Commit db02564e authored by Robbert Krebbers's avatar Robbert Krebbers

Frame preserving updates for auth.

parent cd20e951
......@@ -6,12 +6,14 @@ Add Printing Constructor auth.
Arguments Auth {_} _ _.
Arguments authoritative {_} _.
Arguments own {_} _.
Notation "◯ x" := (Auth ExclUnit x) (at level 20).
Notation "● x" := (Auth (Excl x) ) (at level 20).
Notation "◯ a" := (Auth ExclUnit a) (at level 20).
Notation "● a" := (Auth (Excl a) ) (at level 20).
(* COFE *)
Section cofe.
Context {A : cofeT}.
Implicit Types a b : A.
Implicit Types x y : auth A.
Instance auth_equiv : Equiv (auth A) := λ x y,
authoritative x authoritative y own x own y.
......@@ -42,14 +44,14 @@ Proof.
+ by intros ?; split.
+ by intros ?? [??]; split; symmetry.
+ intros ??? [??] [??]; split; etransitivity; eauto.
* by intros n [x1 y1] [x2 y2] [??]; split; apply dist_S.
* by intros ? [??] [??] [??]; split; apply dist_S.
* by split.
* intros c n; split. apply (conv_compl (chain_map authoritative c) n).
apply (conv_compl (chain_map own c) n).
Canonical Structure authC := CofeT auth_cofe_mixin.
Instance Auth_timeless (x : excl A) (y : A) :
Timeless x Timeless y Timeless (Auth x y).
Instance Auth_timeless (ea : excl A) (b : A) :
Timeless ea Timeless b Timeless (Auth ea b).
Proof. by intros ?? [??] [??]; split; simpl in *; apply (timeless _). Qed.
Global Instance auth_leibniz : LeibnizEquiv A LeibnizEquiv (auth A).
Proof. by intros ? [??] [??] [??]; f_equal'; apply leibniz_equiv. Qed.
......@@ -60,6 +62,8 @@ Arguments authC : clear implicits.
(* CMRA *)
Section cmra.
Context {A : cmraT}.
Implicit Types a b : A.
Implicit Types x y : auth A.
Global Instance auth_empty `{Empty A} : Empty (auth A) := Auth .
Instance auth_validN : ValidN (auth A) := λ n x,
......@@ -120,22 +124,46 @@ Definition auth_cmra_extend_mixin : CMRAExtendMixin (auth A).
intros n x y1 y2 ? [??]; simpl in *.
destruct (cmra_extend_op n (authoritative x) (authoritative y1)
(authoritative y2)) as (z1&?&?&?); auto using authoritative_validN.
(authoritative y2)) as (ea&?&?&?); auto using authoritative_validN.
destruct (cmra_extend_op n (own x) (own y1) (own y2))
as (z2&?&?&?); auto using own_validN.
by exists (Auth (z1.1) (z2.1), Auth (z1.2) (z2.2)).
as (b&?&?&?); auto using own_validN.
by exists (Auth (ea.1) (b.1), Auth (ea.2) (b.2)).
Canonical Structure authRA : cmraT :=
CMRAT auth_cofe_mixin auth_cmra_mixin auth_cmra_extend_mixin.
Instance auth_cmra_identity `{Empty A} : CMRAIdentity A CMRAIdentity authRA.
(** The notations and only work for CMRAs with an empty element. So, in
what follows, we assume we have an empty element. *)
Context `{Empty A, !CMRAIdentity A}.
Global Instance auth_cmra_identity : CMRAIdentity authRA.
split; simpl.
* by apply (@cmra_empty_valid A _).
* by intros x; constructor; rewrite /= left_id.
* apply Auth_timeless; apply _.
Lemma auth_frag_op (a b : A) : (a b) a b.
Lemma auth_frag_op a b : (a b) a b.
Proof. done. Qed.
Lemma auth_update a a' b b' :
( n af, {n} a a ={n}= a' af b ={n}= b' af {n} b)
a a' b b'.
move=> Hab [[] bf1] n // =>-[[bf2 Ha] ?]; do 2 red; simpl in *.
destruct (Hab (S n) (bf1 bf2)) as [Ha' ?]; auto.
{ by rewrite Ha left_id associative. }
split; [by rewrite Ha' left_id associative; apply cmra_includedN_l|done].
Lemma auth_update_op_l a a' b :
(b a) a a' (b a) (b a').
intros; apply auth_update.
by intros n af ? Ha; split; [by rewrite Ha associative|].
Lemma auth_update_op_r a a' b :
(a b) a a' (a b) (a' b).
Proof. rewrite -!(commutative _ b); apply auth_update_op_l. Qed.
End cmra.
Arguments authRA : clear implicits.
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