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   RE: [xml-dev] Subtyping in XML

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> Jeff Lowery scripsit:
> > I guess the point I'm trying to make is that we seem to narrow our
> > definitions of universal types to only those that have validatable
> > membership and universal representation.  There are a lot 
> of well-understood
> > types they fail both criteria.
> > 
> > Prime numbers.
> Say what?  Every prime number has a unique lexical representation,
> and there is an effective test for telling primes from non-primes.

Sorry, I must be abusing terms again.  By 'lexical' I meant something like a
number being expressible as arabic or roman numerals. If that's the wrong
term, give me another.

> That looks like universal representation and validatable 
> membership to me.

Not practically, I didn't think.  If I'm wrong, change it to the type whose
members are the result of  multiplying two primes. I hope that one's still
tough.  Again, abuse of terminology: computable, yes, but not in a practical

I'm guessing that there are types whose members can only be reasoned by
induction, but I could be wrong.   It's the impracticality of validation of
some members that I'm trying to express. And that may vary depending on
local resources. 

> Whether it's important to any particular user to actually validate is
> another concern.  If so, the receiver just specifies a local 
> scheme that
> specifies xsd:integer rather than jl:prime as the type.

Yeah, but he's not really validating the value to the extent necessary to
ensure his computations are giving correct results. 

> Now if you wanted a type without either, consider "beautiful 
> thoughts".

Do you have a rigorous definition for those?  

> -- 
> John Cowan  jcowan@reutershealth.com  www.ccil.org/~cowan  
> www.reutershealth.com
> "If I have not seen as far as others, it is because giants 
> were standing
> on my shoulders."
>         --Hal Abelson


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