A Modal Logic for Termgraph Rewriting

Ph. Balbiani; R. Echahed; A. Herzig

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arXiv · 1003.4369

A Modal Logic for Termgraph Rewriting

Ph. Balbiani·R. Echahed·A. Herzig

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Abstract

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs allow one to describe classical data-structures (possibly with pointers) such as doubly-linked lists, circular lists etc. We show how the proposed logic can faithfully describe (i) termgraphs as well as (ii) the application of a termgraph rewrite rule (i.e. matching and replacement) and (iii) the computation of normal forms with respect to a given rewrite system. We also show how the proposed logic, which is more expressive than propositional dynamic logic, can be used to specify shapes of classical data-structures (e.g. binary trees, circular lists etc.).

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Ph. Balbiani, R. Echahed, A. Herzig. 2010-03-23. A Modal Logic for Termgraph Rewriting. https://arxiv.org/abs/1003.4369

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