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Lambda Calculus & A++

Basic Concepts



The 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.

The Lambda Calculus has stayed alive above all in the context of functional programming. It has gained a major importance in the area of compiler construction for functional languages like Haskell, SML, Miranda and others.

In this article the importance of the Lambda Calculus is extended to non-functional languages like Java, C, and C++ as well. The article uses A++, a programming language directly derived from the Lambda Calculus, as a vehicle to demonstrate the application of the basic ideas of the Lambda Calculus in a multi-paradigm environment.

The Lambda Calculus defines the laws for the formation and
conversion of lambda expressions.



The following pages first present the definitions and rules that make up the core of the Lambda Calculus and thereafter A++, a programming language designed as a tool helping to become thoroughly familiar with the essentials of programming without limitations to specific programming paradigms.     

See also the Appendix: The Lambda Calculus in the online version of the book A++ The Smallest Programming Language in the World.

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Georg P. Loczewski 2003-07-24
New book on A++ and the Lambda Calculus