226 lines
7.2 KiB
HTML
226 lines
7.2 KiB
HTML
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<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8">
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<title>Category Theory for DB-ies</title>
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<meta name="description" content="Mimir">
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<meta name="author" content="Oliver Kennedy">
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<meta name="apple-mobile-web-app-capable" content="yes" />
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<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui">
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<link rel="stylesheet" href="../reveal.js-3.5.0/css/reveal.css">
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<link rel="stylesheet" href="ubodin.css" id="theme">
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<!-- Code syntax highlighting -->
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<link rel="stylesheet" href="../reveal.js-3.5.0/lib/css/zenburn.css">
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<!-- Printing and PDF exports -->
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<script>
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var link = document.createElement( 'link' );
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link.rel = 'stylesheet';
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link.type = 'text/css';
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link.href = window.location.search.match( /print-pdf/gi ) ? '../reveal.js-3.5.0/css/print/pdf.css' : '../reveal.js-3.5.0/css/print/paper.css';
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document.getElementsByTagName( 'head' )[0].appendChild( link );
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</script>
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<!--[if lt IE 9]>
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<script src="../reveal.js-3.5.0/lib/js/html5shiv.js"></script>
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<![endif]-->
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</head>
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<body>
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<div class="reveal">
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<!-- Any section element inside of this container is displayed as a slide -->
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<div class="header">
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<!-- Any Talk-Specific Header Content Goes Here -->
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Category Theory for DB-ies
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</div>
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<div class="footer">
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<!-- Any Talk-Specific Footer Content Goes Here -->
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<div style="float: left; margin-top: 15px; ">
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Exploring <u><b>O</b></u>nline <u><b>D</b></u>ata <u><b>In</b></u>teractions
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</div>
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<img src="graphics/FullText-white.png" height="40" style="float: right;"/>
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</div>
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<div class="slides">
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<section>
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<section>
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<h2>Category Theory for DB-ies</h2>
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<h4>(Or how I learned that mathematicians don't know how to name things)<h4>
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</section>
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<section>
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<img src="graphics/bake_pi.jpg" height="400px">
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</section>
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<section>
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<p>People always say that SQL is "Declarative"</p>
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</section>
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<section>
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<h3>Why is the following replacement ok?</h3>
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<pre><code class="sql">
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SELECT * FROM R WHERE A = 1 AND B = 2
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</code></pre>
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<pre><code class="sql">
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SELECT * FROM (SELECT * FROM R WHERE A = 1) WHERE B = 2
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</code></pre>
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<p class="fragment">(and how is it the same as computing $x + 1 + 2$?)</p>
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</section>
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</section>
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<section>
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<section>
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<h2>Addition is Cool</h2>
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<p class="fragment" data-fragment-index="1">
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<b class="fragment" data-fragment-index="4">Commutative</b>
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$$a + b = b + a$$
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</p>
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<p class="fragment" data-fragment-index="2">
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<b class="fragment" data-fragment-index="4">Associative</b>
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$$(a + b) + c = a + (b + c)$$
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</p>
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<p class="fragment" data-fragment-index="3">
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<b class="fragment" data-fragment-index="4">Neutral Element</b>
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$$0 + a = a$$
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</p>
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</section>
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<section>
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<h2>Addition is Cool</h2>
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<pre><code class="java">
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public int add(int a, int b) { ... }
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add(a, b) == add(b, a)
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add(add(a, b), c) == add(a, add(b, c))
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add(a, 0) == a
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</code></pre>
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</section>
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<section>
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<h2>Math is about Patterns</h2>
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<table style="font-size: smaller;">
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<tr><th>Commutativity</th><th>Associativity</th><th>Neutral Element</th></tr>
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<tr>
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<td>$a + b = b + a$</td>
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<td>$(a + b) + c = a + (b + c)$</td>
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<td>0</td>
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</tr>
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<tr class="fragment">
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<td>$a \texttt{ AND } b = b \texttt{ AND } a$</td>
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<td>$(a \texttt{ AND } b) \texttt{ AND } c = a \texttt{ AND } (b \texttt{ AND } c)$</td>
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<td>TRUE</td>
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</tr>
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<tr class="fragment">
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<td>$a \texttt{ OR } b = b \texttt{ OR } a$</td>
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<td>$(a \texttt{ OR } b) \texttt{ OR } c = a \texttt{ OR } (b \texttt{ OR } c)$</td>
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<td>FALSE</td>
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</tr>
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<tr class="fragment">
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<td>$A \cup B = B \cup A$</td>
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<td>$(A \cup B) \cup C = A \cup (B \cup C)$</td>
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<td>$\emptyset$</td>
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</tr>
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<tr class="fragment" style="font-size: smaller">
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<td>$min(A, B) = min(B, A)$</td>
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<td>$min(min(A, B), C) = min(A, min(B, C))$</td>
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<td>$\infty$</td>
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</tr>
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</table>
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<p class="fragment">Mathematicians call this a <b>Group</b></p>
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</section>
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<section>
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<pre><code class="java">
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interface Group<K> {
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public K getZero() { ... }
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public K add(K a, K b) { ... }
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}
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</code></pre>
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<br/>
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<p class="fragment">
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$$\left<\; K,\; +,\; 0\;\right>$$
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</p>
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</section>
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<section>
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$$\left<\; \mathbb R,\; +,\; 0\;\right>$$
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$$\left<\; \mathbb N,\; +,\; 0\;\right>$$
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$$\left<\; \mathbb B,\; \texttt{AND},\; \texttt{TRUE}\;\right>$$
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$$\left<\; \mathbb B,\; \texttt{OR},\; \texttt{FALSE}\;\right>$$
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$$\left<\; Sets,\; \cup,\; \emptyset\;\right>$$
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$$\left<\; Multisets,\; \uplus,\; \emptyset\;\right>$$
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$$\left<\; \mathbb R,\; min,\; \infty;\right>$$
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</section>
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</section>
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<section>
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<section>
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<h2>Fun With Groups</h2>
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<p>Say define function <tt>size()</tt> that returns the size of a Multisets</p>
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</section>
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</section>
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</div></div>
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<script src="../reveal.js-3.5.0/lib/js/head.min.js"></script>
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<script src="../reveal.js-3.5.0/js/reveal.js"></script>
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<script>
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// Full list of configuration options available at:
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// https://github.com/hakimel/../reveal.js#configuration
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Reveal.initialize({
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controls: false,
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progress: true,
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history: true,
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center: true,
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slideNumber: true,
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transition: 'fade', // none/fade/slide/convex/concave/zoom
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// Optional ../reveal.js plugins
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dependencies: [
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{ src: '../reveal.js-3.5.0/lib/js/classList.js', condition: function() { return !document.body.classList; } },
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{ src: '../reveal.js-3.5.0/plugin/math/math.js',
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condition: function() { return true; },
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mathjax: '../reveal.js-3.5.0/js/MathJax.js'
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},
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{ src: '../reveal.js-3.5.0/plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
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{ src: '../reveal.js-3.5.0/plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
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{ src: '../reveal.js-3.5.0/plugin/highlight/highlight.js', async: true, condition: function() { return !!document.querySelector( 'pre code' ); }, callback: function() { hljs.initHighlightingOnLoad(); } },
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{ src: '../reveal.js-3.5.0/plugin/zoom-js/zoom.js', async: true },
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{ src: '../reveal.js-3.5.0/plugin/notes/notes.js', async: true }
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]
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});
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</script>
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</body>
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</html>
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