Scheme - 積極制御評価器(末尾再帰的特性)

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)
• MIT/GNU Scheme (処理系)

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5(レジスタ計算機での計算)、5.4(積極制御評価器)、5.4.4(評価の実行)、評価器の性能監視、問題 5.26.を解いてみる。

その他参考書籍

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

問題 5.26.

コード(BBEdit)

sample.scm

(load "./eval.scm")
(load "./register.scm")
(load "./eceval.scm")
(start eceval)

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

$ scheme
MIT/GNU Scheme running under MacOSX
Type `^C' (control-C) followed by `H' to obtain information about interrupts.

Copyright (C) 2011 Massachusetts Institute of Technology
This is free software; see the source for copying conditions. There is NO
warranty; not even for MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

Image saved on Saturday October 26, 2013 at 11:02:50 PM
  Release 9.1.1 || Microcode 15.3 || Runtime 15.7 || SF 4.41 || LIAR/C 4.118
  Edwin 3.116

1 ]=> (load "./sample.scm")

;Loading "./sample.scm"...
;  Loading "eval.scm"... done
;  Loading "register.scm"... done
;  Loading "eceval.scm"... done


;;; EC-Eval input:
(define (factorial n)
  (define (iter product counter)
    (if (> counter n)
        product
        (iter (* counter product)
              (+ counter 1))))
  (iter 1 1))

(total-pushes = 3 maximum-depth = 3)
;;; EC-Eval value:
ok

;;; EC-Eval input:
(factorial 1)

(total-pushes = 64 maximum-depth = 10)
;;; EC-Eval value:
1

;;; EC-Eval input:
(factorial 2)

(total-pushes = 99 maximum-depth = 10)
;;; EC-Eval value:
2

;;; EC-Eval input:
(factorial 3)

(total-pushes = 134 maximum-depth = 10)
;;; EC-Eval value:
6

;;; EC-Eval input:
(factorial 4)

(total-pushes = 169 maximum-depth = 10)
;;; EC-Eval value:
24

;;; EC-Eval input:
(factorial 5)

(total-pushes = 204 maximum-depth = 10)
;;; EC-Eval value:
120

;;; EC-Eval input:
^C
Interrupt option (? for help): ;... aborted
;Quit!

1 ]=> ^D
End of input stream reached.
Moriturus te saluto.
$

a.

深さは10。

b.

プッシュ演算の総数は(29 + 35n)回。(確かに、nの線形関数で2つの整数29、35で決まっている。)