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.
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References
J.-P. Banâtre and D. Le Métayer. The Gamma model and its discipline of programming. Science of Computer Programming, 15(1):55–79, 1990.
M. Chen, Y. Choo, and J. Li. Parallel Functional Languages and Compilers. Frontier Series. ACM Press, 1991. Chapter 7.
K.M. Chandy and J. Misra. Parallel Program Design: A foundation. Addison Wesley, 1988.
C. Creveuil. Techniques d'analyse et de mise en oeuvre des programmes Gamma. PhD thesis, U. Rennes, 1991.
D. Gelernter. Generative communication in Linda. ACM Transactions on Programming Languages and Systems, 7(1):80–112, January 1985.
H. Leverge. Reduction operators in Alpha. Technical report, IRISA, November 1991.
Distribution INRIA — Rocquencourt. Maple Reference Manual, 4th Edition, March 1989.
C. Mauras. Alpha: un langage équationnel pour la conception et la programmation d'architectures parallèles synchrones. PhD thesis, U. Rennes, 1989.
C. Morgan. Programming from specifications. C.A.R. Hoare. Prentice Hall Ed., Endlewood Cliffs, N.J., 1990.
S. Rajopadhye. Lacs: A language for affine communication structures. Technical report, IRISA Rennes, 1993.
E. Violard. A mathematical theory and its environment for parallel programming. to appear in PPL, 1994.
E. Violard and G.-R. Perrin. Pei: a language and its refinement calculus for parallel programming. Parallel Computing, 18:1167–1184, 1992.
E. Violard and G.-R. Perrin. Pei: a single unifying model to design parallel programs. PARLE, LNCS, 694:500–516, 1993.
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© 1994 Springer-Verlag Berlin Heidelberg
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Violard, E., Perrin, G.R. (1994). Reduction in Pei . In: Buchberger, B., Volkert, J. (eds) Parallel Processing: CONPAR 94 — VAPP VI. VAPP CONPAR 1994 1994. Lecture Notes in Computer Science, vol 854. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58430-7_11
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DOI: https://doi.org/10.1007/3-540-58430-7_11
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