From transformations to methodology in parallel program development: A case study

Abstract The Bird-Meertens formalism (BMF) of higher-order functions over lists is a mathematical framework supporting formal derivation of algorithms from functional specifications. This paper reports results of a case study on the systematic use of BMF in the process of parallel program development. We develop a parallel program for polynomial multiplication, starting with a straight-forward mathematical specification and arriving at the target processor topology together with a program for each processor of it. The development process is based on formal transformations; design decisions concerning data partitioning, processor interconnections, etc. are governed by formal type analysis and performance estimation rather than made ad hoc . The parallel target implementation is parameterized for an arbitrary number of processors; for the particular number, the target program is both time and cost-optimal. We compare our results with systolic solutions to polynomial multiplication.

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