These classes seem like they might correspond to concepts in category theory: class Functor f where fmap :: (a -> b) -> f a -> f b -- must satisfy: -- fmap id = id -- fmap (p . q) = (fmap p) . (fmap q) class (Functor f) => C1 f where f1 :: f (a -> b) -> f a -> f b class (C1 f) => C2 f where return :: a -> f a -- must satisfy: -- fmap = f1 . return class (C2 f) => Monad f where (>>=) :: f a -> (a -> f b) -> f b -- must satisfy: -- fmap ab fa = fa >>= (return . ab) -- f1 fab fa = fab >>= (\ab -> fmap ab fa) -- (return a) >>= p = p a -- (fa >>= p) >>= q = fa >>= (\a -> p a >>= q) What are good names for C1, C2 and f1? -- Ashley Yakeley, Seattle WA