Skip to main content
SpringerLink
Log in

Lightweight Nontermination Inference with CHCs

  • Conference paper
  • First Online:
Book cover Software Engineering and Formal Methods (SEFM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13085))

Included in the following conference series:

Abstract

Non-termination is an unwanted program property (considered a bug) for some software systems, and a safety property for other systems. In either case, automated discovery of preconditions for non-termination is of interest. We introduce NtHorn, a fast lightweight non-termination analyser, able to deduce non-trivial sufficient conditions for non-termination. Using Constrained Horn Clauses (CHCs) as a vehicle, we show how established techniques for CHC program transformation and abstract interpretation can be exploited for the purpose of non-termination analysis. NtHorn is comparable in power to the state-of-the-art non-termination analysis tools, as measured on standard competition benchmark suites (consisting of integer manipulating programs), while typically solving problems an order of magnitude faster.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bagnara, R., Hill, P.M., Zaffanella, E.: The Parma Polyhedra Library. Sci. Comput. Program. 72(1–2), 3–21 (2008). https://doi.org/10.1016/j.scico.2007.08.001

    Article  MATH  Google Scholar 

  2. Bakhirkin, A.: Recurrent sets for non-termination and safety of programs. Ph.D. thesis, University of Leicester (2016)

    Google Scholar 

  3. Bakhirkin, A., Monniaux, D.: Combining forward and backward abstract interpretation of Horn clauses. In: Ranzato, F. (ed.) SAS 2017. LNCS, vol. 10422, pp. 23–45. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-66706-5_2

    Chapter  Google Scholar 

  4. Ben-Amram, A.M., Doménech, J.J., Genaim, S.: Multiphase-linear ranking functions and their relation to recurrent sets. In: Chang, B.-Y.E. (ed.) SAS 2019. LNCS, vol. 11822, pp. 459–480. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-32304-2_22

    Chapter  Google Scholar 

  5. Ben-Amram, A.M., Genaim, S.: Ranking functions for linear-constraint loops. J. ACM 61(4), 26:1–26:55 (2014). https://doi.org/10.1145/2629488

  6. Borralleras, C., Brockschmidt, M., Larraz, D., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: Proving termination through conditional termination. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 99–117. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_6

    Chapter  Google Scholar 

  7. Brockschmidt, M., Ströder, T., Otto, C., Giesl, J.: Automated detection of non-termination and NullPointerExceptions for Java Bytecode. In: Beckert, B., Damiani, F., Gurov, D. (eds.) FoVeOOS 2011. LNCS, vol. 7421, pp. 123–141. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31762-0_9

    Chapter  Google Scholar 

  8. Bueno, F., Cabeza, D., Carro, M., Hermenegildo, M., López-García, P., Puebla, G.: The Ciao Prolog system: reference manual. Technical Report CLIP 3/97.1, UPM (1997). http://www.clip.dia.fi.upm.es/

  9. Chatterjee, K., Goharshady, E.K., Novotný, P., Žikelić, Đ.: Proving non-termination by program reversal. In: Proceedings of PLDI 2021, pp. 1033–1048. ACM (2021)

    Google Scholar 

  10. Chen, H.-Y., Cook, B., Fuhs, C., Nimkar, K., O’Hearn, P.: Proving nontermination via safety. In: Ábrahám, E., Havelund, K. (eds.) TACAS 2014. LNCS, vol. 8413, pp. 156–171. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54862-8_11

    Chapter  Google Scholar 

  11. Cook, B., Fuhs, C., Nimkar, K., O’Hearn, P.W.: Disproving termination with overapproximation. In: Proceedings of FMCAD 2014, pp. 67–74. IEEE (2014). https://doi.org/10.1109/FMCAD.2014.6987597

  12. Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: Proceedings of POPL 1977, pp. 238–252. ACM (1977). https://doi.org/10.1007/978-3-642-35873-9_10

  13. Cousot, P., Cousot, R., Fähndrich, M., Logozzo, F.: Automatic inference of necessary preconditions. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 128–148. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35873-9_10

    Chapter  Google Scholar 

  14. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of POPL 1978, pp 84–96. ACM (1978). https://doi.org/10.1145/512760.512770

  15. De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Program verification via iterated specialization. Sci. Comput. Program. 95, 149–175 (2014). https://doi.org/10.1016/j.scico.2014.05.017

    Article  Google Scholar 

  16. De Angelis, E., Fioravanti, F., Pettorossi, A., Proietti, M.: Semantics-based generation of verification conditions via program specialization. Sci. Comput. Program. 147, 78–108 (2017). https://doi.org/10.1016/j.scico.2016.11.002

    Article  Google Scholar 

  17. Doménech, J.J., Gallagher, J.P., Genaim, S.: Control-flow refinement by partial evaluation, and its application to termination and cost analysis. Theory Pract. Log. Program. 19(5–6), 990–1005 (2019). https://doi.org/10.1017/S1471068419000310

    Article  MathSciNet  MATH  Google Scholar 

  18. Dutertre, B.: Yices 2.2. In: Biere, A., Bloem, R. (eds.) Computer-Aided Verification, volume 8559 of LNCS, pp. 737–744. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-41528-4

  19. Fioravanti, F., Pettorossi, A., Proietti, M.: Specialization with clause splitting for deriving deterministic constraint logic programs. In: Proceedings of IEEE Conference Systems, Man and Cybernetics. IEEE Press (2002). https://doi.org/10.1109/ICSMC.2002.1167971

  20. Gallagher, J.P.: Tutorial on specialisation of logic programs. In: PEPM’93: Proceedings of 1993 ACM SIGPLAN Symposium on Partial Evaluation and Semantics-Based Program Manipulation, pp. 88–98. ACM (1993). https://doi.org/10.1145/154630.154640

  21. Gallagher, J.P.: Polyvariant program specialisation with property-based abstraction. In: Lisitsa, A., Nemytykh, A.P. (eds.) Proceedings of Seventh International Workshop on Verification and Program Transformation, volume 299 of EPTCS, pp. 34–48 (2019). https://doi.org/10.4204/EPTCS.299.6

  22. Giesl, J., et al.: Proving termination of programs automatically with AProVE. In: Demri, S., Kapur, D., Weidenbach, C. (eds.) IJCAR 2014. LNCS (LNAI), vol. 8562, pp. 184–191. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08587-6_13

    Chapter  Google Scholar 

  23. Grebenshchikov, S., Lopes, N.P., Popeea, C., Rybalchenko, A.: Synthesizing software verifiers from proof rules. In: Vitek, J., Lin, H., Tip, F. (eds.) Proceedings of PLDI 2012, pp. 405–416. ACM (2012). https://doi.org/10.1145/2254064.2254112

  24. Gupta, A., Henzinger, T.A., Majumdar, R., Rybalchenko, A., Xu, R.: Proving non-termination. In: Proceedings of 35th ACM Symposium on Principles of Programming Languages, pp. 147–158. ACM (2008). https://doi.org/10.1145/1328438.1328459

  25. Gurfinkel, A., Kahsai, T., Komuravelli, A., Navas, J.A.: The SeaHorn verification framework. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 343–361. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21690-4_20

    Chapter  Google Scholar 

  26. Heizmann, M., Hoenicke, J., Podelski, A.: Termination analysis by learning terminating programs. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 797–813. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_53

    Chapter  Google Scholar 

  27. Kafle, B., Gallagher, J.P.: Constraint specialisation in Horn clause verification. Sci. Comput. Program. 137, 125–140 (2017). https://doi.org/10.1016/j.scico.2017.01.002

    Article  Google Scholar 

  28. Kafle, B., Gallagher, J.P., Gange, G., Schachte, P., Søndergaard, H., Stuckey, P.J.: An iterative approach to precondition inference using constrained Horn clauses. Theory Pract. Log. Program. 18, 553–570 (2018). https://doi.org/10.1017/S1471068418000091

    Article  MathSciNet  MATH  Google Scholar 

  29. Kafle, B., Gallagher, J.P., Morales, J.F.: Rahft: a tool for verifying Horn clauses using abstract interpretation and finite tree automata. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 261–268. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41528-4_14

    Chapter  Google Scholar 

  30. Kafle, B., Gange, G., Schachte, P., Søndergaard, H., Stuckey, P.J.: Transformation-enabled precondition inference. Theory Pract. Log. Program. 21(6) (2021)

    Google Scholar 

  31. Larraz, D., Nimkar, K., Oliveras, A., Rodríguez-Carbonell, E., Rubio, A.: Proving non-termination using max-SMT. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 779–796. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_52

    Chapter  Google Scholar 

  32. Le, T.C., Qin, S., Chin, W.-N.: Termination and non-termination specification inference. In: Grove, D., Blackburn, S.M. (eds.) Proceedings of PLDI 2015, pp. 489–498. ACM (2015). https://doi.org/10.1145/2737924.2737993

  33. Leike, J., Heizmann, M.: Geometric nontermination arguments. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 266–283. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_16

    Chapter  Google Scholar 

  34. Miné, A.: Inferring sufficient conditions with backward polyhedral under-approximations. Electron. Notes Theor. Comp. Sci. 287, 89–100 (2012). https://doi.org/10.1016/j.entcs.2012.09.009

    Article  MATH  Google Scholar 

  35. Moy, Y.: Sufficient preconditions for modular assertion checking. In: Logozzo, F., Peled, D.A., Zuck, L.D. (eds.) VMCAI 2008. LNCS, vol. 4905, pp. 188–202. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78163-9_18

    Chapter  MATH  Google Scholar 

  36. Peralta, J.C., Gallagher, J.P., Sağlam, H.: Analysis of imperative programs through analysis of constraint logic programs. In: Levi, G. (ed.) SAS 1998. LNCS, vol. 1503, pp. 246–261. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49727-7_15

    Chapter  Google Scholar 

  37. Seghir, M.N., Schrammel, P.: Necessary and sufficient preconditions via eager abstraction. In: Garrigue, J. (ed.) APLAS 2014. LNCS, vol. 8858, pp. 236–254. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12736-1_13

    Chapter  MATH  Google Scholar 

  38. Termination competition 2020: C Integer. https://termcomp.github.io/Y2020/job_41519.html. Accessed 1 June 2021

  39. Velroyen, H., Rümmer, P.: Non-termination checking for imperative programs. In: Beckert, B., Hähnle, R. (eds.) TAP 2008. LNCS, vol. 4966, pp. 154–170. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79124-9_11

    Chapter  Google Scholar 

Download references

Acknowledgements

We thank the three anonymous reviewers for their careful reading of an earlier version of the paper, and their constructive suggestions for how to improve it. Bishoksan Kafle has been partially funded by the Spanish Ministry of Research, Science and Innovation, grant MICINN PID2019-108528RB-C21 ProCode and Madrid P2018/TCS-4339 BLOQUES-CM.

Author information

Authors and Affiliations

  1. IMDEA Software Institute, Madrid, Spain

    Bishoksan Kafle

  2. Faculty of IT, Monash University, Melbourne, Australia

    Graeme Gange & Peter J. Stuckey

  3. Computing and Information Systems, The University of Melbourne, Melbourne, Australia

    Peter Schachte & Harald Søndergaard

Authors
  1. Bishoksan Kafle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Graeme Gange
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Schachte
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Harald Søndergaard
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peter J. Stuckey
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of York, York, UK

    Radu Calinescu

  2. Carnegie Mellon University, Moffett Field, CA, USA

    Corina S. Păsăreanu

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kafle, B., Gange, G., Schachte, P., Søndergaard, H., Stuckey, P.J. (2021). Lightweight Nontermination Inference with CHCs. In: Calinescu, R., Păsăreanu, C.S. (eds) Software Engineering and Formal Methods. SEFM 2021. Lecture Notes in Computer Science(), vol 13085. Springer, Cham. https://doi.org/10.1007/978-3-030-92124-8_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92124-8_22

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92123-1

  • Online ISBN: 978-3-030-92124-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation