Inductive types in homotopy type theory

Details Inductive types in homotopy type theory Inductive types in homotopy type theory

2012-01-18

arxiv.org/abs/1201.3898v1

Mathematics

Logic

21 pages

Scientific paper

Homotopy type theory is an interpretation of Martin-L\"of'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 theory-based proof assistants such as Coq. The present work investigates inductive types in this setting. Modified rules for inductive types, including types of well-founded trees, or W-types, 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.

Affiliated with

Also associated with

No associations

Rating

Inductive types in homotopy type theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Inductive types in homotopy type theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Inductive types in homotopy type theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-253178