Lecture notes on the lambda calculus

TL;DR

These lecture notes provide a comprehensive overview of lambda calculus, covering foundational concepts, theorems, type systems, semantics, and related topics, serving as an educational resource for understanding the theoretical underpinnings of computation.

Contribution

The notes compile and explain key topics in lambda calculus and type theory, integrating various results and concepts from multiple courses into a cohesive educational resource.

Findings

Detailed explanation of untyped and simply-typed lambda calculus

Discussion of the Church-Rosser theorem and normalization

Introduction to denotational semantics and PCF language

Abstract

This is a set of lecture notes that developed out of courses on the lambda calculus that I taught at the University of Ottawa in 2001 and at Dalhousie University in 2007 and 2013. Topics covered in these notes include the untyped lambda calculus, the Church-Rosser theorem, combinatory algebras, the simply-typed lambda calculus, the Curry-Howard isomorphism, weak and strong normalization, polymorphism, type inference, denotational semantics, complete partial orders, and the language PCF.