/-
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