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SEB Lean 4 Contract Template
Generated from: SEB_SOVEREIGN_EVENT_BUS_MASTER_SPECIFICATION.xml
Version: 1.0.0
Target: Lean 4 Formal Verification
This file contains formal specifications and proofs for the Sovereign Event Bus.
All theorems must be proven without `sorry`.
-/
import Mathlib.Data.String.Basic
import Mathlib.Data.List.Basic
import Mathlib.Data.Finmap
import Mathlib.Logic.Basic
import Mathlib.Tactic
namespace SEB
/-! ## Core Types -/
/-- Network access policy -/
inductive NetworkPolicy where
| allow : NetworkPolicy
| deny : NetworkPolicy
| restricted : NetworkPolicy
deriving DecidableEq, Repr
/-- Filesystem access policy -/
inductive FilesystemPolicy where
| readonly : FilesystemPolicy
| readwrite : FilesystemPolicy
| deny : FilesystemPolicy
deriving DecidableEq, Repr
/-- Execution constraints -/
structure Constraints where
network : NetworkPolicy
maxRuntimeMs : Nat
maxMemoryBytes : Nat
filesystem : FilesystemPolicy
h_runtime_positive : 0 < maxRuntimeMs
h_memory_positive : 0 < maxMemoryBytes
deriving Repr
/-- Intent structure -/
structure Intent where
action : String
subject : String
parameters : String -- JSON-encoded parameters
h_action_nonempty : action ≠ ""
h_subject_nonempty : subject ≠ ""
deriving Repr
/-- Authority credentials -/
structure Credentials where
credentialType : String
value : String
signature : Option String
h_type_nonempty : credentialType ≠ ""
h_value_nonempty : value ≠ ""
deriving Repr
/-- Authority structure -/
structure Authority where
principal : String
credentials : Credentials
scope : List String
h_principal_nonempty : principal ≠ ""
deriving Repr
/-- Cryptographic evidence -/
structure Evidence where
evidenceType : String
hash : String
signature : String
timestamp : Nat -- Unix timestamp
h_type_nonempty : evidenceType ≠ ""
h_hash_nonempty : hash ≠ ""
h_signature_nonempty : signature ≠ ""
deriving Repr
/-- Cryptographic seal -/
structure Seal where
hash : String
signature : String
publicKey : String
timestamp : Nat
algorithm : String
h_hash_nonempty : hash ≠ ""
h_signature_nonempty : signature ≠ ""
h_pubkey_nonempty : publicKey ≠ ""
h_algorithm_nonempty : algorithm ≠ ""
deriving Repr
/-- Event envelope -/
structure EventEnvelope where
eventType : String
version : String
id : String
timestamp : Nat
intent : Intent
constraints : Constraints
authority : Authority
evidence : List Evidence
seal : Option Seal
h_type_nonempty : eventType ≠ ""
h_version_nonempty : version ≠ ""
h_id_nonempty : id ≠ ""
deriving Repr
/-! ## Policy Decisions -/
/-- Policy decision type -/
inductive PolicyDecision where
| allow : PolicyDecision
| deny : String → PolicyDecision
| requireEvidence : List String → PolicyDecision
deriving Repr
/-- Policy decision is deterministic -/
theorem policy_decision_deterministic (env : EventEnvelope) (d1 d2 : PolicyDecision) :
d1 = d2 ∨ ∃ (reason : String), d1 = PolicyDecision.deny reason ∧ d2 = PolicyDecision.deny reason := by
sorry -- Proof obligation: implement policy evaluation function
/-! ## Routing -/
/-- Route destination -/
inductive RouteDestination where
| adapter : String → RouteDestination
| queue : String → RouteDestination
| reject : String → RouteDestination
deriving Repr
/-- Routing is deterministic given the same envelope -/
theorem routing_deterministic (env : EventEnvelope) (d1 d2 : RouteDestination) :
d1 = d2 := by
sorry -- Proof obligation: implement routing function
/-! ## Execution Status -/
/-- Execution status -/
inductive ExecutionStatus where
| success : ExecutionStatus
| failure : ExecutionStatus
| timeout : ExecutionStatus
| denied : ExecutionStatus
deriving DecidableEq, Repr
/-- Execution metrics -/
structure ExecutionMetrics where
durationMs : Nat
memoryUsedBytes : Nat
networkCalls : Nat
filesystemOps : Nat
deriving Repr
/-- Execution result -/
structure ExecutionResult where
status : ExecutionStatus
output : String -- JSON-encoded output
evidence : List Evidence
metrics : ExecutionMetrics
deriving Repr
/-! ## Safety Properties -/
/-- An envelope with deny network policy cannot make network calls -/
theorem deny_network_prevents_calls (env : EventEnvelope) (result : ExecutionResult) :
env.constraints.network = NetworkPolicy.deny →
result.metrics.networkCalls = 0 := by
sorry -- Proof obligation: verify execution respects constraints
/-- An envelope with readonly filesystem cannot write -/
theorem readonly_prevents_writes (env : EventEnvelope) (result : ExecutionResult) :
env.constraints.filesystem = FilesystemPolicy.readonly →
result.metrics.filesystemOps = 0 := by
sorry -- Proof obligation: verify execution respects constraints
/-- Execution cannot exceed runtime constraint -/
theorem execution_respects_runtime (env : EventEnvelope) (result : ExecutionResult) :
result.metrics.durationMs ≤ env.constraints.maxRuntimeMs := by
sorry -- Proof obligation: verify execution respects constraints
/-- Execution cannot exceed memory constraint -/
theorem execution_respects_memory (env : EventEnvelope) (result : ExecutionResult) :
result.metrics.memoryUsedBytes ≤ env.constraints.maxMemoryBytes := by
sorry -- Proof obligation: verify execution respects constraints
/-! ## Cryptographic Properties -/
/-- Hash function type -/
def Hash := String
/-- Signature function type -/
def Signature := String
/-- Hash is deterministic -/
axiom hash_deterministic (data : String) : ∃! (h : Hash), h = data
/-- Signature verification -/
axiom verify_signature (data : String) (sig : Signature) (pubkey : String) : Bool
/-- A sealed envelope has a valid signature -/
theorem sealed_envelope_valid (env : EventEnvelope) :
env.seal.isSome →
∃ (s : Seal), env.seal = some s ∧
verify_signature s.hash s.signature s.publicKey = true := by
sorry -- Proof obligation: verify seal validity
/-- Seal hash matches envelope content -/
theorem seal_hash_matches_content (env : EventEnvelope) :
env.seal.isSome →
∃ (s : Seal) (h : Hash),
env.seal = some s ∧
h = s.hash ∧
hash_deterministic (toString env) := by
sorry -- Proof obligation: verify hash correctness
/-! ## Fail-Closed Properties -/
/-- Default policy is deny -/
def defaultPolicy : PolicyDecision := PolicyDecision.deny "no explicit policy"
/-- Without explicit allow, action is denied -/
theorem fail_closed (env : EventEnvelope) (decision : PolicyDecision) :
decision ≠ PolicyDecision.allow →
∃ (reason : String), decision = PolicyDecision.deny reason := by
cases decision with
| allow => contradiction
| deny reason => exact ⟨reason, rfl⟩
| requireEvidence _ => sorry -- Proof obligation: require evidence implies eventual deny
/-! ## Evidence Chain Properties -/
/-- Evidence chain is append-only -/
theorem evidence_append_only (env1 env2 : EventEnvelope) :
env1.id = env2.id →
env1.evidence.length ≤ env2.evidence.length := by
sorry -- Proof obligation: verify evidence immutability
/-- Evidence timestamps are monotonic -/
theorem evidence_timestamps_monotonic (evidence : List Evidence) :
∀ i j, i < j → j < evidence.length →
(evidence.get ⟨i, by omega⟩).timestamp ≤ (evidence.get ⟨j, by omega⟩).timestamp := by
sorry -- Proof obligation: verify timestamp ordering
/-! ## WORM Chain Properties -/
/-- WORM entry is immutable once written -/
axiom worm_immutable (id : String) (data1 data2 : String) :
data1 = data2
/-- WORM chain preserves order -/
axiom worm_ordered (id1 id2 : String) (t1 t2 : Nat) :
t1 < t2 → id1 ≠ id2
/-! ## Governance Properties (MIRROR KITTY) -/
/-- All outputs must be cryptographically sealed -/
theorem mirror_kitty_sealed (result : ExecutionResult) :
result.evidence.length > 0 →
∀ e ∈ result.evidence, e.signature ≠ "" := by
intro h_nonempty e h_in
exact e.h_signature_nonempty
/-- Verification is agent-agnostic -/
theorem mirror_kitty_agent_agnostic (env1 env2 : EventEnvelope) (result : ExecutionResult) :
env1.intent = env2.intent →
env1.constraints = env2.constraints →
result.status = ExecutionStatus.success ∨ result.status = ExecutionStatus.failure := by
sorry -- Proof obligation: verify agent independence
/-- No unverified assumptions -/
theorem mirror_kitty_no_assumptions (env : EventEnvelope) :
env.evidence.length = 0 →
∃ (reason : String), PolicyDecision.deny reason = defaultPolicy := by
intro _
exact ⟨"no explicit policy", rfl⟩
/-! ## Performance Bounds -/
/-- Event processing latency bound -/
axiom event_latency_bound : Nat := 10 -- milliseconds
/-- Seal computation latency bound -/
axiom seal_latency_bound : Nat := 5 -- milliseconds
/-- Total latency is bounded -/
theorem total_latency_bounded (env : EventEnvelope) (result : ExecutionResult) :
result.metrics.durationMs ≤ env.constraints.maxRuntimeMs + event_latency_bound + seal_latency_bound := by
sorry -- Proof obligation: verify latency bounds
end SEB |