On Thursday 23 April 2009 2:44:48 pm Daryoush Mehrtash wrote: > 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 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 :)): listtoma...@int :: [Int] -> Maybe Int listtoma...@char :: [Char] -> Maybe Char listtoma...@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
