Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

  • José Espírito Santo
  • Ralph Matthes
  • Luís Pinto
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)


The intuitionistic fragment of the call-by-name version of Curien and Herbelin’s \({{\overline{\lambda}} \mu \tilde{\mu}}\)-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed λ-calculus. Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa’s translation of Parigot’s λμ-calculus. The embedding simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need “units of garbage” to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding.


Reduction Rule Critical Pair Natural Deduction Sequent Calculus Typing Rule 
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© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • José Espírito Santo
    • 1
  • Ralph Matthes
    • 2
  • Luís Pinto
    • 1
  1. 1.Departamento de Matemática, Universidade do MinhoPortugal
  2. 2.C.N.R.S. and University of Toulouse IIIFrance

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