Source : Free On-Line Dictionary of Computing

Church integer
     
        A representation of integers as functions invented by {Alonzo
        Church}, inventor of {lambda-calculus}.  The integer N is
        represented as a {higher-order function} which applies a given
        function N times to a given expression.  In the {pure
        lambda-calculus} there are no constants but numbers can be
        represented by Church integers.
     
        A {Haskell} function to return a given Church integer could be
        written:
     
        	church n = c
        		   where
        		   c f x = if n == 0 then x else c' f (f x)
        			   where
        			   c' = church (n-1)
     
        A function to turn a Church integer into an ordinary integer:
     
        	unchurch c = c (+1) 0
     
        See also {von Neumann integer}.
     
        (1994-11-29)