Proof Systems for Retracts in Simply Typed Lambda Calculus

  • Colin Stirling
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7966)

Abstract

This paper concerns retracts in simply typed lambda calculus assuming βη-equality. We provide a simple tableau proof system which characterises when a type is a retract of another type and which leads to an exponential decision procedure.

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References

  1. 1.
    Barendregt, H.: Lambda calculi with types. In: Abramsky, S., Gabbay, D., Maibaum, T. (eds.) Handbook of Logic in Computer Science, vol. 2, pp. 118–309. Oxford University Press (1992)Google Scholar
  2. 2.
    Bruce, K., Longo, G.: Provable isomorphisms and domain equations in models of typed languages. In: Proc. 17th Symposium on Theory of Computing, pp. 263–272. ACM (1985)Google Scholar
  3. 3.
    de ’Liguoro, U., Piperno, A., Statman, R.: Retracts in simply typed λβη-calculus. In: Procs. LICS 1992, pp. 461–469 (1992)Google Scholar
  4. 4.
    Loader, R.: Higher-order β-matching is undecidable. Logic Journal of the IGPL 11(1), 51–68 (2003)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Ong, C.-H.L.: On model-checking trees generated by higher-order recursion schemes. In: Procs. LICS 2006, pp. 81–90 (2006)Google Scholar
  6. 6.
    Ong, C.-H.L., Tzevelekos, N.: Functional Reachability. In: Procs. LICS 2009, pp. 286–295 (2009)Google Scholar
  7. 7.
    Padovani, V.: Decidability of fourth-order matching. Mathematical Structures in Computer Science 10(3), 361–372 (2000)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Padovani, V.: Retracts in simple types. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 376–384. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  9. 9.
    Regnier, L., Urzyczyn, P.: Retractions of types with many atoms, pp. 1–16 (2005), http://arxiv.org/abs/cs/0212005
  10. 10.
    Schubert, A.: On the building of affine retractions. Math. Struct. in Comp. Science 18, 753–793 (2008)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Stirling, C.: Higher-order matching, games and automata. In: Procs. LICS 2007, pp. 326–335 (2007)Google Scholar
  12. 12.
    Stirling, C.: Dependency tree automata. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 92–106. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Stirling, C.: Decidability of higher-order matching. Logical Methods in Computer Science 5(3:2), 1–52 (2009)MathSciNetGoogle Scholar
  14. 14.
    Stirling, C.: An introduction to decidability of higher-order matching (2012) (Submitted for Publication), Availble at author’s websiteGoogle Scholar
  15. 15.
    Vorobyov, S.: The “hardest” natural decidable theory. In: Procs. LICS 1997, pp. 294–305 (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Colin Stirling
    • 1
  1. 1.School of InformaticsUniversity of EdinburghUK

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