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> Simple types are very low-level (and programming language specific)
> 'Universal' types do not exist.
In the field of mathematics, I would dare say there are many conceptual
types that are universal. I don't think there's any disagreement about what
an integer is, for instance.
It's when we convert these conceptual types to physical ones that can be
represented on a computer that problems arise: there's no universal physical
binary representation of an integer, nor are their common value ranges in
the various computing languages.
I'm sure someone, somewhere in academia has done work in identifying
universal conceptual types (meta-types?) for strings, etc. What I wonder is
if we need to explicitly adopt universal types as a basis for
specifications, and then develop sets of restricted physical specifications
for languages, machines, etc. On top of that we can build validation engines
for type conversions.
Now, now, hear me out...
Take the set of conceptual integers i. We have a set of values allowed in
XML Schema for integers S(i) which happens to be equivalent: S(i)=i. [1]
The set of XML Schema ints (call this I[i]), is not equivalent to i ([2]);
I(i) is a proper subset of i. However, for every i[x] in i, we should be
able to say if there's an equivalent I(i[x]). That equivalency check would
amount to a constraint check between a physical type and a conceptual type.
Okay, so what's the point? The point is to divide the constraint checking
into two parts: the conceptual check vs. the physical. First question: is
value x a member of conceptual type T? If so, x is conceptually type valid.
But the next question is: is x a member of my physical type system, P? If
not, x is conceptually valid but phyically type invalid for type system P.
Which means x is correct, but not representable in my application's physical
type system.
Because an XML document may have to move through many physical type systems
as it jumps from process to process, it may be useful to distinguish
conceptual validity from that of physical representability. As in "Yeah, x
is an integer, all right. But I can't do a thing with it." Which has the
consequence that as long as you don't have to store x internally, you can
leave it in its textual representation and regurgitate it out to some other
process down the chain.
I think that would be useful; but then again, I just got back from vacation.
[1] http://www.w3.org/TR/xmlschema-2/#integer
[2] http://www.w3.org/TR/xmlschema-2/#int
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