Hector: An Equivalence Checker for a Higher-Order Fragment of ML

  • David Hopkins
  • Andrzej S. Murawski
  • C. -H. Luke Ong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7358)


We present Hector, an observational equivalence checker for a higher-order fragment of ML. The input language is RML, the canonical restriction of standard ML to ground-type references. Hector accepts programs from a decidable fragment of RML identified by us at ICALP’11, which comprises programs of short-type (order at most 2 and arity at most 1) that may contain free variables whose arguments are also of short-type. This is an expressive fragment that contains complex higher-order types, and includes many examples from the literature which have proven challenging to verify using other methods. To our knowledge, Hector is the first fully-automated equivalence checker for higher-order, call-by-value programs. Both sound and complete, the tool relies on the fully abstract game semantics of RML to construct, on-the-fly, visibly pushdown automata which precisely capture program behaviour. These automata are then checked for language equivalence, and if they are inequivalent a counterexample (in the form of a separating context) is constructed.


Model Checker Equivalence Checker Game Model Predicate Abstraction Game Semantic 
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  1. 1.
    Abramsky, S., McCusker, G.: Call-by-Value Games. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414, pp. 1–17. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Chaudhuri, S., Etessami, K., Madhusudan, P.: On-the-Fly Reachability and Cycle Detection for Recursive State Machines. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 61–76. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Alur, R., Madhusudan, P.: Visibly pushdown languages. In: STOC (2004)Google Scholar
  4. 4.
    Bakewell, A., Ghica, D.R.: On-the-Fly Techniques for Game-Based Software Model Checking. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 78–92. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  5. 5.
    Bakewell, A., Ghica, D.R.: Compositional Predicate Abstraction from Game Semantics. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 62–76. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
    Dreyer, D., Neis, G., Birkedal, L.: The impact of higher-order state and control effects on local relational reasoning. In: ICFP, pp. 143–156 (2010)Google Scholar
  7. 7.
    Hopkins, D., Murawski, A.S., Ong, C.-H.L.: A Fragment of ML Decidable by Visibly Pushdown Automata. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 149–161. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  8. 8.
    Hopkins, D., Ong, C.-H.L.: Homer: A Higher-Order Observational Equivalence Model checkER. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 654–660. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Jhala, R., Majumdar, R., Rybalchenko, A.: HMC: Verifying Functional Programs Using Abstract Interpreters. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 470–485. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  10. 10.
    Kobayashi, N.: Model-checking higher-order functions. In: PPDP, pp. 25–36 (2009)Google Scholar
  11. 11.
    Pitts, A.M., Stark, I.D.B.: Operational reasoning for functions with local state. Higher Order Operational Techniques in Semantics (1998)Google Scholar
  12. 12.
    Stark, I.D.B.: Names and Higher-Order Functions. PhD thesis, Univ. of Cambridge (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • David Hopkins
    • 1
  • Andrzej S. Murawski
    • 2
  • C. -H. Luke Ong
    • 1
  1. 1.Department of Computer ScienceUniversity of OxfordUK
  2. 2.Department of Computer ScienceUniversity of LeicesterUK

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