A Tutorial Introduction to the Lambda Calculus

TL;DR

This tutorial provides an accessible introduction to lambda calculus, explaining its role in formalizing computation, and demonstrating how to perform arithmetic, logic, and recursion within this foundational framework.

Contribution

It offers a clear, beginner-friendly explanation of lambda calculus concepts and demonstrates their application in computing tasks, bridging theory and practice.

Findings

Shows how to perform arithmetic and logical operations using lambda calculus

Explains how to define recursive functions without explicit self-reference

Highlights the lambda calculus's role in the foundation of functional programming

Abstract

This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular and has provided a strong theoretical foundation for the family of functional programming languages. This tutorial shows how to perform arithmetical and logical computations using the $\lambda$-calculus and how to define recursive functions, even though $\lambda$-calculus functions are unnamed and thus cannot refer explicitly to themselves.