Re: Proposal: 6NF

Keith H Duggar schreef:

> Bob Badour wrote:
> > Jan Hidders wrote:
> > > Why is that so? In order to allow Z to be a subtype of R
> > > in a database universe we only need to be able to
> > > injectively map the elements of Z to elements of R such
> > > that it is a homomorphism for presumed identical
> > > operations. The latter means for example that if f : Z
> > > -> R is the mapping and +_R the real addition and +_Z
> > > the integer addtion then it should hold that f(a) +_R
> > > f(b) = f(a +Z b). Why is that sufficient? If this holds
> > > then we can define a two-sorted algebra that combines
> > > the two algebras and their operations such that Z is
> > > subset of R. You see that the division for R can then
> > > also be used for Z since it has type RxR->R and Z is a
> > > subset of R. So, in that sense, it is RxR->then
> > > "inherited" by Z.
> > >
> > > So, summarizing, you see that the requirement is not
> > > that the algebra for the subtype should contain all the
> > > operations of the the algebra of the supertype.
> >
> > I don't see that at all, Jan. The Integer inherits the
> > division operation that returns a Real. It's just not part
> > of the integer algebra. The integer type does indeed
> > introduce additional operations, which is why many
> > languages will distinguish between / and div for instance.
>
> Unless I misunderstood one of you, I think you and Jan are
> saying the same thing. Jan said that we /can/ (though need
> not) "define a two-sorted algebra that combines the two
> algebras and their operations" for example:[...]

Indeed. Thanks Keith. I was already wondering if I had explained it that badly. :-)

• Jan Hidders