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Journal of Logic and Computation 1992 2(4):511-547; doi:10.1093/logcom/2.4.511
© 1992 by Oxford University Press
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Original Articles

Abstract Interpretation Frameworks

PATRICK COUSOT, LIENS and RADHIA COUSOT

École Normale Supeérieure 45 rue d'Ulm, 75230 Paris cedex 05, France
LIX, ÉcolePolytechnique 91128 Palaiseau cedex, France cousot{at}dmi.ens.fr and radhia{at}polytechnique.fr

We introduce abstract interpretation frameworks which are variations on the archetypal framework using Galois connections between concrete and abstract semantics, widenings and narrowings and are obtained by relaxation of the original hypotheses. We consider various ways of establishing the correctness of an abstract interpretation depending on how the relation between the concrete and abstract semantics is denned. We insist upon those correspondences allowing for the inducing of the approximate abstract semantics from the concrete one. Furthermore we study various notions of widening and narrowing as a means of obtaining convergence in the iterations used in abstract interpretation.

Keywords: Abstract interpretation; standard and collecting semantics; concrete and abstract semantics; discrete approximation; soundness relation; abstraction; concretization; Galois connections; widening; narrowing


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