Re: Clean Object Class Design -- Circle/Ellipse

"Marc Gluch" <marc.gluch_at_mindtap.com> wrote in message news:3b7f0e59.3694223272_at_news.grpvine1.tx.home.com...
> On Thu, 18 Oct 2001 20:29:43 -0400, "Bob Badour" <bbadour_at_golden.net>
> wrote:
>
> >>>>The only "fool-proof" way of deciding if A is a subtype of B,
> >>>>that I know, is to treat A and B as formal theories.
> >>>>
> >>>>The first questions to consider would be:
> >>>>Are A and B consistent?
> >>>>Does one make more assumptions (postulate more axioms) than the other?
> >>>
> >>>
> >>>Are you arguing that every subtype must postulate more axioms than its
> >>>supertype does?
> >>Yes.
> >>Note that you can't produce the axiomatization of Integers
> >>by extending the axiomatization of Reals (or Rationals).
> >>You actually would have to drop some axioms.
> >
> >Which axioms would I have to drop? The axiom that every integer has a
 real
> >multiplicative inverse? I don't agree that I have to.
>
> Axioms of a theory are expressed in terms of primitives of that theory
> When you say
> Axiom MI: For all x =/= 0 in D there is y in D such that x * y = 1
> you are talking about some domain D.
> For IA = <D, {+.*, = , <}> D is the set of integers and MI holds,
> for RA, D is is the set of rationals (or reals) and MI does not hold.

Marc, what is the point of this? An axiom limited to functions where the argument and result are the same type isn't any good for building a type theory. Bob's point -- that a person's age isn't another person -- is a good example of the lunacy. We're not looking for operations that are self-contained within a given type. We're looking for operations that
map from one type to another type and then exploring what gives between the super-/sub-type relationships in those mappings.

I know you know all this, so what is the point of this thrust? My head is still swimming from trying to follow you guys. Perhaps you can come up for air and give us an update :-? Received on Sun Aug 19 2001 - 06:54:53 CEST