1 665c255d 2023-08-04 jrmu (define (test-case actual expected)
 2 665c255d 2023-08-04 jrmu   (newline)
 3 665c255d 2023-08-04 jrmu   (display "Actual:   ")
 4 665c255d 2023-08-04 jrmu   (display actual)
 5 665c255d 2023-08-04 jrmu   (newline)
 6 665c255d 2023-08-04 jrmu   (display "Expected: ")
 7 665c255d 2023-08-04 jrmu   (display expected)
 8 665c255d 2023-08-04 jrmu   (newline))
 9 665c255d 2023-08-04 jrmu 
10 665c255d 2023-08-04 jrmu ;; Exercise 2.32.  We can represent a set as a list of distinct elements, and we can represent the set of all subsets of the set as a list of lists. For example, if the set is (1 2 3), then the set of all subsets is (() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)). Complete the following definition of a procedure that generates the set of subsets of a set and give a clear explanation of why it works:
11 665c255d 2023-08-04 jrmu 
12 665c255d 2023-08-04 jrmu (define (subsets s)
13 665c255d 2023-08-04 jrmu   (if (null? s)
14 665c255d 2023-08-04 jrmu       '(())
15 665c255d 2023-08-04 jrmu       (let ((rest (subsets (cdr s))))
16 665c255d 2023-08-04 jrmu 	(append rest
17 665c255d 2023-08-04 jrmu 		(map (lambda (subset)
18 665c255d 2023-08-04 jrmu 		       (cons (car s) subset))
19 665c255d 2023-08-04 jrmu 		     rest)))))
20 665c255d 2023-08-04 jrmu 
21 665c255d 2023-08-04 jrmu (test-case (subsets '(1 2 3)) '(() (3) (2) (2 3) (1) (1 3) (1 2) (1 2 3)))
22 665c255d 2023-08-04 jrmu 
23 665c255d 2023-08-04 jrmu ;; what we're doing here is breaking down the problem from originally trying
24 665c255d 2023-08-04 jrmu ;; to find all the subsets of S to instead finding the subsets
25 665c255d 2023-08-04 jrmu ;; of all but the first number
26 665c255d 2023-08-04 jrmu ;; we then take this and add it to all the subsets without the first number
27 665c255d 2023-08-04 jrmu ;; but now with the first number put in the front
28 665c255d 2023-08-04 jrmu