Integrating A First-order Automatic prover In The HOL Environment

The HOL system is a powerful tool for proving higherorder formulae. However, proofs have to be performed interactively and only little automation using tactics is possible. Even though interaction is desirable to guide major and creative backward proof steps of complex proofs, a deluge of simple sub-goals may evolve which all have to be proven manually in order to accomplish the proof. Although these sub-goals are often simple formulae, their proof has not yet been automated in HOL. In this paper it is shown how it is possible to automate these tasks by integrating a first-order automated theorem proving tool, called FAUST, into HOL. It is based on an efficient variant of the well-known sequent calculus. In order to maintain the high confdence in HOL-generated proofs, FAUST is able to generate HOL tactics which may be used to post-justifr the theorem derived by FAUST in HOL. The underlying calculus of FAUST, the tactic generation, as well as experimental results are presented.