Source : Free On-Line Dictionary of Computing

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 abstraction}s (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)