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".

Last updated: 1995-02-03

Nearby terms:

partial evaluation ♦ partial function ♦ partial key ♦ partially ordered set

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