Cyclic proofs of program termination in separation logic

Article


Brotherston, J., Bornat, R. and Calcagno, C. 2008. Cyclic proofs of program termination in separation logic. ACM SIGPLAN Notices - POPL '08. 43 (1), pp. 101-112. https://doi.org/10.1145/1328897.1328453
TypeArticle
TitleCyclic proofs of program termination in separation logic
AuthorsBrotherston, J., Bornat, R. and Calcagno, C.
Abstract

We propose a novel approach to proving the termination of heap-manipulating programs, which combines separation logic with cyclic proof within a Hoare-style proof system.Judgements in this system express (guaranteed) termination of the program when started from a given line in the program and in a state satisfying a given precondition, which is expressed as a formula of separation logic. The proof rules of our system are of two types: logical rules that operate on preconditions; and symbolic execution rules that capture the effect of executing program commands.
Our logical preconditions employ inductively defined predicates to describe heap properties, and proofs in our system are cyclic proofs: cyclic derivations in which some inductive predicate is unfolded infinitely often along every infinite path, thus allowing us to discard all infinite paths in the proof by an infinite descent argument. Moreover, the use of this soundness condition enables us to avoid the explicit construction and use of ranking functions for termination. We also give a completeness result for our system, which is relative in that it relies upon completeness of a proof system for logical implications in separation logic. We give examples illustrating our approach, including one example for which thecorresponding ranking function is non-obvious: termination of the classical algorithm for in-place reversal of a (possibly cyclic) linked list.

Research GroupFoundations of Computing group
PublisherAssociation for Computing Machinery (ACM)
JournalACM SIGPLAN Notices - POPL '08
ISSN0362-1340
Publication process dates
Deposited03 Jul 2013
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.1145/1328897.1328453
LanguageEnglish
Permalink -

https://repository.mdx.ac.uk/item/8429x

  • 22
    total views
  • 0
    total downloads
  • 0
    views this month
  • 0
    downloads this month

Export as

Related outputs

Describing and simulating concurrent quantum systems
Bornat, R., Boender, J., Kammueller, F., Poly, G. and Nagarajan, R. 2020. Describing and simulating concurrent quantum systems. Biere, A. and Parker, D. (ed.) International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 20). Dublin 27 - 30 Apr 2020 Springer. pp. 271-277 https://doi.org/10.1007/978-3-030-45237-7_16
New lace and arsenic: adventures in weak memory with a program logic (v2)
Bornat, R., Alglave, J. and Parkinson, M. 2016. New lace and arsenic: adventures in weak memory with a program logic (v2). arXiv.org arXiv. https://doi.org/10.48550/arXiv.1512.01416
Towards automatic stability analysis for rely-guarantee proofs
Amjad, H. and Bornat, R. 2009. Towards automatic stability analysis for rely-guarantee proofs. in: Jones, N. and Müller-Olm, M. (ed.) Verification, model checking, and abstract interpretation: 10th International Conference, VMCAI 2009, Savannah, GA, USA, January 18-20, 2009. Proceedings Springer.
Separation logic and concurrency
Bornat, R. 2010. Separation logic and concurrency. in: Boca, P., Bowen, J. and Siddiqi, J. (ed.) Formal Methods: State of the Art and New Directions London Springer Verlag. pp. 217-248
Inter-process buffers in separation logic with rely-guarantee
Bornat, R. and Amjad, H. 2010. Inter-process buffers in separation logic with rely-guarantee. Formal Aspects of Computing. 22 (6), pp. 735-772. https://doi.org/10.1007/s00165-009-0141-8
Explanation of two non-blocking shared-variable communication algorithms
Bornat, R. and Amjad, H. 2011. Explanation of two non-blocking shared-variable communication algorithms. Formal Aspects of Computing. https://doi.org/10.1007/s00165-011-0213-4
Variables as resource in Hoare logic.
Bornat, R., Calcagno, C. and Parkinson, M. 2006. Variables as resource in Hoare logic. in: 21st Annual IEEE Symposium on Logic in Computer Science (LICS 2006), Seattle, Washington. Proceedings. IEEE Computer Society. pp. 137-146
Variables as resources in separation logic.
Bornat, R., Calcagno, C. and Yang, H. 2006. Variables as resources in separation logic. 21st Annual Conference on Mathematical Foundations of Programming Semantics (MFPS XXI), Birmingham, UK. Proceedings in Electronic Notes in Theoretical Computer Science. Elsevier B.V.. 155, pp. 247-276. https://doi.org/10.1016/j.entcs.2005.11.059
Modular verification of a non-blocking stack.
Bornat, R., Parkinson, M. and O'Hearn, P. 2007. Modular verification of a non-blocking stack. 34th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL '07), Nice, France. Proceedings.. https://doi.org/10.1145/1190216.1190261
Permission accounting in separation logic.
Bornat, R., Calcagno, C., Parkinson, M. and O'Hearn, P. 2005. Permission accounting in separation logic. 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL '05), Long Beach, California, USA. Proceedings. https://doi.org/10.1145/1047659.1040327