Re: Proposal: 6NF

Marshall wrote:
[...]
> There is no meaningful difference between the two;
> they are alternate, equivalent constructions.

That the actual real/integer/whatever implementation is irrelevant for math development as long as specifications are met has been mentioned many times in this thread. It's unclear why you feel need to regurgitate this trivial fact that no one disputes. Whether or not rationals are "really" a subset of reals is an implementation accident interesting only to the OOP folks and no one else.

The real discussion was *not* whether a math structure implementation matters in math (it does not), but rather whether treating a subtype as a subset in OOP is applicable to various simple mathematical structures. The OOP crowd fails utterly in this regard either when treating their datatypes as abstract specifications:

1. E.g. integers do not form a field so some rational/real properties are lost so the LSP is not satisfied.
2. set/subset talk is irrelevant for abstract specifications in the same way as it is irrelevant with respect to math structures in math.

... or when they try to use a concrete implementations (the only case when they can talk meaningfully about subtypes as subsets):

1. Whether the integers are "really" a subset of reals is an implementation dependent. Should another implementation be chosen, the 'subtype as subset' idea would not work.
2. See (1) above.

> we now have, like, nine different kinds of two? No.
> There's Only One Two, which is exactly the slogan
> of a local TV news channel from years ago.
>
> If we're going to try to say that these various twos are
> all different in anything *except* their construction, then
> I'd say we're in a heap o' trouble, hoss. If you define
> various rational arithmetic functions + - *, they're all going
> to give the same answers for calculations done with two
> either way, so what was the point again? And when we
> come to the case of divide, they *won't* produce the same
> answer, which shows that they weren't the same function
> in the first place, so we have different functions and that
> way we get the same answer again anyway.
>
> The argument that alternative constructions of two
> make for different numbers (or even that there are
> unqiue constructions) is bogus.
>
>
> Marshall
Received on Wed Oct 25 2006 - 17:51:21 CEST