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authorJacques-Henri Jourdan <jacques-henri.jourdan@normalesup.org>2019-07-05 15:15:42 +0200
committerXavier Leroy <xavierleroy@users.noreply.github.com>2019-07-05 15:15:42 +0200
commit998f3c5ff90f6230b722b6094761f5989beea0a5 (patch)
treead107d40768bf6e40ba7d8493b2fa6f01c668231 /cparser/MenhirLib/Interpreter_safe.v
parentda929bc61ccd67d2be2b1e5d3cd9f3cb60f56074 (diff)
downloadcompcert-998f3c5ff90f6230b722b6094761f5989beea0a5.tar.gz
compcert-998f3c5ff90f6230b722b6094761f5989beea0a5.zip
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.
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-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Jacques-Henri Jourdan, INRIA Paris-Rocquencourt *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the GNU General Public License as published by *)
-(* the Free Software Foundation, either version 2 of the License, or *)
-(* (at your option) any later version. This file is also distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-Require Import Streams.
-Require Import Equality.
-Require Import List.
-Require Import Syntax.
-Require Import Alphabet.
-Require Grammar.
-Require Automaton.
-Require Validator_safe.
-Require Interpreter.
-
-Module Make(Import A:Automaton.T) (Import Inter:Interpreter.T A).
-Module Import Valid := Validator_safe.Make A.
-
-(** * A correct automaton does not crash **)
-
-Section Safety_proof.
-
-Hypothesis safe: safe.
-
-Proposition shift_head_symbs: shift_head_symbs.
-Proof. pose proof safe; unfold Valid.safe in H; intuition. Qed.
-Proposition goto_head_symbs: goto_head_symbs.
-Proof. pose proof safe; unfold Valid.safe in H; intuition. Qed.
-Proposition shift_past_state: shift_past_state.
-Proof. pose proof safe; unfold Valid.safe in H; intuition. Qed.
-Proposition goto_past_state: goto_past_state.
-Proof. pose proof safe; unfold Valid.safe in H; intuition. Qed.
-Proposition reduce_ok: reduce_ok.
-Proof. pose proof safe; unfold Valid.safe in H; intuition. Qed.
-
-(** We prove that a correct automaton won't crash : the interpreter will
- not return [Err] **)
-
-Variable init : initstate.
-
-(** The stack of states of an automaton stack **)
-Definition state_stack_of_stack (stack:stack) :=
- (List.map
- (fun cell:sigT noninitstate_type => singleton_state_pred (projT1 cell))
- stack ++ [singleton_state_pred init])%list.
-
-(** The stack of symbols of an automaton stack **)
-Definition symb_stack_of_stack (stack:stack) :=
- List.map
- (fun cell:sigT noninitstate_type => last_symb_of_non_init_state (projT1 cell))
- stack.
-
-(** The stack invariant : it basically states that the assumptions on the
- states are true. **)
-Inductive stack_invariant: stack -> Prop :=
- | stack_invariant_constr:
- forall stack,
- prefix (head_symbs_of_state (state_of_stack init stack))
- (symb_stack_of_stack stack) ->
- prefix_pred (head_states_of_state (state_of_stack init stack))
- (state_stack_of_stack stack) ->
- stack_invariant_next stack ->
- stack_invariant stack
-with stack_invariant_next: stack -> Prop :=
- | stack_invariant_next_nil:
- stack_invariant_next []
- | stack_invariant_next_cons:
- forall state_cur st stack_rec,
- stack_invariant stack_rec ->
- stack_invariant_next (existT _ state_cur st::stack_rec).
-
-(** [pop] conserves the stack invariant and does not crash
- under the assumption that we can pop at this place.
- Moreover, after a pop, the top state of the stack is allowed. **)
-Lemma pop_stack_invariant_conserved
- (symbols_to_pop:list symbol) (stack_cur:stack) A action:
- stack_invariant stack_cur ->
- prefix symbols_to_pop (head_symbs_of_state (state_of_stack init stack_cur)) ->
- match pop symbols_to_pop stack_cur (A:=A) action with
- | OK (stack_new, _) =>
- stack_invariant stack_new /\
- state_valid_after_pop
- (state_of_stack init stack_new) symbols_to_pop
- (head_states_of_state (state_of_stack init stack_cur))
- | Err => False
- end.
-Proof with eauto.
- intros.
- pose proof H.
- destruct H.
- revert H H0 H1 H2 H3.
- generalize (head_symbs_of_state (state_of_stack init stack0)).
- generalize (head_states_of_state (state_of_stack init stack0)).
- revert stack0 A action.
- induction symbols_to_pop; intros.
- - split...
- destruct l; constructor.
- inversion H2; subst.
- specialize (H7 (state_of_stack init stack0)).
- destruct (f2 (state_of_stack init stack0)) as [] eqn:? ...
- destruct stack0 as [|[]]; simpl in *.
- + inversion H6; subst.
- unfold singleton_state_pred in Heqb0.
- now rewrite compare_refl in Heqb0; discriminate.
- + inversion H6; subst.
- unfold singleton_state_pred in Heqb0.
- now rewrite compare_refl in Heqb0; discriminate.
- - destruct stack0 as [|[]]; unfold pop.
- + inversion H0; subst.
- now inversion H.
- + fold pop.
- destruct (compare_eqdec (last_symb_of_non_init_state x) a).
- * inversion H0; subst. clear H0.
- inversion H; subst. clear H.
- dependent destruction H3; simpl.
- assert (prefix_pred (List.tl l) (state_stack_of_stack stack0)).
- unfold tl; destruct l; [constructor | inversion H2]...
- pose proof H. destruct H3.
- specialize (IHsymbols_to_pop stack0 A (action0 n) _ _ H4 H7 H H0 H6).
- revert IHsymbols_to_pop.
- fold (noninitstate_type x); generalize (pop symbols_to_pop stack0 (action0 n)).
- destruct r as [|[]]; intuition...
- destruct l; constructor...
- * apply n0.
- inversion H0; subst.
- inversion H; subst...
-Qed.
-
-(** [prefix] is associative **)
-Lemma prefix_ass:
- forall (l1 l2 l3:list symbol), prefix l1 l2 -> prefix l2 l3 -> prefix l1 l3.
-Proof.
-induction l1; intros.
-constructor.
-inversion H; subst.
-inversion H0; subst.
-constructor; eauto.
-Qed.
-
-(** [prefix_pred] is associative **)
-Lemma prefix_pred_ass:
- forall (l1 l2 l3:list (state->bool)),
- prefix_pred l1 l2 -> prefix_pred l2 l3 -> prefix_pred l1 l3.
-Proof.
-induction l1; intros.
-constructor.
-inversion H; subst.
-inversion H0; subst.
-constructor; eauto.
-intro.
-specialize (H3 x).
-specialize (H4 x).
-destruct (f0 x); simpl in *; intuition.
-rewrite H4 in H3; intuition.
-Qed.
-
-(** If we have the right to reduce at this state, then the stack invariant
- is conserved by [reduce_step] and [reduce_step] does not crash. **)
-Lemma reduce_step_stack_invariant_conserved stack prod buff:
- stack_invariant stack ->
- valid_for_reduce (state_of_stack init stack) prod ->
- match reduce_step init stack prod buff with
- | OK (Fail_sr | Accept_sr _ _) => True
- | OK (Progress_sr stack_new _) => stack_invariant stack_new
- | Err => False
- end.
-Proof with eauto.
-unfold valid_for_reduce.
-intuition.
-unfold reduce_step.
-pose proof (pop_stack_invariant_conserved (prod_rhs_rev prod) stack _ (prod_action' prod)).
-destruct (pop (prod_rhs_rev prod) stack (prod_action' prod)) as [|[]].
-apply H0...
-destruct H0...
-pose proof (goto_head_symbs (state_of_stack init s) (prod_lhs prod)).
-pose proof (goto_past_state (state_of_stack init s) (prod_lhs prod)).
-unfold bind2.
-destruct H0.
-specialize (H2 _ H3)...
-destruct (goto_table (state_of_stack init stack0) (prod_lhs prod)) as [[]|].
-constructor.
-simpl.
-constructor.
-eapply prefix_ass...
-unfold state_stack_of_stack; simpl; constructor.
-intro; destruct (singleton_state_pred x x0); reflexivity.
-eapply prefix_pred_ass...
-constructor...
-constructor...
-destruct stack0 as [|[]]...
-destruct (compare_eqdec (prod_lhs prod) (start_nt init))...
-apply n, H2, eq_refl.
-apply H2, eq_refl.
-Qed.
-
-(** If the automaton is safe, then the stack invariant is conserved by
- [step] and [step] does not crash. **)
-Lemma step_stack_invariant_conserved (stack:stack) buffer:
- stack_invariant stack ->
- match step init stack buffer with
- | OK (Fail_sr | Accept_sr _ _) => True
- | OK (Progress_sr stack_new _) => stack_invariant stack_new
- | Err => False
- end.
-Proof with eauto.
-intro.
-unfold step.
-pose proof (shift_head_symbs (state_of_stack init stack)).
-pose proof (shift_past_state (state_of_stack init stack)).
-pose proof (reduce_ok (state_of_stack init stack)).
-destruct (action_table (state_of_stack init stack)).
-apply reduce_step_stack_invariant_conserved...
-destruct buffer as [[]]; simpl.
-specialize (H0 x); specialize (H1 x); specialize (H2 x).
-destruct (l x)...
-destruct H.
-constructor.
-unfold state_of_stack.
-constructor.
-eapply prefix_ass...
-unfold state_stack_of_stack; simpl; constructor.
-intro; destruct (singleton_state_pred s0 x0)...
-eapply prefix_pred_ass...
-constructor...
-constructor...
-apply reduce_step_stack_invariant_conserved...
-Qed.
-
-(** If the automaton is safe, then it does not crash **)
-Theorem parse_no_err buffer n_steps:
- parse init buffer n_steps <> Err.
-Proof with eauto.
-unfold parse.
-assert (stack_invariant []).
-constructor.
-constructor.
-unfold state_stack_of_stack; simpl; constructor.
-intro; destruct (singleton_state_pred init x)...
-constructor.
-constructor.
-revert H.
-generalize buffer ([]:stack).
-induction n_steps; simpl.
-now discriminate.
-intros.
-pose proof (step_stack_invariant_conserved s buffer0 H).
-destruct (step init s buffer0) as [|[]]; simpl...
-discriminate.
-discriminate.
-Qed.
-
-(** A version of [parse] that uses safeness in order to return a
- [parse_result], and not a [result parse_result] : we have proven that
- parsing does not return [Err]. **)
-Definition parse_with_safe (buffer:Stream token) (n_steps:nat):
- parse_result init.
-Proof with eauto.
-pose proof (parse_no_err buffer n_steps).
-destruct (parse init buffer n_steps)...
-congruence.
-Defined.
-
-End Safety_proof.
-
-End Make.