Skip to main content

Conservativity between logics and typed λ calculi

  • Conference paper
  • First Online:
Types for Proofs and Programs (TYPES 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 806))

Included in the following conference series:

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • [Barendregt 1992]H.P. Barendregt, Typed lambda calculi. In Handbook of Logic in Computer Science, eds. Abramski et al., Oxford Univ. Press.

    Google Scholar 

  • [Barendsen and Geuvers 1989]E. Barendsen and H. Geuvers, λP is conservative over first order predicate logic, Manuscript, Faculty of Mathematics and Computer Science, University of Nijmegen, Netherlands.

    Google Scholar 

  • [Berardi 1988]S. Berardi, Towards a mathematical analysis of the Coquand-Huet calculus of constructions and the other systems in Barendregt's cube. Dept. Computer Science, Carnegie-Mellon University and Dipartimento Matematica, Universita di Torino, Italy.

    Google Scholar 

  • [Berardi 1989]S. Berardi, Talk given at the ‘Jumelage meeting on typed lambda calculus', Edinburgh, September 1989.

    Google Scholar 

  • [Berardi 1990]S. Berardi, Type dependence and constructive mathematics, Ph.D. thesis, Universita di Torino, Italy.

    Google Scholar 

  • [De Bruijn 1980]N.G. de Bruijn, A survey of the project Automath, InTo H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, eds. J.P. Seldin, J.R. Hindley, Academic Press, New York, pp 580–606.

    Google Scholar 

  • [Coquand 1985]Th. Coquand, Une théorie des constructions, Thèse de troisième cycle, Université Paris VII, France, January 1985.

    Google Scholar 

  • [Coquand 1990]Th. Coquand, Metamathematical investigations of a calculus of constructions. In Logic and Computer Science, ed. P.G. Odifreddi, APIC series, vol. 31, Academic Press, pp 91–122.

    Google Scholar 

  • [Coquand and Huet 1988]Th. Coquand and G. Huet, The calculus of constructions, Information and Computation, 76, pp 95–120.

    Article  Google Scholar 

  • [Coquand and Huet 1985]Th. Coquand and G. Huet, Constructions: a higher order proof system for mechanizing mathematics. Proceedings of EUROCAL '85, Linz, LNCS 203.

    Google Scholar 

  • [Gabbay 1981]D.M. Gabbay, Semantical investigations in Heyting's intuitionistic logic, Synthese Library, vol 148, Reidel, Dordrecht.

    Google Scholar 

  • [Geuvers 1989]J.H. Geuvers, Talk given at the ‘Jumelage meeting on typed lambda calculus”, Edinburgh, September 1989.

    Google Scholar 

  • [Geuvers and Nederhof] 1991J.H. Geuvers and M.J. Nederhof, A modular proof of strong normalisation for the calculus of constructions. Journal of Functional Programming, vol 1 (2), pp 155–189.

    Google Scholar 

  • [Geuvers 1993]J.H. Geuvers, Logics and Type systems, PhD. Thesis, University of Nijmegen, Netherlands.

    Google Scholar 

  • [Girard 1972]J.-Y. Girard, Interprétation fonctionelle et élimination des coupures dans l'arithmétique d'ordre supérieur. Ph.D. thesis, Université Paris VII, France.

    Google Scholar 

  • [Girard et al. 1989]J.-Y. Girard, Y. Lafont and P. Taylor, Proofs and types, Camb. Tracts in Theoretical Computer Science 7, Cambridge University Press.

    Google Scholar 

  • [Harper et al. 1987]R. Harper, F. Honsell and G. Plotkin, A framework for defining logics. Proceedings Second Symposium on Logic in Computer Science, (Ithaca, N.Y.), IEEE, Washington DC, pp 194–204.

    Google Scholar 

  • [Howard 1980]W.A. Howard, The formulas-as-types notion of construction. In To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, eds. J.P. Seldin, J.R. Hindley, Academic Press, New York, pp 479–490.

    Google Scholar 

  • [Löb 1976]M. Löb, Embedding first order predicate logic in fragments of intuitionistic logic, J. Symbolic Logic vol 41, 4, pp. 705–719.

    Google Scholar 

  • [Longo and Moggi 1988]G. Longo and E. Moggi, Constructive Natural Deduction and its ‘Modest’ Interpretation. Report CMU-CS-88-131.

    Google Scholar 

  • [Paulin 1989]Ch. Paulin-Mohring, Extraction des programmes dans le calcul des constructions, Thèse, Université Paris VII, France.

    Google Scholar 

  • [Pitts 1992]A.M. Pitts, On an interpretation of second order quantification in first order intuitionistic propositional logic. J. Symbolic Logic vol 57, 1, pp.33–52.

    Google Scholar 

  • [Ruys 1991]M. Ruys, λPω is not conservative over λP2, Master's thesis, University of Nijmegen, Netherlands, November 1991.

    Google Scholar 

  • [Tonino and Fujita 1992]H. Tonino and K.-E. Fujita, On the adequacy of representing higher order intuitionistic logic as a pure type system, Annals of Pure and Applied Logic vol 57, pp 251–276.

    Google Scholar 

  • [Troelstra and Van Dalen 1988]A. Troelstra and D. van Dalen, Constructivism in mathematics, an introduction, Volume I/II, Studies in logic and the foundations of mathematics, vol 121 and volume 123, North-Holland.

    Google Scholar 

  • [Verschuren 1990]E. Verschuren, Conservativity in Barendregt's cube, Master's thesis, University of Nijmegen, Netherlands, December 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Henk Barendregt Tobias Nipkow

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Geuvers, H. (1994). Conservativity between logics and typed λ calculi. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_73

Download citation

  • DOI: https://doi.org/10.1007/3-540-58085-9_73

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58085-0

  • Online ISBN: 978-3-540-48440-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics