On Tue, May 11, 2010 at 2:01 PM, Gordon J. Uszkay
I would like to build a class that includes a method to move data from one arbitrary functor to another, a natural transformation. The structures might be more than just functors, but I can start with that. I ran into some practical issues with resolving the type variables for my multiparameter type class, which I can resolve with functional dependencies. I can also not isolate the natural transformation from my overall operation, muddling it with the element transformation. I was wondering if anyone had any words of advice, example or warning about this kind of function or method in general?
Class (Functor f, Functor g) => Foo f g a where foo :: f a -> g a bar :: (a->b) -> g a -> g b
In general I would shy away from encoding natural transformations as a typeclass describing one family of morphisms of the form f a -> g a. I would avoid it because the choice of function f a -> g a isn't really canonical. There are many potentially valid such functions. foo :: Maybe a -> [a] foo (Just a) = [a] foo Nothing = [] bar :: Maybe a -> [a] bar (Just a) = repeat a bar Nothing = [] baz :: Maybe a -> [a] baz _ = Nothing quux n :: Int -> Maybe a -> [a] quux (Just a) = replicate a n quux Nothing = Nothing With that in mind an arguably better approach would be to define a natural transformation as: type Nat f g = forall a. f a -> g a or even type f :~> g = forall a. f a -> g a and pass them around explicitly then you can encode things like: hylohttp://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/...:: Functorhttp://hackage.haskell.org/packages/archive/base/4.2.0.1/doc/html/Control-Mo...f => Algebrahttp://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/...g b -> (f :~>http://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/...g) -> Coalgebrahttp://hackage.haskell.org/packages/archive/category-extras/0.53.5/doc/html/...f a -> a -> b hylo f e g = f . e . fmap (hylo f e g). g This is important because there can exist such natural transformations that need data out of your current environment: i.e. the natural transformation ((,) x), the quux example above, etc. -Edward Kmett