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From: "Pascal J. Bourguignon" <p...@informatimago.com>
Newsgroups: comp.lang.lisp
Subject: Re: bignums in clisp
Date: Wed, 03 Oct 2012 13:27:21 +0200
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Ian Clifton <ian.clif...@chem.ox.ac.uk> writes:

> Sorry! I just thought it was interesting that such a scheme could (I
> think) be implemented (although you’d have to work out how to do
> indexing of data structures by bignum etc), even though we all know it
> couldn’t possibly work in any useful sense. I recall that Bart Simpson
> once lined up several police bull†horns, the output of one feeding into
> the microphone of the next, in order to produce a stupendously loud
> sound. Of course this wouldn’t work either, but you could attempt the
> experiment.

Well we're speaking of lisp here, so there's a solution.  It's easy to
represent a number bigger than the universe in lisp: just use a sexp!

    (↑↑↑↑  3  3) 

    (↑27↑   3  3) 

    (lessp  '(↑27↑   3  3) (add '(↑27↑   3  3) '(↑↑↑↑  3  3)))

(defun ↑      (x y) (expt x y))
(defun ↑↑    (x y) (expt x (expt y y)))
(defun ↑↑↑  (x y) (expt x (expt y (expt y y))))
(defun ↑↑↑↑ (x y) (expt x (expt y (expt y (expt y y)))))

(↑↑ 3 3) --> 7625597484987

(↑↑↑ 3 3) can't be computed on current hardware, but you can still
represent this number, as the sexp (↑↑↑ 3 3), like you can represent 100
as: (* (expt 5 2) (expt 2 2)) or some other sexp.

And you can write functions like add and lessp that compute
symbolically. (You can use a theorem prover to implement them).

(defun add (a b)
 (cond
  ((and (numberp a) (numberp b))
   (+ a b))
  ((and (numberp a) (zerop a)) b)
  ((and (numberp b) (zerop b)) a)
  (t `(+ ,a ,b))))

(add '(↑27↑   3  3) '(↑↑↑↑  3  3))
--> (+ (↑27↑ 3 3) (↑↑↑↑ 3 3))


-- 
__Pascal Bourguignon__                     http://www.informatimago.com/
A bad day in () is better than a good day in {}.