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Proof-irrelevance out of excluded-middle and choice in the calculus of constructions

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Franco Barbanera  and
Stefano Berardi
Franco Barbanera
Affiliation:
Dipartimento di Informatica, Universita' di Torino, Corso Svizzera 185, 10149 Torino, Italy (e-mail: {barba, stefano} @di.unito.it)
Stefano Berardi
Affiliation:
Dipartimento di Informatica, Universita' di Torino, Corso Svizzera 185, 10149 Torino, Italy (e-mail: {barba, stefano} @di.unito.it)
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Abstract

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We present a short and direct syntactic proof of the fact that adding the axiom of choice and the principle of excluded-middle to Coquand–Huet's Calculus of Constructions gives proof-irrelevance.

Type
Articles
Information
Journal of Functional Programming , Volume 6 , Issue 3 , May 1996 , pp. 519 - 526
Copyright
Copyright © Cambridge University Press 1996

References

Barendregt, H. P. (1992) Typed Lambda Calculi. In Abramski, et al. , editors, Handbook of Logic in Computer Science., Oxford University Press.Google Scholar
Berardi, S. (1994) A formalization in LEGO of a proof of Proof-Irrelevance. Technical Report, Department of Computer Science University of Torino.Google Scholar
Coquand, T. (1990) Metamathematical investigation of a calculus of construction. In Odifreddi, P., editor, Logic and Computer Science. Academic Press.Google Scholar
Coquand, T. and Huet, G. (1988) The Calculus of Constructions. Information and Computation 76.CrossRefGoogle Scholar
Geuvers, H. (1993) Logics and Type Systems. PhD Thesis, University of Nijmegen.Google Scholar
Geuvers, H. (1994) Conservativity between logics and typed λ-calculi. Proc. BRA Workshop on Types for Proofs and Programs.CrossRefGoogle Scholar
Hurkens, A. J. C. (1995) A simplification of Girard's paradox. In Dezani-Ciancaglini, M. and Plotkin, G. editors, Proc. 2nd International Conference on Typed Lambda Calculi and Applications (TLCA'95): Lecture Notes in Computer Science 902.Springer-Verlag.Google Scholar
Pottinger, G. (1989) Definite descriptions and excluded middle in the calculus of constructions. TYPES network, November.Google Scholar
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