On Mon, Feb 07, 2005 at 06:54:50PM -0800, Ashley Yakeley wrote:
These classes seem like they might correspond to concepts in category theory:
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
fmap+return is often called a premonad. I don't know of a good name for fmap+return+f1. Doaitse Swierstra calls the class Sequence and calls f1 (<*>), Conor McBride calls it Idiom, and I'd call it a weakly symmetric lax monoidal functor or a strong lax monoidal functor. There are more equations, too; see http://www.haskell.org/arrows/arrows/Control.Sequence.html Also Conor's hack: http://www.haskell.org//pipermail/haskell/2004-July/014315.html