Abstract
Existing approaches to temporal verification have either sacrificed compositionality in favor of achieving automation or vice-versa. To exploit the best of both worlds, we present a new solution to ensure temporal properties via a Hoare-style verifier and a term rewriting system (T.r.s) on Integrated Dependent Effects. The first contribution is a novel effects logic capable of integrating value-dependent finite and infinite traces into a single disjunctive form, resulting in more concise and expressive specifications. As a second contribution, by avoiding the complex translation into automata, our purely algebraic T.r.s efficiently checks the language inclusion, relying on both inductive and coinductive definitions. We demonstrate the feasibility of our method using a prototype system and a number of case studies. Our experimental results show that our implementation outperforms the automata-based model checker PAT by 31.7% of the average computation time.
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
Notes
- 1.
If the event sequence is possibly empty, i.e. contains
, we call it nullable, formally defined in Definition 1. - 2.
We check the inclusion between the reversed current effects and precondition effects, meaning that, before calling a method, its required effects has just happened.
- 3.
Â
only needs to capture the effects from the current method body, excluding the history effects specified in
. - 4.
As the implementations according to basic regular expressions can be found in prior work [12]. Here, we focus on presenting the definitions and how do we deal with dependent values in the effects, as the key novelties of this work.
- 5.
The proof obligations are discharged using the Z3 SMT prover, while deciding the nullability of effects constructed by symbolic terms, represented by
. - 6.
A residue refers to the remaining event sequences from antecedent after matching up with the consequent. An inclusion with no residue means the antecedent completely/exactly matches with the consequent.
, we call it nullable, formally defined in Definition 
only needs to capture the effects from the current method body, excluding the history effects specified in
.
.References
Arduino. https://create.arduino.cc/projecthub/projects/tags/control
Online demo platform. http://loris-5.d2.comp.nus.edu.sg/EffectNew/index.html?ex=send_valid&type=c&options=sess
Almeida, M., Moreira, N., Reis, R.: Antimirov and Mosses’s rewrite system revisited. Int. J. Found. Comput. Sci. 20(04), 669–684 (2009)
Antimirov, V.: Partial derivatives of regular expressions and finite automata constructions. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 455–466. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59042-0_96
Antimirov, V.M., Mosses, P.D.: Rewriting extended regular expressions. Theor. Comput. Sci. 143(1), 51–72 (1995)
Bezem, M., Klop, J.W., de Vrijer, R.: Terese. Term Rewriting Systems. Cambridge Tracts in Theoretical Computer Science, vol. 55 (2003)
Brotherston, J.: Cyclic proofs for first-order logic with inductive definitions. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 78–92. Springer, Heidelberg (2005). https://doi.org/10.1007/11554554_8
Chin, W.-N., David, C., Nguyen, H.H., Qin, S.: Automated verification of shape, size and bag properties via user-defined predicates in separation logic. Sci. Comput. Program. 77(9), 1006–1036 (2012)
De Wulf, M., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Antichains: a new algorithm for checking universality of finite automata. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 17–30. Springer, Heidelberg (2006). https://doi.org/10.1007/11817963_5
Hofmann, M., Chen, W.: Abstract interpretation from büchi automata. In: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), p. 51. ACM (2014)
Hovland, D.: The inclusion problem for regular expressions. J. Comput. Syst. Sci. 78(6), 1795–1813 (2012)
Keil, M., Thiemann, P.: Symbolic solving of extended regular expression inequalities. arXiv preprint arXiv:1410.3227 (2014)
Koskinen, E., Terauchi, T.: Local temporal reasoning. In: Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), p. 59. ACM (2014)
Malecha, G., Morrisett, G., Wisnesky, R.: Trace-based verification of imperative programs with I/O. J. Symb. Comput. 46(2), 95–118 (2011)
Murase, A., Terauchi, T., Kobayashi, N., Sato, R., Unno, H.: Temporal verification of higher-order functional programs. In: ACM SIGPLAN Notices, vol. 51, p. 57–68. ACM (2016)
Nakata, K., Uustalu, T.: A Hoare logic for the coinductive trace-based big-step semantics of while. In: Gordon, A.D. (ed.) ESOP 2010. LNCS, vol. 6012, pp. 488–506. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-11957-6_26
Nanjo, Y., Unno, H., Koskinen, E., Terauchi, T.: A fixpoint logic and dependent effects for temporal property verification. In: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, pp. 759–768. ACM (2018)
Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: towards flexible verification under fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709–714. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02658-4_59
Acknowledgement
This work is supported by the Academic Research Fund (AcRF) Tier-1 NUS research project R-252-000-A63-114.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Song, Y., Chin, WN. (2020). Automated Temporal Verification of Integrated Dependent Effects. In: Lin, SW., Hou, Z., Mahony, B. (eds) Formal Methods and Software Engineering. ICFEM 2020. Lecture Notes in Computer Science(), vol 12531. Springer, Cham. https://doi.org/10.1007/978-3-030-63406-3_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-63406-3_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-63405-6
Online ISBN: 978-3-030-63406-3
eBook Packages: Computer ScienceComputer Science (R0)