Commit ad5c2676 authored by Robbert Krebbers's avatar Robbert Krebbers

CMRA structure on coPset.

parent fcee7da0
......@@ -60,6 +60,7 @@ algebra/csum.v
algebra/list.v
algebra/updates.v
algebra/gset.v
algebra/coPset.v
program_logic/model.v
program_logic/adequacy.v
program_logic/hoare_lifting.v
......
From iris.algebra Require Export cmra.
From iris.algebra Require Import updates.
From iris.prelude Require Export collections coPset.
(** This is pretty much the same as algebra/gset, but I was not able to
generalize the construction without breaking canonical structures. *)
Inductive coPset_disj :=
| CoPset : coPset coPset_disj
| CoPsetBot : coPset_disj.
Section coPset.
Arguments op _ _ !_ !_ /.
Canonical Structure coPset_disjC := leibnizC coPset_disj.
Instance coPset_disj_valid : Valid coPset_disj := λ X,
match X with CoPset _ => True | CoPsetBot => False end.
Instance coPset_disj_empty : Empty coPset_disj := CoPset .
Instance coPset_disj_op : Op coPset_disj := λ X Y,
match X, Y with
| CoPset X, CoPset Y => if decide (X Y) then CoPset (X Y) else CoPsetBot
| _, _ => CoPsetBot
end.
Instance coPset_disj_pcore : PCore coPset_disj := λ _, Some .
Ltac coPset_disj_solve :=
repeat (simpl || case_decide);
first [apply (f_equal CoPset)|done|exfalso]; set_solver by eauto.
Lemma coPset_disj_valid_inv_l X Y :
(CoPset X Y) Y', Y = CoPset Y' X Y'.
Proof. destruct Y; repeat (simpl || case_decide); by eauto. Qed.
Lemma coPset_disj_union X Y : X Y CoPset X CoPset Y = CoPset (X Y).
Proof. intros. by rewrite /= decide_True. Qed.
Lemma coPset_disj_valid_op X Y : (CoPset X CoPset Y) X Y.
Proof. simpl. case_decide; by split. Qed.
Lemma coPset_disj_ra_mixin : RAMixin coPset_disj.
Proof.
apply ra_total_mixin; eauto.
- intros [?|]; destruct 1; coPset_disj_solve.
- by constructor.
- by destruct 1.
- intros [X1|] [X2|] [X3|]; coPset_disj_solve.
- intros [X1|] [X2|]; coPset_disj_solve.
- intros [X|]; coPset_disj_solve.
- exists (CoPset ); coPset_disj_solve.
- intros [X1|] [X2|]; coPset_disj_solve.
Qed.
Canonical Structure coPset_disjR := discreteR coPset_disj coPset_disj_ra_mixin.
Lemma coPset_disj_ucmra_mixin : UCMRAMixin coPset_disj.
Proof. split; try apply _ || done. intros [X|]; coPset_disj_solve. Qed.
Canonical Structure coPset_disjUR :=
discreteUR coPset_disj coPset_disj_ra_mixin coPset_disj_ucmra_mixin.
End coPset.
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