Combining Lists with Non-Stably Infinite TheoriesReport as inadecuate




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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, 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





Author: Pascal Fontaine - Silvio Ranise - Calogero Zarba -

Source: https://hal.archives-ouvertes.fr/



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