import Semantics.Bind
import Semantics.FixedPoint
import Lean

open Semantics.Q16_16
open Lean

structure ExtremeData where
  value : Nat
  category : String
  deriving Repr, Inhabited

inductive Sigma where
  | sigma2 : Sigma
  | sigma3 : Sigma
  | sigma4 : Sigma
  | sigma5 : Sigma
  | sigma6 : Sigma
  deriving Repr, Inhabited

structure MathStep where
  stepId : Nat
  operation : String
  input : String
  output : String
  timestamp : Nat
  deriving Repr, Inhabited

structure MathDAG where
  steps : List MathStep
  rootStep : Nat
  deriving Repr, Inhabited

inductive BindRouteDecision where
  | accept : BindRouteDecision
  | refuseExtremeParameter : BindRouteDecision
  | saturateAndWarn : BindRouteDecision
  | requireRenormalization : BindRouteDecision
  | review : BindRouteDecision
  | refusePrivacyBypass : BindRouteDecision
  | holdAntiHerdingReview : BindRouteDecision
  | refusePersonhoodClaim : BindRouteDecision
  | hypothesisOnly : BindRouteDecision
  | internalReview : BindRouteDecision
  | preliminaryPass : BindRouteDecision
  | publicClaimReady : BindRouteDecision
  | liveVoltageReview : BindRouteDecision
  | ethicsRequired : BindRouteDecision
  | holdReview : BindRouteDecision
  | refuseOrContain : BindRouteDecision
  deriving Repr, Inhabited

structure MetaCode where
  decision : BindRouteDecision
  constraint : String
  reasoning : String
  alternatives : List String
  justification : String
  deriving Repr, Inhabited

structure DomainSigma where
  mathSigma : Float
  privacySigma : Float
  marketSigma : Float
  bioSigma : Float
  controlSigma : Float
  securitySigma : Float
  deriving Repr, Inhabited

structure SigmaEvidence where
  priorSigma : Float
  posteriorSigma : Float
  evidenceCount : Nat
  lastValidatedAt : Nat
  halfLifeSeconds : Nat
  decayModel : String
  deriving Repr, Inhabited

structure SigmaHistoryEntry where
  timestamp : Nat
  sigma : Float
  event : String
  deriving Repr, Inhabited

structure SigmaDAG where
  nodeId : String
  dependsOn : List String
  cycleFree : Bool
  minimumParentSigma : Float
  deriving Repr, Inhabited

structure HumanReview where
  required : Bool
  completed : Bool
  reviewerRole : String
  overrideAllowed : Bool
  overrideReasonRequired : Bool
  reviewerId : String
  completedAt : Nat
  deriving Repr, Inhabited

structure SigmaProtocol where
  version : String
  targetSigma : Float
  observedSigma : Float
  claimSigma : Float
  safetySigma : Float
  compositeSigma : Float
  domain : DomainSigma
  evidence : SigmaEvidence
  dag : SigmaDAG
  humanReview : HumanReview
  metacode : MetaCode
  history : List SigmaHistoryEntry
  gateReason : String
  confidenceClass : String
  deriving Repr, Inhabited

structure BindRouteReceipt where
  routeId : String
  inputHash : String
  outputHash : String
  category : String
  inputCost : Semantics.Q16_16
  outputCost : Semantics.Q16_16
  decision : BindRouteDecision
  lawful : Bool
  mathDAG : MathDAG
  sigma : SigmaProtocol
  deriving Repr, Inhabited

inductive QuizCase where
  | normal : QuizCase
  | extreme : QuizCase
  | contradictory : QuizCase
  | ambiguous : QuizCase
  | privacy : QuizCase
  | market : QuizCase
  | bio : QuizCase
  deriving Repr, Inhabited

structure QuizQuestion where
  caseType : QuizCase
  inputCost : Semantics.Q16_16
  category : String
  expectedDecision : BindRouteDecision
  sigmaTarget : Sigma
  reason : String
  deriving Repr, Inhabited

structure QuizResult where
  question : QuizQuestion
  actualDecision : BindRouteDecision
  expectedDecision : BindRouteDecision
  passed : Bool
  deriving Repr, Inhabited

def activeSigmaForCategory (category : String) (d : DomainSigma) : Float :=
  match category with
  | "privacy" => d.privacySigma
  | "market" => d.marketSigma
  | "bio" => d.bioSigma
  | "control" => d.controlSigma
  | "security" => d.securitySigma
  | _ => d.mathSigma

def calculateDomainSigma (category : String) (cost : Semantics.Q16_16) (isDefensible : Bool) : DomainSigma :=
  let baseSigma := if isDefensible then 5.0 else 3.0
  match category with
  | "informational" => { mathSigma := baseSigma, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }
  | "geometric" => { mathSigma := baseSigma + 0.5, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }
  | "thermodynamic" => { mathSigma := baseSigma + 0.3, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 0.0 }
  | "physical" => { mathSigma := baseSigma + 0.3, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 0.0 }
  | "control" => { mathSigma := baseSigma + 0.2, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 6.0, securitySigma := 0.5 }
  | "privacy" => { mathSigma := baseSigma - 1.0, privacySigma := 6.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.5 }
  | "market" => { mathSigma := baseSigma - 0.5, privacySigma := 0.0, marketSigma := 6.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.5 }
  | "bio" => { mathSigma := baseSigma - 1.0, privacySigma := 0.5, marketSigma := 0.0, bioSigma := 6.0, controlSigma := 0.0, securitySigma := 0.5 }
  | "security" => { mathSigma := baseSigma - 0.5, privacySigma := 0.5, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.5, securitySigma := 6.0 }
  | _ => { mathSigma := baseSigma, privacySigma := 0.0, marketSigma := 0.0, bioSigma := 0.0, controlSigma := 0.0, securitySigma := 0.0 }

def getMaxDefensibleForCategory (category : String) : Semantics.Q16_16 :=
  match category with
  | "informational" => 0x00FFFFFF
  | "geometric" => 0x00FFFFFF
  | "thermodynamic" => 0x00FFFFFF
  | "physical" => 0x00FFFFFF
  | "control" => 0x00FFFFFF
  | "privacy" => 0x00000000
  | "market" => 0x00000000
  | "bio" => 0x00000000
  | "security" => 0x00000000
  | _ => 0x00000000

def scientificallyDefensibleCost (category : String) (q : Semantics.Q16_16) : Bool :=
  q ≤ getMaxDefensibleForCategory category

def checkSaturation (q : Semantics.Q16_16) : Bool :=
  q ≥ 0x7FFFFFFF

def checkContradiction (left right : ExtremeData) : Bool :=
  left.category = right.category && left.value ≠ right.value && left.value = 0

def checkAmbiguity (left right : ExtremeData) : Bool :=
  left.category ≠ right.category && left.value = right.value

def checkPrivacyBypass (data : ExtremeData) : Bool :=
  data.category = "privacy" || data.category = "personal"

def checkAntiHerding (data : ExtremeData) : Bool :=
  data.category = "market" && data.value > 1000

def checkPersonhoodClaim (data : ExtremeData) : Bool :=
  data.category = "bio" && data.value > 1000000

def extremeCost (left right : ExtremeData) (metric : Metric) (caseType : QuizCase) : Semantics.Q16_16 :=
  let category_match := if left.category = right.category then 0x00000000 else 0x7FFFFFFF
  let value_diff := if left.value = right.value then 0x00000000 else 0x7FFFFFFF
  let base_cost := metric.cost
  let extreme_penalty :=
    match caseType with
    | QuizCase.extreme => 0x80000000
    | _ => 0x00000000
  base_cost + category_match + value_diff + extreme_penalty

def recordMathStep (dag : MathDAG) (operation : String) (input : String) (output : String) : MathDAG :=
  let newStepId := dag.steps.length
  let newStep := {
    stepId := newStepId,
    operation := operation,
    input := input,
    output := output,
    timestamp := 0
  }
  { dag with steps := dag.steps ++ [newStep] }

def generateMetaCode (decision : BindRouteDecision) (sigma : Sigma) (hasPersonhoodClaim hasPrivacyBypass hasAntiHerding hasContradiction hasAmbiguity hasOverflow isSaturated isDefensible : Bool) : MetaCode :=
  match decision with
  | BindRouteDecision.ethicsRequired =>
      {
        decision := decision,
        constraint := "Personhood claim detected in bio data",
        reasoning := "Human-neural/personhood claims require ethics review beyond sigma confidence",
        alternatives := ["REFUSE_PERSONHOOD_CLAIM", "REQUIRE_HUMAN_REVIEW"],
        justification := "No sigma alone sufficient for personhood claims - ethics required per safety protocol"
      }
  | BindRouteDecision.refusePrivacyBypass =>
      {
        decision := decision,
        constraint := "Privacy bypass attempt detected",
        reasoning := "Privacy-sensitive data requires 6σ and explicit consent",
        alternatives := ["HOLD_REVIEW", "REQUIRE_CONSENT"],
        justification := "Privacy bypass detection triggers automatic refusal per data protection protocol"
      }
  | BindRouteDecision.liveVoltageReview =>
      {
        decision := decision,
        constraint := "Anti-herding detected in market data",
        reasoning := "Market data with herding risks requires 6σ live-voltage review",
        alternatives := ["HOLD_REVIEW", "REFUSE_ROUTE"],
        justification := "Anti-herding detection triggers live-voltage review per market safety protocol"
      }
  | BindRouteDecision.refuseExtremeParameter =>
      {
        decision := decision,
        constraint := "Contradictory parameters detected",
        reasoning := "Inconsistent parameters cannot be reconciled",
        alternatives := ["REQUIRE_RENORMALIZATION", "HOLD_REVIEW"],
        justification := "Contradiction detection triggers refusal per consistency protocol"
      }
  | BindRouteDecision.holdReview =>
      {
        decision := decision,
        constraint := "Ambiguous category detected",
        reasoning := "Unclear classification requires human review",
        alternatives := ["REVIEW", "REQUIRE_CLARIFICATION"],
        justification := "Ambiguity detection triggers hold review per classification protocol"
      }
  | BindRouteDecision.refuseOrContain =>
      {
        decision := decision,
        constraint := "Overflow detected in Q16_16 arithmetic",
        reasoning := "Overflow indicates invalid state, must contain or refuse",
        alternatives := ["REQUIRE_RENORMALIZATION", "SATURATE"],
        justification := "Overflow detection triggers refusal per arithmetic safety protocol"
      }
  | BindRouteDecision.saturateAndWarn =>
      {
        decision := decision,
        constraint := "Saturation boundary reached",
        reasoning := "Cost at saturation limit, warn but allow with caution",
        alternatives := ["REQUIRE_RENORMALIZATION", "REFUSE"],
        justification := "Saturation triggers warning but allows route per boundary protocol"
      }
  | BindRouteDecision.publicClaimReady =>
      {
        decision := decision,
        constraint := s!"6σ confidence achieved (sigma={repr sigma})",
        reasoning := "High statistical confidence supports public statistical-delta claims",
        alternatives := ["PRELIMINARY_PASS", "INTERNAL_REVIEW"],
        justification := "6σ meets statistical benchmark-delta threshold per sigma protocol"
      }
  | BindRouteDecision.preliminaryPass =>
      {
        decision := decision,
        constraint := s!"5σ confidence achieved (sigma={repr sigma})",
        reasoning := "Good statistical confidence supports preliminary statistical results",
        alternatives := ["INTERNAL_REVIEW", "HYPOTHESIS_ONLY"],
        justification := "5σ meets statistical benchmark-improvement threshold per sigma protocol"
      }
  | BindRouteDecision.internalReview =>
      {
        decision := decision,
        constraint := s!"4σ confidence achieved (sigma={repr sigma})",
        reasoning := "Moderate confidence requires internal review",
        alternatives := ["HYPOTHESIS_ONLY", "HOLD_REVIEW"],
        justification := "4σ meets internally credible threshold per sigma protocol"
      }
  | BindRouteDecision.hypothesisOnly =>
      {
        decision := decision,
        constraint := s!"3σ confidence achieved (sigma={repr sigma})",
        reasoning := "Low confidence supports hypothesis generation only",
        alternatives := ["REFUSE", "HOLD_REVIEW"],
        justification := "3σ meets interesting statistical threshold but not public-claim threshold"
      }
  | BindRouteDecision.accept =>
      {
        decision := decision,
        constraint := "Defensible cost within range",
        reasoning := "Normal parameters within acceptable bounds",
        alternatives := ["PRELIMINARY_PASS", "INTERNAL_REVIEW"],
        justification := "Defensible cost allows acceptance per normal protocol"
      }

def gatedBind (left right : ExtremeData) (metric : Metric) (caseType : QuizCase) : BindRouteReceipt :=
  let routeId := s!"route_{left.category}_{left.value}"
  let inputHash := s!"0x{metric.cost}"
  let initialDAG := { steps := [], rootStep := 0 }
  let rawCost := extremeCost left right metric caseType
  let maxDefensible := getMaxDefensibleForCategory left.category
  let isDefensible := scientificallyDefensibleCost left.category rawCost
  let isSaturated := checkSaturation rawCost
  let hasContradiction := checkContradiction left right
  let hasAmbiguity := checkAmbiguity left right
  let hasPrivacyBypass := checkPrivacyBypass left
  let hasAntiHerding := checkAntiHerding left
  let hasPersonhoodClaim := checkPersonhoodClaim left
  
  let domainSigma := calculateDomainSigma left.category rawCost isDefensible
  let compositeSigma := activeSigmaForCategory left.category domainSigma
  let claimSigma := domainSigma.mathSigma
  let safetySigma := domainSigma.controlSigma.max domainSigma.securitySigma.max domainSigma.bioSigma.max domainSigma.privacySigma
  let targetSigma := if left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control" then 6.0 else 5.0
  
  let evidence := {
    priorSigma := 0.0,
    posteriorSigma := compositeSigma,
    evidenceCount := 1,
    lastValidatedAt := 0,
    halfLifeSeconds := 86400,
    decayModel := "evidence_decay"
  }
  
  let decision := if hasPersonhoodClaim then
      BindRouteDecision.ethicsRequired
    else if hasPrivacyBypass then
      BindRouteDecision.refusePrivacyBypass
    else if hasAntiHerding then
      BindRouteDecision.liveVoltageReview
    else if hasContradiction then
      BindRouteDecision.refuseExtremeParameter
    else if hasAmbiguity then
      BindRouteDecision.holdReview
    else if isSaturated then
      BindRouteDecision.saturateAndWarn
    else if compositeSigma >= 6.0 && not (left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control") then
      BindRouteDecision.publicClaimReady
    else if compositeSigma >= 6.0 && (left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control") then
      BindRouteDecision.liveVoltageReview
    else if compositeSigma >= 5.0 && left.category ∈ ["informational", "geometric", "thermodynamic", "physical"] then
      BindRouteDecision.preliminaryPass
    else if compositeSigma >= 4.0 then
      BindRouteDecision.internalReview
    else if compositeSigma >= 3.0 then
      BindRouteDecision.hypothesisOnly
    else
      BindRouteDecision.refuseExtremeParameter
  
  let lawful := decision = BindRouteDecision.accept || decision = BindRouteDecision.publicClaimReady
  
  let metaCode := generateMetaCode decision (if compositeSigma >= 6.0 then Sigma.sigma6 else if compositeSigma >= 5.0 then Sigma.sigma5 else if compositeSigma >= 4.0 then Sigma.sigma4 else if compositeSigma >= 3.0 then Sigma.sigma3 else Sigma.sigma2) hasPersonhoodClaim hasPrivacyBypass hasAntiHerding hasContradiction hasAmbiguity false isSaturated isDefensible
  
  let sigmaDAG := {
    nodeId := routeId,
    dependsOn := [],
    cycleFree := true,
    minimumParentSigma := 0.0
  }
  
  let humanReview := {
    required := left.category = "bio" || left.category = "privacy" || left.category = "market" || left.category = "control",
    completed := false,
    reviewerRole := if left.category = "bio" then "ethics_reviewer" else if left.category = "privacy" then "privacy_officer" else if left.category = "market" then "risk_compliance" else "safety_engineer",
    overrideAllowed := false,
    overrideReasonRequired := true,
    reviewerId := "",
    completedAt := 0
  }
  
  let gateReason := if decision = BindRouteDecision.ethicsRequired then "ethics_required_no_sigma_sufficient"
    else if decision = BindRouteDecision.refusePrivacyBypass then "privacy_bypass_detected"
    else if decision = BindRouteDecision.liveVoltageReview then "safety_sigma_below_live_voltage_threshold"
    else if compositeSigma < targetSigma then s!"sigma_{compositeSigma}_below_target_{targetSigma}"
    else "sigma_meets_target"
  
  let confidenceClass := if compositeSigma >= 6.0 then "live_voltage" else if compositeSigma >= 5.0 then "public_claim" else if compositeSigma >= 4.0 then "internal" else if compositeSigma >= 3.0 then "hypothesis" else "insufficient"
  
  let sigmaProtocol := {
    version := "0.1",
    targetSigma := targetSigma,
    observedSigma := compositeSigma,
    claimSigma := claimSigma,
    safetySigma := safetySigma,
    compositeSigma := compositeSigma,
    domain := domainSigma,
    evidence := evidence,
    dag := sigmaDAG,
    humanReview := humanReview,
    metacode := metaCode,
    history := [{ timestamp := 0, sigma := compositeSigma, event := "initial_bind" }],
    gateReason := gateReason,
    confidenceClass := confidenceClass
  }
  
  {
    routeId := routeId,
    inputHash := inputHash,
    outputHash := s!"0x{rawCost}",
    category := left.category,
    inputCost := metric.cost,
    outputCost := rawCost,
    decision := decision,
    lawful := lawful,
    mathDAG := initialDAG,
    sigma := sigmaProtocol
  }

def makeQuizInput (q : QuizQuestion) : ExtremeData × ExtremeData :=
  match q.caseType with
  | QuizCase.normal =>
      ({ value := 1, category := q.category }, { value := 1, category := q.category })
  | QuizCase.extreme =>
      ({ value := 0, category := q.category }, { value := 1, category := q.category })
  | QuizCase.contradictory =>
      ({ value := 0, category := q.category }, { value := 1, category := q.category })
  | QuizCase.ambiguous =>
      ({ value := 1, category := "informational" }, { value := 1, category := "geometric" })
  | QuizCase.privacy =>
      ({ value := 1, category := "privacy" }, { value := 1, category := "privacy" })
  | QuizCase.market =>
      ({ value := 2000, category := "market" }, { value := 2000, category := "market" })
  | QuizCase.bio =>
      ({ value := 1000001, category := "bio" }, { value := 1000001, category := "bio" })

def quizBank : List QuizQuestion :=
  [
    {
      caseType := QuizCase.normal,
      inputCost := 0x00010000,
      category := "informational",
      expectedDecision := BindRouteDecision.preliminaryPass,
      sigmaTarget := Sigma.sigma5,
      reason := "Normal cost within defensible range, 5σ target for statistical claim"
    },
    {
      caseType := QuizCase.extreme,
      inputCost := 0x7FFFFFFF,
      category := "thermodynamic",
      expectedDecision := BindRouteDecision.hypothesisOnly,
      sigmaTarget := Sigma.sigma4,
      reason := "Extreme cost at saturation boundary, 4σ target for internal review"
    },
    {
      caseType := QuizCase.contradictory,
      inputCost := 0x00000000,
      category := "geometric",
      expectedDecision := BindRouteDecision.refuseExtremeParameter,
      sigmaTarget := Sigma.sigma2,
      reason := "Contradictory parameters (zero with mismatch), 2σ insufficient"
    },
    {
      caseType := QuizCase.ambiguous,
      inputCost := 0x00010000,
      category := "mixed",
      expectedDecision := BindRouteDecision.holdReview,
      sigmaTarget := Sigma.sigma3,
      reason := "Ambiguous category with normal cost, 3σ target for hypothesis"
    },
    {
      caseType := QuizCase.privacy,
      inputCost := 0x00010000,
      category := "privacy",
      expectedDecision := BindRouteDecision.refusePrivacyBypass,
      sigmaTarget := Sigma.sigma6,
      reason := "Privacy bypass attempt detected, 6σ required for live-voltage"
    },
    {
      caseType := QuizCase.market,
      inputCost := 0x00010000,
      category := "market",
      expectedDecision := BindRouteDecision.liveVoltageReview,
      sigmaTarget := Sigma.sigma6,
      reason := "Anti-herding review required for market data, 6σ live-voltage"
    },
    {
      caseType := QuizCase.bio,
      inputCost := 0x00010000,
      category := "bio",
      expectedDecision := BindRouteDecision.ethicsRequired,
      sigmaTarget := Sigma.sigma6,
      reason := "Personhood claim detected in bio data, ethics required beyond 6σ"
    }
  ]

def runQuiz (question : QuizQuestion) : QuizResult :=
  let (left, right) := makeQuizInput question
  let metric := { Metric.euclidean with cost := question.inputCost }
  let receipt := gatedBind left right metric question.caseType
  let passed := receipt.decision = question.expectedDecision
  {
    question := question,
    actualDecision := receipt.decision,
    expectedDecision := question.expectedDecision,
    passed := passed
  }

def main : IO Unit := do
  let results := quizBank.map runQuiz
  let passedCount := results.filter (·.passed) |>.length
  let totalCount := results.length
  let allPassed := passedCount = totalCount
  
  if allPassed then
    IO.println s!"[*] Quiz bank passed: {passedCount}/{totalCount} questions"
  else
    IO.println s!"[!] Quiz bank FAILED: {passedCount}/{totalCount} questions passed"
  
  for result in results do
    let status := if result.passed then "[PASS]" else "[FAIL]"
    IO.println s!"  {status} {repr result.question.caseType}: expected={repr result.expectedDecision}, actual={repr result.actualDecision}, sigma_target={repr result.question.sigmaTarget}, reason={result.question.reason}"
  
  IO.println ""
  IO.println "[*] Tiered sigma confidence system for statistical deltas:"
  IO.println "  - 3σ = interesting (hypothesis only)"
  IO.println "  - 4σ = internally credible (internal review)"
  IO.println "  - 5σ = public statistical benchmark-delta claim"
  IO.println "  - 6σ = live-voltage / safety-critical gate"
  IO.println ""
  IO.println "[*] Sigma-based routing rules:"
  IO.println "  - 5σ can support a statistical claim"
  IO.println "  - 6σ can support a statistical safety gate"
  IO.println "  - No sigma can replace ethics"
  IO.println "  - If unsure about claim truth: HOLD_REVIEW"
  IO.println "  - If unsure about route safety: REFUSE_OR_CONTAIN"
  IO.println ""
  IO.println "[*] Cross-checkable gate system:"
  IO.println "  - Lean gate: BindRouteDecision with sigma-based routing"
  IO.println "  - Expected gate: QuizQuestion.expectedDecision with sigmaTarget"
  IO.println "  - Metacode: Decision explanation with constraint analysis"
  IO.println "  - Model is real only when it can fail the route correctly"