Loop optimization plays an important role in compiler optimization and program transformation. Many sophisticated techniques such as loop-invariance code motion, loop restructuring and loop fusion have been developed. This paper introduces a novel technique called loop quasi-invariance code motion. It is a generalization of standard loop-invariance code motion, but based on loop quasi-invariance analysis. Loop quasi-invariance is similar to standard loop-invariance but allows for a finite number of iterations before computations in a loop become invariant. In this paper we define the notion of loop quasi-invariance, present an algorithm for statically computing the optimal unfolding length in While-programs and give a transformation method. Our method can increase the accuracy of program analyses and improve the efficiency of programs by making loops smaller and faster. Our technique is well-suited as supporting transformation in compilers, partial evaluators, and other program transformers.

Deforestation is a well-known program transformation technique which eliminates intermediate data structures that are passed between functions. One of its weaknesses is the inability to deforest programs using accumulating parameters. We show how certain kinds of intermediate lists produced by accumulating parameters can be deforested. In this paper we introduce an accumulative variant of foldr, called rdlof, and show the composition of functions defined by foldr and rdlof. As a simplified instance of foldr and rdlof, we then examine dmap, an accumulative extension of map, and give the corresponding fusion rules. While the associated composition rules cannot capture all deforestation problems, they can handle accumulator fusion of fold- and map-style functions in a simple manner. The rules for accumulator fusion presented here can also be viewed as a restricted composition scheme for attribute grammars, which in turn may help us to bridge the gap between the attribute and functional worlds.