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".