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