Abstract
Two variations of the intersection type assignment system are studied in connection with Böhm-trees. One is the intersection type assignment system with a non-standard subtype relation, by means of which we characterize whereabouts of D in Böhm-trees. The other is a refinement of the intersection type assignment system whose restricted typability is shown to coincide with finiteness of Böhm-trees.
This research was supported in part by JSPS Research Fellowships for Young Scientists.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
S. van Bakel, Complete restrictions of the intersection type descipline, Theoretical Computer Science 102 (1992), 135–163.
H. P. Barendregt, The Lambda Calculus: Its Syntax and Semantics, revised edition, North-Holland, Amsterdam, 1984.
H. P. Barendregt, M. Coppo and M. Dezani-Ciancaglini, A filter lambda model and the completeness of type assignment, Journal of Symbolic Logic 48 (1983), 931–940.
M. Coppo, M. Dezani-Ciancaglini and B. Venneri, Functional characters of solvable terms, Zeitschrift für Mathematische Logik und Grundlagen der Mathmatik 27 (1981), 45–58.
M. Coppo, M. Dezani-Ciancaglini and M. Zacchi, Type theories, normal forms and D∞ lambda-models, Information and Computation 72 (1987), 85–116.
J. Y. Girard, Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieur, Thèse de doctorat d'état, Université Paris VII, 1972.
J. Y. Girard, P. Taylor and Y. Lafont, Proofs and Types, Cambridge University Press, 1989.
J. R. Hindley, The completeness theorem for typing λ-terms, Theoretical Computer Science 22 (1983), 1–17.
F. Honsell and S. Ronchi Delia Rocca, An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus, Journal of Computer and System Sciences 45 (1992), 49–75.
J. L. Krivine, Lambda-Calculus, Types and Models, Ellis Horwood, 1993.
J. C. Mitchell, Type systems for programming languages, Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics, The MIT Press/Elsevier, 1990.
G. D. Plotkin, λ-definability in the full type hierarchy, in: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, ed. J. R. Hindley and J. P. Seldin, Academic Press, New York, 363–373.
G. Pottinger, A type assignment for the strongly normalizable λ-terms, in: To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, ed. J. R. Hindley and J. P. Seldin, Academic Press, New York, 363–373.
R. Statman, Logical relations and the typed lambda calculus, Information and Control 65 (1985), 85–97.
W. W. Tait, Intensional interpretation of functionals of finite type, Journal of Symbolic Logic 32 (1967), 198–212.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kurata, T. (1997). A type theoretical view of Böhm-trees. In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_39
Download citation
DOI: https://doi.org/10.1007/3-540-62688-3_39
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62688-6
Online ISBN: 978-3-540-68438-1
eBook Packages: Springer Book Archive