A mathematical foundation of reflexion?

John Carter cyent@mweb.co.za
Tue, 11 Jan 2000 21:32:44 +0000 (GMT)

On Mon, 10 Jan 2000 btanksley@hifn.com wrote:

> I just wanted to add that
> http://www.latrobe.edu.au/www/philosophy/phimvt/j00syn.html introduces not
> only a facinating computer language, but uses that language as a notation
> for explaining many computer science and mathematics problems in a very
> understandable way (including basic category theory).

I'm extremely impressed. The thing is well named, it is indeed a Joy.

One of the points I was going to make when I joined this group was that
reflection is a brilliant idea but it is hopelessly under utilized in the
"real" world of programming. Even to the extent that many Scheme
implementations seem to bypass macro implementation of features in favour
of hard coding the various features that could have been done by scheme

As such there must be something "unholy" about the current reflective
languages that makes such an obviously tasty feature as reflection so
terribly under utilized.

The next point of observation I was going to make was that one of the very
few languages that its really extensively used as a generated language is
Postscript. ie. Most postscript programs are the output of other programs.
ie. There is something special about PostScript that bares close
inspection for those interested in reflection as a useful daily tool.

I think Joy lays bare that special something about Forth and Postscript.
The homomorphism between syntatic concatenation and functional
composition. If that homomorphism exists, then reasoning
about the program becomes very much easier, and if reasoning becomes
easier it is much easier to write bug free programs.

I haven't enJoy'ed reading a description of a programming language as much
as I have read the write up on Joy. 

I do not think Joy as is a panacea, there are a number of difficiencies
in the semantics that make it unusable, but the idea of creating a
workable algebra of programs is priceless.

John Carter

The Cybernetic Entomologist - cyent@mweb.co.za


"If man realized that the universe, like him, can love and suffer, he
 would be reconciled." - Camus