Combining Lists with Non-Stably Infinite Theories

Pascal Fontaine (1) , Silvio Ranise (2) , Calogero G. Zarba (2)

1 MOSEL - Proof-oriented development of computer-based systems
2 CASSIS - Combination of approaches to the security of infinite states systems

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.

Mots clés: combination; decision procedure; lists; arithmetic

Domaines: Logique en informatique [cs.LO]

Pascal Fontaine, Silvio Ranise, Calogero G. 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⟩