1 (define (memo-proc proc)
2 (let ((already-run? false) (result false))
6 (begin (set! already-run? true)
10 (define-syntax mydelay
11 (rsc-macro-transformer
14 `(memo-proc (lambda () ,exp)))))
16 (apply xfmr (cdr e))))))
18 (define (myforce delayed-object)
21 (define-syntax cons-stream
22 (rsc-macro-transformer
23 (let ((xfmr (lambda (x y) `(cons ,x (mydelay ,y)))))
25 (apply xfmr (cdr e))))))
27 (define (stream-car s)
29 (define (stream-cdr s)
31 (define stream-null? null?)
32 (define the-empty-stream '())
34 (define (integers-starting-from n)
35 (cons-stream n (integers-starting-from (+ n 1))))
37 (define (stream-ref s n)
40 (stream-ref (stream-cdr s) (- n 1))))
41 (define (stream-map proc . argstreams)
42 (if (stream-null? (car argstreams))
45 (apply proc (map stream-car argstreams))
46 (apply stream-map (cons proc (map stream-cdr argstreams))))))
47 (define (stream-for-each proc s)
50 (begin (proc (stream-car s))
51 (stream-for-each proc (stream-cdr s)))))
53 (define (stream-enumerate-interval low high)
58 (stream-enumerate-interval (+ low 1) high))))
59 (define (stream-filter pred s)
62 (let ((scar (stream-car s)))
64 (cons-stream scar (stream-filter pred (stream-cdr s)))
65 (stream-filter pred (stream-cdr s))))))
67 (define (display-stream s)
68 (stream-for-each display-line s))
69 (define (display-line x)
73 (define (test-case actual expected)
78 (display "Expected: ")
82 (define (integers-starting-from n)
83 (cons-stream n (integers-starting-from (+ n 1))))
84 (define integers (integers-starting-from 1))
86 (define (divisible? x y) (= (remainder x y) 0))
88 (stream-filter (lambda (x) (not (divisible? x 7)))
92 (cons-stream a (fibgen b (+ a b))))
93 (define fibs (fibgen 0 1))
100 (not (divisible? x (stream-car s))))
103 ;; (define primes (sieve (integers-starting-from 2)))
104 ;; (test-case (stream-ref primes 25) 101)
106 (define ones (cons-stream 1 ones))
107 (define (add-streams s1 s2)
108 (stream-map + s1 s2))
109 (define integers (cons-stream 1 (add-streams ones integers)))
110 ;; (test-case (stream-ref integers 15) 16)
115 (add-streams (stream-cdr fibs)
118 (define (scale-stream stream factor)
119 (stream-map (lambda (x)
122 (define double (cons-stream 1 (scale-stream double 2)))
127 (stream-filter prime? (integers-starting-from 3))))
130 (cond ((> (square (stream-car ps)) n) true)
131 ((divisible? n (stream-car ps)) false)
132 (else (iter (stream-cdr ps)))))
135 (define (mul-streams s1 s2)
136 (stream-map * s1 s2))
138 (define (partial-sums s)
140 (cons-stream (stream-car s)
145 ;; Exercise 3.56. A famous problem, first raised by R. Hamming, is to enumerate, in ascending order with no repetitions, all positive integers with no prime factors other than 2, 3, or 5. One obvious way to do this is to simply test each integer in turn to see whether it has any factors other than 2, 3, and 5. But this is very inefficient, since, as the integers get larger, fewer and fewer of them fit the requirement. As an alternative, let us call the required stream of numbers S and notice the following facts about it.
149 ;; The elements of (scale-stream S 2) are also elements of S.
151 ;; The same is true for (scale-stream S 3) and (scale-stream 5 S).
153 ;; These are all the elements of S.
155 ;; Now all we have to do is combine elements from these sources. For this we define a procedure merge that combines two ordered streams into one ordered result stream, eliminating repetitions:
157 (define (merge s1 s2)
158 (cond ((stream-null? s1) s2)
159 ((stream-null? s2) s1)
161 (let ((s1car (stream-car s1))
162 (s2car (stream-car s2)))
163 (cond ((< s1car s2car)
166 (merge (stream-cdr s1) s2)))
170 (merge s1 (stream-cdr s2))))
174 (merge (stream-cdr s1) (stream-cdr s2)))))))))
176 ;; (define S (cons-stream 1 (merge <??> <??>)))
178 ;; Fill in the missing expressions in the places marked <??> above.
183 (merge (scale-stream S 2)
184 (merge (scale-stream S 3)
185 (scale-stream S 5)))))
187 (define (test-stream-list stream list)
190 (begin (display "A: ")
191 (display (stream-car stream))
196 (test-stream-list (stream-cdr stream) (cdr list)))))
198 (test-stream-list S '(1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30))