Library zoo_std.optional

Require Import zoo.prelude.
Require Import zoo.base.
Require Export zoo_std.optional__code.
Require Import zoo_std.optional__types.
Require Import zoo.options.

Implicit Type v : val.

Variant optional {A} :=
  | Nothing
  | Anything
  | Something (a : A).
#[global] Arguments optional : clear implicits.
Implicit Type o : optional val.

#[global] Instance optionalｰinhabited A : Inhabited (optional A) :=
  populate Nothing.
#[global] Instance Somethingｰinj A :
  Inj (=) (=) (@Something A).

Definition option۰to_optional {A} (o : option A) :=
  match o with
  | None ⇒
      Nothing
  | Some a ⇒
      Something a
  end.
#[global] Arguments option۰to_optional _ !_ / : assert.

Coercion optional۰to_val o :=
  match o with
  | Nothing ⇒
      §Nothing
  | Anything ⇒
      §Anything
  | Something v ⇒
      ‘Something( v )
  end%V.
#[global] Arguments optional۰to_val !_ / : assert.

#[global] Instance optional۰to_valｰinj :
  Inj (=) (=) optional۰to_val.

Lemma optional۰to_valｰsimilarｰNothing_l o :
  §Nothing%V ≈ o →
  o = Nothing.
Lemma optional۰to_valｰsimilarｰNothingｰr o :
  (o : val) ≈ §Nothing%V →
  o = Nothing.

Lemma optional۰to_valｰsimilarｰAnythingｰl o :
  §Anything%V ≈ o →
  o = Anything.
Lemma optional۰to_valｰsimilarｰAnythingｰr o :
  (o : val) ≈ §Anything%V →
  o = Anything.

Section zoo۰G.
  Context `{zoo۰G : !ZooG Σ}.
  Context τ `{!iType (iPropI Σ) τ}.

  Definition itype۰optional t : iProp Σ :=
      ⌜t = §Nothing%V⌝
    ∨ ⌜t = §Anything%V⌝
    ∨ ∃ v,
      ⌜t = ‘Something( v )%V⌝ ∗
      τ v.
  #[global] Instance itype۰optionalｰitype :
    iType _ itype۰optional.

  Lemma wpｰmatchｰoptional t e1 e2 x e3 Φ :
    itype۰optional t -∗
    ( WP e1 {{ Φ }} ∧
      WP e2 {{ Φ }} ∧
      ∀ v, τ v -∗ WP subst' x v e3 {{ Φ }}
    ) -∗
    WP 𝗺𝗮𝘁𝗰𝗵 t 𝘄𝗶𝘁𝗵 Nothing → e1 | Anything → e2 | Something x → e3 𝗲𝗻𝗱 {{ Φ }}.
End zoo۰G.