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From: steve <sgonedes1977@gmail.com>
Newsgroups: comp.lang.lisp
Subject: Re: Church numerals in early lisp implementations?
References: <875xvkmta1.fsf@yaxenu.org>
Date: Thu, 16 May 2024 16:28:01 -0400
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Julieta Shem <jshem@yaxenu.org> writes:

> McCarthy wrote this in ``History of Lisp''.
>
< > Numbers were originally implemented in LISP I as lists of atoms, and
< > this proved too slow for all but the simplest computations.
>
> Was that Church numerals?  Does anyone have examples of code from back
> then?  I'm picturing things such as
>

I doubt it. check turning machine.

in original lambda-calc numbers where represented as applications of
lambda. check the wiki, it has mostly math since his science would not
fit well with these machines.


>   (defconstant zero nil)
>   (defconstant one (cons nil zero))
>
>   (defun zero? (x) (eq zero x))
>   (defun add1 (x) (cons nil x))
>   (defun sub1 (x) (cdr x))
>
>   (defun add (x y)
>     (cond ((zero? x) y)
>           (t (add (sub1 x) (add1 y)))))
>
>   CL-USER> (add one one)
>   (NIL NIL)
>
> The paragraph continued:
>
< > A reasonably efficient implementation of numbers as atoms in
< > S-expressions was made in LISP 1.5, but in all the early LISPs,
< > numerical computations were still 10 to 100 times slower than in
< > FORTRAN. Efficient numerical computation requires some form of typing
< > in the source language and a distinction between numbers treated by
< > themselves and as elements of S-expressions. Some recent versions of
< > LISP allow distinguishing types, but at the time, this seemed
< > incompatible with other features.


yes, church made the math and the original concepts I believe. Turning
machines were actually usefull if you could find your way into one.