[Aldor-l] 'Domain' in 'SetCategory'?
nic at worldofnic.org
Tue Jul 8 17:27:08 EDT 2008
Bill Naylor pointed me at this discussion, so I've quickly subscribed.
I'm less familiar with Aldor - Axiom 1.x/2.x was more my thing.
I am rather confused as to Aldor's "Type" - from my brief perusing of
the e-mail chain, it appears to be a meta-programming piece of fun,
which you are now stuck with, not derived from a piece of serious
Mathematical design ??? (Pinch of salt required, perhaps).
My view (from my Axiom-centric brain) is to get rid of it. Why should
a both Integer and SetCategory have "Type"? Obj(SetCategory) doesn't
form a Set, but you want to think of it in the same way as the
collection (set) of all Integers? From some purist view, you may want
to use Functors and deal with Classes (things that don't form Sets) in
the same way as you use +(Int, Int) -> Int but In Axiom they are
fundamentally different, and changing that would involve rewriting
pretty much all of it from scratch.
Note: I don't think the notation "Integer \in Obj(Ring)" is my
invention - it may be from Mac Lane, but I can't remember.
If I've got the wrong end of the stick let me know. I'm a bit rusty.
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