Type Theory Courses and Certifications

Topos Institute

Cubical Types for the Working Formalizer - Making Type Theory Accessible

Discover how to effectively use cubical type theory for formalizing mathematics, focusing on automation techniques that simplify complex theoretical concepts for practical applications.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Topos Institute

Fuzzy Type Theory - From Martin-Löf to Fuzzy Sets

Delve into the mathematical foundations of fuzzy type theory and its relationship to Martin-Löf type theory, exploring how it models opinions with parameterized evidence and categorical connections.

• YouTube
• 1 hour 16 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Types, Homotopy, Type Theory, and Verification Workshop

Delve into advanced type theory, homotopy theory, and verification through expert tutorials on cubical models, modal dependent types, and univalent foundations.

• YouTube
• 18 hours 4 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Erik Palmgren: From Type Theory to Setoids and Back

Exploring setoids in constructive mathematics, their implementation in proof assistants, and their role in formalizing Bishop-style mathematics and Martin-Löf type theory models.

• YouTube
• 1 hour 6 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Peter Dybjer - Intuitionistic Type Theory

Explore intuitionistic type theory, inductive definitions, and finite axiomatizations in this advanced lecture on mathematical foundations and type systems.

• YouTube
• 1 hour 10 minutes
• On-Demand
• Free Video

ACM SIGPLAN

Type Theory Session Preview - POPL 2023

Explore type theory fundamentals and recent advancements in this expert-led session preview for POPL 2023, enhancing accessibility of upcoming talks.

• YouTube
• 11 minutes
• On-Demand
• Free Video

ACM SIGPLAN

Martin-Löf Type Theory Mechanization in Coq

Explore an extensive mechanization of Martin-Löf Type Theory in Coq, covering decidability of conversion and type checking, with a certified executable type checker for MLTT.

• YouTube
• 30 minutes
• On-Demand
• Free Video

ACM SIGPLAN

Explicit Refinement Types - A Type Theory with Embedded Proofs

Explore λert, a type theory with explicit proof refinement types. Learn about its soundness, denotational semantics, and formalization in Lean 4.

• YouTube
• 29 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Lean4Lean - Formalizing the Type Theory of Lean

Explore the formalization of Lean's type theory with Mario Carneiro, delving into advanced concepts and techniques for theorem proving and mathematical reasoning.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Hausdorff Center for Mathematics

Condensed Type Theory - Axioms and Applications

Explore condensed sets' topos and internal type theory, examining axioms, predicates, and their interactions. Learn about compact Hausdorff and overt discrete types, with applications in category theory.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Topos Institute

Algebraic Data Types and Self-Reference in Type Theory - From Theory to Version Control

Explore algebraic data types and their extension for self-referential structures, examining semantic interpretations through groupoids and mutation-based approaches for version control systems.

• YouTube
• 1 hour
• On-Demand
• Free Video

Topos Institute

Generalized Algebraic Theory and Dependent Type Theory Semantics

Explore the relationship between Generalized Algebraic Theories and dependent type theory semantics, focusing on Cartmell's work and its modern applications in categories with families.

• YouTube
• 51 minutes
• On-Demand
• Free Video

ACM SIGPLAN

Decidability of Conversion for Type Theory in Type Theory

Delve into the formalization of conversion checking algorithms for dependent type theory, exploring correctness proofs via Kripke logical relations and applications in various type theory variants.

• YouTube
• 24 minutes
• On-Demand
• Free Video

Simons Foundation

A Crash Course on Type Theory

Discover the fundamentals of type theory in this intensive session, building essential mathematical foundations for formal verification and proof systems.

• YouTube
• 1 hour 17 minutes
• On-Demand
• Free Video

Topos Institute

Element Model Type Theory

Delve into a new implementation of generalized algebraic theories in Rust, exploring a type-theoretic approach that integrates e-graphs and enables theory composition for applications in scientific modeling and beyond.

• YouTube
• 1 hour 13 minutes
• On-Demand
• Free Video