Commit 6cd681c3 authored by Ralf Jung's avatar Ralf Jung

prove that we can open invariants around wp_atomic

parent 1f83451a
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......@@ -3,6 +3,7 @@ From Require Import telescopes.
From Require Export atomic.
From iris.proofmode Require Import tactics classes.
From iris.program_logic Require Export weakestpre.
From iris.base_logic Require Import invariants.
Set Default Proof Using "Type".
(* This hard-codes the inner mask to be empty, because we have yet to find an
......@@ -98,6 +99,7 @@ Section lemmas.
Notation iProp := (iProp Σ).
Implicit Types (α : TA iProp) (β : TA TB iProp) (f : TA TB val Λ).
(* Atomic triples imply sequential triples if the precondition is laterable. *)
Lemma atomic_wp_seq e Eo α β f {HL : .. x, Laterable (α x)} :
atomic_wp e Eo α β f -
Φ, .. x, α x - (.. y, β x y - Φ (f x y)) - WP e {{ Φ }}.
......@@ -109,9 +111,20 @@ Section lemmas.
rewrite ->!tele_app_bind. iIntros "HΦ". iApply "HΦ". done.
(* Sequential triples with the empty mask for a physically atomic [e] are atomic. *)
Lemma atomic_seq_wp_atomic e Eo α β f `{!Atomic WeaklyAtomic e} :
( Φ, .. x, α x - (.. y, β x y - Φ (f x y)) - WP e @ {{ Φ }}) -
atomic_wp e Eo α β f.
iIntros "Hwp" (Φ) "AU". iMod "AU" as (x) "[Hα [_ Hclose]]".
iApply ("Hwp" with "Hα"). iIntros (y) "Hβ".
iMod ("Hclose" with "Hβ") as "HΦ".
rewrite ->!tele_app_bind. iApply "HΦ".
(* Sequential triples with a persistent precondition and no initial quantifier
are atomic. *)
Lemma seq_wp_atomic e Eo (α : [tele] iProp) (β : [tele] TB iProp)
Lemma persistent_seq_wp_atomic e Eo (α : [tele] iProp) (β : [tele] TB iProp)
(f : [tele] TB val Λ) {HP : Persistent (α [tele_arg])} :
( Φ, α [tele_arg] - (.. y, β [tele_arg] y - Φ (f [tele_arg] y)) - WP e {{ Φ }}) -
atomic_wp e Eo α β f.
......@@ -124,4 +137,21 @@ Section lemmas.
rewrite ->!tele_app_bind. done.
(* We can open invariants around atomic triples.
(Just for demonstration purposes; we always use [iInv] in proofs.) *)
Lemma wp_atomic_inv e Eo α β f N I :
N Eo
atomic_wp e Eo (λ.. x, I α x) (λ.. x y, I β x y) f -
inv N I - atomic_wp e (Eo N) α β f.
intros ?. iIntros "Hwp #Hinv" (Φ) "AU". iApply "Hwp". iAuIntro.
iInv N as "HI". iApply (aacc_aupd with "AU"); first done.
iIntros (x) "Hα". iAaccIntro with "[HI Hα]"; rewrite ->!tele_app_bind; first by iFrame.
- (* abort *)
iIntros "[HI $]". by eauto with iFrame.
- (* commit *)
iIntros (y). rewrite ->!tele_app_bind. iIntros "[HI Hβ]". iRight.
iExists y. rewrite ->!tele_app_bind. by eauto with iFrame.
End lemmas.
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