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zooqueenandHanzo Dev
d3bff5e2dc
The lean/ proof library (88 files) had ~180 type-check errors across ~45 files plus 31 proof-by-assumption axiom cheats. It now type-checks cleanly under Lean 4.14.0 + Mathlib, with every theorem genuinely proven from definitions. Errors fixed: - Stale Mathlib imports: Data.Nat.Basic / Data.Int.Basic were removed this rev -> Data.Nat.Defs / Data.Int.Defs (57 files). - Shared AI/Agent/Governance/Contract/DeFi/Ecology draft files: same proof-rot as the zoo-labs sibling library (now reconciled): omega missing in-scope bounds, dead tactics after simp, simp over-reduction, doc-comment placement, reserved-word binders, deriving Repr on Finset-bearing structs, noncomputable defs over opaque primitives. - Consensus/Liveness: collapsed a 74-error cascade (undefined shared state model inlined from Safety.lean; the |>. pipe-projection vs comparison parse trap on 14 lines rewritten to explicit dot projection). - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE), Consensus, Protocol, Warp, Trust, GPU, Compute, Network, DeFi: brought structure invariants into scope for omega, Nat-division bounds via Nat.div_le_of_le_mul / Nat.div_mul_le_self, noncomputable over opaque crypto ops, deriving Inhabited for index access. Integrity: - Removed all 31 `theorem X := X_ax` cheats (axiom asserting the identical statement) and proved each from definitions; removed the UNSOUND content_addressed axiom (hash-injectivity over a struct with free fields). - Quorum-intersection theorems (BFT/Quasar/Flare/Warp/BLS/GPU/Bridge): the draft hypothesis 3f<n is insufficient (n unbounded above makes them false); tightened to the optimal-resilience invariant n=3f+1 / 2t>n. Statement intent preserved. - Net axiom change: -35 / +1 (the one addition, honesty_static, is a fixed-validator-set modeling assumption matching sibling files). - Remaining axioms are trusted-base only: opaque crypto primitives (groups, pairings, hardness, hashes, FHE encrypt/decrypt, BLS soundness, forward secrecy, Fisher-Yates uniformity) and protocol modeling assumptions. No sorry/admit/native_decide. Verified all theorems trace to [propext, Classical.choice, Quot.sound] plus those primitives. Co-authored-by: Hanzo Dev <[email protected]>
68 lines
2.0 KiB
Lean4
68 lines
2.0 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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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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