{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE NoImplicitPrelude #-}

module Hcompta.Expr.Trans where

import Data.Function ((.))

-- |
-- * 'trans_lift' is generally not /surjective/
-- * 'trans_apply' is not /injective/
-- * 'trans_apply' . 'trans_lift' == 'id'
-- * 'trans_lift' . 'trans_apply' /= 'id'
class Trans trans repr where
	trans_lift  :: repr a -> trans repr a
	trans_apply :: trans repr a -> repr a
	
	trans_map1 :: (repr a -> repr b) -> (trans repr a -> trans repr b)
	trans_map1 f = trans_lift . f . trans_apply
	
	trans_map2
	 :: (repr a -> repr b -> repr c)
	 -> (trans repr a -> trans repr b -> trans repr c)
	trans_map2 f e1 e2 = trans_lift (f (trans_apply e1) (trans_apply e2))