------------------------------------------------------------------------
-- The Agda standard library
--
-- The Maybe type
------------------------------------------------------------------------
 
{-# OPTIONS --cubical-compatible --safe #-}
 
module Data.Maybe where
 
open import Data.Empty using (⊥)
open import Data.Unit.Base using (⊤)
open import Data.Bool.Base using (T)
open import Data.Maybe.Relation.Unary.All using (All)
open import Data.Maybe.Relation.Unary.Any using (Any; just)
open import Level using (Level)
 
private
  variable
    a : Level
    A : Set a
 
------------------------------------------------------------------------
-- The base type and some operations
 
open import Data.Maybe.Base public
 
------------------------------------------------------------------------
-- Using Any and All to define Is-just and Is-nothing
 
Is-just : Maybe A → Set _
Is-just = Any (λ _ → ⊤)
 
Is-nothing : Maybe A → Set _
Is-nothing = All (λ _ → ⊥)
 
to-witness : ∀ {m : Maybe A} → Is-just m → A
to-witness (just {x = p} _) = p
 
to-witness-T : ∀ (m : Maybe A) → T (is-just m) → A
to-witness-T (just p) _  = p