<fray_fernando@my-deja.com> wrote:
+---------------
| <dzemo@fesb.hr> wrote:
| > Are there doctoral thesis in LISP, closed to mathematics?
| > And whom to ask, where to look?
| 
| Gregory J. Chaitin has written a few math books that use lisp...
+---------------

Yup. See <URL:http://www.cs.umaine.edu/~chaitin/>, especially
<URL:http://www.cs.umaine.edu/~chaitin/lisp.html>.

Though his "Lisp" really isn't. It's closer to a subset of Scheme
[yes, subset -- even smaller than R4RS!!] that's had most of the
parentheses removed. From the second URL above:

	Now actually I don't like to write all these parentheses.
	LISP programmers haven't heard about parenthesis-free
	Polish notation! So I just write

		define (fact N)
		if = N 1  1
		          * N (fact - N 1)

	The other parentheses are understood.

The only reason this works at all is that in his tiny subset all
forms and functions have fixed arity that's already known when
the expression is parsed.

Personally, I find it almost unreadable, and I really, *really*
wish he'd just stuck with standard S-expression notation. (*sigh*) 
At worst it would have lengthened slightly the constant prefix
program his proofs require (currently 410 characters). It wouldn't
have changed the math at all.

On the flip side, the math is sort of interesting. The use of "elegant
Lisp programs" and the Berry paradox to derive an easily-understood
proof that's equivalent to Godel's incompleteness is (IMHO) worth the
minor bit of irritation at his needlessly-incompatible notation.


-Rob

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Rob Warnock, 31-2-510		rpw3@sgi.com
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