Joe Fredette wrote:
I fiddled with my previous idea -- the NatTrans class -- a bit, the results are here[1], I don't know enough really to know if I got the NT law right, or even if the class defn is right.
Any thoughts? Am I doing this right/wrong/inbetween? Is there any use for a class like this? I listed a couple ideas of use-cases in the paste, but I have no idea of the applicability of either of them.
/Joe
A few problems there: (1) The |a| should be natural, i.e. universally qualified in the class methods, not an argument of the typeclass. (2) Just because there's a natural transformation from F to G does not mean there's a "related" natural transformation back. The law you want is, forall (X :: *) (Y :: *) (f :: X -> Y). eta_Y . fmap_F f == fmap_G f . eta_X (3) There can be more than one natural transformation between two functors. Which means a type class is the wrong way to go about things since there can only be one for the set of type parameters. Consider for instance: type F a = [a] type G a = [a] identity :: F a -> G a identity [] = [] identity (x:xs) = (x:xs) reverse :: F a -> G a reverse = go [] where go ys [] = ys go ys (x:xs) = go (x:ys) xs nil :: F a -> G a nil = const [] ... -- Live well, ~wren