Non-wellfounded trees in Homotopy Type Theory
arXiv:1504.02949 · doi:10.4230/LIPIcs.TLCA.2015.17
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.
14 pages, to be published in proceedings of TLCA 2015; ancillary files contain Agda files with formalized proofs