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ICFP 2018
Sun 23 - Sat 29 September 2018 St. Louis, Missouri, United States
Tue 25 Sep 2018 14:07 - 14:30 at Stifel Theatre - Proof Techniques and Mechanization Chair(s): Niki Vazou

Homotopy Type Theory promises a unification of the concepts of equality and equivalence in Type Theory, through the introduction of the univalence principle. However, existing proof assistants based on type theory treat this principle as an axiom, and it is not yet clear how to extend them to handle univalence internally. In this paper, we propose a construction grounded on a univalent version of parametricity to bring the benefits of univalence to the programmer and prover, that can be used on top of existing type theories. In particular, univalent parametricity strengthens parametricity to ensure preservation of type equivalences. We present a lightweight framework implemented in the Coq proof assistant that allows the user to transparently transfer definitions and theorems for a type to an equivalent one, as if they were equal. Our approach handles both type and term dependency. We study how to maximize the effectiveness of these transports in terms of computational behavior, and identify a fragment useful for certified programming on which univalent transport is guaranteed to be effective.

Tue 25 Sep

icfp-2018-papers
13:00 - 14:30: Research Papers - Proof Techniques and Mechanization at Stifel Theatre
Chair(s): Niki VazouUniversity of Maryland, USA
icfp-2018-papers13:00 - 13:22
Talk
Robbert KrebbersDelft University of Technology, Jacques-Henri JourdanCNRS, LRI, Université Paris-Sud, Ralf JungMPI-SWS, Joseph TassarottiCarnegie Mellon University, Jan-Oliver KaiserMPI-SWS, Amin Timanyimec-Distrinet KU-Leuven, Arthur CharguéraudInria, Derek DreyerMPI-SWS
DOI
icfp-2018-papers13:22 - 13:45
Talk
Jan-Oliver KaiserMPI-SWS, Beta ZilianiFAMAF, UNC and CONICET, Robbert KrebbersDelft University of Technology, Yann Régis-GianasIRIF, University Paris Diderot and CNRS, France / INRIA PI.R2, Derek DreyerMPI-SWS
DOI
icfp-2018-papers13:45 - 14:07
Talk
Sven KeidelDelft University of Technology, Netherlands, Casper Bach PoulsenDelft University of Technology, Sebastian ErdwegDelft University of Technology, Netherlands
DOI
icfp-2018-papers14:07 - 14:30
Talk
Nicolas TabareauInria, Éric TanterUniversity of Chile & Inria Paris, Matthieu SozeauInria
DOI