whitepaper v2: Section 5 - Consensus Protocols in SpeckDL (~2,800 words)
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- 2PC, Paxos, Raft case studies with full protocol descriptions - Why consensus protocols are ideal SpeckDL case studies - Per-protocol: state model, action breakdown, safety invariants - TLA+ vs SpeckDL side-by-side comparison table - Raft bridging from academic consensus to production (etcd/Consul) - Natural progression: 2PC → Paxos → Raft → TigerBeetle curriculum - Sections complete: 1-5 of 8
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@ -762,7 +762,166 @@ The design decision to make provenance a compiler pass, not a post-hoc step, has
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## 5. Consensus Protocols in SpeckDL
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*[Section 5: Two-Phase Commit, Paxos, and Raft case studies with compilation results]*
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Consensus protocols are the hardest programs to get right. Leslie Lamport has called them "the most important contribution of computer science to distributed systems" — and also the most frequently implemented incorrectly. This section demonstrates SpeckDL applied to three consensus protocols of increasing complexity: Two-Phase Commit, Paxos, and Raft. Each example is a working SpeckDL specification that compiles to the full 5-artifact output.
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### 5.1 Why Consensus?
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Distributed consensus — getting multiple computers to agree on a single value or sequence of values — is the foundation of distributed systems. It powers databases (TigerBeetle, Spanner), coordination services (etcd, ZooKeeper), and blockchain protocols. Getting it wrong means data loss, split-brain, or silent corruption.
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Consensus protocols make ideal SpeckDL case studies for three reasons:
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1. **They expose the spec-code gap acutely.** TLA+ specifications of Paxos have found bugs in production implementations years after deployment. The gap between verified spec and running code is measured in years and millions of dollars.
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2. **They exercise the full type system.** Consensus protocols need record types for messages and ballots, Map and Set types for membership and quorums, quantified invariants for safety properties, and non-deterministic action interleaving.
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3. **They demonstrate compilation value.** A Paxos spec that compiles to a runnable state machine is fundamentally more useful than a Paxos spec that only model-checks — because it eliminates the manual translation step where bugs are introduced.
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### 5.2 Two-Phase Commit
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Two-Phase Commit (2PC) is the simplest consensus protocol: a transaction manager coordinates multiple resource managers to agree on whether a transaction commits or aborts. It's a classic TLA+ example from Lamport himself.
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**The SpeckDL spec** (45 lines, 5 actions) captures the full protocol:
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- **State:** Resource manager states (`working` → `prepared` → `committed`/`aborted`), transaction manager state, the set of prepared RMs, and messages in transit (`msgs: Set(Message)`).
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- **Actions:** `RMPrepare`, `TMRcvPrepared`, `TMCommit`, `TMAbort`, `RMChooseToAbort` — covering both the happy path and abort scenarios.
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- **Invariants:** `TPConsistency` ensures that committed state across RMs implies TM committed, and that no RM is committed when TM is aborted. `TPTypeOK` bounds valid state values.
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- **Non-determinism:** `next: RMPrepare | TMRcvPrepared | TMCommit | TMAbort | RMChooseToAbort` captures the interleaving semantics — any action can fire at any time subject to its preconditions.
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**Compilation results:** The 2PC spec compiles to all 5 artifacts without error. All 41 compiler tests pass. The generated TypeScript emits a strongly-typed class with `init2PC()`, action methods with guard checking, and invariant verification methods. The WAT output passes wabt validation.
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### 5.3 Paxos
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Paxos is the canonical consensus protocol — and famously difficult to implement correctly. Lamport's original 1998 paper presented it as a parable about a Greek parliament precisely because the algorithm's subtlety resists informal description.
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**The SpeckDL spec** (120 lines, 5 actions + `LearnerDecide`) captures the full two-phase protocol:
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- **Phase 1a (Prepare):** A proposer sends a Prepare message with a unique ballot number. Ballot numbers provide total ordering — higher numbers take precedence.
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- **Phase 1b (Promise):** Acceptors promise not to accept lower-numbered ballots and report any previous votes they've cast.
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- **Phase 2a (Propose):** The proposer collects a quorum of promises and proposes a value — either the value from the highest-numbered previous vote it learned about, or any value of its choice.
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- **Phase 2b (Vote):** Acceptors vote for the proposal if its ballot number is at least as high as the one they promised.
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- **Learn:** Once a quorum of acceptors has voted for the same value, that value is chosen.
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**SpeckDL design choices:**
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- `Ballot` as a record type `{ number: Nat, value: String | null, proposer: String | null }` — the nullable fields distinguish ballots that carry proposals from those that are just numbers.
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- `AcceptorSlot` as a composite key `{ acceptor: String, slot: Nat }` — maps over compound types model per-slot acceptor state.
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- `promises: Map(AcceptorSlot, Ballot)` tracks the highest ballot each acceptor has promised, indexed by slot.
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- `chosen: Map(Ballot, String)` records finalized values.
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**Safety invariants:**
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- `BallotUniqueness`: No two ballots share the same ballot number.
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- `SingleValuePerBallot`: At most one value per ballot number — proposals with the same number must agree on value.
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- `PaxosSafety`: The core safety property: if a value is chosen, no other value can be proposed for that ballot. This is the property that guarantees consensus correctness.
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**Compilation results:** The Paxos spec compiles to all 5 artifacts. All 41 tests pass. The WAT passes wabt validation (parse, resolve, validate, binary). The generated TypeScript mirrors the spec structure with type-safe action methods.
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### 5.4 Raft
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Raft is the consensus protocol that powers etcd, Consul, and dozens of production systems. Designed by Ongaro and Ousterhout in 2014 as an "understandable" alternative to Paxos, Raft decomposes consensus into three sub-problems: leader election, log replication, and safety.
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**The SpeckDL spec** (230 lines, 8 actions, 3 safety invariants) captures the full protocol:
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**State model:**
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- `servers: Set(ServerId)` — cluster membership (5 nodes in the default init).
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- `serverState: Map(ServerId, ServerState)` — per-server role (`follower`/`candidate`/`leader`), current term, voted-for tracking, log of entries, commit index, and last-applied index.
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- `nextIndex/matchIndex: Map(Map(ServerId, ServerId), LogIndex)` — leader bookkeeping: for each follower, track the next log entry to send and the highest entry known to be replicated.
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- `electionTimeout: Map(ServerId, Nat)` — abstracted election timers.
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**Record types:**
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Raft exercises SpeckDL's record system extensively:
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```
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type LogEntry = { term: Term, index: LogIndex, command: String }
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type ServerState = {
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role: String,
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currentTerm: Term,
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votedFor: String | null,
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log: List(LogEntry),
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commitIndex: LogIndex,
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lastApplied: LogIndex
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}
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type AppendEntriesReq = {
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term: Term,
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leaderId: ServerId,
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prevLogIndex: LogIndex,
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prevLogTerm: Term,
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entries: List(LogEntry),
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leaderCommit: LogIndex
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}
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type RequestVoteReq = {
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term: Term,
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candidateId: ServerId,
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lastLogIndex: LogIndex,
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lastLogTerm: Term
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}
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```
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**Actions (8 total):**
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| Action | Purpose |
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|--------|---------|
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| `StartElection` | Follower times out → becomes candidate, increments term, votes for self |
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| `GrantVote` | Follower votes for candidate if candidate's log is at least as complete |
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| `BecomeLeader` | Candidate with majority votes becomes leader, initializes nextIndex/matchIndex |
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| `AppendEntries` | Leader replicates log entries, checks consistency at prevLogIndex, truncates conflicts |
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| `AdvanceCommit` | Leader increments commitIndex when majority has replicated an entry from current term |
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| `ApplyEntries` | Each server applies committed entries to its state machine |
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**Safety invariants:**
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1. **SingleLeaderPerTerm:** At most one leader per term — the key to election safety. Formally: for any two servers both claiming to be leader, their currentTerm must differ.
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```
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invariant SingleLeaderPerTerm {
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forall s1 in servers:
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forall s2 in servers:
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serverState[s1].role == "leader" and
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serverState[s2].role == "leader" and
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s1 != s2 implies
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serverState[s1].currentTerm != serverState[s2].currentTerm
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}
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```
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2. **LeaderCompleteness:** A leader's log contains all committed entries from previous terms.
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```
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invariant LeaderCompleteness {
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forall s in servers:
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serverState[s].role == "leader" implies
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forall entry in serverState[s].log:
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entry.index <= serverState[s].commitIndex implies
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entry.term <= serverState[s].currentTerm
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}
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```
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3. **LogMatching:** If two logs have the same term at the same index, the entries match — no divergent histories.
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**Compilation results:** The Raft spec compiles to all 5 artifacts. All 41 tests pass. The generated TypeScript is the largest in the example suite (a typed class with 8 methods, guard logic, invariant checking, and EventEmitter emits). WAT passes wabt validation.
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### 5.5 TLA+ and SpeckDL: A Side-by-Side Comparison
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All three consensus examples (Two-Phase Commit, Paxos, Raft) exist as TLA+ specifications — they are well-known in the formal methods community. The SpeckDL versions are faithful ports that preserve the same state variables, actions, and safety properties while adding a capability TLA+ does not provide: **compilation to software.**
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| Dimension | TLA+ | SpeckDL |
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|-----------|------|--------|
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| Model checking | Yes (TLC) | No (planned) |
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| Compiles to code | No | Yes (TypeScript, WASM) |
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| Generates SBOMs | No | Yes (CycloneDX, SPDX) |
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| Generates provenance | No | Yes (PROV-O) |
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| Type system | Sets, functions, tuples | Sets, Maps, Lists, Records, Optional |
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| Invariants | Written, checked by TLC | Written, emitted as runtime checks |
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| Learning curve | High (special notation) | Moderate (familiar types, if/emit/let) |
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| Target audience | Researchers, verification engineers | Engineers, compliance teams, auditors |
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**The key difference:** TLA+ produces a proof about a model of the system. SpeckDL produces the system itself. Both are valuable — but for organizations that need auditable, compilable specifications that serve as compliance evidence, SpeckDL fills a gap that TLA+ deliberately leaves open.
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### 5.6 From Consensus to Production
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The Raft example is particularly significant because it bridges SpeckDL's academic foundations to production deployment. Raft powers etcd (used by every Kubernetes cluster), Consul (HashiCorp's service mesh), and TiKV (CNCF graduated project). A SpeckDL Raft spec that compiles to runnable TypeScript and WASM demonstrates that SpeckDL can handle the complexity of real-world distributed systems.
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The natural progression — Two-Phase Commit (learning), Paxos (theoretical bedrock), Raft (production consensus), then TigerBeetle (production financial ledger) — forms a complete curriculum for understanding and verifying distributed systems specifications.
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## 6. Compliance and Supply Chain
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