Lectures related to Lambda Calculus: Church Numerals

Lambda Calculus and Type Safety: An Overview

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

Lambda Calculus: Syntax and Abstractions

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

Lambda Calculus: Operational Semantics and Evaluation Strategies

Covers operational semantics and evaluation strategies in lambda calculus, including redex, alternative evaluation strategies, and Church Booleans.

Semantics in Computer Language Processing: Understanding Meaning

Covers the semantics of programming languages, focusing on the Add language and the role of rewriting rules and CK machines in understanding meaning.

Types in Lambda Calculus

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

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.

Encoding Recursion as Self-Application

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

Closure Conversion: Representation and Transformation

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.

Pen-and-paper session: Lambda Calculus Proofs

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

Type Checking and Reconstruction: Equations and Unification

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

Church Numerals and Conditionals

Explores Church numerals and encoding conditionals in lambda calculus.

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.

Objects Everywhere

Covers pure object orientation, standard classes in Scala, Boolean implementation, and exercises on class implementations.

Functional Programming: Concepts and Implementation

Covers the concepts and implementation of functional programming in Scala, emphasizing functions, immutable data, and data abstraction.

Prime Numbers: Finding and Testing

Covers the definition of a function to determine if a given number is prime.

Coq Workshop: Introduction to Interactive Theorem Proving

Introduces Coq, an interactive theorem assistant based on the Curry-Howard isomorphism.

Control Flow in Python: Conditional Statements and Loops

Covers control flow in Python, focusing on conditional statements and loops.

Conditions and Loops: Basics of Programming

Covers the basics of programming, including types, variables, methods, functions, conditions, loops, and boolean logic.

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.

Foundations of Software

Covers the basics of induction, syntax, abstract vs. concrete syntax, and operational semantics for Booleans.