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1. The Free On-line Dictionary of Computing (18 March 2015)
lambda-calculus

    (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)


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