The problems involved in developing efficient parallel programs have proved harder than those in developing efficient sequential ones, both for programmers and for compilers. Although program calculation has been found to be a promising way to solve these problems in the sequential world, we believe that it needs much more effort to study its effective use in the parallel world. In this paper, we propose a calculational framework for the derivation of efficient parallel programs with two main innovations: - We propose a novel inductive synthesis lemma based on which an elementary but powerful parallelization theorem is developed. - We make the first attempt to construct a calculational algorithm for parallelization, deriving associative operators from data type definition and making full use of existing fusion and tupling calculations. Being more constructive, our method is not only helpful in the design of efficient parallel programs in general but also promising in the construc...

Abstract program schemes, such as scan or homomorphism, can capture a wide range of data parallel programs. While versatile, these schemes are of limited practical use on their own. A key problem is that the more natural sequential specifications may not have associative combine operators required by these schemes. As a result, they often fail to be immediately identified. To resolve this problem, we propose a method to systematically derive parallel programs from sequential definitions. This method is special in that it can automatically invent auxiliary functions needed by associative combine operators. Apart from a formalisation, we also provide new theorems, based on the notion of context preservation, to guarantee parallelization for a precise class of sequential programs. 1 Introduction It is well-recognised that a key problem of parallel computing remains the development of efficient and correct parallel software. This task is further complicated by the variety of parallel arc...

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, we propose