Iris in Lean

2026-09-21

AI Summary

该研究使用Lean的灵活元编程和商类型简化了Iris框架的设计与使用，提高了性能，并通过集成Mathlib库增强了数学依赖任务的处理能力。

Abstract

The Iris framework for concurrent separation logic has been widely used for program verification research. An important factor contributing to the framework's adoption is its high-quality mechanization in Rocq. This mechanization uses a number of Rocq features in sophisticated ways, including a carefully constructed algebraic hierarchy for modeling separation logic resources, and a proof mode for embedded separation logic proofs, which combines custom Ltac with extensible typeclasses. The library has been developed for over a decade with dozens of contributors, with an emphasis on modularity and maintainability. We explore how Lean features like flexible metaprogramming and quotient types can simplify the design and usage of Iris. Using these features, we provide a novel implementation of the Iris proof mode with improved performance, simplify the handling of equivalences through quotient types, build a variant of Diaframe proof automation, and provide convenience features like automatic construction of Iris fixed points. Building on Lean lets us integrate with the extensive Mathlib library, allowing us to re-use results from this library for program verification tasks that have heavy mathematical dependencies, as we demonstrate with an application to probabilistic program verification.

Problem

• concurrent separation logic
• program verification
• metaprogramming
• quotient types

Innovation

• flexible metaprogramming
• quotient types
• proof mode
• Diaframe proof automation
• Mathlib integration