \TERM{in}~\NT{ident}
+\nlsep \epsilon
+\end{rulebox}
+\caption{Grammaires annexes des points fixes}
+\label{gram-fix}
+\end{figure}
+
+La construction $\TERM{Case}$ peut-être considérée comme
+obsolète. Quant au $\TERM{Match}$ de la V6, il disparaît purement et
+simplement.
+
+\begin{figure}
+\begin{rulebox}
+\DEFNT{match-expr}
+       \TERM{match}~\NT{case-items}~\NT{case-type}~\TERM{with}~
+       \NT{branches}~\TERM{end}        &\RNAME{match}
+\nlsep \TERM{match}~\NT{case-items}~\TERM{with}~
+       \NT{branches}~\TERM{end}        &\RNAME{infer-match}
+%%\nlsep \TERM{case}~\NT{constr}~\NT{case-predicate}~\TERM{of}~
+%%      \STAR{\NT{constr}}~\TERM{end}   &\RNAME{case}
+\SEPDEF
+\DEFNT{case-items}
+       \NT{case-item} ~\TERM{\&} ~\NT{case-items}
+\nlsep \NT{case-item}
+\SEPDEF
+\DEFNT{case-item}
+       \NT{constr}~\NT{pred-pattern} &\RNAME{dep-case}
+\nlsep \NT{constr}                   &\RNAME{nodep-case}
+\SEPDEF
+\DEFNT{case-type}
+       \TERM{$\Rightarrow$}~\NT{constr}
+\nlsep \epsilon
+\SEPDEF
+\DEFNT{pred-pattern}
+       \TERM{as}~\NT{ident} ~\TERM{\!:}~\NT{constr}
+\SEPDEF
+\DEFNT{branches}
+       \TERM{|} ~\NT{patterns} ~\TERM{$\Rightarrow$}
+        ~\NT{constr} ~\NT{branches}
+\nlsep \epsilon
+\SEPDEF
+\DEFNT{patterns}
+       \NT{pattern} ~\TERM{\&} ~\NT{patterns}
+\nlsep \NT{pattern}
+\SEPDEF
+\DEFNT{pattern} ...
+\end{rulebox}
+\caption{Grammaires annexes du filtrage}
+\label{gram-match}
+\end{figure}
+
+De manière globale, l'introduction de définitions dans les termes se
+fait avec le symbole $=$, et le $\!:=$ est réservé aux définitions au
+niveau vernac. Il y avait un manque de cohérence dans la
+V6, puisque l'on utilisait $=$ pour le $\TERM{let}$ et $\!:=$ pour les
+points fixes et les commandes vernac.
+
+% OBSOLETE: lieurs multiples supprimes
+%On peut remarquer que $\NT{binder}$ est un sous-ensemble de
+%$\NT{simple-constr}$, à l'exception de $\texttt{(a,b\!\!:T)}$: en tant
+%que lieur, {\tt a} et {\tt b} sont tous deux contraints, alors qu'en
+%tant que terme, seul {\tt b} l'est. Cela qui signifie que l'objectif
+%de rendre compatibles les membres gauches et droits est {\it presque}
+%atteint.
+
+\subsection{Infixes}
+
+\subsubsection{Infixes extensibles}
+
+Le problème de savoir si la liste des symboles pouvant apparaître en
+infixe est fixée ou extensible par l'utilisateur reste à voir.
+
+Notons que la solution où les symboles infixes sont des
+identificateurs que l'on peut définir paraît difficilement praticable:
+par exemple $\texttt{Logic.eq}$ n'est pas un opérateur binaire, mais
+ternaire. Il semble plus simple de garder des déclarations infixes qui
+relient un symbole infixe à un terme avec deux ``trous''. Par exemple:
+
+$$\begin{array}{c|l}
+$infixe$ &  $identificateur$ \\
+\hline
+= & \texttt{Logic.eq _ ?1 ?2} \\
+== & \texttt{JohnMajor.eq _ ?1 _ ?2}
+\end{array}$$
+
+La syntaxe d'une déclaration d'infixe serait par exemple:
+\begin{verbatim}
+Infix "=" 50 := Logic.eq _ ?1 ?2;
+\end{verbatim}
+
+
+\subsubsection{Gestion des précédences}
+
+Les infixes peuvent être soit laissé à Camlp4, ou bien (comme ici)
+considérer que tous les opérateurs ont la même précédence et gérer
+soit même la recomposition des termes à l'aide d'une pile (comme
+Yacc).
+
+
+\subsection{Extensions de syntaxe}
+
+\subsubsection{Litéraux numériques}
+
+La proposition est de considerer les litéraux numériques comme de
+simples identificateurs. Comme il en existe une infinité, il faut un
+nouveau mécanisme pour leur associer une définition. Par exemple, en
+ce qui concerne \texttt{Arith}, la définition de $5$ serait
+$\texttt{S}~4$. Pour \texttt{ZArith}, $5$ serait $\texttt{xI}~2$.
+
+Comme les infixes, les constantes numériques peuvent être qualifiées
+pour indiquer dans quels module est le type que l'on veut
+référencer. Par exemple (si on renomme \texttt{Arith} en \texttt{N} et
+\texttt{ZArith} en \texttt{Z}): \verb+N.5+, \verb+Z.5+.
+
+\begin{eqnarray*}
+\EXTNT{global}
+      \NT{int}
+\end{eqnarray*}
+
+\subsubsection{Nouveaux lieurs}
+
+$$
+\begin{array}{rclr}
+\EXTNT{constr}
+       \TERM{ex}~\PLUS{\NT{binder}}~\TERM{.}~\NT{constr}  &\RNAME{ex}
+\nlsep \TERM{ex}~\PLUS{\NT{binder}}~\TERM{.}~\NT{constr}~\TERM{,}~\NT{constr}
+        &\RNAME{ex2}
+\nlsep \TERM{ext}~\PLUS{\NT{binder}}~\TERM{.}~\NT{constr}  &\RNAME{exT}
+\nlsep \TERM{ext}~\PLUS{\NT{binder}}~\TERM{.}~\NT{constr}~\TERM{,}~\NT{constr}
+        &\RNAME{exT2}
+\end{array}
+$$
+
+Pour l'instant l'existentielle n'admet qu'une seule variable, ce qui
+oblige à écrire des cascades de $\TERM{ex}$.
+
+Pour parser les existentielles avec deux prédicats, on peut considérer
+\TERM{\&} comme un infixe intermédiaire et l'opérateur existentiel en
+présence de cet infixe se transforme en \texttt{ex2}.
+
+\subsubsection{Nouveaux infixes}
+
+Précédences des opérateurs infixes (les plus grands associent moins fort):
+$$
+\begin{array}{l|l|c|l}
+$identificateur$      & $module$     & $infixe/préfixe$ & $précédence$ \\
+\hline
+\texttt{iff}          & $Logic$      & \longleftrightarrow & 100 \\
+\texttt{or}           & $Logic$      & \vee     & 80\, R \\
+\texttt{sum}          & $Datatypes$  & +        & 80\, R \\
+\texttt{and}          & $Logic$      & \wedge   & 70\, R \\
+\texttt{prod}         & $Datatypes$  & *        & 70\, R \\
+\texttt{not}          & $Logic$      & \tilde{} & 60\, L \\
+\texttt{eq _}         & $Logic$      & =        & 50 \\
+\texttt{eqT _}        & $Logic_Type$ & =        & 50 \\
+\texttt{identityT _}  & $Data_Type$  & =        & 50 \\
+\texttt{le}           & $Peano$      & $<=$     & 50 \\
+\texttt{lt}           & $Peano$      & $<$      & 50 \\
+\texttt{ge}           & $Peano$      & $>=$     & 50 \\
+\texttt{gt}           & $Peano$      & $>$      & 50 \\
+\texttt{Zle}          & $zarith_aux$   & $<=$   & 50 \\
+\texttt{Zlt}          & $zarith_aux$   & $<$    & 50 \\
+\texttt{Zge}          & $zarith_aux$   & $>=$   & 50 \\
+\texttt{Zgt}          & $zarith_aux$   & $>$    & 50 \\
+\texttt{Rle}          & $Rdefinitions$ & $<=$   & 50 \\
+\texttt{Rlt}          & $Rdefinitions$ & $<$    & 50 \\
+\texttt{Rge}          & $Rdefinitions$ & $>=$   & 50 \\
+\texttt{Rgt}          & $Rdefinitions$ & $>$    & 50 \\
+\texttt{plus}         & $Peano$        & +      & 40\,L \\
+\texttt{Zplus}        & $fast_integer$ & +      & 40\,L \\
+\texttt{Rplus}        & $Rdefinitions$ & +      & 40\,L \\
+\texttt{minus}        & $Minus$        & -      & 40\,L \\
+\texttt{Zminus}       & $zarith_aux$   & -      & 40\,L \\
+\texttt{Rminus}       & $Rdefinitions$ & -      & 40\,L \\
+\texttt{Zopp}         & $fast_integer$ & -      & 40\,L \\
+\texttt{Ropp}         & $Rdefinitions$ & -      & 40\,L \\
+\texttt{mult}         & $Peano$        & *      & 30\,L \\
+\texttt{Zmult}        & $fast_integer$ & *      & 30\,L \\
+\texttt{Rmult}        & $Rdefinitions$ & *      & 30\,L \\
+\texttt{Rdiv}         & $Rdefinitions$ & /      & 30\,L \\
+\texttt{pow}          & $Rfunctions$   & \hat   & 20\,L \\
+\texttt{fact}         & $Rfunctions$   & !      & 20\,L \\
+\end{array}
+$$
+
+Notons qu'il faudrait découper {\tt Logic_Type} en deux car celui-ci
+définit deux égalités, ou alors les mettre dans des modules différents.
+
+\subsection{Exemples}
+
+\begin{verbatim}
+Definition not (A:Prop) := A->False;
+Inductive eq (A:Set) (x:A) : A->Prop :=
+    refl_equal : eq A x x;
+Inductive ex (A:Set) (P:A->Prop) : Prop :=
+    ex_intro : !x. P x -> ex A P;
+Lemma not_all_ex_not : !(P:U->Prop). ~(!n. P n) -> ?n. ~ P n;
+Fixpoint plus n m : nat {struct n} :=
+  match n with
+    O     => m
+  | (S k) => S (plus k m)
+  end;
+\end{verbatim}
+
+\subsection{Questions ouvertes}
+
+Voici les points sur lesquels la discussion est particulièrement
+ouverte: 
+\begin{itemize}
+\item choix d'autres symboles pour les quantificateurs \TERM{!} et
+  \TERM{?}. En l'état actuel des discussions, on garderait le \TERM{!}
+  pour la qunatification universelle, mais on choisirait quelquechose
+  comme \TERM{ex} pour l'existentielle, afin de ne pas suggérer trop
+  de symétrie entre ces quantificateurs (l'un est primitif, l'autre
+  pas).
+\item syntaxe particulière pour les \texttt{sig}, \texttt{sumor}, etc.
+\item la possibilité d'introduire plusieurs variables du même type est
+  pour l'instant supprimée au vu des problèmes de compatibilité de
+  syntaxe entre les membres gauches et membres droits. L'idée étant
+  que l'inference de type permet d'éviter le besoin de déclarer tous
+  les types.
+\end{itemize}
+
+\subsection{Autres extensions}
+
+\subsubsection{Lieur multiple}
+
+L'écriture de types en présence de polymorphisme est souvent assez
+pénible:
+\begin{verbatim}
+Check !(A:Set) (x:A) (B:Set) (y:B). P A x B y;
+\end{verbatim}
+
+On pourrait avoir des déclarations introduisant à la fois un type
+d'une certaine sorte et une variable de ce type:
+\begin{verbatim}
+Check !(x:A:Set) (y:B:Set). P A x B y;
+\end{verbatim}
+
+Noter que l'on aurait pu écrire:
+\begin{verbatim}
+Check !A x B y. P A (x:A:Set) B (y:B:Set);
+\end{verbatim}
+
+\section{Syntaxe des tactiques}
+
+\subsection{Questions diverses}
+
+Changer ``Pattern nl c ... nl c'' en ``Pattern [ nl ] c ... [ nl ] c''
+pour permettre des chiffres seuls dans la catégorie syntaxique des
+termes.
+
+Par uniformité remplacer ``Unfold nl c'' par ``Unfold [ nl ] c'' ?
+
+Même problème pour l'entier de Specialize (ou virer Specialize ?) ?
+
+\subsection{Questions en suspens}
+
+\verb=EAuto= : deux syntaxes différentes pour la recherche en largeur
+et en profondeur ? Quelle recherche par défaut ?
+
+\section*{Remarques pêle-mêle (HH)}
+
+Autoriser la syntaxe
+
+\begin{verbatim}
+Variable R (a : A) (b : B) : Prop.
+Hypotheses H (a : A) (b : B) : Prop; Y (u : U) : V.
+Variables H (a : A) (b : B), J (k : K) : nat; Z (v : V) : Set.
+\end{verbatim}
+
+Renommer eqT, refl_eqT, eqT_ind, eqT_rect, eqT_rec en eq, refl_equal, etc.
+Remplacer == en =.
+
+Mettre des \verb=?x= plutot que des \verb=?1= dans les motifs de ltac ??
+
+\section{Moulinette}
+
+\begin{itemize}
+
+\item Mettre \verb=/= et * au même niveau dans R.
+
+\item Changer la précédence du - unaire dans R.
+
+\item Ajouter Require Arith par necessite si Require ArithRing ou Require ZArithRing.
+
+\item Ajouter Require ZArith par necessite si Require ZArithRing ou Require Omega.
+
+\item Enlever le Export de Bool, Arith et ZARith de Ring quand inapproprié et
+l'ajouter à côté des Require Ring.
+
+\item Remplacer "Check n" par "n:Check ..."
+
+\item Renommer Variable/Hypothesis hors section en Parameter/Axiom.
+
+\item Renommer les \verb=command0=, \verb=command1=, ... \verb=lcommand= etc en
+\verb=constr0=, \verb=constr1=, ... \verb=lconstr=.
+
+\item Remplacer les noms Coq.omega.Omega par Coq.Omega ...
+
+\item Remplacer AddPath par Add LoadPath (ou + court)
+
+\item Unify + and \{\}+\{\} and +\{\} using Prop $\leq$ Set ??
+
+\item Remplacer Implicit Arguments On/Off par Set/Unset Implicit Arguments.
+
+\item La syntaxe \verb=Intros (a,b)= est inutile, \verb=Intros [a b]= fait l'affaire.
+
+\item Virer \verb=Goal= sans argument (synonyme de \verb=Proof= et sans effets).
+
+\item Remplacer Save. par Qed.
+
+\item Remplacer \verb=Zmult_Zplus_distr= par \verb=Zmult_plus_distr_r=
+et \verb=Zmult_plus_distr= par \verb=Zmult_plus_distr_l=.
+
+\end{itemize}
+
+\end{document}
diff --git a/dev/doc/parse.ml b/dev/doc/parse.ml
new file mode 100644
index 00000000..e537b1f2
--- /dev/null
+++ b/dev/doc/parse.ml
@@ -0,0 +1,183 @@
+
+open Ast
+
+type assoc = L | R | N
+
+let level = function
+  | "--" -> 70,L
+  | "=" -> 70,N
+  | "+" -> 60,L
+  | "++" -> 60,R
+  | "+++" -> 60,R
+  | "-" -> 60,L
+  | "*" -> 50,L
+  | "/" -> 50,L
+  | "**" -> 40,R
+  | ":" -> (100,R)
+  | "->" -> (90,R)
+  | s -> failwith ("unknowm operator '"^s^"'")
+
+let fixity = function
+  | "--" -> [L]
+  | "=" -> [N]
+  | ("+"|"-"|"*"|"/") -> [L;N]
+  | "++" -> [R]
+  | _ -> [L;N;R]
+
+let ground_oper = function
+    ("-"|"+") -> true
+  | _ -> false
+
+let is_prefix op = List.mem L (fixity op)
+let is_infix op = List.mem N (fixity op)
+let is_postfix op = List.mem R (fixity op)
+
+let mk_inf op t1 t2 =
+  if not (is_infix op) then failwith (op^" not infix");
+  Infix(op,t1,t2)
+
+let mk_post op t =
+  if not (is_postfix op) then failwith (op^" not postfix");
+  Postfix(op,t)
+
+
+(* Pb avec ground_oper: pas de diff entre -1 et -(1) *)
+let mk_pre op t =
+  if not (is_prefix op) then failwith (op^" not prefix");
+  if ground_oper op then
+    match t with
+    | Int i -> Int (op^i)
+    | _     -> Prefix(op,t)
+  else Prefix(op,t)
+
+(* teste si on peut reduire op suivi d'un op de niveau (n,a)
+   si la reponse est false, c'est que l'op (n,a) doit se reduire
+   avant *)
+let red_left_op (nl,al) (nr,ar) =
+  if nl < nr then true
+  else
+    if nl = nr then
+      match al,ar with
+        | (L|N), L -> true
+        | R, (R|N) -> false
+        | R, L ->  failwith "conflit d'assoc: ambigu"
+        | (L|N), (R|N) -> failwith "conflit d'assoc: blocage"
+    else false
+
+
+type level = int * assoc
+type stack =
+  | PrefixOper of string list
+  | Term of constr_ast * stack
+  | Oper of string list * string * constr_ast * stack
+
+let rec str_ast = function
+  | Infix(op,t1,t2) -> str_ast t1 ^ " " ^ op ^ " " ^ str_ast t2
+  | Postfix(op,t) -> str_ast t ^ " " ^ op
+  | Prefix(op,t) -> op ^ " " ^ str_ast t
+  | _ -> "_"
+
+let rec str_stack = function
+  | PrefixOper ops -> String.concat " " (List.rev ops)
+  | Term (t,s) -> str_stack s ^ " (" ^ str_ast t ^ ")"
+  | Oper(ops,lop,t,s) ->
+      str_stack (Term(t,s)) ^ " " ^ lop ^ " " ^
+      String.concat " " (List.rev ops) 
+
+let pps s = prerr_endline (str_stack s)
+let err s stk = failwith (s^": "^str_stack stk)
+
+
+let empty = PrefixOper []
+
+let check_fixity_term stk =
+  match stk with
+      Term _ -> err "2 termes successifs" stk
+    | _ -> ()
+
+let shift_term t stk =
+  check_fixity_term stk;
+  Term(t,stk)
+
+let shift_oper op stk =
+  match stk with
+    | Oper(ops,lop,t,s) -> Oper(op::ops,lop,t,s)
+    | Term(t,s) -> Oper([],op,t,s)
+    | PrefixOper ops -> PrefixOper (op::ops)
+
+let is_reducible lv stk =
+  match stk with
+    | Oper([],iop,_,_)  -> red_left_op (level iop) lv
+    | Oper(op::_,_,_,_) -> red_left_op (level op) lv
+    | PrefixOper(op::_) -> red_left_op (level op) lv
+    | _                 -> false
+
+let reduce_head (t,stk) =
+  match stk with
+    | Oper([],iop,t1,s) ->
+        (Infix(iop,t1,t), s)
+    | Oper(op::ops,lop,t',s) ->
+        (mk_pre op t, Oper(ops,lop,t',s))
+    | PrefixOper(op::ops) ->
+        (Prefix(op,t), PrefixOper ops)
+    | _ -> assert false
+
+let rec reduce_level lv (t,s) =
+  if is_reducible lv s then reduce_level lv (reduce_head (t, s))
+  else (t, s)
+
+let reduce_post op (t,s) =
+  let (t',s') = reduce_level (level op) (t,s) in
+  (mk_post op t', s')
+
+let reduce_posts stk =
+  match stk with
+      Oper(ops,iop,t,s) ->
+        let pts1 = reduce_post iop (t,s) in
+        List.fold_right reduce_post ops pts1
+    | Term(t,s) -> (t,s)
+    | PrefixOper _ -> failwith "reduce_posts"
+
+
+let shift_infix op stk =
+  let (t,s) = reduce_level (level op) (reduce_posts stk) in
+  Oper([],op,t,s)
+
+let is_better_infix op stk =
+  match stk with
+    | Oper(ops,iop,t,s) ->
+        is_postfix iop &&
+        List.for_all is_postfix ops &&
+        (not (is_prefix op) || red_left_op (level iop) (level op))
+    | Term _ -> false
+    | _ -> assert false
+
+let parse_oper op stk =
+  match stk with
+    | PrefixOper _ ->
+        if is_prefix op then shift_oper op stk else failwith "prefix_oper"
+    | Oper _ ->
+        if is_infix op then
+          if is_better_infix op stk then shift_infix op stk
+          else shift_oper op stk
+        else if is_prefix op then shift_oper op stk
+        else if is_postfix op then
+          let (t,s) = reduce_post op (reduce_posts stk) in
+          Term(t,s)
+        else assert false
+    | Term(t,s) ->
+        if is_infix op then shift_infix op stk
+        else if is_postfix op then
+          let (t2,s2) = reduce_post op (t,s) in Term(t2,s2)
+        else failwith "infix/postfix"
+
+let parse_term = shift_term
+
+let rec close_stack stk =
+  match stk with
+      Term(t,PrefixOper []) -> t
+    | PrefixOper _ -> failwith "expression sans atomes"
+    | _ ->
+        let (t,s) = reduce_head (reduce_posts stk) in
+        close_stack (Term(t,s))
+
diff --git a/dev/doc/parsing.dep.ps b/dev/doc/parsing.dep.ps
new file mode 100644
index 00000000..723d8c69
--- /dev/null
+++ b/dev/doc/parsing.dep.ps
@@ -0,0 +1,1115 @@
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diff --git a/dev/doc/preamble.tex b/dev/doc/preamble.tex
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+\documentclass[11pt]{article}
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diff --git a/dev/doc/pretyping.dep.ps b/dev/doc/pretyping.dep.ps
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diff --git a/dev/doc/syntax-v8.tex b/dev/doc/syntax-v8.tex
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--- /dev/null
+++ b/dev/doc/syntax-v8.tex
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+
+\documentclass{article}
+
+\usepackage{verbatim}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{array}
+\usepackage{fullpage}
+
+\author{B.~Barras}
+\title{Syntax of Coq V8}
+
+%% Le _ est un caractère normal
+\catcode`\_=13
+\let\subscr=_
+\def_{\ifmmode\sb\else\subscr\fi}
+
+\def\bfbar{\ensuremath{|\hskip -0.22em{}|\hskip -0.24em{}|}}
+\def\TERMbar{\bfbar}
+\def\TERMbarbar{\bfbar\bfbar}
+\def\notv{\text{_}}
+\def\infx#1{\notv#1\notv}
+
+
+%% Macros pour les grammaires
+\def\GR#1{\text{\large(}#1\text{\large)}}
+\def\NT#1{\langle\textit{#1}\rangle}
+\def\NTL#1#2{\langle\textit{#1}\rangle_{#2}}
+\def\TERM#1{{\bf\textrm{\bf #1}}}
+%\def\TERM#1{{\bf\textsf{#1}}}
+\def\KWD#1{\TERM{#1}}
+\def\ETERM#1{\TERM{#1}}
+\def\CHAR#1{\TERM{#1}}
+
+\def\STAR#1{#1*}
+\def\STARGR#1{\GR{#1}*}
+\def\PLUS#1{#1+}
+\def\PLUSGR#1{\GR{#1}+}
+\def\OPT#1{#1?}
+\def\OPTGR#1{\GR{#1}?}
+%% Tableaux de definition de non-terminaux
+\newenvironment{cadre}
+        {\begin{array}{|c|}\hline\\}
+        {\\\\\hline\end{array}}
+\newenvironment{rulebox}
+        {$$\begin{cadre}\begin{array}{r@{~}c@{~}l@{}l@{}r}}
+        {\end{array}\end{cadre}$$}
+\def\DEFNT#1{\NT{#1} & ::= &}
+\def\EXTNT#1{\NT{#1} & ::= & ... \\&|&}
+\def\RNAME#1{(\textsc{#1})}
+\def\SEPDEF{\\\\}
+\def\nlsep{\\&|&}
+\def\nlcont{\\&&}
+\newenvironment{rules}
+        {\begin{center}\begin{rulebox}}
+        {\end{rulebox}\end{center}}
+
+\begin{document}
+
+\maketitle
+
+\section{Meta notations used in this document}
+
+Non-terminals are printed between angle brackets (e.g. $\NT{non-terminal}$) and
+terminal symbols are printed in bold font (e.g. $\ETERM{terminal}$). Lexemes
+are displayed as non-terminals.
+
+The usual operators on regular expressions:
+\begin{center}
+\begin{tabular}{l|l}
+\hfil notation & \hfil  meaning \\
+\hline
+$\STAR{regexp}$ & repeat $regexp$ 0 or more times \\
+$\PLUS{regexp}$ & repeat $regexp$ 1 or more times \\
+$\OPT{regexp}$ & $regexp$ is optional \\
+$regexp_1~\mid~regexp_2$ & alternative
+\end{tabular}
+\end{center}
+
+Parenthesis are used to group regexps. Beware to distinguish this operator
+$\GR{~}$ from the terminals $\ETERM{( )}$, and $\mid$ from terminal
+\TERMbar.
+
+Rules are optionaly annotated in the right margin with:
+\begin{itemize}
+\item a precedence and associativity (L for left, R for right and N for no associativity), indicating how to solve conflicts;
+  lower levels are tighter;
+\item a rule name.
+\end{itemize}
+In order to solve some conflicts, a non-terminal may be invoked with a
+precedence (notation: $\NTL{entry}{prec}$), meaning that rules with higher
+precedence do not apply.
+
+\section{Lexical conventions}
+
+Lexical categories are:
+\begin{rules}
+\DEFNT{ident}
+     \STARGR{\NT{letter}\mid\CHAR{_}}
+     \STARGR{\NT{letter}\mid \NT{digit} \mid \CHAR{'} \mid \CHAR{_}}
+\SEPDEF
+\DEFNT{field}       \CHAR{.}\NT{ident}
+\SEPDEF
+\DEFNT{meta-ident}  \CHAR{?}\NT{ident}   
+\SEPDEF
+\DEFNT{num}         \PLUS{\NT{digit}}
+\SEPDEF
+\DEFNT{int}         \NT{num} \mid \CHAR{-}\NT{num}
+\SEPDEF
+\DEFNT{digit}       \CHAR{0}-\CHAR{9}
+\SEPDEF
+\DEFNT{letter}      \CHAR{a}-\CHAR{z}\mid\CHAR{A}-\CHAR{Z}
+                    \mid\NT{unicode-letter}
+
+\SEPDEF
+\DEFNT{string}      \CHAR{"}~\STARGR{\CHAR{""}\mid\NT{unicode-char-but-"}}~\CHAR{"}
+\end{rules}
+
+Reserved identifiers for the core syntax are:
+\begin{quote}
+\KWD{as},
+\KWD{cofix},
+\KWD{else},
+\KWD{end},
+\KWD{fix},
+\KWD{for},
+\KWD{forall},
+\KWD{fun},
+\KWD{if},
+\KWD{in},
+\KWD{let},
+\KWD{match}, 
+\KWD{Prop},
+\KWD{return}, 
+\KWD{Set},
+\KWD{then},
+\KWD{Type},
+\KWD{with}  
+\end{quote}
+
+Symbols used in the core syntax:
+$$ \KWD{(}
+~~ \KWD{)}
+~~ \KWD{\{}
+~~ \KWD{\}}
+~~ \KWD{:}
+~~ \KWD{,}
+~~ \Rightarrow
+~~ \rightarrow
+~~ \KWD{:=}
+~~ \KWD{_}
+~~ \TERMbar
+~~ \KWD{@}
+~~ \KWD{\%}
+~~ \KWD{.(}
+$$
+
+Note that \TERM{struct} is not a reserved identifier.
+
+\section{Syntax of terms}
+
+\subsection{Core syntax}
+
+The main entry point of the term grammar is $\NTL{constr}{9}$. When no
+conflict can appear, $\NTL{constr}{200}$ is also used as entry point.
+
+\begin{rules}
+\DEFNT{constr}
+       \NT{binder-constr}                             &200R~~ &\RNAME{binders}
+\nlsep \NT{constr}~\KWD{:}~\NT{constr}                &100R &\RNAME{cast}
+\nlsep \NT{constr}~\KWD{:}~\NT{binder-constr}         &100R &\RNAME{cast'}
+\nlsep \NT{constr}~\KWD{$\rightarrow$}~\NT{constr}    &80R  &\RNAME{arrow}
+\nlsep \NT{constr}~\KWD{$\rightarrow$}~\NT{binder-constr} &80R &\RNAME{arrow'}
+\nlsep \NT{constr}~\PLUS{\NT{appl-arg}}               &10L  &\RNAME{apply}
+\nlsep \KWD{@}~\NT{reference}~\STAR{\NTL{constr}{9}}  &10L  &\RNAME{expl-apply}
+\nlsep \NT{constr}~\KWD{.(}
+       ~\NT{reference}~\STAR{\NT{appl-arg}}~\TERM{)}  &1L & \RNAME{proj}
+\nlsep \NT{constr}~\KWD{.(}~\TERM{@}
+       ~\NT{reference}~\STAR{\NTL{constr}{9}}~\TERM{)} &1L & \RNAME{expl-proj}
+\nlsep \NT{constr} ~ \KWD{\%} ~ \NT{ident}            &1L   &\RNAME{scope-chg}
+\nlsep \NT{atomic-constr}                             &0
+\nlsep \NT{match-expr}                                &0
+\nlsep \KWD{(}~\NT{constr}~\KWD{)}                    &0
+\SEPDEF
+\DEFNT{binder-constr}
+       \KWD{forall}~\NT{binder-list}~\KWD{,}~\NTL{constr}{200} 
+          &&\RNAME{prod}
+\nlsep \KWD{fun} ~\NT{binder-list} ~\KWD{$\Rightarrow$}~\NTL{constr}{200}
+          &&\RNAME{lambda}
+\nlsep \NT{fix-expr}
+\nlsep \KWD{let}~\NT{ident-with-params} ~\KWD{:=}~\NTL{constr}{200}
+       ~\KWD{in}~\NTL{constr}{200}  &&\RNAME{let}
+\nlsep \KWD{let}~\NT{single-fix} ~\KWD{in}~\NTL{constr}{200}
+          &&\RNAME{rec-let}
+\nlsep \KWD{let}~\KWD{(}~\OPT{\NT{let-pattern}}~\KWD{)}~\OPT{\NT{return-type}}
+       ~\KWD{:=}~\NTL{constr}{200}~\KWD{in}~\NTL{constr}{200}
+          &&\RNAME{let-case}
+\nlsep \KWD{if}~\NT{if-item}
+       ~\KWD{then}~\NTL{constr}{200}~\KWD{else}~\NTL{constr}{200}
+          &&\RNAME{if-case}
+\SEPDEF
+\DEFNT{appl-arg}
+       \KWD{(}~\NT{ident}~\!\KWD{:=}~\NTL{constr}{200}~\KWD{)}
+          &&\RNAME{impl-arg}
+\nlsep \KWD{(}~\NT{num}~\!\KWD{:=}~\NTL{constr}{200}~\KWD{)}
+          &&\RNAME{impl-arg}
+\nlsep \NTL{constr}{9}
+\SEPDEF
+\DEFNT{atomic-constr}
+       \NT{reference}     && \RNAME{variables}
+\nlsep \NT{sort}          && \RNAME{CIC-sort}
+\nlsep \NT{num}           && \RNAME{number}
+\nlsep \KWD{_}            && \RNAME{hole}
+\nlsep \NT{meta-ident}    && \RNAME{meta/evar}
+\end{rules}
+
+
+
+\begin{rules}
+\DEFNT{ident-with-params}
+       \NT{ident}~\STAR{\NT{binder-let}}~\NT{type-cstr}
+\SEPDEF
+\DEFNT{binder-list}
+       \NT{binder}~\STAR{\NT{binder-let}}
+\nlsep \PLUS{\NT{name}}~\KWD{:}~\NT{constr}
+\SEPDEF
+\DEFNT{binder}
+       \NT{name}      &&\RNAME{infer}
+\nlsep \KWD{(}~\PLUS{\NT{name}}~\KWD{:}~\NT{constr}
+       ~\KWD{)}      &&\RNAME{binder}
+\SEPDEF
+\DEFNT{binder-let}
+       \NT{binder}
+\nlsep \KWD{(}~\NT{name}~\NT{type-cstr}~\KWD{:=}~\NT{constr}~\KWD{)}
+\SEPDEF
+\DEFNT{let-pattern}
+       \NT{name}
+\nlsep \NT{name} ~\KWD{,} ~\NT{let-pattern}
+\SEPDEF
+\DEFNT{type-cstr}
+       \OPTGR{\KWD{:}~\NT{constr}}
+\SEPDEF
+\DEFNT{reference}
+       \NT{ident}                   && \RNAME{short-ident}
+\nlsep \NT{ident}~\PLUS{\NT{field}} && \RNAME{qualid}
+\SEPDEF
+\DEFNT{sort}
+       \KWD{Prop} ~\mid~ \KWD{Set} ~\mid~ \KWD{Type}
+\SEPDEF
+\DEFNT{name}
+       \NT{ident} ~\mid~ \KWD{_}
+\end{rules}
+
+\begin{rules}
+\DEFNT{fix-expr}
+       \NT{single-fix}
+\nlsep \NT{single-fix}~\PLUSGR{\KWD{with}~\NT{fix-decl}}
+      ~\KWD{for}~\NT{ident}
+\SEPDEF
+\DEFNT{single-fix}
+       \NT{fix-kw}~\NT{fix-decl}
+\SEPDEF
+\DEFNT{fix-kw} \KWD{fix} ~\mid~ \KWD{cofix}
+\SEPDEF
+\DEFNT{fix-decl}
+       \NT{ident}~\STAR{\NT{binder-let}}~\OPT{\NT{annot}}~\NT{type-cstr}
+       ~\KWD{:=}~\NTL{constr}{200}
+\SEPDEF
+\DEFNT{annot}
+       \KWD{\{}~\TERM{struct}~\NT{ident}~\KWD{\}}
+\end{rules}
+
+
+\begin{rules}
+\DEFNT{match-expr}
+       \KWD{match}~\NT{match-items}~\OPT{\NT{return-type}}~\KWD{with}
+  ~\OPT{\TERMbar}~\OPT{\NT{branches}}~\KWD{end}        &&\RNAME{match}
+\SEPDEF
+\DEFNT{match-items}
+       \NT{match-item} ~\KWD{,} ~\NT{match-items}
+\nlsep \NT{match-item}
+\SEPDEF
+\DEFNT{match-item}
+       \NTL{constr}{100}~\OPTGR{\KWD{as}~\NT{name}}
+       ~\OPTGR{\KWD{in}~\NTL{constr}{100}}
+\SEPDEF
+\DEFNT{return-type}
+       \KWD{return}~\NTL{constr}{100}
+\SEPDEF
+\DEFNT{if-item}
+       \NT{constr}~\OPTGR{\OPTGR{\KWD{as}~\NT{name}}~\NT{return-type}}
+\SEPDEF
+\DEFNT{branches}
+       \NT{eqn}~\TERMbar~\NT{branches}
+\nlsep \NT{eqn}
+\SEPDEF
+\DEFNT{eqn}
+       \NT{pattern} ~\STARGR{\KWD{,}~\NT{pattern}}
+       ~\KWD{$\Rightarrow$}~\NT{constr}
+\SEPDEF
+\DEFNT{pattern}
+       \NT{reference}~\PLUS{\NT{pattern}}  &1L~~ & \RNAME{constructor}
+\nlsep \NT{pattern}~\KWD{as}~\NT{ident}    &1L & \RNAME{alias}
+\nlsep \NT{pattern}~\KWD{\%}~\NT{ident}    &1L & \RNAME{scope-change}
+\nlsep \NT{reference}                      &0  & \RNAME{pattern-var}
+\nlsep \KWD{_}                             &0  & \RNAME{hole}
+\nlsep \NT{num}                            &0
+\nlsep \KWD{(}~\NT{tuple-pattern}~\KWD{)}
+\SEPDEF
+\DEFNT{tuple-pattern}
+       \NT{pattern}
+\nlsep \NT{tuple-pattern}~\KWD{,}~\NT{pattern} && \RNAME{pair}
+\end{rules}
+
+\subsection{Notations of the prelude (logic and basic arithmetic)}
+
+Reserved notations:
+
+$$
+\begin{array}{l|c}
+\text{Symbol} & \text{precedence} \\
+\hline
+\infx{,}             & 250L \\
+\KWD{IF}~\notv~\KWD{then}~\notv~\KWD{else}~\notv
+                     & 200R \\
+\infx{:}             & 100R \\
+\infx{\leftrightarrow} & 95N \\
+\infx{\rightarrow}   & 90R \\
+\infx{\vee}          & 85R \\
+\infx{\wedge}        & 80R \\
+\tilde{}\notv        & 75R \\
+\begin{array}[c]{@{}l@{}}
+ \infx{=}\quad \infx{=}\KWD{$:>$}\notv \quad \infx{=}=\notv
+ \quad \infx{\neq} \quad  \infx{\neq}\KWD{$:>$}\notv \\
+ \infx{<}\quad\infx{>} \quad \infx{\leq}\quad\infx{\geq}
+ \quad \infx{<}<\notv \quad \infx{<}\leq\notv
+ \quad \infx{\leq}<\notv \quad \infx{\leq}\leq\notv
+\end{array}          & 70N \\
+\infx{+}\quad\infx{-}\quad -\notv   & 50L \\
+\infx{*}\quad\infx{/}\quad /\notv   & 40L \\
+\end{array}
+$$
+
+Existential quantifiers follows the \KWD{forall} notation (with same
+precedence 200), but only one quantified variable is allowed.
+
+\begin{rules}
+\EXTNT{binder-constr}
+       \NT{quantifier-kwd}~\NT{name}~\NT{type-cstr}~\KWD{,}~\NTL{constr}{200} \\
+\SEPDEF
+\DEFNT{quantifier-kwd}
+       \TERM{exists} && \RNAME{ex}
+\nlsep \TERM{exists2} && \RNAME{ex2}
+\end{rules}
+
+$$
+\begin{array}{l|c|l}
+\text{Symbol} & \text{precedence} \\
+\hline
+\notv+\{\notv\}                            & 50 & \RNAME{sumor} \\
+\{\notv:\notv~|~\notv\}                    & 0 & \RNAME{sig} \\
+\{\notv:\notv~|~\notv \& \notv \}          & 0 & \RNAME{sig2} \\
+\{\notv:\notv~\&~\notv \}                  & 0 & \RNAME{sigS} \\
+\{\notv:\notv~\&~\notv \& \notv \}         & 0 & \RNAME{sigS2} \\
+\{\notv\}+\{\notv\}                        & 0 & \RNAME{sumbool} \\
+\end{array}
+$$
+
+%% Strange: nat + {x:nat|x=x} * nat  == ( + ) *
+
+\section{Grammar of tactics}
+
+\def\tacconstr{\NTL{constr}{9}}
+\def\taclconstr{\NTL{constr}{200}}
+
+Additional symbols are:
+$$ \TERM{'}
+~~ \KWD{;}
+~~ \TERM{()}
+~~ \TERMbarbar
+~~ \TERM{$\vdash$}
+~~ \TERM{[}
+~~ \TERM{]}
+~~ \TERM{$\leftarrow$}
+$$
+Additional reserved keywords are:
+$$ \KWD{at}
+~~ \TERM{using}
+$$
+
+\subsection{Basic tactics}
+
+\begin{rules}
+\DEFNT{simple-tactic}
+       \TERM{intros}~\TERM{until}~\NT{quantified-hyp}
+\nlsep \TERM{intros}~\NT{intro-patterns}
+\nlsep \TERM{intro}~\OPT{\NT{ident}}~\OPTGR{\TERM{after}~\NT{ident}}
+%%
+\nlsep \TERM{assumption}
+\nlsep \TERM{exact}~\tacconstr
+%%
+\nlsep \TERM{apply}~\NT{constr-with-bindings}
+\nlsep \TERM{elim}~\NT{constr-with-bindings}~\OPT{\NT{eliminator}}
+\nlsep \TERM{elimtype}~\tacconstr
+\nlsep \TERM{case}~\NT{constr-with-bindings}
+\nlsep \TERM{casetype}~\tacconstr
+\nlsep \KWD{fix}~\OPT{\NT{ident}}~\NT{num}
+\nlsep \KWD{fix}~\NT{ident}~\NT{num}~\KWD{with}~\PLUS{\NT{fix-spec}}
+\nlsep \KWD{cofix}~\OPT{\NT{ident}}
+\nlsep \KWD{cofix}~\NT{ident}~\PLUS{\NT{fix-spec}}
+%%
+\nlsep \TERM{cut}~\tacconstr
+\nlsep \TERM{assert}~\tacconstr
+\nlsep \TERM{assert}~
+  \TERM{(}~\NT{ident}~\KWD{:}~\taclconstr~\TERM{)}
+\nlsep \TERM{assert}~
+  \TERM{(}~\NT{ident}~\KWD{:=}~\taclconstr~\TERM{)}
+\nlsep \TERM{pose}~\tacconstr
+\nlsep \TERM{pose}~
+  \TERM{(}~\NT{ident}~\KWD{:=}~\taclconstr~\TERM{)}
+\nlsep \TERM{generalize}~\PLUS{\tacconstr}
+\nlsep \TERM{generalize}~\TERM{dependent}~\tacconstr
+\nlsep \TERM{set}~\tacconstr~\OPT{\NT{clause}}
+\nlsep \TERM{set}~
+  \TERM{(}~\NT{ident}~\KWD{:=}~\taclconstr~\TERM{)}~\OPT{\NT{clause}}
+\nlsep \TERM{instantiate}~
+  \TERM{(}~\NT{num}~\TERM{:=}~\taclconstr~\TERM{)}~\OPT{\NT{clause}}
+%%
+\nlsep \TERM{specialize}~\OPT{\NT{num}}~\NT{constr-with-bindings}
+\nlsep \TERM{lapply}~\tacconstr
+%%
+\nlsep \TERM{simple}~\TERM{induction}~\NT{quantified-hyp}
+\nlsep \TERM{induction}~\NT{induction-arg}~\OPT{\NT{with-names}}
+       ~\OPT{\NT{eliminator}}
+\nlsep \TERM{double}~\TERM{induction}~\NT{quantified-hyp}~\NT{quantified-hyp}
+\nlsep \TERM{simple}~\TERM{destruct}~\NT{quantified-hyp}
+\nlsep \TERM{destruct}~\NT{induction-arg}~\OPT{\NT{with-names}}
+       ~\OPT{\NT{eliminator}}
+\nlsep \TERM{decompose}~\TERM{record}~\tacconstr
+\nlsep \TERM{decompose}~\TERM{sum}~\tacconstr
+\nlsep \TERM{decompose}~\TERM{[}~\PLUS{\NT{reference}}~\TERM{]}
+       ~\tacconstr
+%%
+\nlsep ...
+\end{rules}
+
+\begin{rules}
+\EXTNT{simple-tactic}
+       \TERM{trivial}~\OPT{\NT{hint-bases}}
+\nlsep \TERM{auto}~\OPT{\NT{num}}~\OPT{\NT{hint-bases}}
+%%
+%%\nlsep \TERM{autotdb}~\OPT{\NT{num}}
+%%\nlsep \TERM{cdhyp}~\NT{ident}
+%%\nlsep \TERM{dhyp}~\NT{ident}
+%%\nlsep \TERM{dconcl}
+%%\nlsep \TERM{superauto}~\NT{auto-args}
+\nlsep \TERM{auto}~\OPT{\NT{num}}~\TERM{decomp}~\OPT{\NT{num}}
+%%
+\nlsep \TERM{clear}~\PLUS{\NT{ident}}
+\nlsep \TERM{clearbody}~\PLUS{\NT{ident}}
+\nlsep \TERM{move}~\NT{ident}~\TERM{after}~\NT{ident}
+\nlsep \TERM{rename}~\NT{ident}~\TERM{into}~\NT{ident}
+%%
+\nlsep \TERM{left}~\OPT{\NT{with-binding-list}}
+\nlsep \TERM{right}~\OPT{\NT{with-binding-list}}
+\nlsep \TERM{split}~\OPT{\NT{with-binding-list}}
+\nlsep \TERM{exists}~\OPT{\NT{binding-list}}
+\nlsep \TERM{constructor}~\NT{num}~\OPT{\NT{with-binding-list}}
+\nlsep \TERM{constructor}~\OPT{\NT{tactic}}
+%%
+\nlsep \TERM{reflexivity}
+\nlsep \TERM{symmetry}~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{transitivity}~\tacconstr
+%%
+\nlsep \NT{inversion-kwd}~\NT{quantified-hyp}~\OPT{\NT{with-names}}~\OPT{\NT{clause}}
+\nlsep \TERM{dependent}~\NT{inversion-kwd}~\NT{quantified-hyp}
+  ~\OPT{\NT{with-names}}~\OPTGR{\KWD{with}~\tacconstr}
+\nlsep \TERM{inversion}~\NT{quantified-hyp}~\TERM{using}~\tacconstr~\OPT{\NT{clause}}
+%%
+\nlsep \NT{red-expr}~\OPT{\NT{clause}}
+\nlsep \TERM{change}~\NT{conversion}~\OPT{\NT{clause}}
+\SEPDEF
+\DEFNT{red-expr}
+       \TERM{red} ~\mid~ \TERM{hnf} ~\mid~ \TERM{compute}
+\nlsep \TERM{simpl}~\OPT{\NT{pattern-occ}}
+\nlsep \TERM{cbv}~\PLUS{\NT{red-flag}}
+\nlsep \TERM{lazy}~\PLUS{\NT{red-flag}}
+\nlsep \TERM{unfold}~\NT{unfold-occ}~\STARGR{\KWD{,}~\NT{unfold-occ}}
+\nlsep \TERM{fold}~\PLUS{\tacconstr}
+\nlsep \TERM{pattern}~\NT{pattern-occ}~\STARGR{\KWD{,}~\NT{pattern-occ}}
+\SEPDEF
+\DEFNT{conversion}
+       \NT{pattern-occ}~\KWD{with}~\tacconstr
+\nlsep \tacconstr
+\SEPDEF
+\DEFNT{inversion-kwd}
+       \TERM{inversion} ~\mid~ \TERM{invesion_clear} ~\mid~
+       \TERM{simple}~\TERM{inversion}
+\end{rules}
+
+Conflicts exists between integers and constrs.
+
+\begin{rules}
+\DEFNT{quantified-hyp}
+       \NT{int}~\mid~\NT{ident}
+\SEPDEF
+\DEFNT{induction-arg}
+       \NT{int}~\mid~\tacconstr
+\SEPDEF
+\DEFNT{fix-spec}
+       \KWD{(}~\NT{ident}~\STAR{\NT{binder}}~\OPT{\NT{annot}}
+       ~\KWD{:}~\taclconstr~\KWD{)}
+\SEPDEF
+\DEFNT{intro-patterns}
+       \STAR{\NT{intro-pattern}}
+\SEPDEF
+\DEFNT{intro-pattern}
+       \NT{name}
+\nlsep \TERM{[}~\NT{intro-patterns}~\STARGR{\TERMbar~\NT{intro-patterns}}
+       ~\TERM{]}
+\nlsep \KWD{(}~\NT{intro-pattern}~\STARGR{\KWD{,}~\NT{intro-pattern}}
+       ~\KWD{)}
+\SEPDEF
+\DEFNT{with-names}
+%       \KWD{as}~\TERM{[}~\STAR{\NT{ident}}~\STARGR{\TERMbar~\STAR{\NT{ident}}}
+%       ~\TERM{]}
+       \KWD{as}~\NT{intro-pattern}
+\SEPDEF
+\DEFNT{eliminator}
+       \TERM{using}~\NT{constr-with-bindings}
+\SEPDEF
+\DEFNT{constr-with-bindings}
+       % dangling ``with'' of ``fix'' can conflict with ``with''
+       \tacconstr~\OPT{\NT{with-binding-list}}
+\SEPDEF
+\DEFNT{with-binding-list}
+       \KWD{with}~\NT{binding-list}
+\SEPDEF
+\DEFNT{binding-list}
+       \PLUS{\tacconstr}
+\nlsep \PLUS{\NT{simple-binding}}
+\SEPDEF
+\DEFNT{simple-binding}
+       \KWD{(}~\NT{quantified-hyp}~\KWD{:=}~\taclconstr~\KWD{)}
+\SEPDEF
+\DEFNT{red-flag}
+       \TERM{beta} ~\mid~ \TERM{iota} ~\mid~ \TERM{zeta}
+       ~\mid~ \TERM{delta} ~\mid~
+       \TERM{delta}~\OPT{\TERM{-}}~\TERM{[}~\PLUS{\NT{reference}}~\TERM{]}
+\SEPDEF
+\DEFNT{clause}
+       \KWD{in}~\TERM{*}
+\nlsep \KWD{in}~\TERM{*}~\KWD{$\vdash$}~\OPT{\NT{concl-occ}}
+\nlsep \KWD{in}~\OPT{\NT{hyp-ident-list}} ~\KWD{$\vdash$} ~\OPT{\NT{concl-occ}}
+\nlsep \KWD{in}~\OPT{\NT{hyp-ident-list}}
+\SEPDEF
+\DEFNT{hyp-ident-list}
+       \NT{hyp-ident}
+\nlsep \NT{hyp-ident}~\KWD{,}~\NT{hyp-ident-list}
+\SEPDEF
+\DEFNT{hyp-ident}
+       \NT{ident}
+\nlsep \KWD{(}~\TERM{type}~\TERM{of}~\NT{ident}~\KWD{)}
+\nlsep \KWD{(}~\TERM{value}~\TERM{of}~\NT{ident}~\KWD{)}
+\SEPDEF
+\DEFNT{concl-occ}
+       \TERM{*} ~\NT{occurrences}
+\SEPDEF
+\DEFNT{pattern-occ}
+       \tacconstr ~\NT{occurrences}
+\SEPDEF
+\DEFNT{unfold-occ}
+       \NT{reference}~\NT{occurrences}
+\SEPDEF
+\DEFNT{occurrences}
+       ~\OPTGR{\KWD{at}~\PLUS{\NT{int}}}
+\SEPDEF
+\DEFNT{hint-bases}
+       \KWD{with}~\TERM{*}
+\nlsep \KWD{with}~\PLUS{\NT{ident}}
+\SEPDEF
+\DEFNT{auto-args}
+       \OPT{\NT{num}}~\OPTGR{\TERM{adding}~\TERM{[}~\PLUS{\NT{reference}}
+       ~\TERM{]}}~\OPT{\TERM{destructuring}}~\OPTGR{\TERM{using}~\TERM{tdb}}
+\end{rules}
+
+\subsection{Ltac}
+
+%% Currently, there are conflicts with keyword \KWD{in}: in the following,
+%% has the keyword to be associated to \KWD{let} or to tactic \TERM{simpl} ?
+%% \begin{center}
+%% \texttt{let x := simpl in ...}
+%% \end{center}
+
+
+\begin{rules}
+\DEFNT{tactic}
+       \NT{tactic} ~\KWD{;} ~\NT{tactic}  &5 &\RNAME{Then}
+\nlsep \NT{tactic} ~\KWD{;}~\TERM{[} ~\OPT{\NT{tactic-seq}} ~\TERM{]}
+         &5 &\RNAME{Then-seq}
+%%
+\nlsep \TERM{try} ~\NT{tactic}     &3R &\RNAME{Try}
+\nlsep \TERM{do} ~\NT{int-or-var} ~\NT{tactic}
+\nlsep \TERM{repeat} ~\NT{tactic}
+\nlsep \TERM{progress} ~\NT{tactic}
+\nlsep \TERM{info} ~\NT{tactic}
+\nlsep \TERM{abstract}~\NTL{tactic}{2}~\OPTGR{\TERM{using}~\NT{ident}}
+%%
+\nlsep \NT{tactic} ~\TERMbarbar ~\NT{tactic} &2R &\RNAME{Orelse}
+%%
+\nlsep \KWD{fun} ~\PLUS{\NT{name}} ~\KWD{$\Rightarrow$}
+       ~\NT{tactic}  &1 &\RNAME{Fun-tac}
+\nlsep \KWD{let} ~\NT{let-clauses} ~\KWD{in} ~\NT{tactic}
+\nlsep \KWD{let} ~\TERM{rec} ~\NT{rec-clauses} ~\KWD{in} ~\NT{tactic}
+\nlsep \KWD{match}~\OPT{\TERM{reverse}}~\TERM{goal}~\KWD{with}
+       ~\OPT{\TERMbar}~\OPT{\NT{match-goal-rules}} ~\KWD{end}
+\nlsep \KWD{match} ~\NT{tactic} ~\KWD{with}
+       ~\OPT{\TERMbar}~\OPT{\NT{match-rules}} ~\KWD{end}
+\nlsep \TERM{first}~\TERM{[} ~\NT{tactic-seq} ~\TERM{]}
+\nlsep \TERM{solve}~\TERM{[} ~\NT{tactic-seq} ~\TERM{]}
+\nlsep \TERM{idtac}
+\nlsep \TERM{fail} ~\OPT{\NT{num}} ~\OPT{\NT{string}}
+\nlsep \TERM{constr}~\KWD{:}~\tacconstr
+\nlsep \TERM{ipattern}~\KWD{:}~\NT{intro-pattern}
+\nlsep \NT{term-ltac}
+\nlsep \NT{reference}~\STAR{\NT{tactic-arg}}  &&\RNAME{call-tactic}
+\nlsep \NT{simple-tactic}
+%%
+\nlsep \NT{tactic-atom}  &0 &\RNAME{atomic}
+\nlsep \KWD{(} ~\NT{tactic} ~\KWD{)}
+\SEPDEF
+\DEFNT{tactic-arg}
+       \TERM{ltac}~\KWD{:}~\NTL{tactic}{0}
+\nlsep \TERM{ipattern}~\KWD{:}~\NT{intro-pattern}
+\nlsep \NT{term-ltac}
+\nlsep \NT{tactic-atom}
+\nlsep \tacconstr
+\SEPDEF
+\DEFNT{term-ltac}
+       \TERM{fresh} ~\OPT{\NT{string}}
+\nlsep \TERM{context} ~\NT{ident} ~\TERM{[} ~\taclconstr ~\TERM{]}
+\nlsep \TERM{eval} ~\NT{red-expr} ~\KWD{in} ~\tacconstr
+\nlsep \TERM{type} ~\tacconstr
+\SEPDEF
+\DEFNT{tactic-atom}
+       \NT{reference}
+\nlsep \TERM{()}
+\SEPDEF
+\DEFNT{tactic-seq}
+       \NT{tactic} ~\TERMbar ~\NT{tactic-seq}
+\nlsep \NT{tactic}
+\end{rules}
+
+
+
+\begin{rules}
+\DEFNT{let-clauses}
+       \NT{let-clause} ~\STARGR{\KWD{with}~\NT{let-clause}}
+\SEPDEF
+\DEFNT{let-clause}
+       \NT{ident} ~\STAR{\NT{name}} ~\KWD{:=} ~\NT{tactic}
+\SEPDEF
+\DEFNT{rec-clauses}
+       \NT{rec-clause} ~\KWD{with} ~\NT{rec-clauses}
+\nlsep \NT{rec-clause}
+\SEPDEF
+\DEFNT{rec-clause}
+       \NT{ident} ~\PLUS{\NT{name}} ~\KWD{:=} ~\NT{tactic}
+\SEPDEF
+\DEFNT{match-goal-rules}
+       \NT{match-goal-rule}
+\nlsep \NT{match-goal-rule} ~\TERMbar ~\NT{match-goal-rules}
+\SEPDEF
+\DEFNT{match-goal-rule}
+       \NT{match-hyps-list} ~\TERM{$\vdash$} ~\NT{match-pattern}
+       ~\KWD{$\Rightarrow$} ~\NT{tactic}
+\nlsep \KWD{[}~\NT{match-hyps-list} ~\TERM{$\vdash$} ~\NT{match-pattern}
+       ~\KWD{]}~\KWD{$\Rightarrow$} ~\NT{tactic}
+\nlsep \KWD{_} ~\KWD{$\Rightarrow$} ~\NT{tactic}
+\SEPDEF
+\DEFNT{match-hyps-list}
+       \NT{match-hyps} ~\KWD{,} ~\NT{match-hyps-list}
+\nlsep \NT{match-hyps}
+\SEPDEF
+\DEFNT{match-hyps}
+       \NT{name} ~\KWD{:} ~\NT{match-pattern}
+\SEPDEF
+\DEFNT{match-rules}
+       \NT{match-rule}
+\nlsep \NT{match-rule} ~\TERMbar ~\NT{match-rules}
+\SEPDEF
+\DEFNT{match-rule}
+       \NT{match-pattern} ~\KWD{$\Rightarrow$} ~\NT{tactic}
+\nlsep \KWD{_} ~\KWD{$\Rightarrow$} ~\NT{tactic}
+\SEPDEF
+\DEFNT{match-pattern}
+       \TERM{context}~\OPT{\NT{ident}}
+       ~\TERM{[} ~\NT{constr-pattern} ~\TERM{]}  &&\RNAME{subterm}
+\nlsep \NT{constr-pattern}
+\SEPDEF
+\DEFNT{constr-pattern}
+       \tacconstr
+\end{rules}
+
+\subsection{Other tactics}
+
+\begin{rules}
+\EXTNT{simple-tactic}
+       \TERM{rewrite} ~\NT{orient} ~\NT{constr-with-bindings}
+         ~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{replace} ~\tacconstr ~\KWD{with} ~\tacconstr
+         ~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{replace} ~\OPT{\NT{orient}} ~\tacconstr
+         ~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{symplify_eq} ~\OPT{\NT{quantified-hyp}}
+\nlsep \TERM{discriminate} ~\OPT{\NT{quantified-hyp}}
+\nlsep \TERM{injection} ~\OPT{\NT{quantified-hyp}}
+\nlsep \TERM{conditional}~\NT{tactic}~\TERM{rewrite}~\NT{orient}
+         ~\NT{constr-with-bindings}~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{dependent}~\TERM{rewrite}~\NT{orient}~\NT{ident}
+\nlsep \TERM{cutrewrite}~\NT{orient}~\tacconstr
+         ~\OPTGR{\KWD{in}~\NT{ident}}
+\nlsep \TERM{absurd} ~\tacconstr
+\nlsep \TERM{contradiction}
+\nlsep \TERM{autorewrite}~\NT{hint-bases}~\OPTGR{\KWD{using}~\NT{tactic}}
+\nlsep \TERM{refine}~\tacconstr
+\nlsep \TERM{setoid_replace} ~\tacconstr ~\KWD{with} ~\tacconstr
+\nlsep \TERM{setoid_rewrite} ~\NT{orient} ~\tacconstr
+\nlsep \TERM{subst} ~\STAR{\NT{ident}}
+%% eqdecide.ml4
+\nlsep \TERM{decide}~\TERM{equality} ~\OPTGR{\tacconstr~\tacconstr}
+\nlsep \TERM{compare}~\tacconstr~\tacconstr
+%% eauto
+\nlsep \TERM{eexact}~\tacconstr
+\nlsep \TERM{eapply}~\NT{constr-with-bindings}
+\nlsep \TERM{prolog}~\TERM{[}~\STAR{\tacconstr}~\TERM{]}
+         ~\NT{quantified-hyp}
+\nlsep \TERM{eauto}~\OPT{\NT{quantified-hyp}}~\OPT{\NT{quantified-hyp}}
+         ~\NT{hint-bases}
+\nlsep \TERM{eautod}~\OPT{\NT{quantified-hyp}}~\OPT{\NT{quantified-hyp}}
+         ~\NT{hint-bases}
+%% tauto
+\nlsep \TERM{tauto}
+\nlsep \TERM{simplif}
+\nlsep \TERM{intuition}~\OPT{\NTL{tactic}{0}}
+\nlsep \TERM{linearintuition}~\OPT{\NT{num}}
+%% contrib/cc
+\nlsep \TERM{cc}
+%% contrib/field
+\nlsep \TERM{field}~\STAR{\tacconstr}
+%% contrib/first-order
+\nlsep \TERM{ground}~\OPT{\NTL{tactic}{0}}
+\nlsep \TERM{ground}~\OPT{\NTL{tactic}{0}}~\KWD{with}~\PLUS{\NT{reference}}
+\nlsep \TERM{ground}~\OPT{\NTL{tactic}{0}}~\KWD{using}~\PLUS{\NT{ident}}
+%%\nlsep \TERM{gtauto}
+\nlsep \TERM{gintuition}~\OPT{\NTL{tactic}{0}}
+%% contrib/fourier
+\nlsep \TERM{fourierZ}
+%% contrib/funind
+\nlsep \TERM{functional}~\TERM{induction}~\tacconstr~\PLUS{\tacconstr}
+%% contrib/jprover
+\nlsep \TERM{jp}~\OPT{\NT{num}}
+%% contrib/omega
+\nlsep \TERM{omega}
+%% contrib/ring
+\nlsep \TERM{quote}~\NT{ident}~\OPTGR{\KWD{[}~\PLUS{\NT{ident}}~\KWD{]}}
+\nlsep \TERM{ring}~\STAR{\tacconstr}
+%% contrib/romega
+\nlsep \TERM{romega}
+\SEPDEF
+\DEFNT{orient}
+       \KWD{$\rightarrow$}~\mid~\KWD{$\leftarrow$}
+\end{rules}
+
+\section{Grammar of commands}
+
+New symbols:
+$$ \TERM{.}
+~~ \TERM{..}
+~~ \TERM{\tt >->}
+~~ \TERM{:$>$}
+~~ \TERM{$<$:}
+$$
+
+New keyword:
+$$ \KWD{where}
+$$
+
+\subsection{Classification of commands}
+
+\begin{rules}
+\DEFNT{vernac}
+       \TERM{Time}~\NT{vernac}  &2~~ &\RNAME{Timing}
+%%
+\nlsep \NT{gallina}~\TERM{.}    &1
+\nlsep \NT{command}~\TERM{.}
+\nlsep \NT{syntax}~\TERM{.}
+\nlsep \TERM{[}~\PLUS{\NT{vernac}}~\TERM{]}~\TERM{.}
+%%
+\nlsep \OPTGR{\NT{num}~\KWD{:}}~\NT{subgoal-command}~\TERM{.} ~~~&0
+\SEPDEF
+\DEFNT{subgoal-command}
+       \NT{check-command}
+\nlsep %\OPT{\TERM{By}}~
+   \NT{tactic}~\OPT{\KWD{..}}
+\end{rules}
+
+\subsection{Gallina and extensions}
+
+\begin{rules}
+\DEFNT{gallina}
+       \NT{thm-token}~\NT{ident}~\STAR{\NT{binder-let}}~\KWD{:}~\NT{constr}
+\nlsep \NT{def-token}~\NT{ident}~\NT{def-body}
+\nlsep \NT{assum-token}~\NT{assum-list}
+\nlsep \NT{finite-token}~\NT{inductive-definition}
+      ~\STARGR{\KWD{with}~\NT{inductive-definition}}
+\nlsep \TERM{Fixpoint}~\NT{fix-decl}~\STARGR{\KWD{with}~\NT{fix-decl}}
+\nlsep \TERM{CoFixpoint}~\NT{fix-decl}~\STARGR{\KWD{with}~\NT{fix-decl}}
+\nlsep \TERM{Scheme}~\NT{scheme}~\STARGR{\KWD{with}~\NT{scheme}}
+%% Extension: record
+\nlsep \NT{record-tok}~\OPT{\TERM{$>$}}~\NT{ident}~\STAR{\NT{binder-let}}
+       ~\KWD{:}~\NT{constr}~\KWD{:=}
+       ~\OPT{\NT{ident}}~\KWD{\{}~\NT{field-list}~\KWD{\}}
+\nlsep \TERM{Ltac}~\NT{ltac-def}~\STARGR{~\TERM{with}~\NT{ltac-def}}
+\end{rules}
+
+\begin{rules}
+\DEFNT{thm-token}
+   \TERM{Theorem} ~\mid~ \TERM{Lemma} ~\mid~ \TERM{Fact} ~\mid~ \TERM{Remark}
+\SEPDEF
+\DEFNT{def-token}
+   \TERM{Definition} ~\mid~ \TERM{Let} ~\mid~
+   \OPT{\TERM{Local}}~\TERM{SubClass}
+\SEPDEF
+\DEFNT{assum-token}
+    \TERM{Hypothesis} ~\mid~ \TERM{Variable} ~\mid~ \TERM{Axiom} ~\mid~
+    \TERM{Parameter}
+\SEPDEF
+\DEFNT{finite-token}
+    \TERM{Inductive} ~\mid~ \TERM{CoInductive}
+\SEPDEF
+\DEFNT{record-tok}
+    \TERM{Record} ~\mid~ \TERM{Structure}
+\end{rules}
+
+
+\begin{rules}
+\DEFNT{def-body}
+       \STAR{\NT{binder-let}}~\NT{type-cstr}~\KWD{:=}
+       ~\OPT{\NT{reduce}}~\NT{constr}
+\nlsep \STAR{\NT{binder-let}}~\KWD{:}~\NT{constr}
+\SEPDEF
+\DEFNT{reduce}
+       \TERM{Eval}~\NT{red-expr}~\KWD{in}
+\SEPDEF
+\DEFNT{ltac-def}
+       \NT{ident}~\STAR{\NT{name}}~\KWD{:=}~\NT{tactic}
+\SEPDEF
+\DEFNT{rec-definition}
+       \NT{fix-decl}~\OPT{\NT{decl-notation}}
+\SEPDEF
+\DEFNT{inductive-definition}
+       \OPT{\NT{string}}~\NT{ident}~\STAR{\NT{binder-let}}~\KWD{:}
+       ~\NT{constr}~\KWD{:=}
+       ~\OPT{\TERMbar}~\OPT{\NT{constructor-list}}
+       ~\OPT{\NT{decl-notation}}
+\SEPDEF
+\DEFNT{constructor-list}
+       \NT{constructor}~\TERMbar~\NT{constructor-list}
+\nlsep \NT{constructor}
+\SEPDEF
+\DEFNT{constructor}
+       \NT{ident}~\STAR{\NT{binder-let}}\OPTGR{\NT{coerce-kwd}~\NT{constr}}
+\SEPDEF
+\DEFNT{decl-notation}
+       \TERM{where}~\NT{string}~\TERM{:=}~\NT{constr}
+\SEPDEF
+\DEFNT{field-list}
+       \NT{field}~\KWD{;}~\NT{field-list}
+\nlsep \NT{field}
+\SEPDEF
+\DEFNT{field}
+       \NT{ident}~\OPTGR{\NT{coerce-kwd}~\NT{constr}}
+\nlsep \NT{ident}~\NT{type-cstr-coe}~\KWD{:=}~\NT{constr}
+\SEPDEF
+\DEFNT{assum-list}
+       \PLUS{\GR{\KWD{(}~\NT{simple-assum-coe}~\KWD{)}}}
+\nlsep \NT{simple-assum-coe}
+\SEPDEF
+\DEFNT{simple-assum-coe}
+       \PLUS{\NT{ident}}~\NT{coerce-kwd}~\NT{constr}
+\SEPDEF
+\DEFNT{coerce-kwd} \TERM{:$>$} ~\mid~ \KWD{:}
+\SEPDEF
+\DEFNT{type-cstr-coe} \OPTGR{\NT{coerce-kwd}~\NT{constr}}
+\SEPDEF
+\DEFNT{scheme}
+       \NT{ident}~\KWD{:=}~\NT{dep-scheme}~\KWD{for}~\NT{reference}
+       ~\TERM{Sort}~\NT{sort}
+\SEPDEF
+\DEFNT{dep-scheme}
+       \TERM{Induction}~\mid~\TERM{Minimality}
+\end{rules}
+
+\subsection{Modules and sections}
+
+\begin{rules}
+\DEFNT{gallina}
+       \TERM{Module}~\NT{ident}~\STAR{\NT{mbinder}}~\OPT{\NT{of-mod-type}}
+       ~\OPTGR{\KWD{:=}~\NT{mod-expr}}
+\nlsep \TERM{Module}~\KWD{Type}~\NT{ident}~\STAR{\NT{mbinder}}
+       ~\OPTGR{\KWD{:=}~\NT{mod-type}}
+\nlsep \TERM{Declare}~\TERM{Module}~\NT{ident}~\STAR{\NT{mbinder}}
+       ~\OPT{\NT{of-mod-type}}
+       ~\OPTGR{\KWD{:=}~\NT{mod-expr}}
+\nlsep \TERM{Section}~\NT{ident}
+\nlsep \TERM{Chapter}~\NT{ident}
+\nlsep \TERM{End}~\NT{ident}
+%%
+\nlsep \TERM{Require}~\OPT{\NT{export-token}}~\OPT{\NT{specif-token}}
+       ~\PLUS{\NT{reference}}
+\nlsep \TERM{Require}~\OPT{\NT{export-token}}~\OPT{\NT{specif-token}}
+       ~\NT{string}
+\nlsep \TERM{Import}~\PLUS{\NT{reference}}
+\nlsep \TERM{Export}~\PLUS{\NT{reference}}
+\SEPDEF
+\DEFNT{export-token}
+       \TERM{Import} ~\mid~ \TERM{Export}
+\SEPDEF
+\DEFNT{specif-token}
+       \TERM{Implementation} ~\mid~ \TERM{Specification}
+\SEPDEF
+\DEFNT{mod-expr}
+       \NT{reference}
+\nlsep \NT{mod-expr}~\NT{mod-expr} & L
+\nlsep \KWD{(}~\NT{mod-expr}~\KWD{)}
+\SEPDEF
+\DEFNT{mod-type}
+       \NT{reference}
+\nlsep \NT{mod-type}~\KWD{with}~\NT{with-declaration}
+\SEPDEF
+\DEFNT{with-declaration}
+                                                          %on forcera les ( )
+                                                          %si exceptionnellemt
+                                                          %un fixpoint ici
+       \TERM{Definition}~\NT{ident}~\KWD{:=}~\NTL{constr}{} %{100}
+\nlsep \TERM{Module}~\NT{ident}~\KWD{:=}~\NT{reference}
+\SEPDEF
+\DEFNT{of-mod-type}
+       \KWD{:}~\NT{mod-type}
+\nlsep \TERM{$<$:}~\NT{mod-type}
+\SEPDEF
+\DEFNT{mbinder}
+       \KWD{(}~\PLUS{\NT{ident}}~\KWD{:}~\NT{mod-type}~\KWD{)}
+\end{rules}
+
+\begin{rules}
+\DEFNT{gallina}
+       \TERM{Transparent}~\PLUS{\NT{reference}}
+\nlsep \TERM{Opaque}~\PLUS{\NT{reference}}
+\nlsep \TERM{Canonical}~\TERM{Structure}~\NT{reference}~\OPT{\NT{def-body}}
+\nlsep \TERM{Coercion}~\OPT{\TERM{Local}}~\NT{reference}~\NT{def-body}
+\nlsep \TERM{Coercion}~\OPT{\TERM{Local}}~\NT{reference}~\KWD{:}
+       ~\NT{class-rawexpr}~\TERM{$>->$}~\NT{class-rawexpr}
+\nlsep \TERM{Identity}~\TERM{Coercion}~\OPT{\TERM{Local}}~\NT{ident}~\KWD{:}
+       ~\NT{class-rawexpr}~\TERM{$>->$}~\NT{class-rawexpr}
+\nlsep \TERM{Implicit}~\TERM{Arguments}~\NT{reference}~\TERM{[}~\STAR{\NT{num}}~\TERM{]}
+\nlsep \TERM{Implicit}~\TERM{Arguments}~\NT{reference}
+\nlsep \TERM{Implicit}~\KWD{Type}~\PLUS{\NT{ident}}~\KWD{:}~\NT{constr}
+\SEPDEF
+\DEFNT{command}
+       \TERM{Comments}~\STAR{\NT{comment}}
+\nlsep \TERM{Pwd}
+\nlsep \TERM{Cd}~\OPT{\NT{string}}
+\nlsep \TERM{Drop} ~\mid~ \TERM{ProtectedLoop} ~\mid~\TERM{Quit}
+%%
+\nlsep \TERM{Load}~\OPT{\TERM{Verbose}}~\NT{ident}
+\nlsep \TERM{Load}~\OPT{\TERM{Verbose}}~\NT{string}
+\nlsep \TERM{Declare}~\TERM{ML}~\TERM{Module}~\PLUS{\NT{string}}
+\nlsep \TERM{Dump}~\TERM{Universes}~\OPT{\NT{string}}
+\nlsep \TERM{Locate}~\NT{locatable}
+\nlsep \TERM{Add}~\OPT{\TERM{Rec}}~\TERM{LoadPath}~\NT{string}~\OPT{\NT{as-dirpath}}
+\nlsep \TERM{Remove}~\TERM{LoadPath}~\NT{string}
+\nlsep \TERM{Add}~\OPT{\TERM{Rec}}~\TERM{ML}~\TERM{Path}~\NT{string}
+%%
+\nlsep \KWD{Type}~\NT{constr}
+\nlsep \TERM{Print}~\NT{printable}
+\nlsep \TERM{Print}~\NT{reference}
+\nlsep \TERM{Inspect}~\NT{num}
+\nlsep \TERM{About}~\NT{reference}
+%%
+\nlsep \TERM{Search}~\NT{reference}~\OPT{\NT{in-out-modules}}
+\nlsep \TERM{SearchPattern}~\NT{constr-pattern}~\OPT{\NT{in-out-modules}}
+\nlsep \TERM{SearchRewrite}~\NT{constr-pattern}~\OPT{\NT{in-out-modules}}
+\nlsep \TERM{SearchAbout}~\NT{reference}~\OPT{\NT{in-out-modules}}
+\nlsep \TERM{SearchAbout}~\TERM{[}~\STAR{\NT{ref-or-string}}~\TERM{]}\OPT{\NT{in-out-modules}}
+\nlsep \KWD{Set}~\NT{ident}~\OPT{\NT{opt-value}}
+\nlsep \TERM{Unset}~\NT{ident}
+\nlsep \KWD{Set}~\NT{ident}~\NT{ident}~\OPT{\NT{opt-value}}
+\nlsep \KWD{Set}~\NT{ident}~\NT{ident}~\PLUS{\NT{opt-ref-value}}
+\nlsep \TERM{Unset}~\NT{ident}~\NT{ident}~\STAR{\NT{opt-ref-value}}
+%%
+\nlsep \TERM{Print}~\TERM{Table}~\NT{ident}~\NT{ident}
+\nlsep \TERM{Print}~\TERM{Table}~\NT{ident}
+\nlsep \TERM{Add}~\NT{ident}~\OPT{\NT{ident}}~\PLUS{\NT{opt-ref-value}}
+%%
+\nlsep \TERM{Test}~\NT{ident}~\OPT{\NT{ident}}~\STAR{\NT{opt-ref-value}}
+%%
+\nlsep \TERM{Remove}~\NT{ident}~\OPT{\NT{ident}}~\PLUS{\NT{opt-ref-value}}
+\SEPDEF
+\DEFNT{check-command}
+       \TERM{Eval}~\NT{red-expr}~\KWD{in}~\NT{constr}
+\nlsep \TERM{Check}~\NT{constr}
+\SEPDEF
+\DEFNT{ref-or-string}
+       \NT{reference}
+\nlsep \NT{string}
+\end{rules}
+
+\begin{rules}
+\DEFNT{printable}
+       \TERM{Term}~\NT{reference}
+\nlsep \TERM{All}
+\nlsep \TERM{Section}~\NT{reference}
+\nlsep \TERM{Grammar}~\NT{ident}
+\nlsep \TERM{LoadPath}
+\nlsep \TERM{Module}~\OPT{\KWD{Type}}~\NT{reference}
+\nlsep \TERM{Modules}
+\nlsep \TERM{ML}~\TERM{Path}
+\nlsep \TERM{ML}~\TERM{Modules}
+\nlsep \TERM{Graph}
+\nlsep \TERM{Classes}
+\nlsep \TERM{Coercions}
+\nlsep \TERM{Coercion}~\TERM{Paths}~\NT{class-rawexpr}~\NT{class-rawexpr}
+\nlsep \TERM{Tables}
+% \nlsep \TERM{Proof}~\NT{reference}  % Obsolete, useful in V6.3 ??
+\nlsep \TERM{Hint}~\OPT{\NT{reference}}
+\nlsep \TERM{Hint}~\TERM{*}
+\nlsep \TERM{HintDb}~\NT{ident}
+\nlsep \TERM{Scopes}
+\nlsep \TERM{Scope}~\NT{ident}
+\nlsep \TERM{Visibility}~\OPT{\NT{ident}}
+\nlsep \TERM{Implicit}~\NT{reference}
+\SEPDEF
+\DEFNT{class-rawexpr}
+       \TERM{Funclass}~\mid~\TERM{Sortclass}~\mid~\NT{reference}
+\SEPDEF
+\DEFNT{locatable}
+       \NT{reference}
+\nlsep \TERM{File}~\NT{string}
+\nlsep \TERM{Library}~\NT{reference}
+\nlsep \NT{string}
+\SEPDEF
+\DEFNT{opt-value}
+       \NT{ident} ~\mid~ \NT{string}
+\SEPDEF
+\DEFNT{opt-ref-value}
+       \NT{reference} ~\mid~ \NT{string}
+\SEPDEF
+\DEFNT{as-dirpath}
+       \KWD{as}~\NT{reference}
+\SEPDEF
+\DEFNT{in-out-modules}
+       \TERM{inside}~\PLUS{\NT{reference}}
+\nlsep \TERM{outside}~\PLUS{\NT{reference}}
+\SEPDEF
+\DEFNT{comment}
+       \NT{constr}
+\nlsep \NT{string}
+\end{rules}
+
+\subsection{Other commands}
+
+%% TODO: min/maj pas a jour
+\begin{rules}
+\EXTNT{command}
+       \TERM{Debug}~\TERM{On}
+\nlsep \TERM{Debug}~\TERM{Off}
+%% TODO: vernac
+\nlsep \TERM{Add}~\TERM{setoid}~\tacconstr~\tacconstr~\tacconstr
+\nlsep \TERM{Add}~\TERM{morphism}~\tacconstr~\KWD{:}~\NT{ident}
+\nlsep \TERM{Derive}~\TERM{inversion_clear}
+         ~\OPT{\NT{num}}~\NT{ident}~\NT{ident}
+\nlsep \TERM{Derive}~\TERM{inversion_clear}
+         ~\NT{ident}~\KWD{with}~\tacconstr~\OPTGR{\TERM{Sort}~\NT{sort}}
+\nlsep \TERM{Derive}~\TERM{inversion}
+         ~\OPT{\NT{num}}~\NT{ident}~\NT{ident}
+\nlsep \TERM{Derive}~\TERM{inversion}
+         ~\NT{ident}~\KWD{with}~\tacconstr~\OPTGR{\TERM{Sort}~\NT{sort}}
+\nlsep \TERM{Derive}~\TERM{dependent}~\TERM{inversion_clear}
+         ~\NT{ident}~\KWD{with}~\tacconstr~\OPTGR{\TERM{Sort}~\NT{sort}}
+\nlsep \TERM{Derive}~\TERM{dependent}~\TERM{inversion}
+         ~\NT{ident}~\KWD{with}~\tacconstr~\OPTGR{\TERM{Sort}~\NT{sort}}
+%% Correctness: obsolete ?
+%\nlsep Correctness
+%\nlsep Global Variable
+%% TODO: extraction
+\nlsep Extraction ...
+%% field
+\nlsep \TERM{Add}~\TERM{Field}~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\tacconstr~\OPT{\NT{minus-div}}
+%% funind
+\nlsep \TERM{Functional}~\TERM{Scheme}~\NT{ident}~\KWD{:=}
+         ~\TERM{Induction}~\KWD{for}~\tacconstr
+         ~\OPTGR{\KWD{with}~\PLUS{\tacconstr}}
+%% ring
+\nlsep \TERM{Add}~\TERM{Ring}~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\tacconstr~\KWD{[}~\PLUS{\tacconstr}~\KWD{]}
+\nlsep \TERM{Add}~\TERM{Semi}~\TERM{Ring}~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\KWD{[}~\PLUS{\tacconstr}~\KWD{]}
+\nlsep \TERM{Add}~\TERM{Abstract}~\TERM{Ring}~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\tacconstr
+\nlsep \TERM{Add}~\TERM{Abstract}~\TERM{Semi}~\TERM{Ring}~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr
+\nlsep \TERM{Add}~\TERM{Setoid}~\TERM{Ring}~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\tacconstr~\tacconstr~\tacconstr~\tacconstr~\tacconstr
+         ~\tacconstr~\KWD{[}~\PLUS{\tacconstr}~\KWD{]}
+\nlsep \TERM{Add}~\TERM{Setoid}~\TERM{Semi}~\TERM{Ring}~\tacconstr~\tacconstr
+         ~\tacconstr~\tacconstr~\tacconstr~\tacconstr
+\nlcont~~~~\tacconstr~\tacconstr~\tacconstr~\tacconstr~\tacconstr
+         ~\KWD{[}~\PLUS{tacconstr}~\KWD{]}
+\SEPDEF
+\DEFNT{minus-div}
+       \KWD{with}~\NT{minus-arg}~\NT{div-arg}
+\nlsep \KWD{with}~\NT{div-arg}~\NT{minus-arg}
+\SEPDEF
+\DEFNT{minus-arg}
+       \TERM{minus}~\KWD{:=}~\tacconstr
+\SEPDEF
+\DEFNT{div-arg}
+       \TERM{div}~\KWD{:=}~\tacconstr
+\end{rules}
+
+\begin{rules}
+\EXTNT{command}
+       \TERM{Write}~\TERM{State}~\NT{ident}
+\nlsep \TERM{Write}~\TERM{State}~\NT{string}
+\nlsep \TERM{Restore}~\TERM{State}~\NT{ident}
+\nlsep \TERM{Restore}~\TERM{State}~\NT{string}
+\nlsep \TERM{Reset}~\NT{ident}
+\nlsep \TERM{Reset}~\TERM{Initial}
+\nlsep \TERM{Back}~\OPT{\NT{num}}
+\end{rules}
+
+\subsection{Proof-editing commands}
+
+\begin{rules}
+\EXTNT{command}
+       \TERM{Goal}~\NT{constr}
+\nlsep \TERM{Proof}~\OPT{\NT{constr}}
+\nlsep \TERM{Proof}~\KWD{with}~\NT{tactic}
+\nlsep \TERM{Abort}~\OPT{\TERM{All}}
+\nlsep \TERM{Abort}~\NT{ident}
+\nlsep \TERM{Existential}~\NT{num}~\KWD{:=}~\NT{constr-body}
+\nlsep \TERM{Qed}
+\nlsep \TERM{Save}~\OPTGR{\NT{thm-token}~\NT{ident}}
+\nlsep \TERM{Defined}~\OPT{\NT{ident}}
+\nlsep \TERM{Suspend}
+\nlsep \TERM{Resume}~\OPT{\NT{ident}}
+\nlsep \TERM{Restart}
+\nlsep \TERM{Undo}~\OPT{\NT{num}}
+\nlsep \TERM{Focus}~\OPT{\NT{num}}
+\nlsep \TERM{Unfocus}
+\nlsep \TERM{Show}~\OPT{\NT{num}}
+\nlsep \TERM{Show}~\TERM{Implicit}~\TERM{Arguments}~\OPT{\NT{num}}
+\nlsep \TERM{Show}~\TERM{Node}
+\nlsep \TERM{Show}~\TERM{Script}
+\nlsep \TERM{Show}~\TERM{Existentials}
+\nlsep \TERM{Show}~\TERM{Tree}
+\nlsep \TERM{Show}~\TERM{Conjecture}
+\nlsep \TERM{Show}~\TERM{Proof}
+\nlsep \TERM{Show}~\TERM{Intro}
+\nlsep \TERM{Show}~\TERM{Intros}
+%% Correctness: obsolete ?
+%%\nlsep \TERM{Show}~\TERM{Programs}
+\nlsep \TERM{Explain}~\TERM{Proof}~\OPT{\TERM{Tree}}~\STAR{\NT{num}}
+%% Go not documented
+\nlsep \TERM{Hint}~\OPT{\TERM{Local}}~\NT{hint}~\OPT{\NT{inbases}}
+%% PrintConstr not documented
+\end{rules}
+
+
+\begin{rules}
+\DEFNT{constr-body}
+       \NT{type-cstr}~\KWD{:=}~\NT{constr}
+\SEPDEF
+\DEFNT{hint}
+       \TERM{Resolve}~\PLUS{\NTL{constr}{9}}
+\nlsep \TERM{Immediate}~\PLUS{\NTL{constr}{9}}
+\nlsep \TERM{Unfold}~\PLUS{\NT{reference}}
+\nlsep \TERM{Constructors}~\PLUS{\NT{reference}}
+\nlsep \TERM{Extern}~\NT{num}~\NT{constr}~\KWD{$\Rightarrow$}~\NT{tactic}
+\nlsep \TERM{Destruct}~\NT{ident}~\KWD{:=}~\NT{num}~\NT{destruct-loc}
+       ~\NT{constr}~\KWD{$\Rightarrow$}~\NT{tactic}
+\nlsep \TERM{Rewrite}~\NT{orient}~\PLUS{\NTL{constr}{9}}
+       ~\OPTGR{\KWD{using}~\NT{tactic}}
+\SEPDEF
+\DEFNT{inbases}
+       \KWD{:}~\PLUS{\NT{ident}}
+\SEPDEF
+\DEFNT{destruct-loc}
+       \TERM{Conclusion}
+\nlsep \OPT{\TERM{Discardable}}~\TERM{Hypothesis}
+\end{rules}
+
+
+\subsection{Syntax extensions}
+
+\begin{rules}
+\DEFNT{syntax}
+       \TERM{Open}~\TERM{Scope}~\NT{ident}
+\nlsep \TERM{Close}~\TERM{Scope}~\NT{ident}
+\nlsep \TERM{Delimit}~\TERM{Scope}~\NT{ident}~\KWD{with}~\NT{ident}
+\nlsep \TERM{Bind}~\TERM{Scope}~\NT{ident}~\KWD{with}~\PLUS{\NT{class-rawexpr}}
+\nlsep \TERM{Arguments}~\TERM{Scope}~\NT{reference}
+       ~\TERM{[}~\PLUS{\NT{name}}~\TERM{]}
+\nlsep \TERM{Infix}~\OPT{\TERM{Local}} %%% ~\NT{prec}~\OPT{\NT{num}}
+       ~\NT{string}~\KWD{:=}~\NT{reference}~\OPT{\NT{modifiers}}
+       ~\OPT{\NT{in-scope}}
+\nlsep \TERM{Notation}~\OPT{\TERM{Local}}~\NT{string}~\KWD{:=}~\NT{constr}
+       ~\OPT{\NT{modifiers}}~\OPT{\NT{in-scope}}
+\nlsep \TERM{Notation}~\OPT{\TERM{Local}}~\NT{ident}~\KWD{:=}~\NT{constr}
+       ~\OPT{\KWD{(}\TERM{only~\TERM{parsing}\KWD{)}}}
+\nlsep \TERM{Reserved}~\TERM{Notation}~\OPT{\TERM{Local}}~\NT{string}
+       ~\OPT{\NT{modifiers}}
+\nlsep \TERM{Tactic}~\TERM{Notation}~\NT{string}~\STAR{\NT{tac-production}}
+       ~\KWD{:=}~\NT{tactic}
+\SEPDEF
+\DEFNT{modifiers}
+       \KWD{(}~\NT{mod-list}~\KWD{)}
+\SEPDEF
+\DEFNT{mod-list}
+       \NT{modifier}
+\nlsep \NT{modifier}~\KWD{,}~\NT{mod-list}
+\SEPDEF
+\DEFNT{modifier}
+       \NT{ident}~\KWD{at}~\NT{num}
+\nlsep \NT{ident}~\STARGR{\KWD{,}~\NT{ident}}~\KWD{at}~\NT{num}
+\nlsep \KWD{at}~\TERM{next}~\TERM{level}
+\nlsep \KWD{at}~\TERM{level}~\NT{num}
+\nlsep \TERM{left}~\TERM{associativity}
+\nlsep \TERM{right}~\TERM{associativity}
+\nlsep \TERM{no}~\TERM{associativity}
+\nlsep \NT{ident}~\NT{syntax-entry}
+\nlsep \TERM{only}~\TERM{parsing}
+\nlsep \TERM{format}~\NT{string}
+\SEPDEF
+\DEFNT{in-scope}
+       \KWD{:}~\NT{ident}
+\SEPDEF
+\DEFNT{syntax-entry}
+       \TERM{ident}~\mid~\TERM{global}~\mid~\TERM{bigint}
+\SEPDEF
+\DEFNT{tac-production}
+       \NT{string}
+\nlsep \NT{ident}~\TERM{(}~\NT{ident}~\TERM{)}
+%%% \SEPDEF
+%%% \DEFNT{prec}
+%%%       \TERM{LeftA}~\mid~\TERM{RightA}~\mid~\TERM{NonA}
+\end{rules}
+
+\end{document}
diff --git a/dev/doc/syntax.mly b/dev/doc/syntax.mly
new file mode 100644
index 00000000..bfc7d5cc
--- /dev/null
+++ b/dev/doc/syntax.mly
@@ -0,0 +1,224 @@
+%{
+open Ast
+open Parse
+%}
+
+%token <string> META INT IDENT
+%token <string> OPER
+%token LPAR RPAR BAR COMMA COLON BANG FUN DOT RARROW LET COLONEQ IN IF
+%token THEN ELSE EVAL AT FOR PROP SET TYPE WILDCARD FIX
+%token COFIX MATCH WITH END AND LBRACE RBRACE STRUCT AS SIMPL PERCENT
+%token EOF
+
+%start main
+%type <Ast.constr_ast> main
+
+%start constr
+%type <Ast.constr_ast> constr
+
+%start simple_constr
+%type <Ast.constr_ast> simple_constr
+
+%%
+
+main:
+          constr EOF { $1 }
+;
+
+
+paren_constr:
+          constr COMMA paren_constr  { Pair($1,$3) }
+        | constr                     { $1 }
+;
+
+constr:
+          binder_constr  { $1 }
+        | oper_constr    { close_stack $1 }
+;
+
+binder_constr:
+          BANG ne_binders DOT constr              { Prod($2, $4) }
+        | FUN ne_binders type_cstr RARROW constr  { Lambda($2,mk_cast $5 $3) }
+        | LET IDENT binders type_cstr COLONEQ constr IN constr
+            { Let($2,mk_lambda $3 (mk_cast $6 $4),$8) }
+        | LET LPAR comma_binders RPAR COLONEQ constr IN constr
+            { LetCase($3,$6,$8) }
+        | IF constr THEN constr ELSE constr       { IfCase($2,$4,$6) }
+        | fix_constr                              { $1 }
+        | EVAL rfun IN constr                     { Eval($2,$4) }
+;
+
+comma_binders:
+          ne_comma_binders  { $1 }
+        |                   { [] }
+;
+
+ne_comma_binders:
+          binder COMMA ne_comma_binders  { $1 :: $3 }
+        | binder                         { [$1] }
+;
+
+rfun:
+          SIMPL  { Simpl }
+;
+
+
+/* 2 Conflits shift/reduce */
+oper_constr:
+          oper_constr oper appl_constr
+            { parse_term $3 (parse_oper $2 $1) }
+        | oper_constr oper binder_constr
+            { parse_term $3 (parse_oper $2 $1) }
+        | oper_constr oper  { parse_oper $2 $1 }
+        |                   { empty }
+        | appl_constr       { parse_term $1 empty }
+;
+
+oper:
+          OPER {$1}
+        | COLON {":"}
+;
+
+appl_constr:
+          simple_constr ne_appl_args  { Appl($1,$2) }
+        | AT global simple_constrs    { ApplExpl($2,$3) }
+        | simple_constr               { $1 }
+;
+
+appl_arg:
+          AT INT COLONEQ simple_constr  { (Some $2,$4) }
+        | simple_constr                 { (None,$1) }
+;
+
+ne_appl_args:
+          appl_arg               { [$1] }
+        | appl_arg ne_appl_args  { $1::$2 }
+;
+
+simple_constr:
+          atomic_constr                           { $1 }
+        | match_constr                            { $1 }
+        | LPAR paren_constr RPAR                  { $2 }
+        | simple_constr PERCENT IDENT { Scope($3,$1) }
+;
+
+simple_constrs:
+          simple_constr simple_constrs  { $1::$2 }
+        |                               { [] }
+;
+
+atomic_constr:
+          global    { Qualid $1 }
+        | PROP      { Prop }
+        | SET       { Set }
+        | TYPE      { Type }
+        | INT       { Int $1 }
+        | WILDCARD  { Hole }
+        | META      { Meta $1 }
+;
+
+global:
+          IDENT DOT global  { $1 :: $3 }
+        | IDENT             { [$1] }
+;
+
+/* Conflit normal */
+fix_constr:
+          fix_kw fix_decl
+            { let (id,_,_,_,_ as fx) = $2 in Fixp($1,[fx],id) }
+        | fix_kw fix_decl fix_decls FOR IDENT  { Fixp($1, $2::$3, $5) }
+;
+
+fix_kw: FIX {Fix} | COFIX {CoFix}
+;
+
+fix_decl:
+          IDENT binders type_cstr annot COLONEQ constr  { ($1,$2,$3,$4,$6) }
+;
+
+fix_decls:
+          AND fix_decl fix_decls  { $2::$3 }
+        | AND fix_decl            { [$2] }
+;
+
+annot:
+          LBRACE STRUCT IDENT RBRACE  { Some $3 }
+        |                             { None }
+;
+
+match_constr:
+          MATCH case_items case_type WITH branches END  { Match($2,$3,$5) }
+;
+
+case_items:
+          case_item                   { [$1] }
+        | case_item COMMA case_items  { $1::$3 }
+;
+
+case_item:
+          constr pred_pattern { ($1,$2) }
+;
+
+case_type:
+          RARROW constr  { Some $2 }
+        |                { None }
+;
+
+pred_pattern:
+          AS IDENT COLON constr  { (Some $2, Some $4) }
+        | AS IDENT               { (Some $2, None) }
+        | COLON constr           { (None, Some $2) }
+        |                        { (None,None) }
+;
+
+branches:
+          BAR branch_list  { $2 }
+        | branch_list      { $1 }
+        |                  { [] }
+;
+
+branch_list:
+          patterns RARROW constr                  { [$1, $3] }
+        | patterns RARROW constr BAR branch_list  { ($1,$3)::$5 }
+;
+
+patterns:
+          pattern                 { [$1] }
+        | pattern COMMA patterns  { $1::$3 }
+;
+
+pattern:
+          pattern AS IDENT       { PatAs($1,$3) }
+        | pattern COLON constr   { PatType($1,$3) }
+        | IDENT simple_patterns  { PatConstr($1,$2) }
+        | simple_pattern         { $1 }
+;
+
+simple_pattern:
+          IDENT              { PatVar $1 }
+        | LPAR pattern RPAR  { $2 }
+;
+
+simple_patterns:
+          simple_pattern                  { [$1] }
+        | simple_pattern simple_patterns  { $1::$2 }
+;
+
+binder:
+          IDENT                 { ($1,Hole) }
+        | LPAR IDENT type_cstr RPAR  { ($2,$3) }
+;
+
+binders:
+          ne_binders  { $1 }
+        |             { [] }
+
+ne_binders:
+          binder             { [$1] }
+        | binder ne_binders  { $1::$2 }
+;
+
+type_cstr:
+          COLON constr  { $2 }
+        |               { Hole }
+;
diff --git a/dev/doc/tactics.dep.ps b/dev/doc/tactics.dep.ps
new file mode 100644
index 00000000..f4de22b7
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@@ -0,0 +1,991 @@
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+  dup 306 /AE
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+  dup 302 /Acircumflex
+  dup 304 /Adieresis
+  dup 300 /Agrave
+  dup 305 /Aring
+  dup 303 /Atilde
+  dup 307 /Ccedilla
+  dup 311 /Eacute
+  dup 312 /Ecircumflex
+  dup 313 /Edieresis
+  dup 310 /Egrave
+  dup 315 /Iacute
+  dup 316 /Icircumflex
+  dup 317 /Idieresis
+  dup 314 /Igrave
+  dup 334 /Udieresis
+  dup 335 /Yacute
+  dup 376 /thorn
+  dup 337 /germandbls
+  dup 341 /aacute
+  dup 342 /acircumflex
+  dup 344 /adieresis
+  dup 346 /ae
+  dup 340 /agrave
+  dup 345 /aring
+  dup 347 /ccedilla
+  dup 351 /eacute
+  dup 352 /ecircumflex
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+  dup 350 /egrave
+  dup 355 /iacute
+  dup 356 /icircumflex
+  dup 357 /idieresis
+  dup 354 /igrave
+  dup 360 /dcroat
+  dup 361 /ntilde
+  dup 363 /oacute
+  dup 364 /ocircumflex
+  dup 366 /odieresis
+  dup 362 /ograve
+  dup 365 /otilde
+  dup 370 /oslash
+  dup 372 /uacute
+  dup 373 /ucircumflex
+  dup 374 /udieresis
+  dup 371 /ugrave
+  dup 375 /yacute
+  dup 377 /ydieresis  
+
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