Minimal classical logic and control operators

  • Authors:
  • Zena M. Ariola;Hugo Herbelin

  • Affiliations:
  • University of Oregon, Eugene, OR;INRIA-uturs, Parc Club Orsay Université, Orsay Cedex, France

  • Venue:
  • ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
  • Year:
  • 2003

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Abstract

We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce's law without enforcing Ex Falso Quodlibet. We show that a "natural" implementation of this logic is Parigot's classical natural deduction. We then move on to the computational side and emphasize that Parigot's λµ corresponds to minimal classical logic. A continuation constant must be added to λµ to get full classical logic. We then map the extended λµ to a new theory of control, λ-C--top, which extends Felleisen's reduction theory. λ-C--top allows one to distinguish between aborting and throwing to a continuation. It is also in correspondence with the proofs of a refinement of Prawitz's natural deduction.