Email this page to a friend

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".

< Previous Terms	Terms Containing partial function	Next Terms >
parsing Parsley Partial Differential Equation LANguage partial equivalence relation partial evaluation	category function partial function total function	partial key partially ordered set partial ordering Partial Response Maximum Likelihood partition