SICP_2.58

#lang racket

(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)
         (make-sum (deriv (addend exp) var)
                   (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
          (make-product (multiplier exp)
                        (deriv (multiplicand exp) var))
          (make-product (deriv (multiplier exp) var)
                        (multiplicand exp))))
        (else
         (error "unknow expression type --DERIV" exp))))

(define (variable? x)
  (symbol? x))

(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))

(define (=number? exp num)
  (and (number? exp) (= exp num)))

(define (** a b)
  (define (iter n result)
      (cond ((= 0 b) 1)
          ((or (< n b) (= n b)) (iter (+ n 1) (* a result)))
          ((> n b) result)))
  (iter 1 1))

(define (sum? x)
  (and (pair? x) (eq? (cadr x) '+)))

(define (product? x)
  (and (pair? x) (eq? (cadr x) '*)))

(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) (+ a1 a2))
         (else (list a1 '+ a2))))

(define (addend s) (car s))
(define (augend s) (caddr s))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list m1 '* m2))))

(define (multiplier p) (car p))
(define (multiplicand p) (caddr p))

;(deriv '(x + (x * x)) 'x)
;(deriv '(x * (x + x)) 'x)

;;;;;;;;;;;;;;(b)
;;;;;;;;;;;;;;不会