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POPL 2019
Sun 13 - Sat 19 January 2019 Cascais, Portugal
Fri 18 Jan 2019 10:35 - 10:57 at Sala I - Dependent Types Chair(s): Andreas Abel

Homotopy type theory proposes higher inductive types (HITs) as a means of defining and reasoning about inductively-generated objects with higher-dimensional structure. As with the univalence axiom, however, homotopy type theory does not specify the computational behavior of HITs. Computational interpretations have now been provided for univalence and specific HITs by way of cubical type theories, which use a judgmental infrastructure of dimension variables. We extend the cartesian cubical computational type theory introduced by Angiuli et al. with a schema for indexed cubical inductive types (CITs), an adaptation of higher inductive types to the cubical setting. In doing so, we isolate the canonical values of a cubical inductive type and prove a canonicity theorem with respect to these values.

Higher Inductive Types in Cubical Computational Type Theory - Slides (slides.pdf)2.50MiB

Fri 18 Jan
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10:35 - 12:03: Research Papers - Dependent Types at Sala I
Chair(s): Andreas AbelGothenburg University
POPL-2019-Research-Papers10:35 - 10:57
Evan CavalloCarnegie Mellon University, Robert Harper
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POPL-2019-Research-Papers10:57 - 11:19
Thorsten AltenkirchUniversity of Nottingham, Ambrus KaposiUniversity of Nottingham, András KovácsEötvös Loránd University
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POPL-2019-Research-Papers11:19 - 11:41
Gaetan Gilbert, Jesper CockxChalmers | University of Gothenburg, Matthieu SozeauInria, Nicolas TabareauInria
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POPL-2019-Research-Papers11:41 - 12:03
Rasmus Ejlers MøgelbergIT University of Copenhagen, Niccolò VeltriIT University of Copenhagen
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