Beagle as a HOL4 external ATP method

10 pages•Published: July 5, 2015

Thibault Gauthier, Cezary Kaliszyk, Chantal Keller and Michael Norrish

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.

Keyphrases: automated theorem proving, beagle, hol4

In: Stephan Schulz, Leonardo De Moura and Boris Konev (editors). PAAR-2014. 4th Workshop on Practical Aspects of Automated Reasoning, vol 31, pages 50-59.

Links:	https://easychair.org/publications/paper/Lt3c
	https://doi.org/10.29007/8xbv

BibTeX entry

@inproceedings{PAAR-2014:Beagle_as_HOL4_external,
  author    = {Thibault Gauthier and Cezary Kaliszyk and Chantal Keller and Michael Norrish},
  title     = {Beagle as a HOL4 external ATP method},
  booktitle = {PAAR-2014. 4th Workshop on Practical Aspects of Automated Reasoning},
  editor    = {Stephan Schulz and Leonardo De Moura and Boris Konev},
  series    = {EPiC Series in Computing},
  volume    = {31},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/Lt3c},
  doi       = {10.29007/8xbv},
  pages     = {50-59},
  year      = {2015}}

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