Principled strength reduction

This paper presents a principled approach for optimizing iterative (or recur-sive) programs. The approach formulates a loop body as a function f and a change operation , incrementalizes f with respect to , and adopts an incrementalized loop body to form a new loop that is more eecient. Three general optimizations are performed as part of the adoption; they systematically handle initializations, termination conditions, and nal return values on exits of loops. These optimizations are either omitted, or done in implicit, limited, or ad hoc ways in previous methods. The new approach generalizes classical loop optimization techniques, notably strength reduction, in optimizing compilers, and it uniies and systematizes various optimization strategies in transformational programming. Such principled strength reduction performs drastic program eeciency improvement via incrementalization and appreciably reduces code size via associated optimizations. We give examples where this approach can systematically produce strength-reduced programs while no previous method can.