linear function

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linear function - Free On-line Dictionary of Computing (26 May 2007) :

  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)