The DICT Development Group

  function
  mapping
  
     1.  (Or "map", "mapping") If D and C are sets
     (the domain and codomain) then a function f from D to C,
     normally written "f : D -> C" is a subset of D x C such that:
  
     1. For each d in D there exists some c in C such that (d,c) is
     an element of f.  I.e. the function is defined for every
     element of D.
  
     2. For each d in D, c1 and c2 in C, if both (d,c1) and (d,c2)
     are elements of f then c1 = c2.  I.e. the function is uniquely
     defined for every element of D.
  
     See also image, inverse, partial function.
  
     2.  Computing usage derives from the mathematical
     term but is much less strict.  In programming (except in
     functional programming), a function may return different
     values each time it is called with the same argument values
     and may have side effects.
  
     A procedure is a function which returns no value but has
     only side-effects.  The C language, for example, has no
     procedures, only functions.  ANSI C even defines a type,
     void, for the result of a function that has no result.
  
     (1996-09-01)