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