Di usion : Calculating E cient Parallel Programs

Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from ready-made components for which e cient implementations are known to exist, making the parallelization process easier. However, programmers often su er from the di culty to choose a combination of proper parallel primitives so as to construct efcient parallel programs. To overcome this di culty, we shall propose a new transformation, called di usion, which can e ciently decompose a recursive de nition into several functions such that each function can be described by some parallel primitive. This allows programmers to describe algorithms in a more natural recursive form. We demonstrate our idea with several interesting examples. Our di usion transformation should be signi cant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.