[Haskell-cafe] Relating functors in Category Theory to Functor
ajb at spamcop.net
ajb at spamcop.net
Tue Jun 29 20:01:56 EDT 2004
G'day all.
Quoting "Iavor S. Diatchki" <diatchki at cse.ogi.edu>:
> 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
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