{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE Safe #-}
{-# LANGUAGE TypeOperators #-}
#if MIN_VERSION_base(4,7,0)
{-# LANGUAGE PolyKinds #-}
#endif
{-|
Module: Control.Transformation
Copyright: (C) 2015 The University of Kansas
License: BSD-style (see the file LICENSE)
Maintainer: Andy Gill
Stability: Experimental
A type class for transformations.
-}
module Control.Transformation (Transformation(..)) where
import Control.Natural ((:~>)(..))
infixr 0 #
-- | A (natural) transformation is inside @t@, and contains @f@ and @g@
-- (typically 'Functor's).
--
-- The order of arguments allows the use of @GeneralizedNewtypeDeriving@ to wrap
-- a ':~>', but maintain the 'Transformation' constraint. Thus, @#@ can be used
-- on abstract data types.
class Transformation f g t | t -> f g where
-- | The invocation method for a natural transformation.
(#) :: t -> f a -> g a
-- {-# RULES "natural free theorem" [~]
-- forall h (r :: (Functor f, Functor g, Transformation f g t) => t) .
-- fmap h . (r #) = (r #) . fmap h
-- #-}
instance Transformation f g (f :~> g) where
Nat f # g = f g