```------------------------------------------------------------------------
-- The Agda standard library
--
-- Sums (disjoint unions)
------------------------------------------------------------------------

{-# OPTIONS --cubical-compatible --safe #-}

module Data.Sum where

open import Agda.Builtin.Equality

open import Data.Bool.Base using (true; false)
open import Data.Unit.Polymorphic.Base using (⊤; tt)
open import Data.Maybe.Base using (Maybe; just; nothing)
open import Function.Base
open import Level
open import Relation.Nullary.Reflects using (invert)
open import Relation.Nullary using (Dec; yes; no; _because_; ¬_)

private
variable
a b : Level
A B : Set a

------------------------------------------------------------------------
-- Re-export content from base module

open import Data.Sum.Base public

------------------------------------------------------------------------

module _ {a b} {A : Set a} {B : Set b} where

isInj₁ : A ⊎ B → Maybe A
isInj₁ (inj₁ x) = just x
isInj₁ (inj₂ y) = nothing

isInj₂ : A ⊎ B → Maybe B
isInj₂ (inj₁ x) = nothing
isInj₂ (inj₂ y) = just y

From-inj₁ : A ⊎ B → Set a
From-inj₁ (inj₁ _) = A
From-inj₁ (inj₂ _) = ⊤

from-inj₁ : (x : A ⊎ B) → From-inj₁ x
from-inj₁ (inj₁ x) = x
from-inj₁ (inj₂ _) = _

From-inj₂ : A ⊎ B → Set b
From-inj₂ (inj₁ _) = ⊤
From-inj₂ (inj₂ _) = B

from-inj₂ : (x : A ⊎ B) → From-inj₂ x
from-inj₂ (inj₁ _) = _
from-inj₂ (inj₂ x) = x

-- Conversion back and forth with Dec

fromDec : Dec A → A ⊎ ¬ A
fromDec ( true because  [p]) = inj₁ (invert  [p])
fromDec (false because [¬p]) = inj₂ (invert [¬p])

toDec : A ⊎ ¬ A → Dec A
toDec (inj₁ p)  = yes p
toDec (inj₂ ¬p) = no ¬p
```