Commit 03ee69f3 authored by Ralf Jung's avatar Ralf Jung

Merge branch 'v2.0' of gitlab.mpi-sws.org:FP/iris-coq into v2.0

parents 42cb296d d885e2e5
......@@ -318,15 +318,32 @@ Proof.
* by intros Hx z ?; exists y; split; [done|apply (Hx z)].
* by intros Hx z n ?; destruct (Hx z n) as (?&<-&?).
Qed.
Lemma ra_updateP_id (P : A Prop) x : P x x : P.
Lemma cmra_updateP_id (P : A Prop) x : P x x : P.
Proof. by intros ? z n ?; exists x. Qed.
Lemma ra_updateP_compose (P Q : A Prop) x :
Lemma cmra_updateP_compose (P Q : A Prop) x :
x : P ( y, P y y : Q) x : Q.
Proof.
intros Hx Hy z n ?. destruct (Hx z n) as (y&?&?); auto. by apply (Hy y).
Qed.
Lemma ra_updateP_weaken (P Q : A Prop) x : x : P ( y, P y Q y) x : Q.
Proof. eauto using ra_updateP_compose, ra_updateP_id. Qed.
Lemma cmra_updateP_weaken (P Q : A Prop) x : x : P ( y, P y Q y) x : Q.
Proof. eauto using cmra_updateP_compose, cmra_updateP_id. Qed.
Lemma cmra_updateP_op (P1 P2 Q : A Prop) x1 x2 :
x1 : P1 x2 : P2 ( y1 y2, P1 y1 P2 y2 Q (y1 y2)) x1 x2 : Q.
Proof.
intros Hx1 Hx2 Hy z n ?.
destruct (Hx1 (x2 z) n) as (y1&?&?); first by rewrite associative.
destruct (Hx2 (y1 z) n) as (y2&?&?);
first by rewrite associative (commutative _ x2) -associative.
exists (y1 y2); split; last rewrite (commutative _ y1) -associative; auto.
Qed.
Lemma cmra_updateP_op' (P1 P2 : A Prop) x1 x2 :
x1 : P1 x2 : P2 x1 x2 : λ y, y1 y2, y = y1 y2 P1 y1 P2 y2.
Proof. eauto 10 using cmra_updateP_op. Qed.
Lemma cmra_update_op x1 x2 y1 y2 : x1 y1 x2 y2 x1 x2 y1 y2.
Proof.
rewrite !cmra_update_updateP; eauto using cmra_updateP_op with congruence.
Qed.
End cmra.
Hint Extern 0 (_ {0} _) => apply cmra_includedN_0.
......@@ -473,13 +490,16 @@ Section prod.
Qed.
Lemma prod_update x y : x.1 y.1 x.2 y.2 x y.
Proof. intros ?? z n [??]; split; simpl in *; auto. Qed.
Lemma prod_updateP (P : A * B Prop) P1 P2 x :
x.1 : P1 x.2 : P2 ( a b, P1 a P2 b P (a,b)) x : P.
Lemma prod_updateP P1 P2 (Q : A * B Prop) x :
x.1 : P1 x.2 : P2 ( a b, P1 a P2 b Q (a,b)) x : Q.
Proof.
intros Hx1 Hx2 HP z n [??]; simpl in *.
destruct (Hx1 (z.1) n) as (a&?&?), (Hx2 (z.2) n) as (b&?&?); auto.
exists (a,b); repeat split; auto.
Qed.
Lemma prod_updateP' P1 P2 x :
x.1 : P1 x.2 : P2 x : λ y, P1 (y.1) P2 (y.2).
Proof. eauto using prod_updateP. Qed.
End prod.
Arguments prodRA : clear implicits.
......
......@@ -185,26 +185,45 @@ Proof.
+ by rewrite Hi; apply Some_Some_includedN, cmra_included_includedN.
+ apply None_includedN.
Qed.
Lemma map_dom_op (m1 m2 : gmap K A) :
dom (gset K) (m1 m2) dom _ m1 dom _ m2.
Lemma map_dom_op m1 m2 : dom (gset K) (m1 m2) dom _ m1 dom _ m2.
Proof.
apply elem_of_equiv; intros i; rewrite elem_of_union !elem_of_dom.
unfold is_Some; setoid_rewrite lookup_op.
destruct (m1 !! i), (m2 !! i); naive_solver.
Qed.
Lemma map_insert_updateP (P : A Prop) (Q : gmap K A Prop) m i x :
x : P ( y, P y Q (<[i:=y]>m)) <[i:=x]>m : Q.
Proof.
intros Hx%option_updateP' HP mf n Hm.
destruct (Hx (mf !! i) n) as ([y|]&?&?); try done.
{ by generalize (Hm i); rewrite lookup_op; simplify_map_equality. }
exists (<[i:=y]> m); split; first by auto.
intros j; move: (Hm j)=>{Hm}; rewrite !lookup_op=>Hm.
destruct (decide (i = j)); simplify_map_equality'; auto.
Qed.
Lemma map_insert_updateP' (P : A Prop) (Q : gmap K A Prop) m i x :
x : P <[i:=x]>m : λ m', y, m' = <[i:=y]>m P y.
Proof. eauto using map_insert_updateP. Qed.
Lemma map_insert_update m i x y : x y <[i:=x]>m <[i:=y]>m.
Proof.
rewrite !cmra_update_updateP; eauto using map_insert_updateP with congruence.
Qed.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma map_update_alloc (m : gmap K A) x :
x m : λ m', i, m' = <[i:=x]>m m !! i = None.
Lemma map_updateP_alloc (Q : gmap K A Prop) m x :
x ( i, m !! i = None Q (<[i:=x]>m)) m : Q.
Proof.
intros ? mf n Hm. set (i := fresh (dom (gset K) (m mf))).
intros ? HQ mf n Hm. set (i := fresh (dom (gset K) (m mf))).
assert (i dom (gset K) m i dom (gset K) mf) as [??].
{ rewrite -not_elem_of_union -map_dom_op; apply is_fresh. }
exists (<[i:=x]>m); split; [exists i; split; [done|]|].
* by apply not_elem_of_dom.
* rewrite -map_insert_op; last by apply not_elem_of_dom.
exists (<[i:=x]>m); split; first by apply HQ, not_elem_of_dom.
rewrite -map_insert_op; last by apply not_elem_of_dom.
by apply map_insert_validN; [apply cmra_valid_validN|].
Qed.
Lemma map_updateP_alloc' m x :
x m : λ m', i, m' = <[i:=x]>m m !! i = None.
Proof. eauto using map_updateP_alloc. Qed.
End properties.
Instance map_fmap_ne `{Countable K} {A B : cofeT} (f : A B) n :
......
......@@ -147,10 +147,12 @@ Proof.
destruct (Hx (unit x) n) as (y'&?&?); rewrite ?cmra_unit_r; auto.
by exists (Some y'); split; [auto|apply cmra_validN_op_l with (unit x)].
Qed.
Lemma option_updateP' (P : A Prop) x :
x : P Some x : λ y, default False y P.
Proof. eauto using option_updateP. Qed.
Lemma option_update x y : x y Some x Some y.
Proof.
intros; apply cmra_update_updateP, (option_updateP (y=)); [|naive_solver].
by apply cmra_update_updateP.
rewrite !cmra_update_updateP; eauto using option_updateP with congruence.
Qed.
End cmra.
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment