------------------------------------------------------------------------
-- The Agda standard library
--
-- The Maybe type
------------------------------------------------------------------------

{-# OPTIONS --without-K --safe #-}

module Data.Maybe where

open import Data.Empty using ()
open import Data.Unit using ()
open import Data.Bool.Base using (T)
open import Data.Maybe.Relation.Unary.All
open import Data.Maybe.Relation.Unary.Any
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  _  )

Is-nothing : Maybe A  Set _
Is-nothing = All  _  )

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