Re: [xsl] Kleene Operators

[Terry Badger <terry_badger@xxxxxxxxx>]

Thank you for responding. Remarks below.



>>----- Original Message ----
>>From: Michael Kay <mike@xxxxxxxxxxxx>
>>To: xsl-list@xxxxxxxxxxxxxxxxxxxxxx
>>Sent: Mon, March 1, 2010 4:00:57 AM
>>Subject: RE: [xsl] Kleene Operators

>
I am lucky to have an adjunct teaching job at RIT teaching 
> xml and xsl and
started to think about the questions they 
> might ask me about why do we use
*,+,?  and wondered if there 
> was some really good answer rather than the
operators result 
> in a closed set. I like the construct and would not
imagine I 
> would have something better or different to offer.

>>Firstly,
I'm surprised that you desribe these operators as coming out of set
>>theory.
I thought they were all to do with the structure of sequences. But
>>I'm not
really sure what the boundaries of "set theory" are supposed to
>>be...

What
little I understood I got from here:
http://en.wikipedia.org/wiki/Kleene_star and
http://en.wikipedia.org/wiki/Monoid
and from the second one I saw
...superscript * is the Kleene star: the set is closed under composition or
concatenation of its elements... and made a jump to sets. 

>>Fundamentally,
if you take the view that the only interesting numbers are
>>zero, one, and
infinity, then the interesting cardinality bounds on finite
>>sequences are
>>  (0, 0)
>> (0, 1)
>>  (0, infinity)
>>  (1, 1)
>>  (1, infinity)

>>giving
five ranges which one might denote as X:, X?, X*, X9, X+. In the
>>Kleene
system, the (0, 0) case is not provided for presumably because it is
>>only of
theoretical interest, and the (1, 1) case doesn't get a symbol
>>because it's
the default. But I've been using X: and X9 internally.

>>When you say "the
operators result in a closed set", I'm wondering exactly
>>what you you have
in mind?

I think the second reference sent me off in that direction; the
strings being operated on that are in the set. 

>>I guess there's an
intersection operator whereby
>>X9.X? = X9, X?.X? = X?, X?.X* = X?, X?.X+ =
X9; and a union operator whereby
>>X?|X+ = X*, etc. But if you include X:,
then X:.X+ doesn't have an
>>intersection within the group: X: represents the
set of empty sequences, X+
>>the set of non-empty sequences, and their
intersection is the empty set,
>>which isn't part of the group.

I guess on
our xml world a null set just vanishes. 
Used in a DTD the *,+,? are just a
great way to formalize what people will be allowed to do when they create
content and leave it at that. 

>>Regards,

>>Michael Kay
>>http://www.saxonica.com/
>>http://twitter.com/michaelhkay