Skip to main content
Springer Nature Link
Log in

Induction in the elementary theory of types and names

  • Conference paper
  • First Online:
CSL '87 (CSL 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 329))

Included in the following conference series:

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.J. Beeson, Foundations of Constructive Mathematics, Springer, Berlin, 1985.

    Google Scholar 

  2. W. Buchholz, S. Feferman, W. Pohlers, W. Sieg, Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies, Lecture Notes in Mathematics 897, Springer, Berlin, 1981.

    Google Scholar 

  3. L. Cardelli and P. Wegner, On understanding types, data abstraction and polymorphism, Computing surveys 17 (1985).

    Google Scholar 

  4. R.L. Constable, S.F. Allen, H.M. Bromley, W.R. Cleveland, J.F. Cremer, R.W. Harper, D.J. Howe, T.B. Knoblock, N.P. Mendler, P. Panangaden, J.T. Sasaki and S.F. Smith, Implementing Mathematics with the Nuprl Proof Development System, Prentice-Hall, Englewood Cliffs, NJ, 1986.

    Google Scholar 

  5. Th. Coquand and G. Huet, Constructions: A higher order proof system for mechanizing mathematics, in: Proceedings EUROCAL 85, Lecture Notes in Computer Science 203, Springer, Berlin, 1985.

    Google Scholar 

  6. N.G. de Bruijn, A survey of AUTOMATH, in: J.P. Seldin and J.R. Hindley (eds.), To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, New York, 1980.

    Google Scholar 

  7. M. Gordon, R. Milner and C. Wadsworth, Edinburgh LCF, Lecture Notes in Computer Science 78, Springer, Berlin, 1979.

    Google Scholar 

  8. S. Feferman, A language and axiom for explicit mathematics, in: Algebra and Logic, Lecture Notes in Mathematics 450, Springer, Berlin, 1975.

    Google Scholar 

  9. S. Feferman, Theories of finite type, in: J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977.

    Google Scholar 

  10. S. Feferman, Constructive theories of functions and classes, in: M. Boffa, D. van Dalen, K. McAloon (eds.), Proceedings of Logic Colloquium '78, North-Holland, Amsterdam, 1979.

    Google Scholar 

  11. S. Feferman, Iterated fixed-point theories: application to Hancock's conjecture, in: G. Metakides (ed.), The Patras Symposium, North-Holland, Amsterdam, 1982.

    Google Scholar 

  12. S. Feferman, A theory of variable types, Revista Colombiana de Mathemáticas, XIX, (1985).

    Google Scholar 

  13. S. Feferman, Weyl vindicated: ”Das Kontinuum” 70 years later, Preprint, Stanford, 1987.

    Google Scholar 

  14. S. Feferman, The polymorphic typed λ-calculus (and all that) in a type-free axiomatic framework, Preprint, Stanford, 1988.

    Google Scholar 

  15. J.-Y. Girard, Une extension de l'interpretation de Gödel a l'analyse, et son application a l'elimination des coupures dans l'analyse et la theorie des types, in: Proceedings 2nd Scandinavian Logic Symposium, North-Holland, Amsterdam, 1971.

    Google Scholar 

  16. J.-Y. Girard, The system F of variable types, fifeteen years later, Theoretical Computer Science 45 (1986).

    Google Scholar 

  17. S. Hayashi and H. Nakano, PX a computational logic, Report Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 1987.

    Google Scholar 

  18. G. Huet, Induction principles formalized in the calculus of constructions, in: H. Ehrig, R. Kowalski, G. Levi and U. Montanari (eds.), Proceedings of TAPSOFT '87, Lecture Notes in Computer Science 249, Springer, Berlin, 1987.

    Google Scholar 

  19. G. Jäger, Type theory and explicit mathematics, in: Proceedings of Logic Colloquium '87, to appear.

    Google Scholar 

  20. P. Martin-Löf, Constructive mathematics and computer programming, in: Proceedings 6th International Congress for Logic, Methodology and Philosophy of Science, North-Holland, Amsterdam, 1982.

    Google Scholar 

  21. Y.N. Moschovakis, Elementary Induction on Abstract Structures, North-Holland, Amsterdam, 1974.

    Google Scholar 

  22. B. Nordstrom and K. Petersson, Types and specifications, in: Proceedings IFIP '83, North-Holland, Amsterdam, 1983.

    Google Scholar 

  23. B. Nordstrom and J. Smith, Propositions, types, and specifications in Martin-Löf's type theory, BIT 24, n. 3 (1984).

    Google Scholar 

  24. J.C. Reynolds, Towards a theory of type structure, in: Proceedings Colloque sur la Programmation, Lecture Notes in Computer Science 19, Springer, Berlin, 1974.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik ETH Zürich, Switzerland

    Gerhard Jäger

Authors
  1. Gerhard Jäger
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Egon Börger Hans Kleine Büning Michael M. Richter

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Jäger, G. (1988). Induction in the elementary theory of types and names. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '87. CSL 1987. Lecture Notes in Computer Science, vol 329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50241-6_33

Download citation

  • DOI: https://doi.org/10.1007/3-540-50241-6_33

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50241-8

  • Online ISBN: 978-3-540-45960-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation