Proof Nets and Explicit Substitutions

  • Roberto Di Cosmo
  • Delia Kesner
  • Emmanuel Polonovski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1784)


We refine the simulation technique introduced in [10] to show strong normalization of λ-calculi with explicit substitutions via termination of cut elimination in proof nets [13]. We first propose a notion of equivalence relation for proof nets that extends the one in [9], and we show that cut elimination modulo this equivalence relation is terminating. We then show strong normalization of the typed version of the λ l-calculus with de Bruijn indices (a calculus with full composition defined in [8]) using a translation from typed λ l to proof nets. Finally, we propose a version of typed λ l with named variables which helps to better understand the complex mechanism of the explicit weakening notation introduced in the λ l-calculus with de Bruijn indices [8].


Linear Logic Reduction Rule Sequent Calculus Typing Rule Strong Normalization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Roberto Di Cosmo
    • 1
  • Delia Kesner
    • 2
  • Emmanuel Polonovski
    • 1
  1. 1.PPSUniversité de Paris VIIParisFrance
  2. 2.LRIUniversité de Paris-SudOrsay CedexFrance

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