LambdaConf 2015 - Introduction to Intuitionistic Type Theory Vlad Patryshev
Traditionally, in Computer Science, sets are assumed to be the basis of a type theory, together with Boolean logic. In this version of type theory, we do not need sets or Boolean logic; intuitionism is enough ("no principle of excluded middle required"). The underlying math is Topos Theory
From playlist LambdaConf 2015
LambdaConf 2015 - Type Theory and its Meaning Explanations Jon Sterling
At the heart of intuitionistic type theory lies an intuitive semantics called the “meaning explanations." Crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer “proof” but “verification”. We’ll explore how type theories of this sort aris
From playlist LambdaConf 2015
There are two different types of reductionism. One is called methodological reductionism, the other one theory reductionism. Methodological reductionism is about the properties of the real world. It’s about taking things apart into smaller things and finding that the smaller things determ
From playlist Philosophy of Science
What are the Types of Numbers? Real vs. Imaginary, Rational vs. Irrational
We've mentioned in passing some different ways to classify numbers, like rational, irrational, real, imaginary, integers, fractions, and more. If this is confusing, then take a look at this handy-dandy guide to the taxonomy of numbers! It turns out we can use a hierarchical scheme just lik
From playlist Algebra 1 & 2
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
Peter Dybjer: Intuitionistic Type Theory (Lecture II)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Peter Dybjer: Intuitionistic Type Theory (Lecture III)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Peter Dybjer: Intuitionistic Type Theory (Lecture I)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
This is a follow up to https://youtu.be/lDhKE2SKF08. In this video we zoom in on Negation and also discuss models such as the 3-valued one for intuitionistic propositional logic. The script I'm using you can find here: https://gist.github.com/Nikolaj-K/1478e66ccc9b7ac2ea565e743c904555
From playlist Logic
Makoto Fujiwara: Bar theorem and bar recursion for continuous functions with continuous modulus
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: (joint work with Tatsuji Kawai) Bar induction is originally discussed by L. E. J. Brouwer under the name of “bar theorem” in his intuitionistic mathematics but first formali
From playlist Workshop: "Constructive Mathematics"
Anders Mörtberg: Yet Another Cartesian Cubical Type Theory yacctt
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions. Abstract: I will discuss recent work on developing a Cartesian cubical type theory inspired by the computational semantics of Computational Higher Type Theory of Angiuli et. al. Th
From playlist Workshop: "Types, Homotopy, Type theory, and Verification"
Martin Hötzel Escardó: Constructive Mathematics in Univalent Type Theory (Lecture II)
The lecture was held within the framework of the Hausdorff Trimester Program: Types, Sets and Constructions
From playlist HIM Lectures: Trimester Program "Types, Sets and Constructions"
Axioms of Constructive Set Theory Explained
In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I
From playlist Logic
Anne Baanen - Computing with or despite the computer - IPAM at UCLA
Recorded 14 February 2023. Anne Baanen of Vrije Universiteit presents "Computing with or despite the computer" at IPAM's Machine Assisted Proofs Workshop. Abstract: I have recently been collaborating on a project where we compute the class number of quadratic number fields, formally verifi
From playlist 2023 Machine Assisted Proofs Workshop
Discussion - Panel: What is the role of Topos in Information and Communication Technologies?
Mérouane Debbah (Huawei Technologies) Olivia Caramello (Università degli Studi dell'Insubria in Como) Daniel Bennequin (Univ. Paris-Diderot) Thierry Coquand (University of Göteborg) Jean-Claude Belfiore (Huawei France)
From playlist 4th Huawei-IHES Workshop on Mathematical Theories for Information and Communication Technologies
Dale Miller: Focused proof systems
HYBRID EVENT Recorded during the meeting Linear Logic Winter School" the January 28, 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
From playlist Logic and Foundations
Squashing theories into Heyting algebras
This is the first of two videos on Heyting algebra, Tarski-Lindenbaum and negation: https://gist.github.com/Nikolaj-K/1478e66ccc9b7ac2ea565e743c904555 Followup video: https://youtu.be/ws6vCT7ExTY
From playlist Logic
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"
Hugo Herbelin: A constructive proof of dependent choice, compatible with classical logic
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: Martin-Löf's type theory has strong existential elimination (dependent sum type) what allows to prove the full axiom of choice. However the theory is intuitionistic. We give
From playlist Workshop: "Constructive Mathematics"