https://www.lvguowei.me/categories/sicp/ Recent content in SICP on Guowei Lv Hugo -- gohugo.io en-us Wed, 04 Aug 2021 15:03:26 +0300 https://www.lvguowei.me/post/sicp-goodness-y-combinator/ Wed, 04 Aug 2021 15:03:26 +0300 https://www.lvguowei.me/post/sicp-goodness-y-combinator/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! I rewatched the Lecture 7A again and found that I never really understand the second half. https://www.lvguowei.me/post/sicp-goodness-metacircular-evaluator-lecture/ Fri, 20 Nov 2020 22:19:03 +0200 https://www.lvguowei.me/post/sicp-goodness-metacircular-evaluator-lecture/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In Lecture 7A: Metacircular Evaluator, Part 1, Mr Sussman said that he was going to fit the whole evaluator on the blackboard. https://www.lvguowei.me/post/sicp-goodness-metacircular-evaluator/ Sat, 26 Sep 2020 20:18:45 +0300 https://www.lvguowei.me/post/sicp-goodness-metacircular-evaluator/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! At the beginning of Chapter 4, we will implement an evaluator. https://www.lvguowei.me/post/sicp-goodness-evaluator-scan/ Fri, 11 Sep 2020 18:40:42 +0300 https://www.lvguowei.me/post/sicp-goodness-evaluator-scan/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Do you have the following questions? https://www.lvguowei.me/post/sicp-goodness-setup-racket-org/ Thu, 06 Aug 2020 23:10:10 +0300 https://www.lvguowei.me/post/sicp-goodness-setup-racket-org/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Recently, I started to write down study notes in one org file. https://www.lvguowei.me/post/sicp-goodness-stream-11/ Fri, 06 Mar 2020 20:53:21 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-11/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In last article we talked about the integral procedure. https://www.lvguowei.me/post/sicp-goodness-stream-10/ Wed, 26 Feb 2020 13:14:23 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-10/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Let’s talk about the integral example in the book. https://www.lvguowei.me/post/sicp-goodness-stream-9/ Fri, 14 Feb 2020 14:02:02 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-9/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! I’ve been quite busy with work related stuff recently and not had enough time for this series. https://www.lvguowei.me/post/sicp-goodness-stream-8/ Fri, 05 Jul 2019 22:37:09 +0300 https://www.lvguowei.me/post/sicp-goodness-stream-8/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! One more example from the book and one related exercise. https://www.lvguowei.me/post/sicp-goodness-stream-7/ Sat, 13 Apr 2019 20:39:53 +0300 https://www.lvguowei.me/post/sicp-goodness-stream-7/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Let’s examine some examples from the book and furthur explore the stream paradigm. https://www.lvguowei.me/post/sicp-goodness-stream-6/ Sat, 06 Apr 2019 20:31:46 +0300 https://www.lvguowei.me/post/sicp-goodness-stream-6/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Let’s do some exercises. https://www.lvguowei.me/post/sicp-goodness-stream-5/ Tue, 19 Mar 2019 21:05:53 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-5/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Streams can also be infinite, let’s look at some examples. https://www.lvguowei.me/post/sicp-goodness-stream-4/ Thu, 14 Mar 2019 20:49:46 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-4/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Let’s do one more exercise. https://www.lvguowei.me/post/sicp-goodness-stream-3/ Wed, 13 Mar 2019 14:55:47 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-3/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! To test our knowledge, let’s do some exercises from the book. https://www.lvguowei.me/post/sicp-goodness-stream-2/ Sun, 10 Mar 2019 13:37:47 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In previous article, we implemented the very basics of stream: cons-stream, stream-car and stream-cdr, now we can implement some util functions based on those. https://www.lvguowei.me/post/sicp-goodness-stream-1/ Thu, 14 Feb 2019 21:36:32 +0200 https://www.lvguowei.me/post/sicp-goodness-stream-1/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Finally, we arrived at one the epic topics in the SICP book, stream. https://www.lvguowei.me/post/sicp-goodness-functional-vs-oo/ Sun, 13 Jan 2019 20:52:15 +0200 https://www.lvguowei.me/post/sicp-goodness-functional-vs-oo/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Functional Programming is coming back in recent years, so people who have been doing Java or C++ for their entire career will want to know what is the difference. https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim-3/ Tue, 25 Dec 2018 20:24:09 +0200 https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim-3/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In part 3 we can finally start talking about the digital circuits. https://www.lvguowei.me/post/sicp-goodness-peter-norvig-review/ Sat, 15 Dec 2018 12:35:51 +0200 https://www.lvguowei.me/post/sicp-goodness-peter-norvig-review/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Today I found the book review from Peter Norvig, and it is such a pleasure to read, enjoy. https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim-2/ Sat, 15 Dec 2018 12:26:36 +0200 https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Agenda Agenda is a data structure, that contains a schedule of things to do. https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim/ Fri, 14 Dec 2018 20:45:49 +0200 https://www.lvguowei.me/post/sicp-goodness-digital-circuits-sim/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! We are building a simulator program for digital circuits, using the Object Oriented view of the world, in Scheme Lisp. https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing-3/ Fri, 16 Nov 2018 20:29:13 +0200 https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing-3/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! A Table to the Rescue In previous article, we see that it becomes quite annoying that each and every one of the generic selectors of the complex number has to do a cond on the types. https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing-2/ Fri, 02 Nov 2018 20:33:51 +0200 https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Tagged Data At the end of previous post, we identified one problem of our current complex number system, which is given a complex number, there is no way to tell whether it is implemented in rectangular form or polar form. https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing/ Sun, 28 Oct 2018 20:17:15 +0200 https://www.lvguowei.me/post/sicp-goodness-data-directed-programming-and-message-passing/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! When I first read about data directed programming in the book, I was surprised. https://www.lvguowei.me/post/sicp-goodness-mutable-data-2/ Fri, 26 Oct 2018 19:55:26 +0300 https://www.lvguowei.me/post/sicp-goodness-mutable-data-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Representing Tables We can build a table data structure by just using pairs. https://www.lvguowei.me/post/sicp-goodness-mutable-data-1/ Mon, 22 Oct 2018 22:26:22 +0300 https://www.lvguowei.me/post/sicp-goodness-mutable-data-1/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Mutable List Structure We introduce 2 operations to change a list: set-car! https://www.lvguowei.me/post/sicp-goodness-environment-model/ Mon, 08 Oct 2018 19:53:20 +0300 https://www.lvguowei.me/post/sicp-goodness-environment-model/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Before introducing assignment operation set! https://www.lvguowei.me/post/sicp-goodness-message-passing/ Sun, 30 Sep 2018 13:40:07 +0300 https://www.lvguowei.me/post/sicp-goodness-message-passing/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In this article, we will see how to construct an object that has internal states by using message passing. https://www.lvguowei.me/post/sicp-goodness-why-assignment-is-still-useful/ Fri, 14 Sep 2018 21:53:35 +0300 https://www.lvguowei.me/post/sicp-goodness-why-assignment-is-still-useful/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In FP world people bash assignment. https://www.lvguowei.me/post/sicp-goodness-the-essence-of-computer-science/ Sun, 09 Sep 2018 19:40:17 +0300 https://www.lvguowei.me/post/sicp-goodness-the-essence-of-computer-science/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! The following text is from the preface to the first edition of SICP. https://www.lvguowei.me/post/sicp-goodness-from-pair-to-flatmap-2/ Sat, 01 Sep 2018 10:12:11 +0300 https://www.lvguowei.me/post/sicp-goodness-from-pair-to-flatmap-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Part I of this series can be found here. https://www.lvguowei.me/post/sicp-goodness-from-pair-to-flatmap/ Sat, 25 Aug 2018 22:07:55 +0300 https://www.lvguowei.me/post/sicp-goodness-from-pair-to-flatmap/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Sequence is an important data structure in any programming language, especially in Lisp. https://www.lvguowei.me/post/sicp-goodness-cont-frac/ Tue, 24 Jul 2018 22:39:43 +0300 https://www.lvguowei.me/post/sicp-goodness-cont-frac/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Writing recursive functions is not an easy task, often requires a different way of thinking. https://www.lvguowei.me/post/sicp-goodness-data-2/ Sun, 15 Jul 2018 20:58:31 +0300 https://www.lvguowei.me/post/sicp-goodness-data-2/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! This is the second part of a two part series, you can find the first part here. https://www.lvguowei.me/post/sicp-goodness-data/ Tue, 10 Jul 2018 21:36:11 +0300 https://www.lvguowei.me/post/sicp-goodness-data/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Let’s begin by asking the question: What is data? https://www.lvguowei.me/post/sicp-goodness-fib/ Fri, 06 Jul 2018 20:35:43 +0300 https://www.lvguowei.me/post/sicp-goodness-fib/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! Every programmer at some point has studied fibonacci numbers, mostly likely as an interview question. https://www.lvguowei.me/post/sicp-goodness-music/ Mon, 02 Jul 2018 20:49:50 +0300 https://www.lvguowei.me/post/sicp-goodness-music/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! The music in the beginning of each lecture is beautiful. https://www.lvguowei.me/post/sicp-goodness-sqrt/ Fri, 29 Jun 2018 20:52:11 +0300 https://www.lvguowei.me/post/sicp-goodness-sqrt/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! There are several epic example problems in the book, the first one of them is of how to calculate the square root of a number. https://www.lvguowei.me/post/sicp-goodness-let/ Thu, 28 Jun 2018 21:59:58 +0300 https://www.lvguowei.me/post/sicp-goodness-let/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! In this post I give my guess of where the new let keyword in JavaScript comes from. https://www.lvguowei.me/post/sicp-goodness-looping/ Sat, 16 Jun 2018 21:07:45 +0300 https://www.lvguowei.me/post/sicp-goodness-looping/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! I was quite shocked when I first read the following text from the book: https://www.lvguowei.me/post/sicp-goodness/ Wed, 13 Jun 2018 22:30:04 +0300 https://www.lvguowei.me/post/sicp-goodness/ Do you think Computer Science equals building websites and mobile apps? Are you feeling that you are doing repetitive and not so intelligent work? Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long? Do you want to understand the soul of Computer Science? If yes, read SICP!!! This is the first post of this SICP Goodness series, in which I discuss some of my own findings from reading the book SICP. https://www.lvguowei.me/post/sicp-quote/ Fri, 06 Oct 2017 20:05:49 +0300 https://www.lvguowei.me/post/sicp-quote/ Since I have to take a long bus trip to work everyday, I decided to use the time to read the SICP (Structure and Interpretation of Computer Programs). And blog along the way to mark the progress. I have read Chapter 1 and watched the video lectures. But I still feel I get planty new things from going through it again. The best part of this book I think is that it spends minimal time and effort in teaching the programming language, the main focus is the thinking and ideas about programming. https://www.lvguowei.me/post/time-and-space-of-recursion/ Sun, 29 May 2016 21:32:14 +0300 https://www.lvguowei.me/post/time-and-space-of-recursion/ 今天通过一个例子，来谈一谈第归的时间和空间效应。 例子很简单，计算 a 的 n 次方。 我们来对比一下两种第归算法的时间和空间的消耗。 第一个方法很直接。思想就是要计算 a 的 n 次方， 只要计算 a 的 (n - 1) 次方， 然后结果在乘以 a 。如下： (define (expt a n) (if (= n 0) 1 (* a (expt a (- n 1))))) 为了更直观的理解这个算法，我们来计算一个例子， 2 的 3 次方。 (expt 2 3) (* 2 (expt 2 2)) (* 2 (* 2 (expt 2 1))) (* 2 (* 2 (* 2 (expt 2 0)))) (* 2 (* 2 (* 2 1))) (* 2 (* 2 2)) (* 2 4) 8 我们能能明显看到这个算法的“形状”是一个三角形。每一行代表一次计算，也可以理解成时间的消耗。而每一列则代表计算机需要记住的内容，比如说一共要乘以几个2，也可以理解成空间的消耗。我们可以看到，随着 n 的增大， 这个算法的时间和空间消耗也随之增大。而且增大的速度都是线性的。时间的消耗随着 n 的增大而增大很好理解， n 大了， 计算花的时间也相应长了。但是空间消耗可不可以不增大呢？下面我们就来看另一种算法。 https://www.lvguowei.me/post/recursion-example/ Thu, 05 May 2016 15:33:59 +0300 https://www.lvguowei.me/post/recursion-example/ 今天读到SICP里的一个介绍recursion的例子，用牛顿猜想来计算平方根。 首先，介绍了计算机程序和数学方程的区别。数学方程大多用的是描述法（declarative）。比如说这个平方根，数学上只需要说： 如果x的平方等于y，而且x大于0，那么x就是y的平方根。 这是一种很高层次的描述，通过描述，来限制答案的域。如果能直接用到计算机里，问题就简单了。大概写出来的程序就是这个样子： func sqrt(x): @ * @ = x; @ > 0; return @; 让计算机去处理计算细节。这当然是一种理想的情况，如果都能这样写程序，那就完事大吉了。这就叫描述性编程(Declarative Programming)。 当然现在还做不到这么绝对，所以我们只能自己写如何进行细节的计算来得到我们的结果。这就叫做命令式变成(Imperative Programming)。 总体来说，描述性编程比命令式编程要容易理解的多，因为不用自己下达命令给计算机，只需要对问题进行描述，计算机自己会找到答案。典型的例子就是xml配置文件，人们把对系统的需求和配置写在一个单独的xml文件里面，然后让计算机自己去执行相应的命令。 好了，现在进入正题。牛顿猜想的原理如下： 要计算x的平方根，先猜想一个答案y，然后用 (y + x / y) / 2 来得到新的优化过猜想。反复进行，知道得到满意的猜想。 首先，我们先来定义一些辅助方程。 (define (abs x) (if (< x 0) (- x) x)) (define (square x) (* x x)) (define (average x y) (/ (+ x y) 2)) 接下来我们来写主程序。 (define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x))) 这个程序用第归的方法实现了牛顿猜想。