Abstract
We extend pure type systems with quotient types and subset types and establish an equivalence between four strong normalisation problems: subset types, quotient types, definitions and the so-called K-rules. As a corollary, we get strong normalisation of ECC with definitions, subset and quotient types.
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References
H. Barendregt. Typed λ-calculi, Handbook of logic in computer science, Abramsky and al eds, OUP 1992.
G. Barthe. Towards a mathematical vernacular, submitted.
G. Barthe. Formalizing mathematics in type theory: fundamentals and case studies, submitted.
G. Barthe. An introduction to quotient and congruence types, manuscript, University of Nijmegen, November 1994.
R. Constable and al. Implementing Mathematics with the NuPrl Proof Development System, Prenctice Hall, 1986.
T. Coquand. A new paradox in type theory, in the proceedings of the 9th Congress of Logic, Methodology and Philosophy of Science.
H. Geuvers. Logics and type systems, Ph.D thesis, University of Nijmegen, 1993.
H. Geuvers. A short and flexible proof of strong normalisation for the Calculus of Constructions, submitted.
M. Hofmann. Extensional concepts in intensional type theory, Ph.D thesis, University of Edinburgh, forthcoming.
M. Hofmann. A simple model for quotient types, in these proceedings.
B. Jacobs. Categorical Logic and Type Theory, in preparation.
B. Jacobs. Quotients in simple Type Theory, submitted.
J. Lambek and P.J. Scott. Introduction to higher-order categorical logic, CUP, 1986.
Z. Luo. Computation and reasoning: a type theory for computer science, OUP, 1994.
N. Mendler. Quotient types via coequalisers in Martin-Lof's type theory, in the informal proceedings of the workshop on logical frameworks, Antibes, May 1990.
R. Nederpelt and al (eds). Selected Papers on Automath, North-Holland, 1994.
B. Nordstrom, K. Petersson and J. Smith. Programming in Martin-Lof's type theory, OUP, 1990.
E. Poll and P. Severi. PTS with definitions, in proceedings of LFCS'94, LNCS 813.
G. Pottinger. Definite descriptions and excluded middle in the theory of constructions, TYPES mailing list, November 1989.
A. Salvesen and J. Smith. The strength of the subset type in Martin-Lof's type theory, proceedings of LICS'88, 1988.
J. Terlouw. Strong normalisation in type systems: a model-theoretical approach, Dirk van Dalen Festschrift, Utrecht, 1993.
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© 1995 Springer-Verlag Berlin Heidelberg
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Barthe, G. (1995). Extensions of pure type systems. 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/BFb0014042
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DOI: https://doi.org/10.1007/BFb0014042
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