SICP Sections 2.1.1-2.1.2

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本文通过具体的程序实例介绍了如何使用抽象编程技巧来实现数据结构的操作，包括分数的简化、线段中点的计算及矩形的周长与面积计算等。文章展示了如何通过构造器和选择器接口来实现数据抽象，使得底层实现细节得以隐藏。

Exercise 2.1

#lang racket
;the greatest common divisor of the two integers
(define (gcd a b)
  (if (= b 0)
      a
      (gcd b (remainder a b))))
;reduce the numerator and the denominator to the lowest terms
(define (make-rat-lowest a b)
  (let ((g (abs (gcd a b))))
    (cons (/ a g) (/ b g))))
;get the answer satisfied the require
(define (make-rat n d)
  (cond ((and (< n 0) (< d 0))
         (make-rat-lowest (- n) (- d)))
        ((and (< d 0) (> n 0))
         (make-rat-lowest (- n) (- d)))
        (else
         (make-rat-lowest n d))))

Exercise 2.2

#lang racket
;segment constructor and selectors
(define (make-segment start end)
  (cons start end))
(define (start-segment segment)
  (car segment))
(define (end-segment segment)
  (cdr segment))
;point constructor and selectors
(define make-point cons)
(define x-point car)
(define y-point cdr)
;middle-point of the designate segment
(define (average x y)
  (/ (+ x y) 2))
(define (midpoint-segment segment)
  (make-point
   (average (x-point (start-segment segment)) (x-point (end-segment segment)))
   (average (y-point (start-segment segment)) (y-point (end-segment segment)))))
;output to the console
(define (print-point p)
  (newline)
  (display "(")
  (display (x-point p))
  (display ",")
  (display (y-point p))
  (display ")"))

(print-point (midpoint-segment (make-segment (make-point 1.0 2.0) (make-point 2.0 2.0))))

Exercise 2.3

#lang racket
;compute the perimeter and area of the rectangle 
;no matter how rect-width and rect-height implemented
(define (rect-perimeter rect)
  (+ (* 2 (rect-width rect))
     (* 2 (rect-height rect))))
(define (rect-area rect)
  (* (rect-width rect)
     (rect-height rect)))
;rectangle constructor and selectors
(define (make-rect p1 p2)
  (make-segment p1 p2))
(define (rect-width rect)
  (abs (- (x-point (start-segment rect))
          (x-point (end-segment rect)))))
(define (rect-height rect)
  (abs (- (y-point (start-segment rect))
          (y-point (end-segment rect)))))

Summarize

wishful thinking是一种很好的编写抽象程序的指导方法，可以使我们编写“期望”的方法，而忽略底层实现。
数据抽象提供了一种 abstraction barriers，通过提供constructor和selector接口，使我们可以直接访问数据结构而忽略其底层实现，也就是说，底层实现可以任意的组织。