{-# LANGUAGE NoRebindableSyntax #-}
module Clean.Core(
  Category(..),Choice(..),Split(..),(:*:),(:+:),

  first,second,left,right,ifThenElse,fail,
  
  module Prelude
  ) where

import Prelude hiding (
  Functor(..),Monad(..),
  sequence,mapM,mapM_,sequence_,(=<<),

  map,(++),filter,length,sum,
  (+),(.),id)
import qualified Prelude as P

ifThenElse b th el = if b then th else el
fail = error

type a:*:b = (a,b)
type a:+:b = Either a b

class Category k where
  id :: k a a
  (.) :: k b c -> k a b -> k a c
instance Category (->) where
  id = P.id
  (.) = (P..)

class Category k => Choice k where
  (<|>) :: k a c -> k b c -> k (a:+:b) c
infixr 3 <|>
instance Choice (->) where
  (f <|> _) (Left a) = f a
  (_ <|> g) (Right b) = g b

class Category k => Split k where
  (<#>) :: k a c -> k b d -> k (a,b) (c,d)
instance Split (->) where f <#> g = \(a,b) -> (f a,g b)

second a = id <#> a
first a = a <#> id
left a = a <|> id
right a = id <|> a