NishMath - #formalization

The Equational Theories Project has achieved a major breakthrough, formalizing all possible implications between a test list of 4694 equational laws in the Lean theorem prover. This involved verifying a staggering 22,033,636 implications (4694 squared) over a period of just over 200 days. The project's success is attributed to a substantial and diverse collection of code, data, and text, highlighting the complexity and scale of the formalization effort. This milestone marks a significant advancement in the field of automated theorem proving, with potential applications in formal verification of mathematical theories and software.

The project leverages the Lean theorem prover, a powerful tool for formalizing mathematics and verifying software. The formalization effort required managing a large volume of code, data, and textual descriptions. Now that the formalization is complete, the project team is focusing on documenting their methodologies and results in a comprehensive paper. This paper will detail the techniques used to tackle the challenge of formalizing such a vast number of implications, offering insights for future research in automated reasoning and formal verification.

The next key step for the Equational Theories Project is drafting the accompanying paper. The current draft is in an incomplete state, but is now the central focus of the project. This paper will serve as a crucial resource for understanding the project's accomplishments and methodologies. While the code and data are essential, the paper will provide the necessary context and explanation to make the formalization accessible and useful to the broader research community.


References :

• leanprover.zulipchat.com: after just over 200 days, the last of the 4694^2 = 22033636 possible implications between our test list of 4694 equational laws has now been formalized in Lean .
• Terence Tao: A key milestone in the Equational Theories Project: after just over 200 days, the last of the 4694^2 = 22033636 possible implications between our test list of 4694 equational laws has now been formalized in Lean .
• teorth.github.io: after just over 200 days, the last of the 4694^2 = 22033636 possible implications between our test list of 4694 equational laws has now been formalized in Lean .

Classification:

• HashTags: #EquationalTheories #FormalVerification #LeanProver
• Company: GitHub
• Target: Mathematics
• Product: Algebra
• Feature: Formalization
• Type: Research
• Severity: Medium