Article

Soundness of the Logical Framework for Its Typed Operational Semantics

Author: Healfdene GoguenAuthors Info & Claims

TLCA '99: Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications

Pages 177 - 197

Published: 07 April 1999 Publication History

Abstract

Typed operational semantics [4,5] is a technique for describing the operational behavior of the terms of type theory. The combination of operational information and types provides a strong induction principle that allows an elegant and uniform treatment of the metatheory of type theory. In this paper, we adapt the new proof of strong normalization by Joachimski and Matthes [6] for the simply-typed λ-calculus to prove soundness of the Logical Framework for its typed operational semantics. This allows an elegant treatment of strong normalization, Church-Rosser, and subject reduction for βv-reduction for the Logical Framework. Along the way, we also give a cleaner presentation of typed operational semantics than has appeared elsewhere.

References

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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.

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A. Compagnoni and H. Goguen. Typed operational semantics for higher order subtyping. Technical Report ECS-LFCS-97-361, Edinburgh Univ., July 1997. Submitted to Information and Computation.

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H. Geuvers. Logics and Type Systems. PhD thesis, Katholieke Universiteit Nijmegen, Sept. 1993.

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H. Goguen. A Typed Operational Semantics for Type Theory. PhD thesis, Edinburgh Univ., Aug. 1994.

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H. Goguen. Typed operational semantics. In Proceedings of TLCA, volume 902 of Lecture Notes in Computer Science, pages 186-200. Springer-Verlag, Apr. 1995.

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F. Joachimski and R. Matthes. Short proofs of strong normalization, 1998. Draft, submitted for publication.

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A. Jones, Z. Luo, and S. Soloviev. Some algorithmic and proof-theoretical aspects of coercive subtyping. In Proceedings of TYPES'96, 1996. To appear.

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Z. Luo. An Extended Calculus of Constructions. PhD thesis, Edinburgh Univ., Nov. 1990.

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J. McKinna and R. Pollack. Pure type systems formalized. In M. Bezem and J. F. Groote, editors, Proceedings of TLCA, pages 289-305. Springer-Verlag, LNCS 664, Mar. 1993.

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B. Nordström, K. Petersson, and J. Smith. Programming in Martin-Löf's Type Theory: An Introduction. Oxford University Press, 1990.

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G. Pottinger. Strong normalization for the terms of the theory of constructions. Technical Report TR 11-7, Odyssey Research Associates, Inc., 1987.

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F. van Raamsdonk and P. Severi. On normalisation. Technical Report CS-R9545, CWI Amsterdam, 1995.

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Cited By

Luo Z(2009)Dependent record types revisitedProceedings of the 1st Workshop on Modules and Libraries for Proof Assistants10.1145/1735813.1735819(30-37)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1735813.1735819
Abel A(2006)Polarized subtyping for sized typesProceedings of the First international computer science conference on Theory and Applications10.1007/11753728_39(381-392)Online publication date: 8-Jun-2006
https://dl.acm.org/doi/10.1007/11753728_39
Harper RPfenning F(2005)On equivalence and canonical forms in the LF type theoryACM Transactions on Computational Logic (TOCL)10.1145/1042038.10420416:1(61-101)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.1145/1042038.1042041
Show More Cited By

Index Terms

Soundness of the Logical Framework for Its Typed Operational Semantics
1. Mathematics of computing
  1. Mathematical analysis
    1. Calculus
      1. Lambda calculus
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program semantics
      1. Operational semantics

Index terms have been assigned to the content through auto-classification.

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cover image Guide Proceedings

TLCA '99: Proceedings of the 4th International Conference on Typed Lambda Calculi and Applications

April 1999

396 pages

ISBN:3540657630

Editor:
Jean-Yves Girard

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 April 1999

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Cited By

Luo Z(2009)Dependent record types revisitedProceedings of the 1st Workshop on Modules and Libraries for Proof Assistants10.1145/1735813.1735819(30-37)Online publication date: 3-Aug-2009
https://dl.acm.org/doi/10.1145/1735813.1735819
Abel A(2006)Polarized subtyping for sized typesProceedings of the First international computer science conference on Theory and Applications10.1007/11753728_39(381-392)Online publication date: 8-Jun-2006
https://dl.acm.org/doi/10.1007/11753728_39
Harper RPfenning F(2005)On equivalence and canonical forms in the LF type theoryACM Transactions on Computational Logic (TOCL)10.1145/1042038.10420416:1(61-101)Online publication date: 1-Jan-2005
https://dl.acm.org/doi/10.1145/1042038.1042041
Abel ACoquand T(2005)Untyped algorithmic equality for martin-löf's logical framework with surjective pairsProceedings of the 7th international conference on Typed Lambda Calculi and Applications10.1007/11417170_4(23-38)Online publication date: 21-Apr-2005
https://dl.acm.org/doi/10.1007/11417170_4
Pfenning F(2001)Logical frameworksHandbook of automated reasoning10.5555/778522.778526(1063-1147)Online publication date: 1-Jan-2001
https://dl.acm.org/doi/10.5555/778522.778526

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