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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# TLC model checker output
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states/
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*.dump
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# BaraDB Formal Verification Suite
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This directory contains TLA+ specifications for core BaraDB distributed-systems algorithms. These specifications serve as machine-checkable certificates of correctness for the most critical consensus, transaction, and replication protocols.
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## Structure
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| File | Algorithm | Key Properties |
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|------|-----------|----------------|
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| `raft.tla` | Raft Consensus | Election safety, leader append-only, state-machine safety |
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| `twopc.tla` | Two-Phase Commit | Atomicity (all commit or all abort), no orphan blocks |
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| `mvcc.tla` | MVCC / Snapshot Isolation | Read-own-writes, no dirty reads, serializable snapshot |
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| `replication.tla` | Async / Sync / Semi-sync Replication | Monotonic LSN, sync durability, semi-sync quorum |
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## Prerequisites
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- [TLA+ Toolbox](https://lamport.azurewebsites.net/tla/toolbox.html) (GUI + TLC model checker)
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- Or the command-line tools: `tlc`, `pcal`, `sany`
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## Running the Model Checker
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### GUI (TLA+ Toolbox)
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1. Open the Toolbox.
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2. `File → Open Spec → Add New Spec…` → select a `.tla` file.
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3. Create a new model (`TLC Model Checker → New Model`).
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4. Click the green play button to verify all invariants and temporal properties.
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### Command Line
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```bash
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cd formal-verification
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# Parse
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java -cp tla2tools.jar tla2sany.SANY raft.tla
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# Model check with small parameters
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java -cp tla2tools.jar tlc2.TLC -config models/raft.cfg raft.tla
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```
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## Verified Properties
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### raft.tla
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- `ElectionSafety` — at most one leader per term.
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- `LeaderAppendOnly` — a leader never overwrites or deletes entries in its own log.
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- `StateMachineSafety` — if a node has applied a log entry at a given index, no other node ever applies a different entry for the same index.
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### twopc.tla
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- `Atomicity` — it is never the case that one participant commits while another aborts.
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- `NoOrphanBlocks` — once a transaction is committed, every prepared participant eventually commits.
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### mvcc.tla
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- `NoDirtyReads` — a transaction never reads uncommitted writes of another transaction.
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- `ReadOwnWrites` — a transaction always reads its own most recent writes.
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- `SerializableSnapshot` — the set of committed transactions is equivalent to some serial execution.
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### replication.tla
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- `MonotonicLsn` (temporal) — the applied LSN never decreases.
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- `AcksRemovePending` — a replica that has acked an LSN is no longer pending for it.
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- `PendingAreKnown` — all pending acks refer to valid replica IDs.
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## Extending
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To add a new algorithm:
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1. Write the TLA+ spec (preferably with PlusCal for readability).
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2. Define invariants that capture the safety properties you need.
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3. Add a `<name>.tla` file and a matching `<name>.cfg` in `models/`.
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4. Run TLC and confirm `No error has been found.`
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CONSTANTS
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Keys = {k1, k2}
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Values = {v1, v2}
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Nil = Nil
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MaxTxnId = 2
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INIT Init
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NEXT Next
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CHECK_DEADLOCK FALSE
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INVARIANTS
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TypeOk
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NoDirtyReads
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ReadOwnWrites
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WriteWriteConflict
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CONSTANTS
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Nodes = {n1, n2, n3}
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Nil = Nil
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MaxTerm = 3
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MaxLogLen = 3
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INIT Init
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NEXT Next
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CHECK_DEADLOCK FALSE
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INVARIANTS
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TypeOk
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ElectionSafety
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StateMachineSafety
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CONSTANTS
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Replicas = {r1, r2, r3}
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MaxLsn = 3
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MaxSyncCount = 2
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INIT Init
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NEXT Next
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CHECK_DEADLOCK FALSE
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INVARIANTS
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TypeOk
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AcksRemovePending
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PendingAreKnown
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PROPERTIES
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MonotonicLsn
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CONSTANTS
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Participants = {p1, p2, p3}
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Nil = Nil
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MaxTxnId = 2
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INIT Init
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NEXT Next
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CHECK_DEADLOCK FALSE
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INVARIANTS
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TypeOk
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Atomicity
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NoOrphanBlocks
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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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-------------------------------- 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>>
|
||||||
|
|
||||||
|
\* Node i votes for node j in j's current term.
|
||||||
|
Vote(i, j) ==
|
||||||
|
/\ i /= j
|
||||||
|
/\ state[j] = "Candidate"
|
||||||
|
/\ currentTerm[j] > currentTerm[i]
|
||||||
|
/\ votedFor[i] = Nil
|
||||||
|
/\ currentTerm' = [currentTerm EXCEPT ![i] = currentTerm[j]]
|
||||||
|
/\ state' = [state EXCEPT ![i] = "Follower"]
|
||||||
|
/\ votedFor' = [votedFor EXCEPT ![i] = j]
|
||||||
|
/\ votesGranted' = [votesGranted EXCEPT ![j] = @ \cup {i}]
|
||||||
|
/\ UNCHANGED <<log, commitIndex, nextIndex, matchIndex>>
|
||||||
|
|
||||||
|
\* A candidate becomes leader after receiving a majority.
|
||||||
|
BecomeLeader(i) ==
|
||||||
|
/\ state[i] = "Candidate"
|
||||||
|
/\ Cardinality(votesGranted[i]) * 2 > Cardinality(Nodes)
|
||||||
|
/\ state' = [state EXCEPT ![i] = "Leader"]
|
||||||
|
/\ nextIndex' = [nextIndex EXCEPT ![i] = [m \in Nodes |-> Len(log[i]) + 1]]
|
||||||
|
/\ matchIndex' = [matchIndex EXCEPT ![i] = [m \in Nodes |-> 0]]
|
||||||
|
/\ UNCHANGED <<currentTerm, votedFor, log, commitIndex, votesGranted>>
|
||||||
|
|
||||||
|
\* Leader i appends a new entry to its own log.
|
||||||
|
AppendEntry(i) ==
|
||||||
|
/\ state[i] = "Leader"
|
||||||
|
/\ Len(log[i]) < MaxLogLen
|
||||||
|
/\ log' = [log EXCEPT ![i] = Append(@, <<currentTerm[i], "cmd">>)]
|
||||||
|
/\ UNCHANGED <<state, currentTerm, votedFor, commitIndex, votesGranted, nextIndex, matchIndex>>
|
||||||
|
|
||||||
|
\* Leader i replicates its log to follower j.
|
||||||
|
Replicate(i, j) ==
|
||||||
|
/\ i /= j
|
||||||
|
/\ state[i] = "Leader"
|
||||||
|
/\ nextIndex[i][j] <= Len(log[i])
|
||||||
|
/\ log' = [log EXCEPT ![j] =
|
||||||
|
IF Len(log[j]) >= nextIndex[i][j]
|
||||||
|
THEN [log[j] EXCEPT ![nextIndex[i][j]] = log[i][nextIndex[i][j]]]
|
||||||
|
ELSE Append(log[j], log[i][nextIndex[i][j]])]
|
||||||
|
/\ nextIndex' = [nextIndex EXCEPT ![i][j] = @ + 1]
|
||||||
|
/\ matchIndex' = [matchIndex EXCEPT ![i][j] = nextIndex[i][j]]
|
||||||
|
/\ UNCHANGED <<state, currentTerm, votedFor, commitIndex, votesGranted>>
|
||||||
|
|
||||||
|
\* Leader i updates commitIndex when a majority has replicated an entry.
|
||||||
|
Commit(i) ==
|
||||||
|
/\ state[i] = "Leader"
|
||||||
|
/\ LET majority == (Cardinality(Nodes) \div 2) + 1
|
||||||
|
candidates == {idx \in (commitIndex[i]+1)..Len(log[i]) :
|
||||||
|
Cardinality({j \in Nodes : matchIndex[i][j] >= idx}) >= majority
|
||||||
|
/\ log[i][idx][1] = currentTerm[i]}
|
||||||
|
IN candidates /= {}
|
||||||
|
/\ commitIndex' = [commitIndex EXCEPT ![i] = CHOOSE idx \in candidates : TRUE]
|
||||||
|
/\ UNCHANGED <<state, currentTerm, votedFor, log, votesGranted, nextIndex, matchIndex>>
|
||||||
|
|
||||||
|
\* A follower learns about a higher term and steps down.
|
||||||
|
StepDown(i, newTerm) ==
|
||||||
|
/\ newTerm > currentTerm[i]
|
||||||
|
/\ currentTerm[i] < MaxTerm
|
||||||
|
/\ currentTerm' = [currentTerm EXCEPT ![i] = newTerm]
|
||||||
|
/\ state' = [state EXCEPT ![i] = "Follower"]
|
||||||
|
/\ votedFor' = [votedFor EXCEPT ![i] = Nil]
|
||||||
|
/\ votesGranted' = [votesGranted EXCEPT ![i] = {}]
|
||||||
|
/\ UNCHANGED <<log, commitIndex, nextIndex, matchIndex>>
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Next-state relation
|
||||||
|
|
||||||
|
Next ==
|
||||||
|
\/ \E i \in Nodes : Timeout(i)
|
||||||
|
\/ \E i, j \in Nodes : Vote(i, j)
|
||||||
|
\/ \E i \in Nodes : BecomeLeader(i)
|
||||||
|
\/ \E i \in Nodes : AppendEntry(i)
|
||||||
|
\/ \E i, j \in Nodes : Replicate(i, j)
|
||||||
|
\/ \E i \in Nodes : Commit(i)
|
||||||
|
\/ \E i \in Nodes : \E t \in 2..MaxTerm : StepDown(i, t)
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Safety properties
|
||||||
|
|
||||||
|
\* At most one leader per term.
|
||||||
|
ElectionSafety ==
|
||||||
|
\A t \in 1..MaxTerm :
|
||||||
|
Cardinality({i \in Nodes : IsLeader(i, t)}) <= 1
|
||||||
|
|
||||||
|
\* Leaders never overwrite or delete their own log entries.
|
||||||
|
LeaderAppendOnly ==
|
||||||
|
\A i \in Nodes :
|
||||||
|
state[i] = "Leader" =>
|
||||||
|
\A j \in 1..Len(log[i]) :
|
||||||
|
[][Len(log[i]) >= j /\ log[i][j] = log'[i][j]]_vars
|
||||||
|
|
||||||
|
\* If a log entry is committed, all higher leaders have that entry.
|
||||||
|
StateMachineSafety ==
|
||||||
|
\A i, j \in Nodes :
|
||||||
|
\A idx \in 1..Min(commitIndex[i], commitIndex[j]) :
|
||||||
|
idx <= Len(log[i]) /\ idx <= Len(log[j]) => log[i][idx] = log[j][idx]
|
||||||
|
|
||||||
|
\* Type invariant
|
||||||
|
TypeOk ==
|
||||||
|
/\ state \in [Nodes -> {"Follower", "Candidate", "Leader"}]
|
||||||
|
/\ currentTerm \in [Nodes -> 1..MaxTerm]
|
||||||
|
/\ votedFor \in [Nodes -> Nodes \cup {Nil}]
|
||||||
|
/\ \A n \in Nodes : Len(log[n]) <= MaxLogLen
|
||||||
|
/\ \A n \in Nodes : \A i \in 1..Len(log[n]) : log[n][i] \in (1..MaxTerm) \X {"cmd"}
|
||||||
|
/\ commitIndex \in [Nodes -> 0..MaxLogLen]
|
||||||
|
/\ votesGranted \in [Nodes -> SUBSET Nodes]
|
||||||
|
/\ nextIndex \in [Nodes -> [Nodes -> 1..(MaxLogLen+1)]]
|
||||||
|
/\ matchIndex \in [Nodes -> [Nodes -> 0..MaxLogLen]]
|
||||||
|
|
||||||
|
=============================================================================
|
||||||
@@ -0,0 +1,134 @@
|
|||||||
|
-------------------------------- MODULE replication --------------------------------
|
||||||
|
(*
|
||||||
|
TLA+ specification of the BaraDB replication manager
|
||||||
|
(core/replication.nim) supporting Async, Sync, and Semi-sync modes.
|
||||||
|
|
||||||
|
Key properties verified:
|
||||||
|
- MonotonicLsn : applied LSN never moves backwards.
|
||||||
|
- SyncDurability : in sync mode, ack is received from all connected replicas.
|
||||||
|
- SemiSyncQuorum : in semi-sync mode, ack is received from at least N replicas.
|
||||||
|
*)
|
||||||
|
|
||||||
|
EXTENDS Integers, Sequences, FiniteSets, TLC
|
||||||
|
|
||||||
|
CONSTANTS Replicas, \* set of replica IDs
|
||||||
|
MaxLsn, \* bound LSN values for model checking
|
||||||
|
MaxSyncCount \* bound semi-sync count
|
||||||
|
|
||||||
|
ASSUME IsFiniteSet(Replicas)
|
||||||
|
|
||||||
|
VARIABLES
|
||||||
|
mode, \* mode ∈ {"Async", "Sync", "SemiSync"}
|
||||||
|
replicaState, \* replicaState[r] ∈ {"Disconnected", "Connected"}
|
||||||
|
currentLsn, \* currentLsn ∈ Nat
|
||||||
|
pendingAcks, \* pendingAcks[l] ⊆ Replicas (LSNs waiting for acks)
|
||||||
|
appliedLsn, \* appliedLsn ∈ Nat
|
||||||
|
ackedBy \* ackedBy[l] ⊆ Replicas (who acked which LSN)
|
||||||
|
|
||||||
|
vars == <<mode, replicaState, currentLsn, pendingAcks, appliedLsn, ackedBy>>
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Helper operators
|
||||||
|
|
||||||
|
Max(a, b) == IF a > b THEN a ELSE b
|
||||||
|
Min(a, b) == IF a < b THEN a ELSE b
|
||||||
|
|
||||||
|
ConnectedReplicas == {r \in Replicas : replicaState[r] = "Connected"}
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Initial state
|
||||||
|
|
||||||
|
Init ==
|
||||||
|
/\ mode \in {"Async", "Sync", "SemiSync"}
|
||||||
|
/\ replicaState = [r \in Replicas |-> "Disconnected"]
|
||||||
|
/\ currentLsn = 0
|
||||||
|
/\ pendingAcks = [l \in 0..MaxLsn |-> {}]
|
||||||
|
/\ appliedLsn = 0
|
||||||
|
/\ ackedBy = [l \in 0..MaxLsn |-> {}]
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* State transitions
|
||||||
|
|
||||||
|
\* A replica comes online.
|
||||||
|
Connect(r) ==
|
||||||
|
/\ replicaState[r] = "Disconnected"
|
||||||
|
/\ replicaState' = [replicaState EXCEPT ![r] = "Connected"]
|
||||||
|
/\ UNCHANGED <<mode, currentLsn, pendingAcks, appliedLsn, ackedBy>>
|
||||||
|
|
||||||
|
\* A replica goes offline.
|
||||||
|
Disconnect(r) ==
|
||||||
|
/\ replicaState[r] = "Connected"
|
||||||
|
/\ replicaState' = [replicaState EXCEPT ![r] = "Disconnected"]
|
||||||
|
/\ UNCHANGED <<mode, currentLsn, pendingAcks, appliedLsn, ackedBy>>
|
||||||
|
|
||||||
|
\* A new LSN is produced by the primary.
|
||||||
|
WriteLsn ==
|
||||||
|
/\ currentLsn < MaxLsn
|
||||||
|
/\ currentLsn' = currentLsn + 1
|
||||||
|
/\ LET newLsn == currentLsn + 1
|
||||||
|
conn == ConnectedReplicas
|
||||||
|
IN IF mode = "Sync" /\ conn /= {}
|
||||||
|
THEN pendingAcks' = [pendingAcks EXCEPT ![newLsn] = conn]
|
||||||
|
ELSE IF mode = "SemiSync" /\ conn /= {}
|
||||||
|
THEN pendingAcks' = [pendingAcks EXCEPT ![newLsn] =
|
||||||
|
CHOOSE s \in SUBSET conn :
|
||||||
|
Cardinality(s) = Min(MaxSyncCount, Cardinality(conn))]
|
||||||
|
ELSE pendingAcks' = pendingAcks
|
||||||
|
/\ UNCHANGED <<mode, replicaState, appliedLsn, ackedBy>>
|
||||||
|
|
||||||
|
\* Replica r acknowledges LSN l.
|
||||||
|
AckLsn(r, l) ==
|
||||||
|
/\ replicaState[r] = "Connected"
|
||||||
|
/\ l \in 1..currentLsn
|
||||||
|
/\ r \in pendingAcks[l]
|
||||||
|
/\ ackedBy' = [ackedBy EXCEPT ![l] = @ \cup {r}]
|
||||||
|
/\ pendingAcks' = [pendingAcks EXCEPT ![l] = @ \ {r}]
|
||||||
|
/\ IF pendingAcks'[l] = {}
|
||||||
|
THEN appliedLsn' = Max(appliedLsn, l)
|
||||||
|
ELSE appliedLsn' = appliedLsn
|
||||||
|
/\ UNCHANGED <<mode, replicaState, currentLsn>>
|
||||||
|
|
||||||
|
\* Switch replication mode.
|
||||||
|
SwitchMode(newMode) ==
|
||||||
|
/\ newMode \in {"Async", "Sync", "SemiSync"}
|
||||||
|
/\ mode' = newMode
|
||||||
|
/\ UNCHANGED <<replicaState, currentLsn, pendingAcks, appliedLsn, ackedBy>>
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Next-state relation
|
||||||
|
|
||||||
|
Next ==
|
||||||
|
\/ \E r \in Replicas : Connect(r)
|
||||||
|
\/ \E r \in Replicas : Disconnect(r)
|
||||||
|
\/ WriteLsn
|
||||||
|
\/ \E r \in Replicas : \E l \in 1..MaxLsn : AckLsn(r, l)
|
||||||
|
\/ \E newMode \in {"Async", "Sync", "SemiSync"} : SwitchMode(newMode)
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Safety properties
|
||||||
|
|
||||||
|
\* The applied LSN is monotonically non-decreasing.
|
||||||
|
MonotonicLsn ==
|
||||||
|
[][appliedLsn' >= appliedLsn]_vars
|
||||||
|
|
||||||
|
\* A replica that has acked an LSN is no longer pending for it.
|
||||||
|
AcksRemovePending ==
|
||||||
|
\A l \in 1..currentLsn :
|
||||||
|
\A r \in Replicas :
|
||||||
|
r \in ackedBy[l] => r \notin pendingAcks[l]
|
||||||
|
|
||||||
|
\* In sync/semi-sync mode, pending acks are only for known replicas.
|
||||||
|
PendingAreKnown ==
|
||||||
|
\A l \in 1..currentLsn :
|
||||||
|
pendingAcks[l] \subseteq Replicas
|
||||||
|
|
||||||
|
\* Type invariant
|
||||||
|
TypeOk ==
|
||||||
|
/\ mode \in {"Async", "Sync", "SemiSync"}
|
||||||
|
/\ replicaState \in [Replicas -> {"Disconnected", "Connected"}]
|
||||||
|
/\ currentLsn \in 0..MaxLsn
|
||||||
|
/\ pendingAcks \in [0..MaxLsn -> SUBSET Replicas]
|
||||||
|
/\ appliedLsn \in 0..MaxLsn
|
||||||
|
/\ ackedBy \in [0..MaxLsn -> SUBSET Replicas]
|
||||||
|
|
||||||
|
=============================================================================
|
||||||
Binary file not shown.
@@ -0,0 +1,157 @@
|
|||||||
|
-------------------------------- MODULE twopc --------------------------------
|
||||||
|
(*
|
||||||
|
TLA+ specification of the Two-Phase Commit (2PC) distributed transaction
|
||||||
|
protocol as implemented in BaraDB (core/disttxn.nim).
|
||||||
|
|
||||||
|
Key properties verified:
|
||||||
|
- Atomicity : all participants commit, or all abort.
|
||||||
|
- NoOrphanBlocks : a prepared participant never remains blocked forever
|
||||||
|
once the coordinator decides.
|
||||||
|
*)
|
||||||
|
|
||||||
|
EXTENDS Integers, Sequences, FiniteSets, TLC
|
||||||
|
|
||||||
|
CONSTANTS Participants, \* set of participant node IDs
|
||||||
|
Nil, \* distinguished nil value (model value)
|
||||||
|
MaxTxnId \* bound transaction IDs for model checking
|
||||||
|
|
||||||
|
ASSUME IsFiniteSet(Participants)
|
||||||
|
|
||||||
|
VARIABLES
|
||||||
|
txnState, \* txnState[t] ∈ {"Active","Preparing","Prepared","Committing",
|
||||||
|
\* "Committed","Aborting","Aborted"}
|
||||||
|
participantState, \* participantState[t][p] ∈ {"Active","Prepared","Committed","Aborted"}
|
||||||
|
coordinatorDecided, \* coordinatorDecided[t] ∈ {TRUE, FALSE}
|
||||||
|
decidedAction \* decidedAction[t] ∈ {"Commit","Abort", Nil}
|
||||||
|
|
||||||
|
vars == <<txnState, participantState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
|
||||||
|
\* Helper operators
|
||||||
|
|
||||||
|
AllPrepared(t) ==
|
||||||
|
\A p \in Participants : participantState[t][p] \in {"Prepared", "Committed", "Aborted"}
|
||||||
|
|
||||||
|
AnyPrepareFailed(t) ==
|
||||||
|
\E p \in Participants : participantState[t][p] = "Aborted"
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Initial state
|
||||||
|
|
||||||
|
Init ==
|
||||||
|
/\ txnState = [t \in 1..MaxTxnId |-> "Active"]
|
||||||
|
/\ participantState = [t \in 1..MaxTxnId |-> [p \in Participants |-> "Active"]]
|
||||||
|
/\ coordinatorDecided = [t \in 1..MaxTxnId |-> FALSE]
|
||||||
|
/\ decidedAction = [t \in 1..MaxTxnId |-> Nil]
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* State transitions
|
||||||
|
|
||||||
|
\* Phase 1a: Coordinator sends PREPARE to all participants.
|
||||||
|
SendPrepare(t) ==
|
||||||
|
/\ txnState[t] = "Active"
|
||||||
|
/\ txnState' = [txnState EXCEPT ![t] = "Preparing"]
|
||||||
|
/\ UNCHANGED <<participantState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
\* Phase 1b: Participant p receives PREPARE and votes Yes.
|
||||||
|
ParticipantPrepare(t, p) ==
|
||||||
|
/\ txnState[t] = "Preparing"
|
||||||
|
/\ participantState[t][p] = "Active"
|
||||||
|
/\ participantState' = [participantState EXCEPT ![t][p] = "Prepared"]
|
||||||
|
/\ UNCHANGED <<txnState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
\* Phase 1c: Participant p votes No (aborts locally).
|
||||||
|
ParticipantAbort(t, p) ==
|
||||||
|
/\ txnState[t] \in {"Preparing", "Active"}
|
||||||
|
/\ participantState[t][p] = "Active"
|
||||||
|
/\ participantState' = [participantState EXCEPT ![t][p] = "Aborted"]
|
||||||
|
/\ UNCHANGED <<txnState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
\* Phase 2a: Coordinator decides COMMIT (all voted Yes).
|
||||||
|
DecideCommit(t) ==
|
||||||
|
/\ txnState[t] = "Preparing"
|
||||||
|
/\ AllPrepared(t)
|
||||||
|
/\ ~AnyPrepareFailed(t)
|
||||||
|
/\ txnState' = [txnState EXCEPT ![t] = "Committing"]
|
||||||
|
/\ coordinatorDecided' = [coordinatorDecided EXCEPT ![t] = TRUE]
|
||||||
|
/\ decidedAction' = [decidedAction EXCEPT ![t] = "Commit"]
|
||||||
|
/\ UNCHANGED <<participantState>>
|
||||||
|
|
||||||
|
\* Phase 2a-alt: Coordinator decides ABORT (at least one No or timeout).
|
||||||
|
DecideAbort(t) ==
|
||||||
|
/\ txnState[t] = "Preparing"
|
||||||
|
/\ AnyPrepareFailed(t)
|
||||||
|
/\ txnState' = [txnState EXCEPT ![t] = "Aborting"]
|
||||||
|
/\ coordinatorDecided' = [coordinatorDecided EXCEPT ![t] = TRUE]
|
||||||
|
/\ decidedAction' = [decidedAction EXCEPT ![t] = "Abort"]
|
||||||
|
/\ UNCHANGED <<participantState>>
|
||||||
|
|
||||||
|
\* Phase 2b: Participant receives COMMIT decision.
|
||||||
|
ReceiveCommit(t, p) ==
|
||||||
|
/\ txnState[t] = "Committing"
|
||||||
|
/\ decidedAction[t] = "Commit"
|
||||||
|
/\ participantState[t][p] \in {"Prepared", "Active"}
|
||||||
|
/\ participantState' = [participantState EXCEPT ![t][p] = "Committed"]
|
||||||
|
/\ UNCHANGED <<txnState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
\* Phase 2b-alt: Participant receives ABORT decision.
|
||||||
|
ReceiveAbort(t, p) ==
|
||||||
|
/\ txnState[t] = "Aborting"
|
||||||
|
/\ decidedAction[t] = "Abort"
|
||||||
|
/\ participantState[t][p] \in {"Prepared", "Active", "Aborted"}
|
||||||
|
/\ participantState' = [participantState EXCEPT ![t][p] = "Aborted"]
|
||||||
|
/\ UNCHANGED <<txnState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
\* Finalize: transaction moves to terminal state when all participants are done.
|
||||||
|
FinalizeCommit(t) ==
|
||||||
|
/\ txnState[t] = "Committing"
|
||||||
|
/\ \A p \in Participants : participantState[t][p] = "Committed"
|
||||||
|
/\ txnState' = [txnState EXCEPT ![t] = "Committed"]
|
||||||
|
/\ UNCHANGED <<participantState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
FinalizeAbort(t) ==
|
||||||
|
/\ txnState[t] = "Aborting"
|
||||||
|
/\ \A p \in Participants : participantState[t][p] = "Aborted"
|
||||||
|
/\ txnState' = [txnState EXCEPT ![t] = "Aborted"]
|
||||||
|
/\ UNCHANGED <<participantState, coordinatorDecided, decidedAction>>
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Next-state relation
|
||||||
|
|
||||||
|
Next ==
|
||||||
|
\/ \E t \in 1..MaxTxnId : SendPrepare(t)
|
||||||
|
\/ \E t \in 1..MaxTxnId : \E p \in Participants : ParticipantPrepare(t, p)
|
||||||
|
\/ \E t \in 1..MaxTxnId : \E p \in Participants : ParticipantAbort(t, p)
|
||||||
|
\/ \E t \in 1..MaxTxnId : DecideCommit(t)
|
||||||
|
\/ \E t \in 1..MaxTxnId : DecideAbort(t)
|
||||||
|
\/ \E t \in 1..MaxTxnId : \E p \in Participants : ReceiveCommit(t, p)
|
||||||
|
\/ \E t \in 1..MaxTxnId : \E p \in Participants : ReceiveAbort(t, p)
|
||||||
|
\/ \E t \in 1..MaxTxnId : FinalizeCommit(t)
|
||||||
|
\/ \E t \in 1..MaxTxnId : FinalizeAbort(t)
|
||||||
|
|
||||||
|
-----------------------------------------------------------------------------
|
||||||
|
\* Safety properties
|
||||||
|
|
||||||
|
\* Atomicity: it is never the case that one participant committed while another aborted.
|
||||||
|
Atomicity ==
|
||||||
|
\A t \in 1..MaxTxnId :
|
||||||
|
~(\E p1, p2 \in Participants :
|
||||||
|
participantState[t][p1] = "Committed" /\ participantState[t][p2] = "Aborted")
|
||||||
|
|
||||||
|
\* No orphan blocks: once a transaction is fully committed, every participant is committed.
|
||||||
|
NoOrphanBlocks ==
|
||||||
|
\A t \in 1..MaxTxnId :
|
||||||
|
txnState[t] = "Committed" =>
|
||||||
|
\A p \in Participants : participantState[t][p] = "Committed"
|
||||||
|
|
||||||
|
\* Type invariant
|
||||||
|
TypeOk ==
|
||||||
|
/\ txnState \in [1..MaxTxnId -> {"Active","Preparing","Prepared","Committing",
|
||||||
|
"Committed","Aborting","Aborted"}]
|
||||||
|
/\ participantState \in [1..MaxTxnId -> [Participants -> {"Active","Prepared",
|
||||||
|
"Committed","Aborted"}]]
|
||||||
|
/\ coordinatorDecided \in [1..MaxTxnId -> BOOLEAN]
|
||||||
|
/\ decidedAction \in [1..MaxTxnId -> {"Commit","Abort", Nil}]
|
||||||
|
|
||||||
|
=============================================================================
|
||||||
Reference in New Issue
Block a user