Re: Relations contain Objects

"James" <jraustin1_at_hotmail.com> wrote in message news:a6e74506.0206141952.1ad530c7_at_posting.google.com...
> > > > Silly, you already know that objects equals domains.
> > >
> > > An object isn't equivalent to the domain or range.
> > > An object is equivalent to an element in either domain or range.
> >
> > Object class equals domain.
> > Object value equals element in domain.
>
> I think part of the problem is that our words have different meanings:
>
> Assuming
> Domain = {M1, M2}
> Range = {Marble}

Range is synonymous with domain and only has meaning for functions in which case one of the domains is sometimes called a range. Domain is the more general term used for relations.

> How does this synch with your
> interpretation?

Your model does not synch with reality. Where do you keep your instantiate function?

> Where is the "type" you are referring to in the scenario?

It makes no sense for every value to make a type independent from its own type. If we have an Integer variable whose value is 3, it makes no sense to pretend we now have a type 3. What would the values of type 3 be?

> > > > Specifically, a relation has a header consisting of a set of N
named,
> > typed
> > > > attributes and a body consisting of a set of N-dimensional tuples
with a
> > > > value corresponding to each of the named, typed attributes.
> > >
> > > Let N = 1
> >
> > If I have a relation variable of 1 dimension, I can quickly and easily
> > derive a 2 dimensional relation using cartesion product.
> > What is your product's equivalent operation?
>
> XDb also implements a 2-dimensional relation

I apologize for lack of clarity. What is your product's equivalent to the relational operation "cartesian product".

> What would a 3 or 4 dimensional relation represent?

Exactly that -- a relation in 3 or 4 dimensions. Alternatively, a set of assertions each describing 3 or 4 entities (or "objects" if one insists).

> Space and Time?

Any dimensions: Temperature, Speed, Electrical Potential, Electrical Current, Employee, Project, Department, Map, Engineering Drawing, Video, Sound Clip, Customer, Naval Vessel...

> > > Although each element has a type, there is no need to consider it at
> > > the logical level. Is there?
> >
> > Type is logically very important!
>
> What is your definition of a type?

A set of values with common semantics and the associated operations on those values.

It happens to equate to Liskov's and Wing's definition in both their 1994 and their 1999 LSP papers: "A Behavioral Notion of Subtyping" and "Behavioral Subtyping Using Invariants and Constraints" respectively.

> It important for what reason?

Semantics (ie. meaning) -- something you need to consider more in your models. If everything is an object and an object is everything and anything, object ceases to have any useful meaning.

> > > > They are the same as mathematical relations.
> > > > Each of the values in every tuple is an object in an OO sense.
>
> In XDb, one tuple is not equal to one object.
> In XDb, each value in a tuple is an object with corresponding data!!!

Huh? You clearly lack a clue.

> > > Although a tuple has a type, is there is no need to consider it at the
> > > logical level?
> >
> > Type is logically very important! For instance, two values of different
type
> > cannot be equal and equality is an important logical concept.
>
> Can you define a type precisely?

Yes, I have done so several times now. A set of values and their associated operations. Received on Sat Jun 15 2002 - 06:46:25 CEST