CIC\(\widehat{~}\): Type-Based Termination of Recursive Definitions in the Calculus of Inductive Constructions

  • Gilles Barthe
  • Benjamin Grégoire
  • Fernando Pastawski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)


Sized types provides a type-based mechanism to enforce termination of recursive definitions in typed λ-calculi. Previous work has provided strong indications that type-based termination provides an appropriate foundation for proof assistants based on type theory; however, most work to date has been confined to non-dependent type systems. In this article, we introduce a variant of the Calculus of Inductive Constructions with sized types and study its meta theoretical properties: subject reduction, normalization, and thus consistency and decidability of type-checking and of size-inference. A prototype implementation has been developed alongside case studies.


Type System Proof Assistant Elimination Rule Inductive Type Inductive Construction 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gilles Barthe
    • 1
  • Benjamin Grégoire
    • 1
  • Fernando Pastawski
    • 1
    • 2
  1. 1.INRIA Sophia-AntipolisFrance
  2. 2.FaMAFUniv. Nacional de CórdobaArgentina

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