Functor hierarchy proposal
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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. Various schemes have been proposed to create a richer hierarchy of Functor classes. Here's a typical example:
class Functor f where fmap :: (a -> b) -> f a -> f b
class (Functor f) => Idiom f where ap :: f (a -> b) -> f a -> f b return :: a -> f a
class (Idiom f) => Monad f where (>>=) :: f a -> (a -> f b) -> f b
satisfying the usual Functor and Monad laws, and
fmap = ap . return ap fab fa = fab >>= (\ab -> fmap ab fa)
The downside of this is that every instance declaration of Monad would have to be accompanied by instance declarations for the superclasses.