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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]>
98 lines
3.5 KiB
Lean4
98 lines
3.5 KiB
Lean4
/-
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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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