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Journal of Logic and Computation Advance Access published online on January 8, 2009
Journal of Logic and Computation, doi:10.1093/logcom/exn066
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© The Author, 2008. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Original Papers

Tableaux and Resource Graphs for Separation Logic

Didier Galmiche and Daniel Méry

LORIA - Université Henri Poincaré, Campus Scientifique, BP 239, Vandœuvre-lès-Nancy, France.
E-mail: galmiche{at}loria.fr

Received 31 December 2007.


  Abstract

Separation logic (SL) is often presented as an assertion language for reasoning about mutable data structures. As recent results about verification in SL have mainly been achieved from a model-checking point of view, our aim in this article is to study SL from a complementary proof-theoretic perspective in order to provide results about proof search in SL. We begin our study with a fragment of SL, denoted SLP, where first-order quantifiers, variables and equality are removed. We first define specific structures, called resource graphs, that capture SLP models by considering heaps as resources via a labelling process. We then provide a tableau calculus that allows us to build such resource graphs from which either proofs, or countermodels can be generated. We finally prove soundess, completeness and termination of our tableau calculus before discussing extensions to various fragments of SL (including full SL) and the related decidability issues.

Keywords: Separation logic; theorem proving; tableaux; countermodels


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