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Homotopy Type Theory in Lean

Presented by: 
Floris van Doorn Carnegie Mellon University
Date: 
Tuesday 11th July 2017 - 11:30 to 12:30
Venue: 
INI Seminar Room 1
Abstract: 
Co-authors: Ulrik Buchholtz (TU Darmstadt), Jakob von Raumer (University of Nottingham)

We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic homotopy theory, and contains many results in that area, among which are the computation of , a formalization of Eilenberg-MacLane spaces and the adjunction of pointed maps and the smash product. We have a novel method of implementing higher inductive types (HITs), where we only take two HITs as primitives and add their computation rules to the kernel of Lean. We define all other HITs in terms of these two primitive ones. Other features include the use of cubical methods, a large algebraic hierarchy and category theory library.

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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons