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.

ion and Performance in the Design of Parallel Programs Der Fakultat fur Mathematik und Informatik der Universitat Passau vorgelegte Zusammenfassung der Veroffentlichungen zur Erlangung der venia legendi von Dr. Sergei Gorlatch Passau, Juli 1997 Contents 1 Introduction 2 2 Outline of the SAT Approach 6 2.1 Performance View . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Abstraction View . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Design in SAT: Stages and Transformations . . . . . . . . . . 9 2.4 SAT and Homomorphisms . . . . . . . . . . . . . . . . . . . . 11 3 List Homomorphisms 12 4 Extraction and Adjustment 14 4.1 The CS-Method . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Mechanizing the CS-Method . . . . . . . . . . . . . . . . . . . 17 4.3 Almost-Homomorphisms: the MSS Problem . . . . . . . . . . 19 5 Composition of Homomorphisms 21 5.1 Rules of Composition . . . . . . . . . . . . . . . . . . . . . . . 21 5.2 Derivation by Transformation...