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

Talks linked

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André Muricy

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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

[FourTetTrack]

Thanks FP Sweden and André! This presentation came just in time, I started learning haskell a couple of months ago and just finished going through Functors and Applicatives.

[valentinussofa]

This lecture is really helpfull. Thank you so much FP Sweden. 🙏