https://github.com/ramsayleung/sicp_solution

We toast the Lisp programmer who pens his thoughts within nests of parentheses.
https://github.com/ramsayleung/sicp_solution

design lisp programming racket scheme sicp

Last synced: 22 days ago
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We toast the Lisp programmer who pens his thoughts within nests of parentheses.

• Host: GitHub
• URL: https://github.com/ramsayleung/sicp_solution
• Owner: ramsayleung
• Created: 2017-10-01T16:13:34.000Z (over 8 years ago)
• Default Branch: master
• Last Pushed: 2025-08-04T06:08:50.000Z (8 months ago)
• Last Synced: 2025-10-28T17:48:28.309Z (5 months ago)
• Topics: design, lisp, programming, racket, scheme, sicp
• Language: Racket
• Homepage: https://ramsayleung.github.io/zh/post/2025/structure_and_interpretation_of_computer_programs/
• Size: 2.24 MB
• Stars: 7
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.org

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README

          
#+LATEX_CLASS: ramsay-org-article

#+LATEX_CLASS_OPTIONS: [oneside,A4paper,12pt]

#+AUTHOR: Ramsay Leung

#+EMAIL: ramsayleung@gmail.com

#+DATE: 2022-11-07 一 21:07

* Structure and Interpretation of Computer Programs

  《计算机程序的构造和解释》题解，使用标准Racket 实现（开发环境是Emacs）

  

  #+begin_quote

  If art interprets our dreams, the computer executes them in the guise of programs!

  如果说艺术解释了我们的梦想，那么计算机就是以程序的名义执行着它们

  #+end_quote

  #+begin_quote

  We toast the Lisp programmer who pens his thoughts within nests of parentheses.

  #+end_quote

  向以括号为画笔的Lisp程序员举杯，干杯！

* 安装依赖

  #+begin_src shell

    raco pkg install --auto --batch # 类似 JavaScript 的 npm install

  #+end_src

* 习题

  习题完成情况:

  - 章节一: 43/46

  - 章节二: 88/97

  - 章节三: 72/82

  - 章节四: TODO

  - 章节五: TODO

* 运行

  运行所有的习题

  #+begin_src shell

    raco test -t .

  #+end_src

  运行指定的习题:

  #+begin_src shell

    raco test chapter1/exercise1-10.scm 

  #+end_src

* 笔记

** chapter2

*** 图形语言

    racket的 =sicp= package 包含了一个画图工具，可以画出类似书中的效果

    #+begin_src scheme

      #lang racket

      (require sicp-pict)

      (define (flipped-pairs painter)

        (let ((painter2 (beside painter (flip-vert painter))))

          (below painter2 painter2)))

      (define (right-split painter n)

        (if (= n 0)

            painter

            (let ((smaller (right-split painter (- n 1))))

              (beside painter (below smaller smaller)))))

      (define (up-split painter n)

        (if (= n 0)

            painter

            (let ((smaller (up-split painter (- n 1))))

              (below painter (beside smaller smaller)))))

      (define (corner-split painter n)

        (if (= n 0)

            painter

            (let ((up (up-split painter (- n 1)))

                  (right (right-split painter (- n 1))))

              (let ((top-left (beside up up))

                    (bottom-right (below right right))

                    (corner (corner-split painter (- n 1))))

                (beside (below painter top-left)

                        (below bottom-right corner))))))

      (define (square-limit painter n)

        (let ((quarter (corner-split painter n)))

          (let ((half (beside (flip-horiz quarter) quarter)))

            (below (flip-vert half) half))))

      (paint (square-limit einstein 6))

    #+end_src

    在 =DrRacket= 的运行效果（只能在DrRacket 运行，在终端无法展示图片）：

    [[file:img/chapter2/square-limit-einstein.png]]

    配合 [[file:chapter2/exercise2-49.org][wave的实现]]，画出来的效果：

[[file:img/chapter2/wave-square-limit.png]]

** chapter3

*** 蒙特卡罗模拟步骤来计算 π 

    3.1 赋值与局部变量, 155 页

    #+begin_quote

    举例来说，6/π^2 是随机选取的两个整数之间没有公因子（也就是说，它们的最大公因子是1）的概率。我们可以利用这一事实做出π的近似值。

    #+end_quote

    完全读不懂这段话，没理解是怎么可以算出π的近似值的。

    查阅完资料都知道:

    随机选取两个正整数，它们互质（即最大公约数GCD为1）的概率是 $\frac{6}{\pi^2}$ , 所谓的 互质指两个数没有公共因子（如8和15互质，但8和12不互质，因为公约数为4）。

     而这一结论是源自数论中关于 *互质数的密度* 的研究，与黎曼ζ函数相关（难怪我看不懂了）。

     而用蒙特卡罗模拟步骤来计算 ${\pi}$:

     随机实验：重复多次随机选取两个整数，检查它们的GCD是否为1。

     例如：

        - (3, 5) → GCD=1（计数+1）

        - (4, 6) → GCD=2（不计数）

     统计概率：

     若总实验次数为 N，其中 k 次GCD=1，则互质概率的估计值为 $\frac{k}{N}$ 

     关联π：

     根据数论结论 $\frac{k}{N} \approx \frac{6}{\pi^2}$，解得 $\pi \approx \sqrt{\frac{6N}{k}}$。

     当直接计算π困难时，可通过概率实验间接逼近。

     这里利用了数论中的概率规律，将π与随机事件联系起来。(高数对于我来说已是雪泥鸿爪，更遑论数论的知识了)

     #+begin_src racket

       #lang racket

       (define (estimate-pi trials)

         (sqrt (/ 6 (monte-carlo trials cesaro-test))))

       (define (cesaro-test)

         (= (gcd (rand) (rand)) 1))

       (define (monte-carlo trials experiment)

         (define (iter trials-remaining trial-passed)

           (cond ((= trials-remaining 0)

                  (/ trials-passed trials))

                 ((experiment)

                  (iter (- trials-remaining 1) (+ trials-passed 1)))

                 (else

                  (iter (- trials-remaining 1) trials-passed))))

         (iter trials 0))

     #+end_src

     这里的蒙特卡罗实现真的是优雅

     而基于流的实现更是优美:

     #+begin_src scheme

       (define (monte-carlo experiment-stream passed failed)

         (define (next passed failed)

           (cons-stream

            (/ passed (+ passed failed))

            (monte-carlo

             (stream-cdr experiment-stream)

             passed

             failed)))

         (if (stream-car experiment-stream)

             (next (+ passed 1) failed)

             (next passed (+ failed 1))))

     #+end_src

** 翻译错误

   第2版，238页，模块化，对象和状态，中文翻译是

   #+begin_quote

   练习3.70

   b) 所有正正数序对 (i,j) 的流，其中要求 i<=j, 而且这里的i或者j可以被2,3或者5整除

   #+end_quote

   原文是:

   #+begin_quote

   the stream of all pairs of positive integers ( i , j ) with i ≤ j , where neither i nor j is divisible by 2, 3, or 5,

   #+end_quote

   https://sarabander.github.io/sicp/html/3_002e5.xhtml#g_t3_002e5

    

   i和j不可以被2,3,5整除，翻译成了可以被2,3或者5整除，意思完全相反，真的是服了。

** 排版错误

   第2版，240页，模块化，对象和状态

   练习3.74 输入信号流和过零点信号流完全没有对齐