Towards Polytypic Parallel Programming

Data parallelism is currently one of the most successful models for programming massively parallel computers. The central idea is to evaluate a uniform collection of data in parallel by simultaneously manipulating each data element in the collection. Despite many of its promising features, the current approach su ers from two problems. First, the main parallel data structures that most data parallel languages currently support are restricted to simple collection data types like lists, arrays or similar structures. But other useful data structures like trees have not been well addressed. Second, parallel programming relies on a set of parallel primitives that capture parallel skeletons of interest. However, these primitives are not well structured, and e cient parallel programming with these primitives is di cult. In this paper, we propose a polytypic framework for developing e cient parallel programs on most data structures. We show how a set of polytypic parallel primitives can be formally de ned for manipulating most data structures, how these primitives can be successfully structured into a uniform recursive de nition, and how an e cient combination of primitives can be derived from a naive speci cation program. Our framework should be signi cant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.