Library zoo_std.option

From zoo Require Import
  prelude.
From zoo.language Require Import
  notations.
From zoo.diaframe Require Import
  diaframe.
From zoo_std Require Export
  base.
From zoo Require Import
  options.

Implicit Types o : option val.
Implicit Types v : val.

Coercion option_to_val o :=
  match o with
  | None ⇒
      §None
  | Some v ⇒
      ‘Some( v )
  end%V.
#[global] Arguments option_to_val !_ / : assert.

#[global] Instance option_to_val_inj :
  Inj (=) (=) option_to_val.

Lemma option_to_val_similar_None_l o :
  §None%V ≈ o →
  o = None.
Lemma option_to_val_similar_None_r o :
  (o : val) ≈ §None%V →
  o = None.

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

  Definition itype_option t : iProp Σ :=
      ⌜t = §None%V⌝
    ∨ ∃ v,
      ⌜t = ‘Some( v )%V⌝ ∗
      τ v.
  #[global] Instance itype_option_itype :
    iType _ itype_option.

  Lemma wp_match_option t e1 x e2 Φ :
    itype_option t -∗
    ( WP e1 {{ Φ }} ∧
      ∀ v, τ v -∗ WP subst' x v e2 {{ Φ }}
    ) -∗
    WP match: t with None ⇒ e1 | Some x ⇒ e2 end {{ Φ }}.
End zoo_G.