EventB

Event-B is a formal method for modelling and reasoning about computer-based systems. It emphasizes correctness by construction through refinement and proof obligations. Models in Event-B are built in two layers: contexts and machines. Contexts declare carrier sets, constants, and axioms; machines declare variables, invariants, and events, which describe state transitions.

A machine's invariants constrain all reachable states, and events specify guarded updates to variables. An event consists of a guard (when it can fire) and an action (how variables change). The combination of contexts and machines allows modular development, with local properties expressed in invariants and global properties enforced by refinement.

Refinement is the central mechanism for progressive detail. A refinement step replaces abstract variables and events with more concrete ones, while proving that the refined machine simulates the abstract one. New events or state variables may be introduced, provided the refinement obligations are discharged.

Proof obligations generated in Event-B verify that invariants are preserved by all events, that the refinement preserves behavior, and that termination or variant measures decrease as required. These obligations are typically discharged with automated theorem provers integrated in development tools.

Event-B was developed in the 1990s by Jean-Raymond Abrial as an extension of the B-Method. It has been implemented in the Rodin platform, which provides editors, proof management, and a library of reusable models. Event-B is used in safety-critical domains, such as avionics and rail.

Notable tools besides Rodin include Atelier B; these environments support modelling, proof orchestration, and model checking. Event-B emphasizes incremental development and formal verification, complementing traditional testing.