Re: [Haskell-cafe] Relating functors in Category Theory to Functor

[Iavor S. Diatchki]

hi,
just a few silly remarks...
[EMAIL PROTECTED] wrote:
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
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
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