Functor hierarchy proposal

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• Functor-Applicative-Monad Proposal

Currently the standard libraries include a Functor class and a Monad class, and Functor is not a superclass of Monad, even though logically every monad is a functor. New classes have been added to HEAD to create a richer hierarchy of Functor classes:

class Functor f where
  fmap :: (a -> b) -> f a -> f b

class Functor f => Applicative f where
  pure :: a -> f a
  (<*>) :: f (a -> b) -> f a -> f b

  (*>) :: Applicative f => f a -> f b -> f b
  fa *> fb = (fmap (const id) fa) <*> fb

I propose that "pure" be renamed "return", "*>" be renamed ">>", and that Monad be made a subclass of Applicative:

class (Applicative f) => Monad f where
  (>>=) :: f a -> (a -> f b) -> f b

The downside of this is that every instance declaration of Monad would have to be accompanied by instance declarations for the superclasses, but see Class system extension proposal.

It might also be useful to split a Pointed class from the Applicative class.

class Pointed f where
    pure :: a -> f a

class (Functor f, Pointed f) => Applicative f where
  (<*>) :: f (a -> b) -> f a -> f b

  (*>) :: Applicative f => f a -> f b -> f b
  fa *> fb = (fmap (const id) fa) <*> fb

Such Pointed functionality by itself could be useful, for example, in a DSL in which it is only possible to embed values and not to lift functions to functions over those embedded values.