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François Bourdoncle, Abstract interpretation by dynamic partitioning

François Bourdoncle, Abstract interpretation by dynamic partitioning

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PARIS RESEARCH LABORATORY d i g i t a l March 1992 18 Fran¸cois Bourdoncle Abstract Interpretation by Dynamic Partitioning
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18 Abstract Interpretation by Dynamic Partitioning Fran¸cois Bourdoncle March 1992
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Publication Notes This paper has also been published in the Journal of Functional Programming. c Digital Equipment Corporation 1992 This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for non-profit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of the Paris Research Laboratory of Digital Equipment Centre Technique Europe, in Rueil-Malmaison, France; an acknowledgement of the authors and individual contributors to the work; and all applicable portions of the copyright notice. Copying, reproducing, or republishing for any other purpose shall require a license with payment of fee to the Paris Research Laboratory. All rights reserved. ii
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Abstract The essential part of abstract interpretation is to build a machine-representable abstract domain expressing interesting properties about the possible states reached by a program at run-time. Many techniques have been developed which assume that one knows in advance the class of properties that are of interest. There are cases however when there are no a priori indications about the “best” abstract properties to use. We introduce a new framework that enables non- unique representations of abstract program properties to be used, and expose a method, called dynamic partitioning, that allows the dynamic determination of interesting abstract domains using data structures built over simpler domains. Finally, we show how dynamic partitioning can be used to compute non-trivial approximations of functions over infinite domains and give an application to the computation of minimal function graphs. R´esum´e L’une des principales difficult´es de l’interpr´etation abstraite consiste `a construire un domaine abstrait, repr´esentable en machine, qui permette d’exprimer un ensemble de propri´et´es suffisant `a d´ecrire de mani`ere pr´ecise l’ensemble des ´etats dans lequel peut se trouver un programme lorsqu’il est ex´ecut´e. De nombreuse techniques d’interpr´etation abstraite ont ´et´e d´evelopp´ees `a partir de l’hypoth`ese que la classe des “bonnes” propri´et´es est, d`es le d´epart, bien identifi´ee. Cependant, dans de nombreux cas, il n’y a aucune indication a priori quant `a l’int´erˆet relatif des diff´erentes classes de propri´et´es envisageables. Nous pr´esentons ici une nouvelle m´ethode, appel´ee partitionnement dynamique, qui autorise la d´etermination dynamique des “bonnes” propri´et´es par l’utilisationde structures de donn´ee construites `a partir d’approximationssimples du domaine concret. Nous montrons en particulier comment des approximations finies et non
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