Foundations of a Formally Verified Graph Library for Coq: the Example of Dijkstra?s Shortest Path Algorithm
Résumé
Despite their wide use and the maturity of their theory, only a few works have focused on the formal verification of graph proper- ties and algorithms. With the growing range and complexity of formally verified applications, the need for formally verified graph libraries natu- rally rises. This is even more relevant for the Coq system, in which the extraction facility motivates the need for efficient structures.
In this work, we propose the core of a graph library (formally verified within the Coq system) that combines the expressivity needed to prove graph properties and efficient purely functional data structures required for algorithms. We illustrate the use of this library with a lightweight formally verified implementation of Dijkstra?s shortest path algorithm. The library, including Dijkstra?s shortest path algorithm, can freely be extracted in different languages including Ocaml and Haskell.