Lectures related to Subtyping and Type Calculus

Foundations of Scala: Modelling and Type Systems

Covers the foundations of Scala, including modelling recursive types, parameterized types, and variance.

Covers subtyping, generics, variance, type bounds, covariance, contravariance, and combinatorial search.

Logical Formulas and Types: Understanding the Kerry Howard Isomorphism

Explores the Kerry Howard Isomorphism, translating logical propositions into types and terms, with a focus on proof by induction and exam preparation.

Subtyping and Polymorphism

Explores subtyping rules, challenges, and its connection to various forms of polymorphism in programming languages.

Algorithmic Subtyping: Transitivity Proof

Explores proving transitivity in algorithmic subtyping through induction and subtype relationships.

Types in Lambda Calculus

Covers types in lambda calculus, including defining types, specifying rules, and proving soundness.

Church Numerals and Conditionals

Explores Church numerals and encoding conditionals in lambda calculus.

Dependent Types in Programming Languages

Explores maps, type operators, equivalence, first-class types, System Fw, Coq, and the challenges of type checking in programming languages.

Lattices for Abstract Interpretation

Covers lattices, abstract interpretation, fixpoint analysis, Hoare logic, and partial orders with extreme elements.

Type Inference

Explores type inference in statically typed languages, using algorithms to assign types to program expressions accurately.

Type Checking and Reconstruction: Equations and Unification

Delves into type checking, reconstruction, equations, unification, Hindley/Milner system, polymorphism, and principal types.

Supremum MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.

Lambda Calculus: Syntax and Abstractions

Introduces terms, abstractions, applications, and values in the lambda calculus.

Encoding Recursion as Self-Application

Explores lambda calculus, higher-order functions, and recursive function encoding.

Generics and Subtyping

Covers advanced concepts in generics and subtyping in Java, focusing on LinkedList implementation and List interface.

Infimum MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the concept of infimum in real numbers and its properties.

Lambda Calculus: Church Numerals

Explores Church numerals, Booleans, pairs, recursion, and behavioral equivalence in Lambda Calculus.

Polymorphism and Proofs

Covers parametric polymorphism, lists construction, tuples, generic methods, merge sort, and proving program properties.

Higher-Order Functions: Lambda

Explores higher-order functions and lambda expressions in Python, showcasing their practical applications and concise syntax.

Verified Functional Programming: Nicolas Voirol public PhD thesis defense

Explores verified functional programming, formal verification, SMT solvers, type checking, Scala features, automation, and dependent types.