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Abstract. Algorithmic skeletons in conjunction with list homomorphisms play an important role in formal development of parallel algorithms. We have designed a notion of homomorphism dedicated to bulk synchronous parallelism. In this paper we derive two application using this theory: sparse matrix vector multiplication and the all nearest smaller values problem. We implement a support for BSP homomorphism in the Orléans Skeleton Library and experiment it with these two applications.

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The All Nearest Smaller Values (ANSV) problem is an important problem for parallel programming as it can be used to solve several problems and is one of the phases of several other parallel algorithms. We formally develop by construction a functional parallel program for solving the ANSV problem using the theory of Bulk Synchronous Parallel (BSP) homomorphisms within the Coq proof assistant. The performances of the Bulk Synchronous Parallel ML program obtained from Coq is compared to a version derived without software support (pen-and-paper) and implemented using the Orléans Skeleton Library of algorithmic skeletons, and to a (unproved correct) direct implementation of the BSP algorithm of He and Huang.

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