Modeling Pointer Redirection as Cyclic Term-graph Rewriting

Abstract

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 ← K → 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.

A Heterogeneous Pushout Approach to Term-Graph Transformation

“…As for σ, it is useful only when one needs to clone some parts of L. We defined rewrite steps as pushouts in an appropriate category as shown in section 4. The proposed rewrite systems offer the possibility to transform cyclic termgraphs either by performing local edge redirections or global edge redirections, as defined in [5] following a DPO approach, but provides also new features not present in [5] such as cloning or deletion of nodes.…”

On Term-Graph Rewrite Strategies

“…One of the main advantages of the class of term-graph rewrite systems described above (see also [8] for a definition of the same class following the categorical doublepush out approach) is the ability to define in a natural way, rule-based programs with good space and/or time complexities, thanks to pointer redirection capabilities. Unfortunately, the expressiveness of this class has a cost : unlike term rewrite system, the property of confluence is no more ensured for orthogonal tGRSs.…”

“…Our rules are close to those used in the language Lean [6] augmented by local redirection of pointers. The categorical definition of tGRSs following the double-pushout approach can be found in [8].…”

“…They also allow one to go beyond the processing of first-order terms by handling efficiently real-world data-structures represented as cyclic graphs such as doubly-linked lists or circular lists, e.g. [8].…”

Adjunction for Garbage Collection with Application to Graph Rewriting

“…In these frameworks a rewrite step is defined as a span L ← K → R where L, K and R are graphs and the arrows represent graph homomorphisms. Let us consider, for instance, the category of graphs defined in [6] (this category is similar to the category Gr of section 3.1 except that graphs are not rooted).…”