A TRANSFORMATION METHOD FOR DYNAMIC-SIZED TABULATION

Tupling is a transformation tactic to obtain new functions, without re dundant calls and/or multiple traversals of common inputs. It achieves this feat by allowing each set (tuple) of function calls to be comput ed recursively from its previous set. In previous works by Chin and Kh oo [8, 9], a safe (terminating) fold/unfold transformation algorithm w as developed for some classes of functions which are guaranteed to be successfully tupled. However, these classes of functions currently use static-sized tables for eliminating the redundant calls. As shown by Richard Bird in [3], there are also other classes of programs whose re dundant calls could only be eliminated by using dynamic-sized tabulati on. This paper proposes a new solution to dynamic-sized tabulation by an extension to the tupling tactic. Our extension uses lambda abstract ions which can be viewed as either dynamic-sized tables or application s of the higher-order generalisation technique to facilitate tupling. Significant speedups could be obtained after the transformed programs were vectorised, as confirmed by experiment.