Model Checking Via ΓCFA

  • Matthew Might
  • Benjamin Chambers
  • Olin Shivers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4349)


We present and discuss techniques for performing and improving the model-checking of higher-order, functional programs based upon abstract interpretation [4]. We use continuation-passing-style conversion to produce an abstractable state machine, and then utilize abstract garbage collection and abstract counting [9] to indirectly prune false branches in the abstract state-to-state transition graph. In the process, we generalize abstract garbage collection to conditional garbage collection; that is, we collect values which an ordinary reaching-based collector would have deemed live when it is provable that such values will never be referenced. In addition, we enhance abstract counting, and then exploit it to more precisely evaluate conditions in the abstract.


Abstract interpretation static analysis abstract counting abstract garbage collection ΓCFA higher-order languages 


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  1. 1.
    Appel, A.W.: Compiling with Continuations. Cambridge University Press, Cambridge (1992)Google Scholar
  2. 2.
    Ball, T., Rajamani, S.K.: The SLAM project: Debugging system software via static analysis. In: Proceedings of the 29th Annual ACM SIGPLAN Conference on the Principles of Programming Languages, Portland, Oregon, pp. 1–3 (January 2002)Google Scholar
  3. 3.
    Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code. In: Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2006, Ottawa, Canada (June 2006)Google Scholar
  4. 4.
    Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: ACM SIGPLAN Symposium on Principles of Programming Languages, Los Angeles, California, vol. 4, pp. 238–252 (January 1977)Google Scholar
  5. 5.
    Cousot, P., Cousot, R.: Systematic design of program analysis frameworks. In: ACM SIGPLAN Symposium on Principles of Programming Languages, San Antonio, Texas, vol. 6, pp. 269–282 (January 1979)Google Scholar
  6. 6.
    Danvy, O.: A first-order one-pass CPS transformation. Theoretical Computer Science 308 1(3), 239–257 (2003)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Leuschel, M., Bendisposto, J.: Animating and model checking b specifications with higher-order recursive functions. In: Abrial, J.-R., Glässer, U. (eds.) Rigorous Methods for Software Construction and Analysis, no. 06191 in Dagstuhl Seminar Proceedings (2006)Google Scholar
  8. 8.
    Might, M.: Logic-flow analysis of higher-order programs. In: Proceedings of the 34th Annual ACM SIGPLAN Conference on the Principles of Programming Languages, Nice, France (January 2007)Google Scholar
  9. 9.
    Might, M., Shivers, O.: Improving Flow Analysis via ΓCFA: Abstract Garbage Collection and Counting. In: Proceedings of the 11th ACM SIGPLAN International Conference on Functional Programming, ICFP 2006, Portland, Oregon (September 2006)Google Scholar
  10. 10.
    Sabry, A., Felleisen, M.: Reasoning about programs in continuation-passing style. Lisp and Symbolic Computation 6(3–4), 289–360 (1993)CrossRefGoogle Scholar
  11. 11.
    Shivers, O.: Control-flow analysis in Scheme. In: Proceedings of the SIGPLAN ’88 Conference on Programming Language Design and Implementation, PLDI, Atlanta, Georgia, pp. 164–174 (June 1988)Google Scholar
  12. 12.
    Steele, J.G.L.: RABBIT: a compiler for SCHEME. Master’s thesis, Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts, Technical report AI-TR-474 (May 1978)Google Scholar
  13. 13.
    Wright, A.K., Jagannathan, S.: Polymorphic splitting: An effective polyvariant flow analysis. ACM Transactions on Programming Languages and Systems 20(1), 166–207 (1998)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Matthew Might
  • Benjamin Chambers
  • Olin Shivers

There are no affiliations available

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