Commit a1ea5292 authored by Robbert Krebbers's avatar Robbert Krebbers
Browse files

Prove adequacy of observational view shifts.

This implements issue #3.
parent 8111cab0
......@@ -87,6 +87,13 @@ Qed.
Instance rvs_iter_mono n : Proper (() ==> ()) (Nat.iter n (λ P, |=r=> P)%I).
Proof. intros P Q HP. induction n; simpl; do 2?f_equiv; auto. Qed.
Lemma rvs_iter_frame_l n R Q :
R Nat.iter n (λ P, |=r=> P) Q Nat.iter n (λ P, |=r=> P) (R Q).
induction n as [|n IH]; simpl; [done|].
by rewrite rvs_frame_l {1}(later_intro R) -later_sep IH.
Lemma wptp_result n e1 t1 v2 t2 σ1 σ2 φ :
nsteps step n (e1 :: t1, σ1) (of_val v2 :: t2, σ2)
world σ1 WP e1 {{ v, φ v }} wptp t1
......@@ -119,6 +126,23 @@ Proof.
iApply wp_safe. iFrame "Hw".
iApply (big_sep_elem_of with "Htp"); apply elem_of_list_fmap; eauto.
Lemma wptp_invariance n e1 e2 t1 t2 σ1 σ2 I φ :
PersistentP I
nsteps step n (e1 :: t1, σ1) (t2, σ2)
(I ={,}=> σ', ownP σ' φ σ')
I world σ1 WP e1 {{ _, True }} wptp t1
Nat.iter (S (S n)) (λ P, |=r=> P) ( φ σ2).
intros ?? HI. rewrite wptp_steps //.
rewrite (Nat_iter_S_r (S n)) rvs_iter_frame_l. apply rvs_iter_mono.
iIntros "[HI H]".
iDestruct "H" as (e2' t2') "(% & (Hw&HE&Hσ) & _)"; subst.
rewrite pvs_eq in HI;
iVs (HI with "HI [Hw HE]") as "> (_ & _ & H)"; first by iFrame.
iDestruct "H" as (σ2') "[Hσf %]".
iDestruct (ownP_agree σ2 σ2' with "[#]") as %<-. by iFrame. eauto.
End adequacy.
Theorem wp_adequacy Σ `{irisPreG Λ Σ} e σ φ :
......@@ -137,3 +161,18 @@ Proof.
iVsIntro. iNext. iApply wptp_safe; eauto.
iFrame "Hw HE Hσ". iSplitL; auto. by iApply Hwp.
Theorem wp_invariance Σ `{irisPreG Λ Σ} (I : iProp Σ) e φ σ1 t2 σ2 :
PersistentP I
( `{irisG Λ Σ}, ownP σ1 ={}=> I WP e {{ _, True }})
( `{irisG Λ Σ}, I ={,}=> σ', ownP σ' φ σ')
rtc step ([e], σ1) (t2, σ2)
φ σ2.
intros ? Hwp HI [n ?]%rtc_nsteps.
eapply (adequacy (M:=iResUR Σ) _ (S (S (S n)))); iIntros "".
rewrite Nat_iter_S. iVs (iris_alloc σ1) as (?) "(Hw & HE & ? & Hσ)".
rewrite pvs_eq in Hwp.
iVs (Hwp _ with "Hσ [Hw HE]") as ">(? & ? & ? & ?)"; first by iFrame.
iVsIntro. iNext. iApply wptp_invariance; eauto. by iFrame.
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