For two functors F, G: C -> D, there is a natural transformation tau from F to G, if for every object a in C, there is morphism tau[a]: F(a) -> G(a) in D.
In Haskell, natural transformations are polymorphic functions, tau :: f a -> g a. For example, maybeToList :: Maybe a -> [a].
actually i think this is a good approximation. not all polymorphic functions are natural
hi, just a few silly remarks... ajb@spamcop.net wrote: transformations, but "simple" ones usually are.
Not quite. A natural transformation is a mapping between _functors_. In this case, maybeToList is a natural transformation between Maybe and []. Expressing this as a typeclass is left as an exercise, but here's a start:
class (Functor f, Functor g) => NaturalTransformation ... where ...
it is not a good idea to have a _class_ for natural transformations as they have little to do with overloading. there can be many different natural transformations between two functors, so it does not make sense to give them all the same name. -iavor