Isomorphism.hs

{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE Safe #-}
-----------------------------------------------------------------------------
-- |
-- Copyright   :  (C) 2011-2015 Edward Kmett
-- License     :  BSD-style (see the file LICENSE)
--
-- Maintainer  :  Edward Kmett <ekmett@gmail.com>
-- Stability   :  provisional
-- Portability :  polykinds
--
----------------------------------------------------------------------------

module Data.Isomorphism
  ( Iso(..)
  ) where

import Control.Category
import Data.Semigroupoid
import Data.Groupoid
import Prelude ()

data Iso k a b = Iso { embed :: k a b, project :: k b a }

instance Semigroupoid k => Semigroupoid (Iso k) where
  Iso f g `o` Iso h i = Iso (f `o` h) (i `o` g)

instance Semigroupoid k => Groupoid (Iso k) where
  inv (Iso f g) = Iso g f

instance Category k => Category (Iso k) where
  Iso f g . Iso h i = Iso (f . h) (i . g)
  id = Iso id id