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A Formalized Proof of Strong Normalization for Guarded Recursive Types

  • Andreas Abel
  • Andrea Vezzosi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8858)

Abstract

We consider a simplified version of Nakano’s guarded fixed-point types in a representation by infinite type expressions, defined coinductively. Smallstep reduction is parametrized by a natural number “depth” that expresses under how many guards we may step during evaluation. We prove that reduction is strongly normalizing for any depth. The proof involves a typed inductive notion of strong normalization and a Kripke model of types in two dimensions: depth and typing context. Our results have been formalized in Agda and serve as a case study of reasoning about a language with coinductive type expressions.

Keywords

Kripke Model Typing Context Type Constructor Strong Normalization Recursive 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 International Publishing Switzerland 2014

Authors and Affiliations

  • Andreas Abel
    • 1
  • Andrea Vezzosi
    • 1
  1. 1.Computer Science and EngineeringChalmers and Gothenburg UniversityGöteborgSweden

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