Apply2Isar: Automatically Converting Isabelle/HOL Apply-Style Proofs to Structured Isar

2026-03-08

AI Summary

This work addresses the poor readability and maintainability of procedural apply-style proof scripts in Isabelle/HOL by introducing Apply2Isar, the first fully automated tool that translates fragile yet efficient apply-style scripts into clear, declarative Isar proofs. The approach leverages an analysis of Isabelle’s internal proof states, combined with syntax tree restructuring and abstraction of proof steps, to balance exploratory efficiency with robustness. Evaluated on a large-scale dataset from the Archive of Formal Proofs, Apply2Isar demonstrates its ability to generate high-quality, human-readable Isar proofs, significantly enhancing the maintainability and reusability of formal proofs.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Reasoning under Uncertainty: Applications
• Intelligent Robots: Other Foundations and Applications

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In Isabelle/HOL, declarative proofs written in the Isar language are widely appreciated for their readability and robustness. However, some users may prefer writing procedural"apply-style"proof scripts since they enable rapid exploration of the search space. To get the best of both worlds, we introduce Apply2Isar, a tool for Isabelle/HOL that automatically converts apply-style scripts to declarative Isar. This allows users to write complex, possibly fragile apply-style scripts, and then automatically convert them to more readable and robust declarative Isar proofs. To demonstrate the efficacy of Apply2Isar in practice, we evaluate it on a large benchmark set consisting of apply-style proofs from the Isabelle Archive of Formal Proofs.

Problem

• Isabelle/HOL
• apply-style proofs
• Isar
• proof conversion
• declarative proofs

Innovation

• Apply2Isar
• Isabelle/HOL
• proof conversion
• declarative proofs
• apply-style proofs