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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)


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