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Every proof assistant: Arend

Andrej Bauer

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For a while now I have been contemplating a series of seminars titled "Every proof assistant" that would be devoted to all the different proof assistants out there. Apart from the established ones (Isabelle/HOL, Coq, Agda, Lean), there are other interesting experimental proof assistants, and some that are still under development, or just proofs of concept. I would like to know more about them, and I suspect I am not the only one.

Getting the authors of proof assistants to travel to Ljubljana and giving talks at our Foundations of mathematics and theoretical computer science seminar has largely become impossible. But luckily research seminars world-wide are rapidly moving online, and so is our Foundations seminar. I am therefore delighted to announce the first "Every proof assistant" seminar:

Arend proof assistant Time: Thursday, April 30, 2020 from 18:00 to 19:00 (Central European Summer Time, UTC+2)

Location: online at Zoom ID 965 4439 5816

Speaker: Valery Isaev (JetBrains research) Proof assistant: Arend proof assistant Abstract: I will discuss Arend, a proof assistant developed at JetBrains Research. The aim of Arend is to provide a powerful system for formalization results in homotopy type theory and in ordinary mathematics. To achieve the latter goal, we prove a flexible class system with subtyping, universe polymorphism with a powerful level inference mechanism, quotient sets with a convenient pattern matching principles for them. We also recently implemented a tactic framework which can be used to automate routine proofs and implement various EDSLs. Homotopic features of Arend include built-in universes of finite homotopy level, higher inductive types, univalence, and path types in the style of cubical type theories. I will talk about these features and also about our plans to implement language extensions that can be used to simplify reasoning about various higher structures. Video recording of the talk is available.

I have a couple more in the pipeline, so follow this blog, the Foundations seminar announcements or my Twitter account @andrejbauer.