# 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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Halberstadt forms as middle center (mz) with partial function of an upper center (oz) a traffic node in the resin foreland.
Partial array A of size (m, n) over [SIGMA], a finite alphabet, is partial function A : [Z.sub.2.sub.+] [right arrow] Z, where [Z.sub.+] is the set of all positive integers.
The patient has regained partial function of knee extensors and remains classified as ASIA Impairment Scale C (AIS C) with a motor incomplete spinal cord injury.
* Pulmonologists know they can never restore normal lung function for their patients with chronic obstructive pulmonary disease; they can only help them hang on with partial function.
where the successive iterations acting over the partial function [f.sub.1] (dom [f.sub.1] = 1 and [f.sub.1] (1) = 1) hold that [[phi].sup.n.sub.fact] ([f.sub.1])(m) = 1 if m = 1 and [[phi].sup.n.sub.fact]([f.sub.1])(m) = m!
University of Illinois scientists have also discovered why it happens: soy restores partial function of that organ's key signalling pathway.
After the concepts and theories are introduced, the equivalence of computable partial function and recursive partial function are demonstrated, in part through proofs of the unsolvability of the halting problem and of the enumeration theorem.
In addition to these ten individuals, two other patients recovered partial function. These two required electrical stimulation of the skin to initiate voiding, and, although residual urine volume was less, they still retained more than 100 milliliters.
--W is a partial function from set IxTm where W[i,t] is a quintuple <U[i], [[sigma][i,t].sup.[PI]], [alpha][[i,t].sup.[psi]], [lambda][[i,t].sup.[conjunction]] [kappa][i,t].sup.K]>: the INTERNAL-WORLD FUNCTION.
1), where mi is the number of partial solutions, for partial function i.
Although the procedure has a high success rate--88% of the grafts retain at least partial function beyond 5 years--it is not practical in Japan, where the concept of cadaveric organ transplantation is only now gaining public support.
First we extend the bisimulation concept in order to handle partial functions. By a partial function we mean a relation that fails to be a function because it is not aplicable for certain arguments in the domain.

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