The linear function, replicated in the use of the lever, was generalized in machines made of many levers.
The increase is very regular, and seems to be a linear function of the height.
Linearity: relation among dependent phenomena that can be described through a linear function.
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.
See also linear argument.
(1995-02-15)