(Normally written with a Greek letter lambda). A branch of mathematical logic developed by Alonzo Church in the late 1930s and early 1940s, dealing with the application of functions to their arguments.The pure lambda-calculus contains no constants - neither numbers nor mathematical functions such as plus - and is untyped.It consists only of lambda abstractions (functions), variables and applications of one function to another.All entities must therefore be represented as functions.For example, the natural number N can be represented as the function which applies its first argument to its second N times (Church integer N).Church invented lambda-calculus in order to set up a foundational project restricting mathematics to quantities with "effective procedures".Unfortunately, the resulting system admits Russell' s paradox in a particularly nasty wayChurch couldn' t see any way to get rid of it, and gave the project up.Most functional programming languages are equivalent to lambda-calculus extended with constants and types.Lisp uses a variant of lambda notation for defining functions but only its purely functional subset is really equivalent to lambda-calculus.See reduction.(1995-04-13)