diff options
Diffstat (limited to 'src/Trace.v')
| -rw-r--r-- | src/Trace.v | 289 |
1 files changed, 207 insertions, 82 deletions
diff --git a/src/Trace.v b/src/Trace.v index 17338ca..1849c44 100644 --- a/src/Trace.v +++ b/src/Trace.v @@ -11,7 +11,6 @@ Require Import Bool Int63 PArray. -Require Structures. Require Import Misc State SMT_terms. Require Import Syntactic Arithmetic Operators Assumptions. Require Import Cnf Euf Lia BVList Bva_checker Array_checker. @@ -34,7 +33,7 @@ Section trace. Variable rho : Valuation.t. - Definition _trace_ := Structures.trace step. + Definition _trace_ := ((list step) * step)%type. (* A checker for such a trace *) @@ -42,7 +41,7 @@ Section trace. Hypothesis is_false_correct : forall c, is_false c -> ~ C.interp rho c. Definition _checker_ (s: S.t) (t: _trace_) (confl:clause_id) : bool := - let s' := Structures.trace_fold check_step s t in + let s' := List.fold_left check_step (fst t) s in (* let s' := PArray.fold_left (fun s a => PArray.fold_left check_step s a) s t in *) is_false (S.get s' confl). (* Register _checker_ as PrimInline. *) @@ -78,7 +77,11 @@ Section trace. intros s t' cid Hf Hv. apply (is_false_correct Hf). apply S.valid_get. - apply Structures.trace_fold_ind; auto. + clear Hf. + rewrite <- List.fold_left_rev_right in *. + induction (List.rev (fst t')); [ apply Hv | ]. + apply valid_check_step. + apply IHl. (* apply PArray.fold_left_ind; auto. *) (* intros a i _ Ha;apply PArray.fold_left_ind;trivial. *) (* intros a0 i0 _ H1;auto. *) @@ -117,37 +120,37 @@ Module Sat_Checker. Definition dimacs := PArray.array (PArray.array _lit). Definition C_interp_or rho c := - afold_left _ _ false orb (Lit.interp rho) c. + afold_left _ false orb (amap (Lit.interp rho) c). Lemma C_interp_or_spec : forall rho c, C_interp_or rho c = C.interp rho (to_list c). Proof. intros rho c; unfold C_interp_or; case_eq (C.interp rho (to_list c)). - unfold C.interp; rewrite List.existsb_exists; intros [x [H1 H2]]; destruct (In_to_list _ _ H1) as [i [H3 H4]]; subst x; apply (afold_left_orb_true _ i); auto. - unfold C.interp; intro H; apply afold_left_orb_false; intros i H1; case_eq (Lit.interp rho (c .[ i])); auto; intro Heq; assert (H2: exists x, List.In x (to_list c) /\ Lit.interp rho x = true). + unfold C.interp; rewrite List.existsb_exists; intros [x [H1 H2]]; destruct (In_to_list _ _ H1) as [i [H3 H4]]; subst x; apply (afold_left_orb_true i); rewrite ?length_amap,?get_amap;auto. + unfold C.interp; intro H; apply afold_left_orb_false; rewrite length_amap; intros i H1; rewrite get_amap; case_eq (Lit.interp rho (c .[ i])); auto; intro Heq; assert (H2: exists x, List.In x (to_list c) /\ Lit.interp rho x = true). exists (c.[i]); split; auto; apply to_list_In; auto. rewrite <- List.existsb_exists in H2; rewrite H2 in H; auto. Qed. Definition valid rho (d:dimacs) := - afold_left _ _ true andb (C_interp_or rho) d. + afold_left _ true andb (amap (C_interp_or rho) d). Lemma valid_spec : forall rho d, valid rho d <-> - (forall i : int, i < length d -> C.interp rho (PArray.to_list (d.[i]))). + (forall i : int, i < length d -> C.interp rho (to_list (d.[i]))). Proof. unfold valid; intros rho d; split; intro H. intros i Hi; case_eq (C.interp rho (to_list (d .[ i]))); try reflexivity. - intro Heq; erewrite afold_left_andb_false in H; try eassumption. + intro Heq; erewrite afold_left_andb_false in H; rewrite ?length_amap, ?get_amap; try eassumption. rewrite C_interp_or_spec; auto. - apply afold_left_andb_true; try assumption; intros i Hi; rewrite C_interp_or_spec; apply H; auto. + apply afold_left_andb_true; rewrite length_amap; intros i Hi; rewrite get_amap, C_interp_or_spec by assumption; apply H; auto. Qed. Inductive certif := | Certif : int -> _trace_ step -> clause_id -> certif. Definition add_roots s (d:dimacs) := - PArray.foldi_right (fun i c s => S.set_clause s i (PArray.to_list c)) d s. + foldi (fun i s => S.set_clause s i (to_list (d.[i]))) 0 (length d) s. Definition checker (d:dimacs) (c:certif) := let (nclauses, t, confl_id) := c in @@ -157,7 +160,8 @@ Qed. forall d s, valid rho d -> S.valid rho s -> S.valid rho (add_roots s d). Proof. - intros rho Hwr d s Hd Hs; unfold add_roots; apply (PArray.foldi_right_Ind _ _ (fun _ a => S.valid rho a)); auto; intros a i Hlt Hv; apply S.valid_set_clause; auto; rewrite valid_spec in Hd; apply Hd; auto. + intros rho Hwr d s Hd Hs; unfold add_roots. +apply (foldi_ind _ (fun _ a => S.valid rho a)); [ apply leb_0 | | ]; auto; intros i a _ Hle Hv; apply S.valid_set_clause; auto; rewrite valid_spec in Hd; apply Hd; auto. Qed. Lemma checker_correct : forall d c, @@ -230,7 +234,7 @@ Module Cnf_Checker. Proof. intros rho rhobv t_form Ht s H; destruct (Form.check_form_correct rho rhobv _ Ht) as [[Ht1 Ht2] Ht3]; intros [pos res|pos cid lf|pos|pos|pos l|pos l|pos l i|pos cid|pos cid|pos cid i]; simpl; try apply S.valid_set_clause; auto. apply S.valid_set_resolve; auto. - apply valid_check_flatten; auto; try discriminate; intros a1 a2; unfold is_true; rewrite Int63Properties.eqb_spec; intro; subst a1; auto. + apply valid_check_flatten; auto; try discriminate; intros a1 a2; unfold is_true; rewrite Int63.eqb_spec; intro; subst a1; auto. apply valid_check_True; auto. apply valid_check_False; auto. apply valid_check_BuildDef; auto. @@ -280,7 +284,7 @@ Module Cnf_Checker. checker_b t_form l b c = true -> Lit.interp (Form.interp_state_var (PArray.get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l = b. Proof. - unfold checker_b; intros t_var t_form l b c; case b; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l); auto; intros H1 H2; elim (checker_correct H2 (rho:=get t_var) (rhobv:=fun _ s => BITVECTOR_LIST.zeros s)); auto; rewrite Lit.interp_neg, H1; auto. + unfold checker_b; intros t_var t_form l b c; case b; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l); auto with smtcoq_core; intros H1 H2; elim (checker_correct H2 (rho:=get t_var) (rhobv:=fun _ s => BITVECTOR_LIST.zeros s)); auto with smtcoq_core; rewrite Lit.interp_neg, H1; auto with smtcoq_core. Qed. Definition checker_eq t_form l1 l2 l (c:certif) := @@ -296,9 +300,9 @@ Module Cnf_Checker. Lit.interp (Form.interp_state_var (PArray.get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l1 = Lit.interp (Form.interp_state_var (PArray.get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l2. Proof. - unfold checker_eq; intros t_var t_form l1 l2 l c; rewrite !andb_true_iff; case_eq (t_form .[ Lit.blit l]); [intros _ _|intros _|intros _|intros _ _ _|intros _ _|intros _ _|intros _ _|intros _ _ _|intros l1' l2' Heq|intros _ _ _ _|intros a ls Heq]; intros [[H1 H2] H3]; try discriminate; rewrite andb_true_iff in H2; rewrite !Int63Properties.eqb_spec in H2; destruct H2 as [H2 H4]; subst l1' l2'; case_eq (Lit.is_pos l); intro Heq'; rewrite Heq' in H1; try discriminate; clear H1; assert (H:PArray.default t_form = Form.Ftrue /\ Form.wf t_form). - unfold checker in H3; destruct c as (nclauses, t, confl); rewrite andb_true_iff in H3; destruct H3 as [H3 _]; destruct (Form.check_form_correct (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) _ H3) as [[Ht1 Ht2] Ht3]; split; auto. - destruct H as [H1 H2]; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l1); intro Heq1; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l2); intro Heq2; auto; elim (checker_correct H3 (rho:=get t_var) (rhobv:=fun _ s => BITVECTOR_LIST.zeros s)); unfold Lit.interp; rewrite Heq'; unfold Var.interp; rewrite Form.wf_interp_form; auto; rewrite Heq; simpl; rewrite Heq1, Heq2; auto. + unfold checker_eq; intros t_var t_form l1 l2 l c; rewrite !andb_true_iff; case_eq (t_form .[ Lit.blit l]); [intros _ _|intros _|intros _|intros _ _ _|intros _ _|intros _ _|intros _ _|intros _ _ _|intros l1' l2' Heq|intros _ _ _ _|intros a ls Heq]; intros [[H1 H2] H3]; try discriminate; rewrite andb_true_iff in H2; rewrite !Int63.eqb_spec in H2; destruct H2 as [H2 H4]; subst l1' l2'; case_eq (Lit.is_pos l); intro Heq'; rewrite Heq' in H1; try discriminate; clear H1; assert (H:PArray.default t_form = Form.Ftrue /\ Form.wf t_form). + unfold checker in H3; destruct c as (nclauses, t, confl); rewrite andb_true_iff in H3; destruct H3 as [H3 _]; destruct (Form.check_form_correct (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) _ H3) as [[Ht1 Ht2] Ht3]; split; auto with smtcoq_core. + destruct H as [H1 H2]; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l1); intro Heq1; case_eq (Lit.interp (Form.interp_state_var (get t_var) (fun _ s => BITVECTOR_LIST.zeros s) t_form) l2); intro Heq2; auto with smtcoq_core; elim (checker_correct H3 (rho:=get t_var) (rhobv:=fun _ s => BITVECTOR_LIST.zeros s)); unfold Lit.interp; rewrite Heq'; unfold Var.interp; rewrite Form.wf_interp_form; auto with smtcoq_core; rewrite Heq; simpl; rewrite Heq1, Heq2; auto with smtcoq_core. Qed. End Cnf_Checker. @@ -433,49 +437,49 @@ Inductive step := |pos orig1 orig2 res|pos orig1 orig2 res |pos orig1 orig2 res|pos orig1 orig2 res|pos orig1 orig2 res|pos orig1 orig2 res |pos cl |pos orig res |pos orig res |pos orig res | pos orig1 orig2 res | pos orig1 orig2 res |pos res|pos res - |pos res |pos prem_id prem concl p|pos lemma plemma concl p]; simpl; try apply S.valid_set_clause; auto. - - apply S.valid_set_resolve; auto. - - apply S.valid_set_weaken; auto. - - apply valid_check_flatten; auto; intros h1 h2 H. - + rewrite (Syntactic.check_hatom_correct_bool _ _ _ Ha1 Ha2 _ _ H); auto. - + rewrite (Syntactic.check_neg_hatom_correct_bool _ _ _ H10 Ha1 Ha2 _ _ H); auto. - - apply valid_check_True; auto. - - apply valid_check_False; auto. - - apply valid_check_BuildDef; auto. - - apply valid_check_BuildDef2; auto. - - apply valid_check_BuildProj; auto. - - apply valid_check_ImmBuildDef; auto. - - apply valid_check_ImmBuildDef2; auto. - - apply valid_check_ImmBuildProj; auto. - - apply valid_check_trans; auto. - - apply valid_check_congr; auto. - - apply valid_check_congr_pred; auto. - - apply valid_check_micromega; auto. - - apply valid_check_diseq; auto. - - apply valid_check_spl_arith; auto. - - apply valid_check_distinct_elim; auto. - - eapply valid_check_bbVar; eauto. - - apply valid_check_bbConst; auto. - - apply valid_check_bbOp; auto. - - apply valid_check_bbNot; auto. - - apply valid_check_bbNeg; auto. - - apply valid_check_bbAdd; auto. - - apply valid_check_bbConcat; auto. - - apply valid_check_bbMult; auto. - - apply valid_check_bbUlt; auto. - - apply valid_check_bbSlt; auto. - - apply valid_check_bbEq; auto. - - apply valid_check_bbDiseq; auto. - - apply valid_check_bbExtract; auto. - - apply valid_check_bbZextend; auto. - - apply valid_check_bbSextend; auto. - - apply valid_check_bbShl; auto. - - apply valid_check_bbShr; auto. - - apply valid_check_roweq; auto. - - apply valid_check_rowneq; auto. - - apply valid_check_ext; auto. - - apply valid_check_hole; auto. - - apply valid_check_forall_inst with lemma; auto. + |pos res |pos prem_id prem concl p|pos lemma plemma concl p]; simpl; try apply S.valid_set_clause; auto with smtcoq_core. + - apply S.valid_set_resolve; auto with smtcoq_core. + - apply S.valid_set_weaken; auto with smtcoq_core. + - apply valid_check_flatten; auto with smtcoq_core; intros h1 h2 H. + + rewrite (Syntactic.check_hatom_correct_bool _ _ _ Ha1 Ha2 _ _ H); auto with smtcoq_core. + + rewrite (Syntactic.check_neg_hatom_correct_bool _ _ _ H10 Ha1 Ha2 _ _ H); auto with smtcoq_core. + - apply valid_check_True; auto with smtcoq_core. + - apply valid_check_False; auto with smtcoq_core. + - apply valid_check_BuildDef; auto with smtcoq_core. + - apply valid_check_BuildDef2; auto with smtcoq_core. + - apply valid_check_BuildProj; auto with smtcoq_core. + - apply valid_check_ImmBuildDef; auto with smtcoq_core. + - apply valid_check_ImmBuildDef2; auto with smtcoq_core. + - apply valid_check_ImmBuildProj; auto with smtcoq_core. + - apply valid_check_trans; auto with smtcoq_core. + - apply valid_check_congr; auto with smtcoq_core. + - apply valid_check_congr_pred; auto with smtcoq_core. + - apply valid_check_micromega; auto with smtcoq_core. + - apply valid_check_diseq; auto with smtcoq_core. + - apply valid_check_spl_arith; auto with smtcoq_core. + - apply valid_check_distinct_elim; auto with smtcoq_core. + - eapply valid_check_bbVar; eauto with smtcoq_core. + - apply valid_check_bbConst; auto with smtcoq_core. + - apply valid_check_bbOp; auto with smtcoq_core. + - apply valid_check_bbNot; auto with smtcoq_core. + - apply valid_check_bbNeg; auto with smtcoq_core. + - apply valid_check_bbAdd; auto with smtcoq_core. + - apply valid_check_bbConcat; auto with smtcoq_core. + - apply valid_check_bbMult; auto with smtcoq_core. + - apply valid_check_bbUlt; auto with smtcoq_core. + - apply valid_check_bbSlt; auto with smtcoq_core. + - apply valid_check_bbEq; auto with smtcoq_core. + - apply valid_check_bbDiseq; auto with smtcoq_core. + - apply valid_check_bbExtract; auto with smtcoq_core. + - apply valid_check_bbZextend; auto with smtcoq_core. + - apply valid_check_bbSextend; auto with smtcoq_core. + - apply valid_check_bbShl; auto with smtcoq_core. + - apply valid_check_bbShr; auto with smtcoq_core. + - apply valid_check_roweq; auto with smtcoq_core. + - apply valid_check_rowneq; auto with smtcoq_core. + - apply valid_check_ext; auto with smtcoq_core. + - apply valid_check_hole; auto with smtcoq_core. + - apply valid_check_forall_inst with lemma; auto with smtcoq_core. Qed. Definition euf_checker (* t_atom t_form *) s t := @@ -490,8 +494,8 @@ Inductive step := ~ (S.valid rho s). Proof. unfold euf_checker; intros (* t_i t_func t_atom t_form *) rho H1 H2 H10; apply _checker__correct. - intros c H; apply C.is_false_correct; auto. - apply step_checker_correct; auto. + intros c H; apply C.is_false_correct; auto with smtcoq_core. + apply step_checker_correct; auto with smtcoq_core. Qed. Inductive certif := @@ -499,15 +503,15 @@ Inductive step := Definition add_roots s d used_roots := match used_roots with - | Some ur => PArray.foldi_right (fun i c_index s => - let c := if c_index < length d then (d.[c_index])::nil else C._true in - S.set_clause s i c) ur s - | None => PArray.foldi_right (fun i c s => S.set_clause s i (c::nil)) d s + | Some ur => foldi (fun i s => + let c := if (ur.[i]) < length d then (d.[ur.[i]])::nil else C._true in + S.set_clause s i c) 0 (length ur) s + | None => foldi (fun i s => S.set_clause s i (d.[i]::nil)) 0 (length d) s end. Definition valid t_i t_func t_atom t_form d := let rho := Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form in - afold_left _ _ true andb (Lit.interp rho) d. + afold_left _ true andb (amap (Lit.interp rho) d). Lemma add_roots_correct : (* forall t_i t_func t_atom t_form, *) let rho := Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form in @@ -516,11 +520,11 @@ Inductive step := forall s d used_roots, S.valid rho s -> valid t_func t_atom t_form d -> S.valid rho (add_roots s d used_roots). Proof. - intros (* t_i t_func t_atom t_form *) rho H1 H2 H10 s d used_roots H3; unfold valid; intro H4; pose (H5 := (afold_left_andb_true_inv _ _ _ H4)); unfold add_roots; assert (Valuation.wf rho) by (destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H1) as [_ H]; auto); case used_roots. - intro ur; apply (foldi_right_Ind _ _ (fun _ a => S.valid rho a)); auto; intros a i H6 Ha; apply S.valid_set_clause; auto; case_eq (ur .[ i] < length d). - intro; unfold C.valid; simpl; rewrite H5; auto. - intros; apply C.interp_true; auto. - apply (foldi_right_Ind _ _ (fun _ a => S.valid rho a)); auto; intros a i H6 Ha; apply S.valid_set_clause; auto; unfold C.valid; simpl; rewrite H5; auto. + intros (* t_i t_func t_atom t_form *) rho H1 H2 H10 s d used_roots H3; unfold valid; intro H4; pose (H5 := (afold_left_andb_true_inv _ H4)); unfold add_roots; assert (Valuation.wf rho) by (destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H1) as [_ H]; auto with smtcoq_core); case used_roots. + intro ur; apply (foldi_ind _ (fun _ a => S.valid rho a)); [ apply leb_0 | | ]; auto with smtcoq_core; intros i a _ H6 Ha; apply S.valid_set_clause; auto with smtcoq_core; case_eq (ur .[ i] < length d). + intro; unfold C.valid; simpl; specialize (H5 (ur.[i])); rewrite length_amap, get_amap in H5 by assumption; unfold rho; rewrite H5; auto with smtcoq_core. + intros; apply C.interp_true; auto with smtcoq_core. + apply (foldi_ind _ (fun _ a => S.valid rho a)); [ apply leb_0 | | ]; auto with smtcoq_core; intros i a _ H6 Ha; apply S.valid_set_clause; auto with smtcoq_core; unfold C.valid; simpl; specialize (H5 i); rewrite length_amap, get_amap in H5 by assumption; unfold rho; rewrite H5; auto with smtcoq_core. Qed. Definition checker (* t_i t_func t_atom t_form *) d used_roots (c:certif) := @@ -534,7 +538,7 @@ Inductive step := Definition setup_checker_step_debug d used_roots (c:certif) := let (nclauses, t, confl) := c in let s := add_roots (S.make nclauses) d used_roots in - (s, Structures.trace_to_list t). + (s, fst t). Definition position_of_step (st:step) := @@ -686,7 +690,7 @@ Inductive step := let (nclauses, t, confl) := c in let s := add_roots (S.make nclauses) d used_roots in let '(_, nb, failure) := - Structures.trace_fold + List.fold_left (fun acc step => match acc with | (s, nb, None) => @@ -698,7 +702,7 @@ Inductive step := else (s, nb, None) | _ => acc end - ) (s, O, None) t + ) (fst t) (s, O, None) in match failure with | Some st => Some (nb, name_of_step st) @@ -711,7 +715,7 @@ Inductive step := checker (* t_i t_func t_atom t_form *) d used_roots c = true -> ~ (valid t_func t_atom t_form d). Proof. - unfold checker; intros (* t_i t_func t_atom t_form *) d used_roots (nclauses, t, confl); rewrite !andb_true_iff; intros [[[H1 H2] H10] H3] H; eelim euf_checker_correct; try eassumption; apply add_roots_correct; try eassumption; apply S.valid_make; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H1) as [_ H4]; auto. + unfold checker; intros (* t_i t_func t_atom t_form *) d used_roots (nclauses, t, confl); rewrite !andb_true_iff; intros [[[H1 H2] H10] H3] H; eelim euf_checker_correct; try eassumption; apply add_roots_correct; try eassumption; apply S.valid_make; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H1) as [_ H4]; auto with smtcoq_core. Qed. Definition checker_b (* t_i t_func t_atom t_form *) l (b:bool) (c:certif) := @@ -723,7 +727,7 @@ Inductive step := checker_b (* t_func t_atom t_form *) l b c = true -> Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l = b. Proof. - unfold checker_b; intros (* t_i t_func t_atom t_form *) l b (nclauses, t, confl); case b; intros H2; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l); auto; intros H1; elim (checker_correct H2); auto; unfold valid; apply afold_left_andb_true; intros i Hi; rewrite get_make; auto; rewrite Lit.interp_neg, H1; auto. + unfold checker_b; intros (* t_i t_func t_atom t_form *) l b (nclauses, t, confl); case b; intros H2; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l); auto with smtcoq_core; intros H1; elim (checker_correct H2); auto with smtcoq_core; unfold valid; apply afold_left_andb_true; rewrite length_amap; intros i Hi; rewrite get_amap by assumption; rewrite get_make; auto with smtcoq_core; rewrite Lit.interp_neg, H1; auto with smtcoq_core. Qed. Definition checker_eq (* t_i t_func t_atom t_form *) l1 l2 l (c:certif) := @@ -740,9 +744,9 @@ Inductive step := Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l1 = Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l2. Proof. - unfold checker_eq; intros (* t_i t_func t_atom t_form *) l1 l2 l (nclauses, t, confl); rewrite !andb_true_iff; case_eq (t_form .[ Lit.blit l]); [intros _ _|intros _|intros _|intros _ _ _|intros _ _|intros _ _|intros _ _|intros _ _ _|intros l1' l2' Heq|intros _ _ _ _|intros a ls Heq]; intros [[H1 H2] H3]; try discriminate; rewrite andb_true_iff in H2; rewrite !Int63Properties.eqb_spec in H2; destruct H2 as [H2 H4]; subst l1' l2'; case_eq (Lit.is_pos l); intro Heq'; rewrite Heq' in H1; try discriminate; clear H1; assert (H:PArray.default t_form = Form.Ftrue /\ Form.wf t_form). - unfold checker in H3; rewrite !andb_true_iff in H3; destruct H3 as [[[H3 _] _] _]; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H3) as [[Ht1 Ht2] Ht3]; split; auto. - destruct H as [H1 H2]; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l1); intro Heq1; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l2); intro Heq2; auto; elim (checker_correct H3); unfold valid; apply afold_left_andb_true; intros i Hi; rewrite get_make; unfold Lit.interp; rewrite Heq'; unfold Var.interp; rewrite Form.wf_interp_form; auto; rewrite Heq; simpl; rewrite Heq1, Heq2; auto. + unfold checker_eq; intros (* t_i t_func t_atom t_form *) l1 l2 l (nclauses, t, confl); rewrite !andb_true_iff; case_eq (t_form .[ Lit.blit l]); [intros _ _|intros _|intros _|intros _ _ _|intros _ _|intros _ _|intros _ _|intros _ _ _|intros l1' l2' Heq|intros _ _ _ _|intros a ls Heq]; intros [[H1 H2] H3]; try discriminate; rewrite andb_true_iff in H2; rewrite !Int63.eqb_spec in H2; destruct H2 as [H2 H4]; subst l1' l2'; case_eq (Lit.is_pos l); intro Heq'; rewrite Heq' in H1; try discriminate; clear H1; assert (H:PArray.default t_form = Form.Ftrue /\ Form.wf t_form). + unfold checker in H3; rewrite !andb_true_iff in H3; destruct H3 as [[[H3 _] _] _]; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) _ H3) as [[Ht1 Ht2] Ht3]; split; auto with smtcoq_core. + destruct H as [H1 H2]; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l1); intro Heq1; case_eq (Lit.interp (Form.interp_state_var (Atom.interp_form_hatom t_i t_func t_atom) (Atom.interp_form_hatom_bv t_i t_func t_atom) t_form) l2); intro Heq2; auto with smtcoq_core; elim (checker_correct H3); unfold valid; apply afold_left_andb_true; rewrite length_amap; intros i Hi; rewrite get_amap by assumption; rewrite get_make; unfold Lit.interp; rewrite Heq'; unfold Var.interp; rewrite Form.wf_interp_form; auto with smtcoq_core; rewrite Heq; simpl; rewrite Heq1, Heq2; auto with smtcoq_core. Qed. @@ -762,7 +766,7 @@ Inductive step := forall t_i t_func, Atom.wt t_i t_func t_atom -> ~ valid t_func t_atom t_form d. Proof. - unfold checker_ext; intros t_atom t_form d used_roots (nclauses, t, confl); rewrite !andb_true_iff; intros [[H1 H2] H3]; intros t_i t_func H10 H; eelim euf_checker_correct; try eassumption; apply add_roots_correct; try eassumption; apply S.valid_make; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) _ H1) as [_ H4]; auto. + unfold checker_ext; intros t_atom t_form d used_roots (nclauses, t, confl); rewrite !andb_true_iff; intros [[H1 H2] H3]; intros t_i t_func H10 H; eelim euf_checker_correct; try eassumption; apply add_roots_correct; try eassumption; apply S.valid_make; destruct (Form.check_form_correct (Atom.interp_form_hatom t_i t_func t_atom) _ H1) as [_ H4]; auto with smtcoq_core. Qed. *) @@ -774,6 +778,127 @@ End Euf_Checker. Unset Implicit Arguments. +(* Register constants for OCaml access *) +Register Sat_Checker.valid as SMTCoq.Trace.Sat_Checker.valid. +Register Sat_Checker.interp_var as SMTCoq.Trace.Sat_Checker.interp_var. +Register Sat_Checker.Certif as SMTCoq.Trace.Sat_Checker.Certif. +Register Sat_Checker.step as SMTCoq.Trace.Sat_Checker.step. +Register Sat_Checker.Res as SMTCoq.Trace.Sat_Checker.Res. +Register Sat_Checker.dimacs as SMTCoq.Trace.Sat_Checker.dimacs. +Register Sat_Checker.certif as SMTCoq.Trace.Sat_Checker.certif. +Register Sat_Checker.theorem_checker as SMTCoq.Trace.Sat_Checker.theorem_checker. +Register Sat_Checker.checker as SMTCoq.Trace.Sat_Checker.checker. + +Register Cnf_Checker.certif as SMTCoq.Trace.Cnf_Checker.certif. +Register Cnf_Checker.Certif as SMTCoq.Trace.Cnf_Checker.Certif. +Register Cnf_Checker.checker_b_correct as SMTCoq.Trace.Cnf_Checker.checker_b_correct. +Register Cnf_Checker.checker_b as SMTCoq.Trace.Cnf_Checker.checker_b. +Register Cnf_Checker.checker_eq_correct as SMTCoq.Trace.Cnf_Checker.checker_eq_correct. +Register Cnf_Checker.checker_eq as SMTCoq.Trace.Cnf_Checker.checker_eq. +Register Cnf_Checker.step as SMTCoq.Trace.Cnf_Checker.step. +Register Cnf_Checker.Res as SMTCoq.Trace.Cnf_Checker.Res. +Register Cnf_Checker.ImmFlatten as SMTCoq.Trace.Cnf_Checker.ImmFlatten. +Register Cnf_Checker.CTrue as SMTCoq.Trace.Cnf_Checker.CTrue. +Register Cnf_Checker.CFalse as SMTCoq.Trace.Cnf_Checker.CFalse. +Register Cnf_Checker.BuildDef as SMTCoq.Trace.Cnf_Checker.BuildDef. +Register Cnf_Checker.BuildDef2 as SMTCoq.Trace.Cnf_Checker.BuildDef2. +Register Cnf_Checker.BuildProj as SMTCoq.Trace.Cnf_Checker.BuildProj. +Register Cnf_Checker.ImmBuildDef as SMTCoq.Trace.Cnf_Checker.ImmBuildDef. +Register Cnf_Checker.ImmBuildDef2 as SMTCoq.Trace.Cnf_Checker.ImmBuildDef2. +Register Cnf_Checker.ImmBuildProj as SMTCoq.Trace.Cnf_Checker.ImmBuildProj. + +Register Euf_Checker.Certif as SMTCoq.Trace.Euf_Checker.Certif. +Register Euf_Checker.certif as SMTCoq.Trace.Euf_Checker.certif. +Register Euf_Checker.checker as SMTCoq.Trace.Euf_Checker.checker. +Register Euf_Checker.checker_correct as SMTCoq.Trace.Euf_Checker.checker_correct. +Register Euf_Checker.checker_b_correct as SMTCoq.Trace.Euf_Checker.checker_b_correct. +Register Euf_Checker.checker_b as SMTCoq.Trace.Euf_Checker.checker_b. +Register Euf_Checker.checker_eq_correct as SMTCoq.Trace.Euf_Checker.checker_eq_correct. +Register Euf_Checker.checker_eq as SMTCoq.Trace.Euf_Checker.checker_eq. +Register Euf_Checker.checker_debug as SMTCoq.Trace.Euf_Checker.checker_debug. +Register Euf_Checker.name_step as SMTCoq.Trace.Euf_Checker.name_step. +Register Euf_Checker.Name_Res as SMTCoq.Trace.Euf_Checker.Name_Res. +Register Euf_Checker.Name_Weaken as SMTCoq.Trace.Euf_Checker.Name_Weaken. +Register Euf_Checker.Name_ImmFlatten as SMTCoq.Trace.Euf_Checker.Name_ImmFlatten. +Register Euf_Checker.Name_CTrue as SMTCoq.Trace.Euf_Checker.Name_CTrue. +Register Euf_Checker.Name_CFalse as SMTCoq.Trace.Euf_Checker.Name_CFalse. +Register Euf_Checker.Name_BuildDef as SMTCoq.Trace.Euf_Checker.Name_BuildDef. +Register Euf_Checker.Name_BuildDef2 as SMTCoq.Trace.Euf_Checker.Name_BuildDef2. +Register Euf_Checker.Name_BuildProj as SMTCoq.Trace.Euf_Checker.Name_BuildProj. +Register Euf_Checker.Name_ImmBuildDef as SMTCoq.Trace.Euf_Checker.Name_ImmBuildDef. +Register Euf_Checker.Name_ImmBuildDef2 as SMTCoq.Trace.Euf_Checker.Name_ImmBuildDef2. +Register Euf_Checker.Name_ImmBuildProj as SMTCoq.Trace.Euf_Checker.Name_ImmBuildProj. +Register Euf_Checker.Name_EqTr as SMTCoq.Trace.Euf_Checker.Name_EqTr. +Register Euf_Checker.Name_EqCgr as SMTCoq.Trace.Euf_Checker.Name_EqCgr. +Register Euf_Checker.Name_EqCgrP as SMTCoq.Trace.Euf_Checker.Name_EqCgrP. +Register Euf_Checker.Name_LiaMicromega as SMTCoq.Trace.Euf_Checker.Name_LiaMicromega. +Register Euf_Checker.Name_LiaDiseq as SMTCoq.Trace.Euf_Checker.Name_LiaDiseq. +Register Euf_Checker.Name_SplArith as SMTCoq.Trace.Euf_Checker.Name_SplArith. +Register Euf_Checker.Name_SplDistinctElim as SMTCoq.Trace.Euf_Checker.Name_SplDistinctElim. +Register Euf_Checker.Name_BBVar as SMTCoq.Trace.Euf_Checker.Name_BBVar. +Register Euf_Checker.Name_BBConst as SMTCoq.Trace.Euf_Checker.Name_BBConst. +Register Euf_Checker.Name_BBOp as SMTCoq.Trace.Euf_Checker.Name_BBOp. +Register Euf_Checker.Name_BBNot as SMTCoq.Trace.Euf_Checker.Name_BBNot. +Register Euf_Checker.Name_BBNeg as SMTCoq.Trace.Euf_Checker.Name_BBNeg. +Register Euf_Checker.Name_BBAdd as SMTCoq.Trace.Euf_Checker.Name_BBAdd. +Register Euf_Checker.Name_BBConcat as SMTCoq.Trace.Euf_Checker.Name_BBConcat. +Register Euf_Checker.Name_BBMul as SMTCoq.Trace.Euf_Checker.Name_BBMul. +Register Euf_Checker.Name_BBUlt as SMTCoq.Trace.Euf_Checker.Name_BBUlt. +Register Euf_Checker.Name_BBSlt as SMTCoq.Trace.Euf_Checker.Name_BBSlt. +Register Euf_Checker.Name_BBEq as SMTCoq.Trace.Euf_Checker.Name_BBEq. +Register Euf_Checker.Name_BBDiseq as SMTCoq.Trace.Euf_Checker.Name_BBDiseq. +Register Euf_Checker.Name_BBExtract as SMTCoq.Trace.Euf_Checker.Name_BBExtract. +Register Euf_Checker.Name_BBZextend as SMTCoq.Trace.Euf_Checker.Name_BBZextend. +Register Euf_Checker.Name_BBSextend as SMTCoq.Trace.Euf_Checker.Name_BBSextend. +Register Euf_Checker.Name_BBShl as SMTCoq.Trace.Euf_Checker.Name_BBShl. +Register Euf_Checker.Name_BBShr as SMTCoq.Trace.Euf_Checker.Name_BBShr. +Register Euf_Checker.Name_RowEq as SMTCoq.Trace.Euf_Checker.Name_RowEq. +Register Euf_Checker.Name_RowNeq as SMTCoq.Trace.Euf_Checker.Name_RowNeq. +Register Euf_Checker.Name_Ext as SMTCoq.Trace.Euf_Checker.Name_Ext. +Register Euf_Checker.Name_Hole as SMTCoq.Trace.Euf_Checker.Name_Hole. +Register Euf_Checker.step as SMTCoq.Trace.Euf_Checker.step. +Register Euf_Checker.Res as SMTCoq.Trace.Euf_Checker.Res. +Register Euf_Checker.Weaken as SMTCoq.Trace.Euf_Checker.Weaken. +Register Euf_Checker.ImmFlatten as SMTCoq.Trace.Euf_Checker.ImmFlatten. +Register Euf_Checker.CTrue as SMTCoq.Trace.Euf_Checker.CTrue. +Register Euf_Checker.CFalse as SMTCoq.Trace.Euf_Checker.CFalse. +Register Euf_Checker.BuildDef as SMTCoq.Trace.Euf_Checker.BuildDef. +Register Euf_Checker.BuildDef2 as SMTCoq.Trace.Euf_Checker.BuildDef2. +Register Euf_Checker.BuildProj as SMTCoq.Trace.Euf_Checker.BuildProj. +Register Euf_Checker.ImmBuildProj as SMTCoq.Trace.Euf_Checker.ImmBuildProj. +Register Euf_Checker.ImmBuildDef as SMTCoq.Trace.Euf_Checker.ImmBuildDef. +Register Euf_Checker.ImmBuildDef2 as SMTCoq.Trace.Euf_Checker.ImmBuildDef2. +Register Euf_Checker.EqTr as SMTCoq.Trace.Euf_Checker.EqTr. +Register Euf_Checker.EqCgr as SMTCoq.Trace.Euf_Checker.EqCgr. +Register Euf_Checker.EqCgrP as SMTCoq.Trace.Euf_Checker.EqCgrP. +Register Euf_Checker.LiaMicromega as SMTCoq.Trace.Euf_Checker.LiaMicromega. +Register Euf_Checker.LiaDiseq as SMTCoq.Trace.Euf_Checker.LiaDiseq. +Register Euf_Checker.SplArith as SMTCoq.Trace.Euf_Checker.SplArith. +Register Euf_Checker.SplDistinctElim as SMTCoq.Trace.Euf_Checker.SplDistinctElim. +Register Euf_Checker.BBVar as SMTCoq.Trace.Euf_Checker.BBVar. +Register Euf_Checker.BBConst as SMTCoq.Trace.Euf_Checker.BBConst. +Register Euf_Checker.BBOp as SMTCoq.Trace.Euf_Checker.BBOp. +Register Euf_Checker.BBNot as SMTCoq.Trace.Euf_Checker.BBNot. +Register Euf_Checker.BBEq as SMTCoq.Trace.Euf_Checker.BBEq. +Register Euf_Checker.BBDiseq as SMTCoq.Trace.Euf_Checker.BBDiseq. +Register Euf_Checker.BBNeg as SMTCoq.Trace.Euf_Checker.BBNeg. +Register Euf_Checker.BBAdd as SMTCoq.Trace.Euf_Checker.BBAdd. +Register Euf_Checker.BBMul as SMTCoq.Trace.Euf_Checker.BBMul. +Register Euf_Checker.BBUlt as SMTCoq.Trace.Euf_Checker.BBUlt. +Register Euf_Checker.BBSlt as SMTCoq.Trace.Euf_Checker.BBSlt. +Register Euf_Checker.BBConcat as SMTCoq.Trace.Euf_Checker.BBConcat. +Register Euf_Checker.BBExtract as SMTCoq.Trace.Euf_Checker.BBExtract. +Register Euf_Checker.BBZextend as SMTCoq.Trace.Euf_Checker.BBZextend. +Register Euf_Checker.BBSextend as SMTCoq.Trace.Euf_Checker.BBSextend. +Register Euf_Checker.BBShl as SMTCoq.Trace.Euf_Checker.BBShl. +Register Euf_Checker.BBShr as SMTCoq.Trace.Euf_Checker.BBShr. +Register Euf_Checker.RowEq as SMTCoq.Trace.Euf_Checker.RowEq. +Register Euf_Checker.RowNeq as SMTCoq.Trace.Euf_Checker.RowNeq. +Register Euf_Checker.Ext as SMTCoq.Trace.Euf_Checker.Ext. +Register Euf_Checker.Hole as SMTCoq.Trace.Euf_Checker.Hole. +Register Euf_Checker.ForallInst as SMTCoq.Trace.Euf_Checker.ForallInst. + + (* Local Variables: coq-load-path: ((rec "." "SMTCoq")) |