LatticeProduct

The componentwise product of two join-semilattices.

Given two Quilted types A and B, the pair (a, b) forms a new join-semilattice whose join (piece) is applied to each component independently:

(a₁, b₁).piece(a₂, b₂) = (a₁.piece(a₂), b₁.piece(b₂))

This is monotone by construction: componentwise join of two semilattices is itself a semilattice. The three lattice laws follow directly from the laws already satisfied by A and B:

• idempotent p.piece(p) == p

• commutative p.piece(q) == q.piece(p)

• associative p.piece(q).piece(r) == p.piece(q.piece(r))

Use on the coordination-free path: combine two CoordinationFree values into a single atomic snapshot via the us.tractat.kuilt.warp.zip combinator in :kuilt-warp.

Type Parameters

Samples

val r1 = ReplicaId("r1")
val r2 = ReplicaId("r2")

// Two replicas each carry a (counter, tags) pair.
val replicaA = LatticeProduct.of(GCounter.of(r1 to 3L), GSet.of("alpha"))
val replicaB = LatticeProduct.of(GCounter.of(r2 to 7L), GSet.of("beta"))

// Componentwise join: counter sums, set unions.
val merged = replicaA.piece(replicaB)
check(merged.first.value == 10L)                      // 3 + 7
check(merged.second.elements == setOf("alpha", "beta"))

// Idempotent: merging again changes nothing.
check(merged.piece(replicaA) == merged)