Complexity of strongly normalising λ-terms via non-idempotent intersection types

  • Authors:

  • Alexis Bernadet;Stéphane Lengrand

  • Affiliations:

  • École Polytechnique, France and École Normale Supérieur de Cachan, France;École Polytechnique, France and CNRS, France

  • Venue:
  • FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
  • Year:
  • 2011

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Abstract

We present a typing system for the λ-calculus, with nonidempotent intersection types. As it is the case in (some) systems with idempotent intersections, a lambda;-term is typable if and only if it is strongly normalising. Non-idempotency brings some further information into typing trees, such as a bound on the longest β-reduction sequence reducing a term to its normal form. We actually present these results in Klop's extension of lambda;-calculus, where the bound that is read in the typing tree of a term is refined into an exact measure of the longest reduction sequence. This complexity result is, for longest reduction sequences, the counterpart of de Carvalho's result for linear head-reduction sequences.