Internal Strategies in a Rewriting Implementation of Tile Systems

Abstract

Tile logic extends rewriting logic, taking into account rewriting with side-effects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation efforts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. The resulting implementation requires a meta-layer to control the rewritings, so that only tile proofs are accepted. However, by exploiting the reflective capabilities of the Maude language, such meta-layer can be specified as a kernel of internal strategies. It turns out that the required strategies are very general and can be reformulated in terms of search algorithms for non-confluent systems equipped with a notion of success. We formalize such strategies, giving their detailed description in Maude, and showing their application to modeling uniform tile systems.We would like to thank Narciso Marti-Oliet for his precious suggestions and comments on a preliminary version of this paper and Manuel Clavel for his help in the area of strategies. We also thank the anonymous referees for their careful reading and their helpful comments.