Modeling Pointer Redirection as Cyclic Term-graph Rewriting

We tackle the problem of data-structure rewriting including global and local pointer redirections. Eachbasic rewrite step may perform three kinds of actions: (i) Local redirection, the aim of which is to redirectspecific pointers determined by means of a pattern ; (ii) Replacement, that may add new information todata-structures ; (iii) Global redirection, which is aimed at redirecting all pointers targeting a node towardsanother one. We define a new framework, following the double-pushout approach, where graph rewrite rulesmay mix these three kinds of actions in a row. We define first the category of graphs we consider and thenwe define rewrite rules as 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, pushouts do not always exist andcomplement pushouts, when they exist, are not unique. Despite these concerns, our definition of rewritingsteps is such that a rewrite rule can always be fired, once a matching is found.