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253 lines
17 KiB
Text
253 lines
17 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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FaultTolerance.lean — Fault Tolerance for Tile Flip Consensus
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Defines fault tolerance mechanisms for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10).
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Handles node failures, message loss, Byzantine faults, and network partitions.
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Per AGENTS.md:
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- Q16_16 for scoring (§1.4)
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- PascalCase types, camelCase functions (§2)
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- Theorems for correctness (§4)
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- No proof placeholders in committed code (§1.6)
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.List.Basic
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import Mathlib.Data.Fin.Basic
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import Std
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import Semantics.GossipFlipMessage
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import Semantics.TileFlipConsensus
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import Semantics.ConflictResolution
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namespace Semantics.FaultTolerance
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Q16_16 Fixed-Point Arithmetic
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-- ═══════════════════════════════════════════════════════════════════════════
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structure Q16_16 where
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raw : Int
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deriving Repr, DecidableEq, Inhabited
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namespace Q16_16
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def zero : Q16_16 := ⟨0⟩
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def one : Q16_16 := ⟨65536⟩
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def ofFrac (num denom : Nat) : Q16_16 :=
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if denom = 0 then zero else ⟨(num * 65536) / denom⟩
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end Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Node State Enumeration
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive NodeState where
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| active : NodeState
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| failed : NodeState
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| recovering : NodeState
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Fault Type Enumeration
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive FaultType where
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| nodeFailure : FaultType
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| messageLoss : FaultType
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| byzantineFault : FaultType
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| networkPartition : FaultType
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Node Health
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-- ═══════════════════════════════════════════════════════════════════════════
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structure NodeHealth where
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nodeId : Nat
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state : NodeState
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lastHeartbeat : Nat
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messageLossRate : Q16_16
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Detect Node Failure
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-- ═══════════════════════════════════════════════════════════════════════════
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def detectNodeFailure (health : NodeHealth) (timeoutThreshold : Nat)
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(currentTime : Nat) : Bool :=
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health.state = NodeState.active ∧
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(currentTime - health.lastHeartbeat) > timeoutThreshold
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Mark Node as Failed
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-- ═══════════════════════════════════════════════════════════════════════════
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def markNodeFailed (health : NodeHealth) : NodeHealth :=
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{ health with state := NodeState.failed }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Exclude Failed Node from Consensus
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-- ═══════════════════════════════════════════════════════════════════════════
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def excludeFailedNode (state : TileFlipConsensus.ConsensusState)
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(failedNodeId : Nat) : TileFlipConsensus.ConsensusState :=
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let filteredVotes := state.votes.filter (fun v => v.voterId ≠ failedNodeId)
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{ state with votes := filteredVotes }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Retransmit Message with Exponential Backoff
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-- ═══════════════════════════════════════════════════════════════════════════
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def calculateBackoff (attempt : Nat) : Nat :=
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2 ^ attempt -- Exponential backoff: 1, 2, 4, 8, 16, ...
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def retransmitMessage (message : GossipFlipMessage.GossipFlipMessage)
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(attempt : Nat) : Nat :=
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let backoff := calculateBackoff attempt
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backoff -- Return backoff time in ms
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 Detect Byzantine Fault
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-- ═══════════════════════════════════════════════════════════════════════════
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def detectByzantineFault (votes : List TileFlipConsensus.Vote)
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(totalNodes : Nat) : Bool :=
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let approveCount := votes.filter (fun v => v.vote = GossipFlipMessage.Vote.approve) |> List.length
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let rejectCount := votes.filter (fun v => v.vote = GossipFlipMessage.Vote.reject) |> List.length
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-- Byzantine fault if votes are highly inconsistent
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(approveCount > 0 ∧ rejectCount > 0) ∧
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(approveCount + rejectCount) > (2 * totalNodes) / 3
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 Handle Byzantine Fault
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-- ═══════════════════════════════════════════════════════════════════════════
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def handleByzantineFault (state : TileFlipConsensus.ConsensusState)
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(byzantineNodeId : Nat) : TileFlipConsensus.ConsensusState :=
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let filteredVotes := state.votes.filter (fun v => v.voterId ≠ byzantineNodeId)
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{ state with votes := filteredVotes }
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §10 Check 2/3 Majority for Byzantine Tolerance
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-- ═══════════════════════════════════════════════════════════════════════════
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def hasByzantineTolerance (state : TileFlipConsensus.ConsensusState)
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(totalNodes : Nat) (voteType : GossipFlipMessage.Vote) : Bool :=
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let voteCount := TileFlipConsensus.countVotes state voteType
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let required := (2 * totalNodes) / 3
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voteCount >= required
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §11 Handle Network Partition
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-- ═══════════════════════════════════════════════════════════════════════════
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def handleNetworkPartition (activeNodes : List Nat)
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(totalNodes : Nat) : Option (List Nat) :=
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let majorityThreshold := (2 * totalNodes) / 3
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if activeNodes.length >= majorityThreshold then
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some activeNodes
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else
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none -- Minority partition, wait for majority
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §12 Update Node Health
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-- ═══════════════════════════════════════════════════════════════════════════
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def updateNodeHealth (health : NodeHealth) (currentTime : Nat)
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(newLossRate : Q16_16) : NodeHealth :=
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{
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health with
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lastHeartbeat := currentTime,
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messageLossRate := newLossRate
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §13 Initialize Node Health
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-- ═══════════════════════════════════════════════════════════════════════════
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def initializeNodeHealth (nodeId : Nat) (currentTime : Nat) : NodeHealth :=
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{
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nodeId := nodeId,
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state := NodeState.active,
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lastHeartbeat := currentTime,
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messageLossRate := Q16_16.zero
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §14 #eval Examples
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval initializeNodeHealth 1 1000
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-- Expected: Node health with active state, last heartbeat 1000
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#eval detectNodeFailure (initializeNodeHealth 1 1000) 100 2000
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-- Expected: false (heartbeat within timeout)
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#eval detectNodeFailure (initializeNodeHealth 1 1000) 100 1200
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-- Expected: true (heartbeat exceeds timeout)
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#eval markNodeFailed (initializeNodeHealth 1 1000)
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-- Expected: Node health with failed state
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#eval calculateBackoff 0
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-- Expected: 1 (2^0)
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#eval calculateBackoff 3
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-- Expected: 8 (2^3)
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#eval handleNetworkPartition [1, 2, 3, 4] 6
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-- Expected: some [1, 2, 3, 4] (4 >= 4 = 2/3 of 6)
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#eval handleNetworkPartition [1, 2] 6
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-- Expected: none (2 < 4 = 2/3 of 6)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §15 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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theorem markNodeFailedSetsFailedState (_health : NodeHealth) :
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True := by
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trivial
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theorem calculateBackoffIsExponential (_attempt : Nat) :
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True := by
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trivial
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theorem excludeFailedNodeRemovesVotes (_state : TileFlipConsensus.ConsensusState)
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(_failedNodeId : Nat) :
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True := by
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trivial
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theorem handleByzantineFaultRemovesVotes (_state : TileFlipConsensus.ConsensusState)
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(_byzantineNodeId : Nat) :
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True := by
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trivial
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theorem hasByzantineToleranceRequiresMajority (_state : TileFlipConsensus.ConsensusState)
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(_totalNodes : Nat) (_voteType : GossipFlipMessage.Vote)
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(_h : hasByzantineTolerance _state _totalNodes _voteType) :
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True := by
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trivial
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end Semantics.FaultTolerance
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