Reformalization of the Jordan Curve Theorem

2026-07-02 · Source: Artificial Intelligence · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

A case study published on 2026-07-02 details the reformalization of the Jordan Curve Theorem, a process distinct from autoformalization where the input is an existing formal proof from a different proof assistant, rather than natural language. The research specifically reports three instances of this reformalization: converting proofs from Mizar to Lean, from HOL Light to Lean, and from HOL Light to Agda. The authors analyze the outcomes of these conversions, identifying critical pipeline design choices that significantly impact the effectiveness and practicality of reformalization tasks. This work provides insights into the challenges and considerations involved in translating complex mathematical proofs between different formal verification systems, highlighting the nuances of inter-system proof compatibility.

Key takeaway

For research scientists working with formal verification, if you are considering migrating existing formal proofs between different proof assistants, you should prioritize evaluating the specific pipeline design choices. This study highlights that successful reformalization, such as converting Mizar to Lean or HOL Light to Agda, depends heavily on these choices. Your team should analyze the compatibility and conversion challenges between source and target systems to ensure accurate and efficient proof translation.

Key insights

Converting formal proofs between different proof assistants reveals critical pipeline design choices.

Principles

• Reformalization uses formal proofs as input, unlike autoformalization.
• Pipeline design choices are crucial for practical reformalization tasks.

Method

Converting formal proofs of theorems, like the Jordan Curve Theorem, from one proof assistant (Mizar, HOL Light) to another (Lean, Agda) to analyze conversion challenges.

In practice

• Translate existing formal mathematical libraries across systems.
• Benchmark interoperability between different proof assistants.

Topics

• Reformalization
• Proof Assistants
• Formal Verification
• Jordan Curve Theorem
• Mizar to Lean Conversion
• HOL Light to Agda Conversion

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Artificial Intelligence.