Advertisement

Rewriting properties of combinators for rudimentary linear logic

  • Monica Nesi
  • Valeria de Paiva
  • Eike Ritter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 816)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Abadi, L. Cardelli, P.-L. Curien, J.-J. Lévy, ‘Explicit substitutions', in Journal of Functional Programming, 1991, Vol. 1, No. 4, pp. 375–416.Google Scholar
  2. 2.
    N. Benton, G. Bierman, V. de Paiva, M. Hyland, ‘Term assignment for intuitionistic linear logic', Technical Report No. 262, Computer Laboratory, University of Cambridge, 1992.Google Scholar
  3. 3.
    G. Bierman, ‘On Intuitionistic Linear Logic', Draft of Ph.D. Thesis, Computer Laboratory, University of Cambridge, 1993.Google Scholar
  4. 4.
    T. Coquand, Th. Ehrhard, ‘An equational presentation of higher order logic', in Proceedings of Category Theory and Computer Science, Lecture Notes in Computer Science 283, Springer-Verlag, 1987, pp. 40–56.Google Scholar
  5. 5.
    G. Cousineau, P.-L. Curien, M. Mauny, ‘The categorical abstract machine', in Science of Computer Programming, 1987, Vol. 8, pp. 173–202.Google Scholar
  6. 6.
    P.-L. Curien, ‘Categorical Combinators, Sequential Algorithms and Functional Programming', Birkhäuser, 1993.Google Scholar
  7. 7.
    P.-L. Curien, T. Hardin, A. Ríos, 'strong normalisation of substitutions', in Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science 1992, Lecture Notes in Computer Science 629, Springer-Verlag, 1992, pp. 209–217.Google Scholar
  8. 8.
    N. Dershowitz, J.-P. Jouannaud, ‘Rewrite Systems', in Handbook of Theoretical Computer Science, Vol. B: Formal Models and Semantics, J. van Leeuwen (ed.), North-Holland, 1990, pp. 243–320.Google Scholar
  9. 9.
    Th. Ehrhard, ‘A categorical semantics of constructions', in Proceedings of the 3rd Annual Symposium on Logic in Computer Science, IEEE, 1988, pp. 264–273.Google Scholar
  10. 10.
    S. J. Garland, J. V. Guttag, ‘A Guide to LP, The Larch Prover', Release 2.2 LP Documentation, MIT, November 1991.Google Scholar
  11. 11.
    J.-Y. Girard, ‘Linear logic', in Theoretical Computer Science, 1987, Vol. 50, pp. 1–102.Google Scholar
  12. 12.
    J.-Y. Girard, P. Taylor, Y. Lafont, ‘Proofs and Types', Cambridge University Press, 1989.Google Scholar
  13. 13.
    T. Hardin, ‘Confluence results for the pure strong categorical logic CCL. λ-calculi as subsystems of CCL', in Theoretical Computer Science, 1989, Vol. 65, pp. 291–342.Google Scholar
  14. 14.
    T. Hardin, A. Laville, ‘Proof of termination of the rewriting system Subst on CCL', in Theoretical Computer Science, 1986, Vol. 46, pp. 305–312.Google Scholar
  15. 15.
    M. Hermann, ‘Vademecum of Divergent Term Rewriting Systems', Technical Report CRIN 88-R-082, Centre de Recherche en Informatique de Nancy, 1988.Google Scholar
  16. 16.
    M. Hermann, ‘Chain Properties of Rule Closures', in Formal Aspects of Computing, 1990, Vol. 2, pp. 207–225.Google Scholar
  17. 17.
    Y. Lafont, ‘The linear abstract machine', in Theoretical Computer Science, 1988, Vol. 59, pp. 157–180.Google Scholar
  18. 18.
    V. de Paiva, E. Ritter, ‘Categorical combinators for symmetric multicategories', unpublished manuscript, 1994.Google Scholar
  19. 19.
    E. Ritter, ‘Categorical Abstract Machines for Higher-Order Lambda Calculi', to appear in Theoretical Computer Science. Also available as Technical Report No. 297, Computer Laboratory, University of Cambridge, 1993.Google Scholar
  20. 20.
    E. Ritter, ‘Normalization for Typed Lambda Calculi with Explicit Substitution', to appear in Proceedings of the 1993 Annual Conference of the European Association for Computer Science Logic CSL 93, Lecture Notes in Computer Science.Google Scholar
  21. 21.
    E. Ritter, V. de Paiva, 'syntactic Multicategories and Categorical Combinators for Linear Logic', presented at the Fifth Biennial Meeting on Category Theory and Computer Science CTCS-5, Amsterdam, September 1993.Google Scholar
  22. 22.
    A. Scedrov, ‘A Brief Guide to Linear Logic', in Bulletin of EATCS, No. 41, June 1990, pp. 154–165.Google Scholar
  23. 23.
    H. Zantema, ‘Termination of term rewriting by interpretation', in Proceedings of the 3rd International Workshop on Conditional Term Rewriting Systems CTRS-92, Lecture Notes in Computer Science 656, Springer-Verlag, 1993, pp. 155–167.Google Scholar
  24. 24.
    H. Zantema, Private Communication, June 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Monica Nesi
    • 1
  • Valeria de Paiva
    • 1
  • Eike Ritter
    • 2
  1. 1.Computer LaboratoryUniversity of CambridgeUK
  2. 2.Computing LaboratoryOxford UniversityUK

Personalised recommendations