Commit 697ac29a authored by Zhen Zhang's avatar Zhen Zhang
Browse files

improve proof

parent 4ee578f6
......@@ -108,14 +108,14 @@ Section generic.
(β: A A val iProp Σ)
(Ei Eo: coPset)
(e: expr) γ : iProp Σ :=
( Q, ( g g' r, (True ={Eo, Ei}=> gFrag γ g)
(gFrag γ g' β g g' r ={Ei, Eo}=> Q r)) - WP e {{ Q }})%I.
( P Q, ( g g' r, (P ={Eo, Ei}=> gFrag γ g)
(gFrag γ g' β g g' r ={Ei, Eo}=> Q r))
- {{ P }} e {{ Q }})%I.
(* Definition atomic_spec γ (f: val): iProp Σ := *)
(* ( a b: val, atomic_triple' (β a b) heapN ( nclose N) (f a b) γ)%I. *)
(* Lemma pcas_atomic_spec (x10 x20: val): *)
(* heapN N heap_ctx WP mk_pcas x10 x20 {{ f, γ, is_pcas γ f }} *)
Lemma update_a: x x': A, (gFullR x gFragR x) ~~> (gFullR x' gFragR x').
intros x x'.
End triple.
End generic.
......@@ -201,7 +201,8 @@ Section atomic_pair.
iClear "Hfrag". (* HFrag should be handled to user? *)
iVsIntro. iExists γ. iAlways.
rewrite /is_pcas.
iIntros (a b Q) "H".
iIntros (a b P Q) "#H".
iAlways. iIntros "HP".
repeat wp_let.
wp_bind (acquire _).
iApply acquire_spec.
......@@ -221,14 +222,15 @@ Section atomic_pair.
rewrite /is_lock.
iDestruct "Hlk" as (l) "(% & _ & % & Hinv)".
iInv N as ([]) ">[Hl _]" "Hclose".
* iVs ("Hvs1" with "[]") as "Hfraga"; first by auto.
* iVs ("Hvs1" with "[HP]") as "Hfraga"; first by auto.
subst. wp_store.
iAssert (β a b (a, a) (b, b) #true) as "Hβ".
{ iPureIntro. left. eauto. }
iAssert (gFrag γ (a, a) gFull γ (a, a) - gFrag γ (b, b) gFull γ (b, b))%I as "H".
{ admit. }
iDestruct ("H" with "[Hfraga HFulla]") as "[HFragb HFullb]"; first by iFrame.
iCombine "HFulla" "Hfraga" as "Ha".
iVs (own_update with "Ha") as "Hb".
{ instantiate (H4:=(gFullR (b, b) gFragR (b, b))).
apply update_a. eauto. }
iDestruct (own_op with "Hb") as "[HFullb HFragb]".
iVs ("Hvs2" with "[HFragb Hβ]"); first by iFrame.
rewrite /lock_inv.
iVsIntro. iVs ("Hclose" with "[-~]").
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