Bounded Parallelism in PowerList and ParList Theories

A very efficient model for recursive, data-parallel programs can be one based on PowerList, PowerArray, and ParList theories. It assures simple and correct design of this kind of programs, allowing work at a high level of abstraction. This high level of abstraction could be reconciled with performance by introducing data-distributions into these theories.%An important advantage of formally introducing distributions is that this allows us to evaluate costs, depending on the number of available processors, which is considered as a parameter. In this paper, we generalize the data distributions defined on PowerLists by introducing data distributions for parallel programs defined using ParList structures. Using these distributions we also define a possibility to transform ParList parallel programs into PowerList parallel programs, which are more efficient. This is an important advantage since PowerList programs could be efficiently mapped on real architecture (e.g. hypercubes).