Library iris.algebra.lib.excl_auth
From iris.algebra Require Export auth excl updates.
From iris.algebra Require Import local_updates.
From iris.prelude Require Import options.
From iris.algebra Require Import local_updates.
From iris.prelude Require Import options.
Authoritative CMRA where the fragment is exclusively owned.
This is effectively a single "ghost variable" with two views, the frament ◯E a
and the authority ●E a.
Definition excl_authR (A : ofe) : cmra :=
authR (optionUR (exclR A)).
Definition excl_authUR (A : ofe) : ucmra :=
authUR (optionUR (exclR A)).
Definition excl_auth_auth {A : ofe} (a : A) : excl_authR A :=
● (Some (Excl a)).
Definition excl_auth_frag {A : ofe} (a : A) : excl_authR A :=
◯ (Some (Excl a)).
Global Typeclasses Opaque excl_auth_auth excl_auth_frag.
Global Instance: Params (@excl_auth_auth) 1 := {}.
Global Instance: Params (@excl_auth_frag) 2 := {}.
Notation "●E a" := (excl_auth_auth a) (at level 10).
Notation "◯E a" := (excl_auth_frag a) (at level 10).
Section excl_auth.
Context {A : ofe}.
Implicit Types a b : A.
Global Instance excl_auth_auth_ne : NonExpansive (@excl_auth_auth A).
Proof. solve_proper. Qed.
Global Instance excl_auth_auth_proper : Proper ((≡) ==> (≡)) (@excl_auth_auth A).
Proof. solve_proper. Qed.
Global Instance excl_auth_frag_ne : NonExpansive (@excl_auth_frag A).
Proof. solve_proper. Qed.
Global Instance excl_auth_frag_proper : Proper ((≡) ==> (≡)) (@excl_auth_frag A).
Proof. solve_proper. Qed.
Global Instance excl_auth_auth_discrete a : Discrete a → Discrete (●E a).
Proof. intros; apply auth_auth_discrete; [apply Some_discrete|]; apply _. Qed.
Global Instance excl_auth_frag_discrete a : Discrete a → Discrete (◯E a).
Proof. intros; apply auth_frag_discrete, Some_discrete; apply _. Qed.
Lemma excl_auth_validN n a : ✓{n} (●E a ⋅ ◯E a).
Proof. by rewrite auth_both_validN. Qed.
Lemma excl_auth_valid a : ✓ (●E a ⋅ ◯E a).
Proof. intros. by apply auth_both_valid_2. Qed.
Lemma excl_auth_agreeN n a b : ✓{n} (●E a ⋅ ◯E b) → a ≡{n}≡ b.
Proof.
rewrite auth_both_validN /= ⇒ -[Hincl Hvalid].
move: Hincl⇒ /Some_includedN_exclusive /(_ I) ?. by apply (inj Excl).
Qed.
Lemma excl_auth_agree a b : ✓ (●E a ⋅ ◯E b) → a ≡ b.
Proof.
intros. apply equiv_dist⇒ n. by apply excl_auth_agreeN, cmra_valid_validN.
Qed.
Lemma excl_auth_agree_L `{!LeibnizEquiv A} a b : ✓ (●E a ⋅ ◯E b) → a = b.
Proof. intros. by apply leibniz_equiv, excl_auth_agree. Qed.
Lemma excl_auth_auth_op_validN n a b : ✓{n} (●E a ⋅ ●E b) ↔ False.
Proof. apply auth_auth_op_validN. Qed.
Lemma excl_auth_auth_op_valid a b : ✓ (●E a ⋅ ●E b) ↔ False.
Proof. apply auth_auth_op_valid. Qed.
Lemma excl_auth_frag_op_validN n a b : ✓{n} (◯E a ⋅ ◯E b) ↔ False.
Proof. by rewrite -auth_frag_op auth_frag_validN. Qed.
Lemma excl_auth_frag_op_valid a b : ✓ (◯E a ⋅ ◯E b) ↔ False.
Proof. by rewrite -auth_frag_op auth_frag_valid. Qed.
Lemma excl_auth_update a b a' : ●E a ⋅ ◯E b ~~> ●E a' ⋅ ◯E a'.
Proof.
intros. by apply auth_update, option_local_update, exclusive_local_update.
Qed.
End excl_auth.
Definition excl_authURF (F : oFunctor) : urFunctor :=
authURF (optionURF (exclRF F)).
Global Instance excl_authURF_contractive F :
oFunctorContractive F → urFunctorContractive (excl_authURF F).
Proof. apply _. Qed.
Definition excl_authRF (F : oFunctor) : rFunctor :=
authRF (optionURF (exclRF F)).
Global Instance excl_authRF_contractive F :
oFunctorContractive F → rFunctorContractive (excl_authRF F).
Proof. apply _. Qed.