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Homotopy Type Theory in Lean

  • Floris van Doorn
  • Jakob von Raumer
  • Ulrik Buchholtz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10499)

Abstract

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory. Of particular interest is the use of just a few primitive notions of higher inductive types, namely quotients and truncations, and the use of cubical methods.

Keywords

Homotopy type theory Formalized mathematics Lean Proof assistants 

Notes

Acknowledgments

We wish to thank the members of the HoTT group at Carnegie Mellon University for many fruitful discussions and Lean hacking sessions, and in particular Steve Awodey and Jeremy Avigad who have been very supportive of our work. Additionally, we deeply appreciate all the times Leonardo de Moura fixed an issue in the Lean kernel to accommodate our library. Lastly, we want to thank all contributors to the HoTT library and the Spectral repository, most notably Egbert Rijke and Mike Shulman.

The first and second authors gratefully acknowledge the support of the Air Force Office of Scientific Research through MURI grant FA9550-15-1-0053. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the AFOSR.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Floris van Doorn
    • 1
  • Jakob von Raumer
    • 2
  • Ulrik Buchholtz
    • 3
  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.University of NottinghamNottinghamUK
  3. 3.TU DarmstadtDarmstadtGermany

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