Reflecting Proofs in First-Order Logic with Equality

  • Evelyne Contejean
  • Pierre Corbineau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3632)


Our general goal is to provide better automation in interactive proof assistants such as Coq. We present an interpreter of proof traces in first-order multi-sorted logic with equality. Thanks to the reflection ability of Coq, this interpreter is both implemented and formally proved sound — with respect to a reflective interpretation of formulae as Coq properties — inside Coq’s type theory. Our generic framework allows to interpret proofs traces computed by any automated theorem prover, as long as they are precise enough: we illustrate that on traces produced by the CiME tool when solving unifiability problems by ordered completion. We discuss some benchmark results obtained on the TPTP library.


Word Problem Critical Pair Sequent Calculus Proof Assistant Interpretation Function 
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-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Evelyne Contejean
    • 1
  • Pierre Corbineau
    • 1
  1. 1.PCRI — LRI (CNRS UMR 8623) & INRIA Futurs, Bât. 490Université Paris-SudOrsay CedexFrance

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