From 4193161c07fdc6e14605e03ffe95a15e01304891 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?L=C3=A9on=20Gondelman?=
Date: Thu, 4 Oct 2018 18:14:47 +0200
Subject: [PATCH] vcgen and dcexpr correctness fixed (vcg_solver remains)
---
theories/vcgen/dcexpr.v | 16 ++--
theories/vcgen/vcgen.v | 190 +++++++++++++++++++++++++---------------
2 files changed, 128 insertions(+), 78 deletions(-)
diff --git a/theories/vcgen/dcexpr.v b/theories/vcgen/dcexpr.v
index 270c93f..7c533e5 100644
--- a/theories/vcgen/dcexpr.v
+++ b/theories/vcgen/dcexpr.v
@@ -383,11 +383,17 @@ Qed.
Global Instance dcexpr_closed X E de :
dcexpr_wf X E de →
- Closed X (cdexpr_interp E de).
-Proof. Admitted.
-(* induction de; simpl; try solve_closed. rewrite /Closed /=.
- split_and. change (Closed [] a_ret). solve_closed. apply (dexpr_closed E d).
-Qed. *)
+ Closed X (dcexpr_interp E de).
+Proof.
+ revert X. induction de; intros; unfold Closed in *; simplify_eq /=;
+ try (destruct_and!; split_and; first split_and; [ apply is_closed_of_val | by apply IHde2 | by apply IHde1]);
+ try (destruct_and!; split_and; first split_and; [ apply is_closed_of_val | by apply IHde1 | by apply IHde2]).
+ - split_and; eauto using is_closed_of_val. by apply dexpr_closed.
+ - split_and; [ apply is_closed_of_val | by apply IHde].
+ - split_and; [ apply is_closed_of_val | by apply IHde].
+ - split_and; first split_and; [ apply is_closed_of_val | apply is_closed_of_val | by apply IHde].
+ - by apply W.is_closed_correct.
+Qed.
(** * Reification of C syntax *)
(** ** LocLookup *)
diff --git a/theories/vcgen/vcgen.v b/theories/vcgen/vcgen.v
index fbd28ea..ee9b11a 100644
--- a/theories/vcgen/vcgen.v
+++ b/theories/vcgen/vcgen.v
@@ -332,7 +332,7 @@ Section vcg.
| dCUnOp op de, S p => vcg_wp E m de R (λ E m dv, vcg_wp_un_op E op dv m Φ) p
| dCSeq de1 de2, S p =>
vcg_wp E m de1 R (λ E m _,
- U (vcg_wp E (denv_unlock m) de2 R Φ p)) p
+ U (vcg_wp E (denv_unlock m) de2 R Φ p)) p
| dCPar de1 de2, S p =>
match vcg_sp' E m de1 with
| Some (m', mNew, dv1) =>
@@ -724,14 +724,12 @@ Section vcg_spec.
(λ v, ⌜v = dval_interp E dv⌝ ∧ denv_interp E mNew).
Proof.
iIntros (Hsp Hwf) "Hm".
- iPoseProof vcg_sp_correct' as "Hawp"; first eassumption.
- pose (vcg_sp_length _ _ _ _ _ _ _ Hsp) as Hlen.
+ iPoseProof vcg_sp_correct' as "Hawp"; first eassumption; first done.
+ pose (vcg_sp_length _ _ _ _ _ _ _ Hsp) as Hlen;
assert (∃ m', ms = [m']) as [m' ->]=>/=.
{ destruct ms as [|m' [|m'' ms'']]; eauto; inversion Hlen. }
- { done. }
- Admitted.
- (* rewrite denv_merge_nil_r. iDestruct ("Hawp" with "Hm") as "[$ $]".
- Qed.*)
+ rewrite denv_merge_nil_r. iDestruct ("Hawp" with "Hm") as "[$ $]".
+ Qed.
Lemma vcg_sp'_correct E de m m' mNew dv R :
vcg_sp' E m de = Some (m', mNew, dv) →
@@ -748,24 +746,41 @@ Section vcg_spec.
pose (vcg_sp_length _ _ _ _ _ _ _ Hsp) as Hlen.
assert (ms = []) as -> by (destruct ms; eauto; inversion Hlen); simplify_eq.
rewrite vcg_sp_correct; last eassumption; simplify_eq; last done. simpl.
- rewrite denv_merge_nil_r. iFrame. eauto 422 with iFrame. simplify_option_eq.
- Admitted.
+ rewrite denv_merge_nil_r. clear Hsp Hlen. simplify_eq /=.
+ by iFrame.
+ Qed.
Lemma vcg_sp_wf' E de ms ms' mNew dv n:
Forall (denv_wf E) ms →
- dcexpr_wf E de →
+ dcexpr_wf [] E de →
vcg_sp E ms de n = Some (ms', mNew, dv) →
Forall (denv_wf E) ms' ∧ denv_wf E mNew ∧ dval_wf E dv .
- Proof. Admitted.
-(* revert ms ms' mNew dv. induction de;
- intros ms ms' mNew dv Hwfms Hwfde Hsp; simplify_eq/=; eauto.
- - simplify_option_eq. split_and?; auto; first by destruct E.
- by eapply vcg_eval_dexpr_wf.
+ Proof.
+ revert de ms ms' mNew dv. induction n as [|n IH];
+ intros de ms ms' mNew dv Hwfms Hwfde Hsp; simplify_eq/=; eauto.
+ { destruct de; simplify_option_eq. split_and?; auto; first by destruct E.
+ by eapply vcg_eval_dexpr_wf. }
+ destruct de; simplify_eq /=.
+ - simplify_option_eq. split_and?; auto; first by destruct E.
+ by eapply vcg_eval_dexpr_wf.
+ - destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq/=.
+ destruct (vcg_sp E (mNew1 :: ms1) (dce_subst E s dv1 de2))
+ as [[[ms2 mNew2] dv2]|] eqn:Hsp2; simplify_eq/=.
+ destruct ms2 as [|t ms2]; simplify_eq/=.
+ apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ assert (Forall (denv_wf E) (mNew1 :: ms1)) as Hwfms2.
+ { apply Forall_cons. split; eauto. }
+ assert (dcexpr_wf [] E (dce_subst E s dv1 de2)) as Hwfsubst.
+ by apply dce_subst_dcexpr_wf.
+ destruct (IH (dce_subst E s dv1 de2) _ _ _ _ Hwfms2 Hwfsubst Hsp2) as (Hall&?&?).
+ apply Forall_cons in Hall. destruct Hall.
+ repeat split; eauto using denv_wf_merge.
- destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq /=.
destruct (is_dloc _ _) as [i|] eqn:Hdl; try apply is_dloc_Some in Hdl as ->; simplify_eq/=.
destruct (denv_delete_frac_2 i ms1 mNew1)
as [[[[ms2 mNew2] q] dv1]|] eqn:Hout1; simplify_eq/=.
- destruct (IHde _ _ _ _ Hwfms Hwfde Hsp1) as (?&?&?).
+ destruct (IH de _ _ _ _ Hwfms Hwfde Hsp1) as (?&?&?).
eapply denv_wf_delete_frac_2 in Hout1; eauto.
destruct Hout1 as (?&?&?).
repeat split; eauto using denv_wf_insert.
@@ -777,8 +792,8 @@ Section vcg_spec.
destruct (denv_delete_full_2 i ms2 (denv_merge mNew1 mNew2))
as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
- destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
- destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
eapply denv_wf_delete_full_2 in Hout1; try eassumption.
destruct Hout1 as (?&?&?).
repeat split; eauto using denv_wf_insert.
@@ -789,8 +804,8 @@ Section vcg_spec.
simplify_eq/=.
destruct (dcbin_op_eval E c dv1 dv2) eqn:Hboe; simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
- destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
- destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
repeat split; eauto. apply denv_wf_merge; eauto.
eapply (dcbin_op_eval_Some_wf _ dv1 dv2); eauto.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hsp1;
@@ -802,8 +817,8 @@ Section vcg_spec.
as [[[ms3 mNew3] dv1]|] eqn:Hout1; simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
destruct (dcbin_op_eval E c dv1 dv2) eqn:Hboe; simplify_eq/=.
- destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
- destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
eapply denv_wf_delete_full_2 in Hout1; try eassumption.
destruct Hout1 as (?&?&?).
repeat split; eauto using denv_wf_insert, denv_wf_merge.
@@ -811,7 +826,7 @@ Section vcg_spec.
eapply (dcbin_op_eval_Some_wf _ dv dv2); eauto.
by eapply denv_wf_merge.
- destruct (vcg_sp E ms de) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq/=.
- destruct (IHde _ _ _ _ Hwfms Hwfde Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de _ _ _ _ Hwfms Hwfde Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
destruct (dun_op_eval E u dv1) as [?|] eqn:Hop; simplify_eq/=.
repeat split; eauto.
eapply dun_op_eval_Some_wf; eauto.
@@ -820,36 +835,37 @@ Section vcg_spec.
as [[[ms2 mNew2] dv2]|] eqn:Hsp2; simplify_eq/=.
destruct ms2 as [|t ms2]; simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
- destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
assert (Forall (denv_wf E) (denv_unlock mNew1 :: ms1)) as Hwfms2.
{ apply Forall_cons. split; eauto. by apply denv_wf_unlock. }
- destruct (IHde2 _ _ _ _ Hwfms2 Hwfde2 Hsp2) as (Hall&?&?).
+ destruct (IH de2 _ _ _ _ Hwfms2 Hwfde2 Hsp2) as (Hall&?&?).
apply Forall_cons in Hall. destruct Hall.
repeat split; eauto using denv_wf_merge.
- destruct (vcg_sp E ms de1) as [[[ms1 mNew1] dv1]|] eqn:Hsp1; simplify_eq/=.
destruct (vcg_sp E ms1 de2) as [[[ms2 mNew2] dv2]|] eqn:Hsp2;
simplify_eq/=.
apply andb_True in Hwfde. destruct Hwfde as [Hwfde1 Hwfde2].
- destruct (IHde1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
- destruct (IHde2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
+ destruct (IH de1 _ _ _ _ Hwfms Hwfde1 Hsp1) as (Hwfms1&HwfNew1&Hwfdv1).
+ destruct (IH de2 _ _ _ _ Hwfms1 Hwfde2 Hsp2) as (?&?&?).
repeat split; eauto. apply denv_wf_merge; eauto.
- Qed. *)
+ Qed.
Lemma vcg_sp'_wf E de m m' mNew dv :
denv_wf E m →
- dcexpr_wf E de →
+ dcexpr_wf [] E de →
vcg_sp' E m de = Some (m', mNew, dv) →
- denv_wf E m' ∧ denv_wf E mNew ∧ dval_wf E dv .
- Proof. Admitted.
-(* rewrite /vcg_sp'. intros Hm Hde Hsp'.
+ denv_wf E m' ∧ denv_wf E mNew ∧ dval_wf E dv.
+ Proof.
+ rewrite /vcg_sp'. intros Hm Hde Hsp'.
assert (Forall (denv_wf E) [m]) as Hms by (econstructor; eauto).
- destruct (vcg_sp E [m] de) as [[[ms ?mNew] ?dv]|] eqn:Hsp; simplify_eq/=.
- destruct ms as [|?m' ms]; simplify_eq/=.
- pose (vcg_sp_length _ _ _ _ _ _ Hsp) as Hlen.
- assert (ms = []) as -> by (destruct ms; eauto; inversion Hlen).
- destruct (vcg_sp_wf' E de [m] [m'] mNew _ Hms Hde Hsp) as (Hm'&?&?).
+ destruct (vcg_sp E [m] de) as [[[ms ?mNew] ?dv]|] eqn:Hsp; simplify_eq.
+ destruct ms as [|?m' ms]; simplify_eq.
+ pose (vcg_sp_length _ _ _ _ _ _ _ Hsp) as Hlen.
+ assert (ms = []) as -> by (destruct ms; eauto; inversion Hlen). simpl in Hsp'.
+ inversion Hsp'. subst.
+ destruct (vcg_sp_wf' E de [m] [m'] mNew _ _ Hms Hde Hsp) as (Hm'&?&?).
repeat split; eauto. by inversion Hm'.
- Qed. *)
+ Qed.
Lemma vcg_wp_awp_continuation_correct R E m de Φ :
denv_wf E m →
@@ -1008,47 +1024,75 @@ Section vcg_spec.
iSplit. iPureIntro. by trans E'. eauto with iFrame.
Qed.
- Lemma vcg_wp_correct R E m de Φ :
- dcexpr_wf E de →
+ Lemma vcg_wp_correct R E m de Φ n:
+ dcexpr_wf [] E de →
denv_wf E m →
denv_interp E m -∗
- vcg_wp E m de R Φ 1024 (*TODO: Fix this *) -∗
+ vcg_wp E m de R Φ n -∗
awp (dcexpr_interp E de) R (vcg_wp_continuation E Φ).
Proof.
- Admitted. (*
- revert Φ E m. induction de; intros Φ E m Hwf; iIntros (Hmwf) "Hm Hwp".
+ revert de Φ E m. induction n as [|n IH]; intros de Φ E m Hwf; iIntros (Hmwf) "Hm Hwp".
+ { simpl; case_match; eauto with iFrame.
+ simpl. case_match.
+ + iApply awp_ret. iApply wp_wand; first by iApply vcg_eval_dexpr_correct.
+ iIntros (? ->). iExists E,_,m. repeat iSplit; eauto with iFrame.
+ iPureIntro. by eapply vcg_eval_dexpr_wf.
+ + by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
+ destruct de; eauto with iFrame.
- simpl. case_match.
+ iApply awp_ret. iApply wp_wand; first by iApply vcg_eval_dexpr_correct.
iIntros (? ->). iExists E,_,m. repeat iSplit; eauto with iFrame.
iPureIntro. by eapply vcg_eval_dexpr_wf.
+ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp").
+ - simpl in Hwf; apply andb_prop_elim in Hwf as [Hwf1 Hwf2].
+ rewrite (IH de1) //. iSpecialize ("Hm" with "Hwp"); fold vcg_wp.
+ assert (Closed [s] (dcexpr_interp E de2)).
+ { by apply dcexpr_closed. }
+ iApply (awp_bind with "[Hm]"); fold dcexpr_interp.
+ { exists (λ: s, dcexpr_interp E de2)%V. by unlock. }
+ iApply (awp_wand with "Hm"). iIntros (v) "Hex".
+ awp_let.
+ iDestruct "Hex" as (Enew dv m' Hpre Hpre' Hm'wf) "(% & Hm & Hwp)".
+ assert (dcexpr_wf [] Enew (dce_subst Enew s dv de2)) as Hwfs.
+ { apply dce_subst_dcexpr_wf; first done. by eapply dcexpr_wf_mono. }
+ rewrite (IH (dce_subst Enew s dv de2)) //.
+ iSpecialize ("Hm" with "Hwp").
+ rewrite (dcexpr_interp_mono _ E Enew _ Hwf2 Hpre').
+ rewrite Hpre -dce_subst_subst_comm.
+ iApply (awp_wand with "Hm").
+ iIntros (v1) "Hex".
+ iDestruct "Hex" as (Ef dvf mf Hpref Hpre3 Hyp4 Hyp5) "(Hm & Hwp)". simpl.
+ iExists Ef, dvf, mf; iSplit; first done. iSplit.
+ iPureIntro. trans Enew ; done.
+ iSplit; first done.
+ iFrame. iPureIntro; done.
- simpl in *. apply andb_prop_elim in Hwf as [Hwf1 Hwf2].
destruct (vcg_sp' E m de1) as [[[m' mNew] dv1]|] eqn:Heqsp; last first.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (? & ? & ?).
- iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde2]"; first done.
+ iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde2]"; try done.
clear Heqsp2 Heqsp.
- iDestruct (IHde1 with "Hm' Hwp") as "Hde1"; try done.
+ iDestruct (IH de1 with "Hm' Hwp") as "Hde1"; try done.
iApply (a_alloc_spec with "Hde1 Hde2"). iIntros "!>" (v1 v2).
iDestruct 1 as (E' dw m'' -> Hpre ? ?) "(Hm' & H)". iIntros "[-> HmNew]".
rewrite (dval_interp_mono E E') //.
rewrite /vcg_wp_alloc mapsto_wand_list_spec. iCombine "HmNew Hm'" as "Hm'".
rewrite (denv_interp_mono E E') // denv_merge_interp.
- iDestruct ("H" with "Hm'") as (n ->) "HΦ". iExists n; iSplit; first done.
+ iDestruct ("H" with "Hm'") as (n' ->) "HΦ". iExists n'; iSplit; first done.
iIntros (l) "Hl". by iApply vcg_wp_continuation_mono; last by iApply "HΦ".
+ specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde1]";
- first done. clear Heqsp.
- iDestruct (IHde2 with "Hm' Hwp") as "Hde2"; try done.
+ try done. clear Heqsp.
+ iDestruct (IH de2 with "Hm' Hwp") as "Hde2"; try done.
iApply (a_alloc_spec with "Hde1 Hde2"). iIntros "!>" (v1 v2).
iIntros "[-> HmNew]". iDestruct 1 as (E' d_new m1 -> ???) "[Hm' H]".
rewrite /vcg_wp_alloc mapsto_wand_list_spec. iCombine "HmNew Hm'" as "Hm'".
rewrite (denv_interp_mono E E') // denv_merge_interp.
rewrite !(dval_interp_mono E E') // .
- iDestruct ("H" with "Hm'") as (n ->) "HΦ". iExists n; iSplit; first done.
+ iDestruct ("H" with "Hm'") as (n' ->) "HΦ". iExists n'; iSplit; first done.
iIntros (l) "Hl". by iApply vcg_wp_continuation_mono; last by iApply "HΦ".
- - rewrite IHde //. iRename "Hm" into "Hawp".
+ - rewrite (IH de) //. iRename "Hm" into "Hawp".
iSpecialize ("Hawp" with "Hwp"); simpl.
iApply (a_load_spec_exists_frac with "[Hawp]").
iApply (awp_wand with "Hawp").
@@ -1068,9 +1112,9 @@ Section vcg_spec.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (? & ? & ?).
- iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde2]"; first done.
+ iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde2]"; try done.
clear Heqsp2 Heqsp.
- iDestruct (IHde1 with "Hm' Hwp") as "Hde1"; try done.
+ iDestruct (IH de1 with "Hm' Hwp") as "Hde1"; try done.
iApply (a_store_spec with "Hde1 Hde2"). iIntros "!>" (v1 v2).
iDestruct 1 as (E' dw m'' ? Hpre ? ?) "(Hm' & H)". iIntros "[-> HmNew]".
rewrite (dval_interp_mono E E') //. subst v1.
@@ -1082,8 +1126,8 @@ Section vcg_spec.
iApply vcg_wp_continuation_mono; last by iApply "H". done.
+ specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct (vcg_sp'_correct with "Hm") as "[Hm' Hde1]";
- first done. clear Heqsp.
- iDestruct (IHde2 with "Hm' Hwp") as "Hde2"; try done.
+ try done. clear Heqsp.
+ iDestruct (IH de2 with "Hm' Hwp") as "Hde2"; try done.
iApply (a_store_spec with "Hde1 Hde2"). iIntros "!>" (v1 v2).
iIntros "[-> HmNew]". iDestruct 1 as (E' d_new m1 ? ? ?) "(% & Hm' & H)".
rewrite (dval_interp_mono E E') //. subst v2.
@@ -1098,11 +1142,11 @@ Section vcg_spec.
destruct (vcg_sp' E m de1) as [[[m' mNew] dv1]|] eqn:Heqsp; last first.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
- iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde2]".
iClear "Hsp"; clear Heqsp2 Heqsp.
- rewrite IHde1; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de1); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iApply (a_bin_op_spec with "Hm' Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "Hex (-> & HmNew)".
iDestruct "Hex" as (E' dv1 m'' Heq Hpre Hm'wf) "(% & Hm' & Hwp)";
@@ -1112,10 +1156,10 @@ Section vcg_spec.
eauto using dval_wf_mono, denv_wf_merge, denv_wf_mono.
{ iApply (denv_interp_mono with "HmNew"); eauto. }
iExists w. iSplit; first done. by iApply vcg_wp_continuation_mono.
- + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde1]"; iClear "Hsp"; clear Heqsp.
- rewrite IHde2; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de2); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iRename "Hm'" into "Hde2".
iApply (a_bin_op_spec with "Hde1 Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "(-> & HmNew) Hex".
@@ -1131,11 +1175,11 @@ Section vcg_spec.
destruct (vcg_sp' E m de1) as [[[m' mNew] dv1]|] eqn:Heqsp; last first.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
- iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde2]".
iClear "Hsp"; clear Heqsp2 Heqsp.
- rewrite IHde1; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de1); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iApply (a_pre_bin_op_spec with "Hm' Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "Hex (-> & HmNew) $".
iDestruct "Hex" as (E' dv1 m'' Heq Hpre Hm'wf) "(% & Hm' & Hwp)";
@@ -1149,10 +1193,10 @@ Section vcg_spec.
iExists l, v, w. iFrame. repeat iSplit; eauto.
* iPureIntro. rewrite (dval_interp_mono E E'); auto.
* rewrite (vcg_wp_continuation_mono E E'); auto.
- + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde1]"; iClear "Hsp"; clear Heqsp.
- rewrite IHde2; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de2); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iRename "Hm'" into "Hde2".
iApply (a_pre_bin_op_spec with "Hde1 Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "(-> & HmNew) Hex $".
@@ -1167,19 +1211,19 @@ Section vcg_spec.
iExists l, v, w. iFrame. repeat iSplit; eauto.
* iPureIntro. rewrite (dval_interp_mono E E'); auto.
* rewrite (vcg_wp_continuation_mono E E'); auto.
- - rewrite IHde //. iApply a_un_op_spec. iSpecialize ("Hm" with "Hwp").
+ - rewrite (IH de) //. iApply a_un_op_spec. iSpecialize ("Hm" with "Hwp").
iApply (awp_wand with "Hm"). iIntros (v) "Hex".
iDestruct "Hex" as (E' dv m' -> Hpre' Hm'wf) "(% & Hm & Hwp)".
iDestruct (vcg_wp_un_op_correct with "Hm Hwp") as (w ?) "Hcont"; auto.
iExists w. iSplit; first done. by iApply vcg_wp_continuation_mono.
- simpl in Hwf; apply andb_prop_elim in Hwf as [Hwf1 Hwf2].
- rewrite IHde1 //. iSpecialize ("Hm" with "Hwp"); fold vcg_wp.
- iApply (a_sequence_spec' with "[Hm]"); fold dcexpr_interp.
+ rewrite (IH de1) //. iSpecialize ("Hm" with "Hwp"); fold vcg_wp.
+ iApply (a_sequence_spec' with "[Hm]"); fold dcexpr_interp. by apply dcexpr_closed.
iNext. iApply (awp_wand with "Hm"). iIntros (v) "Hex".
iDestruct "Hex" as (Enew dv m' Hpre Hpre' Hm'wf) "(% & Hm & Hwp)". simpl.
rewrite denv_unlock_interp.
- iModIntro. rewrite IHde2 //. iSpecialize ("Hm" with "Hwp").
- specialize (dcexpr_interp_mono E Enew de2 Hwf2 Hpre').
+ iModIntro. rewrite (IH de2) //. iSpecialize ("Hm" with "Hwp").
+ specialize (dcexpr_interp_mono [] E Enew de2 Hwf2 Hpre').
intro Heq; rewrite Heq. iApply (awp_wand with "Hm").
iIntros (v1) "Hex".
iDestruct "Hex" as (Ef dvf mf Hpref Hpre3 Hyp4 Hyp5) "(Hm & Hwp)". simpl.
@@ -1193,11 +1237,11 @@ Section vcg_spec.
destruct (vcg_sp' E m de1) as [[[m' mNew] dv1]|] eqn:Heqsp; last first.
+ destruct (vcg_sp' E m de2) as [[[m' mNew] dv2]|] eqn:Heqsp2; last first.
{ by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp"). }
- iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf2 Heqsp2) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde2]".
iClear "Hsp"; clear Heqsp2 Heqsp.
- rewrite IHde1; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de1); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iApply (awp_par with "Hm' Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "Hex (-> & HmNew)".
iDestruct "Hex" as (E' dv1 m'' Heq Hpre Hm'wf) "(% & Hm' & Hwp)";
@@ -1209,10 +1253,10 @@ Section vcg_spec.
eauto using dval_wf_mono, denv_wf_mono, denv_wf_merge).
iFrame. rewrite (denv_interp_mono E) //.
iApply denv_merge_interp. iFrame.
- + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption.
+ + iPoseProof (vcg_sp'_correct) as "Hsp"; first eassumption. done.
specialize (vcg_sp'_wf _ _ _ _ _ _ Hmwf Hwf1 Heqsp) as (?&?&?).
iDestruct ("Hsp" with "Hm") as "[Hm' Hde1]"; iClear "Hsp"; clear Heqsp.
- rewrite IHde2; [| done | done]. iSpecialize ("Hm'" with "Hwp").
+ rewrite (IH de2); [| done | done]. iSpecialize ("Hm'" with "Hwp").
iRename "Hm'" into "Hde2".
iApply (awp_par with "Hde1 Hde2"); fold dcexpr_interp.
iNext. iIntros (v1 v2) "(-> & HmNew) Hex !>".
@@ -1225,7 +1269,7 @@ Section vcg_spec.
eauto using dval_wf_mono, denv_wf_mono, denv_wf_merge).
iFrame. rewrite (denv_interp_mono E) //.
iApply denv_merge_interp. iFrame.
- - simpl. rewrite IHde //. iSpecialize ("Hm" with "Hwp"); fold vcg_wp.
+ - simpl. rewrite (IH de) //. iSpecialize ("Hm" with "Hwp"); fold vcg_wp.
iApply (a_invoke_spec with "Hm"). iIntros (arg) "Hf !> HR".
iDestruct "Hf" as (E' dv1 m' Heq Hpre Hm'wf) "(% & Hm' & Hwp)".
unfold vcg_wp_awp_continuation.
@@ -1235,7 +1279,7 @@ Section vcg_spec.
rewrite (vcg_wp_continuation_mono E) //.
iFrame.
- by iApply (vcg_wp_awp_continuation_correct with "Hm Hwp").
- Qed.*)
+ Qed.
End vcg_spec.
Arguments vcg_wp_awp_continuation _ _ _ _ _ _ _ /.
--
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