Transcription of A Tutorial Introduction to the Lambda Calculus
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A Tutorial Introduction to the Lambda Calculus
A Tutorial Introduction to the Lambda CalculusRa ul Rojas FU Berlin, WS-97/98 AbstractThis paper is a short and painless Introduction to the Calculus . Originallydeveloped in order to study some mathematical properties of effectively com-putable functions, this formalism has provided a strong theoretical foundationfor the family of functional programming languages. We show how to performsome arithmetical computations using the Calculus and how to define recur-sive functions, even though functions in Calculus are not given names and thuscannot refer explicitly to DefinitionThe Calculus can be called thesmallest universal programming language of theworld. The Calculus consists of a single transformation rule (variable substitution)and a single function definition scheme. It was introduced in the 1930s by AlonzoChurch as a way of formalizing the concept of effective computability. The calculusis universal in the sense that any computable function can be expressed and evaluatedusing this formalism.
The expression after the point (in this case a single x) is called the \body" of the de nition. Functions can be applied to expressions. An example of an application is ... Numbers can be represented in lambda calculus starting from zero and writing \suc(zero)" to represent 1, \suc(suc(zero))" to represent 2, and so on. In the lambda calculus ...
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