RE: XPath: all elements with only non-parent children

Hunsberger, Peter writes:
 > > No that wouldn't work, if I remember correctly from my electronics study
 > >
 > >  not(A) and not(B) equals not(A or B)
 > >
 > > I think its called the laws of Morgan or something 
 > > so in your case that would lead to
 > 
 > I believe you're thinking of DeMorgan's law, which states essentially that.
 > However, if I can recall correctly, for DeMorgan's law to apply, the
 > operations in question all have to be commutative and it's not clear to me
 > that that is true for XSLT in general?  The latter is actually an
 > interesting question, since if you can show that all the XSLT operations
 > meet the tests for forming a group then you know you have all other kinds of
 > capabilities with the language...  Perhaps someone who's days of heavy
 > algebra aren't 20 years behind them might care to expand?

DeMorgan's theorem can be proved by complete induction over all
possible inputs.  I don't think it makes any requirements other than
that the functions behave like the boolean opeators they're meant to
emulate.  For example, if there were also type conversions involved,
one might need too be careful when applying DeMorgan's theorem to
XPath expressions.  I've not actually analyzed whether there would be
any screw-cases here or not.




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