To implement Delta-State Conflict-Free Replicated Data Types (δ-CRDTs), you would need to follow the guidelines and concepts outlined in the paper "Efficient State-based CRDTs by Delta-Mutation" by Paulo Sérgio Almeida, Ali Shoker, and Carlos Baquero. Here is a high-level overview of the steps involved:
Define the Join-Semilattice: Start by defining the join-semilattice (S) that represents the state of your δ-CRDT. The join-semilattice should have the properties of being idempotent, associative, and commutative.
Define Delta-Mutators: Delta-mutators are functions that correspond to update operations on the state. They take the current state (X) as a parameter and return a delta-mutation (mδ(X)) in the same join-semilattice (S). These delta-mutations represent the updates induced by the mutator on the current state.
Define Delta-Groups: Delta-groups are either delta-mutations or joins of several delta-groups. They are used to represent multiple delta-mutations that can be joined locally into a delta-group and retained in a buffer for efficiency reasons.
Define Query Functions: Define a set of query functions (Q) that allow accessing and querying the state of the δ-CRDT. These functions should operate on the current state (X) and any received delta-groups (D).
State Transitions: Define the state transitions at each replica by joining the current state (X) with a delta-mutation (mδ(X)) or a received delta-group (D). This can be represented as X' = X ⊔ mδ(X) or X' = X ⊔ D.
Delta-State Shipping: In δ-CRDTs, the effect of applying a mutation (represented by a delta-mutation) is decoupled from the resulting state. This allows shipping the delta-mutation (δ) rather than the entire resulting state (X'). All state transitions in a δ-CRDT, even upon applying mutations locally, are the result of some join with the current state.
Anti-Entropy Algorithm: The paper also presents an anti-entropy algorithm that ensures causal consistency in δ-CRDTs. This algorithm helps synchronize the state between replicas and ensures that all updates are eventually propagated.
It is important to note that implementing δ-CRDTs requires a good understanding of distributed systems and the specific requirements of your application. The paper provides more detailed explanations and examples, so I recommend referring to it for a comprehensive understanding of the implementation process.