# Sharing HOL4 and HOL Light Proof Knowledge

@inproceedings{Gauthier2015SharingHA, title={Sharing HOL4 and HOL Light Proof Knowledge}, author={Thibault Gauthier and C. Kaliszyk}, booktitle={LPAR}, year={2015} }

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…

## 17 Citations

Classification of Alignments Between Concepts of Formal Mathematical Systems

- Computer ScienceCICM
- 2017

This work presents a classification of alignments and design a simple format for describing alignments, as well as an infrastructure for sharing them, and proposes these as a centralized standard for the community.

Higher Order Proof Engineering: Proof Collaboration, Transformation, Checking and Retrieval

- Computer Science
- 2016

An introduction and an overview of related recent advances are given, followed by the proof checking benchmarks of a proof sharing repository, namely OpenTheory (after proof transformation by the upgraded Holide), and ProofCloud, the first proof retrieval engine for higher order proofs.

Proof Artifact Co-training for Theorem Proving with Language Models

- Computer ScienceArXiv
- 2021

PACT is proposed, a general methodology for extracting abundant self-supervised data from kernel-level proof terms for co-training alongside the usual tactic prediction objective and applied to Lean, an interactive proof assistant which hosts some of the most sophisticated formalized mathematics to date.

JEFL: Joint Embedding of Formal Proof Libraries

- Computer ScienceFroCoS
- 2021

This paper compares a previously proposed algorithm for matching concepts across libraries with an unsupervised embedding approach that can help us retrieve similar concepts and argues that the neural embedding Approach has more potential to be integrated into an interactive proof assistant.

A Standard for Aligning Mathematical Concepts

- Computer ScienceFM4M/MathUI/ThEdu/DP/WIP@CIKM
- 2016

This work proposes these as a centralized standard for the community to collect and curate alignments from the different kinds of mathematical corpora, including proof assistant libraries, computer algebra and programming language algorithms, and semi-formal libraries.

Automated Reasoning: 10th International Joint Conference, IJCAR 2020, Paris, France, July 1–4, 2020, Proceedings, Part II

- Computer ScienceIJCAR
- 2020

This paper discusses the design of a hierarchy of structures which combine linear algebra with concepts related to limits, like topology and norms, in dependent type theory, and presents and discusses a solution, coined forgetful inheritance, based on packed classes and unification hints.

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

- Computer ScienceFound. Trends Program. Lang.
- 2019

A survey of the literature presents a holistic understanding of proof engineering for program correctness, covering impact in practice, foundations, proof automation, proof organization, and practical proof development.

A Survey of Languages for Formalizing Mathematics

- Computer ScienceCICM
- 2020

The conclusion is reached that no existing language is truly good enough yet and ideas for possible future improvements are derived.

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