Abstract
This paper introduces typed operational semantics, a class of formal systems which define a reduction to normal form for the welltyped terms of a particular type theory. These systems lead to a new approach to the metatheory for type theories, which we develop here for the simply typed lambda calculus. A similar approach can be used to study systems with dependent types.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
T. Altenkirch. Constructions, Inductive Types and Strong Normalization. PhD thesis, University of Edinburgh, 1993.
H. Barendregt. The Lambda Calculus: its Syntax and Semantics. North Holland, revised edition, 1984.
H. Barendregt. Lambda calculi with types. In S. Abramsky, D. M. Gabbai, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, volume 2. Oxford University Press, 1991.
T. Coquand. An algorithm for testing conversion in type theory. In G. Huet and G. Plotkin, editors, Logical Frameworks. Cambridge University Press, 1991.
T. Coquand and J. Gallier. A proof of strong normalization for the theory of constructions using a Kripke-like interpretation. In Workshop on Logical Frameworks-Preliminary Proceedings, 1990.
H. Geuvers. Logics and Type Systems. PhD thesis, Katholieke Universiteit Nijmegen, Sept. 1993.
H. Goguen. The metatheory of UTT. Submitted to Proceedings of BRA Workshop on Types for Proofs and Programs, 1994.
H. Goguen. A Typed Operational Semantics for Type Theory. PhD thesis, University of Edinburgh, Aug. 1994.
Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, Nov. 1990.
Z. Luo. Computation and Reasoning. Oxford University Press, 1994.
P. Martin-Löf. An intuitionistic theory of types: Predicative part. In H. Rose and J. C. Shepherdson, editors, Logic Colloqium 1973, pages 73–118, 1975.
P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, 1984.
J. McKinna and R. Pollack. Pure type systems formalized. In M. Bezem and J. F. Groote, editors, Proceedings of the International Conference on Typed Lambda Calculi and Applications, pages 289–305. Springer-Verlag, LNCS 664, Mar. 1993.
J. Mitchell. Type systems for programming languages. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science. North Holland, 1990.
A. Salvesen. The Church-Rosser property for pure type systems with βη-reduction, Nov. 1991. Unpublished manuscript.
W. W. Tait. Intensional interpretation of functionals of finite type I. Journal of Symbolic Logic, 32, 1967.
L. van Benthem Jutting, J. McKinna, and R. Pollack. Typechecking in pure type systems. In H. Barendregt and T. Nipkow, editors, Types for Proofs and Programming. Springer-Verlag, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Goguen, H. (1995). Typed operational semantics. In: Dezani-Ciancaglini, M., Plotkin, G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014053
Download citation
DOI: https://doi.org/10.1007/BFb0014053
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-59048-4
Online ISBN: 978-3-540-49178-1
eBook Packages: Springer Book Archive