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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]>
71 lines
2.0 KiB
Lean4
71 lines
2.0 KiB
Lean4
/-
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DeFi Fee Model
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Maker-taker with volume tiers. Permissionless.
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No regulatory fee caps (pure DeFi).
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Maps to:
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- lux/exchange: fee calculation
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- lux/node: fee distribution to validators
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Properties:
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- Makers ≤ takers (incentivize liquidity)
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- Volume tiers: more volume → lower fees
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- Validator revenue: portion of fees to validators
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- Permissionless: fee schedule is on-chain and transparent
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Authors: Zach Kelling (Dec 2025), Woo Bin (Mar 2026)
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace DeFi.FeeModel
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/-- Fee tier -/
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structure FeeTier where
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minVolume : Nat
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makerBps : Nat
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takerBps : Nat
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deriving DecidableEq, Repr, Inhabited
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/-- Standard DeFi tiers -/
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def tiers : List FeeTier :=
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[ ⟨0, 15, 30⟩ -- Tier 1
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, ⟨1000000, 10, 25⟩ -- Tier 2: $1M+
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, ⟨10000000, 5, 15⟩ -- Tier 3: $10M+
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, ⟨100000000, 0, 10⟩ -- Tier 4: $100M+ (zero maker)
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]
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/-- Calculate fee -/
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def fee (tier : FeeTier) (isMaker : Bool) (value : Nat) : Nat :=
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value * (if isMaker then tier.makerBps else tier.takerBps) / 10000
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/-- MAKER ≤ TAKER -/
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theorem maker_le_taker (t : FeeTier) (v : Nat) (h : t.makerBps ≤ t.takerBps) :
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fee t true v ≤ fee t false v := by
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simp [fee]; exact Nat.div_le_div_right (Nat.mul_le_mul_left v h)
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/-- TOP TIER ZERO MAKER -/
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theorem top_tier_zero : (tiers[3]!).makerBps = 0 := by simp [tiers]
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/-- VOLUME DISCOUNT -/
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theorem volume_discount : (tiers[0]!).takerBps > (tiers[3]!).takerBps := by
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simp [tiers]
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/-- 4 TIERS -/
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theorem four_tiers : tiers.length = 4 := rfl
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/-- VALIDATOR SHARE: Portion of fees goes to validators who process trades -/
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def validatorShare (totalFee : Nat) (validatorPct : Nat) : Nat :=
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totalFee * validatorPct / 100
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theorem validator_bounded (totalFee pct : Nat) (h : pct ≤ 100) :
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validatorShare totalFee pct ≤ totalFee := by
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simp only [validatorShare]
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apply Nat.div_le_of_le_mul
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calc totalFee * pct ≤ totalFee * 100 := Nat.mul_le_mul_left totalFee h
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_ = 100 * totalFee := Nat.mul_comm _ _
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end DeFi.FeeModel
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