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LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper)

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Bibliographic Details
Title: LeanLTL: A Unifying Framework for Linear Temporal Logics in Lean (Short Paper)
Authors: Vin, Eric, Miller, Kyle A., Fremont, Daniel J.
Contributors: Eric Vin and Kyle A. Miller and Daniel J. Fremont
Publisher Information: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2025.
Publication Year: 2025
Subject Terms: Interactive Theorem Proving, Lean 4, ddc:004, Linear Temporal Logic
Description: We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with arbitrary Lean expressions, making it straightforward to define properties involving numerical or other types. We prove that standard flavors of LTL can be embedded in our framework. The library also provides automation for reasoning about LeanLTL formulas in a way that facilitates using Lean’s existing tactics. Finally, we provide examples illustrating the utility of the library in reasoning about systems that come from applications.
Document Type: Conference object
File Description: application/pdf
Language: English
DOI: 10.4230/lipics.itp.2025.37
Access URL: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.37
Rights: CC BY
Accession Number: edsair.od......1814..ee988a36e6869bcd85a179b283bf660f
Database: OpenAIRE
Description
Abstract:We propose LeanLTL, a unifying framework for linear temporal logics in Lean 4. LeanLTL supports reasoning about traces that represent either infinite or finite linear time. The library allows traditional LTL syntax to be combined with arbitrary Lean expressions, making it straightforward to define properties involving numerical or other types. We prove that standard flavors of LTL can be embedded in our framework. The library also provides automation for reasoning about LeanLTL formulas in a way that facilitates using Lean’s existing tactics. Finally, we provide examples illustrating the utility of the library in reasoning about systems that come from applications.
DOI:10.4230/lipics.itp.2025.37