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2章前文

この章では対を使って、

ex2.1

(define (make-rat n d)
  (let ((g (abs (gcd n d))))
     (if (< d 0)
         (cons (/ (- n) g) (/ (- d) g))
         (cons (/ n g) (/ d g)))))

ex2.2

(define (make-segment start end) (cons start end))
(define (start-segment p) (car p))
(define (end-segment p) (cdr p))

(define (make-point x y) (cons x y))
(define (x-point p) (car p))
(define (y-point p) (cdr p))

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

ex2.3

;;縦、横で長方形を表現
(define (make-rectangle h w) (cons h w))
(define (height-rectangle r) (make-segment (car r)))
(define (width-rectangle r) (make-segment (cdr r)))
(define (length s)
  (sqrt (+ (square (- (x-point (start-segment s))
		      (x-point (end-segment s))))
	   (square (- (x-point (start-segment s))
		      (x-point (end-segment s))))))

;;高さ,幅で長方形を表現
(define (make-rectangle h w) (cons h w))
(define (height-rectangle r) (car r))
(define (width-rectangle r) (cdr r))

(define (parimeter r)
  (+ (* 2 (height-rectangle r))
     (* 2 (width-rectangle r))))

(define (area r)
  (* (height-rectangle r) (width-rectangle r)))

ex2.4

(define (cons x y)
  (lambda (m) (m x y)))
;;「引数を1つ(m)とり、(m x y)を返す手続き」を返す

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

ex2.5

(define (ex-cons a b)
  (* (expt 2 a) (expt 3 b)))

(define (pair z value result)
  (if (= (remainder z value) 0)
      (pair (/ z value) value (+ result 1))
      result))
(define (ex-car z)
  (pair z 2 0))
(define (ex-cdr z)
  (pair z 3 0))