/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

AgenticOrchestration.lean — Multi-Agent Coordination for Research Automation

This module extends SubagentOrchestrator with agentic research capabilities,
enabling autonomous scientific discovery through coordinated agent teams.

Agent Types:
1. SearchAgent — Literature discovery (wraps ScholarOrchestrator)
2. ExtractAgent — Concept extraction from papers
3. FormalizeAgent — Lean 4 code generation
4. ValidateAgent — Empirical benchmarking
5. SynthesizeAgent — Report compilation

Orchestration via unified field Φ_orchestrate:
Φ_team(team, task) = Σᵢ Φᵢ(agentᵢ) + Σᵢ<ⱼ Φ_coordination(agentᵢ, agentⱼ)

Where coordination field captures:
- Dependency: Agent j needs output from agent i
- Conflict: Agents compete for resources
- Synergy: Agents collaborate on shared goals

Per AGENTS.md §1.4: Q16_16 fixed-point for hardware extraction.
Per AGENTS.md §2: PascalCase types, camelCase functions.
Per AGENTS.md §4: Every def has eval witness or theorem.

TODO(lean-port): Coordinate with SubagentOrchestrator.lean
TODO(lean-port): Define agent communication protocols
TODO(lean-port): Prove orchestration stability (no deadlock)
-/ 

import Mathlib.Data.Nat.Basic
import Mathlib.Data.Real.Basic
import Mathlib.Tactic

namespace Semantics.AgenticOrchestration

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Agent Types and States
-- ═══════════════════════════════════════════════════════════════════════════

/-- Agent specializations. -/
inductive AgentType
  | searchAgent      -- Literature discovery
  | extractAgent     -- Concept extraction
  | formalizeAgent   -- Lean 4 formalization
  | validateAgent    -- Empirical validation
  | synthesizeAgent  -- Report synthesis
  | metaAgent        -- Orchestrates other agents
  deriving Repr, DecidableEq, Inhabited

namespace AgentType

/-- Human-readable names. -/
def name : AgentType → String
  | searchAgent => "SearchAgent"
  | extractAgent => "ExtractAgent"
  | formalizeAgent => "FormalizeAgent"
  | validateAgent => "ValidateAgent"
  | synthesizeAgent => "SynthesizeAgent"
  | metaAgent => "MetaAgent"

/-- Capabilities per agent type. -/
def capabilities : AgentType → List String
  | searchAgent => ["query_scholar", "fetch_pdf", "parse_bibliography"]
  | extractAgent => ["read_pdf", "identify_theorems", "extract_definitions"]
  | formalizeAgent => ["write_lean", "prove_lemmas", "integrate_module"]
  | validateAgent => ["run_benchmarks", "collect_metrics", "compare_baselines"]
  | synthesizeAgent => ["compile_report", "generate_plots", "write_paper"]
  | metaAgent => ["delegate_task", "monitor_progress", "resolve_conflicts"]

end AgentType

/-- Agent state in the orchestration. -/
structure AgentState where
  id : String
  agentType : AgentType
  currentTask : Option String
  completedTasks : List String
  outputBuffer : List String  -- Results ready for other agents
  load : Float  -- 0.0-1.0 (CPU/memory utilization)
  status : AgentStatus
  deriving Repr, Inhabited

/-- Agent status. -/
inductive AgentStatus
  | idle
  | working
  | waiting  -- Blocked on dependency
  | completed
  | failed
  deriving Repr, DecidableEq, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Task Dependencies
-- ═══════════════════════════════════════════════════════════════════════════

/-- Task with dependencies. -/
structure Task where
  id : String
  description : String
  requiredType : AgentType  -- Which agent type can execute
  dependencies : List String  -- Task IDs that must complete first
  estimatedDuration : Float  -- Minutes
  priority : Nat  -- 1 (high) to 5 (low)
  deriving Repr, Inhabited

/-- Research pipeline as task graph. -/
def researchPipeline : List Task :=
  [ { id := "T1", description := "Search literature", requiredType := AgentType.searchAgent
      dependencies := [], estimatedDuration := 10.0, priority := 1 }
  , { id := "T2", description := "Extract concepts", requiredType := AgentType.extractAgent
      dependencies := ["T1"], estimatedDuration := 20.0, priority := 1 }
  , { id := "T3", description := "Generate hypotheses", requiredType := AgentType.extractAgent
      dependencies := ["T2"], estimatedDuration := 15.0, priority := 2 }
  , { id := "T4", description := "Formalize in Lean", requiredType := AgentType.formalizeAgent
      dependencies := ["T3"], estimatedDuration := 60.0, priority := 1 }
  , { id := "T5", description := "Design experiments", requiredType := AgentType.validateAgent
      dependencies := ["T3"], estimatedDuration := 30.0, priority := 2 }
  , { id := "T6", description := "Run benchmarks", requiredType := AgentType.validateAgent
      dependencies := ["T4", "T5"], estimatedDuration := 120.0, priority := 1 }
  , { id := "T7", description := "Synthesize report", requiredType := AgentType.synthesizeAgent
      dependencies := ["T6"], estimatedDuration := 45.0, priority := 1 }
  ]

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Orchestration Field
-- ═══════════════════════════════════════════════════════════════════════════

/-- Individual agent field parameters. -/
structure AgentFieldParams where
  rhoCapability : Float  -- ρ²: capability match to task
  vEfficiency : Float    -- v²: processing speed
  tauLoad : Float        -- τ²: current load (inverse)
  qReliability : Float   -- q²: historical success rate
  deriving Repr, Inhabited

/-- Coordination field parameters between agents. -/
structure CoordinationParams where
  dependencyStrength : Float  -- How much agent j needs agent i
  conflictPenalty : Float     -- Resource competition
  synergyBonus : Float      -- Collaboration benefit
  
  wf_dependency_pos : dependencyStrength ≥ 0
  wf_conflict_nonneg : conflictPenalty ≥ 0
  wf_synergy_pos : synergyBonus ≥ 0
  deriving Repr

/-- Individual agent field: Φᵢ(agentᵢ, task). -/
def agentField (agent : AgentState) (task : Task) (params : AgentFieldParams) : Float :=
  -- Capability match: 1.0 if types match, 0.0 otherwise
  let capabilityMatch : Float := if agent.agentType = task.requiredType then 1.0 else 0.0
  
  -- Efficiency factor
  let efficiency := params.vEfficiency
  
  -- Load penalty (inverse: higher load → lower field)
  let loadFactor := 1.0 - agent.load
  
  -- Reliability bonus
  let reliability := params.qReliability
  
  -- Compute field
  (params.rhoCapability * capabilityMatch + efficiency * loadFactor + reliability)

/-- Coordination field: Φ_coord(agentᵢ, agentⱼ). -/
def coordinationField (agentI agentJ : AgentState) (params : CoordinationParams) : Float :=
  let dependency := params.dependencyStrength
  let conflict := params.conflictPenalty
  let synergy := params.synergyBonus
  
  -- Coordination is positive for synergy, negative for conflict
  dependency + synergy - conflict

/-- Team orchestration field: Σᵢ Φᵢ + Σᵢ<ⱼ Φ_coord. -/
def teamOrchestrationField
    (agents : List AgentState)
    (task : Task)
    (agentParams : AgentFieldParams)
    (coordParams : CoordinationParams) : Float :=
  -- Sum of individual agent fields
  let individualSum := agents.foldl (fun acc agent =>
    acc + agentField agent task agentParams
  ) 0.0
  
  -- Sum of pairwise coordination (simplified: adjacent agents)
  let coordinationSum := match agents with
    | [] => 0.0
    | _ :: [] => 0.0
    | a1 :: a2 :: rest =>
        let init := coordinationField a1 a2 coordParams
        rest.foldl (fun acc (a, prev) =>
          acc + coordinationField prev a coordParams
        ) init (a2 :: rest, a2)
  
  individualSum + coordinationSum

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Task Assignment
-- ═══════════════════════════════════════════════════════════════════════════

/-- Assign task to best available agent using field-weighted selection. -/
def assignTask 
    (task : Task)
    (availableAgents : List AgentState)
    (agentParams : AgentFieldParams) : Option AgentState :=
  -- Filter agents by capability (must match required type)
  let capableAgents := availableAgents.filter (fun a =>
    a.agentType = task.requiredType && a.status = AgentStatus.idle
  )
  
  if capableAgents.isEmpty then
    none
  else
    -- Select agent with highest field value
    some $ capableAgents.foldl (fun best agent =>
      if agentField agent task agentParams > agentField best task agentParams then
        agent
      else
        best
    ) capableAgents.head!

/-- Check if all dependencies are satisfied. -/
def dependenciesSatisfied (task : Task) (completedTasks : List String) : Bool :=
  task.dependencies.all (fun dep => completedTasks.contains dep)

/-- Get ready tasks (dependencies satisfied, not yet assigned). -/
def readyTasks (tasks : List Task) (completedTasks : List String) : List Task :=
  tasks.filter (fun t => 
    dependenciesSatisfied t completedTasks && !completedTasks.contains t.id
  )

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Orchestration Algorithm
-- ═══════════════════════════════════════════════════════════════════════════

/-- Execute one step of orchestration. Returns updated agent states. -/
def orchestrationStep
    (agents : List AgentState)
    (tasks : List Task)
    (completedTasks : List String)
    (agentParams : AgentFieldParams)
    (coordParams : CoordinationParams) : List AgentState × List String :=
  -- Find ready tasks
  let ready := readyTasks tasks completedTasks
  
  -- Assign tasks to agents
  let (updatedAgents, newCompleted) := ready.foldl (fun (accAgents, accCompleted) task =>
    match assignTask task accAgents agentParams with
    | some agent =>
        -- Mark agent as working on task
        let updated := accAgents.map (fun a =>
          if a.id = agent.id then
            { a with 
              status := AgentStatus.working
              currentTask := some task.id
              load := min (a.load + 0.3) 1.0 }
          else a
        )
        (updated, accCompleted)
    | none =>
        -- No available agent, skip
        (accAgents, accCompleted)
  ) (agents, completedTasks)
  
  -- Simulate task completion (in real system, check actual status)
  let finalAgents := updatedAgents.map (fun a =>
    if a.status = AgentStatus.working && a.load >= 0.9 then
      { a with
        status := AgentStatus.completed
        currentTask := none
        completedTasks := a.currentTask.toList ++ a.completedTasks
        load := 0.0
        outputBuffer := a.outputBuffer ++ a.currentTask.toList }
    else if a.status = AgentStatus.working then
      { a with load := min (a.load + 0.1) 1.0 }  -- Progress
    else
      a
  )
  
  let finalCompleted := finalAgents.foldl (fun acc a =>
    acc ++ a.completedTasks
  ) []
  
  (finalAgents, finalCompleted)

/-- Run full orchestration until all tasks complete. -/
def runOrchestration
    (agents : List AgentState)
    (tasks : List Task)
    (agentParams : AgentFieldParams)
    (coordParams : CoordinationParams)
    (maxSteps : Nat := 1000) : List AgentState × List String × Nat :=
  let rec loop (currentAgents : List AgentState) (completed : List String) (steps : Nat) :=
    if steps >= maxSteps || completed.length = tasks.length then
      (currentAgents, completed, steps)
    else
      let (newAgents, newCompleted) := orchestrationStep 
        currentAgents tasks completed agentParams coordParams
      loop newAgents newCompleted (steps + 1)
  
  loop agents [] 0

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Theorems: Orchestration Correctness
-- ═══════════════════════════════════════════════════════════════════════════

-- TODO(lean-port): Add orchestration correctness theorems
-- 1. assignmentRespectsCapabilities: task type matches agent type
-- 2. dependenciesRespected: tasks only start when deps complete
-- 3. orchestrationTerminates: finite termination guarantee
-- 4. synergyImprovesPerformance: higher synergy → faster completion

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Integration with SubagentOrchestrator
-- ═══════════════════════════════════════════════════════════════════════════

/-! ## Layered Orchestration

```
┌─────────────────────────────────────────────────────────────┐
│  LAYER 3: AgenticOrchestration                              │
│  ├── Research pipeline: search → extract → formalize       │
│  ├── Agent teams: specialized workers                        │
│  └── Task graph: dependency management                       │
├─────────────────────────────────────────────────────────────┤
│  LAYER 2: SubagentOrchestrator                               │
│  ├── Domain coordination: compression ↔ field-physics        │
│  ├── Resource allocation: CPU, memory, SRAM                │
│  └── Convergence: multi-domain theorem proving              │
├─────────────────────────────────────────────────────────────┤
│  LAYER 1: Individual Agents                                  │
│  ├── SearchAgent → ScholarOrchestrator (Python)              │
│  ├── FormalizeAgent → GenomicCompression.lean                │
│  └── ValidateAgent → unified_field_validation.py             │
└─────────────────────────────────────────────────────────────┘
```

## Communication Protocol

Agents communicate via:
1. **Message passing**: Async queue (Kafka/RabbitMQ style)
2. **Shared state**: OTOM knowledge graph
3. **Direct RPC**: For synchronous coordination

Message types:
- `TaskRequest`: Assign new task
- `TaskComplete`: Report results
- `DependencyMet`: Notify unblocking
- `ResourceRequest`: Ask for allocation
-/ 

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  Verification Examples
-- ═══════════════════════════════════════════════════════════════════════════

#eval let agents := [
  { id := "A1", agentType := AgentType.searchAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := 0.0, status := AgentStatus.idle },
  { id := "A2", agentType := AgentType.extractAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := 0.0, status := AgentStatus.idle }
]
let tasks := researchPipeline.take 2
let params := { rhoCapability := 1.0, vEfficiency := 1.0, tauLoad := 0.0, qReliability := 1.0 }
let (updated, completed, steps) := runOrchestration agents tasks params 
  { dependencyStrength := 0.5, conflictPenalty := 0.1, synergyBonus := 0.3,
    wf_dependency_pos := by norm_num, wf_conflict_nonneg := by norm_num, wf_synergy_pos := by norm_num }
steps
-- Expected: ~20 steps (simulated)

#eval assignTask researchPipeline[0] [
  { id := "A1", agentType := AgentType.searchAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := 0.0, status := AgentStatus.idle },
  { id := "A2", agentType := AgentType.extractAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := 0.0, status := AgentStatus.idle }
] { rhoCapability := 1.0, vEfficiency := 1.0, tauLoad := 0.0, qReliability := 1.0 }
-- Expected: A1 (searchAgent for search task)

-- ═══════════════════════════════════════════════════════════════════════════
-- §8  Future Work
-- ═══════════════════════════════════════════════════════════════════════════

/-! ## Roadmap

### Immediate (This Week)
- [ ] Connect to SubagentOrchestrator.lean
- [ ] Define agent communication protocol (Lean + Python)
- [ ] Implement Python AgentShim classes

### Short-term (Next 2 Weeks)
- [ ] Full research pipeline: 7 tasks, 5 agents
- [ ] Integration with GenomicCompression + ResearchAgent
- [ ] Demo: Autonomous paper analysis end-to-end

### Medium-term (Next Month)
- [ ] Multi-team orchestration (multiple research projects)
- [ ] Dynamic agent spawning based on workload
- [ ] Paper: "Agentic Orchestration for Scientific Discovery"

## Open Questions

1. **Deadlock prevention**: How to guarantee no circular dependencies?
2. **Fault tolerance**: Agent failure recovery mechanisms?
3. **Scalability**: 10 agents? 100 agents? 1000 agents?
4. **Human-in-the-loop**: When should human review be required?
-/ 

-- TODO(lean-port):
-- 1. Complete all sorry placeholders in theorems
-- 2. Connect to SubagentOrchestrator domain definitions
-- 3. Define agent communication protocol (async message passing)
-- 4. Prove orchestration stability (no deadlock, no starvation)
-- 5. Implement Python AgentShim for each agent type
-- 6. Extract coordination patterns from InternAgent-1.5 paper

end Semantics.AgenticOrchestration