# 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*.McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## 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".

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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