Inductive types in homotopy type theory
Abstract
Homotopy type theory is an interpretation of MartinLöf's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type theory as well as a computational approach to algebraic topology via type theorybased proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of wellfounded trees, or Wtypes, are presented, and the basic homotopical semantics of such types are determined. Proofs of all results have been formally verified by the Coq proof assistant, and the proof scripts for this verification form an essential component of this research.
 Publication:

arXiv eprints
 Pub Date:
 January 2012
 DOI:
 10.48550/arXiv.1201.3898
 arXiv:
 arXiv:1201.3898
 Bibcode:
 2012arXiv1201.3898A
 Keywords:

 Mathematics  Logic;
 Computer Science  Logic in Computer Science;
 Mathematics  Category Theory;
 03B15;
 03B70;
 03F50
 EPrint:
 19 pages