Persistentformal

Persistentformal is a theoretical framework for modeling systems whose state evolves over time while preserving a history of past states. It combines persistence techniques with formal methods to allow reasoning about both current behavior and provenance of changes. Core ideas include persistent state representations, versioned snapshots, and immutable past states that can be queried alongside the latest state.

Semantics and models: A persistentformal model assigns to each moment a state and to each operation a transition that yields a new version without mutating earlier versions. The history is represented as a tree or sequence of states; properties are specified in a temporal or modal logic, enabling verification of invariants across all historical versions. Categorical or algebraic structures may be used to compose system components and to relate histories through morphisms.

Implementation and practice: In practice, persistentformal informs designs of event-sourced systems, versioned data stores, and provenance-aware applications. It supports reasoning about correctness across revisions, rollback, and auditing, while aiding reproducibility of experiments by keeping accessible historical traces. Tools may provide formal specifications, model checkers, and proof assistants integrated with versioned state graphs.

Examples and relation: A simple counter with versioned increments demonstrates how each operation yields a new version while preserving prior states. Related areas include persistent data structures, formal verification, temporal logic, and data provenance. Persistentformal is used conceptually in research on reproducible science and distributed systems with strong audit trails.