An Institution for Event-B

Abstract

This paper presents a formalisation of the Event-B formal specification language in terms of the theory of institutions. The main objective of this paper is to provide: (1) a mathematically sound semantics and (2) modularisation constructs for Event-B using the specification-building operations of the theory of institutions. Many formalisms have been improved in this way and our aim is thus to define an appropriate institution for Event-B, which we call EVT. We provide a definition of EVT and the proof of its satisfaction condition. A motivating example of a traffic-light simulation is presented to illustrate our approach.

A Hybrid Dynamic Logic for Event/Data-Based Systems

“…On the other hand, Event-B supports parameters of events which could be integrated in our logic as well. An institution-based semantics of Event-B has been proposed in [8] which coincides with our semantics of operational specifications for the special case of deterministic state transition predicates. Similarly, our semantics of operational specifications coincides with the unfolding of symbolic transition systems in [17] if we instantiate our generic data domain with algebraic specifications of data types (and consider again only deterministic state transition predicates).…”

Formalizing the Institution for Event-B in the Coq Proof Assistant

“…We will now provide a precise but brief definition for the institution for Event-B, alongside its definition in Coq. For details, we refer the reader to [3]. Throughout, let Status = {ordinary ≤ anticipated ≤ convergent}.…”

“…Given an initialization event which starts n at 0, init :≡ begin n := 0 end, we write the EVT -sentence Init(n = 0). For details on this correspondence, see again [3].…”

“…The theory of institutions [4] was introduced by Joseph Goguen and Rod Burstall to give concrete form to the informal notion of a "logical system", identifying a common structure among the many logics in regular use in computer science. A 2017 paper by Marie Farrell, Rosemary Monahan, and James Power [3] uses the theory of institutions to provide a sound mathematical semantics and modularization constructs for the industrial-strength state-based formal modelling language Event-B [1], providing interoperability with other formalisms. In related work, the Heterogeneous Tool Set (Hets) [7] makes use of institutions to provide heterogeneous specifications.…”

“…Key features include the use of set theory as a modelling notation, the use of refinement to represent systems at different abstraction levels and the use of mathematical proof to verify consistency between refinement levels. The primary purpose of this research is to formalize the work in [3] within the Coq proof assistant, and more generally to provide the rudiments of a Coq library for the theory of institutions.…”