Znotation

Z notation is a formal specification language used to describe and model computing systems. Originating in the 1980s under the direction of Jean-Raymond Abrial and colleagues, it provides a mathematical framework for defining data models, state, and operations in an abstract, machine-independent form. Z specifications focus on correctness properties and are used to aid rigorous design, analysis, and verification in software engineering and safety-critical domains.

Fundamentally, Z rests on classical set theory and first-order predicate logic, with a typed universe of names and concepts. The primary structuring construct is the schema, which groups together a set of declarations (types, variables) and a predicate describing allowed values. State is described by state schemas; operations are described by operation schemas that relate a pre-state to a post-state and typically carry preconditions and postconditions. The schema calculus enables combining and refining schemas through operations such as conjunction, hiding, and import, enabling modular specification of complex systems.

Refinement is a central concept: an abstract specification can be progressively refined into more concrete designs, with each refinement preserving the observable behavior specified by the abstract state and operations. Z supports nondeterminism and abstract data types, allowing designers to postpone implementation decisions until later refinement steps.

Tools and usage: Z specifications are edited in specialized environments and verified with theorem provers and proof systems. Notable tool sets include Z/EVES, the Community Z Tools (CZT) for Eclipse, and AtelierZ. Z remains a reference methodology in academia and in industry for specifying, analyzing, and validating critical systems such as avionics, rail signaling, and safety-critical software.

Relation to other formalisms: Z is closely related to other formal specification approaches such as VDM-OS, B-Method, and Alloy, sharing a focus on precise modeling and verification while differing in refinement philosophy and underlying logic.