The Lambda Calculus


Functions play a prominent role in describing the semantics of a programming language, since the meaning of a computer program can be considered as a function from input values to output values. The lambda calculus is a formal mathematical system devised by Alonzo Church to investigate functions, function application and recursion. It is defined as follows:
Mathematical system for defining functions, proving equations between expressions, and calculating values of expressions.
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. Three other functional programming languages are Lambda calculus also provides the meta-language for formal definitions in denotational semantics. It has a good claim to be the prototype programming language.

Demonstration