From eaf53dcf2ae4ed4a836974f6b8ee08fffc4c8640 Mon Sep 17 00:00:00 2001
From: Jacques-Henri Jourdan <jacques-henri.jourdan@normalesup.org>
Date: Wed, 11 Sep 2019 06:07:18 +0200
Subject: [PATCH] lft_intersect is a Meet instance.
---
theories/lifetime/lifetime.v | 2 +-
theories/lifetime/lifetime_sig.v | 15 +++++++--------
theories/lifetime/model/definitions.v | 4 +---
theories/lifetime/model/primitive.v | 14 +++++++-------
theories/typing/lft_contexts.v | 6 +++---
5 files changed, 19 insertions(+), 22 deletions(-)
diff --git a/theories/lifetime/lifetime.v b/theories/lifetime/lifetime.v
index c169f25e..4a2eb931 100644
--- a/theories/lifetime/lifetime.v
+++ b/theories/lifetime/lifetime.v
@@ -16,7 +16,7 @@ Module Export lifetime : lifetime_sig.
Include creation.
End lifetime.
-Notation lft_intersect_list l := (foldr lft_intersect static l).
+Notation lft_intersect_list l := (foldr (⊓) static l).
Instance lft_inhabited : Inhabited lft := populate static.
diff --git a/theories/lifetime/lifetime_sig.v b/theories/lifetime/lifetime_sig.v
index eb1d9569..77311728 100644
--- a/theories/lifetime/lifetime_sig.v
+++ b/theories/lifetime/lifetime_sig.v
@@ -21,7 +21,7 @@ Module Type lifetime_sig.
(** Definitions *)
Parameter lft : Type.
Parameter static : lft.
- Parameter lft_intersect : lft → lft → lft.
+ Declare Instance lft_intersect : Meet lft.
Parameter lft_ctx : ∀ `{!invG Σ, !lftG Σ}, iProp Σ.
@@ -44,7 +44,6 @@ Module Type lifetime_sig.
Notation "&{ κ , i }" := (idx_bor κ i) (format "&{ κ , i }") : bi_scope.
Infix "⊑" := lft_incl (at level 70) : bi_scope.
- Infix "⊓" := lft_intersect (at level 40) : stdpp_scope.
Section properties.
Context `{!invG Σ, !lftG Σ}.
@@ -53,12 +52,12 @@ Module Type lifetime_sig.
Global Declare Instance lft_inhabited : Inhabited lft.
Global Declare Instance bor_idx_inhabited : Inhabited bor_idx.
- Global Declare Instance lft_intersect_comm : Comm eq lft_intersect.
- Global Declare Instance lft_intersect_assoc : Assoc eq lft_intersect.
- Global Declare Instance lft_intersect_inj_1 κ : Inj eq eq (lft_intersect κ).
- Global Declare Instance lft_intersect_inj_2 κ : Inj eq eq (λ κ', lft_intersect κ' κ).
- Global Declare Instance lft_intersect_left_id : LeftId eq static lft_intersect.
- Global Declare Instance lft_intersect_right_id : RightId eq static lft_intersect.
+ Global Declare Instance lft_intersect_comm : Comm (A:=lft) eq (⊓).
+ Global Declare Instance lft_intersect_assoc : Assoc (A:=lft) eq (⊓).
+ Global Declare Instance lft_intersect_inj_1 (κ : lft) : Inj eq eq (κ ⊓).
+ Global Declare Instance lft_intersect_inj_2 (κ : lft) : Inj eq eq (⊓ κ).
+ Global Declare Instance lft_intersect_left_id : LeftId eq static meet.
+ Global Declare Instance lft_intersect_right_id : RightId eq static meet.
Global Declare Instance lft_ctx_persistent : Persistent lft_ctx.
Global Declare Instance lft_dead_persistent κ : Persistent ([†κ]).
diff --git a/theories/lifetime/model/definitions.v b/theories/lifetime/model/definitions.v
index ede0dc16..f2acef14 100644
--- a/theories/lifetime/model/definitions.v
+++ b/theories/lifetime/model/definitions.v
@@ -17,9 +17,7 @@ Module Export lft_notation.
End lft_notation.
Definition static : lft := (∅ : gmultiset _).
-Definition lft_intersect (κ κ' : lft) : lft := κ ⊎ κ'.
-
-Infix "⊓" := lft_intersect (at level 40) : stdpp_scope.
+Instance lft_intersect : Meet lft := λ κ κ', κ ⊎ κ'.
Inductive bor_state :=
| Bor_in
diff --git a/theories/lifetime/model/primitive.v b/theories/lifetime/model/primitive.v
index 377a8108..e3ab4f51 100644
--- a/theories/lifetime/model/primitive.v
+++ b/theories/lifetime/model/primitive.v
@@ -256,12 +256,12 @@ Qed.
(** Basic rules about lifetimes *)
Instance lft_inhabited : Inhabited lft := _.
Instance bor_idx_inhabited : Inhabited bor_idx := _.
-Instance lft_intersect_comm : Comm eq lft_intersect := _.
-Instance lft_intersect_assoc : Assoc eq lft_intersect := _.
-Instance lft_intersect_inj_1 κ : Inj eq eq (lft_intersect κ) := _.
-Instance lft_intersect_inj_2 κ : Inj eq eq (λ κ', lft_intersect κ' κ) := _.
-Instance lft_intersect_left_id : LeftId eq static lft_intersect := _.
-Instance lft_intersect_right_id : RightId eq static lft_intersect := _.
+Instance lft_intersect_comm : Comm (A:=lft) eq (⊓) := _.
+Instance lft_intersect_assoc : Assoc (A:=lft) eq (⊓) := _.
+Instance lft_intersect_inj_1 κ : Inj eq eq (κ ⊓) := _.
+Instance lft_intersect_inj_2 κ : Inj eq eq (⊓ κ) := _.
+Instance lft_intersect_left_id : LeftId eq static (⊓) := _.
+Instance lft_intersect_right_id : RightId eq static (⊓) := _.
Lemma lft_tok_sep q κ1 κ2 : q.[κ1] ∗ q.[κ2] ⊣⊢ q.[κ1 ⊓ κ2].
Proof. by rewrite /lft_tok -big_sepMS_disj_union. Qed.
@@ -269,7 +269,7 @@ Proof. by rewrite /lft_tok -big_sepMS_disj_union. Qed.
Lemma lft_dead_or κ1 κ2 : [†κ1] ∨ [†κ2] ⊣⊢ [† κ1 ⊓ κ2].
Proof.
rewrite /lft_dead -or_exist. apply exist_proper=> Λ.
- rewrite -sep_or_r -pure_or. do 2 f_equiv. unfold lft_intersect. set_solver.
+ rewrite -sep_or_r -pure_or. do 2 f_equiv. set_solver.
Qed.
Lemma lft_tok_dead q κ : q.[κ] -∗ [† κ] -∗ False.
diff --git a/theories/typing/lft_contexts.v b/theories/typing/lft_contexts.v
index 89829f2e..28fa316e 100644
--- a/theories/typing/lft_contexts.v
+++ b/theories/typing/lft_contexts.v
@@ -51,7 +51,7 @@ Section lft_contexts.
- iDestruct "H" as "[Hq Hq']".
iDestruct "Hq" as (κ0) "(% & Hq & #?)".
iDestruct "Hq'" as (κ0') "(% & Hq' & #?)". simpl in *.
- rewrite (inj (lft_intersect (foldr lft_intersect static κs)) κ0' κ0); last congruence.
+ rewrite (inj ((lft_intersect_list κs) ⊓) κ0' κ0); last congruence.
iExists κ0. by iFrame "∗%".
Qed.
@@ -229,8 +229,8 @@ Section lft_contexts.
iDestruct "HL" as "[HL1 HL2]". rewrite {2}/llctx_interp /llctx_elt_interp.
iDestruct (big_sepL_lookup_acc with "HL2") as "[Hκ Hclose]". done.
iDestruct "Hκ" as (κ0) "(EQ & Htok & #Hend)". simpl. iDestruct "EQ" as %->.
- iAssert (∃ q', q'.[foldr lft_intersect static κs] ∗
- (q'.[foldr lft_intersect static κs] ={F}=∗ llctx_interp L (qL / 2)))%I
+ iAssert (∃ q', q'.[lft_intersect_list κs] ∗
+ (q'.[lft_intersect_list κs] ={F}=∗ llctx_interp L (qL / 2)))%I
with "[> HE HL1]" as "H".
{ move:(qL/2)%Qp=>qL'. clear HL. iClear "Hend".
iInduction Hκs as [|κ κs Hκ ?] "IH" forall (qL').
--
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