Parallel graph rewriting on loosely coupled machine architectures

Abstract

Graph rewriting models are very suited to serve as the basic computational model for functional languages and their implementation. Graphs are used to share computations which is needed to make efficient implementations of functional languages on sequential hardware possible. When graphs are rewritten (reduced) on parallel loosely coupled machine architectures, subgraphs have to be copied from one processor to another such that sharing is lost. In this paper we introduce the notion of lazy copying. With lazy copying it is possible to duplicate a graph without duplicating work. Lazy copying can be combined with simple annotations which control the order of reduction. In principle, only interleaved execution of the individual reduction steps is possible. However, a condition is deduced under which parallel execution is allowed. When only certain combinations of lazy copying and annotations are used it is guarantied that this so-called non-interference condition is fulfilled. Abbreviations for these combinations are introduced. Now complex process behaviours, such as process communication on a loosely coupled parallel machine architecture, can be modelled. This also includes a special case: modelling multiprocessing on a single processor. Arbitrary process topologies can be created. Synchronous and asynchronous process communication can be modelled. The implementation of the language Concurrent Clean, which is based on the proposed graph rewriting model, has shown that complicated parallel algorithms which can go far beyond divide-and-conquer like applications can be expressed.