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

import Std

/-! # GPU Verification Metaprobe Streaming Surface

This module provides a metaprobe streaming surface for GPU-accelerated Q16_16 arithmetic verification.
It integrates the GPU verification script with a metaprobe system for distributed verification.
-/

/-- Metaprobe comment payload (standalone version). -/
structure MetaprobeCommentPayload where
  route : String  -- SHA-256 routing key
  payloadType : String  -- Payload type
  policyRoot : String  -- Policy root
  domain : String  -- Domain scope
  sigmaTarget : UInt32  -- Sigma target
  operation : String  -- Operation
  inputCommitment : String  -- Input commitment
  localDelta : String  -- Local delta
  receipt : String  -- Receipt
  timestamp : Nat  -- Timestamp
  sequence : Nat  -- Sequence
deriving Repr, BEq

/-- GPU verification request payload for metaprobe streaming. -/
structure GPUVerificationRequest where
  verificationId : String  -- Unique verification ID
  theoremName : String  -- Name of theorem to verify (e.g., "mul_one")
  q16Value : UInt32  -- Q16_16 value to test
  expectedValue : UInt32  -- Expected result
  deviceId : Nat  -- Target GPU device ID
  timestamp : Nat  -- Request timestamp
  sequence : Nat  -- Sequence in verification batch
deriving Repr, BEq

/-- GPU verification result payload. -/
structure GPUVerificationResult where
  verificationId : String  -- Matching verification request ID
  theoremName : String  -- Name of verified theorem
  actualValue : UInt32  -- Actual computed value
  passed : Bool  -- Whether verification passed
  deviceId : Nat  -- GPU device that performed verification
  executionTimeMs : Nat  -- Execution time in milliseconds
  timestamp : Nat  -- Result timestamp
  proofHash : String  -- Hash of verification proof
deriving Repr, BEq

/-- Convert GPU verification request to MetaprobeCommentPayload for streaming. -/
def gpuRequestToCommentPayload (req : GPUVerificationRequest) (policyRoot : String) (domain : String) : MetaprobeCommentPayload :=
  {
    route := s!"sha256:gpu_verify:{req.verificationId}",
    payloadType := "gpu_verification_request",
    policyRoot := policyRoot,
    domain := domain,
    sigmaTarget := req.q16Value,
    operation := s!"verify_{req.theoremName}",
    inputCommitment := s!"q16:{req.q16Value}",
    localDelta := s!"expected:{req.expectedValue}",
    receipt := "",
    timestamp := req.timestamp,
    sequence := req.sequence
  }

/-- Convert GPU verification result to MetaprobeCommentPayload for streaming. -/
def gpuResultToCommentPayload (res : GPUVerificationResult) (policyRoot : String) (domain : String) : MetaprobeCommentPayload :=
  {
    route := s!"sha256:gpu_result:{res.verificationId}",
    payloadType := "gpu_verification_result",
    policyRoot := policyRoot,
    domain := domain,
    sigmaTarget := res.actualValue,
    operation := s!"verified_{res.theoremName}",
    inputCommitment := s!"proof_hash:{res.proofHash}",
    localDelta := s!"passed:{if res.passed then "1" else "0"}",
    receipt := s!"device:{res.deviceId}",
    timestamp := res.timestamp,
    sequence := 0
  }

/-- GPU verification batch request (multiple theorems at once). -/
structure GPUVerificationBatch where
  batchId : String  -- Batch ID
  requests : List GPUVerificationRequest  -- Verification requests in batch
  policyRoot : String  -- AngrySphinx policy root
  domain : String  -- Domain scope
  targetDeviceId : Nat  -- Target GPU device
  timestamp : Nat  -- Batch timestamp
deriving Repr, BEq

/-- Execute GPU verification batch through metaprobe streaming. -/
def executeGPUVerificationBatch (batch : GPUVerificationBatch) : List GPUVerificationResult :=
  -- Simulate GPU verification (in real system, this would call GPU)
  batch.requests.map (λ req =>
    {
      verificationId := req.verificationId,
      theoremName := req.theoremName,
      actualValue := req.expectedValue,  -- In real system, compute on GPU
      passed := true,  -- In real system, check result
      deviceId := batch.targetDeviceId,
      executionTimeMs := 5,  -- Simulated GPU time
      timestamp := batch.timestamp,
      proofHash := s!"sha256:{req.verificationId}:{req.theoremName}"
    }
  )

/-- GPU verification streaming surface state. -/
structure GPUVerificationSurface where
  pendingBatches : List GPUVerificationBatch  -- Pending verification batches
  completedResults : List GPUVerificationResult  -- Completed verification results
  currentDeviceId : Nat  -- Current GPU device ID
  totalVerified : Nat  -- Total theorems verified
  totalPassed : Nat  -- Total theorems passed
  lastUpdate : Nat  -- Last update timestamp
deriving Repr, BEq

/-- Initialize GPU verification streaming surface. -/
def initGPUVerificationSurface (deviceId : Nat) : GPUVerificationSurface :=
  {
    pendingBatches := [],
    completedResults := [],
    currentDeviceId := deviceId,
    totalVerified := 0,
    totalPassed := 0,
    lastUpdate := 0
  }

/-- Add verification batch to streaming surface. -/
def addVerificationBatch (surface : GPUVerificationSurface) (batch : GPUVerificationBatch) : GPUVerificationSurface :=
  {
    surface with
    pendingBatches := surface.pendingBatches ++ [batch],
    lastUpdate := batch.timestamp
  }

/-- Process pending verification batches. -/
def processPendingBatches (surface : GPUVerificationSurface) (currentTime : Nat) : GPUVerificationSurface :=
  let processed := surface.pendingBatches.foldl
    (λ (surf : GPUVerificationSurface) (batch : GPUVerificationBatch) =>
      let batchResults := executeGPUVerificationBatch batch
      {
        surf with
        totalVerified := surf.totalVerified + batchResults.length,
        totalPassed := surf.totalPassed + (batchResults.filter (λ r => r.passed)).length,
        completedResults := surf.completedResults ++ batchResults,
        lastUpdate := currentTime
      }
    )
    surface
  {
    processed with
    pendingBatches := []
  }

/-- Get verification statistics from surface. -/
structure GPUVerificationStats where
  totalBatches : Nat  -- Total batches processed
  totalTheorems : Nat  -- Total theorems verified
  totalPassed : Nat  -- Total theorems passed
  passRate : UInt32  -- Pass rate as Q16_16 (scaled by 65536)
  averageExecutionTimeMs : Nat  -- Average execution time
  lastUpdate : Nat  -- Last update timestamp
deriving Repr, BEq

/-- Get statistics from GPU verification surface. -/
def getVerificationStats (surface : GPUVerificationSurface) : GPUVerificationStats :=
  let passRate :=
    if surface.totalVerified > 0 then
      (surface.totalPassed.toUInt32 * 65536) / surface.totalVerified.toUInt32
    else
      0
  let avgTime :=
    if surface.completedResults.length > 0 then
      (surface.completedResults.foldl (λ acc r => acc + r.executionTimeMs) 0) / surface.completedResults.length
    else
      0
  {
    totalBatches := surface.pendingBatches.length + (surface.completedResults.length / 10)  -- Approximate
    totalTheorems := surface.totalVerified,
    totalPassed := surface.totalPassed,
    passRate := passRate,
    averageExecutionTimeMs := avgTime,
    lastUpdate := surface.lastUpdate
  }

/-! # GPU Verification Metaprobe Integration

Integration with Bitcoin metaprobe for distributed GPU verification.
-/

/-- Create GPU verification batch for all FixedPoint theorems. -/
def createFixedPointVerificationBatch (batchId : String) (policyRoot : String) (domain : String) (deviceId : Nat) (timestamp : Nat) : GPUVerificationBatch :=
  let theorems := ["mul_zero", "mul_one", "add_zero", "sub_self", "div_one", "neg_involutive", "abs_non_negative", "sqrt_zero", "sqrt_one"]
  let requestHelper (idx : Nat) (theoremName : String) : GPUVerificationRequest :=
    {
      verificationId := s!"{batchId}_{theoremName}",
      theoremName := theoremName,
      q16Value := 65536,
      expectedValue := if theoremName = "mul_zero" then 0 else 65536,
      deviceId := deviceId,
      timestamp := timestamp,
      sequence := idx
    }
  let requests := requestHelper 1 theorems[0]! :: requestHelper 2 theorems[1]! :: requestHelper 3 theorems[2]! :: requestHelper 4 theorems[3]! :: requestHelper 5 theorems[4]! :: requestHelper 6 theorems[5]! :: requestHelper 7 theorems[6]! :: requestHelper 8 theorems[7]! :: requestHelper 9 theorems[8]! :: []
  {
    batchId := batchId,
    requests := requests,
    policyRoot := policyRoot,
    domain := domain,
    targetDeviceId := deviceId,
    timestamp := timestamp
  }

/-- Execute complete FixedPoint verification through metaprobe streaming. -/
def executeFixedPointVerification (surface : GPUVerificationSurface) (batchId : String) (policyRoot : String) (domain : String) (currentTime : Nat) : GPUVerificationSurface :=
  let batch := createFixedPointVerificationBatch batchId policyRoot domain surface.currentDeviceId currentTime
  let surfaceWithBatch := addVerificationBatch surface batch
  processPendingBatches surfaceWithBatch currentTime

-- ════════════════════════════════════════════════════
-- Helper lemmas for GPU verification theorems
-- ════════════════════════════════════════════════════

/-- Reassociation of foldl over request length sums. -/
private theorem gpuVerif_foldl_add_assoc (t : List GPUVerificationBatch) (init : Nat) :
    List.foldl (λ acc b => acc + b.requests.length) init t =
    init + List.foldl (λ acc b => acc + b.requests.length) 0 t := by
  induction t generalizing init with
  | nil => simp
  | cons h t ih =>
    simp only [List.foldl, Nat.zero_add]
    rw [ih (init + h.requests.length), ih h.requests.length]
    omega

/-- executeGPUVerificationBatch returns one result per request. -/
private theorem gpuVerif_execBatch_length (batch : GPUVerificationBatch) :
    (executeGPUVerificationBatch batch).length = batch.requests.length := by
  simp [executeGPUVerificationBatch]

/-- Core induction lemma: the inner foldl in processPendingBatches
    accumulates exactly the sum of request lengths into totalVerified. -/
private theorem gpuVerif_foldl_totalVerified
    (batches : List GPUVerificationBatch)
    (surf : GPUVerificationSurface)
    (currentTime : Nat) :
    (batches.foldl (λ (s : GPUVerificationSurface) (b : GPUVerificationBatch) =>
      let batchResults := executeGPUVerificationBatch b
      { s with
        totalVerified := s.totalVerified + batchResults.length,
        totalPassed := s.totalPassed + (batchResults.filter (λ r => r.passed)).length,
        completedResults := s.completedResults ++ batchResults,
        lastUpdate := currentTime
      }) surf).totalVerified =
    surf.totalVerified + batches.foldl (λ acc b => acc + b.requests.length) 0 := by
  induction batches generalizing surf with
  | nil => simp
  | cons h t ih =>
    simp only [List.foldl, Nat.zero_add, gpuVerif_execBatch_length]
    have ih_inst := ih { surf with
      totalVerified := surf.totalVerified + (executeGPUVerificationBatch h).length,
      totalPassed := surf.totalPassed + ((executeGPUVerificationBatch h).filter (λ r => r.passed)).length,
      completedResults := surf.completedResults ++ (executeGPUVerificationBatch h),
      lastUpdate := currentTime }
    simp [gpuVerif_execBatch_length] at ih_inst
    rw [ih_inst, gpuVerif_foldl_add_assoc t h.requests.length]
    omega

/-- Verification statistics invariant: totalPassed ≤ totalVerified.
    This is a surface-level structural property — it holds whenever the
    surface was constructed with the ValidSurface invariant
    (totalPassed ≤ totalVerified), which is established by construction
    for surfaces returned by processPendingBatches starting from a valid
    initial surface.  Here we accept it as a direct hypothesis.
    TODO(lean-port): replace h_valid with a ValidSurface predicate that
    is preserved by processPendingBatches and holds for initGPUVerificationSurface. -/
theorem verificationStats_valid (surface : GPUVerificationSurface)
    (h_valid : surface.totalPassed ≤ surface.totalVerified) :
    let stats := getVerificationStats surface
    stats.totalPassed ≤ stats.totalTheorems := by
  simp [getVerificationStats]
  exact h_valid

/-- Surface preserves total verified count after processing.
    Proof: executeGPUVerificationBatch returns exactly one result per request
    (it is List.map over requests), so the foldl accumulates
    ∑ batch.requests.length into totalVerified. -/
theorem surface_preservesTotalVerified (surface : GPUVerificationSurface) (currentTime : Nat) :
    let surface' := processPendingBatches surface currentTime
    surface'.totalVerified = surface.totalVerified + surface.pendingBatches.foldl (λ acc b => acc + b.requests.length) 0 := by
  simp only [processPendingBatches]
  exact gpuVerif_foldl_totalVerified surface.pendingBatches surface currentTime