PROPOSAL: Make Applicative a superclass of Monad

[Isaac Dupree]

Ashley Yakeley wrote:
> For example:
> 
> class Functor f => Applicative f where
>   return :: a -> f a
>   ap :: f (a -> b) -> f a -> f b
>   (>>) :: f a -> f b -> f b
>   (>>) = liftA2 (const id)

for backwards compatibility of everyone who *uses* Applicative, (and 
arguably it is a less ugly notation,) :

(<*>) = ap
(and  pure = return)

I'm not sure, is the word "ap" even as well known as "<*>" right now?  I 
wonder which one we'd prefer to use in Applicative?

> class Applicative m => Monad m where
>   (>>=) :: m a -> (a -> m b) -> m b
>   fail :: String -> m a
>   fail s = error s

I want to add to this Applicative=>Monad class:

     join :: m (m a) -> m a
     join mm = mm >>= id
     m >>= f = join (fmap f m)

What do others think about that?


(P.S. And I guess this hierarchy change is quite independent of the 
difficult task of removing "fail" from Monad, so I won't discuss that 
here/now)

-Isaac