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)