Defining and Reasoning About Recursive Functions: A Practical Tool for the Coq Proof Assistant

  • Gilles Barthe
  • Julien Forest
  • David Pichardie
  • Vlad Rusu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3945)


We present a practical tool for defining and proving properties of recursive functions in the Coq proof assistant. The tool generates from pseudo-code the graph of the intended function as an inductive relation. Then it proves that the relation actually represents a function, which is by construction the function that we are trying to define. Then, we generate induction and inversion principles, and a fixpoint equation for proving other properties of the function. Our tool builds upon state-of-the-art techniques for defining recursive functions, and can also be used to generate executable functions from inductive descriptions of their graph. We illustrate the benefits of our tool on two case studies.


Type Theory Recursive Function Recursive Call Proof Obligation Proof Assistant 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Gilles Barthe
    • 1
  • Julien Forest
    • 1
  • David Pichardie
    • 1
  • Vlad Rusu
    • 2
  1. 1.EVEREST TeamINRIA Sophia-AntipolisFrance
  2. 2.VERTECS TeamIRISA/INRIA RennesFrance

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