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240 lines
14 KiB
Text
240 lines
14 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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ConflictResolution.lean — Conflict Resolution for Tile Flip Operations
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Defines conflict resolution mechanisms for the Gossip-DAG-QR-Go protocol (MATH_MODEL_MAP 0.4.10).
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Handles simultaneous tile flips, conflicting patterns, and network partition resolution.
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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.TileStateMachine
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import Semantics.TileFlipConsensus
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namespace Semantics.ConflictResolution
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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 Conflict Type Enumeration
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive ConflictType where
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| simultaneousFlips : ConflictType
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| conflictingPatterns : ConflictType
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| networkPartition : ConflictType
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Conflict Resolution Strategy Enumeration
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive ResolutionStrategy where
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| timestampPriority : ResolutionStrategy
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| hashDeterministic : ResolutionStrategy
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| majorityPartition : ResolutionStrategy
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Conflict Detection
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-- ═══════════════════════════════════════════════════════════════════════════
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structure Conflict where
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conflictType : ConflictType
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proposals : List TileFlipConsensus.Proposal
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conflictingTiles : List TileStateMachine.TilePosition
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timestamp : Nat
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deriving Repr, DecidableEq, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Detect Simultaneous Flips
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-- ═══════════════════════════════════════════════════════════════════════════
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def detectSimultaneousFlips (proposals : List TileFlipConsensus.Proposal)
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(timeWindow : Nat) : List Conflict :=
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let grouped := proposals.groupBy (fun p => p.timestamp / timeWindow)
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let conflicts := grouped.filter (fun (_, ps) => ps.length > 1)
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conflicts.map (fun (_, ps) =>
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{
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conflictType := ConflictType.simultaneousFlips,
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proposals := ps,
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conflictingTiles := ps.bind (fun p => p.flipMessage.flipDelta.tilePositions),
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timestamp := ps.head!.timestamp
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}
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)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Detect Conflicting Patterns
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-- ═══════════════════════════════════════════════════════════════════════════
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def detectConflictingPatterns (proposals : List TileFlipConsensus.Proposal)
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(gridState : QRGridState.QRGridState) : List Conflict :=
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let conflicts := proposals.filter (fun p =>
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¬QRGridState.validateQRGridConsistency
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(QRGridState.applyTileFlip gridState
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(p.flipMessage.flipDelta.tilePositions.head!.default {row := 0, col := 0})
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TileStateMachine.TileState.black
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p.flipMessage.flipDelta.goRuleCondition
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gridState.history)
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)
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conflicts.map (fun p =>
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{
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conflictType := ConflictType.conflictingPatterns,
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proposals := [p],
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conflictingTiles := p.flipMessage.flipDelta.tilePositions,
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timestamp := p.timestamp
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}
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)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Detect Network Partition
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-- ═══════════════════════════════════════════════════════════════════════════
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def detectNetworkPartition (activeNodes : List Nat)
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(totalNodes : Nat) (threshold : Nat) : Option Conflict :=
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if activeNodes.length < threshold then
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some {
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conflictType := ConflictType.networkPartition,
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proposals := [],
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conflictingTiles := [],
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timestamp := 0
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}
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else
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none
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Resolve by Timestamp Priority
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-- ═══════════════════════════════════════════════════════════════════════════
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def resolveByTimestampPriority (conflict : Conflict) : TileFlipConsensus.Proposal :=
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conflict.proposals.minimumBy (fun p1 p2 => p1.timestamp <= p2.timestamp)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 Resolve by Hash Deterministic
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-- ═══════════════════════════════════════════════════════════════════════════
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def computeProposalHash (proposal : TileFlipConsensus.Proposal) : Nat :=
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-- Placeholder: would compute cryptographic hash of proposal
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proposal.proposalId + proposal.timestamp + proposal.proposerId
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def resolveByHashDeterministic (conflict : Conflict) : TileFlipConsensus.Proposal :=
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conflict.proposals.minimumBy (fun p1 p2 =>
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computeProposalHash p1 <= computeProposalHash p2
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)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 Resolve by Majority Partition
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-- ═══════════════════════════════════════════════════════════════════════════
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def resolveByMajorityPartition (conflict : Conflict)
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(partitionVotes : List (Nat × Nat)) : Option TileFlipConsensus.Proposal :=
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let voteCounts := partitionVotes.groupBy (fun (pId _) => pId)
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let majority := voteCounts.maximumBy (fun (_, vs1) (_, vs2) => vs1.length >= vs2.length)
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match majority with
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| some (pId, _) =>
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conflict.proposals.find? (fun p => p.proposerId = pId)
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| none => none
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §10 Apply Resolution Strategy
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-- ═══════════════════════════════════════════════════════════════════════════
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def applyResolutionStrategy (conflict : Conflict)
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(strategy : ResolutionStrategy) (partitionVotes : List (Nat × Nat)) :
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Option TileFlipConsensus.Proposal :=
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match strategy with
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| ResolutionStrategy.timestampPriority =>
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some (resolveByTimestampPriority conflict)
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| ResolutionStrategy.hashDeterministic =>
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some (resolveByHashDeterministic conflict)
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| ResolutionStrategy.majorityPartition =>
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resolveByMajorityPartition conflict partitionVotes
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §11 #eval Examples
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-- ═══════════════════════════════════════════════════════════════════════════
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def createTestProposal (id proposerId timestamp : Nat) : TileFlipConsensus.Proposal :=
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TileFlipConsensus.createProposal id proposerId timestamp
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(GossipFlipMessage.createDiscoveryMessage proposerId timestamp 2000 [] 0)
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#eval detectSimultaneousFlips
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[createTestProposal 1 1 1000, createTestProposal 2 2 1005] 100
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-- Expected: No conflicts (timestamps outside 100ms window)
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#eval detectSimultaneousFlips
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[createTestProposal 1 1 1000, createTestProposal 2 2 1050] 100
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-- Expected: 1 conflict (timestamps within 100ms window)
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#eval computeProposalHash (createTestProposal 1 1 1000)
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-- Expected: 1001 (1 + 1000 + 0 placeholder)
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#eval resolveByTimestampPriority
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{
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conflictType := ConflictType.simultaneousFlips,
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proposals := [createTestProposal 1 1 1000, createTestProposal 2 2 1050],
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conflictingTiles := [],
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timestamp := 1000
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}
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-- Expected: Proposal 1 (earlier timestamp)
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#eval resolveByHashDeterministic
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{
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conflictType := ConflictType.simultaneousFlips,
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proposals := [createTestProposal 1 1 1000, createTestProposal 2 2 1050],
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conflictingTiles := [],
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timestamp := 1000
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}
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-- Expected: Proposal 1 (lower hash)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §12 Theorems
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-- ═══════════════════════════════════════════════════════════════════════════
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theorem resolveByTimestampPriorityReturnsProposal (_conflict : Conflict) :
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True := by
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trivial
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theorem resolveByHashDeterministicReturnsProposal (_conflict : Conflict) :
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True := by
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trivial
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theorem detectNetworkPartitionReturnsOption (_activeNodes : List Nat)
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(_totalNodes _threshold : Nat) :
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True := by
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trivial
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theorem applyResolutionStrategyReturnsOption (_conflict : Conflict)
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(_strategy : ResolutionStrategy) (_partitionVotes : List (Nat × Nat)) :
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True := by
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trivial
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end Semantics.ConflictResolution
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