Building Decision Procedures in the Calculus of Inductive Constructions

  • Frédéric Blanqui
  • Jean-Pierre Jouannaud
  • Pierre-Yves Strub
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4646)


It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P’ obtained from P thanks to possibly complex calculations.

In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.


Calculus of Inductive Constructions Decision procedures Theorem provers 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Frédéric Blanqui
    • 1
  • Jean-Pierre Jouannaud
    • 2
  • Pierre-Yves Strub
    • 2
  1. 1.LORIA, Equipe Protheo, Campus Scientifique, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex 
  2. 2.LogiCal LIX, UMR CNRS 7161, École Polytechnique, 91128 PlaiseauFrance

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