On Wed, Feb 24, 2016 at 11:22 AM, Kosyrev Serge <_deepfire@feelingofgreen.ru> wrote:

Are you also saying that this cannot be resolved by some kind of a
type families-based type-level 'flip'?

It really can't, no. You can define

type family FlipF f a b where

FlipF f a b = f b a

but FlipF, being a type family, is not first-class. You can't make any instances whatsoever for FlipF f a -- you'll probably get an error about a partially applied type family. What you *can* do is make a Flip newtype:

newtype Flip f a b = Flip {unflip :: f b a}

This behaves perfectly:

instance Bifunctor f => Functor (Flip f a) where

fmap f = Flip . first f . unflip

instance Profunctor f => Contravariant (Flip f a) where

contramap f = Flip . lmap f . unflip

instance Bifunctor f => Bifunctor (Flip f) where

bimap f g (Flip x) = Flip (bimap g f x)