232 lines
7.4 KiB
HTML
232 lines
7.4 KiB
HTML
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<!DOCTYPE html>
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<html>
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<head>
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<meta charset="utf-8">
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<meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1">
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<meta name="viewport" content="width=1024, user-scalable=no">
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<title>Category Theory for Programming</title>
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</head>
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<body class="deck-container">
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<!-- Begin slides. Just make elements with a class of slide. -->
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<section class="slide">
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<h1>Category Theory <span class="and">&</span> Programming
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<div><author style="font-size: .4em"><em class="base01">by</em> Yann Esposito
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<div>
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<twitter style="font-size: .5em">
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<a href="http://twitter.com/yogsototh">@yogsototh</a>,
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</twitter>
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<googleplus style="font-size: .5em">
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<a href="https://plus.google.com/117858550730178181663">+yogsototh</a>
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</googleplus>
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</div>
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</author></div>
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</h1>
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</section>
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<section class="slide">
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<h2>Plan</h2>
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<ul style="font-size: 2em">
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<li class="yellow">Why?</li>
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<li>What?</li>
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<li>How?</li>
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</ul>
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</section>
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<section class="slide">
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<h2>Abstraction Example</h2>
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<p>Something you see very often but in different instances.</p>
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<p>Once you recognize the notion, you see it almost everywhere.</p>
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<ul>
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<li class="slide">Numbers: <em>0</em>,1,2,3,... (3400 BC, real numbers 760 BC)</li>
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<li class="slide">Rational numbers: \(\frac{p}{q}\) (concept is prehistoric)</li>
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<li class="slide">Negative numbers: ..., -3, -2, -1, 0, 1, 2, ... (100-50 BC)</li>
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<li class="slide">Irrational numbers: \(\mathbb{A}\), \(\mathbb{R}\) (500 BC → Pythogoras killed Hippasus because of \(\sqrt{2}\)!)</li>
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<li class="slide">Complex numbers: \(\mathbb{C}\) (100 AD, then 16th century)</li>
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</ul>
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</section>
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<section class="slide">
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<h2>Numbers ⇒ Set Theory (\(\infty\))</h2>
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<table>
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<tr>
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<th>Numbers</th>
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<th>Set Theory</th>
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</tr>
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<tr>
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<td>\(\mathbb{N}\): \((+,0)\)</td>
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<td>Semigroups</td>
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</tr>
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<tr class="slide">
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<td>\(\mathbb{Z}\): \((+,0,\times,1)\)</td>
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<td>Rings</td>
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</tr>
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<tr class="slide">
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<td>\(\mathbb{Q}\)</td>
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<td>Fields</td>
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</tr>
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<tr class="slide">
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<td>\(\mathbb{R}\)</td>
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<td>Complete Fields (<em class="base01">topology</em>)</td>
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</tr>
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<tr class="slide">
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<td>\(\mathbb{C}\)</td>
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<td>Algebræ</td>
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</tr>
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<tr class="slide"><td></td><td>Modules,Vector Spaces, Monoids, ...</td></tr>
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</table>
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<p class="slide">More <strong>general</strong>: more things are sets.<br/>
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<span class="and">&</span> More <strong>precise</strong>: clear distinction between concepts)</p>
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</section>
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<section class="slide">
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<h2>Set Theory ⇒? Category Theory</h2>
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<table>
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<tr>
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<th>Numbers</th>
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<th>Set Theory (\(\infty\))</th>
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<th>Category Theory (relations)</th>
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</tr>
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<tr>
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<td>\(\mathbb{N}\): \((+,0)\)</td>
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<td>Semigroups</td>
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<td>?</td>
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</tr>
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<tr>
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<td>\(\mathbb{Z}\): \((+,0,\times,1)\)</td>
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<td>Rings</td>
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<td>?</td>
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</tr>
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<tr>
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<td>\(\mathbb{Q}\)</td>
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<td>Fields</td>
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<td>?</td>
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</tr>
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<tr>
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<td>\(\mathbb{R}\)</td>
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<td>Complete Fields (<em class="base01">topology</em>)</td>
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<td>?</td>
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</tr>
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<tr>
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<td>\(\mathbb{C}\)</td>
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<td>Algebræ</td>
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<td>?</td>
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</tr>
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<tr><td></td><td>Modules,Vector Spaces, Monoids, ...</td><td>?</td></tr>
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</table>
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</section>
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<section class="slide">
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<h2><span class="yellow">/.*/</span> ⇒? Category Theory</h2>
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<ul>
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<li class="slide">Topology ⇒ Category Theory</li>
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<li class="slide">Quantum Physics ⇒ Category Theory</li>
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<li class="slide">Logic ⇒ Category Theory</li>
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<li class="slide"><b>Programming</b> ⇒ Category Theory</li>
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</ul>
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<p class="slide">More <strong>general</strong>: more things are sets.<br/>
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<span class="and">&</span> More <strong>precise</strong>: clear distinction between concepts)</p>
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</section>
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<section class="slide">
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<h2>too much abstraction?</h2>
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<p>More general <span class="and">&</span> more precise</p>
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</section>
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<section class="slide">
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<h2>Animation, Math & Code</h2>
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<p>Some math \(\sum_{i=1}^\infty \frac{1}{2^x} = 1 \)</p>
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<p class="slide">Another <b>math</b> <em>formula</em> $$\sum_{i=1}^\infty \frac{1}{2^x} = 1$$</p>
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<pre class="slide"><code class="haskell">import Control.Monad
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main :: IO()
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main = do
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putStrLn $ "Hello !"
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</code></pre>
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</section>
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