Re: boolean datatype ... wtf?

On Sep 29, 7:07 am, Erwin <e.sm..._at_myonline.be> wrote:
> On 29 sep, 15:46, paul c <toledobythe..._at_oohay.ac> wrote:
>
>
>
>
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> > On 29/09/2010 4:51 AM, Paul Mansour wrote:
> > ...
>
> > > What is the problem with a Boolean data type?
> > > .
> > > It is fundamental - so fundamental  that in TTM it is the only
> > > required scalar data type:  “We require that at least one built-in
> > > scalar type be supported : Namely, type “Boolean” (BOOLEAN in Tutorial
> > > D”).
>
> > > Date and Darwen go on to give the obvious reasons for this.
>
> > > The fact that DEE and DUM may be interpreted as TRUE and FALSE is not
> > > relevant.  The result of A=B or A>B is not a relation.
>
> > Aren't A=B and A>B relations?
>
> Here we go again ...
>
> But then again, incidentally, he did not say that 'A=B' isn't a
> relation.  He said that _THE RESULT OF_ 'A=B' isn't a relation.
>
> Conceptually, it could be argued that what a language implementation
> achieves when it evaluates an expression such as 'A=B', is to join a
> tuple {A,B} with the EQUALS relation (which is implicitly defined by
> the system) of the pertinent type, and then check whether the result
> of that join is empty or not ...
>
> Fair bit of hairsplitting going on, if you ask me ...- Hide quoted text -

I would argue that we join (ordinary finite) relations with equality predicates much more often that it appeared at the first sight. One operation which utility can rival that of natural join is composition (aka set intersection join). This is merely a natural join projected to the set of distinct attributes. For example composition of

Pets=[nickname specie]

      folly    dog
      scruffy  cat

with

Fed=[name nickname time]

     claire  folly   200
     max   folly    200
     max   folly    300
     max   scruffy  200

is

Pets/^Fed=[name specie time]

           claire  dog  200
           max  cat  200
           max  dog  200
           max  dog  300

It is essentially natural join with the common column "nickname" REMOVEd (to use A-Algebra terminology:-).

Renaming -- which is arguably second most used relational operation -- is composition with equality predicate:

Pets/^[nickname=petname]=[petname specie]

                          folly  dog
                          scruffy  cat