Re: Lambda calculus and it relation to LISP

[David Kastrup]

see@sig.below (Barb Knox) writes:

> In article <9e8ebeb2.0210062058.5c7ab267@posting.google.com>,
> gnuist007@hotmail.com (gnuist) wrote:
> [snip]
> 
> > In the same way I ask for GRADED examples of use of lambda. I am sure many
> > of you can just cut and paste from your collection. Examples to illustrate
> > recursion, etc. And how will you do recursion without/with "LABEL"?
> 
> Lambda calculus does not have Lisp's LABEL/LABELS or DEFUN/DE.  Recursion
> is done via the "Y combinator", which is a very interesting
> self-referential hack (in the good sense).
> 
> For example, here is a recursive factorial function in lambda calculus in
> Lispish syntax (assuming apprioriate definitions for 'if', '<', '*', '-',
> and '1').  It takes one argument (which gets bound to 'n') and returns its
> factorial.
> 
>     ((lambda (f) ((lambda (Y) (f (Y Y))) (lambda (Y) (f (Y Y)))))
>      (lambda (ff n) (if (< n 1) 1 (* n (ff (- n 1))))) )
> 
> Intense, eh?

Also wrong.  This is "Lispish Syntax", actually Scheme.  So we can
check it out:

guile> ((lambda (f) ((lambda (Y) (f (Y Y))) (lambda (Y) (f (Y Y)))))(lambda (ff 
n) (if (< n 1) 1 (* n (ff (- n 1))))) )
standard input:1:27: In expression (f (Y Y)):
standard input:1:27: Wrong number of arguments to #<procedure (ff n)>
ABORT: (wrong-number-of-args)

Type "(backtrace)" to get more information.
guile> (backtrace)

Backtrace:
0* [#<procedure (f)> #<procedure (ff n)>]
1  [#<procedure (Y)> #<procedure (Y)>]
2  (f (Y Y))

Type "(debug-enable 'backtrace)" if you would like a backtrace
automatically if an error occurs in the future.

-- 
David Kastrup, Kriemhildstr. 15, 44793 Bochum
Email: David.Kastrup@t-online.de