Strong Normalization of Classical Natural Deduction with Disjunction

  title={Strong Normalization of Classical Natural Deduction with Disjunction},
  author={Philippe de Groote},
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. 
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