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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 defined. 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.

ASTRÉE is an abstract interpretation-based static program analyzer aiming at proving automatically the absence of run time errors in programs written in the C programming language. It has been applied with success to large embedded control-command safety critical realtime software generated automatically from synchronous specifications, producing a correctness proof for complex software without any false alarm in a few hours of computation. This work was supported in part by the French exploratory project ASTRÉE of the Réseau National de recherche et d'innovation en Technologies Logicielles (RNTL).

Abstract. Abstract interpretation theory formalizes the idea of abstraction of mathematical structures, in particular those involved in the specification of properties and proof methods of computer systems. Verification by abstract interpretation is illustrated on the particular cases of predicate abstraction, which is revisited to handle infinitary abstractions, and on the new parametric predicate abstraction.