Characterizing Convergent Terms in Object Calculi via Intersection Types

  • Ugo de’Liguoro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (\( \varsigma \) -calculus) via intersection types. We consider a λ-calculus with records and its intersection type assignment system. We prove that convergent λ-terms are characterized by their types. The characterization is then inherited by the object calculus via self-application interpretation.


Normal Form Intersection Type Operational Semantic Record Type Type Assignment 
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  1. 1.
    M. Abadi, L. Cardelli, A Theory of Objects, Springer 1996.Google Scholar
  2. 2.
    M. Abadi, L. Cardelli, R. Viswanathan, “An interpretation of objects and object types” Proc. of of POPL’96 1996, 396–409.Google Scholar
  3. 3.
    S. Abramsky, “Domain Theory in Logical Form”, APAL 51, 1991, 1–77.zbMATHMathSciNetGoogle Scholar
  4. 4.
    S. Abramsky, C.-H. L. Ong “Full abstraction in the lazy lambda calculus”, Inf. Comput. 105(2), 1993, 159–267.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    S. van Bakel, Intersection Type Disciplines in Lambda Calculus and Applicative Term Rewriting, Ph.D. Thesis, Mathematisch Centrum, Amsterdam 1993.Google Scholar
  6. 6.
    H.P. Barendregt, M. Coppo, M. Dezani, “A Filter Lambda Model and the Completeness of Type Assignment”, JSL 48, 1983, 931–940.zbMATHCrossRefGoogle Scholar
  7. 7.
    G. Boudol, “A Lambda Calculus for (Strict) Parallel Functions”, Info. Comp. 108, 1994, 51–127.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    K.B. Bruce, “A paradigmatic Object-Oriented design, static typing and semantics”, J. of Fun. Prog. 1(4), 1994, 127–206.MathSciNetCrossRefGoogle Scholar
  9. 9.
    K.B. Bruce, L. Cardelli, B.C. Pierce, “Comparing object encodings”, Proc. of TACS’97, LNCS 1281, 1997, 415–438.Google Scholar
  10. 10.
    K. Crary, “Simple, Efficient Object Encoding using Intersection Types”, CMU Technical Report CMU-CS-99-100.Google Scholar
  11. 11.
    M. Coppo, F. Damiani, P. Giannini, “Inference based analyses of functional programs: dead-code and strictness”, in M. Okada, M. Dezani eds., Theories of Types and Proofs, Mathematical Society of Japan, vol. 2, 1998 [28]}, 143–176.Google Scholar
  12. 12.
    M. Coppo, M. Dezani, B. Venneri, “Functional characters of solvable terms”, Grund. der Math., 27, 1981, 45–58.zbMATHCrossRefGoogle Scholar
  13. 13.
    M. Coppo, A. Ferrari, “Type inference, abstract interpretation and strictness analysis”, TCS 121, 1993, 113–144.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    M. Dezani, E. Giovannetti, U. de Liguoro, “Intersection types, λ-models and Böhm trees”, in M. Okada, M. Dezani eds., Theories of Types and Proofs, Mathematical Society of Japan, vol. 2, 1998 [28]}, 45–97.Google Scholar
  15. 15.
    M. Dezani, F. Honsell, Y. Motohama, “Compositional Characterizations of λ-terms using Intersection Types”, Proc. of MFCS’00, LNCS 1893, 2000, 304–313.Google Scholar
  16. 16.
    M. Dezani, U. de Liguoro, A. Piperno. “A filter model for concurrent lambda-calculus”, Siam J. Comput. 27(5), 1998, 1376–1419.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    L. Egidi, F. Honsell, S. Ronchi della Rocca, “Operational, denotational and logical descriptions: a case study”, Fund. Inf. 16, 1992, 149–169.zbMATHGoogle Scholar
  18. 18.
    K. Fisher, F. Honsell, J.C. Mitchell, “A lambda calculus of objects and method specialization”, Nordic J. Comput. 1, 1994, 3–37.zbMATHMathSciNetGoogle Scholar
  19. 19.
    A. Gordon, G. Rees, “Bisimilarity for first-order calculus of objects with subtyping”, Proc. of POPL’96, 1996, 386–395.Google Scholar
  20. 20.
    H. Ishihara, T. Kurata, “Completeness of intersection and union type assignment systems for call-by-value λ-models”, to appear in TCS.Google Scholar
  21. 21.
    S. Kamin, “Inheritance in Smalltalk-80: a denotational definition”, Proc. of POPL’88, 1988, 80–87.Google Scholar
  22. 22.
    J.L. Krivine, Lambda-calcul, types et modéles, Masson 1990.Google Scholar
  23. 23.
    J.C. Mitchell, Foundations for Programming Languages, MIT Press, 1996.Google Scholar
  24. 24.
    B. Pierce, Programming with Intersection Types and Bounded Polymorphism, Ph.D. Thesis, 1991.Google Scholar
  25. 25.
    G. Pottinger, “A Type Assignment System for Strongly Normalizable λ-terms”, in R. Hindley, J. Seldin eds., To H.B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalisms, Academic Press, 1980, 561–527.Google Scholar
  26. 26.
    J. Reynolds, “The Coherence of Languages with Intersection Types”, LNCS 526, 1991, 675–700.MathSciNetGoogle Scholar
  27. 27.
    D. Scott, “Data types as lattices”, SIAM J. Comput. 5,n. 3, 1976, 522–587.zbMATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    M. Takahashi, M. Okada, M. Dezani eds., Theories of Types and Proofs, Mathematical Society of Japan, vol. 2, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ugo de’Liguoro
    • 1
  1. 1.Dipartimento di InformaticaUniversità di TorinoTorinoItaly

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