Incremental Abstract Interpretation

  • Helmut Seidl
  • Julian ErhardEmail author
  • Ralf Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12065)


Non-incremental static analysis by abstract interpretation has to be rerun every time the code to be analyzed changes. For large code bases, this incurs a significant overhead, in particular, if the individual changes to the code are small. In order to accelerate the analysis on changing code bases, incremental static analysis reuses analysis results computed for earlier versions of the source code where possible. We show that this behavior can seamlessly be achieved for the analysis of C programs if a local generic solver such as the top-down solver is used as the fixed-point engine. This solver maintains a set of stable unknowns for which fixpoint iteration has already stabilized and it recursively destabilizes dependent unknowns on change. We indicate how this machinery can be applied to selectively invalidate results for those unknowns that may be directly or indirectly affected by program changes. We also explain the technical difficulties faced when realizing this basic idea within an analysis infra-structure such as Goblint. We also report the results of a preliminary experimental evaluation concerning the impact of incrementalization on analysis performance.


  1. 1.
    Amato, G., Scozzari, F., Seidl, H., Apinis, K., Vojdani, V.: Efficiently intertwining widening and narrowing. Sci. Comput. Program. 120, 1–24 (2016). Scholar
  2. 2.
    Apinis, K., Seidl, H., Vojdani, V.: Side-effecting constraint systems: a swiss army knife for program analysis. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 157–172. Springer, Heidelberg (2012). Scholar
  3. 3.
    Apinis, K., Seidl, H., Vojdani, V.: Enhancing top-down solving with widening and narrowing. In: Probst, C.W., Hankin, C., Hansen, R.R. (eds.) Semantics, Logics, and Calculi. LNCS, vol. 9560, pp. 272–288. Springer, Cham (2016). Scholar
  4. 4.
    Arzt, S., Bodden, E.: Reviser: efficiently updating IDE-/IFDS-based data-flow analyses in response to incremental program changes. In: Jalote, P., Briand, L.C., van der Hoek, A. (eds.) 36th International Conference on Software Engineering, ICSE 2014, Hyderabad, India, 31 May –07 June 2014, pp. 288–298. ACM (2014).
  5. 5.
    Bolduc, C.: Lessons learned: using a static analysis tool within a continuous integration system. In: 2016 IEEE International Symposium on Software Reliability Engineering Workshops (ISSREW), pp. 37–40. IEEE (2016)Google Scholar
  6. 6.
    Cousot, P., Cousot, R.: Static determination of dynamic properties of recursive programs. In: Neuhold, E. (ed.) Formal Descriptions of Programming Concepts, pp. 237–277. North-Holland Publishing Company, Amsterdam (1977)zbMATHGoogle Scholar
  7. 7.
    Cousot, P., Cousot, R.: Comparing the Galois connection and widening/narrowing approaches to abstract interpretation. In: Bruynooghe, M., Wirsing, M. (eds.) PLILP 1992. LNCS, vol. 631, pp. 269–295. Springer, Heidelberg (1992). Scholar
  8. 8.
    Cousot, P., Cousot, R.: Modular static program analysis. In: Horspool, R.N. (ed.) CC 2002. LNCS, vol. 2304, pp. 159–179. Springer, Heidelberg (2002). Scholar
  9. 9.
    Emanuelsson, P., Nilsson, U.: A comparative study of industrial static analysis tools. Electron. Notes Theor. Comput. Sci. 217, 5–21 (2008)CrossRefGoogle Scholar
  10. 10.
    Frielinghaus, S.S., Seidl, H., Vogler, R.: Enforcing termination of interprocedural analysis. Formal Methods Syst. Design 53(2), 313–338 (2018). Scholar
  11. 11.
    Garcia-Contreras, I., Morales, J.F., Hermenegildo, M.V.: Towards incremental and modular context-sensitive analysis. In: Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018). OpenAccess Series in Informatics (OASIcs). Dagstuhl Press, July 2018. (Extended Abstract)Google Scholar
  12. 12.
    Hermenegildo, M.V., Puebla, G., Marriott, K., Stuckey, P.: Incremental analysis of constraint logic programs. ACM Trans. Program. Lang. Syst. 22(2), 187–223 (2000)CrossRefGoogle Scholar
  13. 13.
    Jones, N.D., Muchnick, S.S.: A flexible approach to interprocedural data flow analysis and programs with recursive data structures. In: DeMillo, R.A. (ed.) Conference Record of the Ninth Annual ACM Symposium on Principles of Programming Languages, Albuquerque, New Mexico, USA, January 1982, pp. 66–74. ACM Press (1982).
  14. 14.
    Muthukumar, K., Hermenegildo, M.: Deriving a fixpoint computation algorithm for top-down abstract interpretation of logic programs. Technical report ACT-DC-153-90, Microelectronics and Computer Technology Corporation (MCC), Austin, TX, April 1990Google Scholar
  15. 15.
    Karbyshev, A.: Monadic parametricity of second-order functionals. Ph.D. thesis, Technical University Munich (2013).
  16. 16.
    Le Charlier, B., Van Hentenryck, P.: A universal top-down fixpoint algorithm. Technical report CS-92-25. CS Department, Brown University (1992)Google Scholar
  17. 17.
    Liqat, U., et al.: Energy consumption analysis of programs based on XMOS ISA-level models. In: Gupta, G., Peña, R. (eds.) LOPSTR 2013. LNCS, vol. 8901, pp. 72–90. Springer, Cham (2014). Scholar
  18. 18.
    O’Hearn, P.W.: Continuous reasoning: scaling the impact of formal methods. In: Dawar, A., Grädel, E. (eds.) Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, 09–12 July 2018, pp. 13–25. ACM (2018).
  19. 19.
    Puebla, G., Hermenegildo, M.: Optimized algorithms for incremental analysis of logic programs. In: Cousot, R., Schmidt, D.A. (eds.) SAS 1996. LNCS, vol. 1145, pp. 270–284. Springer, Heidelberg (1996). Scholar
  20. 20.
    Ramalingam, G., Reps, T.W.: A categorized bibliography on incremental computation. In: Deusen, M.S.V., Lang, B. (eds.) Conference Record of the Twentieth Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, Charleston, South Carolina, USA, January 1993, pp. 502–510. ACM Press (1993).
  21. 21.
    Ramalingam, G., Reps, T.W.: An incremental algorithm for a generalization of the shortest-path problem. J. Algorithms 21(2), 267–305 (1996). Scholar
  22. 22.
    Reps, T.W., Horwitz, S., Sagiv, S.: Precise interprocedural dataflow analysis via graph reachability. In: Cytron, R.K., Lee, P. (eds.) Conference Record of POPL 1995: 22nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, San Francisco, California, USA, 23–25 January 1995, pp. 49–61. ACM Press (1995).
  23. 23.
    Seidl, H., Vogler, R.: Three improvements to the top-down solver. In: Sabel, D., Thiemann, P. (eds.) Proceedings of the 20th International Symposium on Principles and Practice of Declarative Programming, PPDP 2018, Frankfurt am Main, Germany, 03–05 September 2018, pp. 21:1–21:14. ACM (2018).
  24. 24.
    Sharir, M., Pnueli, A.: Two approaches to interprocedural data flow analysis. In: Muchnick, S., Jones, N. (eds.) Program Flow Analysis: Theory and Applications, pp. 189–233. Prentice-Hall, Englewood Cliffs (1981)Google Scholar
  25. 25.
    Vojdani, V., Apinis, K., Rõtov, V., Seidl, H., Vene, V., Vogler, R.: Static race detection for device drivers: the Goblint approach. In: Proceedings of the 31st IEEE/ACM International Conference on Automated Software Engineering, ASE 2016, pp. 391–402. ACM (2016).

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Technische Universität MünchenGarchingGermany

Personalised recommendations