Re: Clean Object Class Design -- Circle/Ellipse

[posted and mailed]

macdonaldrj_at_att.net (Richard MacDonald) wrote in <xEHf7.22358$1p1.1750638_at_bgtnsc04-news.ops.worldnet.att.net>:
>> 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.

In the case of addition we are, but not in the general case. The you have to look at multi sorted algebras, but let's not go there since we're having enough communication problems already...

Martijn Received on Sun Aug 19 2001 - 10:41:54 CEST