UTC Time, Formally Verified

TL;DR

FV Time is a Coq library for verified UTC time conversions that uniquely includes leap seconds, demonstrating a methodology for software verification with practical solutions and tactics.

Contribution

It introduces a verified library for UTC time conversions with leap seconds in Coq, showcasing novel verification techniques and auxiliary tools.

Findings

Successfully verified time conversion functions including leap seconds

Developed a refinement package bridging MathComp and Coq standard library numbers

Created tactics for automatic decidable statement proofs over finite ranges

Abstract

FV Time is a small-scale verification project developed in the Coq proof assistant using the Mathematical Components libraries. It is a library for managing conversions between time formats (UTC and timestamps), as well as commonly used functions for time arithmetic. As a library for time conversions, its novelty is the implementation of leap seconds, which are part of the UTC standard but usually not implemented in existing libraries. Since the verified functions of FV Time are reasonably simple yet non-trivial, it nicely illustrates our methodology for verifying software with Coq. In this paper we present a description of the project, emphasizing the main problems faced while developing the library, as well as some general-purpose solutions that were produced as by-products and may be used in other verification projects. These include a refinement package between proof-oriented MathComp numbers and computation-oriented primitive numbers from the Coq standard library, as well as a set of tactics to automatically prove certain decidable statements over finite ranges through brute-force computation.