Modeling Pointer Redirection as Cyclic Term - graph Rewriting 1 Dominique Duval 2 Rachid Echahed 3 Frédéric Prost

We tackle the problem of data-structure rewriting including global and local pointerredirections. Each basic rewrite step may perform three kinds of actions: (i) Localredirection, the aim of which is to redirect specific pointers determined by meansof a pattern ; (ii) Replacement, that may add new information to data-structures ;(iii) Global redirection, which is aimed at redirecting all pointers targeting a nodetowards another one. We define a new framework, following the double-pushoutapproach, where graph rewrite rules may mix these three kinds of actions in a row.We define first the category of graphs we consider and then we define rewrite rulesas pairs of graph homomorphisms of the form L ← K → R. In our setting, graphK is not arbitrary, it is used to encode pointer redirection. Furthermore, pushoutsdo not always exist and complement pushouts, when they exist, are not unique.Despite these concerns, our definition of rewriting steps is such that a rewrite rulecan always be fired, once a matching is found.