The Lambda CalculusOriginThe Lambda Calculus has been created by the American logician Alonzo Church in the 1930's and is documented in his works published in 1941 under the title `The Calculi of Lambda Conversion'. Alonzo Church wanted to formulate a mathematical logical system and had no intent to create a programming language. The intrinsic relationship of his system to programming was discovered much later in a time in which programming of computers became an issue.DefinitionSyntax of Lambda ExpressionsThe syntax of lambda expressions is defined as follows:
Remark: The parentheses in the syntax of an application are not mandatory. This results from the law of associativity for applications introduced below. More DetailsFor a detailed introduction to the Calculi of Lambda Conversion see Appendix B of the online version of the A++ book. For the reader's convenience a PDFVersion of this article is also available at this address.LiteratureAs a mathematical logical system the Lambda Calculus is covered in detail in [Bar81] and less comprehensively but in a more readable form in [Sto81]. A clear account of the historical origins and basic properties of the lambda calculus is presented by Curry and Fey in their book [CF58]. This view is taken from [Jon87] page 23.From the programmer's point of view the Lambda
Calculus is adressed in [Jon87],
[Kam90], [Cha96].

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