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linear function

noun, Mathematics
Origin of linear function
1855-60 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2015.
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linear function in Technology

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
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.
See also linear argument.

The Free On-line Dictionary of Computing, © Denis Howe 2010
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