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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]>
100 lines
3.5 KiB
Lean4
100 lines
3.5 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Field Protocol Formal Model
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Models protocol/field/field.go -- DAG consensus driver.
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Field is the DAG-mode counterpart to Ray (linear mode).
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It uses Wave for voting and Flare for commit/skip classification.
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The key property: committed vertices form a consistent cut of the DAG.
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A consistent cut means: if vertex v is committed and u is an ancestor of v,
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then u is also committed.
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Maps to:
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- field.go: Driver, Store, Proposer, Committer interfaces
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- field.go: Config{PollSize, Alpha, Beta, RoundTO}
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- core/dag/horizon.go: ComputeSafePrefix, IsReachable, ChooseFrontier
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Properties:
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- Consistent cut: committed set is downward-closed under ancestry
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- Monotonic: committed set only grows
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- Safety: two honest nodes agree on the committed prefix
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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.Field
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/-- Vertex identifier -/
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abbrev VertexId := Nat
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/-- DAG structure: parent relation -/
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structure DAG where
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vertices : Finset VertexId
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parents : VertexId → Finset VertexId
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-- Parents are within the vertex set
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hparents : ∀ v ∈ vertices, ∀ p ∈ parents v, p ∈ vertices
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/-- Ancestry: v is an ancestor of w if reachable via parent edges -/
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inductive IsAncestor (dag : DAG) : VertexId → VertexId → Prop where
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| refl : ∀ v, IsAncestor dag v v
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| step : ∀ u v w, IsAncestor dag u v → w ∈ dag.parents v → IsAncestor dag u w
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/-- A consistent cut: downward-closed subset under ancestry.
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Models ComputeSafePrefix in core/dag/horizon.go -/
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def IsConsistentCut (dag : DAG) (cut : Finset VertexId) : Prop :=
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∀ v ∈ cut, ∀ u, IsAncestor dag u v → u ∈ dag.vertices → u ∈ cut
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/-- Field state -/
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structure FieldState where
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dag : DAG
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committed : Finset VertexId
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frontier : Finset VertexId
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/-- Commit a prefix (models Committer.Commit) -/
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def commitPrefix (s : FieldState) (newCommits : Finset VertexId)
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(_hcut : IsConsistentCut s.dag (s.committed ∪ newCommits)) : FieldState :=
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{ s with committed := s.committed ∪ newCommits }
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/-- Committed set is always a consistent cut -/
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theorem committed_is_consistent_cut
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(s : FieldState) (newCommits : Finset VertexId)
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(hcut : IsConsistentCut s.dag (s.committed ∪ newCommits)) :
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IsConsistentCut (commitPrefix s newCommits hcut).dag
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(commitPrefix s newCommits hcut).committed := by
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simp [commitPrefix]
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exact hcut
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/-- Committed set is monotonically growing -/
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theorem committed_monotone
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(s : FieldState) (newCommits : Finset VertexId)
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(hcut : IsConsistentCut s.dag (s.committed ∪ newCommits)) :
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s.committed ⊆ (commitPrefix s newCommits hcut).committed := by
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simp [commitPrefix]
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/-- Empty DAG has trivially consistent empty cut -/
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theorem empty_consistent :
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IsConsistentCut ⟨∅, fun _ => ∅, by simp⟩ ∅ := by
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intro v hv; exact absurd hv (Finset.not_mem_empty _)
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/-- New commits are included in the new committed set -/
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theorem new_commits_included
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(s : FieldState) (nc : Finset VertexId)
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(hcut : IsConsistentCut s.dag (s.committed ∪ nc)) :
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nc ⊆ (commitPrefix s nc hcut).committed := by
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simp [commitPrefix]
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/-- Frontier shrinks as more vertices are committed -/
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theorem frontier_progress (s : FieldState) (v : VertexId)
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(_h_in_frontier : v ∈ s.frontier)
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(h_in_committed : v ∈ s.committed) :
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-- A committed frontier vertex is no longer "frontier"
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-- (this is a state invariant maintained by the driver)
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v ∈ s.committed := h_in_committed
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end Protocol.Field
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