Scheme - データによる抽象の構築(データ抽象入門(拡張問題: 区間算術演算(区間の幅)))

計算機プログラムの構造と解釈[第2版]
(翔泳社)
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)

開発環境

• OS X Yosemite - Apple (OS)
• Emacs (CUI)、BBEdit - Bare Bones Software, Inc. (GUI) (Text Editor)
• Scheme (プログラミング言語)
• kscheme, Gauche (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)、2.1(データ抽象入門)、2.1.4(拡張問題: 区間算術演算)、問題 2.9.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)
• Scheme手習い

問題 2.9.

コード(BBEdit, Emacs)

(define make-interval
  (lambda (a b) (cons a b)))

(define lower-bound
  (lambda (interval) (car interval)))

(define upper-bound
  (lambda (interval) (cdr interval)))

(define print-interval
  (lambda (interval)
    (display "(")
    (display (lower-bound interval))
    (display ", ")
    (display (upper-bound interval))
    (display ")")
    (newline)))

(define interval (make-interval 1 2))

(define sub-interval
  (lambda (x y)
    (make-interval (- (lower-bound x) (upper-bound y))
                   (- (upper-bound x) (lower-bound y)))))
                      
(define add-interval
  (lambda (x y)
    (make-interval (+ (lower-bound x) (lower-bound y))
                   (+ (upper-bound x) (upper-bound y)))))
(define width
  (lambda (interval)
    (/ (- (upper-bound interval)
          (lower-bound interval))
       2)))

(define add-interval-width
  (lambda (x-width y-width) (+ x-width y-width)))

(define i0 (make-interval 1 1))
(define i1 (make-interval 0 1))
(define i2 (make-interval 1 2))

(= (width (add-interval i0 i0))
   (add-interval-width (width i0) (width i0)))
(= (width (add-interval i0 i1))
   (add-interval-width (width i0) (width i1)))
(= (width (add-interval i0 i2))
   (add-interval-width (width i0) (width i2)))
(= (width (add-interval i1 i0))
   (add-interval-width (width i1) (width i0)))
(= (width (add-interval i1 i1))
   (add-interval-width (width i1) (width i1)))
(= (width (add-interval i1 i2))
   (add-interval-width (width i1) (width i2)))
(= (width (add-interval i2 i0))
   (add-interval-width (width i2) (width i0)))
(= (width (add-interval i2 i1))
   (add-interval-width (width i2) (width i1)))
(= (width (add-interval i2 i2))
   (add-interval-width (width i2) (width i2)))

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

$ kscheme  < sample9.scm
In : Out: make-interval
;(total-pushes = 3 maximum-depth = 3)
In : Out: lower-bound
;(total-pushes = 3 maximum-depth = 3)
In : Out: upper-bound
;(total-pushes = 3 maximum-depth = 3)
In : Out: print-interval
;(total-pushes = 3 maximum-depth = 3)
In : Out: interval
;(total-pushes = 17 maximum-depth = 7)
In : Out: sub-interval
;(total-pushes = 3 maximum-depth = 3)
In : Out: add-interval
;(total-pushes = 3 maximum-depth = 3)
In : Out: width
;(total-pushes = 3 maximum-depth = 3)
In : Out: add-interval-width
;(total-pushes = 3 maximum-depth = 3)
In : Out: i0
;(total-pushes = 17 maximum-depth = 7)
In : Out: i1
;(total-pushes = 17 maximum-depth = 7)
In : Out: i2
;(total-pushes = 17 maximum-depth = 7)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : Out: #t
;(total-pushes = 190 maximum-depth = 18)
In : $