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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]>
119 lines
4.1 KiB
Lean4
119 lines
4.1 KiB
Lean4
/-
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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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simp only [Coeffects.isReproducible] at ha hb
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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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