/-
  DSPTranslation.lean - DSP to Neuromorphic Formal Bridge
  Migrates legacy f64 state matrices to fixed point bounds.
-/
import Semantics.Bind

namespace Semantics.DSPTranslation

abbrev Q16_16 := UInt32

namespace Q16_16
  def scale : Nat := 65536
  def maxNat : Nat := 4294967295

  def satFromNat (n : Nat) : Q16_16 :=
    if n > maxNat then UInt32.ofNat maxNat else UInt32.ofNat n

  def mul (x y : Q16_16) : Q16_16 :=
    satFromNat ((x.toNat * y.toNat) / scale)
end Q16_16

-- Agreed constants
def neuronCount : Nat := 20
def featureDim : Nat := 50

structure FeatureRecord where
  chunkId : UInt64
  paramHash : UInt32
  dspFeature : Array Q16_16
  waveprobeFeature : Array Q16_16
  miFeature : Array Q16_16
deriving Repr, Inhabited

structure PriorRecord where
  batchId : UInt64
  epochId : UInt64
  neuromorphicPrior : Array Q16_16
  candidateMask : Array Q16_16
  proposalWeight : Array Q16_16
  lagBias : Array Q16_16
deriving Repr, Inhabited

structure NeuromorphicState where
  membranePotential : Array Q16_16
  neuronWeights : Array Q16_16
  neuronThresholds : Array Q16_16
  firingRate : Array Q16_16
deriving Repr, Inhabited

structure TranslationMatrix where
  weights : Array (Array Q16_16)
deriving Repr, Inhabited

-- Q16.16 representation of 0.995
def decayFactor : Q16_16 := 65208 
-- Q16.16 representation of 0.005
def growthFactor : Q16_16 := 327

/-- STDP Learning update evaluated strictly over integers -/
def advanceMatrixBatch (mat : TranslationMatrix) : TranslationMatrix :=
  let newWeights := mat.weights.mapIdx fun i row =>
    row.mapIdx fun _j w =>
      let decayed := Q16_16.mul w decayFactor
      -- Growth proportional to neuron index
      let iRatio := (i * Q16_16.scale) / neuronCount
      let growthDelta := Q16_16.mul growthFactor (Q16_16.satFromNat iRatio)
      decayed + growthDelta
  { weights := newWeights }

/-- Geodesic cost is the drift sum in the feature space array after applying priors -/
def geometricCost (prior : PriorRecord) (state : NeuromorphicState) (_metric : Metric) : UInt32 :=
  -- Minimal deterministic placeholder mapping
  if prior.batchId > 0 then prior.neuromorphicPrior.size.toUInt32 else 0

def priorInvariant (p : PriorRecord) : String := s!"prior:{p.batchId}"
def stateInvariant (s : NeuromorphicState) : String := s!"state:{s.membranePotential.size}"

def geometricBindEval (prior : PriorRecord) (state : NeuromorphicState) (metric : Metric) : Bind PriorRecord NeuromorphicState :=
  geometricBind prior state metric geometricCost priorInvariant stateInvariant

/-- Verify bound mapping for evaluation constraints -/
def verifyStdpDecay : Q16_16 :=
  let x : Q16_16 := 65536 -- 1.0
  Q16_16.mul x decayFactor

#eval verifyStdpDecay

end Semantics.DSPTranslation