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λμ-calculus and Böhm's theorem

Published online by Cambridge University Press:  12 March 2014

René David  and
Walter Py
René David
Affiliation:
Laboratoire de Maths, Campus Scientifique, F 73376 le Bourget du Lac, France, E-mail: david@univ-savoie.fr
Walter Py
Affiliation:
Laboratoire de Maths, Campus Scientifique, F 73376 le Bourget du Lac, France
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Abstract

The λμ-calculus is an extension of the λ-calculus that has been introduced by M Parigot to give an algorithmic content to classical proofs. We show that Böhm's theorem fails in this calculus.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 407 - 413
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

[1]Abramsky, S. and Ong, L., Full abstraction in the lazy lambda calculas, Information and Computation, vol. 105 (1993), no. 2.CrossRefGoogle Scholar
[2]Aczel, P., A general church-rosser theorem, Technical report, University of Manchester, 1978.Google Scholar
[3]Klop, J. W., van Oostrom, V., and van Raamsdonk, F., Combinatory reduction systems, introduction and suevey, Theoretical Computer Science, vol. 121 (1993).CrossRefGoogle Scholar
[4]Krivine, J. L., Lambda-calcul, types et modèles, Masson, Paris, 1990.Google Scholar
[5]Nour, K., Non deterministic classical logic: The λ∂-calculas, Private communication.Google Scholar
[6]Parigot, M., λμ-calculas: an algorithmic interpretation of classical natural deduction, Lecture Notes in Artificial Intelligence, no. 624, Springer-Verlag, 1992.Google Scholar
[7]Parigot, M., Classical proofs as programs, Lecture Notes in Computer Science, no. 713, Springer Verlag, 1993.CrossRefGoogle Scholar
[8]Parigot, M., Proofs of strong normalization for second order classical natural deduction, this Journal, vol. 62, (1997), no. 4.Google Scholar
[9]Prawitz, D., Natural deduction, a proof-theoritical study, Almqvist & Wiksell, Stockholm, 1965.Google Scholar
[10]Py, W., Confluence en λμcalcul, Ph.D. thesis, 1998.Google Scholar