diff options
Diffstat (limited to 'src/lia')
-rw-r--r-- | src/lia/Lia.v | 208 | ||||
-rw-r--r-- | src/lia/lia.ml | 223 | ||||
-rw-r--r-- | src/lia/lia.mli | 54 |
3 files changed, 263 insertions, 222 deletions
diff --git a/src/lia/Lia.v b/src/lia/Lia.v index c214c3b..46bbc5d 100644 --- a/src/lia/Lia.v +++ b/src/lia/Lia.v @@ -113,7 +113,7 @@ Section certif. | Some z => (vm, PEc z) | None => let (vm,p) := find_var vm h in - (vm,PEX Z p) + (vm,PEX p) end end. @@ -157,7 +157,7 @@ Section certif. Section Build_form. Definition build_not2 i f := - fold (fun f' => N (N (A:=Formula Z) f')) 1 i f. + fold (fun f' : BFormula (Formula Z) => N (N f')) 1 i f. Variable build_var : vmap -> var -> option (vmap*BFormula (Formula Z)). @@ -166,11 +166,11 @@ Section certif. match f with | Form.Fatom h => match build_formula vm h with - | Some (vm,f) => Some (vm, A f) + | Some (vm,f) => Some (vm, A f tt) | None => None end - | Form.Ftrue => Some (vm, TT (Formula Z)) - | Form.Ffalse => Some (vm, FF (Formula Z)) + | Form.Ftrue => Some (vm, TT) + | Form.Ffalse => Some (vm, FF) | Form.Fnot2 i l => match build_var vm (Lit.blit l) with | Some (vm, f) => @@ -181,7 +181,7 @@ Section certif. end | Form.Fand args => let n := length args in - if n == 0 then Some (vm,TT (Formula Z)) + if n == 0 then Some (vm,TT) else foldi (fun i f1 => match f1 with | Some(vm',f1') => let l := (args.[i]) in match build_var vm' (Lit.blit l) with | Some(vm2,f2) => let f2' := if Lit.is_pos l then f2 else N f2 in Some(vm2,Cj f1' f2') | None => None end | None => None end) 1 (n-1) (let l := args.[0] in match build_var vm (Lit.blit l) with @@ -190,7 +190,7 @@ Section certif. end) | Form.For args => let n := length args in - if n == 0 then Some (vm,FF (Formula Z)) + if n == 0 then Some (vm,FF) else foldi (fun i f1 => match f1 with | Some(vm',f1') => let l := (args.[i]) in match build_var vm' (Lit.blit l) with | Some(vm2,f2) => let f2' := if Lit.is_pos l then f2 else N f2 in Some(vm2,D f1' f2') | None => None end | None => None end) 1 (n-1) (let l := args.[0] in match build_var vm (Lit.blit l) with @@ -211,7 +211,7 @@ Section certif. end | Form.Fimp args => let n := length args in - if n == 0 then Some (vm,TT (Formula Z)) + if n == 0 then Some (vm,TT) else if n <= 1 then let l := args.[0] in match build_var vm (Lit.blit l) with @@ -219,7 +219,7 @@ Section certif. | None => None end else - foldi_down (fun i f1 => match f1 with | Some(vm',f1') => let l := (args.[i]) in match build_var vm' (Lit.blit l) with | Some(vm2,f2) => let f2' := if Lit.is_pos l then f2 else N f2 in Some(vm2,I f2' f1') | None => None end | None => None end) (n-2) 0 (let l := args.[n-1] in + foldi_down (fun i f1 => match f1 with | Some(vm',f1') => let l := (args.[i]) in match build_var vm' (Lit.blit l) with | Some(vm2,f2) => let f2' := if Lit.is_pos l then f2 else N f2 in Some(vm2,I f2' None f1') | None => None end | None => None end) (n-2) 0 (let l := args.[n-1] in match build_var vm (Lit.blit l) with | Some (vm',f) => if Lit.is_pos l then Some (vm',f) else Some (vm',N f) | None => None @@ -295,7 +295,7 @@ Section certif. Definition build_clause vm cl := match build_clause_aux vm cl with - | Some (vm, bf) => Some (vm, I bf (FF _)) + | Some (vm, bf) => Some (vm, I bf None FF) | None => None end. @@ -479,11 +479,11 @@ Section certif. Fixpoint bounded_bformula (p:positive) (bf:BFormula (Formula Z)) := match bf with - | @TT _ | @FF _ | @X _ _ => true - | A f => bounded_formula p f + | @TT _ | @FF _ | @X _ _ _ _ _ => true + | A f _ => bounded_formula p f | Cj bf1 bf2 | D bf1 bf2 - | I bf1 bf2 => bounded_bformula p bf1 && bounded_bformula p bf2 + | I bf1 _ bf2 => bounded_bformula p bf1 && bounded_bformula p bf2 | N bf => bounded_bformula p bf end. @@ -523,7 +523,7 @@ Section certif. check_atom h Typ.TZ -> match build_z_atom h with | Some z => (vm, PEc z) - | None => let (vm0, p) := find_var vm h in (vm0, PEX Z p) + | None => let (vm0, p) := find_var vm h in (vm0, PEX p) end = (vm', pe) -> wf_vmap vm -> wf_vmap vm' /\ @@ -1020,13 +1020,15 @@ Transparent build_z_atom. intros;apply build_formula_atom_correct with (get_type t_i t_func t_atom h);trivial. unfold wt, is_true in wt_t_atom;rewrite forallbi_spec in wt_t_atom. - case_eq (h < length t_atom);intros Heq;unfold get_type;auto. + case_eq (h < length t_atom);intros Heq;unfold get_type;auto with smtcoq_core. unfold get_type'. rewrite !PArray.get_outofbound, default_t_interp, def_t_atom;trivial; try reflexivity. rewrite length_t_interp;trivial. Qed. + Local Notation eval_f := (eval_f (fun x => x)). + Lemma build_not2_pos_correct : forall vm f l i, bounded_bformula (fst vm) f -> (rho (Lit.blit l) <-> eval_f (Zeval_formula (interp_vmap vm)) f) -> Lit.is_pos l -> bounded_bformula (fst vm) (build_not2 i f) /\ (Form.interp interp_form_hatom interp_form_hatom_bv t_form (Form.Fnot2 i l) <-> eval_f (Zeval_formula (interp_vmap vm)) (build_not2 i f)). Proof. @@ -1083,7 +1085,7 @@ Transparent build_z_atom. Proof. intros vm vm' Hnth. unfold is_true;induction bf;simpl;try tauto. - destruct a;unfold bounded_formula;simpl. + destruct t;unfold bounded_formula;simpl. rewrite andb_true_iff;intros (H1, H2). rewrite !(interp_pexpr_le _ _ Hnth);tauto. rewrite andb_true_iff;intros (H1,H2);rewrite IHbf1, IHbf2;tauto. @@ -1123,12 +1125,12 @@ Transparent build_z_atom. (* Ftrue *) intros H H1; inversion H; subst vm'; subst bf; split; auto; split; [omega| ]; do 4 split; auto. (* Ffalse *) - intros H H1; inversion H; subst vm'; subst bf; split; auto; split; [omega| ]; do 3 (split; auto); discriminate. + intros H H1; inversion H; subst vm'; subst bf; split; auto; split; [omega| ]; do 3 (split; auto with smtcoq_core); discriminate. (* Fnot2 *) case_eq (build_var vm (Lit.blit l)); try discriminate; intros [vm0 f] Heq H H1; inversion H; subst vm0; subst bf; destruct (Hbv _ _ _ _ Heq H1) as [H2 [H3 [H4 [H5 H6]]]]; do 3 (split; auto); case_eq (Lit.is_pos l); [apply build_not2_pos_correct|apply build_not2_neg_correct]; auto. (* Fand *) simpl; unfold afold_left; case (length l == 0). - intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto; split; [omega| ]; do 3 (split; auto). + intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto with smtcoq_core; split; [omega| ]; do 3 (split; auto with smtcoq_core). revert vm' bf; apply (foldi_ind2 _ _ (fun f1 b => forall vm' bf, f1 = Some (vm', bf) -> wf_vmap vm -> wf_vmap vm' /\ (Pos.to_nat (fst vm) <= Pos.to_nat (fst vm'))%nat /\ (forall p : positive, (Pos.to_nat p < Pos.to_nat (fst vm))%nat -> nth_error (snd vm) (Pos.to_nat (fst vm - p) - 1) = nth_error (snd vm') (Pos.to_nat (fst vm' - p) - 1)) /\ bounded_bformula (fst vm') bf /\ (b = true <-> eval_f (Zeval_formula (interp_vmap vm')) bf))). intros vm' bf; case_eq (build_var vm (Lit.blit (l .[ 0]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ 0])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H10 [H11 [H12 [H13 H14]]]]; do 4 (split; auto); unfold Lit.interp; rewrite Heq2; auto; simpl; split. intros H3 H4; rewrite <- H14 in H4; rewrite H4 in H3; discriminate. @@ -1136,104 +1138,76 @@ Transparent build_z_atom. intros i a b _ H1; case a; try discriminate; intros [vm0 f0] IH vm' bf; case_eq (build_var vm0 (Lit.blit (l .[ i]))); try discriminate; intros [vm1 f1] Heq H2 H3; inversion H2; subst vm'; subst bf; destruct (IH _ _ (refl_equal (Some (vm0, f0))) H3) as [H5 [H6 [H7 [H8 H9]]]]; destruct (Hbv _ _ _ _ Heq H5) as [H10 [H11 [H12 [H13 H14]]]]; split; auto; split; [eauto with arith| ]; split. intros p H15; rewrite H7; auto; apply H12; eauto with arith. split. - simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto. - simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); try rewrite andb_true_r; try rewrite andb_false_r; try (intros; split; auto); try discriminate; intros [H20 H21]; auto. + simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); try rewrite andb_true_r; try rewrite andb_false_r; try (intros; split; auto with smtcoq_core); try discriminate; intros [H20 H21]; auto with smtcoq_core. (* For *) simpl; unfold afold_left; case (length l == 0). - intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto; split; [omega| ]; do 3 (split; auto); discriminate. + intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto with smtcoq_core; split; [omega| ]; do 3 (split; auto with smtcoq_core); discriminate. revert vm' bf; apply (foldi_ind2 _ _ (fun f1 b => forall vm' bf, f1 = Some (vm', bf) -> wf_vmap vm -> wf_vmap vm' /\ (Pos.to_nat (fst vm) <= Pos.to_nat (fst vm'))%nat /\ (forall p : positive, (Pos.to_nat p < Pos.to_nat (fst vm))%nat -> nth_error (snd vm) (Pos.to_nat (fst vm - p) - 1) = nth_error (snd vm') (Pos.to_nat (fst vm' - p) - 1)) /\ bounded_bformula (fst vm') bf /\ (b = true <-> eval_f (Zeval_formula (interp_vmap vm')) bf))). - intros vm' bf; case_eq (build_var vm (Lit.blit (l .[ 0]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ 0])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H10 [H11 [H12 [H13 H14]]]]; do 4 (split; auto); unfold Lit.interp; rewrite Heq2; auto; simpl; split. + intros vm' bf; case_eq (build_var vm (Lit.blit (l .[ 0]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ 0])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H10 [H11 [H12 [H13 H14]]]]; do 4 (split; auto with smtcoq_core); unfold Lit.interp; rewrite Heq2; auto with smtcoq_core; simpl; split. intros H3 H4; rewrite <- H14 in H4; rewrite H4 in H3; discriminate. - intro H3; case_eq (Var.interp rho (Lit.blit (l .[ 0]))); auto; intro H4; elim H3; rewrite <- H14; auto. - intros i a b _ H1; case a; try discriminate; intros [vm0 f0] IH vm' bf; case_eq (build_var vm0 (Lit.blit (l .[ i]))); try discriminate; intros [vm1 f1] Heq H2 H3; inversion H2; subst vm'; subst bf; destruct (IH _ _ (refl_equal (Some (vm0, f0))) H3) as [H5 [H6 [H7 [H8 H9]]]]; destruct (Hbv _ _ _ _ Heq H5) as [H10 [H11 [H12 [H13 H14]]]]; split; auto; split; [eauto with arith| ]; split. - intros p H15; rewrite H7; auto; apply H12; eauto with arith. + intro H3; case_eq (Var.interp rho (Lit.blit (l .[ 0]))); auto with smtcoq_core; intro H4; elim H3; rewrite <- H14; auto with smtcoq_core. + intros i a b _ H1; case a; try discriminate; intros [vm0 f0] IH vm' bf; case_eq (build_var vm0 (Lit.blit (l .[ i]))); try discriminate; intros [vm1 f1] Heq H2 H3; inversion H2; subst vm'; subst bf; destruct (IH _ _ (refl_equal (Some (vm0, f0))) H3) as [H5 [H6 [H7 [H8 H9]]]]; destruct (Hbv _ _ _ _ Heq H5) as [H10 [H11 [H12 [H13 H14]]]]; split; auto with smtcoq_core; split; [eauto with smtcoq_core arith| ]; split. + intros p H15; rewrite H7; auto with smtcoq_core; apply H12; eauto with smtcoq_core arith. split. - simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto. - simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); try rewrite orb_false_r; try rewrite orb_true_r; auto; try (intros [H20|H20]; auto; discriminate); right; intro H20; discriminate. + simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); try rewrite orb_false_r; try rewrite orb_true_r; auto with smtcoq_core; try (intros [H20|H20]; auto with smtcoq_core; discriminate); right; intro H20; discriminate. (* Fimp *) simpl; unfold afold_right; case (length l == 0). - intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto; split; [omega| ]; do 3 (split; auto). + intro H; inversion H; subst vm'; subst bf; simpl; intro H1; split; auto with smtcoq_core; split; [omega| ]; do 3 (split; auto with smtcoq_core). case (length l <= 1). - case_eq (build_var vm (Lit.blit (l .[ 0]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ 0])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H3 [H4 [H5 [H6 H7]]]]; do 4 (split; auto); unfold Lit.interp; rewrite Heq2; auto; simpl; split. + case_eq (build_var vm (Lit.blit (l .[ 0]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ 0])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H3 [H4 [H5 [H6 H7]]]]; do 4 (split; auto with smtcoq_core); unfold Lit.interp; rewrite Heq2; auto with smtcoq_core; simpl; split. intros H8 H9; rewrite <- H7 in H9; rewrite H9 in H8; discriminate. - intro H8; case_eq (Var.interp rho (Lit.blit (l .[ 0]))); auto; intro H9; rewrite H7 in H9; elim H8; auto. + intro H8; case_eq (Var.interp rho (Lit.blit (l .[ 0]))); auto with smtcoq_core; intro H9; rewrite H7 in H9; elim H8; auto with smtcoq_core. revert vm' bf; apply (foldi_down_ind2 _ _ (fun f1 b => forall vm' bf, f1 = Some (vm', bf) -> wf_vmap vm -> wf_vmap vm' /\ (Pos.to_nat (fst vm) <= Pos.to_nat (fst vm'))%nat /\ (forall p : positive, (Pos.to_nat p < Pos.to_nat (fst vm))%nat -> nth_error (snd vm) (Pos.to_nat (fst vm - p) - 1) = nth_error (snd vm') (Pos.to_nat (fst vm' - p) - 1)) /\ bounded_bformula (fst vm') bf /\ (b = true <-> eval_f (Zeval_formula (interp_vmap vm')) bf))). - intros vm' bf; case_eq (build_var vm (Lit.blit (l .[ length l - 1]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ length l - 1])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H10 [H11 [H12 [H13 H14]]]]; do 4 (split; auto); unfold Lit.interp; rewrite Heq2; auto; simpl; split. + intros vm' bf; case_eq (build_var vm (Lit.blit (l .[ length l - 1]))); try discriminate; intros [vm0 f] Heq; case_eq (Lit.is_pos (l .[ length l - 1])); intros Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq H2) as [H10 [H11 [H12 [H13 H14]]]]; do 4 (split; auto with smtcoq_core); unfold Lit.interp; rewrite Heq2; auto with smtcoq_core; simpl; split. intros H3 H4; rewrite <- H14 in H4; rewrite H4 in H3; discriminate. - intro H3; case_eq (Var.interp rho (Lit.blit (l .[ length l - 1]))); auto; intro H4; elim H3; rewrite <- H14; auto. - intros i a b _ H1; case a; try discriminate; intros [vm0 f0] IH vm' bf; case_eq (build_var vm0 (Lit.blit (l .[ i]))); try discriminate; intros [vm1 f1] Heq H2 H3; inversion H2; subst vm'; subst bf; destruct (IH _ _ (refl_equal (Some (vm0, f0))) H3) as [H5 [H6 [H7 [H8 H9]]]]; destruct (Hbv _ _ _ _ Heq H5) as [H10 [H11 [H12 [H13 H14]]]]; split; auto; split; [eauto with arith| ]; split. - intros p H15; rewrite H7; auto; apply H12; eauto with arith. + intro H3; case_eq (Var.interp rho (Lit.blit (l .[ length l - 1]))); auto with smtcoq_core; intro H4; elim H3; rewrite <- H14; auto with smtcoq_core. + intros i a b _ H1; case a; try discriminate; intros [vm0 f0] IH vm' bf; case_eq (build_var vm0 (Lit.blit (l .[ i]))); try discriminate; intros [vm1 f1] Heq H2 H3; inversion H2; subst vm'; subst bf; destruct (IH _ _ (refl_equal (Some (vm0, f0))) H3) as [H5 [H6 [H7 [H8 H9]]]]; destruct (Hbv _ _ _ _ Heq H5) as [H10 [H11 [H12 [H13 H14]]]]; split; auto with smtcoq_core; split; [eauto with smtcoq_core arith| ]; split. + intros p H15; rewrite H7; auto with smtcoq_core; apply H12; eauto with smtcoq_core arith. split. - simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto. - simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); auto; try discriminate; simpl; intro H; apply H; discriminate. + simpl; rewrite (bounded_bformula_le _ _ H11 _ H8); case (Lit.is_pos (l .[ i])); rewrite H13; auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H12 _ H8) in H9; rewrite <- H9; case_eq (Lit.is_pos (l .[ i])); intro Heq2; simpl; rewrite <- H14; unfold Lit.interp; rewrite Heq2; split; case (Var.interp rho (Lit.blit (l .[ i]))); auto with smtcoq_core; try discriminate; simpl; intro H; apply H; discriminate. (* Fxor *) - simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; split; auto; split; [eauto with arith| ]; split. - intros p H18; rewrite H5; auto; rewrite H10; eauto with arith. + simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; split; auto with smtcoq_core; split; [eauto with smtcoq_core arith| ]; split. + intros p H18; rewrite H5; auto with smtcoq_core; rewrite H10; eauto with smtcoq_core arith. split. - case (Lit.is_pos a); case (Lit.is_pos b); simpl; rewrite H11; rewrite (bounded_bformula_le _ _ H9 _ H6); auto. - simpl; rewrite (interp_bformula_le _ _ H10 _ H6) in H7; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; unfold Lit.interp; rewrite Ha, Hb; simpl; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); case (Var.interp rho (Lit.blit b))); split; auto; try discriminate; simpl. - intros [_ [H20|H20]]; elim H20; reflexivity. - intros _; split; [left; reflexivity|right; intro H20; discriminate]. - intros _; split; [right; reflexivity|left; intro H20; discriminate]. - intros [[H20|H20] _]; discriminate. - intros [_ [H20|H20]]; elim H20; [reflexivity|discriminate]. - intros [[H20|H20] _]; [discriminate|elim H20; reflexivity]. - intros _; split; [right|left]; discriminate. - intros [[H20|H20] _]; [elim H20; reflexivity|discriminate]. - intros [_ [H20|H20]]; elim H20; [discriminate|reflexivity]. - intros _; split; [left|right]; discriminate. - intros [[H20|H20] _]; elim H20; reflexivity. - intros _; split; [right; discriminate|left; intro H21; apply H21; reflexivity]. - intros _; split; [left; discriminate|right; intro H21; apply H21; reflexivity]. - intros [_ [H20|H20]]; elim H20; discriminate. + case (Lit.is_pos a); case (Lit.is_pos b); simpl; rewrite H11; rewrite (bounded_bformula_le _ _ H9 _ H6); auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H10 _ H6) in H7; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; unfold Lit.interp; rewrite Ha, Hb; simpl; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); case (Var.interp rho (Lit.blit b))); split; auto with smtcoq_core; try discriminate; simpl; intuition. (* Fiff *) - simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; split; auto; split; [eauto with arith| ]; split. - intros p H18; rewrite H5; auto; rewrite H10; eauto with arith. + simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; split; auto with smtcoq_core; split; [eauto with smtcoq_core arith| ]; split. + intros p H18; rewrite H5; auto with smtcoq_core; rewrite H10; eauto with smtcoq_core arith. split. - case (Lit.is_pos a); case (Lit.is_pos b); simpl; rewrite H11; rewrite (bounded_bformula_le _ _ H9 _ H6); auto. - simpl; rewrite (interp_bformula_le _ _ H10 _ H6) in H7; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; unfold Lit.interp; rewrite Ha, Hb; simpl; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); case (Var.interp rho (Lit.blit b))); split; auto; try discriminate; simpl. - intros [_ [H20|H20]]; [elim H20; reflexivity|discriminate]. - intros [[H20|H20] _]; [discriminate|elim H20; reflexivity]. - intros _; split; [right|left]; discriminate. - intros [_ [H20|H20]]; elim H20; reflexivity. - intros _; split; [left; reflexivity|right; discriminate]. - intros _; split; [right; intro H20; apply H20; reflexivity|left; discriminate]. - intros [[H20|H20] _]; [ |elim H20]; discriminate. - intros [[H20|H20] _]; elim H20; reflexivity. - intros _; split; [right; discriminate|left; intro H20; apply H20; reflexivity]. - intros _; split; [left; discriminate|right; reflexivity]. - intros [_ [H20|H20]]; [elim H20| ]; discriminate. - intros [[H20|H20] _]; elim H20; [reflexivity|discriminate]. - intros [_ [H20|H20]]; elim H20; [discriminate|reflexivity]. - intros _; split; [left|right]; discriminate. + case (Lit.is_pos a); case (Lit.is_pos b); simpl; rewrite H11; rewrite (bounded_bformula_le _ _ H9 _ H6); auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H10 _ H6) in H7; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; unfold Lit.interp; rewrite Ha, Hb; simpl; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); case (Var.interp rho (Lit.blit b))); split; auto with smtcoq_core; try discriminate; simpl; intuition. (* Fite *) - simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2; case_eq (build_var vm2 (Lit.blit c)); try discriminate; intros [vm3 f3] Heq3 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; destruct (Hbv _ _ _ _ Heq3 H8) as [H13 [H14 [H15 [H16 H17]]]]; split; auto; split; [eauto with arith| ]; split. - intros p H18; rewrite H5; auto; rewrite H10; eauto with arith. - assert (H18: (Pos.to_nat (fst vm1) <= Pos.to_nat (fst vm3))%nat) by eauto with arith. + simpl; case_eq (build_var vm (Lit.blit a)); try discriminate; intros [vm1 f1] Heq1; case_eq (build_var vm1 (Lit.blit b)); try discriminate; intros [vm2 f2] Heq2; case_eq (build_var vm2 (Lit.blit c)); try discriminate; intros [vm3 f3] Heq3 H1 H2; inversion H1; subst vm'; subst bf; destruct (Hbv _ _ _ _ Heq1 H2) as [H3 [H4 [H5 [H6 H7]]]]; destruct (Hbv _ _ _ _ Heq2 H3) as [H8 [H9 [H10 [H11 H12]]]]; destruct (Hbv _ _ _ _ Heq3 H8) as [H13 [H14 [H15 [H16 H17]]]]; split; auto with smtcoq_core; split; [eauto with smtcoq_core arith| ]; split. + intros p H18; rewrite H5; auto with smtcoq_core; rewrite H10; eauto with smtcoq_core arith. + assert (H18: (Pos.to_nat (fst vm1) <= Pos.to_nat (fst vm3))%nat) by eauto with smtcoq_core arith. split. - case (Lit.is_pos a); case (Lit.is_pos b); case (Lit.is_pos c); simpl; rewrite H16; rewrite (bounded_bformula_le _ _ H14 _ H11); rewrite (bounded_bformula_le _ _ H18 _ H6); auto. - simpl; rewrite (interp_bformula_le _ _ H15 _ H11) in H12; rewrite (interp_bformula_le _ vm3) in H7; [ |intros p Hp; rewrite H10; eauto with arith|auto]; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; case_eq (Lit.is_pos c); intro Hc; unfold Lit.interp; rewrite Ha, Hb, Hc; simpl; rewrite <- H17; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); [case (Var.interp rho (Lit.blit b))|case (Var.interp rho (Lit.blit c))]); split; auto; try discriminate; try (intros [[H20 H21]|[H20 H21]]; auto); try (intros _; left; split; auto; discriminate); try (intros _; right; split; auto; discriminate); try (elim H20; discriminate); try (elim H21; discriminate); try (simpl; intro H; left; split; auto; discriminate); try (revert H; case (Var.interp rho (Lit.blit c)); discriminate); try (revert H; case (Var.interp rho (Lit.blit b)); discriminate); try (intro H20; rewrite H20 in H; discriminate); simpl. - intro H; right; split; auto. - intro H; right; split; auto. - intro H; right; split; auto. + case (Lit.is_pos a); case (Lit.is_pos b); case (Lit.is_pos c); simpl; rewrite H16; rewrite (bounded_bformula_le _ _ H14 _ H11); rewrite (bounded_bformula_le _ _ H18 _ H6); auto with smtcoq_core. + simpl; rewrite (interp_bformula_le _ _ H15 _ H11) in H12; rewrite (interp_bformula_le _ vm3) in H7; [ |intros p Hp; rewrite H10; eauto with smtcoq_core arith|auto with smtcoq_core]; case_eq (Lit.is_pos a); intro Ha; case_eq (Lit.is_pos b); intro Hb; case_eq (Lit.is_pos c); intro Hc; unfold Lit.interp; rewrite Ha, Hb, Hc; simpl; rewrite <- H17; rewrite <- H12; rewrite <- H7; (case (Var.interp rho (Lit.blit a)); [case (Var.interp rho (Lit.blit b))|case (Var.interp rho (Lit.blit c))]); split; auto with smtcoq_core; try discriminate; try (intros [[H20 H21]|[H20 H21]]; auto with smtcoq_core); try (intros _; left; split; auto with smtcoq_core; discriminate); try (intros _; right; split; auto with smtcoq_core; discriminate); try (elim H20; discriminate); try (elim H21; discriminate); try (simpl; intro H; left; split; auto with smtcoq_core; discriminate); try (revert H; case (Var.interp rho (Lit.blit c)); discriminate); try (revert H; case (Var.interp rho (Lit.blit b)); discriminate); try (intro H20; rewrite H20 in H; discriminate); simpl. + intro H; right; split; auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core. intro H20; rewrite H20 in H; discriminate. - revert H21; case (Var.interp rho (Lit.blit c)); auto. - right; split; auto; intro H20; rewrite H20 in H; discriminate. - revert H21; case (Var.interp rho (Lit.blit c)); auto. - intro H; right; split; auto. - intro H; right; split; auto. + revert H21; case (Var.interp rho (Lit.blit c)); auto with smtcoq_core. + right; split; auto with smtcoq_core; intro H20; rewrite H20 in H; discriminate. + revert H21; case (Var.interp rho (Lit.blit c)); auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core. intro H; left; split; try discriminate; revert H; case (Var.interp rho (Lit.blit b)); discriminate. - revert H21; case (Var.interp rho (Lit.blit b)); auto. + revert H21; case (Var.interp rho (Lit.blit b)); auto with smtcoq_core. intro H; left; split; try discriminate; revert H; case (Var.interp rho (Lit.blit b)); discriminate. - revert H21; case (Var.interp rho (Lit.blit b)); auto. - intro H; right; split; auto; revert H; case (Var.interp rho (Lit.blit c)); discriminate. - revert H21; case (Var.interp rho (Lit.blit c)); auto. - intro H; right; split; auto; revert H; case (Var.interp rho (Lit.blit c)); discriminate. - revert H21; case (Var.interp rho (Lit.blit c)); auto. - intro H; left; split; auto; revert H; case (Var.interp rho (Lit.blit b)); discriminate. - revert H21; case (Var.interp rho (Lit.blit b)); auto. - intro H; left; split; auto; revert H; case (Var.interp rho (Lit.blit b)); discriminate. - revert H21; case (Var.interp rho (Lit.blit b)); auto. + revert H21; case (Var.interp rho (Lit.blit b)); auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core; revert H; case (Var.interp rho (Lit.blit c)); discriminate. + revert H21; case (Var.interp rho (Lit.blit c)); auto with smtcoq_core. + intro H; right; split; auto with smtcoq_core; revert H; case (Var.interp rho (Lit.blit c)); discriminate. + revert H21; case (Var.interp rho (Lit.blit c)); auto with smtcoq_core. + intro H; left; split; auto with smtcoq_core; revert H; case (Var.interp rho (Lit.blit b)); discriminate. + revert H21; case (Var.interp rho (Lit.blit b)); auto with smtcoq_core. + intro H; left; split; auto with smtcoq_core; revert H; case (Var.interp rho (Lit.blit b)); discriminate. + revert H21; case (Var.interp rho (Lit.blit b)); auto with smtcoq_core. Qed. @@ -1251,8 +1225,8 @@ Transparent build_z_atom. Proof. unfold build_var; apply foldi_down_cont_ind; try discriminate. intros i cont _ Hlen Hrec v vm vm' bf; unfold is_true; intros H1 H2; replace (Var.interp rho v) with (Form.interp interp_form_hatom interp_form_hatom_bv t_form (t_form.[v])). - apply (build_hform_correct cont); auto. - unfold Var.interp; rewrite <- wf_interp_form; auto. + apply (build_hform_correct cont); auto with smtcoq_core. + unfold Var.interp; rewrite <- wf_interp_form; auto with smtcoq_core. Qed. @@ -1285,17 +1259,17 @@ Transparent build_z_atom. unfold build_nlit; intros l vm vm' bf; case_eq (build_form vm (t_form .[ Lit.blit (Lit.neg l)])); try discriminate. intros [vm1 f] Heq H1 H2; inversion H1; subst vm1; subst bf; case_eq (Lit.is_pos (Lit.neg l)); intro Heq2. replace (negb (Lit.interp rho l)) with (Form.interp interp_form_hatom interp_form_hatom_bv t_form (t_form .[ Lit.blit (Lit.neg l)])). - apply build_form_correct; auto. + apply build_form_correct; auto with smtcoq_core. unfold Lit.interp; replace (Lit.is_pos l) with false. - rewrite negb_involutive; unfold Var.interp; rewrite <- wf_interp_form; auto; rewrite Lit.blit_neg; auto. - rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto; intro H; rewrite H in Heq2; discriminate. - simpl; destruct (build_form_correct (t_form .[ Lit.blit (Lit.neg l)]) vm vm' f Heq H2) as [H3 [H4 [H5 [H6 [H7 H8]]]]]; do 4 (split; auto); split. + rewrite negb_involutive; unfold Var.interp; rewrite <- wf_interp_form; auto with smtcoq_core; rewrite Lit.blit_neg; auto with smtcoq_core. + rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto with smtcoq_core; intro H; rewrite H in Heq2; discriminate. + simpl; destruct (build_form_correct (t_form .[ Lit.blit (Lit.neg l)]) vm vm' f Heq H2) as [H3 [H4 [H5 [H6 [H7 H8]]]]]; do 4 (split; auto with smtcoq_core); split. intros H9 H10; pose (H11 := H8 H10); unfold Lit.interp in H9; replace (Lit.is_pos l) with true in H9. - unfold Var.interp in H9; rewrite <- wf_interp_form in H11; auto; rewrite Lit.blit_neg in H11; rewrite H11 in H9; discriminate. - rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto; intro H; rewrite H in Heq2; discriminate. - intro H9; case_eq (Lit.interp rho l); intro Heq3; auto; elim H9; apply H7; unfold Lit.interp in Heq3; replace (Lit.is_pos l) with true in Heq3. - unfold Var.interp in Heq3; rewrite <- wf_interp_form; auto; rewrite Lit.blit_neg; auto. - rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto; intro H; rewrite H in Heq2; discriminate. + unfold Var.interp in H9; rewrite <- wf_interp_form in H11; auto with smtcoq_core; rewrite Lit.blit_neg in H11; rewrite H11 in H9; discriminate. + rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto with smtcoq_core; intro H; rewrite H in Heq2; discriminate. + intro H9; case_eq (Lit.interp rho l); intro Heq3; auto with smtcoq_core; elim H9; apply H7; unfold Lit.interp in Heq3; replace (Lit.is_pos l) with true in Heq3. + unfold Var.interp in Heq3; rewrite <- wf_interp_form; auto with smtcoq_core; rewrite Lit.blit_neg; auto with smtcoq_core. + rewrite Lit.is_pos_neg in Heq2; case_eq (Lit.is_pos l); auto with smtcoq_core; intro H; rewrite H in Heq2; discriminate. Qed. @@ -1403,7 +1377,7 @@ Transparent build_z_atom. rewrite H0, def_t_atom;discriminate. apply H1 in H2;clear H1;rewrite H0 in H2;simpl in H2. rewrite !andb_true_iff in H2;decompose [and] H2;clear H2. - apply Hf with (2:= H0);trivial. auto. + apply Hf with (2:= H0);trivial. auto with smtcoq_core. rewrite wf_interp_form, H;simpl. unfold Atom.interp_form_hatom, Atom.interp_hatom at 1;simpl. rewrite Atom.t_interp_wf, H0;simpl;trivial. @@ -1434,7 +1408,7 @@ Transparent build_z_atom. rewrite H0, def_t_atom;discriminate. apply H1 in H2;clear H1;rewrite H0 in H2;simpl in H2. rewrite !andb_true_iff in H2;decompose [and] H2;clear H2. - simpl; apply Hf with (2:= H0);trivial. auto. + simpl; apply Hf with (2:= H0);trivial. auto with smtcoq_core. rewrite wf_interp_form, H;simpl. unfold Atom.interp_form_hatom, Atom.interp_hatom at 1;simpl. rewrite Atom.t_interp_wf, H0;simpl;trivial. @@ -1480,7 +1454,7 @@ Transparent build_z_atom. case_eq (build_clause empty_vmap cl). intros (vm1, bf) Heq. destruct (build_clause_correct _ _ _ _ Heq). - red;simpl;auto. + red;simpl;auto with smtcoq_core. decompose [and] H0. case_eq (ZTautoChecker bf c);intros Heq2. unfold C.valid;rewrite H5. @@ -1512,11 +1486,11 @@ Transparent build_z_atom. rewrite wf_interp_form, H;simpl. case_eq (Lit.interp rho (a.[0]) || Lit.interp rho (a.[1]) || Lit.interp rho (a.[2])). intros;repeat (rewrite orb_true_iff in H19);destruct H19. destruct H19. - apply (afold_left_orb_true int 0); subst; auto. + apply (afold_left_orb_true int 0); subst; auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. - apply (afold_left_orb_true int 1); auto. + apply (afold_left_orb_true int 1); auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. - apply (afold_left_orb_true int 2); auto. + apply (afold_left_orb_true int 2); auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. intros; repeat (rewrite orb_false_iff in H19);destruct H19. destruct H19. unfold Lit.interp in H19. @@ -1534,7 +1508,7 @@ Transparent build_z_atom. destruct (Typ.reflect_eqb (get_type t_i t_func t_atom b0) Typ.TZ) as [H12|H12]; [intros _|discriminate]. generalize H6. clear H6. destruct (Typ.reflect_eqb (get_type t_i t_func t_atom b0) t) as [H6|H6]; [intros _|discriminate]. - rewrite <- H6. auto. + rewrite <- H6. auto with smtcoq_core. rewrite H26 in H19. case_eq (interp_atom (t_atom .[ b1])); intros t1 v1 Heq1. assert (H50: t1 = Typ.TZ). @@ -1560,11 +1534,11 @@ Transparent build_z_atom. rewrite wf_interp_form, H;simpl. case_eq (Lit.interp rho (a.[0]) || Lit.interp rho (a.[1]) || Lit.interp rho (a.[2])). intros;repeat (rewrite orb_true_iff in H19);destruct H19. destruct H19. - apply (afold_left_orb_true int 0); auto. + apply (afold_left_orb_true int 0); auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. - apply (afold_left_orb_true int 1); auto. + apply (afold_left_orb_true int 1); auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. - apply (afold_left_orb_true int 2); auto. + apply (afold_left_orb_true int 2); auto with smtcoq_core. apply ltb_spec;rewrite H0;compute;trivial. intros; repeat (rewrite orb_false_iff in H19);destruct H19. destruct H19. unfold Lit.interp in H19. @@ -1581,7 +1555,7 @@ Transparent build_z_atom. unfold Var.interp in H23; rewrite H10 in H23. rewrite <-H22, <- H20 in H21. assert (t = Typ.TZ). - rewrite Typ.eqb_spec in H6; rewrite Typ.eqb_spec in H18; subst; auto. + rewrite Typ.eqb_spec in H6; rewrite Typ.eqb_spec in H18; subst; auto with smtcoq_core. rewrite H26 in H19. case_eq (interp_atom (t_atom .[ b0])); intros t1 v1 Heq1. assert (H50: t1 = Typ.TZ). diff --git a/src/lia/lia.ml b/src/lia/lia.ml index 4444816..8dce3e8 100644 --- a/src/lia/lia.ml +++ b/src/lia/lia.ml @@ -13,9 +13,7 @@ (*** Linking SMT Terms to Micromega Terms ***) open Util open Structures.Micromega_plugin_Micromega -open Structures.Micromega_plugin_Coq_micromega -open SmtMisc open SmtForm open SmtAtom @@ -29,14 +27,6 @@ let rec pos_of_int i = then XO(pos_of_int (i lsr 1)) else XI(pos_of_int (i lsr 1)) -let z_of_int i = - if i = 0 - then Z0 - else - if i > 0 - then Zpos (pos_of_int i) - else Zneg (pos_of_int (-i)) - type my_tbl = {tbl:(hatom,int) Hashtbl.t; mutable count:int} @@ -117,8 +107,6 @@ let smt_Atom_to_micromega_formula tbl ha = (* specialized fold *) -let default_constr = lazy (Structures.econstr_of_constr (mkInt 0)) -let default_tag = Structures.Micromega_plugin_Mutils.Tag.from 0 (* morphism for general formulas *) let binop_array g tbl op def t = @@ -135,12 +123,10 @@ let binop_array g tbl op def t = let rec smt_Form_to_coq_micromega_formula tbl l = let v = match Form.pform l with - | Fatom ha -> - A (smt_Atom_to_micromega_formula tbl ha, - default_tag, Lazy.force default_constr) + | Fatom ha -> A (smt_Atom_to_micromega_formula tbl ha, Tt) | Fapp (Ftrue, _) -> TT | Fapp (Ffalse, _) -> FF - | Fapp (Fand, l) -> binop_array smt_Form_to_coq_micromega_formula tbl (fun x y -> C (x,y)) TT l + | Fapp (Fand, l) -> binop_array smt_Form_to_coq_micromega_formula tbl (fun x y -> Cj (x,y)) TT l | Fapp (For, l) -> binop_array smt_Form_to_coq_micromega_formula tbl (fun x y -> D (x,y)) FF l | Fapp (Fxor, l) -> failwith "todo:Fxor" | Fapp (Fimp, l) -> binop_array smt_Form_to_coq_micromega_formula tbl (fun x y -> I (x,None,y)) TT l @@ -162,49 +148,184 @@ let binop_list tbl op def l = | [] -> def | f::l -> List.fold_left (fun x y -> op x (smt_Form_to_coq_micromega_formula tbl y)) (smt_Form_to_coq_micromega_formula tbl f) l +let smt_clause_to_coq_micromega_formula tbl cl = + binop_list tbl (fun x y -> Cj (x,y)) TT (List.map Form.neg cl) -(* let rec binop_list tbl op def l = *) -(* match l with *) -(* | [] -> def *) -(* | [f] -> smt_Form_to_coq_micromega_formula tbl f *) -(* | f::l -> *) -(* op (smt_Form_to_coq_micromega_formula tbl f) (binop_list tbl op def l) *) - -(* and smt_Form_to_coq_micromega_formula tbl l = *) -(* let v = *) -(* match Form.pform l with *) -(* | Fatom ha -> *) -(* A (smt_Atom_to_micromega_formula tbl ha, *) -(* default_tag,default_constr) *) -(* | Fapp (Ftrue, _) -> TT *) -(* | Fapp (Ffalse, _) -> FF *) -(* | Fapp (Fand, l) -> binop_list tbl (fun x y -> C (x,y)) TT l *) -(* | Fapp (For, l) -> binop_list tbl (fun x y -> D (x,y)) FF l *) -(* | Fapp (Fxor, l) -> failwith "todo:Fxor" *) -(* | Fapp (Fimp, l) -> binop_list tbl (fun x y -> I (x,None,y)) TT l *) -(* | Fapp (Fiff, l) -> failwith "todo:Fiff" *) -(* | Fapp (Fite, l) -> failwith "todo:Fite" *) -(* | Fapp (Fnot2 _, l) -> smt_Form_to_coq_micromega_formula tbl l *) -(* in *) -(* if Form.is_pos l then v *) -(* else N(v) *) +(* backported from Coq *) +type ('option,'a,'prf,'model) prover = { + name : string ; (* name of the prover *) + get_option : unit ->'option ; (* find the options of the prover *) + prover : ('option * 'a list) -> ('prf, 'model) Structures.Micromega_plugin_Certificate.res ; (* the prover itself *) + hyps : 'prf -> Structures.Micromega_plugin_Mutils.ISet.t ; (* extract the indexes of the hypotheses really used in the proof *) + compact : 'prf -> (int -> int) -> 'prf ; (* remap the hyp indexes according to function *) + pp_prf : out_channel -> 'prf -> unit ;(* pretting printing of proof *) + pp_f : out_channel -> 'a -> unit (* pretty printing of the formulas (polynomials)*) +} -let smt_clause_to_coq_micromega_formula tbl cl = - binop_list tbl (fun x y -> C(x,y)) TT (List.map Form.neg cl) +let lia_enum = ref true +let max_depth = max_int +let lia_proof_depth = ref max_depth +let get_lia_option () = + (!Structures.Micromega_plugin_Certificate.use_simplex,!lia_enum,!lia_proof_depth) + +let lift_pexpr_prover p l = p (List.map (fun (e,o) -> Structures.Micromega_plugin_Micromega.denorm e , o) l) + +module CacheZ = Structures.Micromega_plugin_Persistent_cache.PHashtable(struct + type prover_option = bool * bool* int + type t = prover_option * ((Structures.Micromega_plugin_Micromega.z Structures.Micromega_plugin_Micromega.pol * Structures.Micromega_plugin_Micromega.op1) list) + let equal = (=) + let hash = Hashtbl.hash +end) + +let memo_zlinear_prover = CacheZ.memo ".lia.cache" (fun ((_,ce,b),s) -> lift_pexpr_prover (Structures.Micromega_plugin_Certificate.lia ce b) s) + +let xhyps_of_cone base acc prf = + let rec xtract e acc = + match e with + | Structures.Micromega_plugin_Micromega.PsatzC _ | Structures.Micromega_plugin_Micromega.PsatzZ | Structures.Micromega_plugin_Micromega.PsatzSquare _ -> acc + | Structures.Micromega_plugin_Micromega.PsatzIn n -> let n = (Structures.Micromega_plugin_Mutils.CoqToCaml.nat n) in + if n >= base + then Structures.Micromega_plugin_Mutils.ISet.add (n-base) acc + else acc + | Structures.Micromega_plugin_Micromega.PsatzMulC(_,c) -> xtract c acc + | Structures.Micromega_plugin_Micromega.PsatzAdd(e1,e2) | Structures.Micromega_plugin_Micromega.PsatzMulE(e1,e2) -> xtract e1 (xtract e2 acc) in + + xtract prf acc + +let hyps_of_pt pt = + + let rec xhyps base pt acc = + match pt with + | Structures.Micromega_plugin_Micromega.DoneProof -> acc + | Structures.Micromega_plugin_Micromega.RatProof(c,pt) -> xhyps (base+1) pt (xhyps_of_cone base acc c) + | Structures.Micromega_plugin_Micromega.CutProof(c,pt) -> xhyps (base+1) pt (xhyps_of_cone base acc c) + | Structures.Micromega_plugin_Micromega.EnumProof(c1,c2,l) -> + let s = xhyps_of_cone base (xhyps_of_cone base acc c2) c1 in + List.fold_left (fun s x -> xhyps (base + 1) x s) s l in + + xhyps 0 pt Structures.Micromega_plugin_Mutils.ISet.empty + +let compact_cone prf f = + let np n = Structures.Micromega_plugin_Mutils.CamlToCoq.nat (f (Structures.Micromega_plugin_Mutils.CoqToCaml.nat n)) in + + let rec xinterp prf = + match prf with + | Structures.Micromega_plugin_Micromega.PsatzC _ | Structures.Micromega_plugin_Micromega.PsatzZ | Structures.Micromega_plugin_Micromega.PsatzSquare _ -> prf + | Structures.Micromega_plugin_Micromega.PsatzIn n -> Structures.Micromega_plugin_Micromega.PsatzIn (np n) + | Structures.Micromega_plugin_Micromega.PsatzMulC(e,c) -> Structures.Micromega_plugin_Micromega.PsatzMulC(e,xinterp c) + | Structures.Micromega_plugin_Micromega.PsatzAdd(e1,e2) -> Structures.Micromega_plugin_Micromega.PsatzAdd(xinterp e1,xinterp e2) + | Structures.Micromega_plugin_Micromega.PsatzMulE(e1,e2) -> Structures.Micromega_plugin_Micromega.PsatzMulE(xinterp e1,xinterp e2) in + + xinterp prf + +let compact_pt pt f = + let translate ofset x = + if x < ofset then x + else (f (x-ofset) + ofset) in + + let rec compact_pt ofset pt = + match pt with + | Structures.Micromega_plugin_Micromega.DoneProof -> Structures.Micromega_plugin_Micromega.DoneProof + | Structures.Micromega_plugin_Micromega.RatProof(c,pt) -> Structures.Micromega_plugin_Micromega.RatProof(compact_cone c (translate (ofset)), compact_pt (ofset+1) pt ) + | Structures.Micromega_plugin_Micromega.CutProof(c,pt) -> Structures.Micromega_plugin_Micromega.CutProof(compact_cone c (translate (ofset)), compact_pt (ofset+1) pt ) + | Structures.Micromega_plugin_Micromega.EnumProof(c1,c2,l) -> Structures.Micromega_plugin_Micromega.EnumProof(compact_cone c1 (translate (ofset)), compact_cone c2 (translate (ofset)), + Structures.Micromega_plugin_Micromega.map (fun x -> compact_pt (ofset+1) x) l) in + compact_pt 0 pt + +let pp_nat o n = Printf.fprintf o "%i" (Structures.Micromega_plugin_Mutils.CoqToCaml.nat n) + +let pp_positive o x = Printf.fprintf o "%i" (Structures.Micromega_plugin_Mutils.CoqToCaml.positive x) + +let pp_z o x = Printf.fprintf o "%s" (Big_int.string_of_big_int (Structures.Micromega_plugin_Mutils.CoqToCaml.z_big_int x)) + +let pp_list op cl elt o l = + let rec _pp o l = + match l with + | [] -> () + | [e] -> Printf.fprintf o "%a" elt e + | e::l -> Printf.fprintf o "%a ,%a" elt e _pp l in + Printf.fprintf o "%s%a%s" op _pp l cl + +let pp_pol pp_c o e = + let rec pp_pol o e = + match e with + | Structures.Micromega_plugin_Micromega.Pc n -> Printf.fprintf o "Pc %a" pp_c n + | Structures.Micromega_plugin_Micromega.Pinj(p,pol) -> Printf.fprintf o "Pinj(%a,%a)" pp_positive p pp_pol pol + | Structures.Micromega_plugin_Micromega.PX(pol1,p,pol2) -> Printf.fprintf o "PX(%a,%a,%a)" pp_pol pol1 pp_positive p pp_pol pol2 in + pp_pol o e + +let pp_psatz pp_z o e = + let rec pp_cone o e = + match e with + | Structures.Micromega_plugin_Micromega.PsatzIn n -> + Printf.fprintf o "(In %a)%%nat" pp_nat n + | Structures.Micromega_plugin_Micromega.PsatzMulC(e,c) -> + Printf.fprintf o "( %a [*] %a)" (pp_pol pp_z) e pp_cone c + | Structures.Micromega_plugin_Micromega.PsatzSquare e -> + Printf.fprintf o "(%a^2)" (pp_pol pp_z) e + | Structures.Micromega_plugin_Micromega.PsatzAdd(e1,e2) -> + Printf.fprintf o "(%a [+] %a)" pp_cone e1 pp_cone e2 + | Structures.Micromega_plugin_Micromega.PsatzMulE(e1,e2) -> + Printf.fprintf o "(%a [*] %a)" pp_cone e1 pp_cone e2 + | Structures.Micromega_plugin_Micromega.PsatzC p -> + Printf.fprintf o "(%a)%%positive" pp_z p + | Structures.Micromega_plugin_Micromega.PsatzZ -> + Printf.fprintf o "0" in + pp_cone o e + +let rec pp_proof_term o = function + | Structures.Micromega_plugin_Micromega.DoneProof -> Printf.fprintf o "D" + | Structures.Micromega_plugin_Micromega.RatProof(cone,rst) -> Printf.fprintf o "R[%a,%a]" (pp_psatz pp_z) cone pp_proof_term rst + | Structures.Micromega_plugin_Micromega.CutProof(cone,rst) -> Printf.fprintf o "C[%a,%a]" (pp_psatz pp_z) cone pp_proof_term rst + | Structures.Micromega_plugin_Micromega.EnumProof(c1,c2,rst) -> + Printf.fprintf o "EP[%a,%a,%a]" + (pp_psatz pp_z) c1 (pp_psatz pp_z) c2 + (pp_list "[" "]" pp_proof_term) rst + +let linear_Z = { + name = "lia"; + get_option = get_lia_option; + prover = memo_zlinear_prover ; + hyps = hyps_of_pt; + compact = compact_pt; + pp_prf = pp_proof_term; + pp_f = fun o x -> pp_pol pp_z o (fst x) +} + +let find_witness p polys1 = + let polys1 = List.map fst polys1 in + match p.prover (p.get_option (), polys1) with + | Structures.Micromega_plugin_Certificate.Model m -> Structures.Micromega_plugin_Certificate.Model m + | Structures.Micromega_plugin_Certificate.Unknown -> Structures.Micromega_plugin_Certificate.Unknown + | Structures.Micromega_plugin_Certificate.Prf prf -> Structures.Micromega_plugin_Certificate.Prf(prf,p) + +let witness_list prover l = + let rec xwitness_list l = + match l with + | [] -> Structures.Micromega_plugin_Certificate.Prf [] + | e :: l -> + match xwitness_list l with + | Structures.Micromega_plugin_Certificate.Model (m,e) -> Structures.Micromega_plugin_Certificate.Model (m,e) + | Structures.Micromega_plugin_Certificate.Unknown -> Structures.Micromega_plugin_Certificate.Unknown + | Structures.Micromega_plugin_Certificate.Prf l -> + match find_witness prover e with + | Structures.Micromega_plugin_Certificate.Model m -> Structures.Micromega_plugin_Certificate.Model (m,e) + | Structures.Micromega_plugin_Certificate.Unknown -> Structures.Micromega_plugin_Certificate.Unknown + | Structures.Micromega_plugin_Certificate.Prf w -> Structures.Micromega_plugin_Certificate.Prf (w::l) in + xwitness_list l + +let witness_list_tags = witness_list -(* backported from Coq-8.8.2 *) -(* val tauto_lia : Mc.z formula -> Certificate.Mc.zArithProof list option *) let tauto_lia ff = let prover = linear_Z in - let cnf_ff,_ = Structures.Micromega_plugin_Coq_micromega.cnf Mc.negate Mc.normalise Mc.zunsat Mc.zdeduce ff in - match witness_list_tags [prover] cnf_ff with - | None -> None - | Some l -> Some (List.map fst l) + let cnf_ff,_ = Structures.Micromega_plugin_Micromega.cnfZ ff in + match witness_list_tags prover cnf_ff with + | Structures.Micromega_plugin_Certificate.Prf l -> Some (List.map fst l) + | _ -> None (* call to micromega solver *) let build_lia_certif cl = let tbl = create_tbl 13 in let f = I(smt_clause_to_coq_micromega_formula tbl cl, None, FF) in - tbl, f, tauto_lia f - + tauto_lia f diff --git a/src/lia/lia.mli b/src/lia/lia.mli index 9d4ee6b..fb58db8 100644 --- a/src/lia/lia.mli +++ b/src/lia/lia.mli @@ -10,60 +10,6 @@ (**************************************************************************) -val pos_of_int : int -> Structures.Micromega_plugin_Micromega.positive -val z_of_int : int -> Structures.Micromega_plugin_Micromega.z -type my_tbl -val get_atom_var : my_tbl -> SmtAtom.hatom -> int -val create_tbl : int -> my_tbl -val smt_Atom_to_micromega_pos : - SmtAtom.hatom -> Structures.Micromega_plugin_Micromega.positive -val smt_Atom_to_micromega_Z : - SmtAtom.hatom -> Structures.Micromega_plugin_Micromega.z -val smt_Atom_to_micromega_pExpr : - my_tbl -> - SmtAtom.hatom -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Micromega.pExpr -val smt_binop_to_micromega_formula : - my_tbl -> - SmtAtom.bop -> - SmtAtom.hatom -> - SmtAtom.hatom -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Micromega.formula -val smt_Atom_to_micromega_formula : - my_tbl -> - SmtAtom.hatom -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Micromega.formula -val binop_array : - ('a -> 'b -> 'c) -> 'a -> ('c -> 'c -> 'c) -> 'c -> 'b array -> 'c -val smt_Form_to_coq_micromega_formula : - my_tbl -> - SmtAtom.Form.t -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula -val binop_list : - my_tbl -> - (Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula) -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula -> - SmtAtom.Form.t list -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula -val smt_clause_to_coq_micromega_formula : - my_tbl -> - SmtAtom.Form.t list -> - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula val build_lia_certif : SmtAtom.Form.t list -> - my_tbl * - Structures.Micromega_plugin_Micromega.z - Structures.Micromega_plugin_Coq_micromega.formula * Structures.Micromega_plugin_Certificate.Mc.zArithProof list option |