Impredicative encodings in HoTT
54 mins 32 secs,
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About this item
| Description: |
Awodey, S
Tuesday 11th July 2017 - 09:00 to 10:00 |
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| Created: | 2017-07-26 12:40 |
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| Collection: | Big proof |
| Publisher: | Isaac Newton Institute |
| Copyright: | Awodey, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
|
| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| Abstract: | We investigate the prospects for impredicative encodings of inductive types (including higher inductive types) in HoTT. It is well-known that encoding inductives using higher-order quantification provides a potential theoretical and practical simplification of the system. Using the further resources available in HoTT allows for a sharpening of the familiar System F style impredicative encodings of inductive types, but this begs the question of whether impredicativity is formally compatible with univalence. We give a realizability model using a combination of topos-theoretic, homotopical, and recent cubical methods. Joint work with Jonas Frey and Pieter Hofstra. |
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