Parigot’s Second Order λμ-Calculus and Inductive Types

  • Ralph Matthes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


A new proof of strong normalization of Parigot’s (second order) λμ-calculus is given by a reduction-preserving embedding into system F (second order polymorphic λ-calculus). The main idea is to use the least stable supertype for any type. These non-strictly positive inductive types and their associated iteration principle are available in system F, and allow to give a translation vaguely related to CPS translations (corresponding to the Kolmogorov embedding of classical logic into intuitionistic logic). However, they simulate Parigot’s μ-reductions whereas CPS translations hide them.

As a major advantage, this embedding does not use the idea of reducing stability (¬¬¬ ¬ ¬) to that for atomic formulae. Therefore, it even extends to non-interleaving positive fixed-point types. As a non-trivial application, strong normalization of λμ-calculus, extended by primitive recursion on monotone inductive types, is established.


Classical Logic Intuitionistic Logic Natural Deduction Elimination Rule Inductive Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ralph Matthes
    • 1
  1. 1.Institut für Informatik der Ludwig-Maximilians-Universität MünchenMünchenGermany

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