Internal strategies in a rewriting implementation of tile systems

Tile logic extends rewriting logic, taking into account rewriting with side-eeects and rewriting synchronization. Since rewriting logic is the semantic basis of several language implementation eeorts, it is interesting to map tile logic back into rewriting logic in a conservative way, to obtain executable speciications 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 reeective capabilities of the Maude language, such meta-layer can be speciied 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-connuent 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.