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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]>
72 lines
2.3 KiB
Lean4
72 lines
2.3 KiB
Lean4
/-
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Nova Protocol Formal Model
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Models protocol/nova/nova.go -- linear blockchain consensus mode.
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Nova wraps Ray (linear decision engine) and provides blockchain semantics.
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It is the simplest consensus mode: blocks form a chain, decided sequentially.
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Maps to:
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- nova.go: Nova struct wrapping ray.Driver
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- nova.go: Config{SampleSize, Alpha, Beta, RoundTO, GenesisHash}
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- nova.go: NewNova, Start, Stop, Status
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Nova delegates all consensus logic to Ray, which delegates voting to Wave.
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The composition: Nova -> Ray -> Wave -> Prism (sampling)
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Properties:
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- Chain property: decided blocks form a valid chain (parent links)
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- Genesis: genesis block is always the first decided block
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- Height monotonicity: block heights are strictly increasing
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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.Nova
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/-- Block in linear chain -/
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structure Block where
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id : Nat
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parentId : Nat
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height : Nat
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/-- Nova chain state -/
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structure NovaState where
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chain : List Block
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lastHeight : Nat
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/-- Genesis state -/
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def genesis (genesisBlock : Block) (_hg : genesisBlock.height = 0) : NovaState :=
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{ chain := [genesisBlock], lastHeight := 0 }
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/-- Append block to chain -/
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def appendBlock (s : NovaState) (b : Block)
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(_hparent : b.parentId = (s.chain.head?.map Block.id).getD 0)
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(_hheight : b.height = s.lastHeight + 1) : NovaState :=
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{ chain := b :: s.chain, lastHeight := b.height }
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/-- Height is strictly increasing -/
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theorem height_increases (s : NovaState) (b : Block)
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(hparent : b.parentId = (s.chain.head?.map Block.id).getD 0)
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(hheight : b.height = s.lastHeight + 1) :
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(appendBlock s b hparent hheight).lastHeight > s.lastHeight := by
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simp [appendBlock, hheight]
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/-- Chain grows on append -/
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theorem chain_grows (s : NovaState) (b : Block)
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(hp : b.parentId = (s.chain.head?.map Block.id).getD 0)
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(hh : b.height = s.lastHeight + 1) :
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(appendBlock s b hp hh).chain.length = s.chain.length + 1 := by
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simp [appendBlock, List.length_cons]
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/-- Genesis has height 0 -/
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theorem genesis_height (b : Block) (hg : b.height = 0) :
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(genesis b hg).lastHeight = 0 := rfl
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/-- Genesis chain has exactly one block -/
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theorem genesis_single (b : Block) (hg : b.height = 0) :
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(genesis b hg).chain.length = 1 := rfl
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end Protocol.Nova
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