partial function

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partial function

[′pär·shəl ′fəŋk·shən]
(computer science)
A partial function from a set A to a set B is a correspondence between some subset of A and B which associates with each element of the subset of A a unique element of B.

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".
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