Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/GpuDutyAssignment.lean

/- 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

GpuDutyAssignment.lean — GPU Translation Surface Duty Assignment in Lean

This module formalizes the GPU translation surface duty assignment system
for the swarm, including duty types, assignment, execution, status tracking,
and statistics.

Per AGENTS.md §1.4: Q16_16 fixed-point for scoring.
Per AGENTS.md §2: PascalCase types, camelCase functions.
Per AGENTS.md §4: Eval witnesses and theorems required.

Integration with SubagentOrchestrator: GPU duties as resource allocation tasks.
-/

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

namespace Semantics.GpuDutyAssignment

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Fixed-Point Scoring (Q16.16)
-- ═══════════════════════════════════════════════════════════════════════════

structure Q16_16 where
  raw : Int
  deriving Repr, DecidableEq, Inhabited, BEq

namespace Q16_16

def zero : Q16_16 := ⟨0⟩
def one : Q16_16 := ⟨65536⟩
def ofNat (n : Nat) : Q16_16 := ⟨n * 65536⟩

instance : LE Q16_16 := ⟨fun a b => a.raw ≤ b.raw⟩
instance : LT Q16_16 := ⟨fun a b => a.raw < b.raw⟩
instance : DecidableRel (fun a b : Q16_16 => a ≤ b) := fun a b => inferInstanceAs (Decidable (a.raw ≤ b.raw))
instance : DecidableRel (fun a b : Q16_16 => a < b) := fun a b => inferInstanceAs (Decidable (a.raw < b.raw))
instance : Add Q16_16 := ⟨fun a b => ⟨a.raw + b.raw⟩⟩
instance : Sub Q16_16 := ⟨fun a b => ⟨a.raw - b.raw⟩⟩
instance : Mul Q16_16 := ⟨fun a b => ⟨(a.raw * b.raw) / 65536⟩⟩
instance : Div Q16_16 := ⟨fun a b => ⟨(a.raw * 65536) / b.raw⟩⟩

end Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Duty Types
-- ═══════════════════════════════════════════════════════════════════════════

inductive DutyType
  | webNavigation
  | contentExtraction
  | formInteraction
  | javascriptExecution
  | screenshotCapture
  | distributedCrawl
  | cloudSync
  | cloudCopy
  | cloudList
  deriving Repr, DecidableEq, Inhabited

namespace DutyType

def toString : DutyType → String
  | webNavigation => "WEB_NAVIGATION"
  | contentExtraction => "CONTENT_EXTRACTION"
  | formInteraction => "FORM_INTERACTION"
  | javascriptExecution => "JAVASCRIPT_EXECUTION"
  | screenshotCapture => "SCREENSHOT_CAPTURE"
  | distributedCrawl => "DISTRIBUTED_CRAWL"
  | cloudSync => "CLOUD_SYNC"
  | cloudCopy => "CLOUD_COPY"
  | cloudList => "CLOUD_LIST"

end DutyType

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Duty Status
-- ═══════════════════════════════════════════════════════════════════════════

inductive DutyStatus
  | pending
  | assigned
  | executing
  | completed
  | failed
  deriving Repr, DecidableEq, Inhabited

namespace DutyStatus

def toString : DutyStatus → String
  | pending => "pending"
  | assigned => "assigned"
  | executing => "executing"
  | completed => "completed"
  | failed => "failed"

end DutyStatus

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  GPU Duty Assignment
-- ═══════════════════════════════════════════════════════════════════════════

structure DutyAssignment where
  dutyId : String
  dutyType : DutyType
  gpuId : Nat
  priority : Nat
  status : DutyStatus
  assignedAt : Nat
  startedAt : Option Nat
  completedAt : Option Nat
  result : Option String
  error : Option String
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  GPU Duty System
-- ═══════════════════════════════════════════════════════════════════════════

structure GpuDutySystem where
  assignments : List DutyAssignment
  availableGpus : List Nat
  totalGpus : Nat
  deriving Repr, Inhabited

namespace GpuDutySystem

/-- Create empty GPU duty system. -/
def empty (totalGpus : Nat) : GpuDutySystem :=
  { assignments := [], availableGpus := List.range totalGpus, totalGpus := totalGpus }

/-- Assign duty to available GPU. -/
def assignDuty (system : GpuDutySystem) (dutyType : DutyType) (priority : Nat) (dutyId : String) : GpuDutySystem :=
  match system.availableGpus with
  | [] => system  -- No GPUs available
  | gpuId :: remaining =>
      let assignment := {
        dutyId := dutyId,
        dutyType := dutyType,
        gpuId := gpuId,
        priority := priority,
        status := DutyStatus.assigned,
        assignedAt := 0,
        startedAt := none,
        completedAt := none,
        result := none,
        error := none
      }
      { system with assignments := assignment :: system.assignments, availableGpus := remaining }

/-- Start duty execution. -/
def startDuty (system : GpuDutySystem) (dutyId : String) : GpuDutySystem :=
  let assignments := system.assignments.map (fun a =>
    if a.dutyId = dutyId then { a with status := DutyStatus.executing, startedAt := some 0 } else a
  )
  { system with assignments := assignments }

/-- Complete duty execution. -/
def completeDuty (system : GpuDutySystem) (dutyId : String) (result : String) : GpuDutySystem :=
  let (completed, remaining) := system.assignments.partition (fun a => a.dutyId = dutyId)
  let completedUpdated := completed.map (fun a => { a with status := DutyStatus.completed, completedAt := some 0, result := some result })
  let freedGpus := completed.map (fun a => a.gpuId)
  { system with assignments := remaining ++ completedUpdated, availableGpus := freedGpus ++ system.availableGpus }

/-- Fail duty execution. -/
def failDuty (system : GpuDutySystem) (dutyId : String) (error : String) : GpuDutySystem :=
  let (failed, remaining) := system.assignments.partition (fun a => a.dutyId = dutyId)
  let failedUpdated := failed.map (fun a => { a with status := DutyStatus.failed, completedAt := some 0, error := some error })
  let freedGpus := failed.map (fun a => a.gpuId)
  { system with assignments := remaining ++ failedUpdated, availableGpus := freedGpus ++ system.availableGpus }

/-- Get pending duties by priority. -/
def getPendingDuties (system : GpuDutySystem) : List DutyAssignment :=
  system.assignments.filter (fun (a : DutyAssignment) => a.status = DutyStatus.pending)

/-- Get system statistics. -/
def getStatistics (system : GpuDutySystem) : Nat :=
  system.assignments.length

end GpuDutySystem

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Integration with SubagentOrchestrator
-- ═══════════════════════════════════════════════════════════════════════════

/-- GPU duty assignment as a resource allocation expert. -/
structure GpuResourceExpert where
  totalGpus : Nat
  availableGpus : Nat
  utilization : Q16_16
  deriving Repr, Inhabited

/-- Create GPU resource expert. -/
def createGpuExpert (totalGpus : Nat) : GpuResourceExpert :=
  { totalGpus := totalGpus
    availableGpus := totalGpus
    utilization := Q16_16.zero }

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

/-- Theorem: Empty system has no assignments. -/
theorem emptySystemHasNoAssignments (totalGpus : Nat) :
    (GpuDutySystem.empty totalGpus).assignments.length = 0 := by
  rfl

/-- Theorem: Statistics equals assignment count. -/
theorem statisticsEqualsAssignments (system : GpuDutySystem) :
    system.getStatistics = system.assignments.length := by
  rfl

-- ═══════════════════════════════════════════════════════════════════════════

end Semantics.GpuDutyAssignment