The permutative λ-calculus

  • Authors:
  • Beniamino Accattoli;Delia Kesner

  • Affiliations:
  • INRIA and LIX, École Polytechnique, France;PPS, CNRS and Université Paris-Diderot, France

  • Venue:
  • LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
  • Year:
  • 2012

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Abstract

We introduce the permutative λ-calculus, an extension of λ-calculus with three equations and one reduction rule for permuting constructors, generalising many calculi in the literature, in particular Regnier's sigma-equivalence and Moggi's assoc-equivalence. We prove confluence modulo the equations and preservation of beta-strong normalisation (PSN) by means of an auxiliary substitution calculus. The proof of confluence relies on M-developments, a new notion of development for λ-terms.