Classical call-by-need and duality

  • Authors:
  • Zena M. Ariola;Hugo Herbelin;Alexis Saurin

  • Affiliations:
  • University of Oregon;Laboratoire PPS, Équipe πr2, CNRS, INRIA & Université Paris Diderot;Laboratoire PPS, Équipe πr2, CNRS, INRIA & Université Paris Diderot

  • Venue:
  • TLCA'11 Proceedings of the 10th international conference on Typed lambda calculi and applications
  • Year:
  • 2011

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Abstract

We study call-by-need from the point of view of the duality between call-by-name and call-by-value. We develop sequent-calculus style versions of call-by-need both in the minimal and classical case. As a result, we obtain a natural extension of call-by-need with control operators. This leads us to introduce a call-by-need λµ-calculus. Finally, by using the dualities principles of λµµ-calculus, we show the existence of a new call-by-need calculus, which is distinct from call-by-name, call-by-value and usual call-by-need theories.