Formal derivation and extraction of a parallel program for the all nearest smaller values problem

Abstract

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.

Calculating Parallel Programs in Coq Using List Homomorphisms

“…The core SyDPaCC presented in this paper is very concise (2 kLoC of Coq, 600 LoC of OCaml 120 LoC of C). Experimental results on the generated programs are presented in [7,14,21] and in the SyDPaCC website.…”

“…We develop the framework SyDPaCC [7,14] for the Coq proof assistant [22] to ease the use of methods based on program transformation and algorithmic skeletons and make them more reliable. More specifically the contributions of this paper are:…”

“…-the support of list homomorphisms in SyDPaCC that previously only supported BSP homomorphisms [14] and the GTA paradigm [7], -improvements of the formalisation of the parallel functional language Bulk Synchronous Parallel ML (BSML) [13] and algorithmic skeletons in Coq, -an application of the framework to produce a parallel program for the maximum prefix sum problem.…”

Parallel Programming with OCaml: A Tutorial

“…The pure semantics of BSML makes the verification of BSML program possible using a proof assistant [28]. This is the foundation of a framework for the Coq proof assistant to support the systematic development of correct parallel programs [29], [30], [31], [32], [33].…”