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

TL;DR

Apply2Isar is a tool that automatically converts procedural apply-style proofs in Isabelle/HOL into more readable and robust declarative Isar proofs, bridging the gap between rapid exploration and formal clarity.

Contribution

We introduce Apply2Isar, a novel tool that automates the conversion of apply-style proofs to Isar, enhancing proof readability and robustness.

Findings

Successfully converts large benchmark set of apply-style proofs

Improves proof readability and robustness

Demonstrates practical efficacy in Isabelle/HOL

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.