Skip to main content

Order-enriched sketches for typed lambda calculi.

  • Part I
  • Conference paper
  • First Online:
Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1488))

  • 1723 Accesses

Abstract

Order-enriched sketches are constructed for which the initial algebras are respectively, the simple typed λ-calculus, the PCF version of the λ-calculus, and the polymorphic typed λ-calculus.

This research was partially supported by the National Science Foundation.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

7 References

  1. M. Barr and C. Wells, Categories for Computer Scientists, Prentice Hall, 1990.

    Google Scholar 

  2. C. Ehresmann, Esquisses et types de structures algébriques, Bull. Instit. Polit., Iasi XIV (1968), 1–14.

    MathSciNet  MATH  Google Scholar 

  3. P. Gabriel and F. Ulmer, Lokal Präsentierbare Kategorien, Lecture Notes in Math., 221, Springer-Verlag, New York, 1971.

    MATH  Google Scholar 

  4. 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 J.E. Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, North-Holland Pub. Co., Amsterdam, London, 1971, 63–92.

    Chapter  Google Scholar 

  5. J.-Y. Girard, Proofs and Types, Translated and with appendices by P. Taylor and Y. Lafont, Cambridge University Press, Cambridge, 1989.

    Google Scholar 

  6. J. W. Gray, Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Mathematics 391, Springer-Verlag, New York, 1974

    MATH  Google Scholar 

  7. J. W. Gray, The Category of Sketches as a model for Algebraic Semantics, in Categories in Computer Science and Logic, J. W. Gray and A. Scedrov, Eds., Contemporary Mathematics 92, Amer. Math. Soc., Providence, R. I., 1989, 109–135.

    Chapter  Google Scholar 

  8. J. W. Gray, The Integration of Logical and Algebraic Types, in Categorical Methods in Computer Science with Aspects from Topology, H. Ehrig et al., Eds., Lecture Notes in Computer Science 393, Springer-Verlag, New York, 1989, 16–35.

    Chapter  Google Scholar 

  9. J. W. Gray, Executable specifications for data type constructors, in preparation.

    Google Scholar 

  10. J. W. Gray, PCF in Mathematica, in preparation.

    Google Scholar 

  11. J. W. Gray, Poly Lambda in Mathematica, in preparation.

    Google Scholar 

  12. G. M. Kelly and R. Street, Sydney Category Theory Seminar, Lecture Notes in Mathematics 420, Springer-Verlag, New York, 1974.

    Book  MATH  Google Scholar 

  13. M. Makkai and R. Pare, Accessible Categories: The foundations of Categorical Model Theory, Contemporary Mathematics 104, Amer. Math. Soc., Providence RI, 1989.

    Book  MATH  Google Scholar 

  14. B. Pierce, S. Dietzen, S. Michaylov, Programming in higher-order typed lambda-calculi, Technical Report CMU-CS-89-111, Carnegie Mellon University.

    Google Scholar 

  15. G. D. Plotkin, LCF considered as a programming language, Theoretical Computer Science 5 (1977), 223–255.

    Article  MathSciNet  MATH  Google Scholar 

  16. J. C. Reynolds, Towards a theory of type structures, in Colloque sur la Programmation, Lecture Notes in Computer Science 19, Springer-Verlag 1974, 408–425.

    Google Scholar 

  17. A. Stouten, Substitution Revisited, Theoretical Computer Science 59 (1988), 317–325.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Gray, J.W. (1991). Order-enriched sketches for typed lambda calculi.. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084216

Download citation

  • DOI: https://doi.org/10.1007/BFb0084216

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics