[Haskell-cafe] lifting restrictions on defining instances

[porges at porg.es]

[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
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