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

	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.

Last updated: 1995-02-15