diff options
Diffstat (limited to 'src/spl/Syntactic.v')
| -rw-r--r-- | src/spl/Syntactic.v | 110 |
1 files changed, 86 insertions, 24 deletions
diff --git a/src/spl/Syntactic.v b/src/spl/Syntactic.v index 7a52694..cc34522 100644 --- a/src/spl/Syntactic.v +++ b/src/spl/Syntactic.v @@ -1,13 +1,9 @@ (**************************************************************************) (* *) (* SMTCoq *) -(* Copyright (C) 2011 - 2016 *) +(* Copyright (C) 2011 - 2019 *) (* *) -(* Michaël Armand *) -(* Benjamin Grégoire *) -(* Chantal Keller *) -(* *) -(* Inria - École Polytechnique - Université Paris-Sud *) +(* See file "AUTHORS" for the list of authors *) (* *) (* This file is distributed under the terms of the CeCILL-C licence *) (* *) @@ -15,9 +11,9 @@ (*** Spl -- a small checker for simplifications ***) - Require Import List PArray Bool Int63 ZMicromega. -Require Import Misc State SMT_terms. +Require Import Misc State SMT_terms BVList. +Require Lia. Local Open Scope array_scope. Local Open Scope int63_scope. @@ -29,7 +25,7 @@ Section CheckAtom. Import Atom. - Variable t_i : PArray.array typ_eqb. + Variable t_i : PArray.array SMT_classes.typ_compdec. Variable t_func : PArray.array (tval t_i). Variable t_atom : PArray.array atom. @@ -73,6 +69,8 @@ Section CheckAtom. Typ.eqb t1 t2 && ((check_hatom a1 b1 && check_hatom a2 b2) || (check_hatom a1 b2 && check_hatom a2 b1)) + | BO_BVand s1, BO_BVand s2 + | BO_BVor s1, BO_BVor s2 => N.eqb s1 s2 && check_hatom a1 b1 && check_hatom a2 b2 | _, _ => false end | Anop o1 l1, Anop o2 l2 => @@ -112,16 +110,62 @@ Section CheckAtom. Lemma check_atom_aux_correct : forall a1 a2, check_atom_aux a1 a2 -> interp t_i t_func t_atom a1 = interp t_i t_func t_atom a2. Proof. - intros [op1|op1 i1|op1 i1 j1|op1 li1|f1 args1]; simpl. + intros [op1|op1 i1|op1 i1 j1|op1 li1|op1 li1|f1 args1]; simpl. (* Constants *) - intros [op2|op2 i2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; pose (H:=reflect_cop_eqb op1 op2); inversion H; try discriminate; subst op1; auto. + - intros [op2|op2 i2|op2 i2 j2|op2 li2|op2 li2|f2 args2]; simpl; try discriminate; pose (H:=reflect_cop_eqb op1 op2); inversion H; try discriminate; subst op1; auto. (* Unary operators *) - intros [op2|op2 i2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; try (case op1; discriminate). + - + intros [op2|op2 i2|op2 i2 j2|op2 li2|op2 li2|f2 args2]; simpl; try discriminate; try (case op1; discriminate). case op1; case op2; try discriminate; try (unfold is_true; rewrite andb_true_iff; intros [_ H]; rewrite (check_hatom_correct _ _ H); auto). - case_eq (get_atom i2); try discriminate; intros [ | | | | ] i Heq H; try discriminate; simpl; unfold apply_unop; rewrite (check_hatom_correct _ _ H); unfold interp_hatom; rewrite (t_interp_wf _ _ _ Hwf Hd i2), Heq; simpl; unfold apply_unop; destruct (t_interp t_i t_func t_atom .[ i]) as [A v]; destruct (Typ.cast A Typ.Tpositive) as [k| ]; auto. - case_eq (get_atom i1); try discriminate; intros [ | | | | ] i Heq H; try discriminate; simpl; unfold apply_unop; rewrite <- (check_hatom_correct _ _ H); unfold interp_hatom; rewrite (t_interp_wf _ _ _ Hwf Hd i1), Heq; simpl; unfold apply_unop; destruct (t_interp t_i t_func t_atom .[ i]) as [A v]; destruct (Typ.cast A Typ.Tpositive) as [k| ]; auto. - (* Binary operators *) - intros [op2|op2 i2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; case op1; case op2; try discriminate; try (unfold is_true; rewrite andb_true_iff; intros [H1 H2]; rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2); auto). + + case_eq (get_atom i2); try discriminate; + intros [ | | | | | | | | i0 n0 n1| n i0| n i0] i Heq H; try discriminate; simpl; + unfold apply_unop; rewrite (check_hatom_correct _ _ H); + unfold interp_hatom; rewrite (t_interp_wf _ _ _ Hwf Hd i2), Heq; simpl; + unfold apply_unop; destruct (t_interp t_i t_func t_atom .[ i]) as [A v]; + destruct (Typ.cast A Typ.Tpositive) as [k| ]; auto. + case_eq (get_atom i1); try discriminate; + intros [ | | | | | | | | i0 n0 n1| n i0| n i0] i Heq H; try discriminate; simpl; + unfold apply_unop. rewrite <- (check_hatom_correct _ _ H); + unfold interp_hatom; rewrite (t_interp_wf _ _ _ Hwf Hd i1), Heq; simpl; + unfold apply_unop; destruct (t_interp t_i t_func t_atom .[ i]) as [A v]; + destruct (Typ.cast A Typ.Tpositive) as [k| ]; auto. + + intros n m n1 m2. simpl. unfold is_true. rewrite !andb_true_iff, beq_nat_true_iff, N.eqb_eq. intros [[-> ->] H]. rewrite (check_hatom_correct _ _ H); auto. + intros n m. simpl. unfold is_true. rewrite andb_true_iff, N.eqb_eq. intros [-> H]. rewrite (check_hatom_correct _ _ H); auto. + intros n m. simpl. unfold is_true. rewrite andb_true_iff, N.eqb_eq. intros [-> H]. rewrite (check_hatom_correct _ _ H); auto. + (* bv_extr *) + intros i n0 n1 i0 n2 n3. + unfold is_true. rewrite andb_true_iff. + intros. destruct H as (Ha, Hb). + inversion Ha. + rewrite !andb_true_iff in H0. + destruct H0 as ((H0a, H0b), H0c). + rewrite N.eqb_eq in H0a, H0b, H0c. + subst. + rewrite (check_hatom_correct _ _ Hb); auto. + (* bv_zextn *) + intros n i n0 i0. + unfold is_true. rewrite andb_true_iff. + intros. destruct H as (Ha, Hb). + inversion Ha. + rewrite !andb_true_iff in H0. + destruct H0 as (H0a, H0b). + rewrite N.eqb_eq in H0a, H0b. + subst. + rewrite (check_hatom_correct _ _ Hb); auto. + (* bv_sextn *) + intros n i n0 i0. + unfold is_true. rewrite andb_true_iff. + intros. destruct H as (Ha, Hb). + inversion Ha. + rewrite !andb_true_iff in H0. + destruct H0 as (H0a, H0b). + rewrite N.eqb_eq in H0a, H0b. + subst. + rewrite (check_hatom_correct _ _ Hb); auto. + (* Binary operators *) + - intros [op2|op2 i2|op2 i2 j2|op2 li2|op2 li2|f2 args2]; simpl; try discriminate; case op1; case op2; try discriminate; try (unfold is_true; rewrite andb_true_iff; intros [H1 H2]; rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2); auto). unfold is_true, interp_bop, apply_binop. rewrite orb_true_iff, !andb_true_iff. intros [[H1 H2]|[H1 H2]]; rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2); destruct (interp_hatom t_i t_func t_atom i2) as [A v1]; destruct (interp_hatom t_i t_func t_atom j2) as [B v2]; destruct (Typ.cast B Typ.TZ) as [k2| ]; destruct (Typ.cast A Typ.TZ) as [k1| ]; auto; rewrite Z.add_comm; reflexivity. unfold is_true, interp_bop, apply_binop. rewrite orb_true_iff, !andb_true_iff. intros [[H1 H2]|[H1 H2]]; rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2); destruct (interp_hatom t_i t_func t_atom i2) as [A v1]; destruct (interp_hatom t_i t_func t_atom j2) as [B v2]; destruct (Typ.cast B Typ.TZ) as [k2| ]; destruct (Typ.cast A Typ.TZ) as [k1| ]; auto; rewrite Z.mul_comm; reflexivity. unfold interp_bop, apply_binop; destruct (interp_hatom t_i t_func t_atom j2) as [B v2]; destruct (interp_hatom t_i t_func t_atom i2) as [A v1]; destruct (Typ.cast B Typ.TZ) as [k2| ]; destruct (Typ.cast A Typ.TZ) as [k1| ]; auto; rewrite Z.gtb_ltb; auto. @@ -129,10 +173,18 @@ Section CheckAtom. unfold interp_bop, apply_binop; destruct (interp_hatom t_i t_func t_atom j2) as [B v2]; destruct (interp_hatom t_i t_func t_atom i2) as [A v1]; destruct (Typ.cast B Typ.TZ) as [k2| ]; destruct (Typ.cast A Typ.TZ) as [k1| ]; auto; rewrite Z.geb_leb; auto. unfold interp_bop, apply_binop; destruct (interp_hatom t_i t_func t_atom j2) as [B v2]; destruct (interp_hatom t_i t_func t_atom i2) as [A v1]; destruct (Typ.cast B Typ.TZ) as [k2| ]; destruct (Typ.cast A Typ.TZ) as [k1| ]; auto; rewrite Z.gtb_ltb; auto. intros A B; unfold is_true; rewrite andb_true_iff, orb_true_iff; change (Typ.eqb B A = true) with (is_true (Typ.eqb B A)); rewrite Typ.eqb_spec; intros [H2 [H1|H1]]; subst B; rewrite andb_true_iff in H1; destruct H1 as [H1 H2]; rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2); auto; simpl; unfold apply_binop; destruct (interp_hatom t_i t_func t_atom j2) as [B v1]; destruct (interp_hatom t_i t_func t_atom i2) as [C v2]; destruct (Typ.cast B A) as [k1| ]; destruct (Typ.cast C A) as [k2| ]; auto; rewrite Typ.i_eqb_sym; auto. + intros s1 s2; unfold is_true; rewrite !andb_true_iff, N.eqb_eq; + intros [[-> H1] H2]; + now rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2). + intros s1 s2; unfold is_true; rewrite !andb_true_iff, N.eqb_eq; + intros [[-> H1] H2]; + now rewrite (check_hatom_correct _ _ H1), (check_hatom_correct _ _ H2). + (* Ternary operators *) + - intros. now contradict H. (* N-ary operators *) - intros [op2|op2 i2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; destruct op1 as [t1]; destruct op2 as [t2]; unfold is_true; rewrite andb_true_iff; change (Typ.eqb t1 t2 = true) with (is_true (Typ.eqb t1 t2)); rewrite Typ.eqb_spec; intros [H1 H2]; subst t2; rewrite (list_beq_compute_interp _ _ _ H2); auto. + - intros [op2|op2 i2|op2 i2 j2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; destruct op1 as [t1]; destruct op2 as [t2]; unfold is_true; rewrite andb_true_iff; change (Typ.eqb t1 t2 = true) with (is_true (Typ.eqb t1 t2)); rewrite Typ.eqb_spec; intros [H1 H2]; subst t2; rewrite (list_beq_compute_interp _ _ _ H2); auto. (* Application *) - intros [op2|op2 i2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; unfold is_true; rewrite andb_true_iff, Int63Properties.eqb_spec; intros [H2 H1]; subst f2; rewrite (list_beq_correct _ _ H1); auto. + - intros [op2|op2 i2|op2 i2 j2|op2 i2 j2|op2 li2|f2 args2]; simpl; try discriminate; unfold is_true; rewrite andb_true_iff, Int63Properties.eqb_spec; intros [H2 H1]; subst f2; rewrite (list_beq_correct _ _ H1); auto. Qed. End AUX. @@ -233,7 +285,10 @@ Section CheckAtom. forall h1 h2, check_neg_hatom h1 h2 -> interp_form_hatom t_i t_func t_atom h1 = negb (interp_form_hatom t_i t_func t_atom h2). Proof. - unfold interp_form_hatom. intros Hwt H1 H2 h1 h2 H3. unfold interp_bool. generalize (check_neg_hatom_correct Hwt H1 H2 _ _ H3). case (interp_hatom t_i t_func t_atom h1). case (interp_hatom t_i t_func t_atom h2). simpl. intros [i| | | ] v1 [j| | | ] v2; intro H; inversion H. rewrite Typ.cast_refl. auto. + unfold interp_form_hatom. intros Hwt H1 H2 h1 h2 H3. unfold interp_bool. generalize (check_neg_hatom_correct Hwt H1 H2 _ _ H3). + case (interp_hatom t_i t_func t_atom h1). + case (interp_hatom t_i t_func t_atom h2). + simpl. intros [ |i| | | | ] v1 [ |j| | | | ] v2; intro H; inversion H. rewrite Typ.cast_refl. auto. Qed. End CheckAtom. @@ -344,6 +399,7 @@ Section FLATTEN. (** Correctness proofs *) Variable interp_atom : atom -> bool. + Variable interp_bvatom : atom -> forall s, BITVECTOR_LIST.bitvector s. Hypothesis default_thf : default t_form = Ftrue. Hypothesis wf_thf : wf t_form. Hypothesis check_atom_correct : @@ -351,10 +407,10 @@ Section FLATTEN. Hypothesis check_neg_atom_correct : forall a1 a2, check_neg_atom a1 a2 -> interp_atom a1 = negb (interp_atom a2). - Local Notation interp_var := (interp_state_var interp_atom t_form). + Local Notation interp_var := (interp_state_var interp_atom interp_bvatom t_form). Local Notation interp_lit := (Lit.interp interp_var). - Lemma interp_Fnot2 : forall i l, interp interp_atom t_form (Fnot2 i l) = interp_lit l. + Lemma interp_Fnot2 : forall i l, interp interp_atom interp_bvatom t_form (Fnot2 i l) = interp_lit l. Proof. intros i l;simpl;apply fold_ind;trivial. intros a;rewrite negb_involutive;trivial. @@ -366,14 +422,14 @@ Section FLATTEN. unfold remove_not;intros l. case_eq (get_form (Lit.blit l));intros;trivial. unfold Lit.interp, Var.interp. - rewrite (wf_interp_form interp_atom t_form default_thf wf_thf (Lit.blit l)), H, interp_Fnot2. + rewrite (wf_interp_form interp_atom interp_bvatom t_form default_thf wf_thf (Lit.blit l)), H, interp_Fnot2. destruct(Lit.is_pos l);trivial. rewrite Lit.is_pos_neg, Lit.blit_neg;unfold Lit.interp;destruct (Lit.is_pos i0);trivial. rewrite negb_involutive;trivial. Qed. Lemma get_and_correct : forall l args, get_and l = Some args -> - interp_lit l = interp interp_atom t_form (Fand args). + interp_lit l = interp interp_atom interp_bvatom t_form (Fand args). Proof. unfold get_and;intros l args. rewrite <- remove_not_correct;unfold Lit.interp;generalize (remove_not l). @@ -384,7 +440,7 @@ Section FLATTEN. Qed. Lemma get_or_correct : forall l args, get_or l = Some args -> - interp_lit l = interp interp_atom t_form (For args). + interp_lit l = interp interp_atom interp_bvatom t_form (For args). Proof. unfold get_or;intros l args. rewrite <- remove_not_correct;unfold Lit.interp;generalize (remove_not l). @@ -527,3 +583,9 @@ Section FLATTEN. Qed. End FLATTEN. + +(* + Local Variables: + coq-load-path: ((rec ".." "SMTCoq")) + End: +*) |