function

n 1: a mathematical relation such that each element of one set is

associated with at least one element of another set

[syn: {mathematical function}]

2: what something is used for; "the function of an auger is to

bore holes"; "ballet is beautiful but what use is it?"

[syn: {purpose}, {role}, {use}]

3: the actions and activities assigned to or required or

expected of a person or group: "the function of a

teacher"; "the government must do its part" or "play its

role" or "do its duty" [syn: {office}, {part}, {role}]

4: a relation such that one thing is dependent on another;

"height is a function of age"; "price is a function of

supply and demand"

5: a formal or official social gathering or ceremony; "it was a

black-tie function"

6: a set sequence of steps, part of larger computer program

[syn: {routine}, {subroutine}, {subprogram}, {procedure}]

v 1: function properly; "The washing machine won't go unless it's

plugged in" [syn: {work}, {operate}, {go}, {run}] [ant:

{malfunction}]

2: serve a purpose, role, or function; "The tree stump serves

as a table"; "The female students served as a control

group"; "This table would serve very well"; "His freedom

served him well"; The table functions as a desk" [syn: {serve}]

3: act as an official in a specific function [syn: {officiate}]

function

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)