A Generalisation of Pre-logical Predicates to Simply Typed Formal Systems

  • Shin-ya Katsumata
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3142)


We generalise the notion of pre-logical predicates [HS02] to arbitrary simply typed formal systems and their categorical models. We establish the basic lemma of pre-logical predicates and composability of binary pre-logical relations in this generalised setting. This generalisation takes place in a categorical framework for typed higher-order abstract syntax and semantics [Fio02,MS03].


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Bar84]
    Barendregt, H.: The Lambda Calculus-Its Sytax and Semantics. North-Holland, Amsterdam (1984)Google Scholar
  2. [Fio02]
    Fiore, M.: Semantic analysis of normalisation by evaluation for typed lambda calculus. In: Proc. PPDP 2002, pp. 26–37. ACM Press, New York (2002)CrossRefGoogle Scholar
  3. [FP94]
    Fiore, M., Plotkin, G.: An axiomatization of computationally adequate domain theoretic models of FPC. In: Proc. LICS 1994, pp. 92–102. IEEE, Los Alamitos (1994)Google Scholar
  4. [FPT99]
    Fiore, M., Plotkin, G., Turi, D.: Abstract syntax and variable binding. In: Proc. LICS 1999, pp. 193–202. IEEE Computer Society Press, Los Alamitos (1999)Google Scholar
  5. [Her93]
    Hermida, C.: Fibrations, Logical Predicates and Indeterminantes. PhD thesis, The University of Edinburgh (1993)Google Scholar
  6. [HLST00]
    Honsell, F., Longley, J., Sannella, D., Tarlecki, A.: Constructive data refinement in typed lambda calculus. In: Tiuryn, J. (ed.) FOSSACS 2000. LNCS, vol. 1784, pp. 161–176. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  7. [Hof99]
    Hoffman, M.: Semantical analysis of higher-order abstract syntax. In: Proc. LICS 1999, pp. 204–213. IEEE Computer Society, Los Alamitos (1999)Google Scholar
  8. [HS02]
    Honsell, F., Sannella, D.: Prelogical relations. INFCTRL: Information and Computation (formerly Information and Control) 178(1), 23–43 (2002)MATHMathSciNetGoogle Scholar
  9. [Jac99]
    Jacobs, B.: Categorical Logic and Type Theory. Elsevier, Amsterdam (1999)MATHGoogle Scholar
  10. [Kat03]
    Katsumata, S.: Behavioural equivalence and indistinguishability in higher-order typed languages. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2003. LNCS, vol. 2755, pp. 284–298. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. [KOPT97]
    Kinoshita, Y., O’Hearn, P.W., Power, A.J., Takeyama, M.: An axiomatic approach to binary logical relations with applications to data refinement. In: Ito, T., Abadi, M. (eds.) TACS 1997. LNCS, vol. 1281, pp. 191–212. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  12. [KP99]
    Kinoshita, Y., Power, J.: Data-refinement for call-by-value programming languages. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 562–576. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  13. [Laf88]
    Lafont, Y.: Logiques, Categories et Machines. PhD thesis, Université de Paris VII (1988)Google Scholar
  14. [Lei01]
    Leiß, H.: Second-order pre-logical relations and representation independence. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 298–314. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  15. [Mit96]
    Mitchell, J.: Foundations for Programming Languages. MIT Press, Cambridge (1996)Google Scholar
  16. [MR92]
    Ma, Q., Reynolds, J.C.: Types, abstractions, and parametric polymorphism, part 2. In: Schmidt, D., Main, M.G., Melton, A.C., Mislove, M.W., Brookes, S.D. (eds.) MFPS 1991. LNCS, vol. 598, pp. 1–40. Springer, Heidelberg (1992)Google Scholar
  17. [MS93]
    Mitchell, J., Scedrov, A.: Notes on sconing and relators. In: Martini, S., Börger, E., Kleine Büning, H., Jäger, G., Richter, M.M. (eds.) CSL 1992. LNCS, vol. 702, pp. 352–378. Springer, Heidelberg (1993)Google Scholar
  18. [MS03]
    Miculan, M., Scagnetto, I.: A framework for typed HOAS and semantics. In: Proc. PPDP 2003, pp. 184–194. ACM Press, New York (2003)CrossRefGoogle Scholar
  19. [PPST00]
    Plotkin, G., Power, J., Sannella, D., Tennent, R.: Lax logical relations. In: Welzl, E., Montanari, U., Rolim, J.D.P. (eds.) ICALP 2000. LNCS, vol. 1853, pp. 85–102. Springer, Heidelberg (2000)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Shin-ya Katsumata
    • 1
  1. 1.Laboratory for Foundations of Computer Science, School of InformaticsThe University of EdinburghEdinburghUK

Personalised recommendations