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.


Normal Form Linear Logic Reduction Rule Reduction Sequence Strongly Normalise 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Beniamino Accattoli
    • 1
  • Delia Kesner
    • 2
  1. 1.INRIA and LIX, École PolytechniqueFrance
  2. 2.PPS, CNRS and Université Paris-DiderotFrance

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