Scheme - データによる抽象の構築(データ抽象入門(抽象の壁(平面上の点、線分、中点)))

計算機プログラムの構造と解釈[第2版]
原著

開発環境

• macOS Sierra - Apple (OS)
• Emacs (Text Editor)
• Scheme (プログラミング言語)
• kscheme (ksi)(github) (処理系)

計算機プログラムの構造と解釈[第2版](ハロルド エイブルソン (著)、ジュリー サスマン (著)、ジェラルド・ジェイ サスマン (著)、Harold Abelson (原著)、Julie Sussman (原著)、Gerald Jay Sussman (原著)、和田 英一 (翻訳)、翔泳社、原著: Structure and Interpretation of Computer Programs (MIT Electrical Engineering and Computer Science)(SICP))の第2章(データによる抽象の構築)、2.1(データ抽象入門)、2.1.2(抽象の壁)、問題2.2.を取り組んでみる。

その他参考書籍

• Instructor's Manual to Accompany Structure & Interpretation of Computer Programs

問題2.2.

コード(Emacs)

(begin
  ;; (load "procedures.scm")
  (newline)
  (define (p x) (display x) (newline))

  (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 (print-point p)
    (display "(")
    (display (x-point p))
    (display ",")
    (display (y-point p))
    (display ")"))
  
  (define (midpoint-segment seg)
    ((lambda (start end)
       (make-point (/ (+ (x-point start) (x-point end)) 2)
                   (/ (+ (y-point start) (y-point end)) 2)))
     (start-segment seg)
     (end-segment seg)))

  (define nums '(1 2 3 4 5))
  (for-each
   (lambda (x1)
     (for-each
      (lambda (y1)
        (for-each
         (lambda (x2)
           (for-each
            (lambda (y2)
              ((lambda (start end)
                 (display "start: ")
                 (print-point start)
                 (display ", end: ")
                 (print-point end)
                 (display ", mid point: ")
                 (print-point (midpoint-segment (make-segment start end)))
                 (newline))
               (make-point x1 y1) (make-point x2 y2)))
            nums))
         nums))
      nums))
   nums)
  'done)

入出力結果(Terminal(kscheme), REPL(Read, Eval, Print, Loop))

$ ksi < sample2.scm
ksi> 
start: (1,1), end: (1,1), mid point: (1,1)
start: (1,1), end: (1,2), mid point: (1,3/2)
start: (1,1), end: (1,3), mid point: (1,2)
start: (1,1), end: (1,4), mid point: (1,5/2)
start: (1,1), end: (1,5), mid point: (1,3)
start: (1,1), end: (2,1), mid point: (3/2,1)
start: (1,1), end: (2,2), mid point: (3/2,3/2)
start: (1,1), end: (2,3), mid point: (3/2,2)
start: (1,1), end: (2,4), mid point: (3/2,5/2)
start: (1,1), end: (2,5), mid point: (3/2,3)
start: (1,1), end: (3,1), mid point: (2,1)
start: (1,1), end: (3,2), mid point: (2,3/2)
start: (1,1), end: (3,3), mid point: (2,2)
start: (1,1), end: (3,4), mid point: (2,5/2)
start: (1,1), end: (3,5), mid point: (2,3)
start: (1,1), end: (4,1), mid point: (5/2,1)
start: (1,1), end: (4,2), mid point: (5/2,3/2)
start: (1,1), end: (4,3), mid point: (5/2,2)
start: (1,1), end: (4,4), mid point: (5/2,5/2)
start: (1,1), end: (4,5), mid point: (5/2,3)
start: (1,1), end: (5,1), mid point: (3,1)
start: (1,1), end: (5,2), mid point: (3,3/2)
start: (1,1), end: (5,3), mid point: (3,2)
start: (1,1), end: (5,4), mid point: (3,5/2)
start: (1,1), end: (5,5), mid point: (3,3)
start: (1,2), end: (1,1), mid point: (1,3/2)
start: (1,2), end: (1,2), mid point: (1,2)
start: (1,2), end: (1,3), mid point: (1,5/2)
start: (1,2), end: (1,4), mid point: (1,3)
start: (1,2), end: (1,5), mid point: (1,7/2)
start: (1,2), end: (2,1), mid point: (3/2,3/2)
start: (1,2), end: (2,2), mid point: (3/2,2)
start: (1,2), end: (2,3), mid point: (3/2,5/2)
start: (1,2), end: (2,4), mid point: (3/2,3)
start: (1,2), end: (2,5), mid point: (3/2,7/2)
start: (1,2), end: (3,1), mid point: (2,3/2)
start: (1,2), end: (3,2), mid point: (2,2)
start: (1,2), end: (3,3), mid point: (2,5/2)
start: (1,2), end: (3,4), mid point: (2,3)
start: (1,2), end: (3,5), mid point: (2,7/2)
start: (1,2), end: (4,1), mid point: (5/2,3/2)
start: (1,2), end: (4,2), mid point: (5/2,2)
start: (1,2), end: (4,3), mid point: (5/2,5/2)
start: (1,2), end: (4,4), mid point: (5/2,3)
start: (1,2), end: (4,5), mid point: (5/2,7/2)
start: (1,2), end: (5,1), mid point: (3,3/2)
start: (1,2), end: (5,2), mid point: (3,2)
start: (1,2), end: (5,3), mid point: (3,5/2)
start: (1,2), end: (5,4), mid point: (3,3)
start: (1,2), end: (5,5), mid point: (3,7/2)
start: (1,3), end: (1,1), mid point: (1,2)
start: (1,3), end: (1,2), mid point: (1,5/2)
start: (1,3), end: (1,3), mid point: (1,3)
start: (1,3), end: (1,4), mid point: (1,7/2)
start: (1,3), end: (1,5), mid point: (1,4)
start: (1,3), end: (2,1), mid point: (3/2,2)
start: (1,3), end: (2,2), mid point: (3/2,5/2)
start: (1,3), end: (2,3), mid point: (3/2,3)
start: (1,3), end: (2,4), mid point: (3/2,7/2)
start: (1,3), end: (2,5), mid point: (3/2,4)
start: (1,3), end: (3,1), mid point: (2,2)
start: (1,3), end: (3,2), mid point: (2,5/2)
start: (1,3), end: (3,3), mid point: (2,3)
start: (1,3), end: (3,4), mid point: (2,7/2)
start: (1,3), end: (3,5), mid point: (2,4)
start: (1,3), end: (4,1), mid point: (5/2,2)
start: (1,3), end: (4,2), mid point: (5/2,5/2)
start: (1,3), end: (4,3), mid point: (5/2,3)
start: (1,3), end: (4,4), mid point: (5/2,7/2)
start: (1,3), end: (4,5), mid point: (5/2,4)
start: (1,3), end: (5,1), mid point: (3,2)
start: (1,3), end: (5,2), mid point: (3,5/2)
start: (1,3), end: (5,3), mid point: (3,3)
start: (1,3), end: (5,4), mid point: (3,7/2)
start: (1,3), end: (5,5), mid point: (3,4)
start: (1,4), end: (1,1), mid point: (1,5/2)
start: (1,4), end: (1,2), mid point: (1,3)
start: (1,4), end: (1,3), mid point: (1,7/2)
start: (1,4), end: (1,4), mid point: (1,4)
start: (1,4), end: (1,5), mid point: (1,9/2)
start: (1,4), end: (2,1), mid point: (3/2,5/2)
start: (1,4), end: (2,2), mid point: (3/2,3)
start: (1,4), end: (2,3), mid point: (3/2,7/2)
start: (1,4), end: (2,4), mid point: (3/2,4)
start: (1,4), end: (2,5), mid point: (3/2,9/2)
start: (1,4), end: (3,1), mid point: (2,5/2)
start: (1,4), end: (3,2), mid point: (2,3)
start: (1,4), end: (3,3), mid point: (2,7/2)
start: (1,4), end: (3,4), mid point: (2,4)
start: (1,4), end: (3,5), mid point: (2,9/2)
start: (1,4), end: (4,1), mid point: (5/2,5/2)
start: (1,4), end: (4,2), mid point: (5/2,3)
start: (1,4), end: (4,3), mid point: (5/2,7/2)
start: (1,4), end: (4,4), mid point: (5/2,4)
start: (1,4), end: (4,5), mid point: (5/2,9/2)
start: (1,4), end: (5,1), mid point: (3,5/2)
start: (1,4), end: (5,2), mid point: (3,3)
start: (1,4), end: (5,3), mid point: (3,7/2)
start: (1,4), end: (5,4), mid point: (3,4)
start: (1,4), end: (5,5), mid point: (3,9/2)
start: (1,5), end: (1,1), mid point: (1,3)
start: (1,5), end: (1,2), mid point: (1,7/2)
start: (1,5), end: (1,3), mid point: (1,4)
start: (1,5), end: (1,4), mid point: (1,9/2)
start: (1,5), end: (1,5), mid point: (1,5)
start: (1,5), end: (2,1), mid point: (3/2,3)
start: (1,5), end: (2,2), mid point: (3/2,7/2)
start: (1,5), end: (2,3), mid point: (3/2,4)
start: (1,5), end: (2,4), mid point: (3/2,9/2)
start: (1,5), end: (2,5), mid point: (3/2,5)
start: (1,5), end: (3,1), mid point: (2,3)
start: (1,5), end: (3,2), mid point: (2,7/2)
start: (1,5), end: (3,3), mid point: (2,4)
start: (1,5), end: (3,4), mid point: (2,9/2)
start: (1,5), end: (3,5), mid point: (2,5)
start: (1,5), end: (4,1), mid point: (5/2,3)
start: (1,5), end: (4,2), mid point: (5/2,7/2)
start: (1,5), end: (4,3), mid point: (5/2,4)
start: (1,5), end: (4,4), mid point: (5/2,9/2)
start: (1,5), end: (4,5), mid point: (5/2,5)
start: (1,5), end: (5,1), mid point: (3,3)
start: (1,5), end: (5,2), mid point: (3,7/2)
start: (1,5), end: (5,3), mid point: (3,4)
start: (1,5), end: (5,4), mid point: (3,9/2)
start: (1,5), end: (5,5), mid point: (3,5)
start: (2,1), end: (1,1), mid point: (3/2,1)
start: (2,1), end: (1,2), mid point: (3/2,3/2)
start: (2,1), end: (1,3), mid point: (3/2,2)
start: (2,1), end: (1,4), mid point: (3/2,5/2)
start: (2,1), end: (1,5), mid point: (3/2,3)
start: (2,1), end: (2,1), mid point: (2,1)
start: (2,1), end: (2,2), mid point: (2,3/2)
start: (2,1), end: (2,3), mid point: (2,2)
start: (2,1), end: (2,4), mid point: (2,5/2)
start: (2,1), end: (2,5), mid point: (2,3)
start: (2,1), end: (3,1), mid point: (5/2,1)
start: (2,1), end: (3,2), mid point: (5/2,3/2)
start: (2,1), end: (3,3), mid point: (5/2,2)
start: (2,1), end: (3,4), mid point: (5/2,5/2)
start: (2,1), end: (3,5), mid point: (5/2,3)
start: (2,1), end: (4,1), mid point: (3,1)
start: (2,1), end: (4,2), mid point: (3,3/2)
start: (2,1), end: (4,3), mid point: (3,2)
start: (2,1), end: (4,4), mid point: (3,5/2)
start: (2,1), end: (4,5), mid point: (3,3)
start: (2,1), end: (5,1), mid point: (7/2,1)
start: (2,1), end: (5,2), mid point: (7/2,3/2)
start: (2,1), end: (5,3), mid point: (7/2,2)
start: (2,1), end: (5,4), mid point: (7/2,5/2)
start: (2,1), end: (5,5), mid point: (7/2,3)
start: (2,2), end: (1,1), mid point: (3/2,3/2)
start: (2,2), end: (1,2), mid point: (3/2,2)
start: (2,2), end: (1,3), mid point: (3/2,5/2)
start: (2,2), end: (1,4), mid point: (3/2,3)
start: (2,2), end: (1,5), mid point: (3/2,7/2)
start: (2,2), end: (2,1), mid point: (2,3/2)
start: (2,2), end: (2,2), mid point: (2,2)
start: (2,2), end: (2,3), mid point: (2,5/2)
start: (2,2), end: (2,4), mid point: (2,3)
start: (2,2), end: (2,5), mid point: (2,7/2)
start: (2,2), end: (3,1), mid point: (5/2,3/2)
start: (2,2), end: (3,2), mid point: (5/2,2)
start: (2,2), end: (3,3), mid point: (5/2,5/2)
start: (2,2), end: (3,4), mid point: (5/2,3)
start: (2,2), end: (3,5), mid point: (5/2,7/2)
start: (2,2), end: (4,1), mid point: (3,3/2)
start: (2,2), end: (4,2), mid point: (3,2)
start: (2,2), end: (4,3), mid point: (3,5/2)
start: (2,2), end: (4,4), mid point: (3,3)
start: (2,2), end: (4,5), mid point: (3,7/2)
start: (2,2), end: (5,1), mid point: (7/2,3/2)
start: (2,2), end: (5,2), mid point: (7/2,2)
start: (2,2), end: (5,3), mid point: (7/2,5/2)
start: (2,2), end: (5,4), mid point: (7/2,3)
start: (2,2), end: (5,5), mid point: (7/2,7/2)
start: (2,3), end: (1,1), mid point: (3/2,2)
start: (2,3), end: (1,2), mid point: (3/2,5/2)
start: (2,3), end: (1,3), mid point: (3/2,3)
start: (2,3), end: (1,4), mid point: (3/2,7/2)
start: (2,3), end: (1,5), mid point: (3/2,4)
start: (2,3), end: (2,1), mid point: (2,2)
start: (2,3), end: (2,2), mid point: (2,5/2)
start: (2,3), end: (2,3), mid point: (2,3)
start: (2,3), end: (2,4), mid point: (2,7/2)
start: (2,3), end: (2,5), mid point: (2,4)
start: (2,3), end: (3,1), mid point: (5/2,2)
start: (2,3), end: (3,2), mid point: (5/2,5/2)
start: (2,3), end: (3,3), mid point: (5/2,3)
start: (2,3), end: (3,4), mid point: (5/2,7/2)
start: (2,3), end: (3,5), mid point: (5/2,4)
start: (2,3), end: (4,1), mid point: (3,2)
start: (2,3), end: (4,2), mid point: (3,5/2)
start: (2,3), end: (4,3), mid point: (3,3)
start: (2,3), end: (4,4), mid point: (3,7/2)
start: (2,3), end: (4,5), mid point: (3,4)
start: (2,3), end: (5,1), mid point: (7/2,2)
start: (2,3), end: (5,2), mid point: (7/2,5/2)
start: (2,3), end: (5,3), mid point: (7/2,3)
start: (2,3), end: (5,4), mid point: (7/2,7/2)
start: (2,3), end: (5,5), mid point: (7/2,4)
start: (2,4), end: (1,1), mid point: (3/2,5/2)
start: (2,4), end: (1,2), mid point: (3/2,3)
start: (2,4), end: (1,3), mid point: (3/2,7/2)
start: (2,4), end: (1,4), mid point: (3/2,4)
start: (2,4), end: (1,5), mid point: (3/2,9/2)
start: (2,4), end: (2,1), mid point: (2,5/2)
start: (2,4), end: (2,2), mid point: (2,3)
start: (2,4), end: (2,3), mid point: (2,7/2)
start: (2,4), end: (2,4), mid point: (2,4)
start: (2,4), end: (2,5), mid point: (2,9/2)
start: (2,4), end: (3,1), mid point: (5/2,5/2)
start: (2,4), end: (3,2), mid point: (5/2,3)
start: (2,4), end: (3,3), mid point: (5/2,7/2)
start: (2,4), end: (3,4), mid point: (5/2,4)
start: (2,4), end: (3,5), mid point: (5/2,9/2)
start: (2,4), end: (4,1), mid point: (3,5/2)
start: (2,4), end: (4,2), mid point: (3,3)
start: (2,4), end: (4,3), mid point: (3,7/2)
start: (2,4), end: (4,4), mid point: (3,4)
start: (2,4), end: (4,5), mid point: (3,9/2)
start: (2,4), end: (5,1), mid point: (7/2,5/2)
start: (2,4), end: (5,2), mid point: (7/2,3)
start: (2,4), end: (5,3), mid point: (7/2,7/2)
start: (2,4), end: (5,4), mid point: (7/2,4)
start: (2,4), end: (5,5), mid point: (7/2,9/2)
start: (2,5), end: (1,1), mid point: (3/2,3)
start: (2,5), end: (1,2), mid point: (3/2,7/2)
start: (2,5), end: (1,3), mid point: (3/2,4)
start: (2,5), end: (1,4), mid point: (3/2,9/2)
start: (2,5), end: (1,5), mid point: (3/2,5)
start: (2,5), end: (2,1), mid point: (2,3)
start: (2,5), end: (2,2), mid point: (2,7/2)
start: (2,5), end: (2,3), mid point: (2,4)
start: (2,5), end: (2,4), mid point: (2,9/2)
start: (2,5), end: (2,5), mid point: (2,5)
start: (2,5), end: (3,1), mid point: (5/2,3)
start: (2,5), end: (3,2), mid point: (5/2,7/2)
start: (2,5), end: (3,3), mid point: (5/2,4)
start: (2,5), end: (3,4), mid point: (5/2,9/2)
start: (2,5), end: (3,5), mid point: (5/2,5)
start: (2,5), end: (4,1), mid point: (3,3)
start: (2,5), end: (4,2), mid point: (3,7/2)
start: (2,5), end: (4,3), mid point: (3,4)
start: (2,5), end: (4,4), mid point: (3,9/2)
start: (2,5), end: (4,5), mid point: (3,5)
start: (2,5), end: (5,1), mid point: (7/2,3)
start: (2,5), end: (5,2), mid point: (7/2,7/2)
start: (2,5), end: (5,3), mid point: (7/2,4)
start: (2,5), end: (5,4), mid point: (7/2,9/2)
start: (2,5), end: (5,5), mid point: (7/2,5)
start: (3,1), end: (1,1), mid point: (2,1)
start: (3,1), end: (1,2), mid point: (2,3/2)
start: (3,1), end: (1,3), mid point: (2,2)
start: (3,1), end: (1,4), mid point: (2,5/2)
start: (3,1), end: (1,5), mid point: (2,3)
start: (3,1), end: (2,1), mid point: (5/2,1)
start: (3,1), end: (2,2), mid point: (5/2,3/2)
start: (3,1), end: (2,3), mid point: (5/2,2)
start: (3,1), end: (2,4), mid point: (5/2,5/2)
start: (3,1), end: (2,5), mid point: (5/2,3)
start: (3,1), end: (3,1), mid point: (3,1)
start: (3,1), end: (3,2), mid point: (3,3/2)
start: (3,1), end: (3,3), mid point: (3,2)
start: (3,1), end: (3,4), mid point: (3,5/2)
start: (3,1), end: (3,5), mid point: (3,3)
start: (3,1), end: (4,1), mid point: (7/2,1)
start: (3,1), end: (4,2), mid point: (7/2,3/2)
start: (3,1), end: (4,3), mid point: (7/2,2)
start: (3,1), end: (4,4), mid point: (7/2,5/2)
start: (3,1), end: (4,5), mid point: (7/2,3)
start: (3,1), end: (5,1), mid point: (4,1)
start: (3,1), end: (5,2), mid point: (4,3/2)
start: (3,1), end: (5,3), mid point: (4,2)
start: (3,1), end: (5,4), mid point: (4,5/2)
start: (3,1), end: (5,5), mid point: (4,3)
start: (3,2), end: (1,1), mid point: (2,3/2)
start: (3,2), end: (1,2), mid point: (2,2)
start: (3,2), end: (1,3), mid point: (2,5/2)
start: (3,2), end: (1,4), mid point: (2,3)
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start: (5,4), end: (4,3), mid point: (9/2,7/2)
start: (5,4), end: (4,4), mid point: (9/2,4)
start: (5,4), end: (4,5), mid point: (9/2,9/2)
start: (5,4), end: (5,1), mid point: (5,5/2)
start: (5,4), end: (5,2), mid point: (5,3)
start: (5,4), end: (5,3), mid point: (5,7/2)
start: (5,4), end: (5,4), mid point: (5,4)
start: (5,4), end: (5,5), mid point: (5,9/2)
start: (5,5), end: (1,1), mid point: (3,3)
start: (5,5), end: (1,2), mid point: (3,7/2)
start: (5,5), end: (1,3), mid point: (3,4)
start: (5,5), end: (1,4), mid point: (3,9/2)
start: (5,5), end: (1,5), mid point: (3,5)
start: (5,5), end: (2,1), mid point: (7/2,3)
start: (5,5), end: (2,2), mid point: (7/2,7/2)
start: (5,5), end: (2,3), mid point: (7/2,4)
start: (5,5), end: (2,4), mid point: (7/2,9/2)
start: (5,5), end: (2,5), mid point: (7/2,5)
start: (5,5), end: (3,1), mid point: (4,3)
start: (5,5), end: (3,2), mid point: (4,7/2)
start: (5,5), end: (3,3), mid point: (4,4)
start: (5,5), end: (3,4), mid point: (4,9/2)
start: (5,5), end: (3,5), mid point: (4,5)
start: (5,5), end: (4,1), mid point: (9/2,3)
start: (5,5), end: (4,2), mid point: (9/2,7/2)
start: (5,5), end: (4,3), mid point: (9/2,4)
start: (5,5), end: (4,4), mid point: (9/2,9/2)
start: (5,5), end: (4,5), mid point: (9/2,5)
start: (5,5), end: (5,1), mid point: (5,3)
start: (5,5), end: (5,2), mid point: (5,7/2)
start: (5,5), end: (5,3), mid point: (5,4)
start: (5,5), end: (5,4), mid point: (5,9/2)
start: (5,5), end: (5,5), mid point: (5,5)
=> done
ksi> $