In
mathematics, a partial function is a
binary relation that associates each
element of a
set, sometimes called its
domain, with at most one element of another (possibly the same) set, called its
codomain. However, not every element of the domain has to be associated with an element of the codomain.An example of a partial function with domain and codomain equal to the
integers, is given by where g(n) is only defined for those nonnegative integers which are
perfect squares, that is are equal to the square of some integer.
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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 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)
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