Skip to main content

Filter Models and Easy Terms

  • Conference paper
  • First Online:
Theoretical Computer Science (ICTCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2202))

Included in the following conference series:

Abstract

We illustrate the use of intersection types as a tool for synthesizing λ-models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of λ-theories induced by graph models is strictly included in the class of λ-theories induced by non-extensional filter models.

Partially supported by MURST Cofin’ 99 TOSCA Project, CNR-GNSAGA and FGV ’99.

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 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. Abramsky. Domain theory in logical form. Ann. Pure Appl. Logic, 51(1-2):1–77, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  2. S. Abramsky and C.-H. L. Ong. Full abstraction in the lazy lambda calculus. Inform. and Comput., 105(2):159–267, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  3. F. Alessi. Strutture di tipi, teoria dei domini e modelli del lambda calcolo. PhD thesis, Torino University, 1991.

    Google Scholar 

  4. J. Baeten and B. Boerboom. ω can be anything it shouldn’t be. Indag.Math., 41:111–120, 1979.

    MathSciNet  Google Scholar 

  5. H. Barendregt. The Lambda Calculus: its Syntax and Semantics. North-Holland, Amsterdam, revised edition, 1984.

    MATH  Google Scholar 

  6. H. Barendregt, M. Coppo, and M. Dezani-Ciancaglini. A filter lambda model and the completeness of type assignment. J. Symbolic Logic, 48(4):931–940, 1983.

    Article  MATH  MathSciNet  Google Scholar 

  7. H. Barendregt et. al. Typed λ-calculus and applications. North-Holland, 2001. (to appear).

    Google Scholar 

  8. A. Berarducci and B. Intrigila. Some new results on easy lambda-terms. Theoret. Comput. Sci., 121:71–88, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  9. A. Berarducci and B. Intrigila. Church-Rosser λ-theories, infinite λ-calculus and consistency problems. In W. Hodges and M. Hyland et al., editors, Logic: From Foundations to applications, pages 33–58. Oxford Sci. Publ., New York, 1996.

    Google Scholar 

  10. M. Coppo and M. Dezani-Ciancaglini. An extension of the basic functionality theory for the λ-calculus. Notre Dame J. Formal Logic, 21(4):685–693, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Coppo, M. Dezani-Ciancaglini, F. Honsell, and G. Longo. Extended type structures and filter lambda models. In Logic colloquium’ 82, pages 241–262. North-Holland, Amsterdam, 1984.

    Google Scholar 

  12. M. Coppo, M. Dezani-Ciancaglini, and B. Venneri. Principal type schemes and λ-calculus semantics. In R. Hindley and J. Seldin, editors, To H. B. Curry: essays on combinatory logic, lambda calculus and formalism, pages 535–560. Academic Press, London, 1980.

    Google Scholar 

  13. M. Coppo, M. Dezani-Ciancaglini, and M. Zacchi. Type theories, normal forms, and D -lambda-models. Inform. and Comput., 72(2):85–116, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  14. M. Dezani-Ciancaglini, F. Honsell, and F. Alessi. A complete characterization of the complete intersection-type theories. In J. Rolim and A. Broder et al., editors, ICALP Workshops 2000, volume 8 of Proceedings in Informatics, pages 287–302. Carleton-Scientific, Canada, 2000.

    Google Scholar 

  15. M. Dezani-Ciancaglini, F. Honsell, and Y. Motohama. Compositional characterization of λ-terms using intersection types. In M. Nielsen and B. Rovan, editors, Mathematical Foundations of Computer Science 2000, volume 1893 of Lecture Notes in Comput. Sci., pages 304–313. Springer, 2000.

    Google Scholar 

  16. P. Di Gianantonio and F. Honsell. An abstract notion of application. In M. Bezem and J.F. Groote, editors, Typed lambda calculi and applications, volume 664 of Lecture Notes in Comput. Sci., pages 124–138. Springer, Berlin, 1993.

    Chapter  Google Scholar 

  17. L. Egidi, F. Honsell, and S. Ronchi Della Rocca. Operational, denotational and logical descriptions: a case study. Fund. Inform., 16(2):149–169, 1992.

    MATH  MathSciNet  Google Scholar 

  18. R. Hindley and G. Longo. Lambda-calculus models and extensionality. Z. Math. Logik Grundlag. Math., 26(4):289–310, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  19. F. Honsell and M. Lenisa. Semantical analysis of perpetual strategies in λ-calculus. Theoret. Comput. Sci., 212(1-2):183–209, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  20. F. Honsell and S. Ronchi Della Rocca. A filter model for μ. Technical report, Torino University, 1984.

    Google Scholar 

  21. F. Honsell and S. Ronchi Della Rocca. An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus. J. Comput. System Sci., 45(1):49–75, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  22. B. Intrigila. A problem on easy terms in λ-calculus. Fund. Inform., 15.1:99–106, 1991.

    MathSciNet  Google Scholar 

  23. G. Jacopini. A condition for identifying two elements of whatever model of combinatory logic. In C. Böhm, editor, λ-calculus and computer science theory, volume 37 of Lecture Notes in Comput. Sci., pages 213–219. Springer, Berlin, 1975.

    Chapter  Google Scholar 

  24. G. Jacopini and M. Venturini Zilli. Easy terms in the lambda calculus. Fund. Inform., 80:225–233, 1985.

    MathSciNet  Google Scholar 

  25. R. Kerth. Isomorphisme et Équivalence Équationnelle entre Modèles du λ-Calcul. PhD thesis, Equipe de Logique Mathématique, Université Paris VII, 1995.

    Google Scholar 

  26. J. Kuper. On the Jacopini technique. Inform. and Comput., 138:101–123, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  27. J. Mitchell. Foundation for Programmimg Languages. MIT Press, 1996.

    Google Scholar 

  28. G. D. Plotkin. Set-theoretical and other elementary models of the λ-calculus. Theoret. Comput. Sci., 121(1-2):351–409, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  29. G. Pottinger. A type assignment for the strongly normalizable λterms. In R. Hindley and J. Seldin, editors, To H. B. Curry: essays on combinatory logic, lambda calculus and formalism, pages 561–577. Academic Press, London, 1980.

    Google Scholar 

  30. A. Pravato, S. Ronchi, and L. Roversi. The call-by-value lambda calculus: a semantic investigation. Math. Struct. in Comput. Sci., 9(5):617–650, 1999.

    Article  MATH  Google Scholar 

  31. D. Scott. Continuous lattices. In F. Lawvere, editor, Toposes, algebraic geometry and logic, volume 274 of Lecture Notes in Math., pages 97–136. Springer, Berlin, 1972.

    Chapter  Google Scholar 

  32. S. Vickers. Topology via logic. Cambridge University Press, Cambridge, 1989.

    MATH  Google Scholar 

  33. C. Zylberajch. Syntaxe et Semantique de la Facilité en Lambda-calcul. PhD thesis, Université Paris VII, 1991.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Alessi, F., Dezani-Ciancaglini, M., Honsell, F. (2001). Filter Models and Easy Terms. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_2

Download citation

  • DOI: https://doi.org/10.1007/3-540-45446-2_2

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42672-1

  • Online ISBN: 978-3-540-45446-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics