The Free On-line Dictionary of Computing (30 December 2018):

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)