From 30b963ae613b3c98ea45a147c091c751e8e0a231 Mon Sep 17 00:00:00 2001
From: Ralf Jung
Date: Wed, 7 Mar 2018 09:24:07 +0100
Subject: [PATCH] update concurrent_stack4
---
.../concurrent_stacks/concurrent_stack4.v | 102 +++++++++++-------
1 file changed, 64 insertions(+), 38 deletions(-)
diff --git a/theories/concurrent_stacks/concurrent_stack4.v b/theories/concurrent_stacks/concurrent_stack4.v
index b15a36d..544aae0 100644
--- a/theories/concurrent_stacks/concurrent_stack4.v
+++ b/theories/concurrent_stacks/concurrent_stack4.v
@@ -2,7 +2,7 @@ From iris.program_logic Require Export weakestpre hoare.
From iris.heap_lang Require Export lang proofmode notation.
From iris.algebra Require Import excl.
-(** Stack 4: With helping, (weak) view-shift spec. *)
+(** Stack 3: Helping, view-shift spec. *)
Definition mk_offer : val :=
λ: "v", ("v", ref #0).
@@ -67,7 +67,7 @@ Section side_channel.
Implicit Types l : loc.
Definition stages γ (P : list val → iProp Σ) (Q : iProp Σ) l (v : val):=
- ((l ↦ #0 ∗ (∀ vs, P vs ==∗ P (v :: vs) ∗ Q))
+ ((l ↦ #0 ∗ (∀ vs, P vs ={⊤ ∖ ↑N}=∗ P (v :: vs) ∗ Q))
∨ (l ↦ #1 ∗ Q)
∨ (l ↦ #1 ∗ own γ (Excl ()))
∨ (l ↦ #2 ∗ own γ (Excl ())))%I.
@@ -79,7 +79,7 @@ Section side_channel.
(∃ l, ⌜v = #l⌝ ∗ (l ↦ NONEV ∨ (∃ v' γ, l ↦ SOMEV v' ∗ is_offer γ P Q v')))%I.
End side_channel.
Section stack_works.
- Context `{!heapG Σ} (N : namespace).
+ Context `{!heapG Σ}.
Implicit Types l : loc.
@@ -141,29 +141,19 @@ Section stack_works.
injection H; intros; subst; auto.
Qed.
- (* View-shift based hole-stack invariant (P). However:
- - The resources for the successful and failing pop must be disjoint.
- Instead, there should be a normal conjunction between them.
- - The updating view shifts have the empty mask.
- Open question: How does this relate to a logically atomic spec? *)
- Theorem stack_works {channelG0 : channelG Σ} P Q Q' Q'' Φ :
+ (* Whole-stack invariant (P). *)
+ Theorem stack_works {channelG0 : channelG Σ} N P Q Q' Q'' Φ :
(∀ (f₁ f₂ : val),
- (□((∀ v vs, P (v :: vs) ==∗ Q v ∗ P vs) -∗
- (P [] ==∗ Q' ∗ P []) -∗
+ (□(((∀ v vs, P (v :: vs) ={⊤ ∖ ↑ N}=∗ Q v ∗ P vs)
+ ∧ (P [] ={⊤ ∖ ↑ N}=∗ Q' ∗ P []) -∗
WP f₁ #() {{ v, (∃ (v' : val), v ≡ SOMEV v' ∗ Q v') ∨ (v ≡ NONEV ∗ Q')}}))
- -∗ (∀ (v : val),
- □ ((∀ vs, P vs ==∗ P (v :: vs) ∗ Q'') -∗ WP f₂ v {{ v, Q'' }}))
+ ∧ (∀ (v : val),
+ □ ((∀ vs, P vs ={⊤ ∖ ↑ N}=∗ P (v :: vs) ∗ Q'') -∗ WP f₂ v {{ v, Q'' }})))
-∗ Φ (f₁, f₂)%V)%I
-∗ P []
-∗ WP mk_stack #() {{ Φ }}.
Proof.
iIntros "HΦ HP".
- (* assert (exists n : namespace, hidden_eq n (nroot .@ "N")) as H *)
- (* by (exists (nroot .@ "N"); unfold hidden_eq; auto). *)
- (* destruct H as (N, Neq). *)
- (* assert (exists n : namespace, hidden_eq n (nroot .@ "N'")) as H *)
- (* by (exists (nroot .@ "N'"); unfold hidden_eq; auto). *)
- (* destruct H as (N', N'eq). *)
wp_let.
wp_let.
wp_alloc m as "Hm".
@@ -179,8 +169,8 @@ Section stack_works.
iMod (inv_alloc (N .@ "stack_inv") _ (stack_inv P #l) with "[Hl HP]") as "#Istack".
{ iNext; iExists l, (InjLV #()), []; iSplit; iFrame; auto. }
wp_let.
- iApply "HΦ".
- - iIntros "!# Hsucc Hfail".
+ iApply "HΦ"; iSplit.
+ - iIntros "!# Hcont".
iLöb as "IH".
wp_rec.
wp_rec.
@@ -206,7 +196,10 @@ Section stack_works.
+ subst.
iDestruct (is_stack_empty with "Hstack") as "%".
subst.
- iMod ("Hfail" with "HP") as "[HQ' HP]".
+ iDestruct "Hcont" as "[_ Hfail]".
+ iDestruct ("Hfail" with "HP") as "Hfail".
+ iDestruct (fupd_mask_mono with "Hfail") as "Hfail";
+ last iMod "Hfail" as "[HQ' HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl' Hstack HP]").
{ iExists l', (InjLV #()), []; iSplit; iFrame; auto. }
iModIntro.
@@ -236,7 +229,10 @@ Section stack_works.
iDestruct "H" as (ys') "%"; subst.
iDestruct "Hstack" as (t') "[% Hstack]".
injection H4; intros; subst.
- iDestruct ("Hsucc" with "[HP]") as "> [HQ HP]"; auto.
+ iDestruct "Hcont" as "[Hsucc _]".
+ iDestruct ("Hsucc" with "HP") as "Hsucc".
+ iDestruct (fupd_mask_mono with "Hsucc") as "Hsucc";
+ last iMod "Hsucc" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl'' Hstack HP]").
{ iExists l'', t', ys'; iSplit; iFrame; auto. }
iModIntro.
@@ -248,7 +244,7 @@ Section stack_works.
{ iExists l'', v', ys; iSplit; iFrame; auto. }
iModIntro.
wp_if.
- iApply ("IH" with "Hsucc Hfail").
+ iApply ("IH" with "Hcont").
* iDestruct "H" as (v' γ') "[Hm' Hstages]".
wp_load.
iDestruct "Hstages" as (v'' l') "[% #Hstages]".
@@ -268,8 +264,15 @@ Section stack_works.
iInv (N .@ "stack_inv") as "Hstack" "Hclose2".
wp_cas_suc.
iDestruct "Hstack" as (l'' v' xs) "[% [Hl'' [Hstack HP]]]".
- iDestruct ("Hmove" with "HP") as "> [HP HQ'']".
- iDestruct ("Hsucc" with "HP") as "> [HQ HP]".
+ iDestruct ("Hmove" with "HP") as "Hmove".
+ iDestruct (fupd_mask_mono with "Hmove") as "Hmove";
+ last iMod "Hmove" as "[HP HQ'']".
+ { apply ndisj_subseteq_difference; try solve_ndisj. }
+ iDestruct "Hcont" as "[Hsucc _]".
+ iDestruct ("Hsucc" with "HP") as "Hsucc".
+ iDestruct (fupd_mask_mono with "Hsucc") as "Hsucc";
+ last (iMod "Hsucc" as "[HQ HP]").
+ { apply ndisj_subseteq_difference; try solve_ndisj. }
iMod ("Hclose2" with "[Hl'' Hstack HP]").
{ iExists l'', v', xs; iSplit; iFrame; auto. }
iModIntro.
@@ -301,7 +304,11 @@ Section stack_works.
** subst.
iDestruct (is_stack_empty with "Hstack") as "%".
subst.
- iMod ("Hfail" with "HP") as "[HQ' HP]".
+ iDestruct "Hcont" as "[_ Hfail]".
+ iDestruct ("Hfail" with "HP") as "Hfail".
+ iDestruct (fupd_mask_mono with "Hfail") as "Hfail";
+ last iMod "Hfail" as "[HQ' HP]"; first by solve_ndisj.
+
iMod ("Hclose" with "[Hl' Hstack HP]").
{ iExists l'', (InjLV #()), []; iSplit; iFrame; auto. }
iModIntro.
@@ -328,7 +335,10 @@ Section stack_works.
iDestruct (is_stack_cons with "Hstack") as "[Hstack H]".
iDestruct "H" as (ys') "%"; subst.
iDestruct "Hstack" as (t') "[% Hstack]"; simplify_eq.
- iDestruct ("Hsucc" with "[HP]") as "> [HQ HP]"; auto.
+ iDestruct "Hcont" as "[Hsucc _]".
+ iDestruct ("Hsucc" with "HP") as "Hsucc".
+ iDestruct (fupd_mask_mono with "Hsucc") as "Hsucc";
+ last iMod "Hsucc" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl''' Hstack HP]").
{ iExists l''', t', ys'; iSplit; iFrame; auto. }
iModIntro.
@@ -340,7 +350,7 @@ Section stack_works.
{ iExists l''', v''', ys; iSplit; iFrame; auto. }
iModIntro.
wp_if.
- iApply ("IH" with "Hsucc Hfail").
+ iApply ("IH" with "Hcont").
+ iDestruct "H" as "[Hl' Hγ']".
wp_cas_fail.
iMod ("Hclose" with "[Hl' Hγ']").
@@ -357,7 +367,10 @@ Section stack_works.
** subst.
iDestruct (is_stack_empty with "Hstack") as "%".
subst.
- iMod ("Hfail" with "HP") as "[HQ' HP]".
+ iDestruct "Hcont" as "[_ Hfail]".
+ iDestruct ("Hfail" with "HP") as "Hfail".
+ iDestruct (fupd_mask_mono with "Hfail") as "Hfail";
+ last iMod "Hfail" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl' Hstack HP]").
{ iExists l'', (InjLV #()), []; iSplit; iFrame; auto. }
iModIntro.
@@ -384,7 +397,10 @@ Section stack_works.
iDestruct (is_stack_cons with "Hstack") as "[Hstack H]".
iDestruct "H" as (ys') "%"; subst.
iDestruct "Hstack" as (t') "[% Hstack]"; simplify_eq.
- iDestruct ("Hsucc" with "[HP]") as "> [HQ HP]"; auto.
+ iDestruct "Hcont" as "[Hsucc _]".
+ iDestruct ("Hsucc" with "HP") as "Hsucc".
+ iDestruct (fupd_mask_mono with "Hsucc") as "Hsucc";
+ last iMod "Hsucc" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl''' Hstack HP]").
{ iExists l''', t', ys'; iSplit; iFrame; auto. }
iModIntro.
@@ -396,7 +412,7 @@ Section stack_works.
{ iExists l''', v''', ys; iSplit; iFrame; auto. }
iModIntro.
wp_if.
- iApply ("IH" with "Hsucc Hfail").
+ iApply ("IH" with "Hcont").
+ iDestruct "H" as "[Hl' Hγ']".
wp_cas_fail.
@@ -414,7 +430,10 @@ Section stack_works.
** subst.
iDestruct (is_stack_empty with "Hstack") as "%".
subst.
- iMod ("Hfail" with "HP") as "[HQ' HP]".
+ iDestruct "Hcont" as "[_ Hfail]".
+ iDestruct ("Hfail" with "HP") as "Hfail".
+ iDestruct (fupd_mask_mono with "Hfail") as "Hfail";
+ last iMod "Hfail" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl' Hstack HP]").
{ iExists l'', (InjLV #()), []; iSplit; iFrame; auto. }
iModIntro.
@@ -441,7 +460,10 @@ Section stack_works.
iDestruct (is_stack_cons with "Hstack") as "[Hstack H]".
iDestruct "H" as (ys') "%"; subst.
iDestruct "Hstack" as (t') "[% Hstack]"; simplify_eq.
- iDestruct ("Hsucc" with "[HP]") as "> [HQ HP]"; auto.
+ iDestruct "Hcont" as "[Hsucc _]".
+ iDestruct ("Hsucc" with "HP") as "Hsucc".
+ iDestruct (fupd_mask_mono with "Hsucc") as "Hsucc";
+ last iMod "Hsucc" as "[HQ HP]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl''' Hstack HP]").
{ iExists l''', t', ys'; iSplit; iFrame; auto. }
iModIntro.
@@ -453,7 +475,7 @@ Section stack_works.
{ iExists l''', v''', ys; iSplit; iFrame; auto. }
iModIntro.
wp_if.
- iApply ("IH" with "Hsucc Hfail").
+ iApply ("IH" with "Hcont").
- iIntros (v) "!# Hpush".
iLöb as "IH".
wp_rec.
@@ -465,7 +487,7 @@ Section stack_works.
iInv (N .@ "mailbox_inv") as "Hmail" "Hclose".
iDestruct "Hmail" as (m') "[>% Hmail]"; simplify_eq.
iMod (own_alloc (Excl ())) as (γ) "Hγ". done.
- iMod (inv_alloc (N .@ "offer_inv") _ (stages γ P Q'' s v) with "[Hs Hpush]") as "#Istages".
+ iMod (inv_alloc (N .@ "offer_inv") _ (stages N γ P Q'' s v) with "[Hs Hpush]") as "#Istages".
{ iLeft; iFrame; auto. }
iDestruct "Hmail" as "[H | H]".
* wp_store.
@@ -502,7 +524,9 @@ Section stack_works.
iDestruct "Hstack" as (l'' v'' xs) "[>% [Hl'' [Hstack HP]]]"; simplify_eq.
destruct (decide (v' = v''%V)).
++ wp_cas_suc.
- iDestruct ("Hpush" with "[HP]") as "> [HP HQ]"; auto.
+ iDestruct ("Hpush" with "HP") as "Hpush".
+ iDestruct (fupd_mask_mono with "Hpush") as "Hpush";
+ last iMod "Hpush" as "[HP HQ]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl'' Hstack HP]").
{ iExists l'', (InjRV (v, v')), (v :: xs); iSplit; iFrame; auto.
iExists v'; iSplit; subst; auto. }
@@ -564,7 +588,9 @@ Section stack_works.
iDestruct "Hstack" as (l'' v''' xs) "[>% [Hl'' [Hstack HP]]]"; simplify_eq.
destruct (decide (v'' = v'''%V)).
++ wp_cas_suc.
- iDestruct ("Hpush" with "[HP]") as "> [HP HQ]"; auto.
+ iDestruct ("Hpush" with "HP") as "Hpush".
+ iDestruct (fupd_mask_mono with "Hpush") as "Hpush";
+ last iMod "Hpush" as "[HP HQ]"; first by solve_ndisj.
iMod ("Hclose" with "[Hl'' Hstack HP]").
{ iExists l'', (InjRV (v, v'')), (v :: xs); iSplit; iFrame; auto.
iExists v''; iSplit; subst; auto. }
--
2.22.0