RE: [ubl-dev] SBS and Restricted Data Types

["G. Ken Holman" <gkholman@CraneSoftwrights.com>]

At 2006-05-04 00:01 +0800, Chin Chee-Kai wrote:
> >>2. a way to say (and maybe
> >>validate/verify) that a schema is a strict subset of another schema
> >>of which it therefore uses the same namespace. Too late for XSD 1.1?
>
>Stephen,
>
>That's an interesting question to ask, or re-phrasing it,
>"is there a way to determine if the entire set of all possible
>instances that are validated as acceptable by a given schema (A)
>are also validated as acceptable by another given schema (B)" ?
>
>Call this "sub-of" operator operating on 2 parameters (A) & (B)
>each of type schema.

I believe there is a way, through itemization by exhaustion, and I 
believe I can do it for UBL schemas and subsets because UBL uses the 
"Garden of Eden" approach where everything is globally defined and 
nothing is anonymously defined locally.  I hope to research this more 
but the essence of my idea is:

  (1) - using XPath files created for the schemas, generate
        the XPath address of every possible element and
        attribute information item of both the smaller schema
        and the larger schema
  (2) - if the set of XPaths of the smaller schema is wholly
        contained within the set of XPaths of the superset schema
        then, by exhaustion, it is proven that the smaller schema
        is a strict subset because information item in the
        exhaustive list generated by the smaller schema isn't
        found in the exhaustive list of the larger schema

>This "sub-of" operator, taking inputs which are schema themselves,
>would likely be outside of the realm in which XSD specifies.
>But of course, whatever XSD does (or doesn't) specify would
>affect the realisability of this "sub-of" operator that you suggested.

My method isn't quick and simple as this, nor does it allow 
operations on schemas as operands ... it is merely proof by proving 
the contrary (that the smaller schema describes an information item 
not allowed in the larger schema) is not true.

And I think I can read an XPath file and a schema expression and 
synthesize a subset schema reflecting the subset constraints ... and 
then use the above proof by exhaustion that the subset schema (while 
not normative) is provably acceptable to use should an application 
wish to use one.

BUT IT WOULDN'T CHANGE THE DEFINITION OF UBL!  An application should 
still (morally, since behaviours are not normative) accept an 
instance of full UBL even if it is only acting on the SBS subset of 
information items ... I think it is dangerous to use a subset schema 
for anything for fear of inadvertently disallowing a valid UBL 
instance just because it includes valid information items that are 
not meaningful to the applicaiton.

This needs more thought and experimentation ... I think I'll have 
some free time around November to look at it.

I hope this helps.

. . . . . . . . . . . Ken

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