Non-wellfounded trees in Homotopy Type Theory

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Non-wellfounded trees in Homotopy Type Theory

Benedikt Ahrens, Paolo Capriotti and 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.