On the Degeneracy of Σ-Types in Presence of Computational Classical Logic

  • Hugo Herbelin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3461)


We show that a minimal dependent type theory based on Σ-types and equality is degenerated in presence of computational classical logic. By computational classical logic is meant a classical logic derived from a control operator equipped with reduction rules similar to the ones of Felleisen’s \({\mathcal C}\) or Parigot’s μ operators. As a consequence, formalisms such as Martin-Löf’s type theory or the (Set-predicative variant of the) Calculus of Inductive Constructions are inconsistent in presence of computational classical logic. Besides, an analysis of the role of the η-rule for control operators through a set-theoretic model of computational classical logic is given.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hugo Herbelin
    • 1
  1. 1.École PolytechniqueLIX – INRIA-Futurs – PCRIPalaiseau Cedex

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