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 (define (merge s1 s2)
146 (cond ((stream-null? s1) s2)
147 ((stream-null? s2) s1)
149 (let ((s1car (stream-car s1))
150 (s2car (stream-car s2)))
151 (cond ((< s1car s2car)
154 (merge (stream-cdr s1) s2)))
158 (merge s1 (stream-cdr s2))))
162 (merge (stream-cdr s1) (stream-cdr s2)))))))))
164 (define (test-stream-list stream list)
167 (begin (display "A: ")
168 (display (stream-car stream))
173 (test-stream-list (stream-cdr stream) (cdr list)))))
175 (define (integrate-series a)
176 (stream-map / a integers))
179 (cons-stream 1 (integrate-series exp-series)))
181 (define cosine-series
184 (integrate-series (stream-map - sine-series))))
188 (integrate-series cosine-series)))
190 (define (mul-series s1 s2)
192 (* (stream-car s1) (stream-car s2))
194 (scale-stream (stream-cdr s2) (stream-car s1))
195 (mul-series (stream-cdr s1) s2))))
197 (define (invert-unit-series s)
201 (mul-series (stream-map - (stream-cdr s))
205 (define (div-series num den)
206 (let ((den-car (stream-car den)))
208 (error "Denominator has zero constant term -- DIV-SERIES")
212 (invert-unit-series (scale-stream den (/ 1 den-car))))
216 (define (sqrt-improve guess x)
217 (define (average x y)
219 (average guess (/ x guess)))
221 (define (sqrt-stream x)
225 (stream-map (lambda (guess)
226 (sqrt-improve guess x))
229 ;; (test-stream-list (stream-map exact->inexact (sqrt-stream 2))
230 ;; '(1 1.5 1.4166 1.4142156 1.41421356))
232 (define (pi-summands n)
234 (stream-map - (pi-summands (+ n 2)))))
236 (scale-stream (partial-sums (pi-summands 1)) 4))
237 ;; (test-stream-list (stream-map exact->inexact pi-stream)
238 ;; '(4 2.6667 3.4667 2.8952 3.3397))
240 (define (euler-transform s)
241 (let ((s0 (stream-ref s 0))
242 (s1 (stream-ref s 1))
243 (s2 (stream-ref s 2)))
245 (- s2 (/ (square (- s2 s1))
246 (+ s0 (* -2 s1) s2)))
247 (euler-transform (stream-cdr s)))))
249 ;; (test-stream-list (stream-map exact->inexact (euler-transform pi-stream))
250 ;; '(3.1667 3.1333 3.1452 3.1397 3.1427))
252 (define (make-tableau transform s)
254 (make-tableau transform
257 ;; (test-stream-list (stream-map exact->inexact (stream-map stream-car (make-tableau euler-transform pi-stream)))
258 ;; '(4 3.1667 3.1421 3.1459935 3.1415927140 3.145926539752927))
260 ;; Exercise 3.63. Louis Reasoner asks why the sqrt-stream procedure was not written in the following more straightforward way, without the local variable guesses:
262 (define (sqrt-stream x)
264 (stream-map (lambda (guess)
265 (sqrt-improve guess x))
268 ;; Alyssa P. Hacker replies that this version of the procedure is considerably less efficient because it performs redundant computation. Explain Alyssa's answer. Would the two versions still differ in efficiency if our implementation of delay used only (lambda () <exp>) without using the optimization provided by memo-proc (section 3.5.1)?
270 ;; by defining guesses, the procedure is able to take advantage of the fact that the previous terms in the stream have been calculated before. When mapping guesses, the delayed objects in the stream which have already been evaluated can simply return their memoized values. Without guesses, each new iteration would require the computation (from scratch) of each previous iteration.
272 ;; without the optimization, the two implementations would be equally inefficient
