References

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Shorthand Words

LUB: Least upper bound

Defines

Monotonic semilattice object

A state-based object, equipped with partial order ≤, noted (S,≤,s0,q,u,m), that has the following properties, is called a monotonic semi-lattice:

Set S of payload values forms a semilattice ordered by ≤.
Merging state s with remote state s′ computes the LUB of the two states, i.e., s - m(s′ ) = s ⊔ s′ .
State is monotonically non-decreasing across updates, i.e., s ≤ s - u

Commutativity

Operations f and g commute, if for any reachable replica state S where their source pre-condition is enabled, the source precondition of f (resp. g) remains enabled in state S - g (resp. S - f), and S - f - g and S - f - g are equivalent abstract states.