The lambda calculus is a formal mathematical system devised by Alonzo Church to investigate functions, function application and recursion. It has influenced many programming languages but none more so than the functional programming languages. Lisp was the first of these although only the "pure" Lisp sublanguage can be called a true functional language. Haskell, Miranda and ML are more recent examples. Lambda calculus also provides the meta-language for formal definitions in denotational semantics. It has a good claim to be the prototype programming language.

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