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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
> 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
Do you have a rigorous definition for those?
> John Cowan email@example.com www.ccil.org/~cowan
> "If I have not seen as far as others, it is because giants
> were standing
> on my shoulders."
> --Hal Abelson