#lang racket
;;;;;;;;;;;;;;;只需先写出按愿望和公式而构造的函数
;;;;;;;;;;;;;;;再加上一些特定的选择函数和构造函数就可以实现这么强大的功能
;;;;;;;;;;;;;;;quote 和 list 的区别
(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))))
((exponentiation?
exp)
(make-product (make-
product (exponent exp)
(make-exponentiation (
base exp) (- (exponent exp)
1)))
(deriv (base exp)
var)))
(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? (car x)
'+)))
;(define (addend s) (cadr s))
;(define (augend s) (caddr s))
(define (product?
x)
(and (pair? x) (eq? (car x)
'*)))
;(define (multiplier p) (cadr p))
;(define (multiplicand p) (caddr p))
(define (exponentiation?
x)
(and (pair? x) (eq? (car x)
'**)))
(define (base e) (cadr e))
(define (exponent e) (caddr e))
(define (make-
exponentiation b1 b2)
(cond ((=number? b2
0)
1)
((=number? b2
1) b1)
((and (number? b1) (number? b2)) (**
b1 b2))
(else (list
'** b1 b2))))
(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 (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))))
;;;;;;;;;;;;test
;(deriv '(* (* x y) (+ x 3)) 'x)
;(deriv '(** (+ x y) 4) 'x)
;(deriv '(+ (* x y) x) 'x)
;;;;;;;;;;;;;2.58
(define (addend s)
(cadr s))
(define (augend s)
(if (
null?
(cdddr s))
(caddr s)
(cons '+ (cddr s))))
(define (multiplier p)
(cadr p))
(define (multiplicand p)
(if (
null?
(cdddr p))
(caddr p)
(cons '* (cddr p))))
;;;;;;;;;;;;test
(deriv '(+ (* x 4) (+ x x) (* x x)) 'x)
(deriv '(* (+ x 4) (* x 4) y (** x 3)) 'y)
1.这几题进一步强化了按愿望实现函数的方法
2.quoto 和 list 的区别 参考
（1）' 是quoto 的缩写
（2）' 后的内容会原样返回，因为 ' 就是个省略了的单引号
（= '3 3） ->#t
（car '（list a b）） ->list (和sicp_2.55同理)
（3）list 是个函数
（list （+ 1 3） （+ 2 5）） -> (4 7)
转载于:https://www.cnblogs.com/tclan126/p/6443803.html
相关资源：数据结构—成绩单生成器
