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1 definition found
From 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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