Abstract

This paper presents BEAGLE TAC, a HOL4 tactic for using Beagle as an external ATP for discharging HOL4 goals. We implement a translation of the higher-order goals to the TFA format of TPTP and add trace output to Beagle to reconstruct the intermediate steps derived by the ATP in HOL4. Our translation combines the characteristics of existing successful translations from HOL to FOL and SMT-LIB, however we needed to adapt certain stages of the translation in order to benefit form the expressivity of the TFA format and the power of Beagle. In our initial experiments, we demonstrate that our system can prove, without any arithmetic lemmas, 81% of the goals solved by Metis.

BibTeX

@inproceedings{TGCKCKMN-PAAR14,
  author    = "Thibault Gauthier and Cezary Kaliszyk and Chantal Keller and
               Michael Norrish",
  title     = "{Beagle} as a {HOL4} External {ATP} Method",
  booktitle = "Proceedings of the 4th Workshop on Practical Aspects of
               Automated Reasoning (PAAR 2014)",
  editor    = "Stephan Schulz and Leonardo De Moura and Boris Konev",
  series    = "EasyChair Proceedings in Computer Science",
  volume    = 31,
  pages     = "50--59",
  year      = 2015
}