Thanks this was helpful.
In many of Conal Elliot's writings I see that he shows that his semantic
function is a natural transformation. Is that just basically showing the
polymorphic nature of his semantic functions, or are there other benifits
you get by showing a particular function is a natural transformation?
Daryoush
On Thu, Apr 23, 2009 at 12:34 PM, Dan Doel
Thanks for this example I get the point now. (at least i think i do :) )
One more question.... This all being on the same category then the functor transformation can also be view as a simple morphism too. In this example the listToMaybe can be viewed as morphism between list and Maybe types
On Thursday 23 April 2009 2:44:48 pm Daryoush Mehrtash wrote: that
are both in the Hask categroy too. right? If so then what would viewing the morphism as natural transformation by you?
listToMaybe in general wouldn't be a morphism in the category, because morphisms would be from concrete types to other concrete types. [1] So, if you'll excuse some notation I just made up (with a little help from GHC core notation :)):
listToMaybe@Int :: [Int] -> Maybe Int listToMaybe@Char :: [Char] -> Maybe Char listToMaybe@String :: [String] -> Maybe String
are all morphisms in the alleged Hask category. Each polymorphic function (similar to the above one, at least) defines a family of morphisms like that. *But*, that's what a natural transformation is: a family of morphisms, one for each object in the category, that commute with functor application in a certain way. Thus, one can look at the fully polymorphic listToMaybe as a natural transformation:
listToMaybe :: [] -> Maybe
-- Dan
[1] Maybe you could make up a category where polymorphic types are objects as well, but that doesn't seem to be the way people typically go about applying category theory to Haskell. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe