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www.0x10086.com |
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<meta name="Description" content="部署小哥."> | ||
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<title>(Re (S a n))</title> | ||
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(Re (S a n)) | ||
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<a class="navbar-item" href="/blog"> | ||
博客 | ||
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每日 | ||
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相册 | ||
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小册 | ||
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2300年前的欧几里得算法 | ||
</h2> | ||
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<p>2300年前的欧几里得算法,做的是这样一件事情:<strong>找出两个数的最大公约数</strong>。</p> | ||
<p>自然语言描述: | ||
<br></br> | ||
<em>计算两个非负整数p和q的最大公约数:若q是0,则最大公约数为p。否则,将p除以q得到余数r,p和q的最大公约数即为q和r的最大公约数。</em> | ||
<br></br></p> | ||
<p>PS: 欧几里得大概是很无聊的,那么奇怪的规律也能找到。</p> | ||
<p><strong>实现:</strong></p> | ||
<pre data-lang="elixir" class="language-elixir "><code class="language-elixir" data-lang="elixir">defmodule Alt do | ||
def gcd(p, 0), do: p | ||
def gcd(p, q), do: gcd(q, rem(p, q)) | ||
end | ||
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IO.puts Alt.gcd(10,4) | ||
#-> 2 | ||
IO.puts Alt.gcd(10,0) | ||
#-> 10 | ||
</code></pre> | ||
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</div> | ||
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<p class="subtitle"><strong>2016-02-01</strong></p> | ||
<p class="subtitle"><strong>false</strong></p> | ||
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</div> | ||
</section> | ||
</body> | ||
<footer class="footer"> | ||
<div class="footer__inner"> | ||
<div class="footer__content"> | ||
<a href="/about">ReSan 👾 1991</a> | ||
</div> | ||
</div> | ||
</footer> | ||
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<!DOCTYPE html> | ||
<html lang="en"> | ||
<head> | ||
<meta charset="utf-8"> | ||
<meta name="Description" content="部署小哥."> | ||
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<title>(Re (S a n))</title> | ||
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<!-- Icon --> | ||
<link rel="apple-touch-icon" sizes="180x180" href="/apple-touch-icon.png"> | ||
<link rel="icon" type="image/png" sizes="32x32" href="/favicon-32x32.png"> | ||
<link rel="icon" type="image/png" sizes="16x16" href="/favicon-16x16.png"> | ||
<link rel="manifest" href="/site.webmanifest"> | ||
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<!-- CSS --> | ||
<link rel="stylesheet" type="text/css" href="/main.css"> | ||
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<!-- Ext Chart --> | ||
<link href="/static/c3.css" rel="stylesheet"> | ||
<script src="https://d3js.org/d3.v5.min.js" charset="utf-8"></script> | ||
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<script> | ||
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function gtag(){dataLayer.push(arguments);} | ||
gtag('js', new Date()); | ||
gtag('config', 'G-5ZZLRFRNRH'); | ||
</script> | ||
</head> | ||
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<body> | ||
<nav class="navbar" > | ||
<div class="navbar-menu is-white is-active"> | ||
<div class="navbar-start"> | ||
<a class="navbar-item" href="/"> | ||
(Re (S a n)) | ||
</a> | ||
</div> | ||
|
||
<div class="navbar-end"> | ||
<a class="navbar-item" href="/blog"> | ||
博客 | ||
</a> | ||
<a class="navbar-item" href="/daily"> | ||
每日 | ||
</a> | ||
<a class="navbar-item" href="/photos"> | ||
相册 | ||
</a> | ||
<a class="navbar-item" href="/books"> | ||
小册 | ||
</a> | ||
</div> | ||
</div> | ||
</nav> | ||
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<section class="section"> | ||
<div class="container"> | ||
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<main class="post"> | ||
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<h2 class="post-title"> | ||
正则序和应用序 | ||
</h2> | ||
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<div class="post-content"> | ||
<p><strong>要点:</strong> | ||
<em>正则序:先展开过程,再求值。 | ||
应用序:先求值,再代入过程。</em></p> | ||
<p>对于以下代码:</p> | ||
<pre data-lang="lisp" class="language-lisp "><code class="language-lisp" data-lang="lisp">(define (p) (p)) | ||
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(define (test x y) | ||
(if (= x 0) | ||
0 | ||
y)) | ||
(test 0 (p)) | ||
</code></pre> | ||
<p>如果解释器采用的是应用序,则程序会不断地执行,因为需要求值<em>p</em>函数,然而<em>p</em>函数返回自己,因此进入死循环。</p> | ||
<pre data-lang="lisp" class="language-lisp "><code class="language-lisp" data-lang="lisp">(test 0 (p)) | ||
(test 0 (p)) | ||
(test 0 (p)) | ||
... | ||
</code></pre> | ||
<hr /> | ||
<p>而对于采用正则序的解释器,程序则能成功输出<code>0</code>,因为,解释器先展开过程,再求值(如果表达式有用到,而这里因为x=0,并没有用到<em>p</em>函数),过程是这样的:</p> | ||
<pre data-lang="lisp" class="language-lisp "><code class="language-lisp" data-lang="lisp">(test 0 (p)) | ||
(if (= 0 0) 0 (p)) | ||
(if #t 0 (p)) | ||
0 | ||
</code></pre> | ||
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</div> | ||
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<!-- | ||
<p class="subtitle"><strong>2016-02-01</strong></p> | ||
<p class="subtitle"><strong>false</strong></p> | ||
--> | ||
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<div class="by-nc-nd"> | ||
<span>署名-非商业性使用-禁止演绎 3.0 国际<a href="https://creativecommons.org/licenses/by-nc-nd/3.0/deed.zh">(CC BY-NC-ND 3.0)</a></span> | ||
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</main> | ||
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</div> | ||
</section> | ||
</body> | ||
<footer class="footer"> | ||
<div class="footer__inner"> | ||
<div class="footer__content"> | ||
<a href="/about">ReSan 👾 1991</a> | ||
</div> | ||
</div> | ||
</footer> | ||
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