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Commit 2ed8bac2 authored by Robbert Krebbers's avatar Robbert Krebbers
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CMRAIdentity instance for option.

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algebra/option.v
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...@@ -63,6 +63,7 @@ Context {A : cmraT}. ...@@ -63,6 +63,7 @@ Context {A : cmraT}.
Instance option_validN : ValidN (option A) := λ n mx, Instance option_validN : ValidN (option A) := λ n mx,
match mx with Some x => ✓{n} x | None => True end. match mx with Some x => ✓{n} x | None => True end.
Global Instance option_empty : Empty (option A) := None.
Instance option_unit : Unit (option A) := fmap unit. Instance option_unit : Unit (option A) := fmap unit.
Instance option_op : Op (option A) := union_with (λ x y, Some (x ⋅ y)). Instance option_op : Op (option A) := union_with (λ x y, Some (x ⋅ y)).
Instance option_minus : Minus (option A) := Instance option_minus : Minus (option A) :=
...@@ -125,6 +126,8 @@ Proof. ...@@ -125,6 +126,8 @@ Proof.
Qed. Qed.
Canonical Structure optionRA := Canonical Structure optionRA :=
CMRAT option_cofe_mixin option_cmra_mixin option_cmra_extend_mixin. CMRAT option_cofe_mixin option_cmra_mixin option_cmra_extend_mixin.
Global Instance option_cmra_identity : CMRAIdentity optionRA.
Proof. split. done. by intros []. by inversion_clear 1. Qed.
Lemma op_is_Some mx my : is_Some (mx ⋅ my) ↔ is_Some mx ∨ is_Some my. Lemma op_is_Some mx my : is_Some (mx ⋅ my) ↔ is_Some mx ∨ is_Some my.
Proof. Proof.
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