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1 definition found for lambda-calculus:

From The Free On-line Dictionary of Computing (27 SEP 03):

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)
     
     




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