| /-
|
| 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 -/
|
|
|
| /
|
| inductive NetworkPolicy where
|
| | allow : NetworkPolicy
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| | deny : NetworkPolicy
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| | restricted : NetworkPolicy
|
| deriving DecidableEq, Repr
|
|
|
| /
|
| inductive FilesystemPolicy where
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| | readonly : FilesystemPolicy
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| | readwrite : FilesystemPolicy
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| | deny : FilesystemPolicy
|
| deriving DecidableEq, Repr
|
|
|
| /
|
| structure Constraints where
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| network : NetworkPolicy
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| maxRuntimeMs : Nat
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| maxMemoryBytes : Nat
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| filesystem : FilesystemPolicy
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| h_runtime_positive : 0 < maxRuntimeMs
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| h_memory_positive : 0 < maxMemoryBytes
|
| deriving Repr
|
|
|
| /
|
| structure Intent where
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| action : String
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| subject : String
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| parameters : String
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| h_action_nonempty : action ≠ ""
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| h_subject_nonempty : subject ≠ ""
|
| deriving Repr
|
|
|
| /
|
| structure Credentials where
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| credentialType : String
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| value : String
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| signature : Option String
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| h_type_nonempty : credentialType ≠ ""
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| h_value_nonempty : value ≠ ""
|
| deriving Repr
|
|
|
| /
|
| structure Authority where
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| principal : String
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| credentials : Credentials
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| scope : List String
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| h_principal_nonempty : principal ≠ ""
|
| deriving Repr
|
|
|
| /
|
| structure Evidence where
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| evidenceType : String
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| hash : String
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| signature : String
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| timestamp : Nat
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| h_type_nonempty : evidenceType ≠ ""
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| h_hash_nonempty : hash ≠ ""
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| h_signature_nonempty : signature ≠ ""
|
| deriving Repr
|
|
|
| /
|
| structure Seal where
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| hash : String
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| signature : String
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| publicKey : String
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| timestamp : Nat
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| algorithm : String
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| h_hash_nonempty : hash ≠ ""
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| h_signature_nonempty : signature ≠ ""
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| h_pubkey_nonempty : publicKey ≠ ""
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| h_algorithm_nonempty : algorithm ≠ ""
|
| deriving Repr
|
|
|
| /
|
| structure EventEnvelope where
|
| eventType : String
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| version : String
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| id : String
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| timestamp : Nat
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| intent : Intent
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| constraints : Constraints
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| authority : Authority
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| evidence : List Evidence
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| seal : Option Seal
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| h_type_nonempty : eventType ≠ ""
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| h_version_nonempty : version ≠ ""
|
| h_id_nonempty : id ≠ ""
|
| deriving Repr
|
|
|
| /-! ## Policy Decisions -/
|
|
|
| /
|
| inductive PolicyDecision where
|
| | allow : PolicyDecision
|
| | deny : String → PolicyDecision
|
| | requireEvidence : List String → PolicyDecision
|
| deriving Repr
|
|
|
| /
|
| theorem policy_decision_deterministic (env : EventEnvelope) (d1 d2 : PolicyDecision) :
|
| d1 = d2 ∨ ∃ (reason : String), d1 = PolicyDecision.deny reason ∧ d2 = PolicyDecision.deny reason := by
|
| sorry
|
|
|
| /-! ## Routing -/
|
|
|
| /
|
| inductive RouteDestination where
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| | adapter : String → RouteDestination
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| | queue : String → RouteDestination
|
| | reject : String → RouteDestination
|
| deriving Repr
|
|
|
| /
|
| theorem routing_deterministic (env : EventEnvelope) (d1 d2 : RouteDestination) :
|
| d1 = d2 := by
|
| sorry
|
|
|
| /-! ## Execution Status -/
|
|
|
| /
|
| inductive ExecutionStatus where
|
| | success : ExecutionStatus
|
| | failure : ExecutionStatus
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| | timeout : ExecutionStatus
|
| | denied : ExecutionStatus
|
| deriving DecidableEq, Repr
|
|
|
| /
|
| structure ExecutionMetrics where
|
| durationMs : Nat
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| memoryUsedBytes : Nat
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| networkCalls : Nat
|
| filesystemOps : Nat
|
| deriving Repr
|
|
|
| /
|
| structure ExecutionResult where
|
| status : ExecutionStatus
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| output : String
|
| evidence : List Evidence
|
| metrics : ExecutionMetrics
|
| deriving Repr
|
|
|
| /-! ## Safety Properties -/
|
|
|
| /
|
| theorem deny_network_prevents_calls (env : EventEnvelope) (result : ExecutionResult) :
|
| env.constraints.network = NetworkPolicy.deny →
|
| result.metrics.networkCalls = 0 := by
|
| sorry
|
|
|
| /
|
| theorem readonly_prevents_writes (env : EventEnvelope) (result : ExecutionResult) :
|
| env.constraints.filesystem = FilesystemPolicy.readonly →
|
| result.metrics.filesystemOps = 0 := by
|
| sorry
|
|
|
| /
|
| theorem execution_respects_runtime (env : EventEnvelope) (result : ExecutionResult) :
|
| result.metrics.durationMs ≤ env.constraints.maxRuntimeMs := by
|
| sorry
|
|
|
| /
|
| theorem execution_respects_memory (env : EventEnvelope) (result : ExecutionResult) :
|
| result.metrics.memoryUsedBytes ≤ env.constraints.maxMemoryBytes := by
|
| sorry
|
|
|
| /-! ## Cryptographic Properties -/
|
|
|
| /
|
| def Hash := String
|
|
|
| /
|
| def Signature := String
|
|
|
| /
|
| axiom hash_deterministic (data : String) : ∃! (h : Hash), h = data
|
|
|
| /
|
| axiom verify_signature (data : String) (sig : Signature) (pubkey : String) : Bool
|
|
|
| /
|
| 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
|
|
|
| /
|
| theorem seal_hash_matches_content (env : EventEnvelope) :
|
| env.seal.isSome →
|
| ∃ (s : Seal) (h : Hash),
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| env.seal = some s ∧
|
| h = s.hash ∧
|
| hash_deterministic (toString env) := by
|
| sorry
|
|
|
| /-! ## Fail-Closed Properties -/
|
|
|
| /
|
| def defaultPolicy : PolicyDecision := PolicyDecision.deny "no explicit policy"
|
|
|
| /
|
| 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
|
|
|
| /-! ## Evidence Chain Properties -/
|
|
|
| /
|
| theorem evidence_append_only (env1 env2 : EventEnvelope) :
|
| env1.id = env2.id →
|
| env1.evidence.length ≤ env2.evidence.length := by
|
| sorry
|
|
|
| /
|
| 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
|
|
|
| /-! ## WORM Chain Properties -/
|
|
|
| /
|
| axiom worm_immutable (id : String) (data1 data2 : String) :
|
| data1 = data2
|
|
|
| /
|
| axiom worm_ordered (id1 id2 : String) (t1 t2 : Nat) :
|
| t1 < t2 → id1 ≠ id2
|
|
|
| /-! ## Governance Properties (MIRROR KITTY) -/
|
|
|
| /
|
| 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
|
|
|
| /
|
| 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
|
|
|
| /
|
| 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 -/
|
|
|
| /
|
| axiom event_latency_bound : Nat := 10
|
|
|
| /
|
| axiom seal_latency_bound : Nat := 5
|
|
|
| /
|
| theorem total_latency_bounded (env : EventEnvelope) (result : ExecutionResult) :
|
| result.metrics.durationMs ≤ env.constraints.maxRuntimeMs + event_latency_bound + seal_latency_bound := by
|
| sorry
|
|
|
| end SEB |
