1 665c255d 2023-08-04 jrmu (define (memo-proc proc)
2 665c255d 2023-08-04 jrmu (let ((already-run? false) (result false))
4 665c255d 2023-08-04 jrmu (if already-run?
6 665c255d 2023-08-04 jrmu (begin (set! already-run? true)
7 665c255d 2023-08-04 jrmu (set! result (proc))
10 665c255d 2023-08-04 jrmu (define-syntax mydelay
11 665c255d 2023-08-04 jrmu (rsc-macro-transformer
13 665c255d 2023-08-04 jrmu (lambda (exp)
14 665c255d 2023-08-04 jrmu `(memo-proc (lambda () ,exp)))))
15 665c255d 2023-08-04 jrmu (lambda (e r)
16 665c255d 2023-08-04 jrmu (apply xfmr (cdr e))))))
18 665c255d 2023-08-04 jrmu (define (myforce delayed-object)
19 665c255d 2023-08-04 jrmu (delayed-object))
21 665c255d 2023-08-04 jrmu (define-syntax cons-stream
22 665c255d 2023-08-04 jrmu (rsc-macro-transformer
23 665c255d 2023-08-04 jrmu (let ((xfmr (lambda (x y) `(cons ,x (mydelay ,y)))))
24 665c255d 2023-08-04 jrmu (lambda (e r)
25 665c255d 2023-08-04 jrmu (apply xfmr (cdr e))))))
27 665c255d 2023-08-04 jrmu (define (stream-car s)
29 665c255d 2023-08-04 jrmu (define (stream-cdr s)
30 665c255d 2023-08-04 jrmu (myforce (cdr s)))
31 665c255d 2023-08-04 jrmu (define stream-null? null?)
32 665c255d 2023-08-04 jrmu (define the-empty-stream '())
34 665c255d 2023-08-04 jrmu (define (integers-starting-from n)
35 665c255d 2023-08-04 jrmu (cons-stream n (integers-starting-from (+ n 1))))
37 665c255d 2023-08-04 jrmu (define (stream-ref s n)
39 665c255d 2023-08-04 jrmu (stream-car s)
40 665c255d 2023-08-04 jrmu (stream-ref (stream-cdr s) (- n 1))))
41 665c255d 2023-08-04 jrmu (define (stream-map proc . argstreams)
42 665c255d 2023-08-04 jrmu (if (stream-null? (car argstreams))
43 665c255d 2023-08-04 jrmu the-empty-stream
44 665c255d 2023-08-04 jrmu (cons-stream
45 665c255d 2023-08-04 jrmu (apply proc (map stream-car argstreams))
46 665c255d 2023-08-04 jrmu (apply stream-map (cons proc (map stream-cdr argstreams))))))
47 665c255d 2023-08-04 jrmu (define (stream-for-each proc s)
48 665c255d 2023-08-04 jrmu (if (stream-null? s)
50 665c255d 2023-08-04 jrmu (begin (proc (stream-car s))
51 665c255d 2023-08-04 jrmu (stream-for-each proc (stream-cdr s)))))
53 665c255d 2023-08-04 jrmu (define (stream-enumerate-interval low high)
54 665c255d 2023-08-04 jrmu (if (> low high)
55 665c255d 2023-08-04 jrmu the-empty-stream
56 665c255d 2023-08-04 jrmu (cons-stream
58 665c255d 2023-08-04 jrmu (stream-enumerate-interval (+ low 1) high))))
59 665c255d 2023-08-04 jrmu (define (stream-filter pred s)
60 665c255d 2023-08-04 jrmu (if (stream-null? s)
61 665c255d 2023-08-04 jrmu the-empty-stream
62 665c255d 2023-08-04 jrmu (let ((scar (stream-car s)))
63 665c255d 2023-08-04 jrmu (if (pred scar)
64 665c255d 2023-08-04 jrmu (cons-stream scar (stream-filter pred (stream-cdr s)))
65 665c255d 2023-08-04 jrmu (stream-filter pred (stream-cdr s))))))
67 665c255d 2023-08-04 jrmu (define (display-stream s)
68 665c255d 2023-08-04 jrmu (stream-for-each display-line s))
69 665c255d 2023-08-04 jrmu (define (display-line x)
71 665c255d 2023-08-04 jrmu (display x))
73 665c255d 2023-08-04 jrmu (define (test-case actual expected)
75 665c255d 2023-08-04 jrmu (display "Actual: ")
76 665c255d 2023-08-04 jrmu (display actual)
78 665c255d 2023-08-04 jrmu (display "Expected: ")
79 665c255d 2023-08-04 jrmu (display expected)
82 665c255d 2023-08-04 jrmu (define (integers-starting-from n)
83 665c255d 2023-08-04 jrmu (cons-stream n (integers-starting-from (+ n 1))))
84 665c255d 2023-08-04 jrmu (define integers (integers-starting-from 1))
86 665c255d 2023-08-04 jrmu (define (divisible? x y) (= (remainder x y) 0))
87 665c255d 2023-08-04 jrmu (define no-sevens
88 665c255d 2023-08-04 jrmu (stream-filter (lambda (x) (not (divisible? x 7)))
91 665c255d 2023-08-04 jrmu (define (fibgen a b)
92 665c255d 2023-08-04 jrmu (cons-stream a (fibgen b (+ a b))))
93 665c255d 2023-08-04 jrmu (define fibs (fibgen 0 1))
95 665c255d 2023-08-04 jrmu (define (sieve s)
96 665c255d 2023-08-04 jrmu (cons-stream
97 665c255d 2023-08-04 jrmu (stream-car s)
98 665c255d 2023-08-04 jrmu (sieve (stream-filter
100 665c255d 2023-08-04 jrmu (not (divisible? x (stream-car s))))
101 665c255d 2023-08-04 jrmu (stream-cdr s)))))
103 665c255d 2023-08-04 jrmu ;; (define primes (sieve (integers-starting-from 2)))
104 665c255d 2023-08-04 jrmu ;; (test-case (stream-ref primes 25) 101)
106 665c255d 2023-08-04 jrmu (define ones (cons-stream 1 ones))
107 665c255d 2023-08-04 jrmu (define (add-streams s1 s2)
108 665c255d 2023-08-04 jrmu (stream-map + s1 s2))
109 665c255d 2023-08-04 jrmu (define integers (cons-stream 1 (add-streams ones integers)))
110 665c255d 2023-08-04 jrmu ;; (test-case (stream-ref integers 15) 16)
112 665c255d 2023-08-04 jrmu (define fibs
113 665c255d 2023-08-04 jrmu (cons-stream 0
114 665c255d 2023-08-04 jrmu (cons-stream 1
115 665c255d 2023-08-04 jrmu (add-streams (stream-cdr fibs)
118 665c255d 2023-08-04 jrmu (define (scale-stream stream factor)
119 665c255d 2023-08-04 jrmu (stream-map (lambda (x)
120 665c255d 2023-08-04 jrmu (* x factor))
122 665c255d 2023-08-04 jrmu (define double (cons-stream 1 (scale-stream double 2)))
124 665c255d 2023-08-04 jrmu (define primes
125 665c255d 2023-08-04 jrmu (cons-stream
127 665c255d 2023-08-04 jrmu (stream-filter prime? (integers-starting-from 3))))
128 665c255d 2023-08-04 jrmu (define (prime? n)
129 665c255d 2023-08-04 jrmu (define (iter ps)
130 665c255d 2023-08-04 jrmu (cond ((> (square (stream-car ps)) n) true)
131 665c255d 2023-08-04 jrmu ((divisible? n (stream-car ps)) false)
132 665c255d 2023-08-04 jrmu (else (iter (stream-cdr ps)))))
133 665c255d 2023-08-04 jrmu (iter primes))
135 665c255d 2023-08-04 jrmu ;; (test-case (stream-ref primes 26) 103
137 665c255d 2023-08-04 jrmu ;; Exercise 3.54. Define a procedure mul-streams, analogous to add-streams, that produces the elementwise product of its two input streams. Use this together with the stream of integers to complete the following definition of the stream whose nth element (counting from 0) is n + 1 factorial:
139 665c255d 2023-08-04 jrmu (define (mul-streams s1 s2)
140 665c255d 2023-08-04 jrmu (stream-map * s1 s2))
142 665c255d 2023-08-04 jrmu (define factorials (cons-stream 1 (mul-streams factorials (stream-cdr integers))))
144 665c255d 2023-08-04 jrmu (test-case (stream-ref factorials 9) 3628800)