View source for Functor hierarchy proposal

#REDIRECT [[Functor-Applicative-Monad Proposal]]

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

<haskell>
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
</haskell>

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

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

The downside of this is that every instance declaration of <tt>Monad</tt> 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 <hask>Pointed</hask> class from the <hask>Applicative</hask> class.

<haskell>
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
</haskell>

Such <hask>Pointed</hask> 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.


[[Category:Proposals]]
[[Category:Functor]]
[[Category: Pages to be removed]]