Strong normalization of classical natural deduction with disjunction

  • Authors:
  • Philippe de Groote

  • Affiliations:
  • LORIA UMR, INRIA, Vandœuvre lès Nancy Cedex, France

  • Venue:
  • TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
  • Year:
  • 2001

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Abstract

We introduce λµ...., an extension of Parigot's λµ-calculus where disjunction is taken as a primitive. The associated reduction relation, which includes the permutative conversions related to disjunction, is Church-Rosser, strongly normalizing, and such that the normal deductions 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.