Monad transformers

{-# LANGUAGE FlexibleInstances, GeneralizedNewtypeDeriving, DeriveFunctor #-}

import Data.Functor.Kan.Ran
import Control.Compose
import Control.Monad
import Control.Monad.Trans
import Data.Pointed

instance (Functor f, Monad g) => Monad(Ran f((:.) f g)) where
	return x = Ran(O. (return<$>). ($x))
	Ran f >>= f2 = Ran(\f3 -> O(join<$>unO(f(unO.($f3).runRan.f2))))

instance (Functor f,  Monad g) => Applicative(Ran f((:.) f g)) where
	pure = return
	(<*>) = ap

newtype Lift g f t = Lift(Ran f((:.) f g) t) deriving (Functor, Applicative, Monad)

instance (Monad g) => MonadTrans(Lift g) where
	lift f = Lift$ Ran(\f2-> O$ f >>= f2 >>= return.return)

-------------------------------------
-- Ex. for various base monads.

tell' :: (Monoid x, Monad f) => x -> Lift((,) x) f ()
tell' x = Lift(Ran(\f->O$(,) x <$> f()))

zero' :: (Monad f, MonadPlus g) => Lift g f x
zero' = Lift(Ran(const$ O$ return mzero))

-- winitzki
class (Monad f) => Rigid f where
	fx ::(t->f x)->f(t->x)

ask' :: (Rigid f) => Lift((->) x) f x
ask' = Lift(Ran(O. fx))