Goal Translation for a Hammer for Coq (Extended Abstract)
{\L}ukasz Czajka (University of Innsbruck), Cezary Kaliszyk, (University of Innsbruck)
TL;DR
This paper extends proof automation tools, called hammers, to advanced type theory systems like Coq by translating Coq logic into formats suitable for automated proof systems and developing a proof reconstruction mechanism.
Contribution
It introduces a novel translation of Coq logic into automated proof system formats and a proof reconstruction method tailored for type theory.
Findings
Successful translation of Coq logic into proof system formats
Development of a proof reconstruction mechanism for type theory
Enhanced automation capabilities for Coq and similar systems
Abstract
Hammers are tools that provide general purpose automation for formal proof assistants. Despite the gaining popularity of the more advanced versions of type theory, there are no hammers for such systems. We present an extension of the various hammer components to type theory: (i) a translation of a significant part of the Coq logic into the format of automated proof systems; (ii) a proof reconstruction mechanism based on a Ben-Yelles-type algorithm combined with limited rewriting, congruence closure and a first-order generalization of the left rules of Dyckhoff's system LJT.
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