lambda-calculus
<mathematics> (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 way; Church 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)
Nearby terms:
Lambada-Calculus « LAMBDA « lambda abstraction «
lambda-calculus » lambda expression » lambda
lifting » LambdaMOO
|
