On 2 Jan 2008, at 5:49 AM, Yitzchak Gale wrote:
Hi Andrew,
Andrew Bromage wrote:
I still say it "isn't a set" in the same way that a group "isn't a
set".
Haskell data types have structure that is respected by Haskell
homomorphisms. Sets don't.
Ah, that's certainly true. But what is that additional structure?
In categories that have a forgetful functor to Set, the interesting
part of their structure comes from the fact that their
morphisms are only a proper subset of the morphisms
in Set.
So in what way are Set morphisms restricted from being
Hask morphisms?
The normal view taken by Haskellers is that the denotations of
Haskell types are CPPOs. So:
(1) Must be monotone
(2) Must be continuous
(Needn't be strict, even though that messes up the resulting category
substantially).
jcc
_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
