## Parallel Programming with Pei

- Guy-Ren, Perrin
- 2007

- Published 1993 in PARLE

I n t r o d u c t i o n It is now admitted that reliable parallel programming techniques should be founded on formal transformations of programs. To manage these transformations safely, a convenient modal has to be defined, to express the successive statements, and the transformation rules. Concerning these transformations the art conditions show two complementary philosophies : the stepwise refinement of programs from a specification and the synthesis of programs from a set of recurrence equations. If a program F ~ satisfies any specification that a program F satisfies, F t is called a refinement of F [Mor90]. This approach requires a logic in order to reason on programs. UNITY [CM88] is a fundamental contribution in this domain. UNITY allows to express specifications and sohtions in the same formalism. UNITY models programs as transition systems. GAMMA [Cre91] uses the same approach as Ut~urY, but is founded on a different model : a program GAMIVIA is a multiset transformer. These two formalisms associated with a refinement calculus are characterized by a non-deterministic computing modal which allows to introduce only necessary sequentiality. Due to the results of Karp, Miller and Winograd [KMW67], the second philosophy lies on a convenient abstract expression of programs in terms of recurrence equations. Indeed, prefiguring architecture evolutions, the introduction of the uniform recurrence equations defines a formal framework where the classical notions of data dependencies, potential parallelism and computation scheduling can be presented. Since this presentation many proposals have generalized this abstract modeling. Affine recurrences on in-

@inproceedings{Violard1993PEIAS,
title={PEI: a Single Unifying Model to Design Parallel Programs},
author={Eric Violard and Guy-Ren{\'e} Perrin},
booktitle={PARLE},
year={1993}
}