Re: Stored fields ordered left to right

Dawn M. Wolthuis <dwolt_at_tincat-group.com> schrieb:
> "Adrian Kubala" <adrian_at_sixfingeredman.net> wrote:
>> Functions are one-way mappings. Many relationships in the world work
>> both ways. It certainly seems useful to distinguish these two kinds of
>> relationships, which relations + functions does but functions alone does
>> not.
>
> This must be another issue of definitions because there are no
> functions in mathematics that are not relations. Functions are a
> particular type of relation.

I had assumed you were talking about representation. There is clearly some difference between, i.e. the function y = x and the relation {<0,0>, <1,1>, <2,2>, ...}. For example, it would be impossible to enumerate that relation explicitly in memory. On the other hand, some functions are such that if you express them implicitly as equations it is harder to solve for some variables than others. That's why I say both representations have merit, but that for the kinds of relations represented in a database it's usually simplest to express them explicitly.

Since you were not talking about relations vs functions in terms of their representation, I don't understand your original point. All functions are relations but not all relations are functions, therefore a function-only database is strictly less expressive than a fully-relational one with no benefits.

On the other hand, if a database allowed you to describe *some* relations as functions and took advantage of algebraic reasoning when creating derived relations from these functions, that would be really neat. But then you'd basically have a kind of Prolog, right? Received on Sat Jan 10 2004 - 23:59:04 CET