function

1. mathematics (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. programming 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)