Autoformalization with large language models
Autoformalization is the process of automatically translating from natural language
mathematics to formal specifications and proofs. A successful autoformalization system …
mathematics to formal specifications and proofs. A successful autoformalization system …
Mathematical language models: A survey
In recent years, there has been remarkable progress in leveraging Language Models (LMs),
encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models …
encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models …
The future is big graphs: a community view on graph processing systems
The future is big graphs: a community view on graph processing systems Page 1 62
COMMUNICATIONS OF THE ACM | SEPTEMBER 2021 | VOL. 64 | NO. 9 contributed articles …
COMMUNICATIONS OF THE ACM | SEPTEMBER 2021 | VOL. 64 | NO. 9 contributed articles …
Thor: Wielding hammers to integrate language models and automated theorem provers
In theorem proving, the task of selecting useful premises from a large library to unlock the
proof of a given conjecture is crucially important. This presents a challenge for all theorem …
proof of a given conjecture is crucially important. This presents a challenge for all theorem …
A formal proof of the Kepler conjecture
T Hales, M Adams, G Bauer, TD Dang… - … of mathematics, Pi, 2017 - cambridge.org
A FORMAL PROOF OF THE KEPLER CONJECTURE Page 1 Forum of Mathematics, Pi (2017),
Vol. 5, e2, 29 pages doi:10.1017/fmp.2017.1 1 A FORMAL PROOF OF THE KEPLER …
Vol. 5, e2, 29 pages doi:10.1017/fmp.2017.1 1 A FORMAL PROOF OF THE KEPLER …
The role of the Mizar Mathematical Library for interactive proof development in Mizar
G Bancerek, C Byliński, A Grabowski… - Journal of Automated …, 2018 - Springer
The Mizar system is one of the pioneering systems aimed at supporting mathematical proof
development on a computer that have laid the groundwork for and eventually have evolved …
development on a computer that have laid the groundwork for and eventually have evolved …
The simplicial model of univalent foundations (after Voevodsky)
K Kapulkin, PLF Lumsdaine - Journal of the European Mathematical …, 2021 - ems.press
We present Voevodsky's construction of a model of univalent type theory in the category of
simplicial sets. To this end, we first give a general technique for constructing categorical …
simplicial sets. To this end, we first give a general technique for constructing categorical …
Premise selection for theorem proving by deep graph embedding
We propose a deep learning-based approach to the problem of premise selection: selecting
mathematical statements relevant for proving a given conjecture. We represent a higher …
mathematical statements relevant for proving a given conjecture. We represent a higher …
Learning to prove theorems via interacting with proof assistants
Humans prove theorems by relying on substantial high-level reasoning and problem-
specific insights. Proof assistants offer a formalism that resembles human mathematical …
specific insights. Proof assistants offer a formalism that resembles human mathematical …
[PDF][PDF] Hammering towards QED
The main ingredients underlying this approach are efficient automatic theorem provers that
can cope with hundreds of axioms, suitable translations of the proof assistant's logic to the …
can cope with hundreds of axioms, suitable translations of the proof assistant's logic to the …