The Free On-line Dictionary of Computing (30 December 2018):

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". (1995-02-03)