From iris.algebra Require Import ofe cmra. Set Default Proof Using "Type". (* Old notation for backwards compatibility. *) (* Deprecated 2016-11-22. Use ofeT instead. *) Notation cofeT := ofeT (only parsing). (* Deprecated 2016-12-09. Use agree instead. *) Module dec_agree. 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_cmra_discrete : CmraDiscrete dec_agreeR. Proof. apply discrete_cmra_discrete. Qed. Global Instance dec_agree_cmra_total : CmraTotal dec_agreeR. Proof. intros x. by exists x. Qed. (* Some properties of this CMRA *) Global Instance dec_agree_core_id (x : dec_agreeR) : CoreId 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.