# linear function

## linear function

noun Mathematics.

Origin:
1855–60

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2013.
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### linear function definition

A recursive function is linear if it is of the form
f x = if p x then q x else h f x
where h is a "linear functional" which means that
(1) for all functions, a, b c and some function ht
h (if a then b else c) = if ht a then h b else h c
Function ht is known as the "predicate transformer" of h.
(2) If for some x,
h (\ y . bottom) x /= bottom
then
for all g, ht g x = True.
I.e. if h g x terminates despite g x not terminating then ht g x doesn't depend on g.
(1995-02-15)

The Free On-line Dictionary of Computing, © Denis Howe 2010 http://foldoc.org
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Example sentences
The fact is that wealth is not a linear function of money.
It suffices to do the math: it is a linear function against an exponential one.
Here is his position with a linear function fit to the data.
Determine the slope and intercepts of the graph of a linear function,
interpreting slope as a constant rate of change.