## 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 -> Cmay 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 otherwisewhere 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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