Casey McCann
{-# LANGUAGE MultiParamTypeClasses, GADTs #-} import qualified Control.Category as Cat
data ChainableFunction a b where CF :: (Num a, Num b) => (a->b) -> (a->b) -> ChainableFunction a b CFId :: ChainableFunction a a
instance Cat.Category ChainableFunction where id = CFId CF g g' . CF f f' = CF (g.f) (\a -> f' a *> g' (f a)) CFId . f = f g . CFId = g
You've probably noticed that I've been ignoring the Module class. Unfortunately, the solution thus far is insufficient; a Module constraint on the CF constructor does work as expected, providing a context with (Module a b, Module b c), but the result requires an instance for Module a c, which neither available, nor easily obtained. I'm not sure how best to handle that issue; if you find the rest of this useful, hopefully it will have given you enough of a start to build a complete solution.
- C.
Thanks for the comment. If we try to use GADT to construct Cat.id, actually (Numa) constraint is redundant because I just want "1" for first derivative of x. However instance (Module a b, Module b c) => Module a c is a must for chain rule... I'm looking at Data.Category suggested by Jason, because it allows subset of Hask object to be applied into parameters