A positive supercompiler

We introduce a positive supercompiler, a version of Turchin's supercompiler maintaining only positive information during transformation, and using folding without generalization. The positive supercompiler can also be regarded as a variant of Wadler's deforestation maintaining an increased amount of information. We compare our algorithm to deforestation and, in less detail, to partial evaluation, Turchin's supercompiler, Generalized Partial Computation (GPC), and partial deduction by classifying these transformers by the amount of information they maintain during transformation. This factor is significant, as a differentiating example reveals: positive supercompilation, Turchin's supercompiler, GPC and partial deduction can specialize a general pattern matcher with respect to a fixed pattern to obtain an efficient matcher very similar to the Knuth-Morris-Pratt algorithm. Deforestation and traditional partial evaluation achieve this effect only after a non-trivial hand rewriting of the general matcher. Capsule Review Supercompilation is a technique of function transformation developed originally by Turchin (1986) for a functional language Refal. The technique uses DRIVING (the forced unfolding guided by functional configurations) to construct a potentially infinite tree of states (configurations) and transitions. This tree is then converted into a self-sufficient graph by reducing some of the configurations to their predecessors, which is similar to folding, or creating new configurations by generalization and redoing the driving. Supercompilation has been shown to do partial evaluation and deforestation, as well as more difficult transformations. Sorensen, Gliick and Jones present and discuss the essential features of supercompilation, using a simplified version of the supercompiler which they call POSITIVE. The reason for this name is that the information which is propagated through the graph during driving includes only POSITIVE elements, i.e. statements that a variable matches a certain pattern, while the NEGATIVE statements that a variable does not match a pattern (which are propagated in Turchin's supercompiler as RESTRICTIONS) are not taken along. Generalization is also not done in the positive supercompiler. These simplifications allow the authors to present supercompilation in more traditional formalism and in more detail, as well as compare it with similar techniques: partial evaluation, deforestation and generalized partial computation. The authors consider in detail one wellknown example of program transformation: the transformation of a naive string matcher by specializing it for a given specific pattern into an efficient algorithm known as KMP (it became a kind of standard test in partial evaluation and similar techniques). They show that while supercompilation (both full and positive) and generalized partial computation solve the problem, 'regular' partial evaluation and deforestation cannot do this without a non-trivial modification in the original unspecialized matcher. 812 M. H. Sorensen, R. Gltick and N. D. Jones