dec_agree.v 1.7 KB
 Ralf Jung committed Feb 23, 2016 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 ``````From algebra Require Export cmra. From algebra Require Import functor upred. Local Arguments validN _ _ _ !_ /. Local Arguments valid _ _ !_ /. Local Arguments op _ _ _ !_ /. Local Arguments unit _ _ !_ /. (* This is isomorphic to optiob, 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 {_}. 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. Instance dec_agree_equiv : Equiv (dec_agree A) := equivL. 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_unit : Unit (dec_agree A) := id. Instance dec_agree_minus : Minus (dec_agree A) := λ x y, x. Definition dec_agree_ra : RA (dec_agree A). Proof. split. - apply _. - apply _. - apply _. - apply _. - intros [?|] [?|] [?|]; simpl; repeat (case_match; simpl); subst; congruence. - intros [?|] [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|]; simpl; repeat (case_match; simpl); try subst; congruence. - intros [?|] [?|] ?; simpl; done. - intros [?|] [?|] ?; simpl; done. - intros [?|] [?|] [[?|]]; simpl; repeat (case_match; simpl); subst; try congruence; []. case=>EQ. destruct EQ. done. Qed. Canonical Structure dec_agreeRA : cmraT := discreteRA dec_agree_ra.``````