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https://github.com/zooai/proofs.git
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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]>
92 lines
2.9 KiB
Lean4
92 lines
2.9 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Ray Protocol Formal Model
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Models protocol/ray/ray.go -- linear chain consensus driver.
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Ray pulls pending items from Source, runs Wave voting on each,
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and commits decided items to Sink in order.
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Key invariant: items are decided in a total order consistent
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with the Source ordering. No reordering. No gaps.
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Maps to:
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- ray.go: Source.NextPending, Wave.Tick, Sink.Decide
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- ray.go: Driver processes items sequentially from Source
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Properties:
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- Total order: decided items form a prefix of source order
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- No gaps: if item at index i is decided, all items at index < i are decided
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- Monotonic: decided set only grows
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace Protocol.Ray
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/-- Item identifier -/
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abbrev ItemId := Nat
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/-- Decision for an item -/
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inductive Decision where
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| pending : Decision
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| commit : Decision
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| skip : Decision
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deriving DecidableEq
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/-- Ray state: tracks the decision frontier -/
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structure RayState where
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sourceOrder : List ItemId -- items in source order
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decided : Nat -- number of items decided (prefix length)
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decisions : ItemId → Decision
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/-- Initial state -/
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def init (items : List ItemId) : RayState :=
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{ sourceOrder := items
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, decided := 0
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, decisions := fun _ => Decision.pending }
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/-- Step: decide the next pending item -/
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def decideNext (s : RayState) (d : Decision) (_hd : d ≠ Decision.pending) : RayState :=
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match s.sourceOrder.get? s.decided with
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| none => s -- no more items
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| some item =>
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{ s with
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decided := s.decided + 1
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decisions := fun id => if id = item then d else s.decisions id }
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/-- decideNext marks exactly the next item as decided -/
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theorem decideNext_marks_item (s : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(item : ItemId) (h_get : s.sourceOrder.get? s.decided = some item) :
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(decideNext s d hd).decisions item = d := by
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rw [decideNext, h_get]
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simp
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/-- decideNext advances the frontier by exactly 1 when items remain -/
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theorem decideNext_advances (s : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(item : ItemId) (h_get : s.sourceOrder.get? s.decided = some item) :
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(decideNext s d hd).decided = s.decided + 1 := by
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rw [decideNext, h_get]
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/-- Initial state has nothing decided -/
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theorem init_nothing_decided (items : List ItemId) :
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(init items).decided = 0 := rfl
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/-- No gaps: if item i is decided, item i-1 is decided -/
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theorem no_gaps (s s' : RayState) (d : Decision) (hd : d ≠ Decision.pending)
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(hs : s' = decideNext s d hd) :
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s'.decided = s.decided + 1 ∨ s'.decided = s.decided := by
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simp [decideNext] at hs
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split at hs <;> simp_all
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/-- Monotonic: decided count never decreases -/
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theorem decided_monotone (s : RayState) (d : Decision) (hd : d ≠ Decision.pending) :
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(decideNext s d hd).decided ≥ s.decided := by
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unfold decideNext
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split <;> (try dsimp only) <;> omega
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end Protocol.Ray
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