Programming with Universal Properties
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Often, categorists will speak about "universal properties" when discussing basic constructions. Understanding what these are can be one of the more confusing aspects of coming to terms with category theory. But it turns out that there is one weird trick that lets us take universal properties and translate them directly into executable code. In doing so, we can better understand just what it means for something to be a universal property, and for that matter, how to think of the relationship between functions and data. The insights from this sort of approach are broadly applicable to real-world practice when we think about how to structure our data to capture just what it should, and nothing else. This talk will start from the very basics, and hopefully leave the audience with a taste of practical categorical intuition, summarized in the slogan "Asking what and asking how are asking the same thing."
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Programming with Universal Properties
Gershom Bazerman
Gershom is a software developer in New York City. He is an organizer of the NY Haskell Users Group and the NY Homotopy Type Theory Reading group, and a member of the Haskell.org committee. He has written a number of widely used Haskell packages, most notably the JMacro library for programmatic generation of JavaScript. He has a particular interest in popularizing results of research related to and deriving from the mathematical foundations of computer science. He occasionally contributes blog articles at the Comonad Reader.