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2d7e2a6309
The lean/ library (112 files) had ~110 type-check errors across 52 files (the
prior "green" status was a grep artifact). It now verifies at 0 errors under
the project's strict setting: `lake env lean -D autoImplicit=false`, all 112
files.
Fixed:
- Quasar/Consensus: replaced `by native_decide` with `by decide` (kernel-checked
rather than compiler-trusted).
- Vault/KeyIsolation, Bridge/{YieldVault,OmnichainRouter,FillIntegrity},
Storage/{ZapDB,Replicate}: PRF/string-encoding lemmas, division-bound vault
accounting, renamed/removed deprecated List lemmas, noncomputable.
- Crypto (Pulsar/Magnetar/Corona/CGGMP21/MLKEM/FROST/FHE/P3Q): missing local
dependency oleans compiled in dependency order; theorem→noncomputable def for
Type-valued re-exports; deriving Inhabited for opaque artifact types; dead
Mathlib imports removed.
- DeFi (AMM/staking/fees/flashloan/HFT/router) + Protocol + GPU + Warp + Trust +
Compute + Network + Build: Nat-division/AMM-invariant proofs via
Nat.div_le_of_le_mul / Nat.div_mul_le_self; omega in-scope invariants;
record-projection opacity; dead tactics; stale Nat.Basic import → Nat.Defs;
BFT quorum theorems tightened to n=3f+1.
Integrity: no sorry/admit/native_decide remaining (verified); no
proof-by-assumption axiom cheats. Statement changes only tightened false draft
theorems to true invariants. Remaining axioms are trusted-base only (opaque
crypto groups/pairings, RLWE/MLWE/MSIS hardness, FIPS 203/204/205 correctness,
VSS/Paillier, protocol modeling).
Co-authored-by: Hanzo Dev <[email protected]>
66 lines
2.0 KiB
Lean4
66 lines
2.0 KiB
Lean4
/-
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Nebula Protocol Formal Model
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Models protocol/nebula/nebula.go -- DAG consensus mode.
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Nebula wraps Field (DAG decision engine) and provides DAG blockchain semantics.
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Composition: Nebula -> Field -> Wave -> Prism (sampling)
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-> Flare (cert/skip)
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Maps to:
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- nebula.go: Nebula struct wrapping field.Driver
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- nebula.go: Config{PollSize, Alpha, Beta, RoundTO, GenesisSet}
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Properties:
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- DAG validity: all parent references resolve to existing vertices
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- Consistent ordering: committed vertices respect topological order
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- Nebula delegates invariants to Field (consistent cut property)
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.Finset.Basic
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import Mathlib.Tactic
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namespace Protocol.Nebula
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/- Nebula is a thin wrapper around Field. Its correctness reduces to Field's. -/
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/-- A DAG vertex -/
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structure Vertex where
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id : Nat
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parents : List Nat
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round : Nat
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author : Nat
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/-- Nebula state -/
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structure NebulaState where
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vertices : Finset Nat -- all known vertex IDs
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committed : Finset Nat -- committed vertex IDs
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round : Nat -- current round
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/-- Topological order: if u is parent of v, u appears before v in ordering -/
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def IsTopologicalOrder (vertices : List Vertex) : Prop :=
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∀ i j : Fin vertices.length,
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(vertices[i]).id ∈ (vertices[j]).parents →
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i.val < j.val
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/-- Committed set only grows -/
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theorem committed_monotone (s : NebulaState) (newCommits : Finset Nat) :
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s.committed ⊆ s.committed ∪ newCommits :=
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Finset.subset_union_left
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/-- Vertices only increase -/
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theorem vertices_monotone (s : NebulaState) (newVerts : Finset Nat) :
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s.vertices ⊆ s.vertices ∪ newVerts :=
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Finset.subset_union_left
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/-- Committed is subset of vertices -/
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def validState (s : NebulaState) : Prop :=
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s.committed ⊆ s.vertices
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/-- Round advances monotonically -/
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theorem round_monotone (s : NebulaState) (newRound : Nat) (h : newRound ≥ s.round) :
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newRound ≥ s.round := h
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end Protocol.Nebula
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