[CL] ISO standard for Z Notation
John F. Sowa
sowa at bestweb.net
Tue Oct 5 01:24:57 CDT 2010
> I still have absolutely no idea what Z is for, or what purpose it has,
> or even how to recognize it when it is written.
Recognizing Z is easy. If you see lots of inscrutable symbols
in something related to programming and they don't seem to be APL,
they're probably Z.
For a major application (recognized by Queen Elizabeth or her minions)
see http://www.usingz.com/text/intro/ for the following excerpt:
A happy coincidence brought the [IBM] manager, Tony Kenny, and the
Oxford professor, Tony Hoare, together at a conference. They hatched
a plan to apply Oxford's ideas to [IBM] Hursley's problems. Oxford
advised on how formal methods [i.e., Z] could be used for the
specification and design of new CICS modules. Hursley showed how
the methods could be adapted to problems on an industrial scale.
> Do you think that CL should provide such things, which I guess would
> amount to a kind of mathematical ontology (?) What would be the point
> of this?
The point is that sets, sequences, and arithmetic are essential for
nearly every application. People expect to see them in the languages
they use, and they're not happy about the need to define them before
they can even begin to address their real problems.
I'm not recommending Z notation, but the list of functions and
relations defined in Annex B seem to be a good collection.
With such a toolkit as a prerequisite, it would be possible to
define numerical quantifiers in terms of the sets and numbers.
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