Data parallelism and functional programming

Data parallelism is often seen as a form of explicit parallelism for SIMD and vector machines, and data parallel programming as an explicit programming paradigm for these architectures. Data parallel languages possess certain software qualities as well, which justifies their use in higher level programming and specification closer to the algorithm domain. Thus, it is interesting to study how the data parallel paradigm can be best realized in a declarative setting, since declarative languages offer a pure view of computation which is good for these purposes. For numerical computing the functional programming paradigm is especially attractive, since numerical algorithms often are specified by recursion equations and thus can be translated more or less directly into recursive functional programs. Merging the data parallel and functional paradigms then yields languages and formalisms where many algorithms can be expressed in a very succinct fashion. In this paper we review data parallelism, functional programming, and existing approaches to the integration of the two paradigms. We then proceed to describe a formalism for data parallel functional programming, allowing very simple languages, where the view of aggregate data is particularly abstract. We explain how various data parallel operations can be expressed in this formalism. Finally, we conclude with a discussion of issues for languages based directly on the formalism.