-- Disjoint sum type; also used as logical disjunction.

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

module Tools.Sum where

data _⊎_ (A B : Set) : Set where
  inj₁ : A  A  B
  inj₂ : B  A  B

-- Idempotency.

id :  {A}  A  A  A
id (inj₁ x) = x
id (inj₂ x) = x

-- Symmetry.

sym :  {A B}  A  B  B  A
sym (inj₁ x) = inj₂ x
sym (inj₂ x) = inj₁ x