## Section: New Results

### Cubical type theory and univalent foundations

Participants : Cyril Cohen, Anders Mörtberg, Benedikt Ahrens [ASCOLA project-team, Inria and LINA Nantes] , Mark Bickford [Cornell Unversity, USA] , Thierry Coquand [Chalmers and Göteborg University, Sweden] , Simon Huber [Chalmers University, Sweden] , Ralph Matthes [CNRS, University of Toulouse] .

This work mainly concerns Univalent Foundations and Homotopy Type Theory, especially in the form of cubical type theory. The code is visible at https://github.com/mortberg/cubicaltt. This year, Anders Mörtberg has been working on formalizing cubical set models in univalent type theory and on extending cubical type theory with a general class of higher inductive types, in collaboration with Cyril Cohen, Thierry Coquand and Simon Huber.

Anders Mörtberg extended work with Ralph Matthes, Benedikt Ahrens and Vladimir Voevodsky on the representation of syntax of programming languages using category theory in univalent type theory. This paper was accepted for publication in JAR.

Anders Mörtberg also prepared a series of lectures introducing to cubical type theory. this lead to invited talks at the workshops "Type Theory based Tools (TTT)", and "Syntax and Semantics of Type Theory".