TY - JOUR
AU1 - Bauer, Andrej
AU2 - Gross, Jason
AU3 - Lumsdaine, Peter LeFanu
AU4 - Shulman, Michael
AU5 - Sozeau, Matthieu
AU6 - Spitters, Bas
AB -  The HoTT Library A Formalization of Homotopy Type Theory in Coq Andrej Bauer University of Ljubljana, Slovenia Andrej.Bauer@andrej.com Jason Gross MIT, USA jgross@mit.edu Peter LeFanu Lumsdaine Stockholm University, Sweden p.l.lumsdaine@math.su.se Michael Shulman University of San Diego, USA shulman@sandiego.edu Matthieu Sozeau § Inria, France mattam@mattam.org Bas Spitters ¶ Aarhus University, Denmark spitters@cs.au.dk Abstract We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher inductive types, and significant amounts of synthetic homotopy theory, as well as category theory and modalities. The library has been used as a basis for several independent developments. We discuss the decisions that led to the design of the library, and we comment on the interaction of homotopy type theory with recently introduced features of Coq, such as universe polymorphism and private inductive types. Categories and Subject Descriptors F.4.1 [Mathematical Logic and Formal Languages]: Mathematical Logic This Keywords Homotopy type theory, Univalent foundations, Coq, Higher inductive types, Universe polymorphism 1. Introduction Homotopy type theory is a novel approach to developing mathematics in Martin-L¨ f's type theory, based on interpreo tations of the theory into abstract 
TI - The HoTT library: a formalization of homotopy type theory in Coq
DA - 2017-01-16
UR - https://www.deepdyve.com/lp/association-for-computing-machinery/the-hott-library-a-formalization-of-homotopy-type-theory-in-coq-FNcZnSPSjV
DP - DeepDyve
ER -