From iris.algebra Require Export cmra. 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 {A : Type} `{∀ x y : A, Decision (x = y)}. Instance dec_agree_valid : Valid (dec_agree A) := λ x, if x is DecAgree _ then True else False. Canonical Structure dec_agreeC : cofeT := 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. split. - apply _. - intros x y cx ? [=<-]; eauto. - apply _. - intros [?|] [?|] [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] ? [=<-]; by repeat (simplify_eq/= || case_match). - intros [?|]; by repeat (simplify_eq/= || case_match). - intros [?|] [?|] ?? [=<-]; eauto. - by intros [?|] [?|] ?. Qed. Canonical Structure dec_agreeR : cmraT := discreteR (dec_agree A) dec_agree_ra_mixin. (* 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. End dec_agree. Arguments dec_agreeC : clear implicits. Arguments dec_agreeR _ {_}.