• From: Liam R E Quin <liam@w...>
• To: "Costello, Roger L." <costello@m...>
• Date: Sun, 05 Jan 2014 02:40:01 -0500

On Sat, 2014-01-04 at 18:13 +0000, Costello, Roger L. wrote:
> [...] Sets are the foundation of mathematics, so by using set
> operations to create new XML languages we have at our disposal the
> entire power of mathematics!

Although Bertrand Russell tried to recast all of mathematics on set
theory, he failed, and instead famously proved it to be impossible. You
could say he cut himself not shaving.

More seriously, both set theory nor automata theory and the algebra of
grammars are equally rigorously mathematically defined.

In practice I think the use cases for a^n . b^n are pretty weak, as more
often you want (a, b)^n or, at a higher level, to record relationships
between individual a and b items. This is the same as in relational
algebra, and the tenets of Normal Forms applies to XML as much as to
relational data (although not, as I recall, in the way Henry Thompson
described, but rather in the entity relationship modeling sense).

Successful XML is rooted in the ground and does not fly with the clouds.
Mathematics is powerless in the face of expediency.

Best,

Liam


-- 
Liam Quin - XML Activity Lead, W3C, http://www.w3.org/People/Quin/
Pictures from old books: http://fromoldbooks.org/
Ankh: irc.sorcery.net irc.gnome.org freenode/#xml

• References:
  • Using Set Operations to Create Powerful New XML Languages
    • From: "Costello, Roger L." <costello@m...>