A history of formal methods in railways

The engineering of industrial systems, particularly in safety-critical domains such as railways, demands rigorous verification and validation processes to ensure system dependability. Formal methods have emerged as powerful tools to complement traditional software engineering practices. In the railway sector, which increasingly relies on complex, distributed, and cyber-physical control systems, formal methods have demonstrated particular value for many decades now. In this paper, we provide a retrospective overview of the application of formal methods and tools in the railway domain, with emphasis on two prominent verification approaches and one frequently verified railway system: modeling and validation with the B method and tools and formal verification of interlocking systems by model checking. We explore their role in the design and development of key railway systems, highlighting both academic research and industrial success stories, as witnessed by international projects and initiatives. We conclude with an outlook on the potential of integrating AI and formal methods to enhance the efficiency of next-generation railway systems.