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Non-Wellfounded Trees in Homotopy Type Theory

Authors Benedikt Ahrens, Paolo Capriotti, Régis Spadotti

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Keywords
  • Homotopy Type Theory
  • coinductive types
  • computer theorem proving
  • Agda

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Abstract

We prove a conjecture about the constructibility of conductive types - in the principled form of indexed M-types - in Homotopy Type Theory. The conjecture says that in the presence of inductive types, coinductive types are derivable. Indeed, in this work, we construct coinductive types in a subsystem of Homotopy Type Theory; this subsystem is given by Intensional Martin-Löf type theory with natural numbers and Voevodsky's Univalence Axiom. Our results are mechanized in the computer proof assistant Agda.

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Benedikt Ahrens, Paolo Capriotti, and Régis Spadotti. Non-Wellfounded Trees in Homotopy Type Theory. In 13th International Conference on Typed Lambda Calculi and Applications (TLCA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 38, pp. 17-30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015) https://doi.org/10.4230/LIPIcs.TLCA.2015.17

Author Details

Benedikt Ahrens
Paolo Capriotti
Régis Spadotti

References

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