练习2.2-练习2.10

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版权声明：本文为博主原创文章，转载请注明出处：http://blog.jerkybible.com/2014/01/15/2014-01-15-练习2.2-练习2.10/

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1.练习2.2

(define (make-segment start end)
  (cons start end))

(define (start-segment seg)
  (car seg))

(define (end-segment seg)
  (cdr seg))

(define (make-point x y)
  (cons x y))

(define (x-point p)
  (car p))

(define (y-point p)
  (cdr p))

(define (midpoint-segment seg)
  (make-point (/ (+ (x-point (start-segment seg))
		    (x-point (end-segment seg))) 2)
	      (/ (+ (y-point (start-segment seg))
		    (y-point (end-segment seg))) 2)))

2.练习2.3首次定义：

(define (make-rect start end)
  (cons start end))

(define (start-rect seg)
  (car seg))

(define (end-rect seg)
  (cdr seg))

(define (width rect)
  (abs (- (y-point (end-rect rect))
	  (y-point (start-rect rect)))))

(define (length rect)
  (abs (- (x-point (end-rect rect))
	  (x-point (start-rect rect)))))

(define (girth rect)
  (* (+ (width rect)
	(length rect))
     2))

(define (area rect)
  (* (width rect)
     (length rect)))

二次定义：

(define (make-rect start length width)
  (cons start
	(cons length width)))

(define (start-rect seg)
  (car seg))

(define (end-rect seg)
  (cons (+ (x-point (start-rect seg))
	   (car (cdr seg)))
	(+ (y-point (start-rect seg))
	   (cdr (cdr seg)))))

3.练习2.4

(define (cons x y)
  (lambda (m) (m x y)))

(define (car z)
  (z (lambda (p q) p)))

(define (cdr z)
  (z (lambda (p q) q)))

4.练习2.5

(define (cons a b)
  (* (pow 2 a)
     (pow 3 b)))

(define (car c)
  (define (iter n result)
    (if (not (= (remainder n 2) 0))
	result
	(iter (/ n 2) (+ result 1))))
  (iter c 0))

(define (cdr c)
  (define (iter n result)
    (if (not (= (remainder n 3) 0))
	result
	(iter (/ n 3) (+ result 1))))
  (iter c 0))

5.练习2.6

(define one
  (lambda (f) (lambda (x) (f x))))

(define two
  (lambda (f) (lambda (x) (f (f x)))))

(define (add a b)
  (lambda (f) (lambda (x) ((b f) ((a f) x)))))

6.练习2.7

(define (make-interval x y)
  (cons x y))

(define (upper-bound c)
  (cdr c))

(define (lower-bound c)
  (car c))

7.练习2.8

(define (sub-interval x y)
  (let ((a (- (lower-bound x) (lower-bound y)))
	(b (- (upper-bound x) (upper-bound y))))
    (make-interval (min a b)
		   (max a b))))

8.练习2.9

(define (width-interval a)
  (/ (- (upper-bound a)
	(lower-bound a))
     2))

9.练习2.10

(define (div-interval x y)
  (if (and (<= (lower-bound y) 0) (>= (upper-bound y) 0))
      (error "ERROR!!!")
      (mul-interval x
		       (make-interval (/ 1.0 (upper-bound y))
				      (/ 1.0 (lower-bound y))))))