Data-Structure Rewriting

TL;DR

This paper introduces a formal framework for data-structure rewriting using graph transformations, defining local and global redirection steps with a focus on pointer redirection and pattern-based modifications.

Contribution

It develops a novel approach to data-structure rewriting based on the double pushout method, accommodating non-unique inverse pushouts and ensuring rule applicability.

Findings

Defines a category of graphs suitable for rewriting

Introduces local and global redirection steps for pointers

Ensures rewrite rules can always be applied once matched

Abstract

We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a pattern, as well as adding new information to an existing data ; and (ii) Global Redirection steps which are aimed to redirect all pointers targeting a node towards another one. We define these two rewriting steps following the double pushout approach. We define first the category of graphs we consider and then define rewrite rules as pairs of graph homomorphisms of the form "L <- K ->R". Unfortunately, inverse pushouts (complement pushouts) are not unique in our setting and pushouts do not always exist. Therefore, we define rewriting steps so that a rewrite rule can always be performed once a matching is found.