Commit cd20e951 authored by Robbert Krebbers's avatar Robbert Krebbers

Some forgotten Proper instances.

parent d885e2e5
......@@ -20,10 +20,16 @@ Instance auth_dist : Dist (auth A) := λ n x y,
Global Instance Auth_ne : Proper (dist n ==> dist n ==> dist n) (@Auth A).
Proof. by split. Qed.
Global Instance Auth_proper : Proper (() ==> () ==> ()) (@Auth A).
Proof. by split. Qed.
Global Instance authoritative_ne: Proper (dist n ==> dist n) (@authoritative A).
Proof. by destruct 1. Qed.
Global Instance authoritative_proper : Proper (() ==> ()) (@authoritative A).
Proof. by destruct 1. Qed.
Global Instance own_ne : Proper (dist n ==> dist n) (@own A).
Proof. by destruct 1. Qed.
Global Instance own_proper : Proper (() ==> ()) (@own A).
Proof. by destruct 1. Qed.
Instance auth_compl : Compl (auth A) := λ c,
Auth (compl (chain_map authoritative c)) (compl (chain_map own c)).
......
......@@ -143,12 +143,12 @@ Class CMRAMonotone {A B : cmraT} (f : A → B) := {
(** * Frame preserving updates *)
Definition cmra_updateP {A : cmraT} (x : A) (P : A Prop) := z n,
{S n} (x z) y, P y {S n} (y z).
Instance: Params (@cmra_updateP) 3.
Instance: Params (@cmra_updateP) 1.
Infix "⇝:" := cmra_updateP (at level 70).
Definition cmra_update {A : cmraT} (x y : A) := z n,
{S n} (x z) {S n} (y z).
Infix "⇝" := cmra_update (at level 70).
Instance: Params (@cmra_update) 3.
Instance: Params (@cmra_update) 1.
(** * Properties **)
Section cmra.
......@@ -193,6 +193,17 @@ Proof.
intros x x' Hx y y' Hy.
by split; intros [z ?]; exists z; [rewrite -Hx -Hy|rewrite Hx Hy].
Qed.
Global Instance cmra_update_proper :
Proper (() ==> () ==> iff) (@cmra_update A).
Proof.
intros x1 x2 Hx y1 y2 Hy; split=>? z n; [rewrite -Hx -Hy|rewrite Hx Hy]; auto.
Qed.
Global Instance cmra_updateP_proper :
Proper (() ==> pointwise_relation _ iff ==> iff) (@cmra_updateP A).
Proof.
intros x1 x2 Hx P1 P2 HP; split=>Hup z n;
[rewrite -Hx; setoid_rewrite <-HP|rewrite Hx; setoid_rewrite HP]; auto.
Qed.
(** ** Validity *)
Lemma cmra_valid_validN x : x n, {n} x.
......
......@@ -27,6 +27,14 @@ Inductive excl_dist `{Dist A} : Dist (excl A) :=
| ExclUnit_dist n : ExclUnit ={n}= ExclUnit
| ExclBot_dist n : ExclBot ={n}= ExclBot.
Existing Instance excl_dist.
Global Instance Excl_ne : Proper (dist n ==> dist n) (@Excl A).
Proof. by constructor. Qed.
Global Instance Excl_proper : Proper (() ==> ()) (@Excl A).
Proof. by constructor. Qed.
Global Instance Excl_inj : Injective () () (@Excl A).
Proof. by inversion_clear 1. Qed.
Global Instance Excl_dist_inj n : Injective (dist n) (dist n) (@Excl A).
Proof. by inversion_clear 1. Qed.
Program Definition excl_chain
(c : chain (excl A)) (x : A) (H : maybe Excl (c 1) = Some x) : chain A :=
{| chain_car n := match c n return _ with Excl y => y | _ => x end |}.
......@@ -66,10 +74,6 @@ Proof.
Qed.
Canonical Structure exclC : cofeT := CofeT excl_cofe_mixin.
Global Instance Excl_inj : Injective () () (@Excl A).
Proof. by inversion_clear 1. Qed.
Global Instance Excl_dist_inj n : Injective (dist n) (dist n) (@Excl A).
Proof. by inversion_clear 1. Qed.
Global Instance Excl_timeless (x : A) : Timeless x Timeless (Excl x).
Proof. by inversion_clear 2; constructor; apply (timeless _). Qed.
Global Instance ExclUnit_timeless : Timeless (@ExclUnit A).
......
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