From ae3a4b2d2b5fcf7136cf168013d1a77bc8ed29e7 Mon Sep 17 00:00:00 2001
From: Jacques-Henri Jourdan <jacques-henri.jourdan@normalesup.org>
Date: Wed, 2 Aug 2017 22:34:07 +0200
Subject: [PATCH] Cleaning up the lifetime logic.
---
theories/lifetime/lifetime.v | 15 +++++++++++++++
theories/lifetime/lifetime_sig.v | 13 ++++---------
theories/lifetime/model/accessors.v | 16 ----------------
3 files changed, 19 insertions(+), 25 deletions(-)
diff --git a/theories/lifetime/lifetime.v b/theories/lifetime/lifetime.v
index e5cbde2a..b2b78797 100644
--- a/theories/lifetime/lifetime.v
+++ b/theories/lifetime/lifetime.v
@@ -26,6 +26,21 @@ Section derived.
Context `{invG Σ, lftG Σ}.
Implicit Types κ : lft.
+Lemma bor_acc_atomic_cons E κ P :
+ ↑lftN ⊆ E →
+ lft_ctx -∗ &{κ} P ={E,E∖↑lftN}=∗
+ (▷ P ∗ ∀ Q, ▷ (▷ Q ={∅}=∗ ▷ P) -∗ ▷ Q ={E∖↑lftN,E}=∗ &{κ} Q) ∨
+ ([†κ] ∗ |={E∖↑lftN,E}=> True).
+Proof.
+ iIntros (?) "#LFT HP".
+ iMod (bor_acc_atomic_strong with "LFT HP") as "[H|[??]]"; first done.
+ - iLeft. iDestruct "H" as (κ') "(#Hκκ' & $ & Hclose)". iIntros "!>* HPQ HQ".
+ iMod ("Hclose" with "[HPQ] HQ") as "Hb".
+ + iNext. iIntros "? _". by iApply "HPQ".
+ + iApply (bor_shorten with "Hκκ' Hb").
+ - iRight. by iFrame.
+Qed.
+
Lemma bor_acc_atomic E κ P :
↑lftN ⊆ E →
lft_ctx -∗ &{κ}P ={E,E∖↑lftN}=∗
diff --git a/theories/lifetime/lifetime_sig.v b/theories/lifetime/lifetime_sig.v
index f2dd298f..0492383b 100644
--- a/theories/lifetime/lifetime_sig.v
+++ b/theories/lifetime/lifetime_sig.v
@@ -62,12 +62,12 @@ Module Type lifetime_sig.
Global Declare Instance lft_intersect_right_id : RightId eq static lft_intersect.
Global Declare Instance lft_ctx_persistent : PersistentP lft_ctx.
- Global Declare Instance lft_dead_persistent κ : PersistentP (lft_dead κ).
+ Global Declare Instance lft_dead_persistent κ : PersistentP ([†κ]).
Global Declare Instance lft_incl_persistent κ κ' : PersistentP (κ ⊑ κ').
- Global Declare Instance idx_bor_persistent κ i P : PersistentP (idx_bor κ i P).
+ Global Declare Instance idx_bor_persistent κ i P : PersistentP (&{κ,i} P).
- Global Declare Instance lft_tok_timeless q κ : TimelessP (lft_tok q κ).
- Global Declare Instance lft_dead_timeless κ : TimelessP (lft_dead κ).
+ Global Declare Instance lft_tok_timeless q κ : TimelessP (q.[κ]).
+ Global Declare Instance lft_dead_timeless κ : TimelessP ([†κ]).
Global Declare Instance idx_bor_own_timeless q i : TimelessP (idx_bor_own q i).
Global Instance idx_bor_params : Params (@idx_bor) 5.
@@ -151,11 +151,6 @@ Module Type lifetime_sig.
□ ((∀ q, lft_tok q κ ={↑lftN}=∗ ∃ q',
lft_tok q' κ' ∗ (lft_tok q' κ' ={↑lftN}=∗ lft_tok q κ)) ∗
(lft_dead κ' ={↑lftN}=∗ lft_dead κ)) -∗ κ ⊑ κ'.
- (* Same for some of the derived lemmas. *)
- Parameter bor_acc_atomic_cons : ∀ E κ P,
- ↑lftN ⊆ E → lft_ctx -∗ &{κ} P ={E,E∖↑lftN}=∗
- (▷ P ∗ ∀ Q, ▷ (▷ Q ={∅}=∗ ▷ P) -∗ ▷ Q ={E∖↑lftN,E}=∗ &{κ} Q) ∨
- ([†κ] ∗ |={E∖↑lftN,E}=> True).
End properties.
diff --git a/theories/lifetime/model/accessors.v b/theories/lifetime/model/accessors.v
index 053a65ce..1dbe1206 100644
--- a/theories/lifetime/model/accessors.v
+++ b/theories/lifetime/model/accessors.v
@@ -262,20 +262,4 @@ Proof.
+ iMod (lft_incl_dead with "Hle H†") as "$". done.
iApply fupd_intro_mask'. solve_ndisj.
Qed.
-
-(* These derived lemmas are needed inside the model. *)
-Lemma bor_acc_atomic_cons E κ P :
- ↑lftN ⊆ E →
- lft_ctx -∗ &{κ} P ={E,E∖↑lftN}=∗
- (▷ P ∗ ∀ Q, ▷ (▷ Q ={∅}=∗ ▷ P) -∗ ▷ Q ={E∖↑lftN,E}=∗ &{κ} Q) ∨
- ([†κ] ∗ |={E∖↑lftN,E}=> True).
-Proof.
- iIntros (?) "#LFT HP".
- iMod (bor_acc_atomic_strong with "LFT HP") as "[H|[??]]"; first done.
- - iLeft. iDestruct "H" as (κ') "(#Hκκ' & $ & Hclose)". iIntros "!>* HPQ HQ".
- iMod ("Hclose" with "[HPQ] HQ") as "Hb".
- + iNext. iIntros "? _". by iApply "HPQ".
- + iApply (bor_shorten with "Hκκ' Hb").
- - iRight. by iFrame.
-Qed.
End accessors.
--
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