Re: Proposal: 6NF

From: Marshall <marshall.spight_at_gmail.com>
Date: 19 Oct 2006 15:33:15 -0700

On Oct 19, 7:06 am, "vc" <boston..._at_hotmail.com> wrote:
> Jan Hidders wrote:
> > 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, [....].
> >
> > You keep on making the same mistake. The expression a +[mod 4] b has a
> > well defined result if a and b are from any subset of {0, 1, 2, 3}.
>
> Consider the subset {2, 3}. What is the result of (2+3) mod 4 ? If
> you say it's '1', what is '1'? There is no such element in {2, 3}.

> > > 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.
>
> Objects in subclass B = {2, 3} won't understand 'plusMod4' because the
> operation does not exist in B, it was lost as soon as you've subsetted
> A = {0,1,2,3}. That is of course if you understand 'operation' in the
> ordinary mathematical sense such that the set is closed under it. If
> you have to go outside the set in question, it ain't no operation no
> more in the accepted mathematical sense.

class ModFour {
private final int val;
ModFour(int i) {
if (i < 0 || i > 3) throw new RuntimeException();     val = i;
}

}

public class TwoOrThree extends ModFour {   TwoOrThree(int i) {
super(i);
if (i < 2 || i > 3) throw new RuntimeException();   }

Marshall Received on Fri Oct 20 2006 - 00:33:15 CEST

Original text of this message