-----------------------------------------------------------------------------
--
-- Module      :  Data.DualCategory.Instances.Categories.Kleisli
-- Copyright   :
-- License     :  BSD3
--
-- Maintainer  :
-- Stability   :
-- Portability :
--
-- |
--
-----------------------------------------------------------------------------

{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE UndecidableInstances #-}

module Data.DualCategory.Instances.Categories.Kleisli (

) where

import Control.Arrow (Kleisli(Kleisli))
import qualified Control.Arrow as A
import Control.Categorical.Bifunctor (PFunctor, QFunctor, Bifunctor, first, second, bimap)
import Control.Category.Associative (Associative, associate, disassociate)
import Control.Category.Braided (Braided, braid, Symmetric, braid, swap)

instance (Monad m) => PFunctor (,) (Kleisli m) (Kleisli m) where
  first = A.first

instance (Monad m) => QFunctor (,) (Kleisli m) (Kleisli m) where
  second = A.second

instance (Monad m) => Bifunctor (,) (Kleisli m) (Kleisli m) (Kleisli m) where
  bimap = (A.***)

instance (Monad m, Bifunctor p (Kleisli m) (Kleisli m) (Kleisli m), Associative (->) p) => Associative (Kleisli m) p where
  associate = Kleisli (return . associate)
  disassociate = Kleisli (return . disassociate)

instance (Monad m, Associative (Kleisli m) p, Braided (->) p) => Braided (Kleisli m) p where
  braid = Kleisli (return . braid)

instance Braided (Kleisli m) p => Symmetric (Kleisli m) p