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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]>
120 lines
4.1 KiB
Lean4
120 lines
4.1 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Coeffect Algebra
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Effects: what a computation DOES to the world.
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Coeffects: what a computation NEEDS from the world.
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A pure build needs nothing external (coeffects = ∅).
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An impure build needs time, random, network, filesystem, etc.
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The tensor product (⊗ = append) combines coeffects.
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Maps to:
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- hanzo/runtime: sandbox coeffect tracking
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- hanzo/attest: discharge proof generation
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- lux/node: build reproducibility checking
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Properties:
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- Pure is identity for tensor
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- Tensor is associative
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- Pure ⊗ pure = pure
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- Time and random are non-reproducible
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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 Build.Coeffect
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/-- What a build needs from the world -/
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inductive Coeffect where
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| pure -- Needs nothing
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| filesystem (path : String) -- Non-CA file access
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| filesystemCA (hash : Nat) -- Content-addressed file
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| network (host : String) -- Non-CA network
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| networkCA (hash : Nat) -- Content-addressed network
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| time -- Wall clock (non-reproducible)
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| random -- Entropy (non-reproducible)
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| gpu (device : String) -- GPU access (non-deterministic)
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| auth (provider : String) -- Credential access (ephemeral)
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| tee (attestation : Nat) -- TEE hardware attestation
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deriving DecidableEq, Repr
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/-- A coeffect set (tensor = append) -/
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abbrev Coeffects := List Coeffect
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/-- Pure coeffect set (empty = needs nothing) -/
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def Coeffects.pure : Coeffects := []
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/-- Check if coeffects are pure -/
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def Coeffects.isPure (r : Coeffects) : Bool := r.isEmpty
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/-- Check if coeffects allow reproducible builds -/
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def Coeffects.isReproducible (r : Coeffects) : Bool :=
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r.all fun c => match c with
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| .pure | .filesystemCA _ | .networkCA _ | .tee _ => true
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| .time | .random | .gpu _ | .auth _ => false
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| .filesystem _ | .network _ => false
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-- ═══════════════════════════════════════════════════════════════
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-- THEOREMS
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-- ═══════════════════════════════════════════════════════════════
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/-- Empty coeffects are pure -/
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theorem empty_is_pure : Coeffects.isPure [] = true := rfl
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/-- Pure coeffects are reproducible -/
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theorem pure_is_reproducible : Coeffects.isReproducible [] = true := rfl
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/-- Tensor with pure is identity (right) -/
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theorem tensor_pure_right (r : Coeffects) : r ++ [] = r :=
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List.append_nil r
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/-- Tensor with pure is identity (left) -/
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theorem tensor_pure_left (r : Coeffects) : [] ++ r = r := rfl
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/-- Tensor is associative -/
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theorem tensor_assoc (a b c : Coeffects) : (a ++ b) ++ c = a ++ (b ++ c) :=
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List.append_assoc a b c
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/-- Pure ⊗ pure = pure -/
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theorem tensor_pure_pure (a b : Coeffects)
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(ha : a.isPure) (hb : b.isPure) : (a ++ b).isPure := by
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simp [Coeffects.isPure, List.isEmpty_iff] at *
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simp [ha, hb]
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/-- Reproducible ⊗ reproducible = reproducible -/
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theorem tensor_reproducible (a b : Coeffects)
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(ha : a.isReproducible) (hb : b.isReproducible) :
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(a ++ b).isReproducible := by
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simp only [Coeffects.isReproducible, List.all_append, Bool.and_eq_true]
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exact ⟨ha, hb⟩
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/-- Time is not reproducible -/
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theorem time_not_reproducible :
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Coeffects.isReproducible [.time] = false := rfl
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/-- Random is not reproducible -/
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theorem random_not_reproducible :
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Coeffects.isReproducible [.random] = false := rfl
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/-- GPU is not reproducible -/
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theorem gpu_not_reproducible (d : String) :
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Coeffects.isReproducible [.gpu d] = false := rfl
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/-- Auth is not reproducible -/
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theorem auth_not_reproducible (p : String) :
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Coeffects.isReproducible [.auth p] = false := rfl
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/-- Content-addressed filesystem IS reproducible -/
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theorem ca_filesystem_reproducible (h : Nat) :
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Coeffects.isReproducible [.filesystemCA h] = true := rfl
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/-- TEE attestation IS reproducible -/
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theorem tee_reproducible (a : Nat) :
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Coeffects.isReproducible [.tee a] = true := rfl
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end Build.Coeffect
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