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There's one loophole I've been thinking is needed for some local types
(types that are not universal):
A local type might only be rigorously defined for a subset of members.
This would allow local types to be "frayed around the edges" as it were.
Calendar systems might be an example, where there a could be ambiguity about
dates in the past (not of events, but of actual dates). Local types that are
frayed at one edge or another could only support value mappings to other
local or universal types where membership is well-defined.
This allows some unavoidable slop in a local (established) type system
without forcing other types to adjust to the uncertainties.
BTW, this all would be offtopic except that there seems to be no agreement
on what constitutes an appropriate universal type system for XML. It seems
a worthwhile effort to deconstruct the notion of what a data type is.
>
> No. I want to be able to define any simple type I want. This includes:
>
> 1) types based on mathematical axioms and proofs
> 2) types whose values are determined by laws of nature (empirical and
> repeatable)
> 3) types based on rigidly defined international standards
> I also want:
> 4) types based on specific locale
>
> All of these would have clearly defined membership (value spaces).
>
> Some of these values spaces would not be computable.
>
> Of those that are computable, some would be prohibitively expensive to
> validate.
>
> All, however, would allow the unambiguous communication of a concept.
>
> All types must have at least one lexical representation to be
> meaningful.
>
> A type may have a universal lexical representation, or it may not.
>
> A universal lexical representation must be capable of
> depicting all values
> of the type.
>
> A type may have both universal and local representations, or
> only local
> representations.
>
> Local lexical representations may only allow depiction of
> _some_ values of
> a type.
>
> For those types with universal representations, a local
> representation _may_
> have a defined mapping to the universal representation.
>
> For types lacking an accepted universal lexical rep, then
> each local rep
> _may_ describe mappings to other local reps.
>
> A local rep _may_ have only a partial mapping to another local rep.
>
> Existence of a universal lexical space does not prohibit direct
> locale-to-locale mappings.
>
> All respresentations of values in a locale must have a
> provable mapping to
> one and only one universal rep (if it exists).
> Implementations of such
> mappings do not have to be provided or made available.
>
> Local representations can be intersected with where partial
> mappings are
> available. The resulting lexical and value space must be well defined.
>
> --------
>
> In other words, types first and formost define a concept of
> membership.
> Such definitions must be formal and unambiguous.
>
> If it's validatable, great.
>
> If it has a universal representation, great.
>
> If it has one or neither, it's still useful for articulating
> what a data
> value _is_.
>
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