Web Reference: Abstract This paper is a short and painless introduction to the calculus. Originally developed in order to study some mathematical properties of e ectively com- putable functions, this formalism has provided a strong theoretical foundation for the family of functional programming languages. Lambda Calculus The Lambda calculus is an abstract mathematical theory of computation, involving λ λ functions. The lambda calculus can be thought of as the theoretical foundation of functional programming. The lambda calculus (or λ-calculus) was introduced by Alonzo Church and Stephen Cole Kleene in the 1930s to describe functions in an unambiguous and compact manner. Many real languages are based on the lambda calculus, such as Lisp, Scheme, Haskell, and ML.
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