import Semantics.Bind
import Semantics.FixedPoint
import Semantics.NICProbe
import Lean.Data.Json

namespace Semantics.ASICTopology

/-! ## TopoASIC — ASIC Topology Abstraction Layer

**Core Inversion:**
- Normal view: ASIC = specific chip, fixed function, limited use
- TopoASIC view: ASIC = topology of constrained transformations, routing surface, operation manifold, interfaceable substrate

**Principle:** An ASIC is a crystallized algorithm; TopoASIC treats the crystal as terrain.

**Key Question:** Not "What was this ASIC designed to do?" but "What lawful transformations can this topology perform cheaply?"

**Definition:**
TopoASIC = fixed hardware operation graph + bandwidth/latency/energy constraints + admissible transform set + routing interface + verification receipts

**Capability Vector:**
Each ASIC node: [operation_family, throughput, latency, precision, memory_access_shape, branching_penalty, routing_flexibility, energy_per_transform, thermal_ceiling, verification_surface]

**General Routing Equation:**
Workload W → projection P(W) → ASIC topology T → admissible route R_T → receipt

**Route Validity:**
- cost(P(W), T) < threshold
- semantic_loss < threshold
- verification_pass = true

**Keeper Law:** Do not ask what the chip is. Ask what shape of computation the chip makes easy.

Per AGENTS.md: Lean is source of truth, Q16_16 fixed-point for hardware-native execution.
-/

open Semantics.Q16_16

/-- ASIC topology node types (RTL8126 specific). -/
inductive ASICNode
  | dmaEngine  -- DMA address translation engine
  | checksumUnit  -- Checksum computation unit
  | txQueue  -- Transmit queue (ring buffer)
  | rxQueue  -- Receive queue (ring buffer)
  | descriptorTable  -- Descriptor memory layout
  | macPhy  -- MAC/PHY physical layer
  | registerSpace  -- MMIO register space
deriving Repr, BEq, DecidableEq

/-- ASIC topology edge types (connections between nodes). -/
inductive ASICEdge
  | dmaToQueue  -- DMA engine to queue
  | queueToDescriptor  -- Queue to descriptor table
  | descriptorToChecksum  -- Descriptor to checksum unit
  | checksumToMac  -- Checksum to MAC/PHY
  | macToPhy  -- MAC to PHY
  | registerControl  -- Register space control path
deriving Repr, BEq, DecidableEq

/-- Operation family classification for capability vector. -/
inductive OperationFamily
  | hashPipeline  -- Hash-like pipeline operations
  | memoryLane  -- Memory access operations
  | busSegment  -- Bus transfer operations
  | pipelineStage  -- Sequential pipeline operations
  | accumulator  -- Accumulation operations
  | serializer  -- Serialization operations
  | validator  -- Validation/verification operations
  | checksumCompute  -- Checksum computation
  | addressTranslate  -- Address translation
  | ringBuffer  -- Ring buffer operations
deriving Repr, BEq, DecidableEq

/-- Memory access shape classification. -/
inductive MemoryAccessShape
  | linearSequential  -- Linear sequential access
  | randomAccess  -- Random access
  | strided  -- Strided access
  | circular  -- Circular/ring access
  | scatterGather  -- Scatter-gather access
deriving Repr, BEq, DecidableEq

/-- Capability vector for ASIC topology node (TopoASIC specification). -/
structure CapabilityVector where
  operationFamily : OperationFamily
  throughput : Semantics.Q16_16  -- Operations per unit time
  latency : Semantics.Q16_16  -- Operation latency
  precision : Semantics.Q16_16  -- Precision (bits of accuracy)
  memoryAccessShape : MemoryAccessShape
  branchingPenalty : Semantics.Q16_16  -- Cost of branching
  routingFlexibility : Semantics.Q16_16  -- How flexible routing can be (0-1)
  energyPerTransform : Semantics.Q16_16  -- Energy cost per operation
  thermalCeiling : Semantics.Q16_16  -- Thermal limit
  verificationSurface : Semantics.Q16_16  -- Verification capability (0-1)
deriving Repr

/-- ASIC topology node with geometric properties and capability vector (TopoASIC). -/
structure ASICTopologyNode where
  nodeId : Nat
  nodeType : ASICNode
  position : Array Semantics.Q16_16  -- Position in ASIC topology space
  capacity : Nat  -- Processing capacity (packets/ops)
  latency : Semantics.Q16_16  -- Operation latency
  curvature : Semantics.Q16_16  -- Topology curvature at this node
  torsion : Semantics.Q16_16  -- Topology torsion at this node
  capability : CapabilityVector  -- TopoASIC capability vector
deriving Repr

/-- ASIC topology edge with geometric properties. -/
structure ASICTopologyEdge where
  sourceNodeId : Nat
  targetNodeId : Nat
  edgeType : ASICEdge
  weight : Semantics.Q16_16  -- Edge weight (cost/bandwidth)
  length : Semantics.Q16_16  -- Geodesic length
  flowCapacity : Semantics.Q16_16  -- Flow capacity
deriving Repr

/-- Complete ASIC topology structure. -/
structure ASICTopology where
  nodes : Array ASICTopologyNode
  edges : Array ASICTopologyEdge
  globalCurvature : Semantics.Q16_16  -- Overall manifold curvature
  globalTorsion : Semantics.Q16_16  -- Overall manifold torsion
  dimension : Nat  -- Topology dimension
deriving Repr

/-- Default RTL8126 ASIC topology with capability vectors (TopoASIC specification). -/
def rtl8126Topology : ASICTopology := {
  nodes := #[  -- 7 nodes representing RTL8126 components with capability vectors
    {
      nodeId := 0,
      nodeType := ASICNode.dmaEngine,
      position := #[zero, zero, zero],
      capacity := 1000,
      latency := 0x00000020,
      curvature := zero,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.addressTranslate,
        throughput := 0x00010000,  -- Q16_16: 1.0
        latency := 0x00000020,
        precision := 0x00004000,  -- 64-bit precision
        memoryAccessShape := MemoryAccessShape.scatterGather,
        branchingPenalty := 0x00000500,  -- Low branching penalty
        routingFlexibility := 0x00008000,  -- 0.5 flexibility
        energyPerTransform := 0x00000100,
        thermalCeiling := 0x00020000,
        verificationSurface := 0x00004000  -- Low verification capability
      }
    },
    {
      nodeId := 1,
      nodeType := ASICNode.txQueue,
      position := #[0x00010000, zero, zero],
      capacity := 256,
      latency := 0x00000010,
      curvature := 0x00000500,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.ringBuffer,
        throughput := 0x00020000,  -- Q16_16: 2.0
        latency := 0x00000010,
        precision := 0x00001000,
        memoryAccessShape := MemoryAccessShape.circular,
        branchingPenalty := 0x00001000,
        routingFlexibility := 0x00002000,  -- Low flexibility (fixed ring)
        energyPerTransform := 0x00000050,
        thermalCeiling := 0x00010000,
        verificationSurface := 0x00001000
      }
    },
    {
      nodeId := 2,
      nodeType := ASICNode.rxQueue,
      position := #[zero, 0x00010000, zero],
      capacity := 256,
      latency := 0x00000010,
      curvature := 0x00000500,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.ringBuffer,
        throughput := 0x00020000,
        latency := 0x00000010,
        precision := 0x00001000,
        memoryAccessShape := MemoryAccessShape.circular,
        branchingPenalty := 0x00001000,
        routingFlexibility := 0x00002000,
        energyPerTransform := 0x00000050,
        thermalCeiling := 0x00010000,
        verificationSurface := 0x00001000
      }
    },
    {
      nodeId := 3,
      nodeType := ASICNode.descriptorTable,
      position := #[0x00010000, 0x00010000, zero],
      capacity := 512,
      latency := 0x00000040,
      curvature := zero,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.memoryLane,
        throughput := 0x00008000,
        latency := 0x00000040,
        precision := 0x00004000,
        memoryAccessShape := MemoryAccessShape.linearSequential,
        branchingPenalty := 0x00000800,
        routingFlexibility := 0x00004000,
        energyPerTransform := 0x00000080,
        thermalCeiling := 0x00008000,
        verificationSurface := 0x00002000
      }
    },
    {
      nodeId := 4,
      nodeType := ASICNode.checksumUnit,
      position := #[zero, zero, 0x00010000],
      capacity := 2000,
      latency := 0x00000050,
      curvature := zero,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.checksumCompute,
        throughput := 0x00040000,  -- Q16_16: 4.0 (high throughput)
        latency := 0x00000050,
        precision := 0x00001000,  -- 16-bit precision
        memoryAccessShape := MemoryAccessShape.linearSequential,
        branchingPenalty := 0x00000200,  -- Very low branching penalty (pipeline)
        routingFlexibility := 0x00001000,  -- Very low flexibility (fixed algorithm)
        energyPerTransform := 0x00000030,
        thermalCeiling := 0x00015000,
        verificationSurface := 0x00008000  -- High verification capability
      }
    },
    {
      nodeId := 5,
      nodeType := ASICNode.macPhy,
      position := #[0x00020000, zero, zero],
      capacity := 5000,
      latency := 0x00000100,
      curvature := zero,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.serializer,
        throughput := 0x00050000,
        latency := 0x00000100,
        precision := 0x00001000,
        memoryAccessShape := MemoryAccessShape.linearSequential,
        branchingPenalty := 0x00001500,
        routingFlexibility := 0x00003000,
        energyPerTransform := 0x00000200,
        thermalCeiling := 0x00030000,
        verificationSurface := 0x00002000
      }
    },
    {
      nodeId := 6,
      nodeType := ASICNode.registerSpace,
      position := #[zero, 0x00020000, zero],
      capacity := 100,
      latency := 0x00000200,
      curvature := zero,
      torsion := zero,
      capability := {
        operationFamily := OperationFamily.validator,
        throughput := 0x00001000,
        latency := 0x00000200,
        precision := 0x00004000,
        memoryAccessShape := MemoryAccessShape.randomAccess,
        branchingPenalty := 0x00002000,
        routingFlexibility := 0x00010000,  -- High flexibility (control path)
        energyPerTransform := 0x00000100,
        thermalCeiling := 0x00005000,
        verificationSurface := 0x00010000
      }
    }
  ],
  edges := #[  -- Edges representing data flow
    { sourceNodeId := 0, targetNodeId := 1, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
    { sourceNodeId := 0, targetNodeId := 2, edgeType := ASICEdge.dmaToQueue, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 },
    { sourceNodeId := 1, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
    { sourceNodeId := 2, targetNodeId := 3, edgeType := ASICEdge.queueToDescriptor, weight := 0x00005000, length := 0x00000500, flowCapacity := 0x00015000 },
    { sourceNodeId := 3, targetNodeId := 4, edgeType := ASICEdge.descriptorToChecksum, weight := 0x00008000, length := 0x00000800, flowCapacity := 0x00018000 },
    { sourceNodeId := 4, targetNodeId := 5, edgeType := ASICEdge.checksumToMac, weight := 0x00003000, length := 0x00000300, flowCapacity := 0x00010000 },
    { sourceNodeId := 5, targetNodeId := 5, edgeType := ASICEdge.macToPhy, weight := 0x00002000, length := 0x00000200, flowCapacity := 0x00008000 },
    { sourceNodeId := 6, targetNodeId := 0, edgeType := ASICEdge.registerControl, weight := 0x00010000, length := 0x00001000, flowCapacity := 0x00020000 }
  ],
  globalCurvature := 0x00000200,
  globalTorsion := zero,
  dimension := 3
}

/-- Find node by ID in ASIC topology. -/
def findNode (topology : ASICTopology) (nodeId : Nat) : Option ASICTopologyNode :=
  topology.nodes.find? (λ n => n.nodeId = nodeId)

/-- Find edges from a node in ASIC topology. -/
def findEdgesFrom (topology : ASICTopology) (nodeId : Nat) : Array ASICTopologyEdge :=
  topology.edges.filter (λ e => e.sourceNodeId = nodeId)

/-- Compute geodesic distance between two nodes in ASIC topology. -/
def geodesicDistance (topology : ASICTopology) (sourceId targetId : Nat) : Semantics.Q16_16 :=
  match findNode topology sourceId, findNode topology targetId with
  | some sourceNode, some targetNode =>
    let rec euclideanDistance (i : Nat) (acc : Semantics.Q16_16) : Semantics.Q16_16 :=
      if i >= sourceNode.position.size then acc
      else
        let diff := sourceNode.position[i]! - targetNode.position[i]!
        let squared := diff * diff
        euclideanDistance (i + 1) (acc + squared)
    let squaredDist := euclideanDistance 0 zero
    -- Simplified square root: use linear approximation for small values
    squaredDist / 0x00010000  -- Rough sqrt approximation
  | _, _ => 0x7FFFFFFF  -- Infinity if nodes not found

/-- Optimal path through ASIC topology based on geometric properties. -/
structure ASICOptimalPath where
  path : List Nat  -- Node IDs in optimal path
  totalCost : Semantics.Q16_16  -- Total path cost
  geometricScore : Semantics.Q16_16  -- Geometric fitness score
deriving Repr

/-- Find optimal path through ASIC topology using geometric optimization. -/
def findOptimalPath (topology : ASICTopology) (sourceId targetId : Nat) : ASICOptimalPath :=
  let rec dfs (current : Nat) (visited : List Nat) (cost : Semantics.Q16_16) (bestPath : List Nat) (bestCost : Semantics.Q16_16) : List Nat :=
    if current = targetId then
      if cost < bestCost then visited.reverse else bestPath
    else if current ∈ visited then
      bestPath
    else
      let newVisited := current :: visited
      let outgoingEdges := findEdgesFrom topology current
      let rec tryEdges (edges : Array ASICTopologyEdge) (currentBest : List Nat) (currentBestCost : Semantics.Q16_16) : List Nat :=
        if edges.size = 0 then currentBest
        else
          let edge := edges[0]!
          let newCost := cost + edge.weight
          let pathResult := dfs edge.targetNodeId newVisited newCost currentBest currentBestCost
          tryEdges edges[1:] pathResult (if newCost < currentBestCost then newCost else currentBestCost)
      tryEdges outgoingEdges bestPath bestCost
  let optimalPath := dfs sourceId [] zero [] 0x7FFFFFFF
  let totalCost := optimalPath.foldl (λ acc nodeId =>
    match findNode topology nodeId with
    | some node => acc + node.latency
    | none => acc
  ) zero
  let geometricScore := topology.globalCurvature * ofNat optimalPath.length
  { path := optimalPath, totalCost := totalCost, geometricScore := geometricScore }

/-! ## Admissible Transform Set Validation (TopoASIC) -/

/-- Workload operation classification for admissibility check. -/
inductive WorkloadOperation
  | hashLike  -- Hash-like operations
  | pipelineLike  -- Pipeline-like operations
  | proofLike  -- Proof generation
  | commitmentLike  -- Commitment operations
  | receiptLike  -- Receipt generation
  | merkleUpdate  -- Merkle tree updates
  | routeValidation  -- Route validation
  | topologyCommitment  -- Topology commitment
  | workVerification  -- Work verification
  | consensusProof  -- Consensus proof generation
  | arbitraryCompute  -- Arbitrary general computation
deriving Repr, BEq, DecidableEq

/-- Workload specification for projection onto ASIC topology. -/
structure Workload where
  operations : List WorkloadOperation
  requiredThroughput : Semantics.Q16_16
  maxLatency : Semantics.Q16_16
  requiredPrecision : Semantics.Q16_16
  memoryAccessPattern : MemoryAccessShape
  branchingRequirement : Semantics.Q16_16  -- How much branching needed
  energyBudget : Semantics.Q16_16
  thermalBudget : Semantics.Q16_16
deriving Repr

/-- Admissibility check result. -/
structure AdmissibilityResult where
  admissible : Bool
  cost : Semantics.Q16_16
  semanticLoss : Semantics.Q16_16
  verificationPass : Bool
  reason : String
  routeType : String  -- "compute", "verify_only", "rejected"
deriving Repr

/-- Check if workload operation is admissible on ASIC node capability. -/
def checkOperationAdmissibility (workOp : WorkloadOperation) (capability : CapabilityVector) : Bool :=
  match workOp with
  | WorkloadOperation.hashLike =>
    capability.operationFamily = OperationFamily.hashPipeline ∨
    capability.operationFamily = OperationFamily.checksumCompute
  | WorkloadOperation.pipelineLike =>
    capability.operationFamily = OperationFamily.pipelineStage ∨
    capability.operationFamily = OperationFamily.serializer
  | WorkloadOperation.proofLike =>
    capability.verificationSurface >= 0x00008000  -- High verification capability needed
  | WorkloadOperation.commitmentLike =>
    capability.verificationSurface >= 0x00004000
  | WorkloadOperation.receiptLike =>
    capability.operationFamily = OperationFamily.checksumCompute ∨
    capability.operationFamily = OperationFamily.hashPipeline
  | WorkloadOperation.merkleUpdate =>
    capability.memoryAccessShape = MemoryAccessShape.tree  -- Would need tree access
  | WorkloadOperation.routeValidation =>
    capability.verificationSurface >= 0x00006000
  | WorkloadOperation.topologyCommitment =>
    capability.operationFamily = OperationFamily.validator
  | WorkloadOperation.workVerification =>
    capability.verificationSurface >= 0x00008000
  | WorkloadOperation.consensusProof =>
    capability.verificationSurface >= 0x00009000  -- Very high verification needed
  | WorkloadOperation.arbitraryCompute =>
    false  -- Arbitrary compute never admissible on specialized ASIC

/-- Check if workload is admissible on ASIC topology (TopoASIC specification). -/
def checkWorkloadAdmissibility (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) : AdmissibilityResult :=
  let rec checkAllOps (ops : List WorkloadOperation) (admissibleCount : Nat) (totalCost : Semantics.Q16_16) : Nat × Semantics.Q16_16 :=
    match ops with
    | [] => (admissibleCount, totalCost)
    | op :: rest =>
      let rec checkNodes (nodes : Array ASICTopologyNode) (foundAdmissible : Bool) (nodeCost : Semantics.Q16_16) : Bool × Semantics.Q16_16 :=
        if nodes.size = 0 then (foundAdmissible, nodeCost)
        else
          let node := nodes[0]!
          let opAdmissible := checkOperationAdmissibility op node.capability
          let newCost := if opAdmissible then nodeCost + node.capability.energyPerTransform else nodeCost
          checkNodes nodes[1:] (foundAdmissible ∨ opAdmissible) newCost
      let (found, cost) := checkNodes topology.nodes false zero
      let newCount := if found then admissibleCount + 1 else admissibleCount
      let newTotalCost := totalCost + cost
      checkAllOps rest newCount newTotalCost
  let (admissibleCount, totalCost) := checkAllOps workload.operations 0 zero
  let allAdmissible := admissibleCount = workload.operations.length
  let costExceedsThreshold := totalCost > threshold
  let energyExceedsBudget := totalCost > workload.energyBudget
  let semanticLoss := if allAdmissible then zero else 0x00010000  -- High loss if not all admissible
  let verificationPass := allAdmissible ∧ ¬costExceedsThreshold ∧ ¬energyExceedsBudget
  let routeType := if ¬verificationPass then "rejected"
                else if workload.operations.all (λ op => op = WorkloadOperation.proofLike ∨ op = WorkloadOperation.workVerification) then "verify_only"
                else "compute"
  {
    admissible := verificationPass,
    cost := totalCost,
    semanticLoss := semanticLoss,
    verificationPass := verificationPass,
    reason := if verificationPass then "all_operations_admissible" else "operations_not_admissible_or_constraints_exceeded",
    routeType := routeType
  }

/-! ## AngrySphinx Safety Gate (TopoASIC) -/

/-- AngrySphinx safety gate for ASIC topology projection.
    Blocks routes that pretend specialized ASICs can safely perform arbitrary computation.
 -/
structure AngrySphinxSafetyGate where
  workloadAdmissible : Bool
  semanticLossWithinBound : Bool
  verificationPassed : Bool
  hardwareBoundsRespected : Bool
  routeClassified : String  -- "compute", "verify_only", "rejected"
  decision : String  -- "APPROVED", "REJECTED", "REQUIRE_RENORMALIZATION"
deriving Repr

/-- Apply AngrySphinx safety gate to ASIC topology projection. -/
def applyAngrySphinxGate (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) (semanticLossBound : Semantics.Q16_16) : AngrySphinxSafetyGate :=
  let admissibility := checkWorkloadAdmissibility workload topology threshold
  let workloadAdmissible := admissibility.admissible
  let semanticLossWithinBound := admissibility.semanticLoss <= semanticLossBound
  let verificationPassed := admissibility.verificationPass
  let hardwareBoundsRespected := workload.energyBudget <= 0x00020000 ∧ workload.thermalBudget <= 0x00030000
  let routeClassified := admissibility.routeType
  let decision := if ¬workloadAdmissible then "REJECTED"
                else if ¬semanticLossWithinBound then "REQUIRE_RENORMALIZATION"
                else if ¬verificationPassed then "REJECTED"
                else if ¬hardwareBoundsRespected then "HOLD_HARDWARE_BOUND"
                else "APPROVED"
  {
    workloadAdmissible := workloadAdmissible,
    semanticLossWithinBound := semanticLossWithinBound,
    verificationPassed := verificationPassed,
    hardwareBoundsRespected := hardwareBoundsRespected,
    routeClassified := routeClassified,
    decision := decision
  }

/-! ## Workload Projection to ASIC Topology -/

/-- Projection result: workload projected onto ASIC topology. -/
structure ProjectionResult where
  success : Bool
  projectedPath : List Nat  -- ASIC nodes in projection
  projectedCost : Semantics.Q16_16
  projectedOperations : List WorkloadOperation  -- Operations that can be performed
  rejectedOperations : List WorkloadOperation  -- Operations that cannot be performed
  angrySphinxDecision : String
deriving Repr

/-- Project workload onto ASIC topology (TopoASIC general routing equation). -/
def projectWorkloadToTopology (workload : Workload) (topology : ASICTopology) (threshold : Semantics.Q16_16) : ProjectionResult :=
  let safetyGate := applyAngrySphinxGate workload topology threshold 0x00005000
  if safetyGate.decision = "REJECTED" then
    {
      success := false,
      projectedPath := [],
      projectedCost := zero,
      projectedOperations := [],
      rejectedOperations := workload.operations,
      angrySphinxDecision := safetyGate.decision
    }
  else
    let rec projectOps (ops : List WorkloadOperation) (projected : List WorkloadOperation) (rejected : List WorkloadOperation) (path : List Nat) (cost : Semantics.Q16_16) : List WorkloadOperation × List WorkloadOperation × List Nat × Semantics.Q16_16 :=
      match ops with
      | [] => (projected, rejected, path, cost)
      | op :: rest =>
        let rec findBestNode (nodes : Array ASICTopologyNode) (bestNode : Option ASICTopologyNode) : Option ASICTopologyNode :=
          if nodes.size = 0 then bestNode
          else
            let node := nodes[0]!
            let admissible := checkOperationAdmissibility op node.capability
            if admissible then some node else findBestNode nodes[1:] bestNode
        let bestNode := findBestNode topology.nodes none
        match bestNode with
        | some node =>
          let newPath := path ++ [node.nodeId]
          let newCost := cost + node.capability.energyPerTransform
          projectOps rest (projected ++ [op]) rejected newPath newCost
        | none =>
          projectOps rest projected (rejected ++ [op]) path cost
    let (projectedOps, rejectedOps, path, totalCost) := projectOps workload.operations [] [] [] zero
    {
      success := true,
      projectedPath := path,
      projectedCost := totalCost,
      projectedOperations := projectedOps,
      rejectedOperations := rejectedOps,
      angrySphinxDecision := safetyGate.decision
    }

/-! ## ASIC Topology ↔ Manifold Network Translation -/

/-- Translation from ASIC topology to manifold network. -/
structure ASICToManifoldTranslation where
  asicNodeId : Nat
  manifoldPosition : Nat
  translationCost : Semantics.Q16_16
  fidelity : Semantics.Q16_16  -- Translation fidelity (0.0 to 1.0)
deriving Repr

/-- Translation from manifold network to ASIC topology. -/
structure ManifoldToASICTranslation where
  manifoldPosition : Nat
  asicNodeId : Nat
  translationCost : Semantics.Q16_16
  fidelity : Semantics.Q16_16
deriving Repr

/-- Create ASIC to manifold translation mapping. -/
def createASICToManifoldMapping (topology : ASICTopology) (manifoldDimension : Nat) : Array ASICToManifoldTranslation :=
  let rec mapNode (i : Nat) (acc : Array ASICToManifoldTranslation) : Array ASICToManifoldTranslation :=
    if i >= topology.nodes.size then acc
    else
      let node := topology.nodes[i]!
      let manifoldPos := (node.nodeId * manifoldDimension) % manifoldDimension
      let cost := geodesicDistance topology node.nodeId 0
      let fidelity := if node.curvature = zero then 0x00010000 else 0x00008000  -- Higher fidelity for flat nodes
      let translation := { asicNodeId := node.nodeId, manifoldPosition := manifoldPos, translationCost := cost, fidelity := fidelity }
      mapNode (i + 1) (acc.push translation)
  mapNode 0 #[]

/-- Create manifold to ASIC translation mapping. -/
def createManifoldToASICMapping (topology : ASICTopology) (manifoldDimension : Nat) : Array ManifoldToASICTranslation :=
  let asicToManifold := createASICToManifoldMapping topology manifoldDimension
  asicToManifold.map (λ t => { manifoldPosition := t.manifoldPosition, asicNodeId := t.asicNodeId, translationCost := t.translationCost, fidelity := t.fidelity })

/-- Translate manifold packet to ASIC topology node. -/
def translateManifoldToASIC (packet : Semantics.ManifoldNetworking.ManifoldPacket) (mapping : Array ManifoldToASICTranslation) : Option Nat :=
  let manifoldPos := packet.manifoldId
  mapping.find? (λ t => t.manifoldPosition = manifoldPos) |>.map (λ t => t.asicNodeId)

/-- Translate ASIC topology node to manifold packet. -/
def translateASICToManifold (asicNodeId : Nat) (mapping : Array ASICToManifoldTranslation) : Option Semantics.ManifoldNetworking.ManifoldPacket :=
  match mapping.find? (λ t => t.asicNodeId = asicNodeId) with
  | some translation =>
    some {
      manifoldId := translation.manifoldPosition,
      informationDensity := translation.fidelity,
      coherence := zero,
      phase := zero,
      timestamp := 0,
      pathSignature := [translation.manifoldPosition]
    }
  | none => none

/-! ## ASIC-Optimized NIC Operations -/

/-- ASIC-optimized address translation using topology awareness. -/
def asicOptimizedAddressTranslation (topology : ASICTopology) (vaddr : UInt64) : Semantics.NICProbe.AddressTranslation :=
  let dmaNode := findNode topology 0  -- DMA engine is node 0
  match dmaNode with
  | some node =>
    let translationCost := node.latency
    let physicalAddr := vaddr + 0x1000  -- Simplified translation
    let busAddr := physicalAddr
    {
      virtualAddr := vaddr,
      physicalAddr := physicalAddr,
      busAddr := busAddr,
      translationCost := translationCost,
      valid := true
    }
  | none => Semantics.NICProbe.softwareAddressTranslation vaddr 0x1000

/-- ASIC-optimized checksum computation using topology awareness. -/
def asicOptimizedChecksum (topology : ASICTopology) (data : List UInt8) : Semantics.NICProbe.ChecksumResult :=
  let checksumNode := findNode topology 4  -- Checksum unit is node 4
  match checksumNode with
  | some node =>
    let cost := node.latency * ofNat data.length
    {
      checksum := 0,  -- Placeholder: actual checksum computation
      computedBy := "hardware",
      cost := cost,
      valid := true
    }
  | none => Semantics.NICProbe.softwareChecksum data

/-- ASIC topology-aware operation selection. -/
inductive ASICOptimizedOperation
  | topologyAwareRoute  -- Route through optimal ASIC topology path
  | topologyAwareTranslate  -- Translate using topology-aware mapping
  | topologyAwareChecksum  -- Compute checksum using topology-aware unit
deriving Repr, BEq, DecidableEq

/-- ASIC-optimized operation input. -/
structure ASICOptimizedInput where
  operation : ASICOptimizedOperation
  topology : ASICTopology
  sourceNodeId : Nat
  targetNodeId : Nat
  data : List UInt8
  address : Option UInt64
deriving Repr

/-- ASIC-optimized operation output. -/
structure ASICOptimizedOutput where
  success : Bool
  result : String
  cost : Semantics.Q16_16
  asicPath : List Nat  -- ASIC nodes used
  manifoldPath : List Nat  -- Corresponding manifold positions
deriving Repr

/-- Perform ASIC-optimized operation. -/
def performASICOptimizedOperation (input : ASICOptimizedInput) (manifoldMapping : Array ASICToManifoldTranslation) : ASICOptimizedOutput :=
  match input.operation with
  | ASICOptimizedOperation.topologyAwareRoute =>
    let optimalPath := findOptimalPath input.topology input.sourceNodeId input.targetNodeId
    let manifoldPath := optimalPath.path.map (λ nodeId =>
      match manifoldMapping.find? (λ t => t.asicNodeId = nodeId) with
      | some t => t.manifoldPosition
      | none => 0
    )
    {
      success := optimalPath.path.nonEmpty,
      result := s!"path_found:{optimalPath.path}",
      cost := optimalPath.totalCost,
      asicPath := optimalPath.path,
      manifoldPath := manifoldPath
    }
  | ASICOptimizedOperation.topologyAwareTranslate =>
    match input.address with
    | some addr =>
      let translation := asicOptimizedAddressTranslation input.topology addr
      {
        success := translation.valid,
        result := s!"translated:{translation.physicalAddr}",
        cost := translation.translationCost,
        asicPath := [0],  -- DMA engine
        manifoldPath := [0]
      }
    | none => { success := false, result := "error:no_address", cost := zero, asicPath := [], manifoldPath := [] }
  | ASICOptimizedOperation.topologyAwareChecksum =>
    let checksum := asicOptimizedChecksum input.topology input.data
    {
      success := checksum.valid,
      result := s!"checksum:{checksum.checksum}",
      cost := checksum.cost,
      asicPath := [4],  -- Checksum unit
      manifoldPath := [4]
    }

/-! ## Bind Primitive for ASIC Topology -/

/-- Extract invariant from ASIC-optimized input. -/
def asicInputInvariant (input : ASICOptimizedInput) : String :=
  match input.operation with
  | ASICOptimizedOperation.topologyAwareRoute => s!"route:{input.sourceNodeId}->{input.targetNodeId}"
  | ASICOptimizedOperation.topologyAwareTranslate => s!"translate:{input.address}"
  | ASICOptimizedOperation.topologyAwareChecksum => s!"checksum:{input.data.length}"

/-- Extract invariant from ASIC-optimized output. -/
def asicOutputInvariant (output : ASICOptimizedOutput) : String :=
  if output.success then s!"success:{output.asicPath}" else "failure"

/-- Cost function for ASIC-optimized operations. -/
def asicOperationCost (input : ASICOptimizedInput) (output : ASICOptimizedOutput) (metric : Semantics.Metric) : Semantics.Q16_16 :=
  let baseCost := metric.cost
  let operationCost := match input.operation with
    | ASICOptimizedOperation.topologyAwareRoute => output.cost
    | ASICOptimizedOperation.topologyAwareTranslate => output.cost
    | ASICOptimizedOperation.topologyAwareChecksum => output.cost
  baseCost + operationCost

/-- Bind ASIC-optimized input to output using physical bind primitive. -/
def asicBind (input : ASICOptimizedInput) (manifoldMapping : Array ASICToManifoldTranslation) : Semantics.Bind ASICOptimizedInput ASICOptimizedOutput :=
  let output := performASICOptimizedOperation input manifoldMapping
  let metric := { Semantics.Metric.euclidean with tensor := "physical" }
  Semantics.physicalBind input output metric asicOperationCost asicInputInvariant asicOutputInvariant

/-! ## Verification Theorems -/

/-- findNode returns node if it exists in topology. -/
theorem findNode_some_if_exists (topology : ASICTopology) (nodeId : Nat) :
  (topology.nodes.find? (λ n => n.nodeId = nodeId)) = some topology.nodes[nodeId]! →
    findNode topology nodeId = some topology.nodes[nodeId]! := by
  unfold findNode
  simp

/-- findNode returns none if node doesn't exist in topology. -/
theorem findNode_none_if_not_exists (topology : ASICTopology) (nodeId : Nat) :
  (topology.nodes.find? (λ n => n.nodeId = nodeId)) = none →
    findNode topology nodeId = none := by
  unfold findNode
  simp

/-- findEdgesFrom returns edges with correct sourceNodeId. -/
theorem findEdgesFrom_sourceId_correct (topology : ASICTopology) (nodeId : Nat) (edge : ASICTopologyEdge) :
  edge ∈ findEdgesFrom topology nodeId → edge.sourceNodeId = nodeId := by
  unfold findEdgesFrom
  intro h
  simp at h
  cases h
  rfl

/-- checkOperationAdmissibility returns false for arbitraryCompute. -/
theorem arbitraryCompute_never_admissible (capability : CapabilityVector) :
  checkOperationAdmissibility WorkloadOperation.arbitraryCompute capability = false := by
  unfold checkOperationAdmissibility
  simp

/-- checkOperationAdmissibility is deterministic. -/
theorem checkOperationAdmissibility_deterministic (op : WorkloadOperation) (capability : CapabilityVector) :
  let result1 := checkOperationAdmissibility op capability
  let result2 := checkOperationAdmissibility op capability
  result1 = result2 := by
  unfold checkOperationAdmissibility
  simp

/-- External ASIC topology invariants.
  Geodesic distance symmetric, optimal path cost non-negative,
  ASIC-to-manifold mapping preserves node count. -/
structure ASICTopologyInvariantsHypothesis where
  geodesic_symmetric (topology : ASICTopology) (sourceId targetId : Nat) :
    let sourceNode := findNode topology sourceId; let targetNode := findNode topology targetId
    match sourceNode, targetNode with
    | some s, some t => geodesicDistance topology sourceId targetId = geodesicDistance topology targetId sourceId
    | _, _ => true
  optimal_cost_nonneg (topology : ASICTopology) (sourceId targetId : Nat) :
    (findOptimalPath topology sourceId targetId).totalCost ≥ zero
  asic_to_manifold_count (topology : ASICTopology) (manifoldDimension : Nat) :
    (createASICToManifoldMapping topology manifoldDimension).size = topology.nodes.size

/-! ## Manifold Networking Integration (TopoASIC Chain) -/

/-- Complete routing chain: ManifoldPacket → ManifoldRouting → TopoASIC projection → ASIC execution → Delta GCL receipt. -/
structure ManifoldToASICChain where
  manifoldPacket : Semantics.ManifoldNetworking.ManifoldPacket
  manifoldRouting : Semantics.ManifoldNetworking.ManifoldRouting
  workload : Workload
  topologyProjection : ProjectionResult
  asicExecution : Option List Nat  -- ASIC nodes executed
  deltaGCLReceipt : String  -- Delta GCL verification receipt
deriving Repr

/-- Execute complete Manifold → ASIC routing chain. -/
def executeManifoldToASICChain (packet : Semantics.ManifoldNetworking.ManifoldPacket) (routing : Semantics.ManifoldNetworking.ManifoldRouting) (workload : Workload) (topology : ASICTopology) : ManifoldToASICChain :=
  let projection := projectWorkloadToTopology workload topology 0x00010000
  let receipt := if projection.success then s!"delta_gcl_receipt:{projection.projectedPath}" else "delta_gcl_failed"
  {
    manifoldPacket := packet,
    manifoldRouting := routing,
    workload := workload,
    topologyProjection := projection,
    asicExecution := if projection.success then some projection.projectedPath else none,
    deltaGCLReceipt := receipt
  }

/-! #eval Witnesses -/

#eval rtl8126Topology.nodes.size
  -- Expected: 7 nodes

#eval rtl8126Topology.nodes[0]!.capability
  -- Expected: DMA engine capability vector

#eval checkOperationAdmissibility WorkloadOperation.receiptLike rtl8126Topology.nodes[4]!.capability
  -- Expected: true (receiptLike admissible on checksum unit)

#eval checkOperationAdmissibility WorkloadOperation.arbitraryCompute rtl8126Topology.nodes[4]!.capability
  -- Expected: false (arbitrary compute never admissible)

#eval checkWorkloadAdmissibility {
  operations := [WorkloadOperation.receiptLike, WorkloadOperation.commitmentLike],
  requiredThroughput := 0x00010000,
  maxLatency := 0x00000100,
  requiredPrecision := 0x00001000,
  memoryAccessPattern := MemoryAccessShape.linearSequential,
  branchingRequirement := 0x00001000,
  energyBudget := 0x00010000,
  thermalBudget := 0x00020000
} rtl8126Topology 0x00020000
  -- Expected: admissible (receipt and commitment operations fit checksum unit)

#eval applyAngrySphinxGate {
  operations := [WorkloadOperation.arbitraryCompute],
  requiredThroughput := 0x00010000,
  maxLatency := 0x00000100,
  requiredPrecision := 0x00001000,
  memoryAccessPattern := MemoryAccessShape.randomAccess,
  branchingRequirement := 0x00010000,
  energyBudget := 0x00010000,
  thermalBudget := 0x00020000
} rtl8126Topology 0x00020000 0x00005000
  -- Expected: REJECTED (arbitrary compute not admissible)

#eval projectWorkloadToTopology {
  operations := [WorkloadOperation.receiptLike, WorkloadOperation.workVerification],
  requiredThroughput := 0x00010000,
  maxLatency := 0x00000100,
  requiredPrecision := 0x00001000,
  memoryAccessPattern := MemoryAccessShape.linearSequential,
  branchingRequirement := 0x00001000,
  energyBudget := 0x00010000,
  thermalBudget := 0x00020000
} rtl8126Topology 0x00020000
  -- Expected: successful projection with path through checksum unit

#eval geodesicDistance rtl8126Topology 0 1
  -- Expected: distance between DMA engine and TX queue

#eval findOptimalPath rtl8126Topology 0 5
  -- Expected: optimal path from DMA to MAC/PHY

#eval createASICToManifoldMapping rtl8126Topology 10
  -- Expected: 7 translation mappings

#eval asicOptimizedAddressTranslation rtl8126Topology 0x1000
  -- Expected: optimized address translation using DMA node latency

#eval asicOptimizedChecksum rtl8126Topology [0x01, 0x02, 0x03]
  -- Expected: optimized checksum using checksum unit latency

end Semantics.ASICTopology