Modeling Pointer Redirection as Cyclic Term-graph Rewriting

We tackle the problem of data-structure rewriting including global and local pointer redirections. Each basic rewrite step may perform three kinds of actions: (i) Local redirection, the aim of which is to redirect specific pointers determined by means of a pattern; (ii) Replacement, that may add new information to data-structures; (iii) Global redirection, which is aimed at redirecting all pointers targeting a node towards another one. We define a new framework, following the double-pushout approach, 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 rules as pairs of graph homomorphisms of the form L R. In our setting, graph K is not arbitrary, it is used to encode pointer redirection. Furthermore, pushouts do 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 rule can always be fired, once a matching is found.