A Model of Type Theory in Cubical Sets
Ahrens, Benedikt, Frumin, Dan, Maggesi, Marco, van der Weide, Niels · arXiv (Cornell University) · 2014
We present a model of type theory with dependent product, sum, and identity, in cubical sets. We describe a universe and explain how to transform an equivalence between two types into an equality. We also explain how to model propositional truncation and the circle. While not expressed internally in type theory, the model is expressed in a constructive metalogic. Thus it is a step towards a computational interpretation of Voevodsky's Univalence Axiom.