proofs/tla/DAGZChain.tla

---------------------------- MODULE DAGZChain ----------------------------
(*
 * TLA+ Specification of DAG Z-Chain Consensus
 *
 * Source: lux/node/vms/zkvm/vm.go              (ZK UTXO VM)
 *         lux/node/vms/zkvm/nullifier_db.go    (spent-nullifier set)
 *         lux/node/vms/zkvm/proof_verifier.go  (Groth16/Plonk verify)
 *         lux/node/vms/zkvm/dag_vertex.go      (DAG vertex adapter)
 *         lux/consensus/engine/dag/            (nebula finality)
 *
 * Protocol summary:
 *   Z-Chain operates the standard ZK-UTXO model (nullifiers, commitments,
 *   proofs) under a DAG consensus engine. The conflict rule reduces to
 *   nullifier-set intersection — a dramatic simplification over the EVM
 *   r/w-set rule because the full state *is* the nullifier set (plus the
 *   Merkle commitments tree).
 *
 *   Conflict rule:
 *     conflicts(v1, v2) == (v1.nulls \cap v2.nulls) # {}
 *
 *   BuildVertex guarantees antichain siblings have disjoint nullifier
 *   sets. Accept runs Groth16/Plonk batch verification in parallel; the
 *   batch is sound iff each proof is individually sound (standard
 *   cryptographic assumption).
 *
 * Key properties (checked with TLC):
 *   NoDoubleSpend   : No nullifier appears in two accepted vertices.
 *   OrderFree       : Any topo order of the DAG yields the same Z-state.
 *   BatchSound      : A batch-verified vertex is accepted only if every
 *                     proof individually verifies (modelled as a non-
 *                     deterministic choice bounded by the verify predicate).
 *   Liveness        : Every valid proof is eventually finalised.
 *
 * Go-to-TLA+ mapping:
 *   v.Nullifiers                 -> v.nulls
 *   v.Outputs                    -> v.commits
 *   NullifierDB.IsNullifierSpent -> spent
 *   ProofVerifier.Verify         -> VerifyVertex
 *   BuildVertex                  -> Propose
 *   nebula.Finalize              -> Finalize
 *)

EXTENDS Integers, FiniteSets, Sequences, TLC

\* --------------------------------------------------------------------------
\* CONSTANTS
\* --------------------------------------------------------------------------

CONSTANTS
    Nullifiers,       \* Universe of possible nullifiers
    Commitments,      \* Universe of possible UTXO commitments
    MaxVertices

ASSUME Cardinality(Nullifiers) > 0
ASSUME Cardinality(Commitments) > 0
ASSUME MaxVertices \in Nat \ {0}

VertexId == 1..MaxVertices

\* Ranks are layered as 1 + maxParentRank starting at 1, and a chain of
\* accepted vertices is bounded by MaxVertices, so every reachable rank lies
\* in 1..MaxVertices. Bounding the field here keeps Vertex a FINITE set; with
\* `rank : Nat` it was infinite and TLC could not enumerate `\E v \in Vertex`
\* in the Next relation ("can't enumerate the value of the rank field: Nat").
RankRange == 1..MaxVertices

Vertex ==
  [ id      : VertexId,
    nulls   : SUBSET Nullifiers,
    commits : SUBSET Commitments,
    parents : SUBSET VertexId,
    rank    : RankRange ]

\* --------------------------------------------------------------------------
\* VARIABLES
\* --------------------------------------------------------------------------

VARIABLES
    accepted,   \* Accepted vertices
    spent,      \* Set of nullifiers spent (state)
    committed,  \* Set of commitments (state)
    finalRank   \* Highest finalised antichain rank

vars == <<accepted, spent, committed, finalRank>>

\* --------------------------------------------------------------------------
\* HELPERS
\* --------------------------------------------------------------------------

Conflicts(v1, v2) == (v1.nulls \cap v2.nulls) # {}

Antichain(r) == { v \in accepted : v.rank = r }

\* Verification predicate — opaque for model checking; we simply assume
\* proposed vertices have valid proofs. The batch-verify soundness is
\* captured separately in the Lean proof (batch_sound axiom).
VerifyVertex(v) == v.nulls # {} \/ v.commits # {}  \* non-trivial tx

\* --------------------------------------------------------------------------
\* TYPE INVARIANT
\* --------------------------------------------------------------------------

TypeOK ==
    /\ accepted \subseteq Vertex
    /\ spent \subseteq Nullifiers
    /\ committed \subseteq Commitments
    /\ finalRank \in Nat

\* --------------------------------------------------------------------------
\* INITIAL STATE
\* --------------------------------------------------------------------------

Init ==
    /\ accepted = {}
    /\ spent = {}
    /\ committed = {}
    /\ finalRank = 0

\* --------------------------------------------------------------------------
\* ACTIONS
\* --------------------------------------------------------------------------

Propose(newV) ==
    /\ newV \in Vertex
    /\ newV.id \notin { v.id : v \in accepted }
    /\ Cardinality(accepted) < MaxVertices
    /\ VerifyVertex(newV)
    \* No double-spend: none of newV.nulls are in spent yet.
    /\ newV.nulls \cap spent = {}
    \* Parents are accepted.
    /\ \A p \in newV.parents : \E v \in accepted : v.id = p
    \* Rank is one more than max parent rank.
    /\ newV.rank =
         IF newV.parents = {} THEN 1
         ELSE 1 + CHOOSE maxR \in { v.rank : v \in {x \in accepted : x.id \in newV.parents} } :
                      \A v \in accepted :
                        v.id \in newV.parents => v.rank <= maxR
    \* Sibling disjointness (the BuildVertex contract).
    /\ \A v \in accepted : v.rank = newV.rank => ~Conflicts(v, newV)
    /\ accepted'   = accepted \cup {newV}
    /\ spent'      = spent \cup newV.nulls
    /\ committed'  = committed \cup newV.commits
    /\ UNCHANGED finalRank

Finalize ==
    /\ finalRank + 1 \in { v.rank : v \in accepted }
    /\ \A v, w \in Antichain(finalRank + 1) : v # w => ~Conflicts(v, w)
    /\ finalRank' = finalRank + 1
    /\ UNCHANGED <<accepted, spent, committed>>

Next ==
    \/ \E v \in Vertex : Propose(v)
    \/ Finalize

Spec == Init /\ [][Next]_vars /\ WF_vars(Finalize)

\* --------------------------------------------------------------------------
\* PROPERTIES
\* --------------------------------------------------------------------------

\* Every nullifier is spent at most once across all accepted vertices.
NoDoubleSpend ==
    \A v1, v2 \in accepted :
        v1.id # v2.id => Conflicts(v1, v2) = FALSE

\* The spent set is monotone — it never shrinks.
SpentMonotone == [] ([spent \subseteq spent']_vars)

\* Within any finalised antichain, all vertices have disjoint nullifiers.
AntichainDisjoint ==
    \A r \in 1..finalRank :
        \A v1, v2 \in Antichain(r) : v1.id # v2.id => ~Conflicts(v1, v2)

\* Liveness: every accepted vertex is eventually finalised.
\*
\* Quantify over the FINITE set of possible ranks (1..MaxVertices), not over
\* the type Vertex. Vertex carries a `rank : Nat` field, making it infinite;
\* TLC cannot enumerate `\A v \in Vertex` inside a temporal (~>) formula
\* ("can't enumerate the value of the rank field: Nat"). Ranks are layered
\* 1 + maxParentRank and bounded by the vertex count, so every reachable rank
\* lies in 1..MaxVertices. "Every accepted vertex is eventually finalised" is
\* equivalent to "every populated rank is eventually <= finalRank".
Liveness ==
    \A r \in 1..MaxVertices :
        (\E v \in accepted : v.rank = r) ~> (finalRank >= r)

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