Lambda calculus, considered to be the mathematical basis for programming language, is a calculus developed by Alonzo Church and Stephen Kleene in the 1930s to express all computableï¿½functions.ï¿½ In an effort to formalize the concept of computability (also known as constructibility and effective calculability), Church and Kleene developed a powerful language with a simpleï¿½ syntax and few grammar restrictions. The language deals with the application of a function to its arguments (a function is a set of rules) and expresses any entity as either a variable, the application of one function to another, or as a "lambda abstraction" (a function in which the Greek letterï¿½lambda is defined as the abstraction operator). Lambda calculus, and the closely related theories of combinators and type systems, are important foundations in the study of mathematics, logic, and computer programming language.
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