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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]>
96 lines
2.9 KiB
Lean4
96 lines
2.9 KiB
Lean4
/-
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Quasar Protocol Formal Model
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Models protocol/quasar/ -- BLS+Corona hybrid quantum consensus.
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Quasar is the finality engine. It collects blocks from all chains
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and produces quantum-final aggregate blocks with dual signatures:
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- BLS (classical, fast): 96-byte aggregated signatures
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- Corona (post-quantum, larger): ~4KB lattice-based threshold signatures
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Maps to:
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- quasar/bls.go: BLS signature aggregation (quorum = 2f+1)
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- quasar/core.go: Quasar struct, chain buffers, quantum finality
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- quasar/engine.go: Engine implementation
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- quasar/horizon.go: Event horizon (pending blocks)
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Properties:
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- BLS aggregation correctness: agg_verify(agg_sig, agg_pk, msg) iff all individual sigs valid
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- Quorum threshold: 2f+1 signatures required for finality
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- Dual signature: quantum block has both BLS and Corona sigs
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- Epoch monotonicity: quantum height only increases
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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 Protocol.Quasar
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/-- Signature types -/
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structure BLSSig where
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bytes : List UInt8
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valid : Bool
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structure CoronaSig where
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bytes : List UInt8
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valid : Bool
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/-- Quasar signature = BLS + Corona (models quasar.QuasarSig) -/
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structure QuasarSig where
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bls : BLSSig
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corona : CoronaSig
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/-- Quantum block (models quasar.QuantumBlock) -/
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structure QuantumBlock where
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height : Nat
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sourceBlocks : List Nat -- block hashes
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signature : QuasarSig
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/-- Quasar state -/
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structure QuasarState where
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quantumHeight : Nat
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finalized : List QuantumBlock
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/-- BLS aggregation: aggregate of valid sigs is valid -/
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axiom bls_aggregation_sound :
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∀ (sigs : List BLSSig),
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(∀ s ∈ sigs, s.valid = true) →
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sigs ≠ [] →
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-- Aggregated signature is valid (bilinear pairing property)
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∃ (agg : BLSSig), agg.valid = true
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/-- Quantum height is monotonically increasing -/
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def addBlock (s : QuasarState) (b : QuantumBlock)
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(_h : b.height > s.quantumHeight) : QuasarState :=
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{ quantumHeight := b.height
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, finalized := b :: s.finalized }
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theorem height_monotone (s : QuasarState) (b : QuantumBlock)
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(h : b.height > s.quantumHeight) :
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(addBlock s b h).quantumHeight > s.quantumHeight := by
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simp [addBlock]
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exact h
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/-- Quorum intersection for BLS signatures:
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Two quorums of 2f+1 from n=3f+1 validators share f+1 members.
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At least one shared member is honest. -/
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theorem bls_quorum_intersection
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(n f : Nat) (hf : n = 3 * f + 1)
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(q1 q2 : Nat)
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(hq1 : q1 ≥ 2 * f + 1) (hq2 : q2 ≥ 2 * f + 1) :
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q1 + q2 > n := by
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omega
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/-- Dual signature validity: both components must be valid -/
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def isValidQuantumSig (qs : QuasarSig) : Bool :=
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qs.bls.valid && qs.corona.valid
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/-- A finalized block has both BLS and Corona valid -/
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theorem quantum_finality_requires_both
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(qs : QuasarSig) (h : isValidQuantumSig qs = true) :
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qs.bls.valid = true ∧ qs.corona.valid = true := by
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simp [isValidQuantumSig] at h
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exact h
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end Protocol.Quasar
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