Lectures related to Lambda Calculus: Syntax and Abstractions

Lambda Calculus and Type Safety: An Overview

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

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

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.

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.

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.

Python Programming: List Comprehensions and Higher Order Functions

Explores advanced Python programming concepts, focusing on list comprehensions and higher order functions.

Functional Programming: Concepts and Implementation

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

Lambda Calculus: Operational Semantics and Evaluation Strategies

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

Algorithms & Growth of Functions

Covers optimization algorithms, stable matching, and Big-O notation for algorithm efficiency.

Type Checking and Reconstruction: Equations and Unification

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

Weak Derivatives: Definition and Properties

Covers weak derivatives, their properties, and applications in functional analysis.

Python Modules and Functions

Covers Python libraries, modules, scoping, functions, lambdas, and practical examples.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Differentiating under the integral sign

Explores differentiating under the integral sign and continuity of functions in integrals.

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.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Types in Lambda Calculus

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

Python Complement: Numpy, Scipy, Matplotlib

Covers advanced Python topics like numpy operations, scipy linear algebra, and matplotlib for creating figures.

Foundations of Software

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

Hoare Logic: Foundations and Applications

Covers Hoare Logic, its foundations, applications, and significance in program verification.