On the Setoid Model of Type Theory - Erik Palmgren
Erik Palmgren University of Stockholm October 18, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Natural Models of Type Theory - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics March 28, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
David McAllester - Dependent Type Theory from the Perspective of Mathematics, Physics, and (...)
Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type theory naturally generalizes the Bourbaki notion of structure and provides a universal notion of isomorphism and symmetry. This comes with a universal
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Functional Programming: Type Systems
What comes to your mind when you hear the word "type"? Do you think of an integer or string? Do you think of an object type from your favorite OOP language? Do you think about never ending religious debates regarding static vs dynamic types? Do you realize that these things hardly scratch
From playlist Functional Programming
Bas Spitters: Modal Dependent Type Theory and the Cubical Model
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: In recent years we have seen several new models of dependent type theory extended with some form of modal necessity operator, including nominal type theory, guarded and c
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
You’re probably familiar with types in programming languages, such as “integer” or “list of integers.” But what if your type system were powerful enough to express types like “non-negative integer” or “list of strings where each string is at least eight characters long”? Welcome to the wor
From playlist Software Development
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Type theory and formalization of mathematics - Anders Mörtberg
Short Talks by Postdoctoral Members Anders Mörtberg - September 28, 2015 http://www.math.ias.edu/calendar/event/88254/1443464100/1443465000 More videos on http://video.ias.edu
From playlist Short Talks by Postdoctoral Members
Tests, Games, and Martin-Lof's Meaning Explanations for Intuitionistic Type Theory - Peter Dybjer
Peter Dybjer November 30, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Homotopy Group - (1)Dan Licata, (2)Guillaume Brunerie, (3)Peter Lumsdaine
(1)Carnegie Mellon Univ.; Member, School of Math, (2)School of Math., IAS, (3)Dalhousie Univ.; Member, School of Math April 11, 2013 In this general survey talk, we will describe an approach to doing homotopy theory within Univalent Foundations. Whereas classical homotopy theory may be des
From playlist Mathematics
Steve Awodey: Type theories and polynomial monads
Abstract: A system of dependent type theory T gives rise to a natural transformation p : Terms → Types of presheaves on the category Ctx of contexts, termed a "natural model of T". This map p in turn determines a polynomial endofunctor P : Ctxˆ → Ctxˆ on the category of all presheaves. It
From playlist Topology
Directed Type Theory Warren - Michael Warren
Michael Warren Dalhousie University; Member, School of Mathematics April 10, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Univalence from a computer science point-of-view - Dan Licata
Vladimir Voevodsky Memorial Conference Topic: Univalence from a computer science point-of-view Speaker: Dan Licata Affiliation: Wesleyan University Date: September 14, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Egbert Rijke: Daily applications of the univalence axiom - lecture 1
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 21, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Combinatorics
On Voevodsky's univalence principle - André Joyal
Vladimir Voevodsky Memorial Conference Topic: On Voevodsky's univalence principle Speaker: André Joyal Affiliation: Université du Québec á Montréal Date: September 11, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
A Computer-Checked Proof that the Fundamental Group of the Circle is the Integers - Daniel Licata
Daniel Licata Carnegie Mellon University; Member, School of Mathematics November 26, 2012 This talk is designed for a general mathematical audience; no prior knowledge of type theory is presumed. One of the main goals for the special year on univalent foundations is the development of a l
From playlist Mathematics
Type Systems I - Vladimir Voevodsky
Vladimir Voevodsky Institute for Advanced Study November 28, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics