Yes, I have tried both implementations at the start and solved it by choosing for the following: type family F a :: * -> * type FList a x = Either () (a,x) type instance F [a] = FList a instance (Functor (F [a])) where fmap _ (Left _) = Left () fmap f (Right (a,x)) = Right (a,f x) The option was: type family F a x :: * type instance F [a] x = Either() (a,x) instance (Functor (F [a])) where -- error, not enough parameters passed to F fmap _ (Left _) = Left () fmap f (Right (a,x)) = Right (a,f x) So, indeed, with either implementation I have a problem.
I have my suspicions about your mentioning of both Functor (F d) and Functor (F a) in the signature. Which implementation of fmap do you want? Or should they be both the same (i.e. F d ~ F a)?
This is an hard question to which the answer is both. In the definition of an hylomorphism I want the fmap from (F d): hylo :: (Functor (F d)) => d -> (F d c -> c) -> (a -> F d a) -> a -> c hylo d g h = g . fmap (hylo d g h) . h However, those constraints I have asked about would allow me to encode a paramorphism as an hylomorphism: class Mu a where inn :: F a a -> a out :: a -> F a a para :: (Mu a, Functor (F a),Mu d, Functor (F d),F d a ~ F a (a,a), F d c ~ F a (c,a)) => d -> (F a (c,a) -> c) -> a -> c para d f = hylo d f (fmap (id /\ id) . out) In para, I would want the fmap from (F a) but that would be implicitly forced by the usage of out :: a -> F a a Sorry for all the details, ignore them if they are too confusing. Do you think there might be a definition that would satisfy me both Functor instances and equality? Thanks for your pacience, hugo