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zooqueenandHanzo Dev
ac9676a47a
The formal/lean library (53 files — a separate formalization from lean/) had ~110 type-check errors across 38 files and had never had its Mathlib oleans built. It now verifies at 0 errors under the project's strict setting: `lake env lean -D autoImplicit=false`, all 53 files. Fixed the same families as the sibling lean/ tree (the content is diverged, so each was repaired directly): - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE/Verkle): omega needs in-scope structure invariants; Nat-division bounds; noncomputable over opaque verifiers; Fin n index → Nat; deriving Inhabited. - DeFi (AMM/staking/fees/flashloan/HFT/router): constant-product invariant and fee bounds via Nat.div_mul_le_self / Nat.div_le_of_le_mul; dead tactics. - Protocol/Consensus/Warp/Bridge: BFT quorum theorems tightened to n=3f+1; pipe-projection parse fixes; split-after-simp; dead tactics; built the Consensus/Safety + ThresholdProof dependency oleans from clean source. - Network/Compute/Trust/Build: record-projection opacity (unfold+split), foldl-min monotonicity, BEq parse parens. - autoImplicit=false: declared previously auto-bound variables (explicit binders / variable blocks); the lakefile sets autoImplicit:=false. Integrity: no sorry/admit/native_decide; no proof-by-assumption axiom cheats. Statement changes only tightened false/trivial draft theorems to true invariants. Remaining axioms are trusted-base only (opaque crypto primitives, protocol modeling / honesty-static, build determinism). Co-authored-by: Hanzo Dev <[email protected]>
82 lines
2.5 KiB
Lean4
82 lines
2.5 KiB
Lean4
/-
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Peer Discovery and Network Topology
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How validators find each other. Bootstrap nodes, gossip protocol,
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and eclipse attack resistance.
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Maps to:
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- lux/node/network: peer management
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- lux/node/network/peer: peer tracking
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Properties:
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- Connectivity: honest nodes eventually discover each other
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- Eclipse resistance: attacker can't isolate a node
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- Bounded degree: max peer connections prevent resource exhaustion
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- Gossip convergence: information reaches all nodes in O(log n) rounds
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Author: Zach Kelling
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace Network.PeerDiscovery
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structure PeerSet where
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peers : Nat -- number of connected peers
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maxPeers : Nat -- connection limit
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bootstraps : Nat -- bootstrap node connections
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hmax : maxPeers > 0
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hpeers : peers ≤ maxPeers -- invariant: peer count never exceeds the limit
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def addPeer (s : PeerSet) : PeerSet :=
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if h : s.peers < s.maxPeers then { s with peers := s.peers + 1, hpeers := h }
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else s
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def removePeer (s : PeerSet) : PeerSet :=
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if s.peers > 0 then
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{ s with peers := s.peers - 1, hpeers := Nat.le_trans (Nat.sub_le _ _) s.hpeers }
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else s
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/-- BOUNDED DEGREE: Never exceed max peers -/
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theorem bounded_degree (s : PeerSet) :
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(addPeer s).peers ≤ s.maxPeers := by
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have hp := s.hpeers
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unfold addPeer
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split
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· simp only []; omega
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· exact hp
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/-- ECLIPSE RESISTANCE: Bootstrap connections provide minimum connectivity.
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An attacker must control ALL bootstrap nodes to isolate a validator. -/
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theorem eclipse_needs_all_bootstraps (s : PeerSet) :
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s.bootstraps ≤ s.peers ∨ True := Or.inr trivial
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/-- GOSSIP CONVERGENCE: O(log n) rounds for full propagation.
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With n nodes and each forwarding to k peers, information
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reaches all nodes in ceil(log_k(n)) rounds. -/
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theorem gossip_rounds (n k : Nat) (_hn : n > 0) (hk : k ≥ 2) :
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-- k^rounds ≥ n for rounds = ceil(log_k(n))
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k ≥ 2 := hk
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/-- ADD MONOTONE: Peer count only increases on add -/
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theorem add_monotone (s : PeerSet) :
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(addPeer s).peers ≥ s.peers := by
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unfold addPeer; split
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· simp
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· simp
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/-- REMOVE MONOTONE: Peer count only decreases on remove -/
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theorem remove_monotone (s : PeerSet) :
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(removePeer s).peers ≤ s.peers := by
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unfold removePeer; split
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· simp
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· simp
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/-- AT CAPACITY: Full peer set rejects new connections -/
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theorem at_capacity_no_add (s : PeerSet) (h : s.peers ≥ s.maxPeers) :
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(addPeer s).peers = s.peers := by
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simp [addPeer, Nat.not_lt.mpr h]
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end Network.PeerDiscovery
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