Bijection.hs

{-# LANGUAGE DerivingStrategies, LambdaCase #-}

module Bijection (type Bijection, swap) where

import Data.Semigroup
import Data.Monoid

newtype Bijection a = Bijection { appBijection :: a -> a }
  deriving (Semigroup, Monoid) via (Endo a)

swap :: Eq a => a -> a -> NatBijection
swap p q = Bijection $ \case
  x | x == p -> q
    | x == q -> p
    | otherwise -> x