Hennessy-Milner Logic in CSLib, the Lean Computer Science Library

TL;DR

This paper formalizes Hennessy-Milner Logic within the Lean CSLib library, providing syntax, semantics, and a complete proof of the Hennessy-Milner theorem, emphasizing generality, reusability, and automation.

Contribution

It introduces a parametric, reusable formalization of HML in CSLib, including the full metatheory and integration with Lean's automation tools.

Findings

Complete formalization of HML in CSLib

Proof of Hennessy-Milner theorem for image-finite LTSs

Reusable library code available for systems using CSLib

Abstract

We present a library-level formalisation of Hennessy-Milner Logic (HML) - a foundational logic for labelled transition systems (LTSs) - for the Lean Computer Science Library (CSLib). Our development includes the syntax, satisfaction relation, and denotational semantics of HML, as well as a complete metatheory including the Hennessy-Milner theorem - bisimilarity coincides with theory equivalence for image-finite LTSs. Our development emphasises generality and reusability: it is parametric over arbitrary LTSs, definitions integrate with CSLib's infrastructure (such as the formalisation of bisimilarity), and proofs leverage Lean's automation (notably the grind tactic). All code is publicly available in CSLib and can be readily applied to systems that use its LTS API.