1 665c255d 2023-08-04 jrmu (define (map proc items)
 2 665c255d 2023-08-04 jrmu   (if (null? items)
 3 665c255d 2023-08-04 jrmu       '()
 4 665c255d 2023-08-04 jrmu       (cons (proc (car items))
 5 665c255d 2023-08-04 jrmu 	    (map proc (cdr items)))))
 6 665c255d 2023-08-04 jrmu 
 7 665c255d 2023-08-04 jrmu (define (scale-list items factor)
 8 665c255d 2023-08-04 jrmu   (map (lambda (x) (* x factor))
 9 665c255d 2023-08-04 jrmu        items))
10 665c255d 2023-08-04 jrmu 
11 665c255d 2023-08-04 jrmu ;; Exercise 2.21.  The procedure square-list takes a list of numbers as argument and returns a list of the squares of those numbers.
12 665c255d 2023-08-04 jrmu 
13 665c255d 2023-08-04 jrmu (define (square-list-map nums)
14 665c255d 2023-08-04 jrmu   (map (lambda (x) (* x x)) nums))
15 665c255d 2023-08-04 jrmu 
16 665c255d 2023-08-04 jrmu (define (square-list-recurse nums)
17 665c255d 2023-08-04 jrmu   (if (null? nums)
18 665c255d 2023-08-04 jrmu       '()
19 665c255d 2023-08-04 jrmu       (cons (* (car nums) (car nums))
20 665c255d 2023-08-04 jrmu 	    (square-list-recurse (cdr nums)))))
21 665c255d 2023-08-04 jrmu 
22 665c255d 2023-08-04 jrmu (define (test-case actual expected)
23 665c255d 2023-08-04 jrmu   (load-option 'format)
24 665c255d 2023-08-04 jrmu   (newline)
25 665c255d 2023-08-04 jrmu   (format #t "Actual: ~A Expected: ~A" actual expected))
26 665c255d 2023-08-04 jrmu 
27 665c255d 2023-08-04 jrmu (test-case (square-list-recurse (list 1 2 3 4)) '(1 4 9 16))
28 665c255d 2023-08-04 jrmu (test-case (square-list-map (list 1 2 3 4)) '(1 4 9 16))
29 665c255d 2023-08-04 jrmu 
30 665c255d 2023-08-04 jrmu  Exercise 2.22.  Louis Reasoner tries to rewrite the first square-list procedure of exercise 2.21 so that it evolves an iterative process:
31 665c255d 2023-08-04 jrmu 
32 665c255d 2023-08-04 jrmu (define (square-list items)
33 665c255d 2023-08-04 jrmu   (define (iter things answer)
34 665c255d 2023-08-04 jrmu     (if (null? things)
35 665c255d 2023-08-04 jrmu         answer
36 665c255d 2023-08-04 jrmu         (iter (cdr things) 
37 665c255d 2023-08-04 jrmu               (cons (square (car things))
38 665c255d 2023-08-04 jrmu                     answer))))
39 665c255d 2023-08-04 jrmu   (iter items nil))
40 665c255d 2023-08-04 jrmu 
41 665c255d 2023-08-04 jrmu Unfortunately, defining square-list this way produces the answer list in the reverse order of the one desired. Why?
42 665c255d 2023-08-04 jrmu 
43 665c255d 2023-08-04 jrmu Louis then tries to fix his bug by interchanging the arguments to cons:
44 665c255d 2023-08-04 jrmu 
45 665c255d 2023-08-04 jrmu (define (square-list items)
46 665c255d 2023-08-04 jrmu   (define (iter things answer)
47 665c255d 2023-08-04 jrmu     (if (null? things)
48 665c255d 2023-08-04 jrmu         answer
49 665c255d 2023-08-04 jrmu         (iter (cdr things)
50 665c255d 2023-08-04 jrmu               (cons answer
51 665c255d 2023-08-04 jrmu                     (square (car things))))))
52 665c255d 2023-08-04 jrmu   (iter items nil))
53 665c255d 2023-08-04 jrmu 
54 665c255d 2023-08-04 jrmu This doesn't work either. Explain.