Stages and Transformations in Parallel Programming

An approach, called SAT (Stages And Transformations), is introduced to support the derivation of parallel distributed-memory programs. During the design, a program is viewed as a single thread of stages, with parallelism concentrated within stages; the target program is of the SPMD format. The design process is based on the transformation rules of the Bird-Meertens formalism of higher-order functions over lists. The approach is illustrated by three case studies which include: a systematic method of constructing list homomorphisms, a scalable, load-balanced implementation of divide-and-conquer based on a specialized topology and a formal derivation of a time and cost optimal parallel algorithm for straightforward polynomial multiplication.