A Tutorial Introduction to the Lambda Calculus

This paper is a concise and painless introduction to the λ-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 λ-calculus and how to define recursive functions, even though λ-calculus functions are unnamed and thus cannot refer explicitly to themselves.