5 code implementations • 14 Oct 2016 • Andrej Bauer, Jason Gross, Peter LeFanu Lumsdaine, Mike Shulman, Matthieu Sozeau, Bas Spitters
We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant.
Logic in Computer Science Logic 03B70, 03B15, 55U35 F.4.1
1 code implementation • 10 May 2016 • Kuen-Bang Hou, Eric Finster, Dan Licata, Peter LeFanu Lumsdaine
This paper continues investigations in "synthetic homotopy theory": the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory We present a mechanized proof of the Blakers-Massey connectivity theorem, a result relating the higher-dimensional homotopy groups of a pushout type (roughly, a space constructed by gluing two spaces along a shared subspace) to those of the components of the pushout.
Logic in Computer Science Algebraic Topology 55U35 (Abstract and axiomatic homotopy theory), 03B15 (Higher-order logic and type theory), 03B70 (Logic in computer science) F.4.1
1 code implementation • 2 Apr 2013 • Jeremy Avigad, Chris Kapulkin, Peter LeFanu Lumsdaine
Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant.
Logic Logic in Computer Science Category Theory 03B70, 55U35 D.2.4; F.4.1
