Re: Proposal: 6NF
Date: 19 Oct 2006 05:55:08 -0700
Message-ID: <1161262508.205808.208850_at_i3g2000cwc.googlegroups.com>
vc wrote:
> Jan Hidders wrote:
> [...]
>
> A much simpler example. Let {0, 1, 2, 3} be a set of four integers
> with addition modulo 4. Then, none of its subsets, except {0} and
> {0, 2}, retains the addition mod 4 operation which makes the idea of
> 'subtype as subset' utterly silly, [....].
> Also, the OOP hypothetical programmer would expect that a subtype
> would have, informally speaking, *more*
> properties/operations/'methods', not less: the basic class properties
> plus some new ones. So at the intuitive level with typical languages
> like Java, 'subtype as subset' does not make much sense either, at
> least with respect to even the simplest mathematical objects.
No, also from that perspective it works correctly. The superclass A
would contain objects that understand the message plusMod4 with an
argument that is in class A and return a result in class A. The objects
in the subclass B would also understand this message with an argument
in class A and return a result in class A. So there is no problem with
defining the extensions of class B such that it is a subset of class A.
So, again, no problem whatsoever.
- Jan Hidders