Polynomial Functors: Jackpot by André Muricy

The category of polynomial functors and (dependent) lenses has tons of expressive power, and can be used to model various applications whose connection may not be obvious. André Muricy presents polynomial functors and their relevance in applied category theory, starting with their representation in Haskell, then describing the usefulness of dependent types for fully expressing them, and ending with application examples. Polynomial Functors A Mathematical Theory of Interaction: Polynomial Functors course (based on the book): Talks linked Scientific and software engineering examples of applied category theory How applied category theory puts thinking on rails Some extra links Topos blog with tag polynomial functors: Categorical systems theory book André Muricy Video sponsor – Ada Beat Merch If you want to spread functional programming and support the channel, buy something from the shop: Chapters: 00:00 Intro by Magnus Sedlacek 00:49 Polynomial Functors: Jackpot by André Muricy Santos 01:51 Intro of André Muricy Santos 04:57 What you need to get the most out of this talk 07:26 Motivation, part 1 – why (applied) category theory 10:21 Except sometimes a pretty fantastic thing come along 11:28 Why polynomial functors, specifically? 12:01 What I hope to give you 12:35 First: a bit of more perspective on regular functors 14:01 So what are polynomial functors? 16:30 How can we map between them? 18:38 The Haskell way is limited 19:43 Enter Agda 21:57 Time to show how this is useful 22:10 Dynamical systems 23:35 This is known as a Moore machine 25:53 Lenses can then be used to wire systems together 26:59 Concrete examples (Fibonacci sequence generator and Turing machine) 28:46 Some Agda code 29:18 Recurrent neural networks: reservoir computing 32:44 What else could we model in this way? 35:10 Thanks! 36:58 Q&A #funcprogsweden