Mon 20 Jan 2020 17:12 - 17:34 at Maurepas - Homotopy Type Theory and PC chairs' report Chair(s): Floris van Doorn

Ordinals and ordinal notation systems play an important role in program verification, since they can be used to prove termination of programs. We present three ordinal notation systems representing ordinals below $\varepsilon_0$ in type theory, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. As case studies, we show how basic ordinal arithmetic can be developed for these systems, and how they admit a transfinite induction principle. We prove that all three notation systems are equivalent, so that we can transport results between them using the univalence principle. All our constructions have been implemented in cubical Agda.

 Slides (ordinals_cpp.pdf) 2.19MiB

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 16:50 - 17:56 Homotopy Type Theory and PC chairs' reportCPP at Maurepas Chair(s): Floris van DoornUniversity of Pittsburgh 16:5022mTalk Cubical Synthetic Homotopy TheoryCPPAnders MörtbergDepartment of Mathematics, Stockholm University, Loïc PujetGallinette Project-Team, Inria DOI Pre-print Media Attached File Attached 17:1222mTalk Three equivalent ordinal notation systems in Cubical AgdaCPPFredrik Nordvall ForsbergUniversity of Strathclyde, Chuangjie XuLudwig-Maximilians-Universität München, Neil GhaniUniversity of Strathclyde DOI Pre-print Media Attached File Attached 17:3422mTalk PC Chairs' reportCPPJasmin BlanchetteVrije Universiteit Amsterdam, Cătălin HriţcuInria Paris DOI Media Attached File Attached