Dave Bayer wrote:
Let me be as concise as I can, for a second try.
One can't make a function-valued monad into an instance of Category, because a Category takes two type arguments, while a Monad takes one? [...] I simply can't believe that I'm the first person to stumble over this. Either this is a famous rough edge, and others can list off a dozen similar circumstances where one gets stuck, or there's an easy work-around I'm just not seeing.
Can anyone confirm that it's simply not possible to plumb type classes the way I want to plumb them? If so, should I be proposing a language extension on a different mailing list?
You want a composition of functors Wrap m ~ m ° (->) but since higher-kinded polymorphism is a bit limited in Haskell (decidability!), I don't think there's a way to make this an instance of Category directly. The usual solution is to make Wrap a newtype newtype Wrap m a b = Wrap (m (a -> b)) instance Monad m => Category (Wrap m) where ... and live with it. If you want to be a bit more generic, you can use a newtype to denote functor composition {-# LANGUAGE TypeSynonymInstances #-} newtype f `O` g a b = O (f (g a b)) instance Monad m => Category (m `O` (->)) where id = return id f . g = liftM2 (.) f g But in both cases, there is no way around the fact that the Category class needs a new type as argument. Regards, Heinrich Apfelmus -- http://apfelmus.nfshost.com