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A-translation and looping combinators in pure type systems

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Thierry Coquand  and
Hugo Herbelin
Thierry Coquand
Affiliation:
(e-mail: coquand@cs.chalmers.se)
Hugo Herbelin
Affiliation:
(e-mail: herbelin@margaux.inria.fr)
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Abstract

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We present here a generalization of A-translation to a class of pure type systems. We apply this translation to give a direct proof of the existence of a looping combinator in a large class of inconsistent type systems, a class which includes type systems with a type of all types. This is the first non-automated solution to this problem.

Type
Articles
Information
Journal of Functional Programming , Volume 4 , Issue 1 , January 1994 , pp. 77 - 88
Copyright
Copyright © Cambridge University Press 1994

References

Barendregt, H. (1991) Introduction to Generalized Type System. J. Functional Programming, 1 (2) 04: 125–154.CrossRefGoogle Scholar
Coquand, T. (1991) A New Paradox in Type Theory. In Proceedings 9th International Congress of Logic, Methodology and Philosophy of Science, Uppsala, 08.Google Scholar
Friedman, H. (1978) Classical and Intuitionistically Provably Recursive Functions. In Higher Set Theory, Müller, G. H. and Scott, D. S., editors, Springer-Verlag, Lecture Notes 669, 21–27.CrossRefGoogle Scholar
Geuvers, H. and Nederhof, M.-J. (1991) Modular proof of strong normalisation for the calculus of constructions. J. Functional Programming, 1 (2) 04: 155–189.Google Scholar
Girard, J. Y. (1972) Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieur. Thése de doctorat d'état d'université Paris 7.Google Scholar
Howe, D. J. (1987) The computational behaviour of Girard's paradox. In Proceedings Second Symposium of Logic in Computer Science,(Ithaca, NY),(IEEE Press), 205–214.Google Scholar
Kolmogorov, A. N. (1967) On the principle of excluded middle. 1925. In From Frege to Gödel: a source book in mathematical logic, 1879–1931, Van Heijenoort, J., editor, Harvard University Press.Google Scholar
Leivant, D. (1985) Syntactic translations and provable recursive functions. J. Symbolic Logic, 50: 682–688.Google Scholar
Meyer, A. R. and Reinhold, M. B. (1986) “type” is not a type. In Conference record Thirteenth Annual ACM Symposium on Principles of Programming Languages,ACM SIGACT, SIGPLAN, 287–295.Google Scholar
Murthy, C. (1990) Extracting Constructive Content From Classical Proofs. PhD Thesis, Cornell University.Google Scholar
Paulin, C. (1989) Extraction de programmes dans le Calcul des Constructions. Thése de doctorat de l'universitéParis 7.Google Scholar
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