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68 lines
2.5 KiB
Lean4
68 lines
2.5 KiB
Lean4
/-
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LeanCTX Formal Verification — Scope Isolation Proofs
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Proves that agents can only access context items within their
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assigned scope.
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Mirrors: rust/src/server/role_guard.rs, http_server/team.rs
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-/
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import LeanCtxProofs.Basic
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namespace LeanCtxProofs.Policy.ScopeIsolation
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/-- Check if a path is within a scope (any allowed prefix matches). -/
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def inScope (scope : Scope) (path : String) : Bool :=
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scope.allowedPrefixes.any (path.startsWith ·)
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/-- Scope-guarded context ref expansion. Returns none if out of scope. -/
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def expandRef (agent : Agent) (ref : ContextRef) (items : List ContextItem) :
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Option ContextItem :=
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if inScope agent.scope ref.itemId then
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items.find? (·.id == ref.itemId)
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else
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none
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-- ============================================================================
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-- Scope Isolation Theorems
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-- ============================================================================
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/-- **Theorem 1: An agent with empty scope cannot expand any ref.** -/
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theorem empty_scope_blocks_all (agent : Agent) (ref : ContextRef) (items : List ContextItem)
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(h_empty : agent.scope.allowedPrefixes = []) :
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expandRef agent ref items = none := by
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unfold expandRef inScope
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simp [h_empty, List.any]
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/-- **Theorem 2: Expansion only succeeds for in-scope refs.** -/
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theorem expansion_requires_scope (agent : Agent) (ref : ContextRef) (items : List ContextItem)
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(h_out : inScope agent.scope ref.itemId = false) :
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expandRef agent ref items = none := by
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unfold expandRef
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simp [h_out]
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/-- **Theorem 3: Scope with matching prefix grants access.** -/
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theorem matching_prefix_grants_access (pfx : String) (path : String)
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(h : path.startsWith pfx = true) :
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inScope ⟨[pfx]⟩ path = true := by
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unfold inScope
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simp [List.any, h]
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/-- **Theorem 4: Scope is prefix-monotone — adding prefixes can only expand access.** -/
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theorem scope_monotone (scope : Scope) (newPfx : String) (path : String)
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(h : inScope scope path = true) :
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inScope { allowedPrefixes := newPfx :: scope.allowedPrefixes } path = true := by
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unfold inScope at *
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simp [List.any_cons, Bool.or_eq_true]
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simp [List.any_eq_true] at h
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exact Or.inr h
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/-- **Theorem 5: If expansion returns Some, the item ID was in scope.** -/
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theorem expansion_implies_in_scope (agent : Agent) (ref : ContextRef)
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(items : List ContextItem) (item : ContextItem)
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(h : expandRef agent ref items = some item) :
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inScope agent.scope ref.itemId = true := by
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unfold expandRef at h
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split at h <;> simp_all
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end LeanCtxProofs.Policy.ScopeIsolation
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