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.

Lambda Calculus and Type Safety: An Overview

Provides an overview of lambda calculus, type safety, and type inference in programming languages.

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.

Simply Typed Lambda Calculus: Foundations and Properties

Covers the simply typed lambda calculus, focusing on its syntax, semantics, and type system properties such as progress and preservation.

Types in Lambda Calculus

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

Algorithmic Subtyping: Transitivity Proof

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

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.

Math-101(en) / Min/Max, Inf/Sup

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

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.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Supremum

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.

Pen-and-paper session: Lambda Calculus Proofs

Delves into Lambda Calculus proofs, emphasizing structural induction and variable manipulation.

Generics and Subtyping

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