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λμ-calculus and Böhm's theorem

  • René David (a1) and Walter Py (a2)
Abstract
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.

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[1]Abramsky S. and Ong L., Full abstraction in the lazy lambda calculas, Information and Computation, vol. 105 (1993), no. 2.
[2]Aczel P., A general church-rosser theorem, Technical report, University of Manchester, 1978.
[3]Klop J. W., van Oostrom V., and van Raamsdonk F., Combinatory reduction systems, introduction and suevey, Theoretical Computer Science, vol. 121 (1993).
[4]Krivine J. L., Lambda-calcul, types et modèles, Masson, Paris, 1990.
[5]Nour K., Non deterministic classical logic: The λ∂-calculas, Private communication.
[6]Parigot M., λμ-calculas: an algorithmic interpretation of classical natural deduction, Lecture Notes in Artificial Intelligence, no. 624, Springer-Verlag, 1992.
[7]Parigot M., Classical proofs as programs, Lecture Notes in Computer Science, no. 713, Springer Verlag, 1993.
[8]Parigot M., Proofs of strong normalization for second order classical natural deduction, this Journal, vol. 62, (1997), no. 4.
[9]Prawitz D., Natural deduction, a proof-theoritical study, Almqvist & Wiksell, Stockholm, 1965.
[10]Py W., Confluence en λμcalcul, Ph.D. thesis, 1998.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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