Combining Lists with Non-Stably Infinite Theories

Pascal Fontaine 1 Silvio Ranise 2 Calogero Zarba 2
1 MOSEL - Proof-oriented development of computer-based systems
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
2 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : In program verification one has often to reason about lists over elements of a given nature. Thus, it becomes important to be able to combine the theory of lists with a generic theory $T$ modeling the elements. This combination can be achieved using the Nelson-Oppen method only if $T$ is stably infinite. The goal of this paper is to relax the stable-infiniteness requirement. More specifically, we provide a new method that is able to combine the theory of lists with any theory $T$ of the elements, regardless of whether $T$ is stably infinite or not. The crux of our combination method is to guess an arrangement over a set of variables that is larger than the one considered by Nelson and Oppen. Furthermore, our results entail that it is also possible to combine $T$ with the more general theory of lists with a length function.
Keywords : combination decision procedure lists arithmetic
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Conference papers
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Pascal Fontaine, Silvio Ranise, Calogero Zarba. Combining Lists with Non-Stably Infinite Theories. 11th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR'04), Mar 2005, Montevideo/Uruguay, pp.51--66, ⟨10.1007/b106931⟩. ⟨inria-00000481⟩

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