diff options
Diffstat (limited to 'src/spl/Operators.v')
| -rw-r--r-- | src/spl/Operators.v | 67 |
1 files changed, 41 insertions, 26 deletions
diff --git a/src/spl/Operators.v b/src/spl/Operators.v index c597fe9..f0aba15 100644 --- a/src/spl/Operators.v +++ b/src/spl/Operators.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 *) (* *) @@ -16,8 +12,6 @@ (*** Spl -- a small checker for simplifications ***) -(* Add LoadPath ".." as SMTCoq. *) -(* Add LoadPath "../lia" as SMTCoq.lia. *) Require Import List PArray Bool Int63 ZMicromega. Require Import Misc State SMT_terms. @@ -171,9 +165,16 @@ Section Operators. (get_atom a = Atom.Abop (Atom.BO_eq A) x y \/ get_atom a = Atom.Abop (Atom.BO_eq A) y x))). Proof. - intros A dist diseq; unfold check_diseqs; rewrite andb_true_iff, PArray.forallb_spec, check_diseqs_complete_spec, length_mapi; split; intros [H1 H2]; split. - clear H2; intros i Hi; generalize (H1 _ Hi); rewrite get_mapi; auto; case_eq (Lit.is_pos (diseq .[ i])); try discriminate; intro Heq1; case_eq (get_form (Lit.blit (diseq .[ i]))); try discriminate; intros a Heq2; case_eq (get_atom a); try discriminate; intros [ | | | | | | |B]; try discriminate; intros h1 h2 Heq3; case_eq (Typ.eqb A B); try discriminate; change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec; intro; subst B; case_eq (h1 == h2); try discriminate; rewrite eqb_false_spec; intro H2; case_eq (check_in h1 dist); try discriminate; case_eq (check_in h2 dist); try discriminate; rewrite !check_in_spec; intros H3 H4 _; split; try discriminate; exists a; split; auto; exists h1, h2; repeat split; auto; rewrite <- In2_In; auto. - clear H1; intros x y Hxy; destruct (H2 _ _ Hxy) as [i [H1 H4]]; clear H2; rewrite get_mapi in H4; auto; exists i; split; auto; generalize H4; case_eq (Lit.is_pos (diseq .[ i])); intro Heq; try (intros [H|H]; discriminate); case_eq (get_form (Lit.blit (diseq .[ i]))); [intros a| | |intros a1 a2|intros a1|intros a1|intros a1|intros a1 a2|intros a1 a2|intros a1 a2 a3]; intro Heq2; try (intros [H|H]; discriminate); case_eq (get_atom a); [intros a1|intros a1 a2|intros [ | | | | | | |B] h1 h2|intros a1 a2|intros a1 a2]; intro Heq3; try (intros [H|H]; discriminate); case_eq (Typ.eqb A B); try (intros _ [H|H]; discriminate); change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec; intro; subst B; case_eq (h1 == h2); try (intros _ [H|H]; discriminate); rewrite eqb_false_spec; intro H10; case (check_in h1 dist); try (intros [H|H]; discriminate); case (check_in h2 dist); try (intros [H|H]; discriminate); simpl; intro H3; split; try discriminate; exists a; split; auto; destruct H3 as [H3|H3]; inversion H3; subst; auto. + intros A dist diseq; unfold check_diseqs; rewrite andb_true_iff, + PArray.forallb_spec, check_diseqs_complete_spec, length_mapi; split; intros [H1 H2]; split. + clear H2; intros i Hi; generalize (H1 _ Hi); rewrite get_mapi; + auto; case_eq (Lit.is_pos (diseq .[ i])); try discriminate; intro Heq1; case_eq (get_form (Lit.blit (diseq .[ i]))); + try discriminate; intros a Heq2; case_eq (get_atom a); try discriminate; intros [ | | | | | | | B | | | | | | | | | | | | | ]; try discriminate; intros h1 h2 Heq3; case_eq (Typ.eqb A B); try discriminate; change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec; intro; subst B; case_eq (h1 == h2); try discriminate; rewrite eqb_false_spec; intro H2; case_eq (check_in h1 dist); try discriminate; case_eq (check_in h2 dist); try discriminate; rewrite !check_in_spec; intros H3 H4 _; split; try discriminate; exists a; split; auto; exists h1, h2; repeat split; auto; rewrite <- In2_In; auto. + clear H1; intros x y Hxy; destruct (H2 _ _ Hxy) as [i [H1 H4]]; clear H2; rewrite get_mapi in H4; auto; exists i; split; auto; generalize H4; + + case_eq (Lit.is_pos (diseq .[ i])); intro Heq; try (intros [H|H]; discriminate); case_eq (get_form (Lit.blit (diseq .[ i]))); [intros a| | |intros a1 a2|intros a1|intros a1|intros a1|intros a1 a2|intros a1 a2| intros a1 a2 a3|intros a ls]; intro Heq2; try (intros [H|H]; discriminate); case_eq (get_atom a); [intros a1|intros a1 a2|intros [ | | | | | | | B | | | | | | | | | | | | | ] h1 h2|intros a1 a2|intros a1 a2 | intros a1 a2]; intro Heq3; try (intros [H|H]; discriminate); try (case_eq (Typ.eqb A B); try (intros _ [H|H]; discriminate); change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec; intro; subst B; case_eq (h1 == h2); try (intros _ [H|H]; discriminate); rewrite eqb_false_spec; intro H10; case (check_in h1 dist); try (intros [H|H]; discriminate); case (check_in h2 dist); try (intros [H|H]; discriminate); simpl; intro H3; split; try discriminate; exists a; split; auto; destruct H3 as [H3|H3]; inversion H3; subst; auto). +intros. destruct H0; now contradict H0. + clear H2; intros i Hi; rewrite get_mapi; auto; destruct (H1 _ Hi) as [H2 [a [H3 [h1 [h2 [H4 [H5 H6]]]]]]]; clear H1; replace (Lit.is_pos (diseq .[ i])) with false by (case_eq (Lit.is_pos (diseq .[ i])); auto); rewrite H3, H4, Typ.eqb_refl; simpl; replace (h1 == h2) with false by (case_eq (h1 == h2); auto; rewrite eqb_spec; intro H; elim H5; auto); simpl; rewrite <- In2_In, <- !check_in_spec in H6; auto; destruct H6 as [H6 H7]; rewrite H6, H7; auto. clear H1; intros x y Hxy; destruct (H2 _ _ Hxy) as [i [H1 [H3 [a [H4 [H6 H5]]]]]]; clear H2; exists i; split; auto; rewrite get_mapi; auto; replace (Lit.is_pos (diseq .[ i])) with false by (case_eq (Lit.is_pos (diseq .[ i])); auto); rewrite H4; assert (H7 := or_introl (In2 y x dist) Hxy); rewrite <- In2_In, <- !check_in_spec in H7; auto; destruct H7 as [H7 H8]; destruct H5 as [H5|H5]; rewrite H5, Typ.eqb_refl; [replace (x == y) with false by (case_eq (x == y); auto; rewrite eqb_spec; auto)|replace (y == x) with false by (case_eq (y == x); auto; rewrite eqb_spec; auto)]; simpl; rewrite H7, H8; auto. Qed. @@ -246,14 +247,14 @@ Section Operators. get_atom hb = Atom.Abop (Atom.BO_eq ty) y x). Proof. intros f1 f2; unfold check_distinct_two_args; split. - case (get_form f1); try discriminate; intro ha; case (get_form f2); try discriminate; intro hb; case_eq (get_atom ha); try discriminate; intros [A] [ |x [ |y [ |l]]] Heq1; try discriminate; case_eq (get_atom hb); try discriminate; intros [ | | | | | | |B] x' y' Heq2; try discriminate; rewrite !andb_true_iff, orb_true_iff, !andb_true_iff; change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec, !Int63Properties.eqb_spec; intros [H1 [[H2 H3]|[H2 H3]]]; subst B x' y'; exists ha, hb, A, x, y; auto. + case (get_form f1); try discriminate; intro ha; case (get_form f2); try discriminate; intro hb; case_eq (get_atom ha); try discriminate; intros [A] [ |x [ |y [ |l]]] Heq1; try discriminate; case_eq (get_atom hb); try discriminate; intros [ | | | | | | |B | | | | | | | | | | | | | ] x' y' Heq2; try discriminate; rewrite !andb_true_iff, orb_true_iff, !andb_true_iff; change (Typ.eqb A B = true) with (is_true (Typ.eqb A B)); rewrite Typ.eqb_spec, !Int63Properties.eqb_spec; intros [H1 [[H2 H3]|[H2 H3]]]; subst B x' y'; exists ha, hb, A, x, y; auto. intros [ha [hb [A [x [y [H1 [H2 [H3 [H4|H4]]]]]]]]]; rewrite H1, H2, H3, H4, Typ.eqb_refl, !eqb_refl; auto; rewrite orb_true_r; auto. Qed. Section Valid1. - Variables (t_i : array typ_eqb) + Variables (t_i : array SMT_classes.typ_compdec) (t_func : array (Atom.tval t_i)) (ch_atom : Atom.check_atom t_atom) (ch_form : Form.check_form t_form) @@ -261,8 +262,10 @@ Section Operators. Local Notation interp_form_hatom := (Atom.interp_form_hatom t_i t_func t_atom). + Local Notation interp_form_hatom_bv := + (Atom.interp_form_hatom_bv t_i t_func t_atom). Local Notation rho := - (Form.interp_state_var interp_form_hatom t_form). + (Form.interp_state_var interp_form_hatom interp_form_hatom_bv t_form). Let wf_t_atom : Atom.wf t_atom. Proof. destruct (Atom.check_atom_correct _ ch_atom); auto. Qed. @@ -271,10 +274,10 @@ Section Operators. Proof. destruct (Atom.check_atom_correct _ ch_atom); auto. Qed. Lemma default_t_form : default t_form = Ftrue. - Proof. destruct (Form.check_form_correct interp_form_hatom _ ch_form) as [[H _] _]; auto. Qed. + Proof. destruct (Form.check_form_correct interp_form_hatom interp_form_hatom_bv _ ch_form) as [[H _] _]; auto. Qed. Lemma wf_t_form : wf t_form. - Proof. destruct (Form.check_form_correct interp_form_hatom _ ch_form) as [[_ H] _]; auto. Qed. + Proof. destruct (Form.check_form_correct interp_form_hatom interp_form_hatom_bv _ ch_form) as [[_ H] _]; auto. Qed. Local Hint Immediate wf_t_atom default_t_atom default_t_form wf_t_form. @@ -354,7 +357,7 @@ Section Operators. | _, _ => false end. - Variables (t_i : array typ_eqb) + Variables (t_i : array SMT_classes.typ_compdec) (t_func : array (Atom.tval t_i)) (ch_atom : Atom.check_atom t_atom) (ch_form : Form.check_form t_form) @@ -362,8 +365,10 @@ Section Operators. Local Notation interp_form_hatom := (Atom.interp_form_hatom t_i t_func t_atom). + Local Notation interp_form_hatom_bv := + (Atom.interp_form_hatom_bv t_i t_func t_atom). Local Notation rho := - (Form.interp_state_var interp_form_hatom t_form). + (Form.interp_state_var interp_form_hatom interp_form_hatom_bv t_form). Hypothesis interp_check_var : forall x y, check_var x y -> Var.interp rho x = Var.interp rho y. @@ -395,9 +400,9 @@ Section Operators. Lemma interp_check_form_aux : forall a b, check_form_aux a b -> - Form.interp interp_form_hatom t_form a = Form.interp interp_form_hatom t_form b. + Form.interp interp_form_hatom interp_form_hatom_bv t_form a = Form.interp interp_form_hatom interp_form_hatom_bv t_form b. Proof. - intros [a| | |i1 l1|a1|a1|a1|l1 l2|l1 l2|l1 l2 l3] [b| | |j1 m1|a2|a2|a2|j1 j2|j1 j2|j1 j2 j3]; simpl; try discriminate;auto. + intros [a| | |i1 l1|a1|a1|a1|l1 l2|l1 l2|l1 l2 l3|a l1] [b| | |j1 m1|a2|a2|a2|j1 j2|j1 j2|j1 j2 j3|b m1]; simpl; try discriminate;auto. (* Atom *) unfold is_true; rewrite Int63Properties.eqb_spec; intro; subst a; auto. (* Interesting case *) @@ -485,7 +490,7 @@ Section Operators. Section Valid. - Variables (t_i : array typ_eqb) + Variables (t_i : array SMT_classes.typ_compdec) (t_func : array (Atom.tval t_i)) (ch_atom : Atom.check_atom t_atom) (ch_form : Form.check_form t_form) @@ -493,18 +498,20 @@ Section Operators. Local Notation interp_form_hatom := (Atom.interp_form_hatom t_i t_func t_atom). + Local Notation interp_form_hatom_bv := + (Atom.interp_form_hatom_bv t_i t_func t_atom). Local Notation rho := - (Form.interp_state_var interp_form_hatom t_form). + (Form.interp_state_var interp_form_hatom interp_form_hatom_bv t_form). Let wf_rho : Valuation.wf rho. - Proof. destruct (Form.check_form_correct interp_form_hatom _ ch_form); auto. Qed. + Proof. destruct (Form.check_form_correct interp_form_hatom interp_form_hatom_bv _ ch_form); auto. Qed. Let default_t_form : default t_form = Ftrue. - Proof. destruct (Form.check_form_correct interp_form_hatom _ ch_form) as [[H _] _]; auto. Qed. + Proof. destruct (Form.check_form_correct interp_form_hatom interp_form_hatom_bv _ ch_form) as [[H _] _]; auto. Qed. Let wf_t_form : wf t_form. - Proof. destruct (Form.check_form_correct interp_form_hatom _ ch_form) as [[_ H] _]; auto. Qed. + Proof. destruct (Form.check_form_correct interp_form_hatom interp_form_hatom_bv _ ch_form) as [[_ H] _]; auto. Qed. Local Hint Immediate wf_rho default_t_form wf_t_form. @@ -522,7 +529,7 @@ Section Operators. Lemma interp_check_form : forall a b, check_form a b -> - Form.interp interp_form_hatom t_form a = Form.interp interp_form_hatom t_form b. + Form.interp interp_form_hatom interp_form_hatom_bv t_form a = Form.interp interp_form_hatom interp_form_hatom_bv t_form b. Proof. apply interp_check_form_aux, interp_check_hform; auto. Qed. @@ -547,3 +554,11 @@ Section Operators. End Valid. End Operators. + + + +(* + Local Variables: + coq-load-path: ((rec ".." "SMTCoq")) + End: +*) |