Reflecting proofs in first-order logic with equality

Authors:
Evelyne Contejean;Pierre Corbineau
Affiliations:
PCRI — LRI (CNRS UMR 8623) & INRIA Futurs, Bât. 490, Université Paris-Sud, Orsay Cedex, France;PCRI — LRI (CNRS UMR 8623) & INRIA Futurs, Bât. 490, Université Paris-Sud, Orsay Cedex, France
Venue:
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Year:
2005

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Abstract

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.