Farms, pipes, streams and reforestation:reasoning about structured parallel processes using types and hylomorphisms

The increasing importance of parallelism has motivated the creation of better abstractions for writing parallel software, including structured parallelism using nested algorithmic skeletons. Such approaches provide high-level abstractions that avoid common problems, such as race conditions, and often allow strong cost models to be defined. However, choosing a combination of algorithmic skeletons that yields good parallel speedups for a program on some specific parallel architecture remains a difficult task. In order to achieve this, it is necessary to simultaneously reason both about the costs of different parallel structures and about the semantic equivalences between them. This paper presents a new type-based mechanism that enables strong static reasoning about these properties. We exploit well-known properties of a very general recursion pattern, hylomorphisms, and give a denotational semantics for structured parallel processes in terms of these hylomorphisms. Using our approach, it is possible to determine formally whether it is possible to introduce a desired parallel structure into a program without altering its functional behaviour, and also to choose a version of that parallel structure that minimises some given cost model