Scheme - データによる抽象の構築(抽象データの多重表現(データ主導プログラミングと加法性(メッセージパッシング, 構成子)))

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(Text Editor)
Scheme (プログラミング言語)
kscheme, Gauche, GNU Guile (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)、2.4(抽象データの多重表現)、2.4.3(データ主導プログラミングと加法性)、問題2.75.を解いてみる。

その他参考書籍

問題2.75.

コード(Emacs)


  (begin
  (newline)
  (define error
    (lambda (message value)
      (display message)
      (display " ")
      (display value)
      (newline)))
  (define print
    (lambda (x)
      (display x)
      (newline)))
  (define for-each
    (lambda (proc items)
      (if (not (null? items))
          (begin (proc (car items))
                 (for-each proc (cdr items))))))
  (define square (lambda (x) (* x x)))
  (define average (lambda (x y) (/ (+ x y) 2)))
  (define abs (lambda (x) (if (< x 0)
                              (* -1 x)
                              x)))  
  (define accumulate
    (lambda (combiner null-value term a next b)
      (define inner
        (lambda (x result)
          (if (> x b)
              result
              (inner (next x)
                     (combiner (term x)
                               result)))))
      (inner a null-value)))
  (define expt
    (lambda (base n)
      (define (iter n result)
        (if (= n 0)
            result
            (iter (- n 1)
                  (* result base))))
      (iter n 1)))
  (define inc (lambda (n) (+ n 1)))
  (define (factorial n)
    (define (iter product counter)
      (if (> counter n)
          product
          (iter (* counter product)
                (+ counter 1))))
    (iter 1 1))
  (define sqrt
    (lambda (x)
      (define sqrt-iter
        (lambda (guess x)
          (if (good-enough? guess x)
              guess
              (sqrt-iter (improve guess x)
                         x))))
      (define good-enough?
        (lambda (guess x)
          (< (abs (- (square guess) x)) 0.001)))
      (define improve
        (lambda (guess x)
          (average guess (/ x guess))))
      (sqrt-iter 1.0 x)))
  ;; 三角関数(正弦、余弦は級数で近似
  (define sin
    (lambda (x)
      (accumulate + 0.0 (lambda (n)
                          (let ((a (+ (* 2 n) 1)))
                            (* (/ (expt -1 n)
                                  (factorial a))
                               (expt x a))))
                  0 inc 10)))
  (define cos
    (lambda (x)
      (accumulate + 0.0 (lambda (n)
                          (let ((a (* 2 n)))
                            (* (/ (expt -1 n)
                                  (factorial a))
                               (expt x a))))
                  0 inc 10)))
  (define make-from-mag-ang
    (lambda (mag ang)
      (define dispatch
        (lambda (op)
          (cond ((eq? op (quote magnitude)) mag)                 
                ((eq? op (quote angle)) ang)
                ((eq? op (quote real-part))
                 (* mag (cos ang)))
                ((eq? op (quote imag-part))
                 (* mag (sin ang)))
                (else
                 (error "Unknown op -- MAKE-FROM-MAG_ANG" op)))))
      dispatch))
  
  (define apply-generic  (lambda (op arg) (arg op)))
  (define real-part
    (lambda (z)
      (apply-generic (quote real-part) z)))
  (define imag-part
    (lambda (z)
      (apply-generic (quote imag-part) z)))
  (define magnitude
    (lambda (z)
      (apply-generic (quote magnitude) z)))
  (define angle
    (lambda (z)
      (apply-generic (quote angle) z)))
  (define pi 3.14)  
  (define z1 (make-from-mag-ang (sqrt 2) (/ pi 4)))
  (define z2 (make-from-mag-ang (sqrt 2) (/ (* 3 pi) 4)))
  (define z3 (make-from-mag-ang (sqrt 2) (/ (* 5 pi) 4)))
  (define z4 (make-from-mag-ang (sqrt 2) (/ (* 7 pi) 4)))
  (define z5 (make-from-mag-ang (sqrt 2) (/ pi -4)))
  (define z6 (make-from-mag-ang (sqrt 2) (/ (* 3 pi) -4)))
  (define z7 (make-from-mag-ang (sqrt 2) (/ (* 5 pi) -4)))
  (define z8 (make-from-mag-ang (sqrt 2) (/ (* 7 pi) -4)))

  (for-each (lambda (z)
              (print (magnitude z))
              (print (angle z))
              (print (real-part z))
              (print (imag-part z))
              (newline))
            (list z1 z2 z3 z4 z5 z6 z7 z8))

  (quote done))

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

$ kscheme < sample75.scm
kscm> 
0.141421568627450980389e1
0.785e0
0.100039958654282907642e1
0.999603258573029749964e0

0.141421568627450980389e1
0.235499999999999999999e1
-0.998806296718297620819e0
0.100119528012292478922e1

0.141421568627450980389e1
0.392499999999999999998e1
-0.100199032461097535973e1
-0.998008699056392693924e0

0.141421568627450980389e1
0.549499999999999999998e1
0.997233157837646648377e0
-0.100277931949570678565e1

0.141421568627450980389e1
-0.785e0
0.100039958654282907642e1
-0.999603258573029749964e0

0.141421568627450980389e1
-0.235499999999999999999e1
-0.998806296718297620819e0
-0.100119528012292478922e1

0.141421568627450980389e1
-0.392499999999999999998e1
-0.100199032461097535973e1
0.998008699056392693924e0

0.141421568627450980389e1
-0.549499999999999999998e1
0.997233157837646648377e0
0.100277931949570678565e1

done
kscm> $

Kamimura's blog

2015年6月23日火曜日

Scheme - データによる抽象の構築(抽象データの多重表現(データ主導プログラミングと加法性(メッセージパッシング, 構成子)))

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