Chapter

Parallel Processing: CONPAR 94 — VAPP VI

Volume 854 of the series Lecture Notes in Computer Science pp 112-123

Date:

Reduction in Pei

  • E. ViolardAffiliated withLaboratoire d'Informatique, University of Franche-Comté
  • , G. -R. PerrinAffiliated withLaboratoire d'Informatique, University of Franche-Comté

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Abstract

Reduction is one of the major issues in data parallel languages: it can be defined as a rule of program refinement. This article presents a theoretical framework, called Pei, the foundation of a formalism for parallel programming, where this rule can easily be expressed and applied. This formalism is founded on a small but powerful set of primitives: they are three operations on data fields and inverse operations. They induce a clear refinement calculus to transform specifications in executable programs by ensuring a safe process of design or optimization. We show how this approach allows to generalize the classical notion of reduction, by introducing a geometrical reduction and a functional one.

Keywords

Multiset Parallel programming Reduction operator Refinement Transformations