Parallel primitives (skeletons) intend to encourage programmers to build a parallel program from ready-made components for which efficient implementations are known to exist, making the parallelization process easier. However, programmers often suffer from the difficulty to choose a combination of proper parallel primitives so as to construct efficient parallel programs. To overcome this difficulty, we shall propose a new transformation, called diffusion, which can efficiently decompose a recursive definition 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 diffusion transformation should be significant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.

This paper presents an equational formulation of an objectoriented data model. In this model, a database is represented as a system of equations over a set of oid’s, and a database query is a transformation of a system of equations into another system of equations. During the query processing, our model maintains an equivalence relation over oid’s that relates oid’s corresponding to the same “real-world entity. ” By this mechanism, the model achieves a declarative set-based query language and views for objects with identity. Moreover, the query primitives are designed so that queries including object traversal can be evaluated in a data-parallel fashion. 1

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 suffers 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 efficient parallel programming with these primitives is difficult. In this paper, we propose a polytypic framework for developing efficient parallel programs on most data structures. We showhow a set of polytypic parallel primitives can be formally defined for manipulating most data structures, how these primitives can be successfully structured into a uniform recursive definition, and how an efficient combination of primitives can be derived from a naive specification program. Our framework should be significant not only in development of new parallel algorithms, but also in construction of parallelizing compilers.