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#Dependent Types

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Institute for Advanced Study

On Voevodsky's Univalence Principle - André Joyal

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Explorez le principe d'univalence de Voevodsky avec André Joyal, examinant ses implications pour la théorie des types et les catégories dans cette conférence commémorative approfondie.
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25 Lesons
1 hour 23 minutes
On-Demand
Free-Video
Institute for Advanced Study

Univalent Foundations and the Equivalence Principle - Benedikt Ahrens

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Explore univalent foundations and the equivalence principle in mathematics, covering type theory, dependent types, and their applications to structures like monoids and categories.
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29 Lesons
1 hour 1 minute
On-Demand
Free-Video
Hausdorff Center for Mathematics

Peter Dybjer - Intuitionistic Type Theory - Lecture I

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Explore intuitionistic type theory's foundations, historical context, and applications in mathematics and computer science with Prof. Peter Dybjer's comprehensive lecture.
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17 Lesons
1 hour 1 minute
On-Demand
Free-Video
Schmid College, Chapman University

From HoTT to HOTT - Exploring Homotopy Type Theory

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Explore the evolution from Homotopy Type Theory (HoTT) to Higher-Order Type Theory (HOTT) in this insightful lecture by Michael Shulman.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
ACM SIGPLAN

Type Theory Session Preview - POPL 2023

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Explore type theory fundamentals and recent advancements in this expert-led session preview for POPL 2023, enhancing accessibility of upcoming talks.
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1 Lesons
11 minutes
On-Demand
Free-Video
ACM SIGPLAN

Combining Dependency, Grades, and Adjoint Logic in Type Systems

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Explore new dependent type systems combining graded/linear types with modal operators and Adjoint Logic. Delve into meta-theoretic properties and graded substitution in advanced type theory.
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1 Lesons
19 minutes
On-Demand
Free-Video
ACM SIGPLAN

A Dependently Typed Language with Dynamic Equality

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Explore a novel dependently typed language with dynamic equality, addressing usability issues in type systems and providing clearer error messages through runtime equality checking.
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8 Lesons
19 minutes
On-Demand
Free-Video
ACM SIGPLAN

Internalizing Indistinguishability with Dependent Types

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Explore a novel type system combining dependency tracking and dependent types, internalizing indistinguishability for enhanced information flow control and program equivalence reasoning.
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1 Lesons
20 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

HOL with Dependent Types and Subtyping

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Explore advanced type theory concepts combining Higher-Order Logic, dependent types, and subtyping for enhanced formal reasoning and theorem proving capabilities.
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1 Lesons
33 minutes
On-Demand
Free-Video
GOTO Conferences

What Are Types For, Or Are They Only Against? - Exploring Type Systems in Programming

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Explore the purpose and benefits of types in programming, examining their role beyond just preventing errors, with insights into functional programming concepts and type theory.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
ACM SIGPLAN

One-Pass CPS Translation of Dependent Types

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Explore type-preserving CPS translation for dependently typed languages, focusing on optimizing techniques to eliminate administrative redexes in the Calculus of Constructions.
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1 Lesons
13 minutes
On-Demand
Free-Video
Strange Loop Conference

Proof Theory Impressionism - Blurring the Curry-Howard Line

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Exploring approaches to bridge the gap between proof assistants and production languages, focusing on Rust and its potential for incorporating provable system capabilities.
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1 Lesons
35 minutes
On-Demand
Free-Video
Strange Loop Conference

Scala vs Idris - Dependent Types, Now and in the Future

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Exploring dependent types in Scala and Idris: current capabilities, limitations, and future possibilities. Demonstrates rich type systems' potential for program verification and static constraint capture in functional programming.
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1 Lesons
40 minutes
On-Demand
Free-Video
Strange Loop Conference

A Little Taste of Dependent Types

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Explore dependent types, uniting programming and mathematical proofs. Learn about Pie, a tiny dependently typed language, and see a proof that's also a program.
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13 Lesons
39 minutes
On-Demand
Free-Video
Strange Loop Conference

Dependent Types in Haskell

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Explore dependent types in Haskell, their influence on GHC, and practical applications through an extended example. Learn about current capabilities, challenges, and surprises in language design.
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12 Lesons
39 minutes
On-Demand
Free-Video
GOTO Conferences

A Taste of Type Theory

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Explore the foundations of type theory in programming, from algebraic data types to dependent types, with insights on mathematical connections and future developments in the field.
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11 Lesons
54 minutes
On-Demand
Free-Video
EuroPython Conference

Bulletproof Python - Writing Fewer Tests with a Typed Code Base

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Explore how a fully typed Python codebase can reduce the need for extensive testing, leveraging dependent types and exhaustiveness checking to enhance code reliability and efficiency.
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1 Lesons
26 minutes
On-Demand
Free-Video
ACM SIGPLAN

An Intrinsically Typed Compiler for Algebraic Effect Handlers

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Explore type-preserving compilation for algebraic effect handlers, focusing on safety in continuation capture and resumption using stack polymorphism in an Agda-implemented compiler.
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4 Lesons
16 minutes
On-Demand
Free-Video
ACM SIGPLAN

A Calculus of Inductive Linear Constructions

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Explore a novel calculus combining linear and dependent types, addressing challenges in linear dependent types research and enabling efficient resource management in programming.
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1 Lesons
22 minutes
On-Demand
Free-Video
ACM SIGPLAN

An Intrinsically-typed Probabilistic Programming Language in Coq - Extended Abstract

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Explore formalization of intrinsically-typed probabilistic programming language in Coq, focusing on syntax, evaluation, and formal verification applications.
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1 Lesons
24 minutes
On-Demand
Free-Video
ACM SIGPLAN

A Type System for Feature Engineering in Machine Learning

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Explore a dependent type system for feature engineering, enhancing machine learning model inputs through advanced data operations and compiler techniques.
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1 Lesons
22 minutes
On-Demand
Free-Video
ACM SIGPLAN

A Type-Theoretic Account of Quantum Computation

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Explore type-theoretic concepts for describing and proving properties of quantum computations, focusing on quantum circuits using Coq's dependent and polymorphic types.
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1 Lesons
28 minutes
On-Demand
Free-Video
ACM SIGPLAN

Binding Syntax for Dependently-Typed Programs - WITS'24

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Explore innovative binding syntax for dependently-typed programs, enhancing ergonomics while maintaining fixed grammar for improved error messaging.
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1 Lesons
25 minutes
On-Demand
Free-Video
ACM SIGPLAN

Efficient Evaluation with Controlled Definition Unfolding - WITS'24

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Explore efficient evaluation techniques in polymorphic and dependently typed languages, focusing on controlled definition unfolding for improved user interaction and unification processes.
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1 Lesons
29 minutes
On-Demand
Free-Video
Code Sync

Examples of Easy Dependently Typed Programming in Idris

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Explore practical applications of dependently typed programming in Idris, focusing on everyday software correctness without complex proofs. Suitable for those familiar with algebraic data types and FP functions.
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1 Lesons
21 minutes
On-Demand
Free-Video
ACM SIGPLAN

Dependently-Typed Programming with Logical Equality Reflection

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Explore System DE, a calculus for dependently-typed programming with equality reflection. Learn about termination tracking, inductive proofs, and performance-safety trade-offs in functional languages.
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1 Lesons
31 minutes
On-Demand
Free-Video
ACM SIGPLAN

Graded Modal Dependent Type Theory with Universe and Erasure - Formalized

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Explore a graded modal type theory with dependent types, erasure, and formalized meta-theoretic properties. Delve into its universe, extraction function, and soundness proofs for open programs.
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1 Lesons
30 minutes
On-Demand
Free-Video
ACM SIGPLAN

Martin-Löf Type Theory Mechanization in Coq

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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.
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1 Lesons
30 minutes
On-Demand
Free-Video
NashKnolX

Unleashing the Power of Type-Level Programming in Scala

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Dive deep into advanced Scala techniques, exploring type-level programming for powerful compile-time computations and fine-grained type control.
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1 Lesons
37 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

A Type-Theoretic Framework for Certified Meta-programming

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Explore a type-theoretic framework for certified meta-programming, delving into advanced concepts and techniques in programming language theory and formal verification.
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1 Lesons
57 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Lean4Lean - Formalizing the Type Theory of Lean

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Explore the formalization of Lean's type theory with Mario Carneiro, delving into advanced concepts and techniques for theorem proving and mathematical reasoning.
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1 Lesons
54 minutes
On-Demand
Free-Video
ACM SIGPLAN

GHC Status Report - Haskell Compiler Updates and Improvements

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Explore GHC's latest developments, including quality-of-life improvements, WebAssembly support, dependent types, and linear types in this comprehensive status report.
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17 Lesons
1 hour 22 minutes
On-Demand
Free-Video