Re: Operationalize orthogonality
Date: Wed, 31 May 2006 02:04:07 GMT
Message-ID: <rQ6fg.34544$YI5.13890_at_tornado.ohiordc.rr.com>
Pickie wrote:
> Tony D wrote:
>
>>The only type absolutely required is the boolean type. You could (and I >>stress, *could*) attempt to model everything from there on up in terms >>of relations and booleans, but that would require a frightening degree >>of circumlocution.
>
> How would you represent a count (IE the non-negative integers) using
> only booleans and relations?
You shouldn't. The point is that the relational model requires only boolean scalars and the corresponding nullary, unary, and binary operators. Beyond that, an RDBMS is expected to provide a mechanism whereby other types and operators can be defined. What types? Well, integers, rationals, characters, and strings are undoubtedly useful. How 'bout internet addresses? Points? Complex numbers? States? Music? Telephone numbers? Mass? Length? Raster images? Vector drawings? You bet! It's all up to the user of the database system The only thing the relational model demands is that, for each type, an operator must be provided that can determine whether two values of the same type are different.
How would you represent a text string? I
> ask because these seem to me to be basic concepts (or primitive types?)
> and both of them have simple ways to represent a boolean (zero and
> empty string respectively being false, all else true).
It is expected that various RDBMSs would provide "off the shelf" support for the types you consider primitive. But it could well be that a user would want to define a numeric type that did arithmetic a bit differently than they way you were probably taught in school. My running example is that proposed by Iverson and made manifest in APL and J: any value divided by itself is 1 - including "zero divided by zero." Rationals are considered equal if they're close to each other. How close? There's an epsilon value - commonly called fuzz - that specifies closeness.
At a "higher" level, consider states: we all recognize that TX and Texas and Tex. are the same value, right? (I'm not talking about the sequence of characters -- I'm talking about what they represent.) An RDMS should provide a mechanism whereby a user can define a STATE type which happens to know that all these are acceptable representations of the same value. Received on Wed May 31 2006 - 04:04:07 CEST