On Strong Normalization of the Calculus of Constructions with Type-Based Termination

  • Benjamin Grégoire
  • Jorge Luis Sacchini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6397)


Termination of recursive functions is an important property in proof assistants based on dependent type theories; it implies consistency and decidability of type checking. Type-based termination is a mechanism for ensuring termination that uses types annotated with size information to check that recursive calls are performed on smaller arguments. Our long-term goal is to extend the Calculus of Inductive Constructions with a type-based termination mechanism and prove its logical consistency. In this paper, we present an extension of the Calculus of Constructions (including universes and impredicativity) with sized natural numbers, and prove strong normalization and logical consistency. Moreover, the proof can be easily adapted to include other inductive types.


Recursive Function Recursive Call Typing Rule Proof Assistant Inductive Type 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Benjamin Grégoire
    • 1
  • Jorge Luis Sacchini
    • 1
  1. 1.INRIA Sophia Antipolis - MéditerranéeFrance

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