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Yann Esposito 2012-11-26 16:44:41 +01:00
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@ -73,7 +73,7 @@
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>About this presentation</li>
<li>General overview</li>
<li>Math <span class="and"><span class="and">&amp;</span></span> Abstraction</li>
<li>Programming <span class="and"><span class="and">&amp;</span></span> Abstraction</li>
<li>Categories <span class="and"><span class="and">&amp;</span></span> Abstraction</li>
@ -84,7 +84,7 @@
</ul>
</section>
<section class="slide">
<h2 id="category-theory">Category Theory</h2>
<h2 id="category-theory-high-level">Category Theory: High level</h2>
<ul>
<li>Central position in contemporary mathematics/computer science/physics.</li>
<li>General mathematical theory of structures and of systems of structures.</li>
@ -97,36 +97,23 @@
</ul>
</section>
<section class="slide">
<h2 id="about-this-presentation">About this presentation</h2>
<ul>
<li>A lot of slides, but short with pictures,</li>
<li>General Ideas → Definitions → Examples using Haskell,</li>
<li>About very fundamental Math, but I'll try not to digress.</li>
</ul>
<img src="categories/img/head_explode.jpg" alt="head explode" style="width: 80%"/>
</section>
<section class="slide">
<h2 id="category-theory-goal">Category Theory Goal?</h2>
<p>Many different approach about Category Theory:</p>
<ul>
<li><a href="http://math.ucr.edu/home/baez/rosetta.pdf">Homogeneous vocabulary and notations</a></li>
<li><a href="http://math.ucr.edu/home/baez/rosetta.pdf">Bridge between disciplines</a></li>
<li><a href="http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf">Better definition of equality</a></li>
<li><a href="www.math.harvard.edu/~mazur/preprints/when_is_one.pdf">Generalization by default</a></li>
<li>Better math foundations</li>
</ul>
</section>
<section class="slide">
<h2 id="what-can-category-theory-do-for-us">What can Category Theory do for us?</h2>
<h2 id="category-theory-for-programming">Category Theory for programming?</h2>
<img class="right" src="categories/img/buddha.png" alt="buddha"/>
<ul>
<li>Ability to see problem differently</li>
<li>Ability to abstract at the right level</li>
<li>Reduce bugs by separating concepts</li>
<li>Make generalisation easier</li>
<li>Help code organisation</li>
<li>Reduce bugs by clarifying concepts</li>
</ul>
<p>What did they already done?</p>
<p>Example In Haskell:</p>
<ul>
<li>Functors, Applicative Functor, Monads, Arrows</li>
<li>Generalize <code>fold</code></li>
<li>...</li>
<li>Functors</li>
<li>Monads</li>
<li><code>fold</code> generalisation</li>
<li>Applicative Functors, Arrows, ...</li>
</ul>
</section>
<section class="slide">

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@ -2,7 +2,7 @@
<ul style="font-size: 2em; font-weight:bold">
<li><span class="yellow">Why?
<ul class="base01" style="border-left: 2px solid; padding-left: 1em; font-size: .6em; float: right; font-weight: bold; margin: 0 0 0 1em">
<li>About this presentation</li>
<li>General overview</li>
<li>Math <span class="and">&amp;</span> Abstraction</li>
<li>Programming <span class="and">&amp;</span> Abstraction</li>
<li>Categories <span class="and">&amp;</span> Abstraction</li>

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@ -1,4 +1,4 @@
<h2 id="category-theory">Category Theory</h2>
<h2 id="category-theory-high-level">Category Theory: High level</h2>
<ul>
<li>Central position in contemporary mathematics/computer science/physics.</li>
<li>General mathematical theory of structures and of systems of structures.</li>

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@ -1,5 +1,5 @@
Category Theory
---------------
Category Theory: High level
---------------------------
- Central position in contemporary mathematics/computer science/physics.
- General mathematical theory of structures and of systems of structures.

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@ -1,6 +0,0 @@
<h2 id="about-this-presentation">About this presentation</h2>
<ul>
<li>A lot of slides, but short with pictures,</li>
<li>General Ideas → Definitions → Examples using Haskell,</li>
<li>About very fundamental Math, but I'll try not to digress.</li>
</ul>

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@ -1,6 +0,0 @@
About this presentation
-----------------------
- A lot of slides, but short with pictures,
- General Ideas → Definitions → Examples using Haskell,
- About very fundamental Math, but I'll try not to digress.

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@ -0,0 +1 @@
<img src="categories/img/head_explode.jpg" alt="head explode" style="width: 80%"/>

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@ -1,9 +0,0 @@
<h2 id="category-theory-goal">Category Theory Goal?</h2>
<p>Many different approach about Category Theory:</p>
<ul>
<li><a href="http://math.ucr.edu/home/baez/rosetta.pdf">Homogeneous vocabulary and notations</a></li>
<li><a href="http://math.ucr.edu/home/baez/rosetta.pdf">Bridge between disciplines</a></li>
<li><a href="http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf">Better definition of equality</a></li>
<li><a href="www.math.harvard.edu/~mazur/preprints/when_is_one.pdf">Generalization by default</a></li>
<li>Better math foundations</li>
</ul>

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@ -1,10 +0,0 @@
Category Theory Goal?
---------------------
Many different approach about Category Theory:
- [Homogeneous vocabulary and notations](http://math.ucr.edu/home/baez/rosetta.pdf)
- [Bridge between disciplines](http://math.ucr.edu/home/baez/rosetta.pdf)
- [Better definition of equality](http://www.math.harvard.edu/~mazur/preprints/when_is_one.pdf)
- [Generalization by default](www.math.harvard.edu/~mazur/preprints/when_is_one.pdf)
- Better math foundations

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@ -1,12 +1,15 @@
<h2 id="what-can-category-theory-do-for-us">What can Category Theory do for us?</h2>
<h2 id="category-theory-for-programming">Category Theory for programming?</h2>
<img class="right" src="categories/img/buddha.png" alt="buddha"/>
<ul>
<li>Ability to see problem differently</li>
<li>Ability to abstract at the right level</li>
<li>Reduce bugs by separating concepts</li>
<li>Make generalisation easier</li>
<li>Help code organisation</li>
<li>Reduce bugs by clarifying concepts</li>
</ul>
<p>What did they already done?</p>
<p>Example In Haskell:</p>
<ul>
<li>Functors, Applicative Functor, Monads, Arrows</li>
<li>Generalize <code>fold</code></li>
<li>...</li>
<li>Functors</li>
<li>Monads</li>
<li><code>fold</code> generalisation</li>
<li>Applicative Functors, Arrows, ...</li>
</ul>

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@ -1,12 +1,16 @@
What can Category Theory do for us?
-----------------------------------
Category Theory for programming?
--------------------------------
<img class="right" src="categories/img/buddha.png" alt="buddha"/>
- Ability to see problem differently
- Ability to abstract at the right level
- Reduce bugs by separating concepts
- Make generalisation easier
- Help code organisation
- Reduce bugs by clarifying concepts
What did they already done?
Example In Haskell:
- Functors, Applicative Functor, Monads, Arrows
- Generalize `fold`
- ...
- Functors
- Monads
- `fold` generalisation
- Applicative Functors, Arrows, ...

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