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, 79 insertions, 0 deletions

diff --git a/MenhirLib/Main.v b/MenhirLib/Main.v
new file mode 100644
index 00000000..f6158074
--- /dev/null
+++ b/MenhirLib/Main.v
@@ -0,0 +1,79 @@
+(****************************************************************************)
+(*                                                                          *)
+(*                                   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.            *)
+(*                                                                          *)
+(****************************************************************************)
+
+Require Grammar Automaton Interpreter_correct Interpreter_complete.
+From Coq Require Import Syntax Arith.
+
+Module Make(Export Aut:Automaton.T).
+Export Aut.Gram.
+Export Aut.GramDefs.
+
+Module Import Inter := Interpreter.Make Aut.
+Module Correct := Interpreter_correct.Make Aut Inter.
+Module Complete := Interpreter_complete.Make Aut Inter.
+
+Definition complete_validator:unit->bool := Complete.Valid.is_complete.
+Definition safe_validator:unit->bool := ValidSafe.is_safe.
+Definition parse (safe:safe_validator ()=true) init log_n_steps buffer :
+  parse_result (symbol_semantic_type (NT (start_nt init))):=
+  parse (ValidSafe.safe_is_validator safe) init buffer log_n_steps.
+
+(** Correction theorem. **)
+Theorem parse_correct
+  (safe:safe_validator ()= true) init log_n_steps buffer:
+  match parse safe init log_n_steps buffer with
+    | Parsed_pr sem buffer_new =>
+      exists word (pt : parse_tree (NT (start_nt init)) word),
+        buffer = (word ++ buffer_new)%buf /\
+        pt_sem pt = sem
+    | _ => True
+  end.
+Proof. apply Correct.parse_correct. Qed.
+
+(** Completeness theorem. **)
+Theorem parse_complete
+  (safe:safe_validator () = true) init log_n_steps word buffer_end:
+  complete_validator () = true ->
+  forall tree:parse_tree (NT (start_nt init)) word,
+  match parse safe init log_n_steps (word ++ buffer_end) with
+  | Fail_pr => False
+  | Parsed_pr sem_res buffer_end_res =>
+    sem_res = pt_sem tree /\ buffer_end_res = buffer_end /\
+    pt_size tree <= 2^log_n_steps
+  | Timeout_pr => 2^log_n_steps < pt_size tree
+  end.
+Proof.
+  intros. now apply Complete.parse_complete, Complete.Valid.complete_is_validator.
+Qed.
+
+(** Unambiguity theorem. **)
+Theorem unambiguity:
+  safe_validator () = true -> complete_validator () = true -> inhabited token ->
+  forall init word,
+  forall (tree1 tree2:parse_tree (NT (start_nt init)) word),
+    pt_sem tree1 = pt_sem tree2.
+Proof.
+  intros Hsafe Hcomp [tok] init word tree1 tree2.
+  pose (buf_end := cofix buf_end := (tok :: buf_end)%buf).
+  assert (Hcomp1 := parse_complete Hsafe init (pt_size tree1) word buf_end
+                                   Hcomp tree1).
+  assert (Hcomp2 := parse_complete Hsafe init (pt_size tree1) word buf_end
+                                   Hcomp tree2).
+  destruct parse.
+  - destruct Hcomp1.
+  - exfalso. eapply PeanoNat.Nat.lt_irrefl. etransitivity; [|apply Hcomp1].
+    eapply Nat.pow_gt_lin_r. constructor.
+  - destruct Hcomp1 as [-> _], Hcomp2 as [-> _]. reflexivity.
+Qed.
+
+End Make.