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

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Automata, Languages and Programming (ICALP 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3142))

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Abstract

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].

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References

  1. Barendregt, H.: The Lambda Calculus-Its Sytax and Semantics. North-Holland, Amsterdam (1984)

    Google Scholar 

  2. Fiore, M.: Semantic analysis of normalisation by evaluation for typed lambda calculus. In: Proc. PPDP 2002, pp. 26–37. ACM Press, New York (2002)

    Chapter  Google Scholar 

  3. 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. 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. Hermida, C.: Fibrations, Logical Predicates and Indeterminantes. PhD thesis, The University of Edinburgh (1993)

    Google Scholar 

  6. 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)

    Chapter  Google Scholar 

  7. 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. Honsell, F., Sannella, D.: Prelogical relations. INFCTRL: Information and Computation (formerly Information and Control) 178(1), 23–43 (2002)

    MATH  MathSciNet  Google Scholar 

  9. Jacobs, B.: Categorical Logic and Type Theory. Elsevier, Amsterdam (1999)

    MATH  Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. 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)

    Chapter  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. Lafont, Y.: Logiques, Categories et Machines. PhD thesis, Université de Paris VII (1988)

    Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Mitchell, J.: Foundations for Programming Languages. MIT Press, Cambridge (1996)

    Google Scholar 

  16. 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. 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. Miculan, M., Scagnetto, I.: A framework for typed HOAS and semantics. In: Proc. PPDP 2003, pp. 184–194. ACM Press, New York (2003)

    Chapter  Google Scholar 

  19. 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)

    Chapter  Google Scholar 

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Katsumata, Sy. (2004). A Generalisation of Pre-logical Predicates to Simply Typed Formal Systems. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_70

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  • DOI: https://doi.org/10.1007/978-3-540-27836-8_70

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22849-3

  • Online ISBN: 978-3-540-27836-8

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