Section: New Results

Termination under Strategies

Participants : Horatiu Cirstea, Sergueï Lenglet, Pierre-Etienne Moreau.

Several approaches for proving the confluence and the termination of term rewriting systems have been proposed  [10] and the corresponding techniques have been implemented in tools like Aprove  [17] and TTT2  [26] . On the other hand, there are relatively few works on the study of these properties in the context of strategic rewriting and the corresponding results were generally obtained for some specific strategies and not within a generic framework. It would thus be interesting to reformulate these notions in the general formalism we have previously proposed  [15] and to establish confluence and termination conditions similar to the ones used in standard rewriting.

We have first focused on the termination property and we targeted the rewriting strategies of the Tom language. We propose a direct approach which consists in translating Tom strategies into a rewriting system which is not guided by a given evaluation strategy and we show that our systematic transformation preserves the termination. This allowed us to take advantage of the termination proof techniques available for standard rewriting and in particular to use existing termination tools (such as Aprove and TTT2) to prove the termination of strategic rewriting systems. The efficiency and scalability of these latter tools has a direct impact on the performances of our approach especially for complex strategies for which an important number of rewrite rules could be generated. We have nevertheless proposed a meta-level implementation of the automatic transformation which improves significantly the performances of the approach. The corresponding tool is available at http://gforge.inria.fr/projects/tom .