Strengthening invariants for efficient computation

This paper presents program analyses and transformations for strengthening invariants for the purpose of efficient computation. Finding the stronger invariants corresponds to discovering a general class of auxiliary information for any incremental computation problem. Combining the techniques with previous techniques for caching intermediate results, we obtain a systematic approach that transforms non-incremental programs into efficient incremental programs that use and maintain useful auxiliary information as well as useful intermediate results. The use of auxiliary information allows us to achieve a greater degree of incrementality than otherwise possible. Applications of the approach include strength reduction in optimizing compilers and finite differencing in transformational programming.