### Improve iPvs to deal with mask changing viewshifts.

parent 2cec343c
 ... @@ -42,17 +42,20 @@ Global Instance fsa_split_fsa {A} (fsa : FSA Λ Σ A) E Φ : ... @@ -42,17 +42,20 @@ Global Instance fsa_split_fsa {A} (fsa : FSA Λ Σ A) E Φ : FrameShiftAssertion fsaV fsa → FSASplit (fsa E Φ) E fsa fsaV Φ. FrameShiftAssertion fsaV fsa → FSASplit (fsa E Φ) E fsa fsaV Φ. Proof. done. Qed. Proof. done. Qed. Lemma tac_pvs_intro Δ E Q : Δ ⊢ Q → Δ ⊢ |={E}=> Q. Lemma tac_pvs_intro Δ E1 E2 Q : E1 = E2 → Δ ⊢ Q → Δ ⊢ |={E1,E2}=> Q. Proof. intros ->. apply pvs_intro. Qed. Proof. intros -> ->. apply pvs_intro. Qed. Lemma tac_pvs_elim Δ Δ' E1 E2 E3 i p P' P Q : Lemma tac_pvs_elim Δ Δ' E1 E2 E3 i p P' E1' E2' P Q : envs_lookup i Δ = Some (p, P') → P' = (|={E1,E2}=> P)%I → envs_lookup i Δ = Some (p, P') → P' = (|={E1',E2'}=> P)%I → (E1' = E1 ∧ E2' = E2 ∧ E2 ⊆ E1 ∪ E3 ∨ E2 = E2' ∪ E1 ∖ E1' ∧ E2' ⊥ E1 ∖ E1' ∧ E1' ⊆ E1 ∧ E2' ⊆ E1' ∪ E3) → envs_replace i p false (Esnoc Enil i P) Δ = Some Δ' → envs_replace i p false (Esnoc Enil i P) Δ = Some Δ' → E2 ⊆ E1 ∪ E3 → Δ' ⊢ (|={E2,E3}=> Q) → Δ ⊢ |={E1,E3}=> Q. Δ' ⊢ (|={E2,E3}=> Q) → Δ ⊢ |={E1,E3}=> Q. Proof. Proof. intros ? -> ?? HQ. rewrite envs_replace_sound //; simpl. intros ? -> HE ? HQ. rewrite envs_replace_sound //; simpl. by rewrite always_if_elim right_id pvs_frame_r wand_elim_r HQ pvs_trans. rewrite always_if_elim right_id pvs_frame_r wand_elim_r HQ. destruct HE as [(?&?&?)|(?&?&?&?)]; subst; first (by apply pvs_trans). etrans; [eapply pvs_mask_frame'|apply pvs_trans]; auto; set_solver. Qed. Qed. Lemma tac_pvs_elim_fsa {A} (fsa : FSA Λ Σ A) fsaV Δ Δ' E i p P' P Q Φ : Lemma tac_pvs_elim_fsa {A} (fsa : FSA Λ Σ A) fsaV Δ Δ' E i p P' P Q Φ : ... @@ -97,17 +100,20 @@ Proof. ... @@ -97,17 +100,20 @@ Proof. Qed. Qed. End pvs. End pvs. Tactic Notation "iPvsIntro" := apply tac_pvs_intro. Tactic Notation "iPvsIntro" := apply tac_pvs_intro; first try fast_done. Tactic Notation "iPvsCore" constr(H) := Tactic Notation "iPvsCore" constr(H) := match goal with match goal with | |- _ ⊢ |={_,_}=> _ => | |- _ ⊢ |={_,_}=> _ => eapply tac_pvs_elim with _ _ H _ _ _; eapply tac_pvs_elim with _ _ H _ _ _ _ _; [env_cbv; reflexivity || fail "iPvs:" H "not found" [env_cbv; reflexivity || fail "iPvs:" H "not found" |let P := match goal with |- ?P = _ => P end in |let P := match goal with |- ?P = _ => P end in reflexivity || fail "iPvs:" H ":" P "not a pvs with the right mask" reflexivity || fail "iPvs:" H ":" P "not a pvs with the right mask" |env_cbv; reflexivity |first |try (rewrite (idemp_L (∪)); reflexivity)|] [left; split_and!; [reflexivity|reflexivity|try (rewrite (idemp_L (∪)); reflexivity)] |right; split; first reflexivity] |env_cbv; reflexivity|] | |- _ => | |- _ => eapply tac_pvs_elim_fsa with _ _ _ _ H _ _ _ _; eapply tac_pvs_elim_fsa with _ _ _ _ H _ _ _ _; [env_cbv; reflexivity || fail "iPvs:" H "not found" [env_cbv; reflexivity || fail "iPvs:" H "not found" ... ...
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