Abstract

List homomorphisms are functions that can be computed in parallel using the divide-and-conquer paradigm. We study the problem of finding a homomorphic representation of a given function, based on the Bird-Meertens theory of lists. A previous work proved that to each pair of leftward and rightward sequential representations of a function, based on cons- and snoc-lists, respectively, there is also a representation as a homomorphism. Our contribution is a mechanizable method to extract the homomorphism representation from a pair of sequential representations. The method is decomposed to a generalization problem and an inductive claim, both solvable by term rewriting techniques. To solve the former we present a sound generalization procedure which yields the required representation, and terminates under reasonable assumptions. We illustrate the method and the procedure by the parallelization of the scan-function (parallel prefix). The inductive claim is provable automatically. Keywords: P...

Citations