Re: Proposal: 6NF

From: Jan Hidders <>
Date: 19 Oct 2006 05:55:08 -0700
Message-ID: <>

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}.

> 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
Received on Thu Oct 19 2006 - 14:55:08 CEST

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