Coq is a formal proof management system. It provides a formal language to write mathematical definitions, executable algorithms and theorems together with an environment for semi-interactive ...

Formal theorem proving has emerged as a critical benchmark for assessing the reasoning capabilities of large language models (LLMs), with significant implications for mathematical automation. While ...

LeanDojo is an open-source platform for automating the proof of theorems with large language models. Developed by Caltech, Nvidia, MIT, UC Santa Barbara, and UT Austin, it interacts with the Lean ...

Traditional methods, relying solely on formal proof data, overlook valuable informal reasoning processes crucial to human mathematicians. The absence of natural language thought processes in formal ...

The field of formal verification is all about using mathematically rigorous techniques and tools to prove properties about systems. The applications of formal verification vary widely. There are ...

This repository contains a small Prolog-based equational theorem proving system. Based on term rewriting, this system facilitates theorem proving by equational transformation based on user-defined ...

DeepSeek AI has announced the release of DeepSeek-Prover-V2, a groundbreaking open-source large language model specifically designed for formal theorem proving within the Lean 4 environment. This ...

The field of theorem proving and higher‐order logic represents a confluence of computer science, mathematics and formal logic. It encompasses the automated and interactive approaches to establishing ...

“You don’t have to believe in God, but you have to believe in The Book,” the Hungarian mathematician Paul Erdős once said. The Book, which only exists in theory, contains the most elegant proofs of ...