SICP_2.58 

 1 #lang racket
 2 
 3 (define (deriv exp var)
 4   (cond ((number? exp) 0)
 5         ((variable? exp)
 6          (if (same-variable? exp var) 1 0))
 7         ((sum? exp)
 8          (make-sum (deriv (addend exp) var)
 9                    (deriv (augend exp) var)))
10         ((product? exp)
11          (make-sum
12           (make-product (multiplier exp)
13                         (deriv (multiplicand exp) var))
14           (make-product (deriv (multiplier exp) var)
15                         (multiplicand exp))))
16         (else
17          (error "unknow expression type --DERIV" exp))))
18 
19 (define (variable? x)
20   (symbol? x))
21 
22 (define (same-variable? v1 v2)
23   (and (variable? v1) (variable? v2) (eq? v1 v2)))
24 
25 (define (=number? exp num)
26   (and (number? exp) (= exp num)))
27 
28 (define (** a b)
29   (define (iter n result)
30       (cond ((= 0 b) 1)
31           ((or (< n b) (= n b)) (iter (+ n 1) (* a result)))
32           ((> n b) result)))
33   (iter 1 1))
34 
35 (define (sum? x)
36   (and (pair? x) (eq? (cadr x) '+)))
37 
38 (define (product? x)
39   (and (pair? x) (eq? (cadr x) '*)))
40 
41 (define (make-sum a1 a2)
42   (cond ((=number? a1 0) a2)
43         ((=number? a2 0) a1)
44         ((and (number? a1) (number? a2)) (+ a1 a2))
45          (else (list a1 '+ a2))))
46 
47 (define (addend s) (car s))
48 (define (augend s) (caddr s))
49 
50 (define (make-product m1 m2)
51   (cond ((or (=number? m1 0) (=number? m2 0)) 0)
52         ((=number? m1 1) m2)
53         ((=number? m2 1) m1)
54         ((and (number? m1) (number? m2)) (* m1 m2))
55         (else (list m1 '* m2))))
56 
57 (define (multiplier p) (car p))
58 (define (multiplicand p) (caddr p))
59 
60 ;(deriv '(x + (x * x)) 'x)
61 ;(deriv '(x * (x + x)) 'x)
62 
63 ;;;;;;;;;;;;;;(b)
64 ;;;;;;;;;;;;;;不会

 

posted @ 2017-02-26 16:56  lan126  阅读(198)  评论(0)  编辑  收藏  举报