question about kinds

I have the following definition:

class Traversable d where traverse :: d a -> (Maybe a, [d a])

And the standard binary tree data type:

data Tree a = Branch (Tree a) (Tree a) | Leaf a

I can define both Tree and [] to be instances of Traversable:

instance Traversable Tree where traverse (Leaf a) = (Just a, []) traverse (Branch t1 t2) = (Nothing, [t1,t2])

instance Traversable [] where traverse [] = (Nothing, []) traverse (x:xs) = (Just x, [xs])

Now, I want to say that if some data type 'd' is Traversable and another data type 'e' is Traversable, then the "combined data type" is Traversable. That is, for example, I want to say that a Tree of Lists is traversable, or that a List of Trees, or a List of Lists is traversable. But I can say neither:

instance Traversable (Tree []) where ...

or:

instance (Traversable a, Traversable b) => Traversable (a b) where ..

Because of the obvious kind errors. What I suppose I need is some sort of lambda expansion over kinds, so I could say:

instance (Traversable a, Traversable b) => Traversable (\x -> a b x)

or something like that. Obviously this doesn't exist. How can I get around this? - Hal -- Hal Daume III "Computer science is no more about computers | hdaume@isi.edu than astronomy is about telescopes." -Dijkstra | www.isi.edu/~hdaume