Research-Stack/0-Core-Formalism/lean/external/OTOM/DSPTranslation.lean

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/-
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