I was inspired by George Pollard's posthttp://www.haskell.org/pipermail/haskell-cafe/2009-July/063981.htmlat haskell-cafe and tried to implement the non-polymorphic Functor class ( I named it Functor' ). I changed some names and added reasonable constraints. type family NewPt f a class Functor' f where type Point f map ∷ (a ~ Point f, b ~ Point g, g ~ NewPt f b, Functor' g) ⇒ (a → b) → f → g I would like to be able to write: type OldPt f = NewPt f (Point f) class (f ~ OldPt f) ⇒ Functor' f ... but ghc says it's not implemented yet (version 6.12.1). However, it's not the main problem. Now I can write some instances: type instance NewPt [a] b = [b] instance Functor' [a] where type Point [a] = a map = fmap type instance NewPt ByteString a = ByteString instance Functor' ByteString where type Point ByteString = Word8 map = BS.map But I can't write instance for Set: type instance NewPt (Set a) b = Set b instance Ord a ⇒ Functor' (Set a) where type Point (Set a) = a map = Set.map ghci complains: Could not deduce (Ord a1) from the context (g ~ NewPt (Set a) a1, a1 ~ Point g, Functor' g) arising from a use of `Set.map' at ... The type of Set.map is Set.map :: (Ord a, Ord b) => (a -> b) -> Set a -> Set b (Ord a) is in the instance context, and what about b? Type of map for Set instance would be: original: map ∷ (a ~ Point f, b ~ Point g, g ~ NewPt f b, Functor' g) ⇒ (a → b) → f → g substitute: f → Set a, g → Set b map :: Functor' (Set b) ⇒ (a →b) →Set a →Set b (Ord b) must be deduced from (Functor (Set b)) but it doesn't. I don't know whether it's my mistake somewhere or ghc problem. (Sorry for my English, it's not perfect). -- All the best, Alexey