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International Conference on Typed Lambda Calculi and Applications

TLCA 2001: Typed Lambda Calculi and Applications pp 182–196Cite as

Strong Normalization of Classical Natural Deduction with Disjunction

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2044))

Abstract

We introduce λμ →∧∨⊥ an extension of Parigot’s λμ-calculus where disjunction is taken as a primitive. The associated reduction rela- tion, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal de- ductions satisfy the subformula property. From a computer science point of view, λμ →∧∨⊥ may be seen as the core of a typed cbn functional language featuring product, coproduct, and control operators.

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Author information

Authors and Affiliations

  1. LORIA UMR no 7503 - INRIA, Campus Scientifique, B.P. 239, 54506, Vandœvre lès Nancy Cedex, France

    Philippe de Groote

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  1. Philippe de Groote
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Editor information

Editors and Affiliations

  1. Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, USA

    Samson Abramsky

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© 2001 Springer-Verlag Berlin Heidelberg

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de Groote, P. (2001). Strong Normalization of Classical Natural Deduction with Disjunction. In: Abramsky, S. (eds) Typed Lambda Calculi and Applications. TLCA 2001. Lecture Notes in Computer Science, vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45413-6_17

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  • DOI: https://doi.org/10.1007/3-540-45413-6_17

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41960-0

  • Online ISBN: 978-3-540-45413-7

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