An Introduction to the Lambda Calculus

Authors:
Zoltán Csörnyei;Gergely Dévai
Affiliations:
Department of Programming Languages and Compilers, Eötvös Loránd University, Budapest;Department of Programming Languages and Compilers, Eötvös Loránd University, Budapest
Venue:
Central European Functional Programming School
Year:
2008

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Abstract

Lambda calculus (驴-calculus) is one of the most well-known formal models of computer science. It is the basis for functional programming like Turing machines are the foundation of imperative programming. These two systems are equivalent and both can be used to formulate and investigate fundamental questions about solvability and computability.First, we introduce the reader to the basics of 驴-calculus: its syntax and transformation rules. We discuss the most important properties of the system related to normal forms of 驴-expressions. We present the recursive version of 驴-calculus and finally give the classical results that establish the link between 驴-calculus, partial recursive functions and Turing machines.