Commit 4397cde3 authored by Robbert Krebbers's avatar Robbert Krebbers

Move update stuff to its own file (it used to be in cmra.v).

parent a20c86e3
Pipeline #1450 passed with stage
......@@ -56,6 +56,7 @@ algebra/upred_big_op.v
algebra/frac.v
algebra/csum.v
algebra/list.v
algebra/updates.v
program_logic/model.v
program_logic/adequacy.v
program_logic/hoare_lifting.v
......
From iris.algebra Require Export excl.
From iris.algebra Require Export excl updates.
From iris.algebra Require Import upred.
Local Arguments valid _ _ !_ /.
Local Arguments validN _ _ _ !_ /.
......
This diff is collapsed.
From iris.algebra Require Export cmra.
From iris.algebra Require Export cmra updates.
From iris.algebra Require Import upred.
Local Arguments pcore _ _ !_ /.
Local Arguments cmra_pcore _ !_ /.
......
From iris.algebra Require Export cmra.
From iris.algebra Require Export cmra updates.
Record DRAMixin A `{Equiv A, Core A, Disjoint A, Op A, Valid A} := {
(* setoids *)
......
From iris.algebra Require Export cmra.
From iris.algebra Require Export cmra updates.
From iris.prelude Require Export gmap.
From iris.algebra Require Import upred.
......
From iris.algebra Require Export cmra.
From iris.algebra Require Export cmra updates.
From iris.algebra Require Import upred.
From iris.prelude Require Import finite.
......
From iris.algebra Require Export cmra.
From iris.algebra Require Export cmra updates.
From iris.prelude Require Export list.
From iris.algebra Require Import upred.
......
From iris.algebra Require Export cmra.
(** * Local updates *)
(** The idea is that lemams taking this class will usually have L explicit,
and leave Lv implicit - it will be inferred by the typeclass machinery. *)
Class LocalUpdate {A : cmraT} (Lv : A Prop) (L : A A) := {
local_update_ne n :> Proper (dist n ==> dist n) L;
local_updateN n x y : Lv x {n} (x y) L (x y) {n} L x y
}.
Arguments local_updateN {_ _} _ {_} _ _ _ _ _.
(** * Frame preserving updates *)
Definition cmra_updateP {A : cmraT} (x : A) (P : A Prop) := n mz,
{n} (x ? mz) y, P y {n} (y ? mz).
Instance: Params (@cmra_updateP) 1.
Infix "~~>:" := cmra_updateP (at level 70).
Definition cmra_update {A : cmraT} (x y : A) := n mz,
{n} (x ? mz) {n} (y ? mz).
Infix "~~>" := cmra_update (at level 70).
Instance: Params (@cmra_update) 1.
(** ** CMRAs *)
Section cmra.
Context {A : cmraT}.
Implicit Types x y : A.
Global Instance cmra_updateP_proper :
Proper (() ==> pointwise_relation _ iff ==> iff) (@cmra_updateP A).
Proof.
rewrite /pointwise_relation /cmra_updateP=> x x' Hx P P' HP;
split=> ? n mz; setoid_subst; naive_solver.
Qed.
Global Instance cmra_update_proper :
Proper (() ==> () ==> iff) (@cmra_update A).
Proof.
rewrite /cmra_update=> x x' Hx y y' Hy; split=> ? n mz ?; setoid_subst; auto.
Qed.
(** ** Local updates *)
Global Instance local_update_proper (L : A A) Lv :
LocalUpdate Lv L Proper (() ==> ()) L.
Proof. intros; apply (ne_proper _). Qed.
Lemma local_update (L : A A) `{!LocalUpdate Lv L} x y :
Lv x (x y) L (x y) L x y.
Proof.
by rewrite cmra_valid_validN equiv_dist=>?? n; apply (local_updateN L).
Qed.
Global Instance op_local_update x : LocalUpdate (λ _, True) (op x).
Proof. split. apply _. by intros n y1 y2 _ _; rewrite assoc. Qed.
Global Instance id_local_update : LocalUpdate (λ _, True) (@id A).
Proof. split; auto with typeclass_instances. Qed.
Global Instance exclusive_local_update y :
LocalUpdate Exclusive (λ _, y) | 1000.
Proof. split. apply _. by intros ?????%exclusiveN_r. Qed.
(** ** Frame preserving updates *)
Lemma cmra_update_updateP x y : x ~~> y x ~~>: (y =).
Proof. split=> Hup n z ?; eauto. destruct (Hup n z) as (?&<-&?); auto. Qed.
Lemma cmra_updateP_id (P : A Prop) x : P x x ~~>: P.
Proof. intros ? n mz ?; eauto. Qed.
Lemma cmra_updateP_compose (P Q : A Prop) x :
x ~~>: P ( y, P y y ~~>: Q) x ~~>: Q.
Proof. intros Hx Hy n mz ?. destruct (Hx n mz) as (y&?&?); naive_solver. Qed.
Lemma cmra_updateP_compose_l (Q : A Prop) x y : x ~~> y y ~~>: Q x ~~>: Q.
Proof.
rewrite cmra_update_updateP.
intros; apply cmra_updateP_compose with (y =); naive_solver.
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.
Global Instance cmra_update_preorder : PreOrder (@cmra_update A).
Proof.
split.
- intros x. by apply cmra_update_updateP, cmra_updateP_id.
- intros x y z. rewrite !cmra_update_updateP.
eauto using cmra_updateP_compose with subst.
Qed.
Lemma cmra_update_exclusive `{!Exclusive x} y:
y x ~~> y.
Proof. move=>??[z|]=>[/exclusiveN_r[]|_]. by apply cmra_valid_validN. 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 n mz ?.
destruct (Hx1 n (Some (x2 ? mz))) as (y1&?&?).
{ by rewrite /= -cmra_opM_assoc. }
destruct (Hx2 n (Some (y1 ? mz))) as (y2&?&?).
{ by rewrite /= -cmra_opM_assoc (comm _ x2) cmra_opM_assoc. }
exists (y1 y2); split; last rewrite (comm _ y1) cmra_opM_assoc; 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.
(** ** Frame preserving updates for total CMRAs *)
Section total_updates.
Context `{CMRATotal A}.
Lemma cmra_total_updateP x (P : A Prop) :
x ~~>: P n z, {n} (x z) y, P y {n} (y z).
Proof.
split=> Hup; [intros n z; apply (Hup n (Some z))|].
intros n [z|] ?; simpl; [by apply Hup|].
destruct (Hup n (core x)) as (y&?&?); first by rewrite cmra_core_r.
eauto using cmra_validN_op_l.
Qed.
Lemma cmra_total_update x y : x ~~> y n z, {n} (x z) {n} (y z).
Proof. rewrite cmra_update_updateP cmra_total_updateP. naive_solver. Qed.
Context `{CMRADiscrete A}.
Lemma cmra_discrete_updateP (x : A) (P : A Prop) :
x ~~>: P z, (x z) y, P y (y z).
Proof.
rewrite cmra_total_updateP; setoid_rewrite <-cmra_discrete_valid_iff.
naive_solver eauto using 0.
Qed.
Lemma cmra_discrete_update `{CMRADiscrete A} (x y : A) :
x ~~> y z, (x z) (y z).
Proof.
rewrite cmra_total_update; setoid_rewrite <-cmra_discrete_valid_iff.
naive_solver eauto using 0.
Qed.
End total_updates.
End cmra.
(** ** CMRAs with a unit *)
Section ucmra.
Context {A : ucmraT}.
Implicit Types x y : A.
Lemma ucmra_update_unit x : x ~~> .
Proof.
apply cmra_total_update=> n z. rewrite left_id; apply cmra_validN_op_r.
Qed.
Lemma ucmra_update_unit_alt y : ~~> y x, x ~~> y.
Proof. split; [intros; trans |]; auto using ucmra_update_unit. Qed.
End ucmra.
Section cmra_transport.
Context {A B : cmraT} (H : A = B).
Notation T := (cmra_transport H).
Lemma cmra_transport_updateP (P : A Prop) (Q : B Prop) x :
x ~~>: P ( y, P y Q (T y)) T x ~~>: Q.
Proof. destruct H; eauto using cmra_updateP_weaken. Qed.
Lemma cmra_transport_updateP' (P : A Prop) x :
x ~~>: P T x ~~>: λ y, y', y = cmra_transport H y' P y'.
Proof. eauto using cmra_transport_updateP. Qed.
End cmra_transport.
(** * Product *)
Section prod.
Context {A B : cmraT}.
Implicit Types x : A * B.
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 n mz [??]; simpl in *.
destruct (Hx1 n (fst <$> mz)) as (a&?&?); first by destruct mz.
destruct (Hx2 n (snd <$> mz)) as (b&?&?); first by destruct mz.
exists (a,b); repeat split; destruct mz; 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.
Lemma prod_update x y : x.1 ~~> y.1 x.2 ~~> y.2 x ~~> y.
Proof.
rewrite !cmra_update_updateP.
destruct x, y; eauto using prod_updateP with subst.
Qed.
Global Instance prod_local_update
(LA : A A) `{!LocalUpdate LvA LA} (LB : B B) `{!LocalUpdate LvB LB} :
LocalUpdate (λ x, LvA (x.1) LvB (x.2)) (prod_map LA LB).
Proof.
constructor.
- intros n x y [??]; constructor; simpl; by apply local_update_ne.
- intros n ?? [??] [??];
constructor; simpl in *; eapply local_updateN; eauto.
Qed.
End prod.
(** * Option *)
Section option.
Context {A : cmraT}.
Implicit Types x y : A.
Global Instance option_fmap_local_update (L : A A) Lv :
LocalUpdate Lv L
LocalUpdate (λ mx, if mx is Some x then Lv x else False) (fmap L).
Proof.
split; first apply _.
intros n [x|] [z|]; constructor; by eauto using (local_updateN L).
Qed.
Global Instance option_const_local_update Lv y :
LocalUpdate Lv (λ _, y)
LocalUpdate (λ mx, if mx is Some x then Lv x else False) (λ _, Some y).
Proof.
split; first apply _.
intros n [x|] [z|]; constructor; by eauto using (local_updateN (λ _, y)).
Qed.
Lemma option_updateP (P : A Prop) (Q : option A Prop) x :
x ~~>: P ( y, P y Q (Some y)) Some x ~~>: Q.
Proof.
intros Hx Hy; apply cmra_total_updateP=> n [y|] ?.
{ destruct (Hx n (Some y)) as (y'&?&?); auto. exists (Some y'); auto. }
destruct (Hx n None) as (y'&?&?); rewrite ?cmra_core_r; auto.
by exists (Some y'); auto.
Qed.
Lemma option_updateP' (P : A Prop) x :
x ~~>: P Some x ~~>: from_option P False.
Proof. eauto using option_updateP. Qed.
Lemma option_update x y : x ~~> y Some x ~~> Some y.
Proof.
rewrite !cmra_update_updateP; eauto using option_updateP with congruence.
Qed.
End option.
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