Games, Automata and Matching

  • Colin Stirling
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4603)

Abstract

Higher-order matching is the problem given t = u where t, u are terms of simply typed λ-calculus and u is closed, is there a substitution θ such that tθ and u have the same normal form with respect to βη-equality: can t be pattern matched to u? The problem was conjectured to be decidable by Huet [4]. Loader showed that it is undecidable when β-equality is the same normal form by encoding λ-definability as matching [6].

References

  1. 1.
    Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S., Tommasi, M.: Tree Automata Techniques and Applications. Draft Book (2002), http://l3ux02.univ-lille3.fr/tata/
  2. 2.
    Comon, H., Jurski, Y.: Higher-order matching and tree automata. In: Nielsen, M. (ed.) CSL 1997. LNCS, vol. 1414, pp. 157–176. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  3. 3.
    Dowek, G.: Higher-order unification and matching. In: Robinson, A., Voronkov, A. (ed.) Handbook of Automated Reasoning, vol. 2, pp. 1009–1062, North-Holland (2001)Google Scholar
  4. 4.
    Huet, G.: Rèsolution d’èquations dans les langages d’ordre 1, 2, ... ω. Thèse de doctorat d’ètat, Universitè Paris VII (1976)Google Scholar
  5. 5.
    Jung, A., Tiuryn, J.: A new characterisation of lambda definability. In: Bezem, M., Groote, J.F. (eds.) TLCA 1993. LNCS, vol. 664, pp. 245–257. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  6. 6.
    Loader, R.: Higher-order β-matching is undecidable. Logic Journal of the IGPL 11(1), 51–68 (2003)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Ong, C.-H.L.: On model-checking trees generated by higher-order recursion schemes. In: Procs LICS, pp. 81–90 (Longer version available from Ong’s web page) (2006)Google Scholar
  8. 8.
    Padovani, V.: Decidability of fourth-order matching. Mathematical Structures in Computer Science 10(3), 361–372 (2001)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Schubert, A.: Linear interpolation for the higher-order matching problem. In: Bidoit, M., Dauchet, M. (eds.) CAAP 1997, FASE 1997, and TAPSOFT 1997. LNCS, vol. 1214, pp. 441–452. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  10. 10.
    Stirling, C.: Modal and Temporal Properties of Processes. In: Texts in Computer Science, Springer, Heidelberg (2001)Google Scholar
  11. 11.
    Stirling, C.: Higher-order matching and games. In: Ong, L. (ed.) CSL 2005. LNCS, vol. 3634, pp. 119–134. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Stirling, C.: A game-theoretic approach to deciding higher-order matching. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 348–359. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Colin Stirling
    • 1
  1. 1.School of Informatics, University of Edinburgh 

Personalised recommendations