Reflecting proofs in first-order logic with equality

Reflecting proofs in first-order logic with equality (2005)

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by Evelyne Contejean , Pierre Corbineau

Venue:	In Proceedings of EUROSPEECH’97
Citations:	10 - 3 self

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Datum	Value	Source
TITLE	Reflecting proofs in first-order logic with equality	INFERENCE
AUTHOR NAME	Evelyne Contejean	SVM HeaderParse 0.2
AUTHOR AFFIL	PCRI — LRI (CNRS UMR 8623) & INRIA Futurs	SVM HeaderParse 0.2
AUTHOR ADDR	Bât. 490, Université Paris-Sud, Centre d’Orsay; 91405 Orsay Cedex, France	SVM HeaderParse 0.2
AUTHOR NAME	Pierre Corbineau	SVM HeaderParse 0.2
AUTHOR AFFIL	PCRI — LRI (CNRS UMR 8623) & INRIA Futurs	SVM HeaderParse 0.2
AUTHOR ADDR	Bât. 490, Université Paris-Sud, Centre d’Orsay; 91405 Orsay Cedex, France	SVM HeaderParse 0.2
ABSTRACT	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. The aim of this paper is twofold: first we want to validate a reflective approach for proofs in interactive proof assistants, and second show how to provide a better automation for such assistants. Both aspects can be achieved by using external provers designed to automatically solve some problems of interest: these provers can “feed ” the assistant with large proofs, and help to compare the direct and the reflective approaches, and they can also release the user from (parts of) the proof.	SVM HeaderParse 0.2
YEAR	2005	INFERENCE
VENUE	In Proceedings of EUROSPEECH’97	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	7--22	INFERENCE
CITATIONS	14 found	ParsCit 1.0