Source : Free On-Line Dictionary of Computing

partial function
     
        A function which is not defined for all arguments of its input
        type.  E.g.
     
        	f(x) = 1/x if x /= 0.
     
        The opposite of a {total function}.  In {denotational
        semantics}, a partial function
     
        	f : D -> C
     
        may be represented as a total function
     
        	ft : D' -> lift(C)
     
        where D' is a superset of D and
     
        	ft x = f x	if x in D
        	ft x = bottom	otherwise
     
        where lift(C) = C U {bottom}.  Bottom ({LaTeX} {\perp})
        denotes "undefined".
     
        (1995-02-03)