New parser based on new version of the Coq backend of Menhir (#276)

What's new:

1. A rewrite of the Coq interpreter of Menhir automaton, with
   dependent types removing the need for runtime checks for the
   well-formedness of the LR stack. This seem to cause some speedup on
   the parsing time (~10% for lexing + parsing).

2. Thanks to 1., it is now possible to avoid the use of int31 for
   comparing symbols: Since this is only used for validation,
   positives are enough.

3. Speedup of Validation: on my machine, the time needed for compiling
   Parser.v goes from about 2 minutes to about 1 minute. This seem to
   be related to a performance bug in the completeness validator and
   to the use of positive instead of int31.

3. Menhir now generates a dedicated inductive type for
   (semantic-value-carrying) tokens (in addition to the already
   existing inductive type for (non-semantic-value-carrying)
   terminals. The end result is that the OCaml support code for the
   parser no longer contain calls to Obj.magic. The bad side of this
   change is that the formal specification of the parser is perhaps
   harder to read.

4. The parser and its library are now free of axioms (I used to use
   axiom K and proof irrelevance for easing proofs involving dependent
   types).

5. Use of a dedicated custom negative coinductive type for the input
   stream of tokens, instead of Coq stdlib's `Stream`. `Stream` is a
   positive coinductive type, which are now deprecated by Coq.

6. The fuel of the parser is now specified using its logarithm instead
   of its actual value. This makes it possible to give large fuel
   values instead of using the `let rec fuel = S fuel` hack.

7. Some refactoring in the lexer, the parser and the Cabs syntax tree.

The corresponding changes in Menhir have been released as part of
version 20190626. The `MenhirLib` directory is identical to the
content of the `src` directory of the corresponding `coq-menhirlib`
opam package except that:
   - In order to try to make CompCert compatible with several Menhir
     versions without updates, we do not check the version of menhir
     is compatible with the version of coq-menhirlib. Hence the
     `Version.v` file is not present in CompCert's copy.
   - Build-system related files have been removed.

1 files changed, 162 insertions, 0 deletions

diff --git a/MenhirLib/Grammar.v b/MenhirLib/Grammar.v
new file mode 100644
index 00000000..a371318b
--- /dev/null
+++ b/MenhirLib/Grammar.v
@@ -0,0 +1,162 @@
+(****************************************************************************)
+(*                                                                          *)
+(*                                   Menhir                                 *)
+(*                                                                          *)
+(*           Jacques-Henri Jourdan, CNRS, LRI, Université Paris Sud         *)
+(*                                                                          *)
+(*  Copyright Inria. All rights reserved. This file is distributed under    *)
+(*  the terms of the GNU Lesser General Public License as published by the  *)
+(*  Free Software Foundation, either version 3 of the License, or (at your  *)
+(*  option) any later version, as described in the file LICENSE.            *)
+(*                                                                          *)
+(****************************************************************************)
+
+From Coq Require Import List Syntax Orders.
+Require Import Alphabet.
+
+(** The terminal non-terminal alphabets of the grammar. **)
+Module Type Alphs.
+  Parameters terminal nonterminal : Type.
+  Declare Instance TerminalAlph: Alphabet terminal.
+  Declare Instance NonTerminalAlph: Alphabet nonterminal.
+End Alphs.
+
+(** Definition of the alphabet of symbols, given the alphabet of terminals
+    and the alphabet of non terminals **)
+Module Symbol(Import A:Alphs).
+
+  Inductive symbol :=
+    | T: terminal -> symbol
+    | NT: nonterminal -> symbol.
+
+  Program Instance SymbolAlph : Alphabet symbol :=
+    { AlphabetComparable := {| compare := fun x y =>
+        match x, y return comparison with
+          | T _, NT _ => Gt
+          | NT _, T _ => Lt
+          | T x, T y => compare x y
+          | NT x, NT y => compare x y
+        end |};
+      AlphabetFinite := {| all_list :=
+        map T all_list++map NT all_list |} }.
+  Next Obligation.
+    destruct x; destruct y; intuition; apply compare_antisym.
+  Qed.
+  Next Obligation.
+    destruct x; destruct y; destruct z; intuition; try discriminate.
+    apply (compare_trans _ t0); intuition.
+    apply (compare_trans _ n0); intuition.
+  Qed.
+  Next Obligation.
+    intros x y.
+    destruct x; destruct y; try discriminate; intros.
+    rewrite (compare_eq t t0); now intuition.
+    rewrite (compare_eq n n0); now intuition.
+  Defined.
+  Next Obligation.
+    rewrite in_app_iff.
+    destruct x; [left | right]; apply in_map; apply all_list_forall.
+  Qed.
+
+End Symbol.
+
+(** A curryfied function with multiple parameters **)
+Definition arrows_right: Type -> list Type -> Type :=
+  fold_right (fun A B => A -> B).
+
+Module Type T.
+  Include Alphs <+ Symbol.
+
+  (** [symbol_semantic_type] maps a symbols to the type of its semantic
+     values. **)
+  Parameter symbol_semantic_type: symbol -> Type.
+
+  (** The type of productions identifiers **)
+  Parameter production : Type.
+  Declare Instance ProductionAlph : Alphabet production.
+
+  (** Accessors for productions: left hand side, right hand side,
+     and semantic action. The semantic actions are given in the form
+     of curryfied functions, that take arguments in the reverse order. **)
+  Parameter prod_lhs: production -> nonterminal.
+  (* The RHS of a production is given in reversed order, so that symbols  *)
+  Parameter prod_rhs_rev: production -> list symbol.
+  Parameter prod_action:
+    forall p:production,
+      arrows_right
+        (symbol_semantic_type (NT (prod_lhs p)))
+        (map symbol_semantic_type (prod_rhs_rev p)).
+
+  (** Tokens are the atomic elements of the input stream: they contain
+     a terminal and a semantic value of the type corresponding to this
+     terminal. *)
+  Parameter token : Type.
+  Parameter token_term : token -> terminal.
+  Parameter token_sem :
+    forall tok : token, symbol_semantic_type (T (token_term tok)).
+End T.
+
+Module Defs(Import G:T).
+
+  (** The semantics of a grammar is defined in two stages. First, we
+    define the notion of parse tree, which represents one way of
+    recognizing a word with a head symbol. Semantic values are stored
+    at the leaves.
+
+      This notion is defined in two mutually recursive flavours:
+    either for a single head symbol, or for a list of head symbols. *)
+  Inductive parse_tree:
+    forall (head_symbol:symbol) (word:list token), Type :=
+
+  (** Parse tree for a terminal symbol. *)
+  | Terminal_pt:
+    forall (tok:token), parse_tree (T (token_term tok)) [tok]
+
+  (** Parse tree for a non-terminal symbol.  *)
+  | Non_terminal_pt:
+    forall (prod:production) {word:list token},
+      parse_tree_list (prod_rhs_rev prod) word ->
+      parse_tree (NT (prod_lhs prod)) word
+
+  (* Note : the list head_symbols_rev is reversed. *)
+  with parse_tree_list:
+    forall (head_symbols_rev:list symbol) (word:list token), Type :=
+
+  | Nil_ptl: parse_tree_list [] []
+
+  | Cons_ptl:
+    forall {head_symbolsq:list symbol} {wordq:list token},
+      parse_tree_list head_symbolsq wordq ->
+
+    forall {head_symbolt:symbol} {wordt:list token},
+      parse_tree head_symbolt wordt ->
+
+      parse_tree_list (head_symbolt::head_symbolsq) (wordq++wordt).
+
+  (** We can now finish the definition of the semantics of a grammar,
+    by giving the semantic value assotiated with a parse tree. *)
+  Fixpoint pt_sem {head_symbol word} (tree:parse_tree head_symbol word) :
+    symbol_semantic_type head_symbol :=
+    match tree with
+    | Terminal_pt tok => token_sem tok
+    | Non_terminal_pt prod ptl => ptl_sem ptl (prod_action prod)
+    end
+  with ptl_sem {A head_symbols word} (tree:parse_tree_list head_symbols word) :
+    arrows_right A (map symbol_semantic_type head_symbols) -> A :=
+    match tree with
+    | Nil_ptl => fun act => act
+    | Cons_ptl q t => fun act => ptl_sem q (act (pt_sem t))
+    end.
+
+  Fixpoint pt_size {head_symbol word} (tree:parse_tree head_symbol word) :=
+    match tree with
+      | Terminal_pt _ => 1
+      | Non_terminal_pt _ l => S (ptl_size l)
+    end
+  with ptl_size {head_symbols word} (tree:parse_tree_list head_symbols word) :=
+    match tree with
+      | Nil_ptl => 0
+      | Cons_ptl q t =>
+         pt_size t + ptl_size q
+    end.
+End Defs.