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ICFP 2019
Sun 18 - Fri 23 August 2019 Berlin, Germany
Mon 19 Aug 2019 15:43 - 16:06 at Aurora Borealis - Type Theory Chair(s): Jennifer Paykin

Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to homotopy type theory and univalent foundations, in particular to the univalence axiom and higher inductive types. This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of higher inductive types. These new primitives make function and propositional extensionality as well as quotient types directly definable with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. This extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

Mon 19 Aug

icfp-2019-papers
15:20 - 16:30: Research Papers - Type Theory at Aurora Borealis
Chair(s): Jennifer PaykinGalois, Inc.
icfp-2019-papers15:20 - 15:43
Talk
icfp-2019-papers15:43 - 16:06
Talk
Andrea VezzosiChalmers University of Technology, Anders MörtbergDepartment of Mathematics, Stockholm University, Andreas AbelGothenburg University
icfp-2019-papers16:06 - 16:30
Talk
Joseph EremondiUniversity of British Columbia, Éric TanterUniversity of Chile & Inria Paris, Ronald GarciaUniversity of British Columbia
Pre-print