Re: Principle of Orthogonal Design(B

On Feb 5, 9:06 pm, Marshall <marshall.spi..._at_gmail.com> wrote:
> On Feb 5, 4:55 am, thesabote..._at_gmail.com wrote:
>
>
>
> > On Feb 3, 1:02 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
>
> > > On 2 feb, 13:50, mAsterdam <mAster..._at_vrijdag.org> wrote:
> > > [huge snips]
> > > > I think 'named perspective' was just an unfamiliar
> > > > label to a familiar concept.
>
> > > Yes. The named perspective is the usual perspective where tuples are
> > > defined as functions from attribute names to domain values, and the
> > > unnamed perspective is where they are defined as sequences. The latter
> > > is sometimes preferred in theoretical work because it is closer to how
> > > logicians formalize things (in P(x,y,z) there are no attribute names,
> > > just the 1st, 2nd and 3rd place in the predicate) and it simplifies
> > > notation sometimes.
>
> > I would echo that this is an important distinction to be aware of. I
> > personally favour the named perspective for a couple of reasons:
> > first, when Codd introduced attribute names there was an implicit
> > shift from a traditional ordered mathematical tuple, to a "tuple"
> > being viewed as an (unordered) partial function. Second, without the
> > attribute name a datum is in fact no datum at all, but rather simply
> > noise. Attributes are as much a component of the data under
> > consideration as the value they are mapped to. Hence, to disregard (or
> > rather externalize) attributes from a mathematical model of data seems
> > rather imprudent.
>
> It is a tricky issue. The approach usually used in predicate logic
> is to leave attributes unnamed and bind them to names with
> specific constructs within the context of a single sentence.
> If we bind the attributes directly to names, we get some
> convenience in the common case, but we also raise some
> issues.
>
> A common case in SQL is that we want to join two tables
> via an attribute that is the primary key of one table and a
> foreign key in another table, and they have the same name.
> Often the join is written out longhand anyway:
>
> SELECT ... from R, S WHERE R.RId = S.Rid
>
> The WHERE clause here is annoyingly boilerplate. Natural
> join, and named attributes, seem the obvious antidote to
> this boilerplate.
>
> However, suppose we have a binary predicate P over
> domain X and we want to assert it is reflexive? In predicate
> logic we can use the same name twice and express this
> very conveniently:
>
> Ax in X: P(x,x)

In my own work I prefer to view the input of the predicate as a set, given attributes are no longer ordered. So to state reflexivity I'd have:

$B"O(Bx P( { a:x, b:x } )

With the : notation just being a shorthand to represent an ordered pair. In fact, if one considers the full enumeration of the binary predicate (denoted as S), one can state reflexivity as:

$B"O(Bx { a:x, b:x } $B":(B S

Which I find kind of neat - that sort of notation allows one to get completely set-theoretic on a data model ass.

Hmmm. I really must remember to use that terminology in a paper some time.

>
> How would we do this if P's attributes were already bound
> to the names "x" and "y"? Renaming? Joining with the equality
> predicate? It seems messy, but perhaps I am overthinking it.
>
> If we have a trinary predicate P, how do we express that it
> is commutative? Associative?
>
> Any thoughts welcome.
>
> Marshall
Received on Wed Feb 06 2008 - 00:50:28 CET