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) ))

 (define (good-enough? guess0 guess1)
  (< (abs (- (/ guess0 guess1) )) 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)) (*  guess))
     )
 )
 (define (good-enough? guess0 guess1)
  (< (abs (- (/ guess0 guess1) )) 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))