[Ack, missed the reply-all button...] This was part of my motivation behind the 'removing polymorphism from Functor' thing... to select a different parameter we'd essentially need type-level lambdas... I'll use 'Λ' (capital lambda) for it: instance Functor (Λ a. X a b) where fmap f (X a b) = X (f a) b We don't have these [1], but we *do* have type families, which are kind of like type-level lambdas turned 'inside out' (at least to my eyes), so my idea was to separate this out: type family Point :: * type instance Point (X a b) = a class Functor f where fmap :: (Point f -> Point f) -> f -> f Here I began to run into problems which are a bit irrelevant to this discussion :) [1]: I'm not sure of the exact connection, but see, e.g. Oleg's construction of computation at the type level (http://okmij.org/ftp/Haskell/TypeLC.lhs), wherein he notes the "primary role of type application rather than that of abstraction". - George