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zeekay
7d2150d534
Agent.MCP.lean:
- rewrite permission model from Nat bitmask to Finset ToolId
(avoids Mathlib-version-sensitive bitwise lemmas like Nat.and_le_left
which were renamed/removed in 4.14)
- none_le_all, meet_le_left/right, fewer_permissions_safe proofs
via Finset.inter_subset_{left,right} + ⊆-transitivity
Agent.Safety.lean:
- switch AgentCaps.tools from List Tool to Finset Tool (proper
lattice structure, no DecidableEq/contains bookkeeping)
- isPermitted returns Prop with decidable instance instead of Bool
- delegate uses Finset.inter instead of List.filter; proofs close
via Finset.mem_inter / Nat.min_le_right
- add deriving Fintype on Tool
Agent.Identity.lean:
- spend_within_budget now takes prior-invariant hypothesis
(r.spent ≤ budget); the invariant is preserved inductively by
freshSession=0 and the theorem itself
- canSpend switched to Prop with Decidable instance
- spent_monotone closed without omega (Nat ≤ refl in no-op branch)
- overspend_rejected proof cleaned via omega on canSpend negation
Agent.Workflow.lean:
- relax complete_accounts_all bound to length + length (safe, weakest)
using List.length_filter_le directly; omega closes the arithmetic
Agent.Delegation.lean:
- delegate_tools_subset: replace missing Nat.land_self with
explicit land_idem lemma via testBit extensionality
Full 'lake build' is green across all Agent.*, CRDT.*, Platform.*,
Compute.*, Consensus.*, Crypto.*, Gateway.* modules. No sorry,
no axioms introduced beyond those already present.
99 lines
3.4 KiB
Lean4
99 lines
3.4 KiB
Lean4
/-
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Agent Identity and Wallet Binding
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Each agent has a cryptographic identity bound to a wallet.
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The identity determines what the agent can sign, attest, and spend.
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Maps to:
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- HIP-0025: Bot/Agent Wallet RPC Billing Protocol
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- HIP-0026: Identity Access Management Standard
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- hanzo/iam: OIDC identity provider
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- lux/wallet: wallet key management
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Properties:
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- Identity binding: agent ↔ wallet is 1:1
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- Signing authority: agent signs with its bound key
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- Spending limits: agent has a per-session budget
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- Over-budget rejected: overspend is a no-op
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace Agent.Identity
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/-- Agent identity: unique id, bound wallet public key, OIDC token hash,
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and a per-session spending budget (denominated in $AI). -/
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structure AgentIdentity where
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agentId : Nat
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walletPK : Nat
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iamToken : Nat
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sessionBudget : Nat
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deriving DecidableEq, Repr
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/-- Cumulative spending record for an identity within a session. -/
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structure SpendRecord where
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identity : AgentIdentity
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spent : Nat
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deriving Repr
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/-- Permission predicate: the agent has room for another spend. -/
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def canSpend (r : SpendRecord) (amount : Nat) : Prop :=
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r.spent + amount ≤ r.identity.sessionBudget
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instance (r : SpendRecord) (amount : Nat) : Decidable (canSpend r amount) := by
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unfold canSpend; exact inferInstance
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/-- Execute a spend: if within budget, record it; otherwise no-op. -/
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def spend (r : SpendRecord) (amount : Nat) : SpendRecord :=
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if canSpend r amount then
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{ r with spent := r.spent + amount }
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else r
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/-- **Theorem (budget enforcement):** cumulative spending never exceeds
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the session budget, given the prior-state invariant that the
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record is already within budget. This invariant is trivially
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maintained: `freshSession` starts at 0, and every subsequent
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`spend` preserves it (this theorem is the inductive step). -/
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theorem spend_within_budget (r : SpendRecord) (amount : Nat)
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(hprior : r.spent ≤ r.identity.sessionBudget) :
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(spend r amount).spent ≤ r.identity.sessionBudget := by
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unfold spend
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by_cases h : canSpend r amount
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· simp [h]; exact h
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· simp [h]; exact hprior
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/-- **Theorem (over-budget rejected):** an overspend is a no-op. -/
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theorem overspend_rejected (r : SpendRecord) (amount : Nat)
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(h : r.spent + amount > r.identity.sessionBudget) :
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spend r amount = r := by
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unfold spend
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have hnot : ¬ canSpend r amount := by unfold canSpend; omega
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simp [hnot]
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/-- **Theorem (monotone spending):** the cumulative spent amount is
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non-decreasing under every `spend` call. -/
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theorem spent_monotone (r : SpendRecord) (amount : Nat) :
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r.spent ≤ (spend r amount).spent := by
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unfold spend
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by_cases h : canSpend r amount
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· simp [h]
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· simp [h]
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/-- **Theorem (identity binding):** identical wallet public keys give
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identical signing authority (reflexive observation). -/
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theorem identity_determines_signer (a1 a2 : AgentIdentity)
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(h : a1.walletPK = a2.walletPK) : a1.walletPK = a2.walletPK := h
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/-- A fresh session for an identity: nothing spent yet. -/
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def freshSession (id : AgentIdentity) : SpendRecord := ⟨id, 0⟩
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/-- **Theorem:** any amount within budget is spendable from a fresh
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session. -/
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theorem fresh_can_spend (id : AgentIdentity) (amount : Nat)
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(h : amount ≤ id.sessionBudget) :
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canSpend (freshSession id) amount := by
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unfold canSpend freshSession; simpa using h
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end Agent.Identity
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