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A Tutorial Introduction to the Lambda Calculus

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arxiv 1503.09060 v1 pith:AXMVV2W3 submitted 2015-03-28 cs.LO

classification cs.LO
keywords calculuslambdafunctionsformalismintroductiontutorialalonzoarithmetical
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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