Re: no names allowed, we serve types only

On Feb 23, 12:49 am, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 22 feb, 15:39, Jan Hidders <hidd..._at_gmail.com> wrote:

> > There is indeed a problem with the subtype = subset principle, or at
> > least the one that I had in mind:
>
> > - if t1 <= t2 then [[t1]] is a subset of [[t2]]
>
> > where [[t]] denotes the set of all values that are of type t. Sorry
> > for being unclear about that.
>
> > The restriction that f in the definition should be uniquely defined is
> > implied by this principle, which IMNSHO makes it not ad-hoc or
> > gratuitous but rather well-founded. The proof is left to the reader as
> > an exercise. ;-)

My problem is that there may be existing types t1,t2,t3,t4 and an existing declared relation-type with H2 = {t3,t4}. Someone wants to create a new relation-type with H1 = {t1,t2} that subtypes H2, perhaps where it is required that t1,t3 represent one role and t2,t4 represent another. However it happens that both t1 and t2 subtype both t3 and t4 so therefore it cannot be done because of ambiguity. That seems unreasonable.

> PS. Note that the corrected definition can be compactly formulated:
>
> Definition: H1 <= H2 if
> for each type t2 in H2
> there is exactly one type t1 in H1
> such that t1 <= t2.

That doesn't seem right to me - by that definition H1 might have more attributes than H2 and yet be considered a subtype. Received on Tue Feb 23 2010 - 01:33:04 CET