Skip to main content
SpringerLink
Log in
Book cover

Italian Conference on Theoretical Computer Science

ICTCS 2003: Theoretical Computer Science pp 202–215Cite as

Logical Semantics for the First Order ς-Calculus

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2841))

Abstract

We investigate logical semantics of the first order ς-calculus. An assignment system of predicates to first order typed terms of the OB1 calculus is introduced. We define retraction models for that calculus and an interpretation of terms, types and predicates into such models. The assignment system is then proved to be sound and complete w.r.t. retraction models.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abadi, M., Cardelli, L.: A Theory of Objects. Springer, Heidelberg (1996)

    MATH  Google Scholar 

  2. Abadi, M., Plotkin, G.D.: A Per Model of Polymorphism and Recursive Types. In: Proc. of IEEE-LICS, pp. 3355–3365 (1990)

    Google Scholar 

  3. Abramsky, S.: Observation Equivalence and Testing Equivalence. Theoretical Computer Science 53, 225–241 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  4. Abramsky, S.: Domain Theory in Logical Form. APAL 51, 1–77 (1991)

    MATH  MathSciNet  Google Scholar 

  5. Amadio, R.: Recursion over Realizability Structures. Info. Comp. 91, 55–85 (1991); Theoretical Computer Science 102(1), 135–163 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  6. van Bakel, S.: Intersection Type Assignment Systems. Theoretical Computer Science 151(2), 385–435 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  7. Barendregt, H.P., Coppo, M., Dezani, M.: A Filter Lambda Model and the Completeness of Type Assignment. JSL 48, 931–940 (1983)

    Article  MATH  Google Scholar 

  8. Bruce, K.B., Mitchell, J.C.: PER models of subtyping, recursive types and higher-order polymorphism. In: Proc. of ACM-POPL 1992 (1992)

    Google Scholar 

  9. Cardone, F.: Relational semantics for recursive types and bounded quantification. In: Ronchi Della Rocca, S., Ausiello, G., Dezani-Ciancaglini, M. (eds.) ICALP 1989. LNCS, vol. 372, pp. 164–178. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  10. Coppo, M., Dezani, M., Venneri, B.: Functional characters of solvable terms. Grund. Der Math. 27, 45–58 (1981)

    Article  MATH  Google Scholar 

  11. Dezani, M., Giovannetti, E., de’ Liguoro, U.: Intersection types, λ-models and Böhm trees. In: [19], pp. 45-97

    Google Scholar 

  12. de’Liguoro, U.: Characterizing convergent terms in object calculi via intersection types. In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, p. 315. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  13. de’Liguoro, U.: Subtyping in logical form. In: ITRS 2002. ENTCS, vol. 70.1, Elsevier, Amsterdam (2002)

    Google Scholar 

  14. Kamin, S.: Inheritance in Smalltalk-80: a denotational definition. In: Proc. of POPL 1988, pp. 80–87 (1988)

    Google Scholar 

  15. Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. of ACM 32(1), 137–161 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  16. Krivine, J.L.: Lambda-calcul, types et modèles, Masson (1990)

    Google Scholar 

  17. Mitchell, J.C.: Foundations for Programming Languages. MIT Press, Cambridge (1996)

    Google Scholar 

  18. Scott, D.: Data types as lattices. SIAM J. Comput. 5(3), 522–587 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  19. Takahashi, M., Okada, M., Dezani, M. (eds.): Theories of Types and Proofs. Mathematical Society of Japan, vol. 2 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computing, Imperial College, 180 Queen’s Gate, London, SW7 2BZ, UK

    Steffen van Bakel

  2. Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149, Torino, Italy

    Ugo de’Liguoro

Authors
  1. Steffen van Bakel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ugo de’Liguoro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica e Applicazioni, Università degli Studi di Salerno, Via Ponte Don Melillo, I-84084, Fisciano, SA, Italy

    Carlo Blundo

  2. Department of Computer Science, University of Bologna,  

    Cosimo Laneve

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van Bakel, S., de’Liguoro, U. (2003). Logical Semantics for the First Order ς-Calculus. In: Blundo, C., Laneve, C. (eds) Theoretical Computer Science. ICTCS 2003. Lecture Notes in Computer Science, vol 2841. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45208-9_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-45208-9_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-20216-5

  • Online ISBN: 978-3-540-45208-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation