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.
Preview
Unable to display preview. Download preview PDF.
References
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.
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.
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.
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.
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.
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.
Jean-Louis Krivine. Lambda-calcul, types et modèles. Etudes et Recherches en Informatique. Masson, 1990.
Daniel Leivant. Typing and computational properties of lambda-expressions. Theoretical Computer Science, 44:51–68, 1986.
Xavier Leroy. Typage polymorphe d'un langage algorithmique. PhD thesis, University of Paris 7, June 1992.
Ines Margaria and Maddalena Zacchi. Principal typing in a ∀∧-discipline. Journal of Logic Computation, 5(3): 367–381, 1995.
Robin Milner. A theory of type polymorphism in programming. Computer and System Sciences, 17(3):348–375, 1978.
Benjamin Pierce. Programming with Intersection Types and Bounded Quantification. PhD thesis, Carnegie Mellon University, 1991.
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.
John C. Reynolds. Preliminary design of the programming language Forsythe. Technical Report CMU-CS-88-159, Carnegie Mellon University, June 1988.
John C. Reynolds. Syntactic control of interference, part 2. Technical Report CMU-CS-89-130, Carnegie Mellon University, April 1989.
Simona Ronchi Della Rocca. Principal type scheme and unification for intersection type discipline. Theoretical Computer Science, 59:181–209, 1988.
Simona Ronchi Della Rocca and Betti Venneri. Principal type schemes for an extended type theory. Theoretical Computer Science, 28:151–169, 1984.
émilie Sayag and Michel Mauny. Characterization of principal types of normal forms in intersection type system. Technical report, INRIA, 1996. To appear.
Zhong Shao and Andrew W. Appel. Smartest recompilation. Technical Report CS-TR-395-92, Princeton University, October 1992.
Steffen van Bakel. Complete restrictions of the intersection type discipline. Theoretical Computer Science, 102:135–163, 1992.
Steffen van Bakel. Principal type schemes for strict type assignment system. Logic and Computation, 3(6):643–670, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/3-540-62034-6_61
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62034-1
Online ISBN: 978-3-540-49631-1
eBook Packages: Springer Book Archive