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 mvcc --------------------------------
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(*
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TLA+ specification of MVCC (Multi-Version Concurrency Control) with
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Snapshot Isolation as implemented in BaraDB (core/mvcc.nim + storage/lsm.nim).
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Key properties verified:
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- NoDirtyReads : a transaction never reads uncommitted data.
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- ReadOwnWrites : a transaction reads its own most recent writes.
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- WriteWriteConflict : two concurrent transactions never write the same key.
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*)
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EXTENDS Integers, Sequences, FiniteSets, TLC
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CONSTANTS Keys, \* set of keys
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Values, \* set of possible values
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Nil, \* distinguished nil value (model value)
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MaxTxnId \* bound transaction IDs for model checking
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ASSUME IsFiniteSet(Keys) /\ IsFiniteSet(Values)
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VARIABLES
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db, \* db[k] = sequence of <<txnId, value, committed>> versions
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txnState, \* txnState[t] ∈ {"Active", "Committed", "Aborted"}
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txnStartTs, \* txnStartTs[t] ∈ Nat (monotonic timestamp)
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writeSet, \* writeSet[t] ∈ SUBSET Keys
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readSet, \* readSet[t] ∈ SUBSET Keys
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globalClock \* global counter for timestamps
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vars == <<db, txnState, txnStartTs, writeSet, readSet, globalClock>>
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-----------------------------------------------------------------------------
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\* Helper operators
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\* The latest committed version of key k visible to transaction t
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CommittedVersion(k, t) ==
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LET versions == db[k]
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visible == {i \in 1..Len(versions) :
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versions[i][3] = TRUE /\ versions[i][1] < txnStartTs[t]}
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IN IF visible = {} THEN Nil
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ELSE versions[CHOOSE i \in visible : \A j \in visible : j <= i => versions[j][1] <= versions[i][1]]
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\* Has transaction t already written key k?
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HasWritten(t, k) == k \in writeSet[t]
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-----------------------------------------------------------------------------
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\* Initial state
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Init ==
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/\ db = [k \in Keys |-> << >>]
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/\ txnState = [t \in 1..MaxTxnId |-> "Active"]
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/\ txnStartTs = [t \in 1..MaxTxnId |-> 0]
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/\ writeSet = [t \in 1..MaxTxnId |-> {}]
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/\ readSet = [t \in 1..MaxTxnId |-> {}]
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/\ globalClock = 1
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-----------------------------------------------------------------------------
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\* State transitions
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\* Begin a transaction: assign a start timestamp.
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BeginTxn(t) ==
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/\ txnState[t] = "Active"
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/\ txnStartTs[t] = 0
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/\ txnStartTs' = [txnStartTs EXCEPT ![t] = globalClock]
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/\ globalClock' = globalClock + 1
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/\ UNCHANGED <<db, txnState, writeSet, readSet>>
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\* Read key k by transaction t.
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Read(t, k) ==
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/\ txnState[t] = "Active"
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/\ txnStartTs[t] > 0
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/\ readSet' = [readSet EXCEPT ![t] = @ \cup {k}]
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/\ UNCHANGED <<db, txnState, txnStartTs, writeSet, globalClock>>
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\* Write key k with value v by transaction t.
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Write(t, k, v) ==
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/\ txnState[t] = "Active"
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/\ txnStartTs[t] > 0
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/\ k \notin writeSet[t]
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/\ writeSet' = [writeSet EXCEPT ![t] = @ \cup {k}]
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/\ db' = [db EXCEPT ![k] = Append(@, <<t, v, FALSE>>)]
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/\ UNCHANGED <<txnState, txnStartTs, readSet, globalClock>>
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\* Commit transaction t: mark its versions as committed (first-committer-wins).
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CommitTxn(t) ==
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/\ txnState[t] = "Active"
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/\ txnStartTs[t] > 0
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/\ ~(\E t2 \in 1..MaxTxnId : t2 /= t /\ txnState[t2] = "Committed" /\
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\E k \in Keys : k \in writeSet[t] /\ k \in writeSet[t2])
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/\ txnState' = [txnState EXCEPT ![t] = "Committed"]
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/\ db' = [k \in Keys |->
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IF k \in writeSet[t]
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THEN LET last == Len(db[k])
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lastTxn == db[k][last][1]
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IN IF lastTxn = t
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THEN [db[k] EXCEPT ![last] = <<t, db[k][last][2], TRUE>>]
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ELSE db[k]
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ELSE db[k]]
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/\ UNCHANGED <<txnStartTs, writeSet, readSet, globalClock>>
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\* Abort transaction t: leave versions as uncommitted (garbage).
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AbortTxn(t) ==
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/\ txnState[t] = "Active"
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/\ txnState' = [txnState EXCEPT ![t] = "Aborted"]
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/\ UNCHANGED <<db, txnStartTs, writeSet, readSet, globalClock>>
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-----------------------------------------------------------------------------
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\* Next-state relation
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Next ==
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\/ \E t \in 1..MaxTxnId : BeginTxn(t)
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\/ \E t \in 1..MaxTxnId : \E k \in Keys : Read(t, k)
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\/ \E t \in 1..MaxTxnId : \E k \in Keys : \E v \in Values : Write(t, k, v)
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\/ \E t \in 1..MaxTxnId : CommitTxn(t)
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\/ \E t \in 1..MaxTxnId : AbortTxn(t)
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-----------------------------------------------------------------------------
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\* Safety properties
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\* A committed transaction only wrote versions that are now marked committed.
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NoDirtyReads ==
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\A t \in 1..MaxTxnId :
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\A k \in Keys :
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\A i \in 1..Len(db[k]) :
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db[k][i][3] = TRUE =>
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db[k][i][1] \in {tx \in 1..MaxTxnId : txnState[tx] = "Committed"}
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\* If a transaction has written a key, its own read of that key sees the latest local value.
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ReadOwnWrites ==
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\A t \in 1..MaxTxnId :
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\A k \in Keys :
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k \in writeSet[t] =>
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LET versions == db[k]
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myWrites == {i \in 1..Len(versions) : versions[i][1] = t}
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IN myWrites /= {}
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\* Snapshot isolation: no two committed transactions write the same key (first-committer-wins).
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WriteWriteConflict ==
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\A t1, t2 \in 1..MaxTxnId :
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t1 /= t2 /\ txnState[t1] = "Committed" /\ txnState[t2] = "Committed" =>
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~(\E k \in Keys : k \in writeSet[t1] /\ k \in writeSet[t2])
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\* Type invariant
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TypeOk ==
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/\ \A k \in Keys : Len(db[k]) <= MaxTxnId * 2
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/\ \A k \in Keys : \A i \in 1..Len(db[k]) : db[k][i] \in (1..MaxTxnId) \X Values \X BOOLEAN
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/\ txnState \in [1..MaxTxnId -> {"Active", "Committed", "Aborted"}]
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/\ txnStartTs \in [1..MaxTxnId -> 0..(MaxTxnId+1)]
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/\ writeSet \in [1..MaxTxnId -> SUBSET Keys]
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/\ readSet \in [1..MaxTxnId -> SUBSET Keys]
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/\ globalClock \in 1..(MaxTxnId + 1)
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=============================================================================
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