Scheme - データによる抽象の構築(階層データ構造と閉包性(例: 図形言語(フレーム(構成子, 選択子の2通りの実装方法(cons, list)))))

計算機プログラムの構造と解釈
Gerald Jay Sussman, Julie Sussman
Harold Abelson (原著) 和田 英一 (翻訳)

開発環境

• OS X Mavericks - Apple(OS)
• Emacs (CUI)、BBEdit - Bare Bones Software, Inc. (GUI) (Text Editor)
• Scheme (プログラミング言語)
• Gauche (処理系)
• Racket (プログラミング言語)
• DrRacket (開発環境)

計算機プログラムの構造と解釈(Gerald Jay Sussman(原著)、Julie Sussman(原著)、Harold Abelson(原著)、和田 英一(翻訳)、ピアソンエデュケーション、原書: Structure and Interpretation of Computer Programs (MIT Electrical Engineering and Computer Science)(SICP))の2(データによる抽象の構築)、2.2(階層データ構造と閉包性)、2.2.4(例: 図形言語)、フレーム、問題 2.47.を解いてみる。

その他参考書籍

• Instructor's Manual to Accompany Structure & Interpretation of Computer Programs
• プログラミングGauche (Kahuaプロジェクト (著), 川合 史朗 (監修), オライリージャパン)

問題 2.47.

コード(BBEdit, Emacs)

sample.scm

#!/usr/bin/env gosh
;; -*- coding: utf-8 -*-

;; これまでに書いた手続き
(load "./procedures.scm")

(define (make-frame origin edge1 edge2)
  (list origin edge1 edge2))

(define (origin-frame frame)
  (car frame))

(define (edge1-frame frame)
  (car (cdr frame)))

(define (edge2-frame frame)
  (car (cdr (cdr frame))))

(define (make-frame1 origin edge1 edge2)
  (cons origin (cons edge1 edge2)))

(define (origin-frame1 frame)
  (car frame))

(define (edge1-frame1 frame)
  (car (cdr frame)))

(define (edge2-frame1 frame)
  (cdr (cdr frame)))

(define v1 (make-vect 0 0))
(define v2 (make-vect 1 1))
(define v3 (make-vect 2 3))
(define v4 (make-vect 4 5))
(define vectors (list v1 v2 v3 v4))
(define frames (flatmap (lambda (origin)
                          (flatmap (lambda (edge1)
                                      (map (lambda (edge2)
                                             (make-frame origin
                                                         edge1
                                                         edge2))
                                           vectors))
                                    vectors))
                        vectors))
(define frames1 (flatmap (lambda (origin)
                           (flatmap (lambda (edge1)
                                      (map (lambda (edge2)
                                             (make-frame1 origin
                                                          edge1
                                                          edge2))
                                           vectors))
                                    vectors))
                         vectors))

(for-each (lambda (frame)
            (print "frame:" frame
                   " origin:" (origin-frame frame)
                   " edge1:" (edge1-frame frame)
                   " edge2:" (edge2-frame frame)))
          frames)

(for-each (lambda (frame1)
            (print "frame1:" frame1
                   " origin:" (origin-frame1 frame1)
                   " edge1:" (edge1-frame1 frame1)
                   " edge2:" (edge2-frame1 frame1)))
          frames1)

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

$ ./sample.scm
frame:((0 0) (0 0) (0 0)) origin:(0 0) edge1:(0 0) edge2:(0 0)
frame:((0 0) (0 0) (1 1)) origin:(0 0) edge1:(0 0) edge2:(1 1)
frame:((0 0) (0 0) (2 3)) origin:(0 0) edge1:(0 0) edge2:(2 3)
frame:((0 0) (0 0) (4 5)) origin:(0 0) edge1:(0 0) edge2:(4 5)
frame:((0 0) (1 1) (0 0)) origin:(0 0) edge1:(1 1) edge2:(0 0)
frame:((0 0) (1 1) (1 1)) origin:(0 0) edge1:(1 1) edge2:(1 1)
frame:((0 0) (1 1) (2 3)) origin:(0 0) edge1:(1 1) edge2:(2 3)
frame:((0 0) (1 1) (4 5)) origin:(0 0) edge1:(1 1) edge2:(4 5)
frame:((0 0) (2 3) (0 0)) origin:(0 0) edge1:(2 3) edge2:(0 0)
frame:((0 0) (2 3) (1 1)) origin:(0 0) edge1:(2 3) edge2:(1 1)
frame:((0 0) (2 3) (2 3)) origin:(0 0) edge1:(2 3) edge2:(2 3)
frame:((0 0) (2 3) (4 5)) origin:(0 0) edge1:(2 3) edge2:(4 5)
frame:((0 0) (4 5) (0 0)) origin:(0 0) edge1:(4 5) edge2:(0 0)
frame:((0 0) (4 5) (1 1)) origin:(0 0) edge1:(4 5) edge2:(1 1)
frame:((0 0) (4 5) (2 3)) origin:(0 0) edge1:(4 5) edge2:(2 3)
frame:((0 0) (4 5) (4 5)) origin:(0 0) edge1:(4 5) edge2:(4 5)
frame:((1 1) (0 0) (0 0)) origin:(1 1) edge1:(0 0) edge2:(0 0)
frame:((1 1) (0 0) (1 1)) origin:(1 1) edge1:(0 0) edge2:(1 1)
frame:((1 1) (0 0) (2 3)) origin:(1 1) edge1:(0 0) edge2:(2 3)
frame:((1 1) (0 0) (4 5)) origin:(1 1) edge1:(0 0) edge2:(4 5)
frame:((1 1) (1 1) (0 0)) origin:(1 1) edge1:(1 1) edge2:(0 0)
frame:((1 1) (1 1) (1 1)) origin:(1 1) edge1:(1 1) edge2:(1 1)
frame:((1 1) (1 1) (2 3)) origin:(1 1) edge1:(1 1) edge2:(2 3)
frame:((1 1) (1 1) (4 5)) origin:(1 1) edge1:(1 1) edge2:(4 5)
frame:((1 1) (2 3) (0 0)) origin:(1 1) edge1:(2 3) edge2:(0 0)
frame:((1 1) (2 3) (1 1)) origin:(1 1) edge1:(2 3) edge2:(1 1)
frame:((1 1) (2 3) (2 3)) origin:(1 1) edge1:(2 3) edge2:(2 3)
frame:((1 1) (2 3) (4 5)) origin:(1 1) edge1:(2 3) edge2:(4 5)
frame:((1 1) (4 5) (0 0)) origin:(1 1) edge1:(4 5) edge2:(0 0)
frame:((1 1) (4 5) (1 1)) origin:(1 1) edge1:(4 5) edge2:(1 1)
frame:((1 1) (4 5) (2 3)) origin:(1 1) edge1:(4 5) edge2:(2 3)
frame:((1 1) (4 5) (4 5)) origin:(1 1) edge1:(4 5) edge2:(4 5)
frame:((2 3) (0 0) (0 0)) origin:(2 3) edge1:(0 0) edge2:(0 0)
frame:((2 3) (0 0) (1 1)) origin:(2 3) edge1:(0 0) edge2:(1 1)
frame:((2 3) (0 0) (2 3)) origin:(2 3) edge1:(0 0) edge2:(2 3)
frame:((2 3) (0 0) (4 5)) origin:(2 3) edge1:(0 0) edge2:(4 5)
frame:((2 3) (1 1) (0 0)) origin:(2 3) edge1:(1 1) edge2:(0 0)
frame:((2 3) (1 1) (1 1)) origin:(2 3) edge1:(1 1) edge2:(1 1)
frame:((2 3) (1 1) (2 3)) origin:(2 3) edge1:(1 1) edge2:(2 3)
frame:((2 3) (1 1) (4 5)) origin:(2 3) edge1:(1 1) edge2:(4 5)
frame:((2 3) (2 3) (0 0)) origin:(2 3) edge1:(2 3) edge2:(0 0)
frame:((2 3) (2 3) (1 1)) origin:(2 3) edge1:(2 3) edge2:(1 1)
frame:((2 3) (2 3) (2 3)) origin:(2 3) edge1:(2 3) edge2:(2 3)
frame:((2 3) (2 3) (4 5)) origin:(2 3) edge1:(2 3) edge2:(4 5)
frame:((2 3) (4 5) (0 0)) origin:(2 3) edge1:(4 5) edge2:(0 0)
frame:((2 3) (4 5) (1 1)) origin:(2 3) edge1:(4 5) edge2:(1 1)
frame:((2 3) (4 5) (2 3)) origin:(2 3) edge1:(4 5) edge2:(2 3)
frame:((2 3) (4 5) (4 5)) origin:(2 3) edge1:(4 5) edge2:(4 5)
frame:((4 5) (0 0) (0 0)) origin:(4 5) edge1:(0 0) edge2:(0 0)
frame:((4 5) (0 0) (1 1)) origin:(4 5) edge1:(0 0) edge2:(1 1)
frame:((4 5) (0 0) (2 3)) origin:(4 5) edge1:(0 0) edge2:(2 3)
frame:((4 5) (0 0) (4 5)) origin:(4 5) edge1:(0 0) edge2:(4 5)
frame:((4 5) (1 1) (0 0)) origin:(4 5) edge1:(1 1) edge2:(0 0)
frame:((4 5) (1 1) (1 1)) origin:(4 5) edge1:(1 1) edge2:(1 1)
frame:((4 5) (1 1) (2 3)) origin:(4 5) edge1:(1 1) edge2:(2 3)
frame:((4 5) (1 1) (4 5)) origin:(4 5) edge1:(1 1) edge2:(4 5)
frame:((4 5) (2 3) (0 0)) origin:(4 5) edge1:(2 3) edge2:(0 0)
frame:((4 5) (2 3) (1 1)) origin:(4 5) edge1:(2 3) edge2:(1 1)
frame:((4 5) (2 3) (2 3)) origin:(4 5) edge1:(2 3) edge2:(2 3)
frame:((4 5) (2 3) (4 5)) origin:(4 5) edge1:(2 3) edge2:(4 5)
frame:((4 5) (4 5) (0 0)) origin:(4 5) edge1:(4 5) edge2:(0 0)
frame:((4 5) (4 5) (1 1)) origin:(4 5) edge1:(4 5) edge2:(1 1)
frame:((4 5) (4 5) (2 3)) origin:(4 5) edge1:(4 5) edge2:(2 3)
frame:((4 5) (4 5) (4 5)) origin:(4 5) edge1:(4 5) edge2:(4 5)
frame1:((0 0) (0 0) 0 0) origin:(0 0) edge1:(0 0) edge2:(0 0)
frame1:((0 0) (0 0) 1 1) origin:(0 0) edge1:(0 0) edge2:(1 1)
frame1:((0 0) (0 0) 2 3) origin:(0 0) edge1:(0 0) edge2:(2 3)
frame1:((0 0) (0 0) 4 5) origin:(0 0) edge1:(0 0) edge2:(4 5)
frame1:((0 0) (1 1) 0 0) origin:(0 0) edge1:(1 1) edge2:(0 0)
frame1:((0 0) (1 1) 1 1) origin:(0 0) edge1:(1 1) edge2:(1 1)
frame1:((0 0) (1 1) 2 3) origin:(0 0) edge1:(1 1) edge2:(2 3)
frame1:((0 0) (1 1) 4 5) origin:(0 0) edge1:(1 1) edge2:(4 5)
frame1:((0 0) (2 3) 0 0) origin:(0 0) edge1:(2 3) edge2:(0 0)
frame1:((0 0) (2 3) 1 1) origin:(0 0) edge1:(2 3) edge2:(1 1)
frame1:((0 0) (2 3) 2 3) origin:(0 0) edge1:(2 3) edge2:(2 3)
frame1:((0 0) (2 3) 4 5) origin:(0 0) edge1:(2 3) edge2:(4 5)
frame1:((0 0) (4 5) 0 0) origin:(0 0) edge1:(4 5) edge2:(0 0)
frame1:((0 0) (4 5) 1 1) origin:(0 0) edge1:(4 5) edge2:(1 1)
frame1:((0 0) (4 5) 2 3) origin:(0 0) edge1:(4 5) edge2:(2 3)
frame1:((0 0) (4 5) 4 5) origin:(0 0) edge1:(4 5) edge2:(4 5)
frame1:((1 1) (0 0) 0 0) origin:(1 1) edge1:(0 0) edge2:(0 0)
frame1:((1 1) (0 0) 1 1) origin:(1 1) edge1:(0 0) edge2:(1 1)
frame1:((1 1) (0 0) 2 3) origin:(1 1) edge1:(0 0) edge2:(2 3)
frame1:((1 1) (0 0) 4 5) origin:(1 1) edge1:(0 0) edge2:(4 5)
frame1:((1 1) (1 1) 0 0) origin:(1 1) edge1:(1 1) edge2:(0 0)
frame1:((1 1) (1 1) 1 1) origin:(1 1) edge1:(1 1) edge2:(1 1)
frame1:((1 1) (1 1) 2 3) origin:(1 1) edge1:(1 1) edge2:(2 3)
frame1:((1 1) (1 1) 4 5) origin:(1 1) edge1:(1 1) edge2:(4 5)
frame1:((1 1) (2 3) 0 0) origin:(1 1) edge1:(2 3) edge2:(0 0)
frame1:((1 1) (2 3) 1 1) origin:(1 1) edge1:(2 3) edge2:(1 1)
frame1:((1 1) (2 3) 2 3) origin:(1 1) edge1:(2 3) edge2:(2 3)
frame1:((1 1) (2 3) 4 5) origin:(1 1) edge1:(2 3) edge2:(4 5)
frame1:((1 1) (4 5) 0 0) origin:(1 1) edge1:(4 5) edge2:(0 0)
frame1:((1 1) (4 5) 1 1) origin:(1 1) edge1:(4 5) edge2:(1 1)
frame1:((1 1) (4 5) 2 3) origin:(1 1) edge1:(4 5) edge2:(2 3)
frame1:((1 1) (4 5) 4 5) origin:(1 1) edge1:(4 5) edge2:(4 5)
frame1:((2 3) (0 0) 0 0) origin:(2 3) edge1:(0 0) edge2:(0 0)
frame1:((2 3) (0 0) 1 1) origin:(2 3) edge1:(0 0) edge2:(1 1)
frame1:((2 3) (0 0) 2 3) origin:(2 3) edge1:(0 0) edge2:(2 3)
frame1:((2 3) (0 0) 4 5) origin:(2 3) edge1:(0 0) edge2:(4 5)
frame1:((2 3) (1 1) 0 0) origin:(2 3) edge1:(1 1) edge2:(0 0)
frame1:((2 3) (1 1) 1 1) origin:(2 3) edge1:(1 1) edge2:(1 1)
frame1:((2 3) (1 1) 2 3) origin:(2 3) edge1:(1 1) edge2:(2 3)
frame1:((2 3) (1 1) 4 5) origin:(2 3) edge1:(1 1) edge2:(4 5)
frame1:((2 3) (2 3) 0 0) origin:(2 3) edge1:(2 3) edge2:(0 0)
frame1:((2 3) (2 3) 1 1) origin:(2 3) edge1:(2 3) edge2:(1 1)
frame1:((2 3) (2 3) 2 3) origin:(2 3) edge1:(2 3) edge2:(2 3)
frame1:((2 3) (2 3) 4 5) origin:(2 3) edge1:(2 3) edge2:(4 5)
frame1:((2 3) (4 5) 0 0) origin:(2 3) edge1:(4 5) edge2:(0 0)
frame1:((2 3) (4 5) 1 1) origin:(2 3) edge1:(4 5) edge2:(1 1)
frame1:((2 3) (4 5) 2 3) origin:(2 3) edge1:(4 5) edge2:(2 3)
frame1:((2 3) (4 5) 4 5) origin:(2 3) edge1:(4 5) edge2:(4 5)
frame1:((4 5) (0 0) 0 0) origin:(4 5) edge1:(0 0) edge2:(0 0)
frame1:((4 5) (0 0) 1 1) origin:(4 5) edge1:(0 0) edge2:(1 1)
frame1:((4 5) (0 0) 2 3) origin:(4 5) edge1:(0 0) edge2:(2 3)
frame1:((4 5) (0 0) 4 5) origin:(4 5) edge1:(0 0) edge2:(4 5)
frame1:((4 5) (1 1) 0 0) origin:(4 5) edge1:(1 1) edge2:(0 0)
frame1:((4 5) (1 1) 1 1) origin:(4 5) edge1:(1 1) edge2:(1 1)
frame1:((4 5) (1 1) 2 3) origin:(4 5) edge1:(1 1) edge2:(2 3)
frame1:((4 5) (1 1) 4 5) origin:(4 5) edge1:(1 1) edge2:(4 5)
frame1:((4 5) (2 3) 0 0) origin:(4 5) edge1:(2 3) edge2:(0 0)
frame1:((4 5) (2 3) 1 1) origin:(4 5) edge1:(2 3) edge2:(1 1)
frame1:((4 5) (2 3) 2 3) origin:(4 5) edge1:(2 3) edge2:(2 3)
frame1:((4 5) (2 3) 4 5) origin:(4 5) edge1:(2 3) edge2:(4 5)
frame1:((4 5) (4 5) 0 0) origin:(4 5) edge1:(4 5) edge2:(0 0)
frame1:((4 5) (4 5) 1 1) origin:(4 5) edge1:(4 5) edge2:(1 1)
frame1:((4 5) (4 5) 2 3) origin:(4 5) edge1:(4 5) edge2:(2 3)
frame1:((4 5) (4 5) 4 5) origin:(4 5) edge1:(4 5) edge2:(4 5)
$