1 665c255d 2023-08-04 jrmu ;; Exercise 2.5.  Show that we can represent pairs of nonnegative integers using only numbers and arithmetic operations if we represent the pair a and b as the integer that is the product 2^a 3^b. Give the corresponding definitions of the procedures cons, car, and cdr. 
 2 665c255d 2023-08-04 jrmu 
 3 665c255d 2023-08-04 jrmu (define (expt base n)
 4 665c255d 2023-08-04 jrmu   (if (= n 0)
 5 665c255d 2023-08-04 jrmu       1
 6 665c255d 2023-08-04 jrmu       (* base (expt base (- n 1)))))
 7 665c255d 2023-08-04 jrmu 
 8 665c255d 2023-08-04 jrmu (define (cons a b)
 9 665c255d 2023-08-04 jrmu   (* (expt 2 a)
10 665c255d 2023-08-04 jrmu      (expt 3 b)))
11 665c255d 2023-08-04 jrmu 
12 665c255d 2023-08-04 jrmu (define (car x)
13 665c255d 2023-08-04 jrmu   (if (not (= (remainder x 2) 0))
14 665c255d 2023-08-04 jrmu       0
15 665c255d 2023-08-04 jrmu       (1+ (car (/ x 2)))))
16 665c255d 2023-08-04 jrmu (define (cdr x)
17 665c255d 2023-08-04 jrmu   (if (not (= (remainder x 3) 0))
18 665c255d 2023-08-04 jrmu       0
19 665c255d 2023-08-04 jrmu       (1+ (cdr (/ x 3)))))
20 665c255d 2023-08-04 jrmu 
21 665c255d 2023-08-04 jrmu (define (test-case actual expected)
22 665c255d 2023-08-04 jrmu   (load-option 'format)
23 665c255d 2023-08-04 jrmu   (newline)
24 665c255d 2023-08-04 jrmu   (format #t "Actual: ~A Expected: ~A" actual expected))
25 665c255d 2023-08-04 jrmu 
26 665c255d 2023-08-04 jrmu (test-case (car (cons 5 9)) 5)
27 665c255d 2023-08-04 jrmu (test-case (cdr (cons 5 9)) 9)
28 665c255d 2023-08-04 jrmu (test-case (car (cons 12 25)) 12)
29 665c255d 2023-08-04 jrmu (test-case (cdr (cons 12 25)) 25)
30 665c255d 2023-08-04 jrmu (test-case (car (cons 0 1)) 0)
31 665c255d 2023-08-04 jrmu (test-case (cdr (cons 1 0)) 0)
32 665c255d 2023-08-04 jrmu (test-case (car (cons 0 6)) 0)
33 665c255d 2023-08-04 jrmu (test-case (cdr (cons 9 0)) 0)
34 665c255d 2023-08-04 jrmu