G'day all.
Quoting "Iavor S. Diatchki"
just a few silly remarks...
Not so silly...
actually i think this is a good approximation. not all polymorphic functions are natural transformations, but "simple" ones usually are.
I've found when studying category theory that expressing this stuff in Haskell REALLY helps. Haskell was a familiar notation, where category theory notation was not. Being able to freely translate between the two helps. In this case, recognising _which_ polymorphic functions are natural transformations help you understand what a natural transformation is. A natural transformation in Haskell is a function of the form: tau :: f a -> g a where f and g are specific Functors. In the book by Saunders MacLane, there was one remark about natural transformations which really helps. He noted that a natural transformation is one that's done
it is not a good idea to have a _class_ for natural transformations as they have little to do with overloading.
Indeed. If you actually want to get work done in Haskell, making a class for this is a bad idea. But then there are easier ways to do this, too: http://www.haskell.org/hawiki/StudyGroup/GraphExamplesInHaskell My point is that Haskell is a good and (for most people on this mailing list) familiar notation for expressing these concepts. Cheers, Andrew Bromage