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<title>Learn Haskell Fast and Hard</title>
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<body lang="en" class="article" data-twttr-rendered="true">
<div id="content">
<div id="titre">
<h1>
Learn Haskell Fast and Hard
</h1>
<h2>
用 Haskell 开阔你的视野
</h2>
</div>
<div id="afterheader">
<div class="corps">
<p><img alt="Magritte pleasure principle" src="./Learn Haskell Fast and Hard_files/magritte_pleasure_principle.jpg"></p>
<div class="intro">
<p><span class="sc"><abbr title="Too long; didn't read">长文</abbr>: </span> 这是一份浓缩过的 Haskell 教程.</p>
<blockquote><center><hr style="width:30%;float:left;border-color:#CCCCD0;margin-top:1em">
<span class="sc"><b>目录</b></span>
<hr style="width:30%;float:right;border-color:#CCCCD0;margin-top:1em"></center>
<div class="toc">
<ul>
<li><a href="#introduction">介绍</a>
<ul>
<li><a href="#install">安装</a></li>
<li><a href="#don-t-be-afraid">别担心</a></li>
<li><a href="#very-basic-haskell">基础的 Haskell</a>
<ul>
<li><a href="#function-declaration">函数声明</a></li>
<li><a href="#a-type-example">类型的例子</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#essential-haskell">Haskell 要点</a>
<ul>
<li><a href="#notations">记法</a>
<ul>
<li><a href="#arithmetic">算术</a></li>
<li><a href="#logic">逻辑</a></li>
<li><a href="#powers">Powers</a></li>
<li><a href="#lists">Lists</a></li>
<li><a href="#strings">Strings</a></li>
<li><a href="#tuples">Tuples</a></li>
<li><a href="#deal-with-parentheses">处理圆括号</a></li>
</ul>
</li>
<li><a href="#useful-notations-for-functions">常用函数记法</a></li>
</ul>
</li>
<li><a href="#hard-part">难点</a>
<ul>
<li><a href="#functional-style">函数风格</a>
<ul>
<li><a href="#higher-order-functions">高阶函数</a></li>
</ul>
</li>
<li><a href="#types">类型</a>
<ul>
<li><a href="#type-inference">类型推断</a></li>
<li><a href="#type-construction">类型构造</a></li>
<li><a href="#recursive-type">递归类型</a></li>
<li><a href="#trees">Trees</a></li>
</ul>
</li>
<li><a href="#infinite-structures">无限结构</a></li>
</ul>
</li>
<li><a href="#hell-difficulty-part">超难的地方</a>
<ul>
<li><a href="#deal-with-io">处理 IO</a></li>
<li><a href="#io-trick-explained">IO 手法解析</a></li>
<li><a href="#monads">Monads</a>
<ul>
<li><a href="#maybe-monad">Maybe 是 monad</a></li>
<li><a href="#the-list-monad">List monad</a></li>
</ul>
</li>
</ul>
</li>
<li><a href="#appendix">附录</a>
<ul>
<li><a href="#more-on-infinite-tree">更多关于 Infinite Tree</a></li>
</ul>
</li>
</ul>
</div>
</blockquote>
</div>
<div class="intro">
<p>我坚信所有开发者的都该来学 Haskell.
我不认为所有人应该成为 Haskell 的超级忍者,
但至少, 他们能发现 Haskell 的存在提供些什么.
学习 Haskell 打开你的思维.</p>
<p>主流语言共通的基础:</p>
<ul>
<li>变量</li>
<li>循环</li>
<li>指针<sup id="fnref:0001"><a href="#fn:0001" rel="footnote">1</a></sup></li>
<li>数据类型, 对象和类(对于大多数)</li>
</ul>
<p>Haskell 非常特别.
这门语言应用了很多我从未听说的概念.
其中很多会助你成为更好的程序员.</p>
<p>然而, 学习 Haskell 可能很难.
对我就这样.
在这篇文章, 我尝试提供我学习过程中所认为缺少的.</p>
<p>这篇文章的进度会很难被跟上.
这是有意为之的.
世上没有学习 Haskell 的捷径.
只有难题和挑战.
但我相信这是一件好事.
因为 Haskell 很难, 所以她会很有趣.</p>
<p>学 Haskell 的常规办法是的看两本书.
第一本 <a href="http://learnyouahaskell.com/">“Learn You a Haskell”</a> 接着是
<a href="http://www.realworldhaskell.org/">“Real World Haskell”</a>.
我也相信这是正确的途径/
但是, 为了学会所有 Haskell 索要表达的, 你需要阅读全部的细节.</p>
<p>同时, 本文对 Haskell 各个方面一个简短和浓缩的概览.
我还加了我学习 Haskell 时我所缺少的资源.
<p>本文包括五个部分:</p>
<ul>
<li>介绍: 一个简短的例子来表明 Haskell 的友好性.</li>
<li>基础的 Haskell: Haskell 语法, 和一些必需的记法.</li>
<li>难点:
<ul>
<li>函数风格; 一个渐进的例子, 从命令式到函数式风格</li>
<li>类型; 类型和标准 binary tree 的例子</li>
<li>无穷类型; 操作一个 infinite binary tree!</li>
</ul>
</li>
<li>超难的地方
<ul>
<li>处理 IO; 一个很迷你的例子</li>
<li>IO 手法解析; 我理解 IO 所缺失的隐藏细节</li>
<li>Monads; 难以置信我们能怎样生成</li>
</ul>
</li>
<li>附录:
<ul>
<li>更多关于 infinite tree; 关于 infinite trees 更数学化的讨论</li>
</ul>
</li>
</ul>
<blockquote>
<p>注: 每次你都会看到一个文件后缀为 <code>.lhs</code> 的分隔,
你可以点击文件名下载这些文件.
如果你把文件存为<code>filename.lhs</code>, 你可以运行之 </p>
<pre>runhaskell filename.lhs
</pre>
<p>某些大概不能运行, 但绝大多数该可以.
你应该能看到这下面有个链接.</p>
</blockquote>
</div>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/00_hello_world.lhs" class="cut">01_basic/10_Introduction/<strong>00_hello_world.lhs</strong></a></p>
<h2 id="introduction">介绍</h2>
<h3 id="install">安装</h3>
<p><img alt="Haskell logo" src="./Learn Haskell Fast and Hard_files/Haskell-logo.png"></p>
<ul>
<li><a href="http://www.haskell.org/platform">Haskell Platform</a> 是安装 Haskell 的标准方法..</li>
</ul>
<p>工具:</p>
<ul>
<li><code>ghc</code>: 编译器, 类似于对 <code>C</code> 而言的 gcc.</li>
<li><code>ghci</code>: 交互式的 Haskell (REPL)</li>
<li><code>runhaskell</code>: 不编译而直接运行 Haskell 程序. 方便, 但对比经过编译的程序显得很慢.</li>
</ul>
<h3 id="don-t-be-afraid">别担心</h3>
<p><img alt="The Scream" src="./Learn Haskell Fast and Hard_files/munch_TheScream.jpg"></p>
<p>很多 Haskell 的书籍文章一开始的介绍用的是那些深奥的程序(快速排序, Fibonacci, 等等...).
我想做的恰恰相反.
首先我不会给你看任何 Haskell 的超能力.
我会从 Haskell 与其他编程语言之间的相似点开始.
让我们开始看惯例的 "Hello World".</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">main</span> = putStrLn <span class="string">"Hello World!"</span>
</code></pre>
</div>
<p>要运行的话, 可以把代码存为 <code>hello.hs</code> 然后执行:</p>
<pre><code class="zsh avrasm">~ runhaskell ./hello<span class="preprocessor">.hs</span> Hello World!
</code></pre>
<p>你也可以下载这份文本的 Haskell 代码.
你应该能看到标题"介绍"上方有个链接.
把文件下载保存为 <code>00_hello_world.lhs</code> 然后执行:</p>
<pre><code class="zsh markdown">~ runhaskell 00<span class="emphasis">_hello_</span>world.lhs
Hello World!
</code></pre>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/00_hello_world.lhs" class="cut">01_basic/10_Introduction/<strong>00_hello_world.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/10_hello_you.lhs" class="cut">01_basic/10_Introduction/<strong>10_hello_you.lhs</strong></a></p>
<p>现在, 一个询问你姓名并根据你输入的姓名回答"Hello"的程序:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">main</span> = <span class="keyword">do</span>
print <span class="string">"What is your name?"</span>
name <- getLine
print (<span class="string">"Hello "</span> ++ name ++ <span class="string">"!"</span>)
</code></pre>
</div>
<p>首先, 让我们跟一些命令式语言写的类似程序对比:</p>
<pre><code class="python"> <span class="comment"># Python</span>
<span class="keyword">print</span> <span class="string">"What is your name?"</span>
name = raw_input()
<span class="keyword">print</span> <span class="string">"Hello %s!"</span> % name
</code></pre>
<pre><code class="ruby"> <span class="comment"># Ruby</span>
<span class="identifier"><span class="keymethods">puts</span></span> <span class="string">"What is your name?"</span>
<span class="identifier"><span class="keymethods">name</span></span> = <span class="identifier"><span class="keymethods">gets</span></span>.<span class="identifier"><span class="keymethods">chomp</span></span>
<span class="identifier"><span class="keymethods">puts</span></span> <span class="string">"Hello <span class="subst">#{<span class="identifier"><span class="keymethods">name</span></span>}</span>!"</span>
</code></pre>
<pre><code class="c tex">// In C
<span class="special">#</span>include <stdio.h>
int main (int argc, char **argv) <span class="special">{</span>
char name<span class="special">[</span>666<span class="special">]</span>; // <- An Evil Number!
// What if my name is more than 665 character long?
printf("What is your name?<span class="command">\n</span>");
scanf("<span class="comment">%s", name);</span>
printf("Hello <span class="comment">%s!\n", name);</span>
return 0;
<span class="special">}</span>
</code></pre>
<p>结构是一样的, 但有些语法差异.
这分教程主体部分会专门用来解释原因.</p>
<p>Haskell 里有个<code>main</code> 函数, 然后每个对象有它的类型.
<code>main</code> 的类型是 <code>IO ()</code>.
意味着, <code>main</code> 将引起副作用.</p>
<p>反正记住 Haskell 可以更像主流命令式语言.</p>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/10_hello_you.lhs" class="cut">01_basic/10_Introduction/<strong>10_hello_you.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/20_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>20_very_basic.lhs</strong></a></p>
<h3 id="very-basic-haskell">基础的 Haskell</h3>
<p><img alt="Picasso minimal owl" src="./Learn Haskell Fast and Hard_files/picasso_owl.jpg"></p>
<p>继续文章之前你需要注意 Haskell 一些本质的属性.</p>
<p><em>函数式</em></p>
<p>Haskell 是一门函数式语言.
如果你有命令式语言背景, 那你会有很多需要学的.
希望其中很多心概念甚至能在命令式编程里帮到你.
<p><em>自动静态类型</em></p>
<p>不像<code>C</code>, <code>C++</code> or <code>Java</code>里那个样子, 类型系统这里使用来帮助你的.</p>
<p><em>纯</em></p>
<p>一般来说你的函数不会修改任何外部的内容.
就是用, 她无法修改变量的值, 不能获取用户输入, 不能读取屏幕字符, 不能发射火箭.
另一面, 并行计算是很容易实现的.
Haskell 理清了哪里副作用将出现以及哪里你是纯的.
同时, 难懂你的程序将会容易非常多.
纯的部分程序很多 bug 都被预防掉了.
<p>而且纯函数遵循着 Haskell 的基本定律.
<blockquote>
<p>用相同的参数调用相同的函数往往有相同的返回值.</p>
</blockquote>
<p><em>惰性</em></p>
<p>默认的惰性是种很不寻常的语言设计.
默认情况下, Haskell 只有在必要是才进行求值.
一种结果是, 她提供给常优雅的方式来处理无限结构.
<p>最后一个关于你该怎样阅读 Haskell 代码的注意点.
对我, 那就像阅读科学文献.
一些部分很清晰, 但等你看到个公式, 就要集中精神慢慢读.
同时, 学习 Haskell, 你不懂语法的细节真的不很重要.
如果你遇到 <code>>>=</code>, <code><$></code>, <code><-</code> 或者其他古怪的符号, 干脆跳过去看代码的流程.</p>
<h4 id="function-declaration">函数声明</h4>
<p>你大概习惯这样声明函数</p>
<p>In <code>C</code>:</p>
<pre><code class="c perl"><span class="keyword">int</span> f(<span class="keyword">int</span> <span class="keyword">x</span>, <span class="keyword">int</span> <span class="keyword">y</span>) {
<span class="keyword">return</span> <span class="keyword">x</span><span class="variable">*x</span> + <span class="keyword">y</span><span class="variable">*y</span>;
}
</code></pre>
<p>In Javascript:</p>
<pre><code class="javascript"><span class="function"><span class="keyword">function</span> <span class="title">f</span><span class="params">(x,y)</span> {</span>
<span class="keyword">return</span> x*x + y*y;
}
</code></pre>
<p>in Python:</p>
<pre><code class="python"><span class="function"><span class="keyword">def</span> <span class="title">f</span><span class="params">(x,y)</span>:</span>
<span class="keyword">return</span> x*x + y*y
</code></pre>
<p>in Ruby:</p>
<pre><code class="ruby"><span class="function"><span class="keyword">def</span> <span class="title">f</span><span class="params">(<span class="identifier">x</span>,<span class="identifier">y</span>)</span></span>
<span class="identifier">x</span>*<span class="identifier">x</span> + <span class="identifier">y</span>*<span class="identifier">y</span>
<span class="identifier"><span class="keyword">end</span></span>
</code></pre>
<p>In Scheme:</p>
<pre><code class="scheme lisp"><span class="list">(<span class="title">define</span><span class="body"> <span class="list">(<span class="title">f</span><span class="body"> x y</span>)</span>
<span class="list">(<span class="title">+</span><span class="body"> <span class="list">(<span class="title">*</span><span class="body"> x x</span>)</span> <span class="list">(<span class="title">*</span><span class="body"> y y</span>)</span></span>)</span></span>)</span>
</code></pre>
<p>最后, Haskell 的方式:</p>
<pre><code class="haskell"><span class="title">f</span> x y = x*x + y*y
</code></pre>
<p>很干净. 没括号, 没 <code>def</code>.</p>
<p>记住, Haskell 经常用到函数和类型.
就这样定义它们非常简单.
语法为了这些对象专门考虑的.
<h4 id="a-type-example">类型的例子</h4>
<p>通常的办法是声明你函数的类型.
这不是非有不可的.
编译器足够聪明去替你给出类型.</p>
<p>Let’s play a little.</p>
<p>我们写写看.</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="comment">-- We declare the type using ::</span>
<span class="title">f</span> :: <span class="label">Int</span> -> <span class="label">Int</span> -> <span class="label">Int</span>
<span class="title">f</span> x y = x*x + y*y
<span class="title">main</span> = print (f <span class="number">2</span> <span class="number">3</span>)
</code></pre>
</div>
<pre><code class="markdown">~ runhaskell 20<span class="emphasis">_very_</span>basic.lhs
13
</code></pre>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/20_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>20_very_basic.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/21_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>21_very_basic.lhs</strong></a></p>
<p>再试试</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">f</span> :: <span class="label">Int</span> -> <span class="label">Int</span> -> <span class="label">Int</span>
<span class="title">f</span> x y = x*x + y*y
<span class="title">main</span> = print (f <span class="number">2.3</span> <span class="number">4.2</span>)
</code></pre>
</div>
<p>你看到这个报错:</p>
<pre><code class="vbscript"><span class="number">21</span>_very_basic.lhs:<span class="number">6</span>:<span class="number">23</span>:
No instance <span class="keyword">for</span> (Fractional <span class="built_in">Int</span>)
arising from the literal `<span class="number">4.2</span><span class="comment">'</span>
Possible fix: add an instance declaration <span class="keyword">for</span> (Fractional <span class="built_in">Int</span>)
<span class="keyword">In</span> the <span class="built_in">second</span> argument of `f<span class="comment">', namely `4.2'</span>
<span class="keyword">In</span> the first argument of `print<span class="comment">', namely `(f 2.3 4.2)'</span>
<span class="keyword">In</span> the expression: print (f <span class="number">2.3</span> <span class="number">4.2</span>)
</code></pre>
<p>问题: <code>4.2</code> 不属于 Int.</p>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/21_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>21_very_basic.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/22_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>22_very_basic.lhs</strong></a></p>
<p>解决方案,
别声明 <code>f</code> 的类型.
Haskell 会为我们推断出尽可能通用的类型:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">f</span> x y = x*x + y*y
<span class="title">main</span> = print (f <span class="number">2.3</span> <span class="number">4.2</span>)
</code></pre>
</div>
<p>运行成功.
好, 我们不需要声明新函数的每个类型.
比如, 用 <code>C</code>, 你得声明函数为<code>int</code>, 为 <code>float</code>, 为 <code>long</code>, 为 <code>double</code>, 等等...</p>
<p>但是, 我们该怎么去声明类型?
要看 Haskell 推出来的类型, 得运行 ghci:</p>
<pre><span class="low">
%</span> ghci<span class="low"><code>
GHCi, version 7.0.4: http://www.haskell.org/ghc/ :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer-gmp ... linking ... done.
Loading package base ... linking ... done.
Loading package ffi-1.0 ... linking ... done.
Prelude></code></span> let f x y = x*x + y*y
<span class="low"><code>Prelude></code></span> :type f
<code>f :: Num a => a -> a -> a</code>
</pre>
<p>呃? 这个古怪的类型什么意思?</p>
<pre><code class="perl">Num <span class="string">a =></span> a -> a -> a
</code></pre>
<p>首先, 仔细看右边的部分 <code>a -> a -> a</code>.
为了理解, 来看一列步进的例子:</p>
<table>
<tbody>
<tr>
<td>类型的写法</td>
<td>意义</td>
</tr>
<tr>
<td><code>Int</code></td>
<td><code>Int</code>类型</td>
</tr>
<tr>
<td><code>Int -> Int</code></td>
<td>类型由 <code>Int</code> 到 <code>Int</code> 的函数 </td>
</tr>
<tr>
<td><code>Float -> Int</code></td>
<td>类型由 <code>Float</code> 到 <code>Int</code> 的函数</td>
</tr>
<tr>
<td><code>a -> Int</code></td>
<td>任意类型到 <code>Int</code> 的函数</td>
</tr>
<tr>
<td><code>a -> a</code></td>
<td>类型由某个 <code>a</code> 到同个 <code>a</code> 的函数 </td>
</tr>
<tr>
<td><code>a -> a -> a</code></td>
<td>接收两个参数类型 <code>a</code> 返回 <code>a</code> 类型的函数</td>
</tr>
</tbody>
</table>
<p>在类型 <code>a -> a -> a</code> 里, 字母 <code>a</code> 是个 <em>类型变量</em>.
意思是<code>f</code> 是有两个参数的函数而且两个参数和返回值是相同的类型.
类型变量 <code>a</code> 能表示多种类型.
比如 <code>Int</code>, <code>Integer</code>, <code>Float</code>...</p>
<p>所以不像强制类型的 <code>C</code> 声明函数为 <code>int</code>, <code>long</code>, <code>float</code>, <code>double</code>, 等等...
我们定义函数就像是动态语言.</p>
<p>通常 <code>a</code> 能是任意类型.
比如 <code>String</code>, <code>Int</code>, 也有更复杂的类型, 像 <code>Trees</code>, 其他的函数, 等等...
不过这里我们的类型加了前缀 <code>Num a => </code>. </p>
<p><code>Num</code> 是个 <em>类型类</em>.
类型类可以理解为一些类型的集合.
<code>Num</code> 仅包含表现为数字的几个类型.
更简单说, <code>Num</code> 类中的类型能运行一套特定的函数, 尤其是 <code>(+)</code> 和 <code>(*)</code>.</p>
<p>类型类是很强大的语言构建.
这能被用来做一些特别强大的事.
后面会再细说.</p>
<p>最后, <code>Num a => a -> a -> a</code> 是说:</p>
<p>用 <code>a</code> 表示一个属于 <code>Num</code> 类型类的类型.
这是个类型由 <code>a</code> 到 (<code>a -> a</code>) 的函数.</p>
<p>是的, 怪.
事实上 Haskell 没一个函数真有两个参数.
反而所有函数都只有一个参数.
但我们会发现接收两个参数等同于接收一个参数再返回一个来接收第二个参数的函数.</p>
<p>更直白地 <code>f 3 4</code> 等于是 <code>(f 3) 4</code>.
注意 <code>f 3</code> 是个函数:</p>
<pre><code class="perl">f :: Num a :: a -> a -> a
g :: Num a :: a -> a
g = f <span class="number">3</span>
g <span class="keyword">y</span> ⇔ <span class="number">3</span><span class="variable">*3</span> + <span class="keyword">y</span><span class="variable">*y</span>
</code></pre>
<p>函数有另一个记法.
lambda 记法让我们能创建函数而不带函数名.
称为匿名函数.
像这样写:</p>
<pre><code class="tex">g = <span class="command">\y</span> -> 3*3 + y*y
</code></pre>
<p>用 <code>\</code> 是因为它像 <code>λ</code> 而且属于 ASCII.</p>
<p>如果你没习惯函数式编程, 你的脑子该开始热了.
可以去做真实应用了.</p>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/22_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>22_very_basic.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/23_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>23_very_basic.lhs</strong></a></p>
<p>但那之前, 我们要确认下类型系统能像预期那样运行:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">f</span> :: <span class="label">Num</span> a => a -> a -> a
<span class="title">f</span> x y = x*x + y*y
<span class="title">main</span> = print (f <span class="number">3</span> <span class="number">2.4</span>)
</code></pre>
</div>
<p>运行正常, 因为, <code>3</code> 同时是 Float 和 Integer 合法的分数写法.
因为 <code>2.4</code> 是分数, <code>3</code> 也就作为分数解释.</p>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/23_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>23_very_basic.lhs</strong> </a></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/24_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>24_very_basic.lhs</strong></a></p>
<p>如果强制让函数接收两个不同的类型, 运行会出错:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">f</span> :: <span class="label">Num</span> a => a -> a -> a
<span class="title">f</span> x y = x*x + y*y
<span class="title">x</span> :: <span class="label">Int</span>
<span class="title">x</span> = <span class="number">3</span>
<span class="title">y</span> :: <span class="label">Float</span>
<span class="title">y</span> = <span class="number">2.4</span>
<span class="title">main</span> = print (f x y) <span class="comment">-- won't work because type x ≠ type y</span>
</code></pre>
</div>
<p>编译器报错.
两个参数必须类型一致.</p>
<p>如果你坚持这个想法不好, 那么就让编译器帮你从一个类型转到另一个, 你很应该看这个不错(也有趣)的视频:
<a href="https://www.destroyallsoftware.com/talks/wat">WAT</a></p>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/10_Introduction/24_very_basic.lhs" class="cut">01_basic/10_Introduction/<strong>24_very_basic.lhs</strong> </a></p>
<h2 id="essential-haskell">基础的 Haskell</h2>
<p><img alt="Kandinsky Gugg" src="./Learn Haskell Fast and Hard_files/kandinsky_gugg.jpg"></p>
<p>我建议你这部分只是浏览.
当作一份手册.
Haskell 有大量特性.
很多信息这里没有给出.
看起费解的记法了可以回来看.</p>
<p>我用 <code>⇔</code> 符号标示两个表达式等价.
这是个元符号, <code>⇔</code> 不属于 Haskell 语法.
我也会用 <code>⇒</code> 标示 Haskell 表达式的返回值.</p>
<h3 id="notations">记法</h3>
<h5 id="arithmetic">算术</h5>
<pre><code class="markdown">3 + 2 <span class="bullet">* 6 / 3 ⇔ 3 + ((2*</span>6)/3)
</code></pre>
<h5 id="logic">逻辑</h5>
<pre><code class="python"><span class="built_in">True</span> || <span class="built_in">False</span> ⇒ <span class="built_in">True</span>
<span class="built_in">True</span> && <span class="built_in">False</span> ⇒ <span class="built_in">False</span>
<span class="built_in">True</span> == <span class="built_in">False</span> ⇒ <span class="built_in">False</span>
<span class="built_in">True</span> /= <span class="built_in">False</span> ⇒ <span class="built_in">True</span> (/=) <span class="keyword">is</span> the operator <span class="keyword">for</span> different
</code></pre>
<h5 id="powers">Powers</h5>
<pre><code class="perl"><span class="keyword">x</span>^n <span class="keyword">for</span> n an integral (understand Int <span class="keyword">or</span> Integer)
<span class="keyword">x</span><span class="variable">**</span><span class="keyword">y</span> <span class="keyword">for</span> <span class="keyword">y</span> any kind of number (Float <span class="keyword">for</span> example)
</code></pre>
<p><code>Integer</code> 没有上限, 而你的设备会到极限:</p>
<pre><code class="parser3"><span class="number">4</span><span class="keyword">^103</span>
<span class="number">102844034832575377634685573909834406561420991602098741459288064</span>
</code></pre>
<p>对!
还有分数 FTW!
但你需要 import 一个模块 <code>Data.Ratio</code>:</p>
<pre><code class="avrasm">$ ghci
....
Prelude> :m Data<span class="preprocessor">.Ratio</span>
Data<span class="preprocessor">.Ratio</span>> (<span class="number">11</span> % <span class="number">15</span>) * (<span class="number">5</span> % <span class="number">3</span>)
<span class="number">11</span> % <span class="number">9</span>
</code></pre>
<h5 id="lists">Lists</h5>
<pre><code class="css"><span class="attr_selector">[]</span> ⇔ <span class="tag">empty</span> <span class="tag">list</span>
<span class="attr_selector">[1,2,3]</span> ⇔ <span class="tag">List</span> <span class="tag">of</span> <span class="tag">integral</span>
<span class="attr_selector">["foo","bar","baz"]</span> ⇔ <span class="tag">List</span> <span class="tag">of</span> <span class="tag">String</span>
1:<span class="attr_selector">[2,3]</span> ⇔ <span class="attr_selector">[1,2,3]</span>, (<span class="pseudo">:)</span> <span class="tag">prepend</span> <span class="tag">one</span> <span class="tag">element</span>
1<span class="pseudo">:2</span>:<span class="attr_selector">[]</span> ⇔ <span class="attr_selector">[1,2]</span>
<span class="attr_selector">[1,2]</span> ++ <span class="attr_selector">[3,4]</span> ⇔ <span class="attr_selector">[1,2,3,4]</span>, (++) <span class="tag">concatenate</span>
<span class="attr_selector">[1,2,3]</span> ++ <span class="attr_selector">["foo"]</span> ⇔ <span class="tag">ERROR</span> <span class="tag">String</span> ≠ <span class="tag">Integral</span>
<span class="attr_selector">[1..4]</span> ⇔ <span class="attr_selector">[1,2,3,4]</span>
<span class="attr_selector">[1,3..10]</span> ⇔ <span class="attr_selector">[1,3,5,7,9]</span>
<span class="attr_selector">[2,3,5,7,11..100]</span> ⇔ <span class="tag">ERROR</span>! <span class="tag">I</span> <span class="tag">am</span> <span class="tag">not</span> <span class="tag">so</span> <span class="tag">smart</span>!
<span class="attr_selector">[10,9..1]</span> ⇔ <span class="attr_selector">[10,9,8,7,6,5,4,3,2,1]</span>
</code></pre>
<h5 id="strings">Strings</h5>
<p>Haskell 里 strings 是 <code>Char</code> 组成的 list.</p>
<pre><code class="objectivec"><span class="string">'a'</span> :: Char
<span class="string">"a"</span> :: [Char]
<span class="string">""</span> ⇔ []
<span class="string">"ab"</span> ⇔ [<span class="string">'a'</span>,<span class="string">'b'</span>] ⇔ <span class="string">'a'</span>:<span class="string">"b"</span> ⇔ <span class="string">'a'</span>:[<span class="string">'b'</span>] ⇔ <span class="string">'a'</span>:<span class="string">'b'</span>:[]
<span class="string">"abc"</span> ⇔ <span class="string">"ab"</span>++<span class="string">"c"</span>
</code></pre>
<blockquote>
<p><em>注意</em>:
实际编写代码是你不应该用 char 的 list 来表示文本.
大多数情况你应该用 <code>Data.Text</code>.
如果你想像是 ASCII char 的文本流, 你该用 <code>Data.ByteString</code>.</p>
</blockquote>
<h5 id="tuples">Tuples</h5>
<p>两个元素的 tuple 类型为 <code>(a,b)</code>.
tuple 允许元素属于不同类型.</p>
<pre><code class="avrasm">-- All these tuple are valid
(<span class="number">2</span>,<span class="string">"foo"</span>)
(<span class="number">3</span>,<span class="string">'a'</span>,[<span class="number">2</span>,<span class="number">3</span>])
((<span class="number">2</span>,<span class="string">"a"</span>),<span class="string">"c"</span>,<span class="number">3</span>)
fst (<span class="built_in">x</span>,<span class="built_in">y</span>) ⇒ <span class="built_in">x</span>
snd (<span class="built_in">x</span>,<span class="built_in">y</span>) ⇒ <span class="built_in">y</span>
fst (<span class="built_in">x</span>,<span class="built_in">y</span>,<span class="built_in">z</span>) ⇒ ERROR: fst :: (a,b) -> a
snd (<span class="built_in">x</span>,<span class="built_in">y</span>,<span class="built_in">z</span>) ⇒ ERROR: snd :: (a,b) -> b
</code></pre>
<h5 id="deal-with-parentheses">处理圆括号</h5>
<p>可以用两个函数还下一部分括号: <code>($)</code> 和 <code>(.)</code>.</p>
<pre><code class="perl">-- By default:
f g h <span class="keyword">x</span> ⇔ (((f g) h) <span class="keyword">x</span>)
-- the $ replace parenthesis from the $
-- to the end of the expression
f g $ h <span class="keyword">x</span> ⇔ f g (h <span class="keyword">x</span>) ⇔ (f g) (h <span class="keyword">x</span>)
f $ g h <span class="keyword">x</span> ⇔ f (g h <span class="keyword">x</span>) ⇔ f ((g h) <span class="keyword">x</span>)
f $ g $ h <span class="keyword">x</span> ⇔ f (g (h <span class="keyword">x</span>))
-- (.) the composition function
(f . g) <span class="keyword">x</span> ⇔ f (g <span class="keyword">x</span>)
(f . g . h) <span class="keyword">x</span> ⇔ f (g (h <span class="keyword">x</span>))
</code></pre>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/20_Essential_Haskell/10a_Functions.lhs" class="cut">01_basic/20_Essential_Haskell/<strong>10a_Functions.lhs</strong></a></p>
<h3 id="useful-notations-for-functions">常用函数记法</h3>
<p>留意下:</p>
<pre><code class="lua">x :: Int ⇔ x is of <span class="built_in">type</span> Int
x :: a ⇔ x can be of any <span class="built_in">type</span>
x :: Num a => a ⇔ x can be any <span class="built_in">type</span> a
such that a belongs to Num <span class="built_in">type</span> class
f :: a -> b ⇔ f is a <span class="function"><span class="keyword">function</span> <span class="title">from</span> <span class="title">a</span> <span class="title">to</span> <span class="title">b</span>
<span class="title">f</span> :: <span class="title">a</span> -> <span class="title">b</span> -> <span class="title">c</span> ⇔ <span class="title">f</span> <span class="title">is</span> <span class="title">a</span> <span class="title">function</span> <span class="title">from</span> <span class="title">a</span> <span class="title">to</span> <span class="params">(b→c)</span></span>
f :: (a -> b) -> c ⇔ f is a <span class="function"><span class="keyword">function</span> <span class="title">from</span> <span class="params">(a→b)</span></span> to c
</code></pre>
<p>在函数定义前声明其类型不是强制性的.
Haskell 会自行推断出最宽泛的类型.
但声明类型是一个好的实践.</p>
<p><em>中缀表示法</em></p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">square</span> :: <span class="label">Num</span> a => a -> a
<span class="title">square</span> x = x^<span class="number">2</span>
</code></pre>
</div>
<p>注意 <code>^</code> 用了中缀表示法.
每个中缀表示法有对应的前缀表示法.
只要加上括号.</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">square'</span> x = (^) x <span class="number">2</span>
<span class="title">square''</span> x = (^<span class="number">2</span>) x
</code></pre>
</div>
<p>两边的 <code>x</code> 可以约掉.
这叫做 η-reduction.</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">square'''</span> = (^<span class="number">2</span>)
</code></pre>
</div>
<p>注意我们可以定义含有 <code>'</code> 的函数名.
Here:</p>
<blockquote>
<p><code>square</code> ⇔ <code>square'</code> ⇔ <code>square''</code> ⇔ <code>square '''</code></p>
</blockquote>
<p><em>判别</em></p>
<p>absolute 函数的一个实现.</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">absolute</span> :: (<span class="label">Ord</span> a, <span class="label">Num</span> a) => a -> a
<span class="title">absolute</span> x = <span class="keyword">if</span> x >= <span class="number">0</span> <span class="keyword">then</span> x <span class="keyword">else</span> -x
</code></pre>
</div>
<p>注意: Haskell 表达式 <code>if .. then .. else</code> 很像
C 语言操作符 <code>¤?¤:¤</code>. 不能遗漏后面的 <code>else</code>.</p>
<p>另一个等价的版本:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="title">absolute'</span> x
| x >= <span class="number">0</span> = x
| otherwise = -x
</code></pre>
</div>
<blockquote>
<p>关于表示法的警告: Haskell 里缩进<em>很重要</em>.
好比 Python, 出错的缩进会破坏代码.</p>
</blockquote>
<div style="display:none">
<div class="codehighlight">
<pre><code class="haskell"><span class="title">main</span> = <span class="keyword">do</span>
print $ square <span class="number">10</span>
print $ square' <span class="number">10</span>
print $ square'' <span class="number">10</span>
print $ square''' <span class="number">10</span>
print $ absolute <span class="number">10</span>
print $ absolute (-<span class="number">10</span>)
print $ absolute' <span class="number">10</span>
print $ absolute' (-<span class="number">10</span>)
</code></pre>
</div>
</div>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/01_basic/20_Essential_Haskell/10a_Functions.lhs" class="cut">01_basic/20_Essential_Haskell/<strong>10a_Functions.lhs</strong> </a></p>
<h2 id="hard-part">难点</h2>
<p>现在开始讲难点.</p>
<h3 id="functional-style">函数风格</h3>
<p><img alt="Biomechanical Landscape by H.R. Giger" src="./Learn Haskell Fast and Hard_files/hr_giger_biomechanicallandscape_500.jpg"></p>
<p>这一章, 我会给个关于 Haskell 令人印象深刻的重构能力的小例子.
我们会选个问题然后用标准的命令式办法去解决掉.
然后我会让代码演进.
最终结果会更优雅更容易接受.</p>
<p>来解决以下问题:</p>
<blockquote>
<p>给定 integer 的 list, 返回 list 中偶数的和.</p>
<p>例如:
<code>[1,2,3,4,5] ⇒ 2 + 4 ⇒ 6</code></p>
</blockquote>
<p>为展示函数式和命令式方案的不同,
我开始会提供一个命令式的方案 (JavaScript):</p>
<pre><code class="javascript"><span class="function"><span class="keyword">function</span> <span class="title">evenSum</span><span class="params">(list)</span> {</span>
<span class="keyword">var</span> result = <span class="number">0</span>;
<span class="keyword">for</span> (<span class="keyword">var</span> i=<span class="number">0</span>; i< list.length ; i++) {
<span class="keyword">if</span> (list[i] % <span class="number">2</span> ==<span class="number">0</span>) {
result += list[i];
}
}
<span class="keyword">return</span> result;
}
</code></pre>
<p>但 Haskell 里没有变量, 也没循环.
一个不用循环而完成相同结果的解法是用递归.</p>
<blockquote>
<p><em>注意</em>:<br>
在命令式语言里递归通常被认为缓慢.
但在函数式编程里通常不是那种状况.
大多数情况下 Haskell 会把递归函数处理得很高效</p>
</blockquote>
<p>这是个 <code>C</code> 版本的递归函数.
注意简单起见, 我设定第一个 <code>0</code> 值表示 int list 的结尾.</p>
<pre><code class="c perl"><span class="keyword">int</span> evenSum(<span class="keyword">int</span> <span class="variable">*list</span>) {
<span class="keyword">return</span> accumSum(<span class="number">0</span>,list);
}
<span class="keyword">int</span> accumSum(<span class="keyword">int</span> n, <span class="keyword">int</span> <span class="variable">*list</span>) {
<span class="keyword">int</span> <span class="keyword">x</span>;
<span class="keyword">int</span> <span class="variable">*xs</span>;
<span class="keyword">if</span> (<span class="variable">*list</span> == <span class="number">0</span>) { <span class="regexp">//</span> <span class="keyword">if</span> the list is empty
<span class="keyword">return</span> n;
} <span class="keyword">else</span> {
<span class="keyword">x</span> = list[<span class="number">0</span>]; <span class="regexp">//</span> let <span class="keyword">x</span> be the first element of the list
xs = list+<span class="number">1</span>; <span class="regexp">//</span> let xs be the list without <span class="keyword">x</span>
<span class="keyword">if</span> ( <span class="number">0</span> == (<span class="keyword">x</span><span class="variable">%2</span>) ) { <span class="regexp">//</span> <span class="keyword">if</span> <span class="keyword">x</span> is even
<span class="keyword">return</span> accumSum(n+<span class="keyword">x</span>, xs);
} <span class="keyword">else</span> {
<span class="keyword">return</span> accumSum(n, xs);
}
}
}
</code></pre>
<p>
考虑下这段代码. 我们会把它转成 Haskell.
但这之前, 我要介绍下我们会用到的三个简单却使用的函数:</p>
<pre><code class="haskell"><span class="title">even</span> :: <span class="label">Integral</span> a => a -> <span class="label">Bool</span>
<span class="title">head</span> :: [a] -> a
<span class="title">tail</span> :: [a] -> [a]
</code></pre>
<p><code>even</code> 验证数字是否偶数.</p>
<pre><code class="haskell"><span class="title">even</span> :: <span class="label">Integral</span> a => a -> <span class="label">Bool</span>
<span class="title">even</span> <span class="number">3</span> ⇒ <span class="label">False</span>
<span class="title">even</span> <span class="number">2</span> ⇒ <span class="label">True</span>
</code></pre>
<p><code>head</code> 返回 list 第一个元素:</p>
<pre><code class="haskell"><span class="title">head</span> :: [a] -> a
<span class="title">head</span> [<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>] ⇒ <span class="number">1</span>
<span class="title">head</span> [] ⇒ <span class="label">ERROR</span>
</code></pre>
<p><code>tail</code> 返回第一个元素以外所有元素:</p>
<pre><code class="haskell"><span class="title">tail</span> :: [a] -> [a]
<span class="title">tail</span> [<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>] ⇒ [<span class="number">2</span>,<span class="number">3</span>]
<span class="title">tail</span> [<span class="number">3</span>] ⇒ []
<span class="title">tail</span> [] ⇒ <span class="label">ERROR</span>
</code></pre>
<p>记下, 对任一非空 list <code>l</code>,
<code>l ⇔ (head l):(tail l)</code></p>
<hr>
<p><a href="http://yannesposito.com/Scratch/en/blog/Haskell-the-Hard-Way/code/02_Hard_Part/11_Functions.lhs" class="cut">02_Hard_Part/<strong>11_Functions.lhs</strong></a></p>
<p>Haskell 第一个解法.
函数 <code>evenSum</code> 返回列表里所有偶数的和:</p>
<div class="codehighlight">
<pre><code class="haskell"><span class="comment">-- Version 1</span>
<span class="title">evenSum</span> :: [<span class="label">Integer</span>] -> <span class="label">Integer</span>
<span class="title">evenSum</span> l = accumSum <span class="number">0</span> l
<span class="title">accumSum</span> n l = <span class="keyword">if</span> l == []
<span class="keyword">then</span> n
<span class="keyword">else</span> <span class="keyword">let</span> x = head l
xs = tail l
<span class="keyword">in</span> <span class="keyword">if</span> even x
<span class="keyword">then</span> accumSum (n+x) xs
<span class="keyword">else</span> accumSum n xs
</code></pre>
</div>
<p>对函数的测试可以用 <code>ghci</code>:</p>
<pre>% ghci
<span class="low">GHCi, version 7.0.3: http://www.haskell.org/ghc/ :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer-gmp ... linking ... done.
Loading package base ... linking ... done.
Prelude></span> :load 11_Functions.lhs