Trimmed abstract: “This thesis proposes a new framework for the combination of multiple abstractions in the abstract interpretation theory. Its core concept is the structuring of the abstract semantics by following the usual distinction between expressions and statements. This can be achieved by a convenient architecture where abstractions are separated in two layers: value abstractions, in charge of the expression semantics, and state abstractions (or abstract domains), in charge of the statement semantics.

This design leads naturally to an elegant communication system where the abstract states, when interpreting a statement, interact and exchange information through abstract values, that express properties about expressions. While the values form the communication interface between states, they are also standard elements of the abstract interpretation framework. The communication system is thus embedded in the abstract semantics, and the usual tools of abstract interpretation apply naturally to value abstractions. For instance, different kinds of value abstractions can be composed through the existing methods of combination of abstractions, enabling even further interaction between the components of the abstract semantics.

This thesis explores the possibilities offered by this framework. We discuss efficient strategies to compute precise value abstractions from the properties inferred by abstract domains, and illustrate the means of communication between different state abstractions. Our architecture also features a direct collaboration for the emission of alarms that report the possible errors of a program.

The general system of abstractions combination has been implemented within EVA, the new version of the abstract interpreter provided by the Frama-C platform. Thus, EVA enjoys a modular and extensible architecture designed to facilitate the introduction of new abstractions and to enable rich interactions between them. Thanks to this work, five new domains from the literature have been implemented in less than a year, enhancing both the scope and the precision of the analyzer.”