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86 lines
2.6 KiB
Lean4
86 lines
2.6 KiB
Lean4
/-
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Validator Economics and Slashing
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Staking economics for Lux validators. Stake-weighted voting.
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Slashing for provable misbehavior.
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Maps to:
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- lux/node/vms/platformvm: validator staking
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- lux/consensus: stake-weighted BFT
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- HIP-0024: Hanzo L1 validator requirements
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Properties:
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- Stake-weighted: voting power ∝ stake
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- Slashing is loss-bounded: cannot lose more than stake
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- Honest validators are never slashed (safety)
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- Minimum stake enforced
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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 Consensus.Validator
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/-- Validator with stake -/
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structure Validator where
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id : Nat
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stake : Nat
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isHonest : Bool
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slashed : Nat -- amount already slashed
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deriving DecidableEq, Repr
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/-- Validator set -/
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structure ValidatorSet where
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validators : List Validator
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minStake : Nat
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totalStake : Nat
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/-- Voting power: proportional to stake -/
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def votingPower (v : Validator) (totalStake : Nat) : Nat :=
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if totalStake = 0 then 0 else v.stake * 1000 / totalStake -- basis points
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/-- Slash a validator for misbehavior -/
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def slash (v : Validator) (penalty : Nat) : Validator :=
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{ v with slashed := v.slashed + min penalty (v.stake - v.slashed) }
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/-- SLASHING BOUNDED: Cannot lose more than stake -/
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theorem slash_bounded (v : Validator) (penalty : Nat)
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(h : v.slashed ≤ v.stake) :
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(slash v penalty).slashed ≤ v.stake := by
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simp [slash]; omega
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/-- SLASHING MONOTONE: Slashed amount only increases -/
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theorem slash_monotone (v : Validator) (penalty : Nat) :
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(slash v penalty).slashed ≥ v.slashed := by
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simp [slash]
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/-- HONEST NEVER SLASHED: Only provable misbehavior triggers slash.
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This is a protocol property (axiomatized). -/
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axiom honest_no_slash :
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∀ (v : Validator), v.isHonest = true → v.slashed = 0
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/-- MINIMUM STAKE: Below minimum cannot validate -/
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def meetsMinimum (vs : ValidatorSet) (v : Validator) : Bool :=
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v.stake ≥ vs.minStake
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theorem below_minimum_rejected (vs : ValidatorSet) (v : Validator)
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(h : v.stake < vs.minStake) :
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meetsMinimum vs v = false := by
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simp [meetsMinimum, Nat.not_le.mpr h]
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/-- STAKE-WEIGHTED POWER: Higher stake → more voting power -/
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theorem more_stake_more_power (v1 v2 : Validator) (total : Nat)
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(h : v1.stake > v2.stake) (ht : total > 0) :
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votingPower v1 total ≥ votingPower v2 total := by
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simp [votingPower, Nat.ne_of_gt ht]
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exact Nat.div_le_div_right (by omega)
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/-- TOTAL STAKE: Sum of all validator stakes -/
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def computeTotalStake (vs : List Validator) : Nat :=
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vs.foldl (fun acc v => acc + v.stake) 0
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theorem empty_zero_stake : computeTotalStake [] = 0 := rfl
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end Consensus.Validator
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