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arXiv · 1504.02949

Non-wellfounded trees in Homotopy Type Theory

Benedikt Ahrens·Paolo Capriotti·Régis Spadotti
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Abstract

We prove a conjecture about the constructibility of coinductive 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, Régis Spadotti. 2015-04-12. Non-wellfounded trees in Homotopy Type Theory. https://doi.org/10.4230/lipics.tlca.2015.17

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