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.

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