1 ;; Exercise 1.30.  The sum procedure above generates a linear recursion. The procedure can be rewritten so that the sum is performed iteratively. Show how to do this by filling in the missing expressions in the following definition:
2 
3 (define (product term a next b)
4   (if (> a b)
5       1
6       (* (term a)
7 	 (product term (next a) next b))))
8 
9 (define (product-iter term a next b)
10   (define (iter i result)
11     (if (> i b)
12 	result
13 	(iter (next i) (* (term i) result))))
14   (iter a 1))
15 
16 (define (factorial n)
17   (product (lambda (x) x)
18 	   1
19 	   (lambda (x) (+ x 1))
20 	   n))
21 
22 (define (factorial-iter n)
23   (product-iter (lambda (x) x)
24 		1
25 		(lambda (x) (+ x 1))
26 		n))
27 
28 ;; pi/4 = 2*4*4*6*6*8*...
29 ;;        ---------------
30 ;;        3*3*5*5*7*7*...
31 
32 (define (pi iterations)
33   (* 4.0
34      (product (lambda (x)
35 		(if (odd? x)
36 		    (/ (+ x 1) (+ x 2))
37 		    (/ (+ x 2) (+ x 1))))
38 	      1
39 	      (lambda (x) (+ x 1))
40 	      iterations)))
41 
42 (define (test-case actual expected)
43   (load-option 'format)
44   (newline)
45   (format #t "Actual: ~A Expected: ~A" actual expected))
46 
47 (test-case (factorial 0) 1)
48 (test-case (factorial 1) 1)
49 (test-case (factorial 2) 2)
50 (test-case (factorial 3) 6)
51 (test-case (factorial 4) 24)
52 (test-case (factorial 5) 120)
53 (test-case (factorial 6) 720)
54 (test-case (factorial 7) 5040)
55 (test-case (factorial-iter 7) 5040)
56 
57 (test-case (pi 10000) 3.1415)