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 skeletons intend to encourage programmers to build...

With the increasing popularity of parallel programming environments such as PC clusters, more and more sequential programmers, with little knowledge about parallel architectures and parallel programming, are hoping to write parallel programs. Numerous attempts have been made to develop high-level parallel programming libraries that use abstraction to hide low-level concerns and reduce difficulties in parallel programming. Among them, libraries of parallel skeletons have emerged as a promising way towards this direction. Unfortunately, these libraries are not well accepted by sequential programmers, because of incomplete elimination of lower-level details, ad-hoc selection of library functions, unsatisfactory performance, or lack of convincing application examples. This paper addresses principle of designing skeleton libraries of parallel programming and reports implementation details and practical applications of a skeleton library SkeTo. The SkeTo library is unique in its feature that it has a solid theoretical foundation based on the theory of Constructive Algorithmics, and is practical to be used to describe various parallel computations in a sequential manner. 1.

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 addresses a new framework for designing and implementing skeleton libraries, in which each skeleton should not only be efficiently implemented as is usually done, but also be equipped with a structured interface to combine it efficiently with other skeletons. We illustrate our idea with a new skeleton library for parallel programming in C++. It is simple and efficient to use just like other C++ libraries. A distinctive feature of the library is its modularity: Our optimization framework treats newly defined skeletons equally to existing ones if the interface is given. Our current experiments are encouraging, indicating that this approach is promising both theoretically and in practice.

Correctness-preserving program transformation has recently received a particular attention for compiler optimization in functional programming [Kelsey and Hudak 1989; Appel 1992; Peyton Jones 1996]. By implementing a compiler using many passes, each of which is a transformation for a particular optimization, one can attain a modular compiler. It is no surprise that the modularity would increase if transformations are structured, i.e. constructed in a modular way. Indeed, the program transformation in calculational form (or program calculation) can help us to attain this goal.

. Systematic parallelization of sequential programs remains a major challenge in parallel computing. Traditional approaches using program schemes tend to be narrower in scope, as the properties which enable parallelism are difficult to capture via ad-hoc schemes. In [CTH98], a systematic approach to parallelization based on the notion of preserving the context of recursive sub-terms has been proposed. This approach can be used to derive a class of divide-and-conquer algorithms. In this paper, we enhance the methodology by using invariants to guide the parallelization process. The enhancement enables the parallelization of a class of recursive functions with conditional and tupled constructs, which were not possible previously. We further show how such invariants can be discovered and verified systematically, and demonstrate the power of our methodology by deriving a parallel code for maximum segment product. To the best of our knowledge, this is the first systematic parall...

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We show how programming pearls can be systematically derived via fusion, followed by tupling transformations. By focusing on the elimination of intermediate data structures (fusion) followed by the elimination of redundant calls (tupling), we systematically realise both space and time efficient algorithms from naive specifications. We illustrate our approach using a well-known maximum segment sum (MSS) problem, and a less-known maximum segment product (MSP) problem. While the two problems share similar specifications, their optimised codes are significantly different. This divergence in the transformed codes do not pose any difficulty. By relying on modular techniques, we are able to systematically reuse both code and transformation in our derivation.