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...

We study the use of well-defined building blocks for SPMD programming of machines with distributed memory. Our general framework is based on homomorphisms, functions that capture the idea of dataparallelism and have a close correspondence with collective operations of the MPI standard, e.g., scan and reduction. We prove two composition rules: under certain conditions, a composition of a scan and a reduction can be transformed into one reduction, and a composition of two scans into one scan. As an example of decomposition, we transform a segmented reduction into a composition of partial reduction and all-gather. The performance gain and overhead of the proposed composition and decomposition rules are assessed analytically for the hypercube and compared with the estimates for some other parallel models.

Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, we have defined a classification of subexpressions based on their data-parallelism. Then, skeleton-based parallel programs are generated from the classification. To extend the scope of parallelization, we have adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows. Keywords: data parallelism, parallelization, functional languages, parallel skeletons, data flow analysis, static slice 1.

Divide-and-conquer algorithms are suitable for modern parallel machines, tending to have large amounts of inherent parallelism and working well with caches and deep memory hierarchies. Among others, list homomorphisms are a class of recursive functions on lists, which match very well with the divide-and-conquer paradigm. However, direct programming with list homomorphisms is a challenge for many programmers. In this paper, we propose and implement a novel system that can automatically derive costoptimal list homomorphisms from a pair of sequential programs, based on the third homomorphism theorem. Our idea is to reduce extraction of list homomorphisms to derivation of weak right inverses. We show that a weak right inverse always exists and can be automatically generated from a wide class of sequential programs. We demonstrate our system with several nontrivial examples, including the maximum prefix sum problem, the prefix sum computation, the maximum segment sum problem, and the line-ofsight problem. The experimental results show practical efficiency of our automatic parallelization algorithm and good speedups of the generated parallel programs.

Programming with parallel skeletons is an attractive framework because it encourages programmers to develop efficient and portable parallel programs. However, extracting parallelism from sequential specifications and constructing efficient parallel programs using the skeletons are still difficult tasks. In this paper, we propose an analytical approach to transforming recursive functions on general recursive data structures into compositions of parallel skeletons. Using static slicing, wehave defined a classification of subexpressions based on their data-parallelism. Then, skeleton-based parallel programs are generated from the classification. To extend the scope of parallelization, wehave adopted more general parallel skeletons which do not require the associativity of argument functions. In this way, our analytical method can parallelize recursive functions with complex data flows. Keywords: data parallelism, parallelization, functional languages, parallel skeletons, data flow analysis, static slice 1.