skip to content
 

Impredicative encodings in HoTT

Presented by: 
Steve Awodey Carnegie Mellon University
Date: 
Tuesday 11th July 2017 - 09:00 to 10:00
Venue: 
INI Seminar Room 1
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.
The video for this talk should appear here if JavaScript is enabled.
If it doesn't, something may have gone wrong with our embedded player.
We'll get it fixed as soon as possible.
Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons