Commit 998df552 authored by Ralf Jung's avatar Ralf Jung

implement dec_agree (no lemmas about it yet)

parent d3700ebd
......@@ -47,6 +47,7 @@ algebra/base.v
algebra/dra.v
algebra/cofe_solver.v
algebra/agree.v
algebra/dec_agree.v
algebra/excl.v
algebra/iprod.v
algebra/functor.v
......
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.
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