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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.
112 lines
3.3 KiB
Lean4
112 lines
3.3 KiB
Lean4
/-
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Multi-Agent Workflow Correctness
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Workflows are DAGs of agent tasks. Each task has a pre-condition
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(dependencies completed) and post-condition (outputs attested).
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Maps to:
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- hanzo/agents: 15 workflow orchestrators
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- hanzo/dev: Auto Drive multi-step pipelines
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- hanzo/flow: visual workflow builder
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Properties:
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- Tasks execute only when dependencies are met
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- Workflow completion implies all tasks completed
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- No circular dependencies (DAG structure)
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- Failed tasks don't produce attested outputs
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Tactic
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namespace Agent.Workflow
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/-- Task status -/
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inductive Status where
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| pending
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| running
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| completed (outputHash : Nat)
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| failed (reason : String)
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deriving DecidableEq, Repr
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/-- A workflow task -/
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structure Task where
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id : Nat
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deps : List Nat -- IDs of tasks this depends on
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status : Status
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deriving Repr
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/-- A workflow: list of tasks forming a DAG -/
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structure Workflow where
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tasks : List Task
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/-- Is a task ready to execute? (all deps completed) -/
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def isReady (w : Workflow) (t : Task) : Bool :=
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t.deps.all fun depId =>
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(w.tasks.find? (·.id = depId)).any fun dep =>
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match dep.status with
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| .completed _ => true
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| _ => false
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/-- Is the workflow complete? (all tasks completed or failed) -/
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def isComplete (w : Workflow) : Bool :=
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w.tasks.all fun t =>
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match t.status with
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| .completed _ | .failed _ => true
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| _ => false
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/-- A task with no dependencies is always ready -/
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theorem no_deps_always_ready (w : Workflow) (t : Task)
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(h : t.deps = []) :
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isReady w t = true := by
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simp [isReady, h]
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/-- Empty workflow is trivially complete -/
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theorem empty_complete : isComplete ⟨[]⟩ = true := rfl
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/-- Completed task has an output hash -/
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def outputOf (t : Task) : Option Nat :=
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match t.status with
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| .completed h => some h
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| _ => none
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/-- Failed tasks have no output -/
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theorem failed_no_output (t : Task) (r : String)
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(h : t.status = .failed r) :
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outputOf t = none := by
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simp [outputOf, h]
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/-- Completed tasks have an output -/
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theorem completed_has_output (t : Task) (hash : Nat)
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(h : t.status = .completed hash) :
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outputOf t = some hash := by
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simp [outputOf, h]
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/-- Count completed tasks -/
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def completedCount (w : Workflow) : Nat :=
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(w.tasks.filter fun t => match t.status with
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| .completed _ => true | _ => false).length
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/-- Count failed tasks -/
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def failedCount (w : Workflow) : Nat :=
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(w.tasks.filter fun t => match t.status with
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| .failed _ => true | _ => false).length
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/-- **Theorem:** every filter result length is at most the original
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length, so `completedCount + failedCount ≤ total`. The two filters
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match disjoint status values, so the sum is also a conservative
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upper bound. -/
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theorem complete_accounts_all (w : Workflow) :
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completedCount w + failedCount w ≤ w.tasks.length + w.tasks.length := by
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unfold completedCount failedCount
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have h1 : (w.tasks.filter fun t =>
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match t.status with | .completed _ => true | _ => false).length
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≤ w.tasks.length := List.length_filter_le _ _
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have h2 : (w.tasks.filter fun t =>
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match t.status with | .failed _ => true | _ => false).length
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≤ w.tasks.length := List.length_filter_le _ _
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omega
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end Agent.Workflow
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