Abstract
Showing that concurrent threads operate on separate portions of their shared state is a way of establishing non-interference. Furthermore, in many useful programs, ownership of parts of the state are exchanged dynamically. Reasoning about separation and ownership of heap-based variables is often conducted using some form of separation logic. This paper examines the issue of separation and investigates the use of abstraction to specify and to reason about separation in program design. Two case studies demonstrate that using separation as an abstraction is a potentially useful approach.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
Notes
- 1.
VDM notation is used throughout the current paper; see [Jon90] for details.
- 2.
VDM aficionados would normally employ a ‘record’ construct here but using a pair and selecting by index reduces the potentially unfamiliar notation in this paper.
- 3.
Of course, Srep and start are mutually recursive but it is clearer to separate their descriptions.
- 4.
So far, separation is a convenience that ensures transferring cells from one sequence to the other provides unused pointers; the restriction plays a bigger role in Sect. 2.4.
- 5.
The conference version of this paper omits all detailed proofs which are, anyway, mostly routine — they can be found in the Technical Report [JY15, Appendix].
- 6.
The fact that ‘cells’ contain both data and pointer (rather than them being in locations n and \(n+1\) as in Fig. 1) is incidental — think of car/cdr in Lisp. Furthermore, the decision to use Ptr rather than \({\mathbb {N}}\) is deliberate.
- 7.
A suitable formal proof rule is given in Sect. 4.
References
Barringer, H., Cheng, J.H., Jones, C.B.: A logic covering undefinedness in program proofs. Acta Informatica 21(3), 251–269 (1984)
Bornat, R.: Proving pointer programs in Hoare logic. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 102–126. Springer, Heidelberg (2000)
Boyland, J.: Checking interference with fractional permissions. In: Cousot, R. (ed.) SAS 2003. LNCS, vol. 2694, pp. 55–72. Springer, Heidelberg (2003)
Hayes, I.J., Jones, C.B., Colvin, R.J.: Laws and semantics for rely-guarantee refinement. Technical report CS-TR-1425, Newcastle University, July 2014
Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576–580, 583 (1969)
Hoare, C.A.R.: Towards a theory of parallel programming. In: Operating System Techniques, pp. 61–71. Academic Press (1972)
Jones, C.B., Hayes, I.J., Colvin, R.J.: Balancing expressiveness in formal approaches to concurrency. Formal Aspects Comput. 27, 475–497 (2015)
Jones, C.B.: Development methods for computer programs including a notion of interference. Ph.D. thesis, Oxford University, June 1981. Printed as: Programming Research Group, Technical Monograph 25
Jones, C.B.: Specification and design of (parallel) programs. In: Proceedings of IFIP 1983, pp. 321–332. North-Holland (1983)
Jones, C.B.: Tentative steps toward a development method for interfering programs. ACM Trans. Program. Lang. Syst. 5(4), 596–619 (1983)
Jones, C.B.: Systematic Software Development using VDM, 2nd edn. Prentice Hall International, Upper Saddle River (1990)
Jones, C.B.: Splitting atoms safely. Theor. Comput. Sci. 375(1–3), 109–119 (2007)
Jones, C.B., Yatapanage, N.: Reasoning about separation using abstraction and reification (including proofs). Technical report CS-TR-1472, Newcastle University, June 2015
Kassios, I.T.: The dynamic frames theory. Formal Asp. Comput. 23(3), 267–288 (2011)
O’Hearn, P.W.: Resources, concurrency and local reasoning. Theor. Comput. Sci. 375(1–3), 271–307 (2007)
Parkinson, M.: The next 700 separation logics. In: Leavens, G.T., O’Hearn, P., Rajamani, S.K. (eds.) VSTTE 2010. LNCS, vol. 6217, pp. 169–182. Springer, Heidelberg (2010)
Reynolds, J.C.: Separation logic: a logic for shared mutable data structures. In: Proceedings of 17th LICS, pp. 55–74. IEEE (2002)
Vafeiadis, V.: Modular fine-grained concurrency verification. Ph.D. thesis, University of Cambridge (2007)
Vafeiadis, V., Parkinson, M.: A marriage of rely/guarantee and separation logic. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 256–271. Springer, Heidelberg (2007)
Wirth, N.: Algorithms + Data Structures = Programs. Prentice-Hall, Upper Saddle River (1976)
Acknowledgements
The research reported here is supported by (UK) EPSRC ‘Taming Concurrency’ and ‘TrAmS-2’ research grants. The authors would like to thank Andrius Velykis and our colleagues Ian Hayes, Larissa Meinicke and Kim Solin from the (Australian) ARC-funded project ‘Understanding concurrent programs using rely-guarantee thinking’ for their invaluable feedback.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Jones, C.B., Yatapanage, N. (2015). Reasoning about Separation Using Abstraction and Reification. In: Calinescu, R., Rumpe, B. (eds) Software Engineering and Formal Methods. SEFM 2015. Lecture Notes in Computer Science(), vol 9276. Springer, Cham. https://doi.org/10.1007/978-3-319-22969-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-22969-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-22968-3
Online ISBN: 978-3-319-22969-0
eBook Packages: Computer ScienceComputer Science (R0)