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The geometry of conservative programs

Published online by Cambridge University Press:  17 October 2017

EMMANUEL HAUCOURT
EMMANUEL HAUCOURT*
Affiliation:
LIX - UMR 7161, Campus de l'École Polytechnique, 1 rue Honoré d'Estienne d'Orves, Bât. Alan Turing, 91120 Palaiseau, France Email: emmanuel.haucourt@lix.polytechnique.fr
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Abstract

The programs, we consider are written in a restricted form of the language introduced by Dijkstra (1968). A program is said to be conservative when each of its loops restores all the resources it consumes. We define the geometric model of such a program and prove that the collection of directed paths on it is a reasonable over-approximation of its set of execution traces. In particular, two directed paths that are close enough with respect to the uniform distance result in the same action on the memory states of the system. The same holds for weakly dihomotopic directed paths. As a by-product, we obtain a notion of independence, which is favourably compared to more common ones. The geometric models actually belong to a handy class of local pospaces whose elements are called isothetic regions. The local pospaces we use differ from the original ones, we carefully explain why the alternative notion should be preferred. The title intentionally echoes the article by Carson and Reynolds (1987).

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Issue 10 , November 2018 , pp. 1723 - 1769
Copyright
Copyright © Cambridge University Press 2017 

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