Computability in higher types and the universal domain Pω

  • G. Longo
  • S. Martini
Contibuted Papers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 166)


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  1. BL [1980]
    Barendregt, H., Longo, G., Equality of lambda-terms in the model Tω, in: To H.B. Curry: Essays on Combinatory Logic Lambda Calculus and Formalism, Hindley and Seldin (Eds), Academic Press, New York, 303–337.Google Scholar
  2. BL [1981]
    Barendregt,H., Longo,G., Recursion theoretic operators and morphisms of numbered sets, Fundamenta Mathematicae, CXIX (1982), to appear.Google Scholar
  3. CDL [1983]
    Coppo,M., Dezani-Ciancaglini,M., Longo,G., Applicative Information Systems, Conference on Trees in Algebra and Programming Ausiello, Protasi (eds), Springer-Verlag LNCS 159 (revised: Info. Contr., to appear).Google Scholar
  4. Er [1972]
    Ershov,Yu.L., Computable Functionals of finite types, Algebra and Logic vol. 11 n. 4.Google Scholar
  5. Er [1976]
    Ershov,Yu.L., Model C of partial continuous functionals, in: Logic Colloquium 76, Gandy, Hyland (Eds), North-Holland, 1977.Google Scholar
  6. GL [1982]
    Giannini,P., Longo,G., Effectively given domains and lambda-calculus semantics, Nota Scientifica, D.I. Università di Pisa.Google Scholar
  7. Gö [1958]
    Gödel, K., Uber eine bicher noch nicht benützte Erweiterung des finiten Standpunktes, Dialettica vol. 12 (1958), 280–287.Google Scholar
  8. Hyl [1979]
    Hyland, M., Filter Spaces and Continuous functionals, Annals Math Logic, 16 (1979) 101–143.Google Scholar
  9. KP [1979]
    Kanda,A., Park,D., When are two effectively given domains identical?, Proc. 4th GI Conf in T.C.S., Aachen, LNCS 67, Springer-Verlag.Google Scholar
  10. Kle [1959]
    Kleene,S., Countable Functionals, in: Constructivity in Mathematics, Heyting (Ed), North-Holland.Google Scholar
  11. Kre [1959]
    Kreisel,G., Interpretation of analysis by means of constructive functionals of finite types, in Constructivity in Mathematics, Heyting (Ed), North-Holland.Google Scholar
  12. Lo [1982a]
    Longo,G., Set-theoretical models of lambda-calculus: theories, expansions, isomorphisms, Annals Pure Applied Logic (formely: Ann. Math. Logic) 24, 153–188.Google Scholar
  13. Lo [1982b]
    Longo,G., Hereditary Partial Effective Functionals in any finite type, Preliminary note, Forshungsinstitut f. Math. ETH Zürich.Google Scholar
  14. LM [1983]
    Longo,G., Moggi,E., The Hereditary Partial Effective Functionals and Recursion Theory in higher types, J. Symb. Logic (to appear).Google Scholar
  15. LM [1984]
    Longo,G., Moggi,E., Gödel-numberings, principal morphisms, combinatory algebras, Nota Sci. 9-83-21. Dip. Informatica, Pisa.Google Scholar
  16. MS [1955]
    Myhill,J., Shepherdson,C., Effective operations on partial recursive functions, Zeit. Math. Logik, 1, 310–317.Google Scholar
  17. Nor [1980]
    Normann,D., Recursion on the Countable Functionals LNM 811 Springer-Verlag, Berlin.Google Scholar
  18. Pl [1978]
    Plotkin, G., Tω as a universal domain, J. Comp. and Syst. Sciences vol. 17, 2 (1978), 209–236.Google Scholar
  19. Ro [1967]
    Rogers,H., Theory of Recursive Functions and Effective Computability, Mc Graw-Hill, New York.Google Scholar
  20. Scott [1972]
    Scott,D., Continuous lattices, in Toposes, Algebraic Geometry and Logic (Law v ere ed), Springer-Verlag LNM 274, 97–136.Google Scholar
  21. Scott [1976]
    Scott,D., Data types as lattices, SIAM J. Comp. 5,3,522–587.Google Scholar
  22. Scott [1981]
    Scott;D., Lectures on a Mathematical Theory of Computation. Oxford University Computing Laboratory, Technical Monograph PRG-19.Google Scholar
  23. Smyth [1977]
    Smyth, M., Effectively given domains, Theor. Comp. Science 5 (1977) 257–274.Google Scholar
  24. Smyth [1979]
    Smyth,M., Computability in Categories, Theory of Computation Report, University of Warwick.Google Scholar
  25. Tro [1973]
    Troelstra,A., Metamathematical Investigation of Intuitionistic Arithmetic and Analysis, LNM 344 Springer-Verlag, Berlin.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • G. Longo
    • 1
  • S. Martini
    • 1
  1. 1.Dipartimento di InformaticaUniversità di PisaPisa

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