流（3.5.1~3.5.2）

;流实现的行为方式;delay和force的实现(define (memo-proc proc)  (let ((already-run? false) (result false))    (lambda ()      (if already-run?          result          (begin            (set! already-run? true)            (set! result (proc))            result)))));(delay exp)应该等价于下面这个式子,但不能用define,目前不知道该如何绑定(memo-proc (lambda () exp))(define (test-func)  (define (fib n)    (if (< n 2)        n        (+ (fib (- n 1)) (fib (- n 2)))))  (fib 30))(define promise (memo-proc (lambda () (test-func))))(define (my-force delayed-project)  (delayed-project));分别求值下面两个表达式，比较速度(my-force promise)(my-force promise);3.50(define (my-stream-map proc . argstreams)  (if (empty-stream? (car argstreams))      the-empty-stream      (cons-stream       (apply proc (map stream-car argstreams))       (apply my-stream-map              (cons proc                    (map stream-cdr argstreams))))))(define a (cons-stream 1 (cons-stream 2 (cons-stream 3 the-empty-stream))))(define b (cons-stream 1 (cons-stream 2 (cons-stream 3 the-empty-stream))))(define c (cons-stream 1 (cons-stream 2 (cons-stream 3 the-empty-stream))))(define (display-stream stream)  (if (empty-stream? stream)      the-empty-stream      (cons (stream-car stream)            (display-stream (stream-cdr stream)))))(display-stream (my-stream-map + a b c));3.51(define (stream-enumerate-interval low high)  (if (> low high)      the-empty-stream      (cons-stream low                   (stream-enumerate-interval (+ 1 low) high))))(define (display-line x)  (newline)  (display x))(define (show x)  (display-line x)  x)(define x (stream-map show (stream-enumerate-interval 0 10)))(stream-ref x 5)(stream-ref x 7);3.52(define (stream-filter pred? stream)  (cond ((empty-stream? stream)         the-empty-stream)        ((pred? (stream-car stream))         (cons-stream (stream-car stream)                      (stream-filter pred? (stream-cdr stream))))        (else (stream-filter pred? (stream-cdr stream)))))(define sum 0)(define (accum x)  (set! sum (+ x sum))  sum)(define seq (stream-map accum (stream-enumerate-interval 1 20)))(define y (stream-filter even? seq))(define z (stream-filter (lambda (x) (= (remainder x 5) 0))                         seq))(stream-ref y 7)(display-stream z);无穷流(define (integers-starting-from n)  (cons-stream n               (integers-starting-from (+ n 1))))(define integers (integers-starting-from 1))(define no-sevens  (stream-filter   (lambda (x) (not (= (remainder x 7) 0))) integers))(define (fibgen a b)  (cons-stream a (fibgen b (+ a b))))(define (divsible? x y)  (= (remainder x y) 0))(define (sieve stream)  (cons-stream   (stream-car stream)   (sieve    (stream-filter     (lambda (x)       (not (divsible? x (stream-car stream))))     (stream-cdr stream)))))(define primes (sieve (integers-starting-from 2)));隐式地定义流(define ones (cons-stream 1 ones))(define (add-streams s1 s2)  (stream-map + s1 s2))(define (scale-stream stream factor)  (stream-map (lambda (x) (* x factor)) stream))(define double (cons-stream 1  (scale-stream double 2)))(define primes (cons-stream 2                            (stream-filter prime?                                           (integers-starting-from                                            3))))(define (prime? x)  (define (iter ps)    (let ((p (stream-car ps)))      (cond ((> (square p) x) true)            ((= (remainder x p) 0) false)            (else (iter (stream-cdr ps))))))  (iter primes));3.53(define s (cons-stream 1 (add-streams s s)))(stream-ref s 8);3.54(define (mul-streams s1 s2)  (cons-stream   (* (stream-car s1)      (stream-car s2))   (mul-streams    (stream-cdr s1)    (stream-cdr s2))))(define factorials  (cons-stream 1 (mul-streams factorials                              (integers-starting-from 2))));3.55(define (partial-sums s)  (define the-partial-sums    (cons-stream (stream-car s)                 (add-streams (stream-cdr s) the-partial-sums)))  the-partial-sums);nice and elegant,相当于从相反的方向构建(define (partial-sums-2 s)  (define the-partial-sums    (add-streams s (cons-stream 0 the-partial-sums)))  the-partial-sums)(define z (partial-sums-2 integers));3.56(define (merge s1 s2)  (cond ((empty-stream? s1) s2)        ((empty-stream? s2) s1)        (else (let ((s1car (stream-car s1))                    (s2car (stream-car s2)))                (cond ((< s1car s2car)                       (cons-stream s1car                        (merge (stream-cdr s1) s2)))                      ((= s1car s2car)                       (cons-stream s1car                        (merge (stream-cdr s1)                               (stream-cdr s2))))                      (else                       (cons-stream s2car                                    (merge s1 (stream-cdr s2)))))))))(define s (cons-stream 1 (merge (scale-stream s 2)                                (merge (scale-stream s 3)                                       (scale-stream s 5)))));3.58这个过程求的是radix进制下(num/den)的小数部分,需假设num<den(define (expand num den radix)  (cons-stream   (quotient (* num radix) den)   (expand (remainder (* num radix) den) den radix)))(define z (expand 1 7 10))(define (show-n s n)  (if (= n 0)      '()      (cons (stream-car s)            (show-n (stream-cdr s) (- n 1)))))(show-n z 6)(show-n z 12);3.59;;a(define (integrate-series s)  (stream-map / s integers))(define exp-series  (cons-stream 1 (integrate-series exp-series)))(show-n exp-series 8);;b(define cosine-series  (cons-stream 1               (scale-stream                (integrate-series sine-series)                -1)))(define sine-series  (cons-stream 0               (integrate-series cosine-series)))(show-n cosine-series 9)(show-n sine-series 9);3.60(define (mul-series s1 s2);  (cons-stream (* (stream-car s1) (stream-car s2))               (add-streams                (scale-stream (stream-cdr s2)                              (stream-car s1))                (mul-series (stream-cdr s1) s2))))(define (mul-series-2 s1 s2);o(n^2)  (add-streams   (scale-stream s2 (stream-car s1))   (cons-stream    0    (mul-series-2 (stream-cdr s1) s2))))(define sine*cosine (mul-series sine-series cosine-series))(show-n sine*cosine 10);3.61(define (1/S s)  (define the-1/S    (cons-stream 1                 (mul-series (scale-stream (stream-cdr s) -1)                             the-1/S)))  the-1/S);warning:下面这个版本直接用递归，由于每次调用1/S时都会产生一个新的流，所以在计算过程中，记忆功能实际上并没有用到，但是算过一次后，两者的表现是一样的，读者可以分别运行两个版本多次比较差别(define (1/S s)  (cons-stream 1               (mul-series (scale-stream (stream-cdr s) -1)                           (1/S s))));3.62(define (div-series s1 s2)  (if (= (stream-car s2) 0)      (error "div-series: divided by zero!")      (mul-series s1 (1/S s2))))(define tan-series (div-series sine-series cosine-series))(show-n tan-series 9)