-- M002: Entropy Encoding Kernel Module
-- Source: shannon_entropy_v1 (3-Mathematical-Models)
-- Kernel Function: DeltaCompressor
--
-- Shannon entropy H(X) = -Σ p(x) log₂ p(x)
-- Used for adaptive compression ratio estimation.
-- Truth Seal: [ SSS-ENE-ENTROPY-2026-05-03 ]

module M002_EntropyEncoding where

import BaseTypes
import Semantics.Q0_16 (Q0_16)

structure SymbolDistribution where
  symbols   : Array UInt8
  counts    : Array Nat
  total     : Nat
  
def shannonEntropy (dist : SymbolDistribution) : Q0_16 :=
  let entropy := dist.counts.foldl (\acc count =>
    if count == 0 then acc
    else
      let p := count.toFloat / dist.total.toFloat
      acc - p * log₂ p
  ) 0.0
  Q0_16.ofFloat (entropy / 8.0)  -- Normalize to [0,1] (max entropy = 8 bits)

-- Kernel interface: estimate compression ratio from entropy
def estimateCompressionRatio (data : Array UInt8) : IO CompressionEstimate := do
  let freqTable := frequencyTable data
  let entropy := shannonEntropy freqTable
  
  -- Theoretical minimum size = entropy × original_size
  -- Actual compression depends on model overhead
  let theoreticalRatio := entropy  -- Q0_16 [0,1]
  let modelOverhead := Q0_16.ofFloat 0.05  -- 5% for codon tables
  let predictedRatio := add theoreticalRatio modelOverhead
  
  return {
    entropy := entropy
    theoreticalRatio := theoreticalRatio
    predictedCompressedSize := (data.size.toFloat * predictedRatio.toFloat).toNat
    confidence := Q0_16.sub Q0_16.one (abs (Q0_16.sub entropy Q0_16.half))
  }

end M002_EntropyEncoding