datalattice

Data lattice, or datalattice, is a formal framework used in distributed data systems to model the growth and combination of information across replicas. In a datalattice, possible data states are elements of a partially ordered set, ordered by information content: A ≤ B if B contains at least as much information as A. The least upper bound (join) of two states represents merging their information, while the greatest lower bound (meet) represents the information common to both states. The structure typically includes a bottom element, denoting an empty or initial state, and often a top element representing universal information, depending on the application.

Key properties include monotonicity of information growth and the associativity, commutativity, and idempotence of the join operation. These properties ensure that repeated merges of state updates converge toward a stable result, a feature leveraged by conflict-free replicated data types (CRDTs) and other eventual consistency mechanisms.

Common examples of datalattices include the powerset lattice under set union (where join is union and meet is intersection), boolean lattices, and product lattices used to model multi-field records. In practice, datalattices are designed so that merge operations are monotone, deterministic, and commutative, enabling safe, concurrent updates without explicit coordination.

Limitations include the need to design appropriate lattice structures for complex data, potential performance overhead from merging and version tracking, and the possibility that some data types do not form a natural lattice.

See also: lattice theory, CRDTs, eventual consistency, distributed databases.