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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)


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