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From Dirk-Willem van Gulik <di...@webweaving.org>
Subject Re: A mathematical vision of XML leads to interesting conclusions
Date Sun, 19 Dec 1999 16:30:04 GMT

On Sat, 18 Dec 1999, Stefano Mazzocchi wrote:

> True, the above can be done thru XSLT transformations, but it's much
> more complex and Donald and I both think XSLT may fail to cover all the
> cases for useful inheritance.
> This is why we ask for your comments on such thing, hopefully to be
> included in the XInclude effort or in another W3C note, but think that
> inheritance should be a fundamental feature of the XML model.

Assuming the grammar is context free; it follows that the Null projection
exists. You can write this in XSL, thus there is at least one way of
writing every valid transformation. A valid transformation can be
decomposed in a sequence of the Injection, Bijection, etc. Thus within 
XSLT each possible expression is covered. 

If you play with this (or if you try a simple Taylor like expansion by
hand in Mathematica) you quickly find that it is not that good though
in a common sense; i.e. it gets weildy to write down. But that is propably
more an issue for namespaces which themselves have projection which
themselves cannot be decomposed as a transformation. (Say, for the sake of
the argument a rand() :-)

But I fail to see any obstacl for inheritance; as that only requires an
Injection, Bijection and Transposition.


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