International Workshop on Aliasing, Confinement and Ownership in Object-Oriented Programming
Information and Computation
A theorem prover for Boolean BI
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Proof search for propositional abstract separation logics via labelled sequents
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
A proof system for separation logic with magic wand
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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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.