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A unifying theory of dependent types: the schematic approach

  • Zhaohui Luo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 620)

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References

  1. [Bac88]
    R. Backhouse. On the meaning and construction of the rules in Martin-Löf s theory of types. In A. Avron et al, editor, Workshop on General Logic. LFCS Report Series, ECS-LFCS-88-52, Dept. of Computer Science, University of Edinburgh, 1988.Google Scholar
  2. [BM91]
    R. Burstall and J. McKinna. Deliverables: an approach to program development in the calculus of constructions. LFCS report ECS-LFCS-91-133, Dept of Computer Science, University of Edinburgh, 1991.Google Scholar
  3. [CH88]
    Th. Coquand and G. Huet. The calculus of constructions. Information and Computation, 76(2/3), 1988.Google Scholar
  4. [Coq89]
    Th. Coquand. Metamathematical investigations of a calculus of constructions. manuscript, 1989.Google Scholar
  5. [Coq91]
    Th. Coquand. An algorithm for testing conversion in Type Theory. In G. Huet and G. Plotkin, editors, Logical Frameworks. Cambridge University Press, 1991.Google Scholar
  6. [CPM90]
    Th. Coquand and Ch. Paulin-Mohring. Inductively denned types. Lecture Notes in Computer Science, 417, 1990.Google Scholar
  7. [Dum75]
    M. Dummett. The philosophical basis of intuitionistic logic. In H. Rose and J. Shepherdson, editors, Proc. of the Logic Colloquium, 1973. North Holland, 1975. Reprinted in P. Benacerraf and H. Putnam (eds.), Philosophy of Mathematics: selected readings, Campbridge University Press.Google Scholar
  8. [Dum91]
    M. Dummett. The Logical Basis of Metaphysics. Duckworth, 1991.Google Scholar
  9. [Dyb89]
    P. Dybjer. An inversion principle for Martin-Löfs type theory. In P. Dybjer et al, editor, Workshop on Programming Logic. Programming Methodology Group, Report 54, 1989.Google Scholar
  10. [Dyb91]
    P. Dybjer. Inductive sets and families in Martin-Löfs type theory and their set-theoretic semantics. In G. Huet and G. Plotkin, editors, Logical Frameworks. Cambridge University Press, 1991.Google Scholar
  11. [GL91]
    H. Goguen and Z. Luo. Inductive data types: Well-ordering types revisited. submitted manuscript, 1991.Google Scholar
  12. [HHP87]
    R. Harper, F. Honsell, and G. Plotkin. A framework for defining logics. Proc. 2nd Ann. Symp. on Logic in Computer Science, 1987.Google Scholar
  13. [LPT89]
    Z. Luo, R. Pollack, and P. Taylor. How to Use LEGO: a preliminary user's manual. LFCS Technical Notes LFCS-TN-27, Dept. of Computer Science, Edinburgh University, 1989.Google Scholar
  14. [Luo89]
    Z. Luo. ECC, an extended calculus of constructions. In Proc. of the Fourth Ann. Symp. on Logic in Computer Science, Asilomar, California, U.S.A., June 1989.Google Scholar
  15. [Luo90a]
    Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Also as Report CST-65-90/ECS-LFCS-90-118, Department of Computer Science, University of Edinburgh.Google Scholar
  16. [Luo90b]
    Z. Luo. A problem of adequacy: conservativity of calculus of constructions over higher-order logic. Technical report, LFCS report series ECS-LFCS-90-121, Department of Computer Science, University of Edinburgh, 1990.Google Scholar
  17. [Luo91a]
    Z. Luo. A higher-order calculus and theory abstraction. Information and Computation, 90(1):107–137, 1991.CrossRefGoogle Scholar
  18. [Luo91b]
    Z. Luo. Program specification and data refinement in type theory. Proc. of the Fourth Inter. Joint Conf. on the Theory and Practice of Software Development (TAPSOFT), 1991. Also as LFCS report ECS-LFCS-91-131, Dept. of Computer Science, Edinburgh University.Google Scholar
  19. [ML75]
    P. Martin-Löf. An intuitionistic theory of types: predicative part. In H.Rose and J.C.Shepherdson, editors, Logic Colloquium'73,1975.Google Scholar
  20. [ML84]
    P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, 1984.Google Scholar
  21. [NPS90]
    B. Nordström, K. Petersson, and J. Smith. Programming in Martin-Löfs Type Theory: an introduction. Oxford University Press, 1990.Google Scholar
  22. [Ore90]
    C.-E. Ore. The Extended Calculus of Constructions (ECC) with inductive types. To appear in Information and Computation, 1990.Google Scholar
  23. [Pol89]
    R. Pollack. The theory of LEGO. manuscript, 1989.Google Scholar
  24. [Pol90]
    R. Pollack. The Tarski fixpoint theorem. communication on TYPES e-mail network, 1990.Google Scholar
  25. [Pra74]
    D. Prawitz. On the idea of a general proof theory. Synthese, 27, 1974.Google Scholar
  26. [Smi88]
    J. Smith. The independence of Peano's fourth axiom from Martin-Löfs type theory without universes. Journal of Symbolic Logic, 53(3), 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Zhaohui Luo
    • 1
  1. 1.Department of Computer ScienceUniversity of EdinburghEdinburghUK

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