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 denotationalsemantics, 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)