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Characterization of the principal type of normal forms in an intersection type system

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Book cover Foundations of Software Technology and Theoretical Computer Science (FSTTCS 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1180))

Abstract

We introduce a restriction of the intersection type discipline that leads to a principal type property in the classical sense for normal forms. We characterize completely the structure of principal types of normal forms and we give an algorithm that reconstructs normal forms from types.

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References

  1. Henk P. Barendregt, Mario Coppo, and Mariangiola Dezani-Ciancaglini. A filter lambda model and the completeness of type assignment. Journal of Symbolic Logic, 48(4):931–940, 1983.

    Google Scholar 

  2. Felice Cardone and Mario Coppo. Two extensions of Curry's type inference system. In P. Odifreddi, editor, Logic in Computer Science, volume 31, pages 19–75. APIC Studies in Data Processing, Academic Press, 1990.

    Google Scholar 

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

    Google Scholar 

  4. Mario Coppo, Mariangiola Dezani-Ciancaglini, and Betti Venneri. Principal type schemes and λ-calculus semantics. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry: Essays in Combinatory Logic, Lambda-calculus and Formalism, pages 536–560. Academic Press, London, 1980.

    Google Scholar 

  5. Mario Coppo, Mariangiola Dezani-Ciancaglini, and Betti Venneri. Functional characters of solvable terms. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik, 27:45–58, 1981.

    Google Scholar 

  6. Philippa Gardner. Discovering needed reductions using type theory. In M. Hagiya and John C. Mitchell, editors, Proceedings of TACS'94, volume 789 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

    Google Scholar 

  7. Jean-Louis Krivine. Lambda-calcul, types et modèles. Etudes et Recherches en Informatique. Masson, 1990.

    Google Scholar 

  8. Daniel Leivant. Typing and computational properties of lambda-expressions. Theoretical Computer Science, 44:51–68, 1986.

    Google Scholar 

  9. Xavier Leroy. Typage polymorphe d'un langage algorithmique. PhD thesis, University of Paris 7, June 1992.

    Google Scholar 

  10. Ines Margaria and Maddalena Zacchi. Principal typing in a ∀∧-discipline. Journal of Logic Computation, 5(3): 367–381, 1995.

    Google Scholar 

  11. Robin Milner. A theory of type polymorphism in programming. Computer and System Sciences, 17(3):348–375, 1978.

    Google Scholar 

  12. Benjamin Pierce. Programming with Intersection Types and Bounded Quantification. PhD thesis, Carnegie Mellon University, 1991.

    Google Scholar 

  13. Garel Pottinger. A type assignment for the strongly normalizable λ-terms. In J. R. Hindley and J. P. Seldin, editors, To H.B. Curry: Essays in Combinatory Logic, λ-Calculus and Formalism, pages 561–577. Academic Press, 1980.

    Google Scholar 

  14. John C. Reynolds. Preliminary design of the programming language Forsythe. Technical Report CMU-CS-88-159, Carnegie Mellon University, June 1988.

    Google Scholar 

  15. John C. Reynolds. Syntactic control of interference, part 2. Technical Report CMU-CS-89-130, Carnegie Mellon University, April 1989.

    Google Scholar 

  16. Simona Ronchi Della Rocca. Principal type scheme and unification for intersection type discipline. Theoretical Computer Science, 59:181–209, 1988.

    Google Scholar 

  17. Simona Ronchi Della Rocca and Betti Venneri. Principal type schemes for an extended type theory. Theoretical Computer Science, 28:151–169, 1984.

    Google Scholar 

  18. émilie Sayag and Michel Mauny. Characterization of principal types of normal forms in intersection type system. Technical report, INRIA, 1996. To appear.

    Google Scholar 

  19. Zhong Shao and Andrew W. Appel. Smartest recompilation. Technical Report CS-TR-395-92, Princeton University, October 1992.

    Google Scholar 

  20. Steffen van Bakel. Complete restrictions of the intersection type discipline. Theoretical Computer Science, 102:135–163, 1992.

    Google Scholar 

  21. Steffen van Bakel. Principal type schemes for strict type assignment system. Logic and Computation, 3(6):643–670, 1993.

    Google Scholar 

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V. Chandru V. Vinay

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© 1996 Springer-Verlag Berlin Heidelberg

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Sayag, E., Mauny, M. (1996). Characterization of the principal type of normal forms in an intersection type system. In: Chandru, V., Vinay, V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1996. Lecture Notes in Computer Science, vol 1180. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62034-6_61

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  • DOI: https://doi.org/10.1007/3-540-62034-6_61

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  • Print ISBN: 978-3-540-62034-1

  • Online ISBN: 978-3-540-49631-1

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