Skip to main content
View expanded cover

International Conference on Intelligent Computer Mathematics

CICM 2018: Intelligent Computer Mathematics pp 111–117Cite as

Aligator.jl – A Julia Package for Loop Invariant Generation

Part of the Lecture Notes in Computer Science book series (LNAI,volume 11006)

Abstract

We describe the Aligator.jl software package for automatically generating all polynomial invariants of the rich class of extended P-solvable loops with nested conditionals. Aligator.jl is written in the programming language Julia and is open-source. Aligator.jl transforms program loops into a system of algebraic recurrences and implements techniques from symbolic computation to solve recurrences, derive closed form solutions of loop variables and infer the ideal of polynomial invariants by variable elimination based on Gröbner basis computation.

All authors are supported by the ERC Starting Grant 2014 SYMCAR 639270. We also acknowledge funding from the Wallenberg Academy Fellowship 2014 TheProSE, the Swedish VR grant GenPro D0497701, and the Austrian FWF research projects RiSE S11409-N23 and W1255-N23. Maximilian Jaroschek is also supported by the FWF project Y464-N18.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-96812-4_10
  • Chapter length: 7 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-96812-4
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.

References

  1. Decker, W., Greuel, G.M., Pfister, G., Schönemann, H.: Singular 4-1-0—a computer algebra system for polynomial computations (2016). http://www.singular.uni-kl.de

  2. Humenberger, A., Jaroschek, M., Kovács, L.: Invariant generation for multi-path loops with polynomial assignments. In: Dillig, I., Palsberg, J. (eds.) VMCAI. LNCS, vol. 10747, pp. 226–246. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-73721-8_11

    CrossRef  Google Scholar 

  3. Julia. https://julialang.org/

  4. Kovács, L.: Aligator: a mathematica package for invariant generation (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 275–282. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-71070-7_22

    CrossRef  Google Scholar 

  5. Meurer, A., Smith, C.P., Paprocki, M., Čertík, O., Kirpichev, S.B., Rocklin, M., Kumar, A., Ivanov, S., Moore, J.K., Singh, S., Rathnayake, T., Vig, S., Granger, B.E., Muller, R.P., Bonazzi, F., Gupta, H., Vats, S., Johansson, F., Pedregosa, F., Curry, M.J., Terrel, A.R., Roučka, S., Saboo, A., Fernando, I., Kulal, S., Cimrman, R., Scopatz, A.: SymPy: symbolic computing in Python. PeerJ Comput. Sci. 3, e103 (2017). https://doi.org/10.7717/peerj-cs.103

    CrossRef  Google Scholar 

  6. Rodríguez-Carbonell, E., Kapur, D.: Generating all polynomial invariants in simple loops. J. Symb. Comput. 42(4), 443–476 (2007). https://doi.org/10.1016/j.jsc.2007.01.002

    MathSciNet  CrossRef  MATH  Google Scholar 

  7. SageMath. http://www.sagemath.org/

  8. Wolfram, S.: An Elementary Introduction to the Wolfram Language. Wolfram Media Inc. (2017). https://www.wolfram.com/language/elementary-introduction/2nd-ed/

Download references

Author information

Authors and Affiliations

  1. TU Wien, Vienna, Austria

    Andreas Humenberger, Maximilian Jaroschek & Laura Kovács

  2. JKU Linz, Linz, Austria

    Maximilian Jaroschek

  3. Chalmers, Gothenburg, Sweden

    Laura Kovács

Authors
  1. Andreas Humenberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maximilian Jaroschek
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Laura Kovács
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Humenberger .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Bayern, Germany

    Florian Rabe

  2. Department of Computing and Software, McMaster University, Hamilton, Ontario, Canada

    William M. Farmer

  3. University of Cambridge, Cambridge, United Kingdom

    Grant O. Passmore

  4. Department of Computer Science, The George Washington University, Washington, District of Columbia, USA

    Abdou Youssef

Rights and permissions

Reprints and Permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Humenberger, A., Jaroschek, M., Kovács, L. (2018). Aligator.jl – A Julia Package for Loop Invariant Generation. In: Rabe, F., Farmer, W., Passmore, G., Youssef, A. (eds) Intelligent Computer Mathematics. CICM 2018. Lecture Notes in Computer Science(), vol 11006. Springer, Cham. https://doi.org/10.1007/978-3-319-96812-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-96812-4_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96811-7

  • Online ISBN: 978-3-319-96812-4

  • eBook Packages: Computer ScienceComputer Science (R0)