Sharing HOL4 and HOL Light Proof Knowledge

Abstract

Abstract. New proof assistant developments often involve concepts similar to already formalized ones. When proving their properties, a human can often take inspiration from the existing formalized proofs available in other provers or libraries. In this paper we propose and evaluate a number of methods, which strengthen proof automation by learning from proof libraries of different provers. Certain conjectures can be proved directly from the dependencies induced by similar proofs in the other library. Even if exact correspondences are not found, learning-reasoning systems can make use of the association between proved theorems and their characteristics to predict the relevant premises. Such external help can be further combined with internal advice. We evaluate the proposed knowledge-sharing methods by reproving the HOL Light and HOL4 standard libraries. The learning-reasoning system HOL(y)Hammer, whose single best strategy could automatically find proofs for 30% of the HOL Light problems, can prove 40% with the knowledge from HOL4.

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

“…Vampire in 300 s solves 27 842 problems. Future work includes joint evaluation of the system on problems translated from different ITP libraries, similar to [9].…”

“…With ATPs being increasingly used and trained on large ITP libraries [2,3,6,8,16,18], it is more and more rewarding to develop methods that learn to reason without relying on the particular terminology adopted in a single project. Initial experiments in this direction using concept alignment [10] methods have already shown performance improvements by transferring knowledge between the HOL libraries [9]. Structural analogies (or even terminology duplications) are however common already in a single large ITP library [17] and their automated detection can lead to new proof ideas and a number of other interesting applications [11].…”

Goal-Oriented Conjecturing for Isabelle/HOL

“…Gauthier et al described conjecturing across proof corpora [4]. While PGT creates conjectures by mutating the original goal, Gauthier et al produced conjectures by using statistical analogies extracted from large formal libraries [5].…”

QED at Large: A Survey of Engineering of Formally Verified Software

“…For example, users may have to reformulate properties to facilitate library reuse (Hales et al, 2017), or to encode data structures in specific ways to aid in automation of proofs about them (Gonthier, 2008). Proof development environments need to allow users to efficiently write, check, and share proofs (Faithfull et al, 2018); proof libraries need to allow easy search and seamless integration of results into local developments (Gauthier and Kaliszyk, 2015). Evolving projects face the possibility of previous proofs breaking due to seemingly unrelated changes, justifying design principles (Woos et al, 2016) as well as support for quick error detection (Celik et al, 2017) and repair .…”