SICP 题解集合

1.1（略）

1.2

biwascheme> 
(/ (+ 5 4 (- 2 (- 3 (+ 6 (/ 4 5)))))
   (* 3 (- 6 2) (- 2 7)))
=> -0.24666666666666667

1.3

biwascheme> 
(define (BiggerSum x y z)
    (define s1 (+ x y))
    (define s2 (+ x z))
    (define s3 (+ y z))
    (cond ((and (> s1 s2) (> s1 s3)) s1)
          ((and (> s2 s1) (> s2 s3)) s2)
          (else s3)
    )
)
biwascheme> (BiggerSum 2 1 3)
=> 5

1.4   (略）

1.5

若解释器采用正则序求值，Ben可以看到解释器顺利返回0；

若解释器采用应用序，则程序会陷入无限循环。

1.6  (略）

1.7  

(define (square x)
 (* x x))
 
(define (improve guess x)
 (average guess (/ x guess)))
 
(define (average x y)
 (/ (+ x y) 2))
 
(define (good-enough? guess0 guess1)
 (< (abs (- (/ guess0 guess1) 1)) 0.001))

(define (sqrt-iter guess x)
 (define new-guess (improve guess x))
 (if (good-enough? guess new-guess)
    guess
    (sqrt-iter new-guess x)))
(define (sqrt x)
 (sqrt-iter 1.0 x))

1.8

(define (square x)
 (* x x))
(define (improve guess x)
 (/ (+ (/ x (square guess)) (* 2 guess)) 
    3)
)
(define (good-enough? guess0 guess1)
 (< (abs (- (/ guess0 guess1) 1)) 0.001))
(define (cube-root-iter guess x)
 (define new-guess (improve guess x))
 (if (good-enough? guess new-guess)
    guess
    (cube-root-iter new-guess x)))
(define (cube-root x)
 (cube-root-iter 1.0 x))