No abstract

No abstract

No abstract

No abstract

We study the proof-theoretic and computational

This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.

This paper describes formalizations of Tait's normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in a non-trivial setting.

The European Rail Traffic Management System (ERTMS) is a state-of-the-art train control system designed as a standard for railways across Europe. It generalises traditional discrete interlocking systems to a world in which trains hold on-board equipment for signalling, and trains and interlockings communicate via radio block processors. The ERTMS aims at improving performance and capacity of rail traffic systems without compromising their safety. The ERTMS system is of hybrid nature, in contrast to classical railway signalling systems which deal with discrete data only. Consequently, the switch to ERTMS poses a number of research questions to the formal methods community, most prominently: How can safety be guaranteed? In this paper we present the first formal modelling of ERTMS comprising all subsystems participating in its control cycle. We capture what safety means in physical and in logical terms, and we demonstrate that it is feasible to prove safety of ERTMS systems utilising Real-Time Maude model-checking by considering a number of bi-directional track layouts. ERTMS is currently being installed in many countries. It will be the main train control standard for the foreseeable future. The concepts presented in this paper offer applicable methods supporting the design of dependable ERTMS systems. We demonstrate model-checking to be a viable option in the analysis of large and complex real-time systems. Furthermore, we establish Real-Time Maude as a modelling and verification tool applicable to the railway domain. The approach given in this paper is a rigorous one. In order to avoid modelling errors, we follow a systematic approach: First, as a requirement specification, we identify the event-response structures present in the ERTMS. Then, we model these structures in Real-Time Maude in a traceable way, i.e., specification text in Real-Time Maude can be directly mapped to requirements. We explore our models by checking if they have the desired behaviour, and apply systematic model-exploration through error injection-both these steps are carried out using the formal method Real-Time Maude. Finally, we analyse ERTMS by model-checking, thus applying a formal method to the railway domain, and we mathematically prove that our analysis of ERTMS by model-checking is complete, i.e., that it guarantees safety at all times.