ExtendedB

ExtendedB (EB) is a formal method for specification and verification of software systems that extends the B-Method. EB provides a mathematically precise language for describing system behavior and supports rigorous reasoning about correctness.

In EB, a system is modeled as a collection of machines that encapsulate state variables, invariants, an initialisation operation, and a set of events that describe state transitions. Invariants specify properties that must hold for every reachable state. The initialisation operation defines the starting state, and events represent atomic transitions that may modify state while preserving the invariants. EB supports refinement, allowing an abstract model to be progressively developed into a concrete implementation while preserving correctness.

EB expands the expressive power of B by adding richer data types and logical constructs, enabling more direct modeling of real-time behavior, concurrency, and complex data structures. It employs formal semantics based on set theory and first-order logic, and proof obligations are generated to verify that invariants are maintained by all events and refinements. Proofs can be carried out interactively or automatically, often with tool support including model checkers and theorem provers.

The method has been used in safety- and security-critical industries and in academic research to model software architectures, control systems, and communication protocols. While EB remains part of the broader B-method family, its ideas have influenced later developments such as Event-B and related refinement strategies.

See also: B-method, Event-B, formal methods.