{-# LANGUAGE GADTs #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE FlexibleInstances #-}
module Data.Semifunctor.Associative where
import Prelude hiding ((.), id)
import Control.Arrow
import Control.Comonad
import Data.Functor.Bind
import Data.Functor.Extend
import Data.Semifunctor
class Semifunctor p (Product k k) k => Associative k p where
associate :: k (p(p(a,b),c)) (p(a,p(b,c)))
instance Associative (->) (Bi Either) where
associate (Bi (Left (Bi (Left a)))) = Bi (Left a)
associate (Bi (Left (Bi (Right b)))) = Bi (Right (Bi (Left b)))
associate (Bi (Right c)) = Bi (Right (Bi (Right c)))
instance Associative (->) (Bi (,)) where
associate (Bi (Bi (a,b),c)) = Bi(a, Bi(b, c))
kleisliAssociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Associative (->) p) => Kleisli m (p(p(a,b),c)) (p(a,p(b,c)))
kleisliAssociate = Kleisli (return . associate)
instance (Bind m, Monad m) => Associative (Kleisli m) (Bi Either) where
associate = kleisliAssociate
instance (Bind m, Monad m) => Associative (Kleisli m) (Bi (,)) where
associate = kleisliAssociate
cokleisliAssociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Associative (->) p) => Cokleisli m (p(p(a,b),c)) (p(a,p(b,c)))
cokleisliAssociate = Cokleisli (associate . extract)
instance (Extend m, Comonad m) => Associative (Cokleisli m) (Bi (,)) where
associate = cokleisliAssociate
class Semifunctor p (Product k k) k => Disassociative k p where
disassociate :: k (p(a,p(b,c))) (p(p(a,b),c))
instance Disassociative (->) (Bi Either) where
disassociate (Bi (Left a)) = Bi (Left (Bi (Left a)))
disassociate (Bi (Right (Bi (Left b)))) = Bi (Left (Bi (Right b)))
disassociate (Bi (Right (Bi (Right b)))) = Bi (Right b)
instance Disassociative (->) (Bi (,)) where
disassociate (Bi(a, Bi(b, c))) = Bi (Bi (a,b),c)
kleisliDisassociate :: (Monad m, Semifunctor p (Product (Kleisli m) (Kleisli m)) (Kleisli m), Disassociative (->) p) => Kleisli m (p(a,p(b,c))) (p(p(a,b),c))
kleisliDisassociate = Kleisli (return . disassociate)
instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi Either) where
disassociate = kleisliDisassociate
instance (Bind m, Monad m) => Disassociative (Kleisli m) (Bi (,)) where
disassociate = kleisliDisassociate
cokleisliDisassociate :: (Comonad m, Semifunctor p (Product (Cokleisli m) (Cokleisli m)) (Cokleisli m), Disassociative (->) p) => Cokleisli m (p(a,p(b,c))) (p(p(a,b),c))
cokleisliDisassociate = Cokleisli (disassociate . extract)
instance (Extend m, Comonad m) => Disassociative (Cokleisli m) (Bi (,)) where
disassociate = cokleisliDisassociate