Re: Notions of Type

From: J M Davitt <jdavitt_at_aeneas.net>
Date: Fri, 18 Aug 2006 02:46:40 GMT
Message-ID: <kS9Fg.77099$Eh1.22703@tornado.ohiordc.rr.com>

paul c wrote:
> J M Davitt wrote:
>

>> David Cressey wrote:
>>
>>> "Marshall" <marshall.spight_at_gmail.com> wrote in message
>>> news:1155833602.403082.5690_at_h48g2000cwc.googlegroups.com...
>>>

> ...
>

>>> I'm surprised the PROJECT is such a problem.  Maybe I should stay out 
>>> of the
>>> discussion,  because this is a little over my head.  But here goes, 
>>> anyway:
>>>
>>> Why can't you define a "set of attributes"  as a relation?  I'm thinking
>>> that an empty relation  (one with no tuples) has exactly the same
>>> information content as a "set of attributes".  If you do that,  why 
>>> can't
>>> you say,
>>>
>>> PROJECT <relation>, <empty relation>  ->  <relation>
>>>
>>>
>>> Or have I violated some other aspect of the formalism?
>>
>>
>> Wait a minute...
>>
>>   PROJECT <relation> <set of attributes> -> <relation>
>>
>> right?  And the question is, "Does this definition of
>> PROJECT demonstrate lack of algebraic closure?"  I think
>>
>>   PROJECT <relation> <relation> -> <relation>
>>
>> is a step in the wrong direction and don't think such a
>> thing is necessary for closure.  I think that the fact
>> that one of the operands and the result are relations is
>> what provides closure.

>
>
> Earlier, Bob B said about the "set of attributes": "It is a relation of
> degree 1 and cardinality N representing a set of N attribute names".
> Maybe you are right and saying that isn't necessary, but his stance
> seems to me to obviate the question.
>
> (I don't know if it matters that if his approach is right, projection
> wouldn't depend on whatever the name of the single attribute is - I
> presume that it would have the same name and type as all headers in the
> db, eg., just another axiom in the form of the catalog.)
>
> p

In some regard, BB's relation is just fine. In D+D's works, a set of attributes wouldn't be a relation value: no heading.

This is one of the areas, I think, where we've been writing "relation" and, in the D+D sense, some think "relation values" and others, in the RA sense (to the extent I understand it), think "relations."

There are differences in the definition of operations in the two; is this one instance?

[Or, it could just be me...] Received on Thu Aug 17 2006 - 21:46:40 CDT