From iris.algebra Require Import ofe cmra.
(* Old notation for backwards compatibility. *)
(* Deprecated 2016-11-22. Use ofeT instead. *)
Notation cofeT := ofeT (only parsing).
(* Deprecated 2016-12-09. Use agree instead. *)
(* The module is called dec_agree_deprecated because if it was just dec_agree,
it would still be imported by "From iris Import dec_agree", and people would
not notice they use sth. deprecated. *)
Module dec_agree_deprecated.
Local Arguments validN _ _ _ !_ /.
Local Arguments valid _ _ !_ /.
Local Arguments op _ _ _ !_ /.
Local Arguments pcore _ _ !_ /.
(* This is isomorphic to option, but has a very different RA structure. *)
Inductive dec_agree (A : Type) : Type :=
| DecAgree : A → dec_agree A
| DecAgreeBot : dec_agree A.
Arguments DecAgree {_} _.
Arguments DecAgreeBot {_}.
Instance maybe_DecAgree {A} : Maybe (@DecAgree A) := λ x,
match x with DecAgree a => Some a | _ => None end.
Section dec_agree.
Context `{EqDecision A}.
Implicit Types a b : A.
Implicit Types x y : dec_agree A.
Instance dec_agree_valid : Valid (dec_agree A) := λ x,
if x is DecAgree _ then True else False.
Canonical Structure dec_agreeC : ofeT := leibnizC (dec_agree A).
Instance dec_agree_op : Op (dec_agree A) := λ x y,
match x, y with
| DecAgree a, DecAgree b => if decide (a = b) then DecAgree a else DecAgreeBot
| _, _ => DecAgreeBot
end.
Instance dec_agree_pcore : PCore (dec_agree A) := Some.
Definition dec_agree_ra_mixin : RAMixin (dec_agree A).
Proof.
apply ra_total_mixin; apply _ || eauto.
- intros [?|] [?|] [?|]; by repeat (simplify_eq/= || case_match).
- intros [?|] [?|]; by repeat (simplify_eq/= || case_match).
- intros [?|]; by repeat (simplify_eq/= || case_match).
- by intros [?|] [?|] ?.
Qed.
Canonical Structure dec_agreeR : cmraT :=
discreteR (dec_agree A) dec_agree_ra_mixin.
Global Instance dec_agree_total : CMRATotal dec_agreeR.
Proof. intros x. by exists x. Qed.
(* Some properties of this CMRA *)
Global Instance dec_agree_persistent (x : dec_agreeR) : Persistent x.
Proof. by constructor. Qed.
Lemma dec_agree_ne a b : a ≠ b → DecAgree a ⋅ DecAgree b = DecAgreeBot.
Proof. intros. by rewrite /= decide_False. Qed.
Lemma dec_agree_idemp (x : dec_agree A) : x ⋅ x = x.
Proof. destruct x; by rewrite /= ?decide_True. Qed.
Lemma dec_agree_op_inv (x1 x2 : dec_agree A) : ✓ (x1 ⋅ x2) → x1 = x2.
Proof. destruct x1, x2; by repeat (simplify_eq/= || case_match). Qed.
Lemma DecAgree_included a b : DecAgree a ≼ DecAgree b ↔ a = b.
Proof.
split. intros [[c|] [=]%leibniz_equiv]. by simplify_option_eq. by intros ->.
Qed.
End dec_agree.
Arguments dec_agreeC : clear implicits.
Arguments dec_agreeR _ {_}.
End dec_agree_deprecated.