/-
  SLUQ.lean - SLUQ Decision Engine Formalization
-/
import Semantics.Bind

namespace Semantics.SLUQ

inductive SLUQState
| Stable   -- 00 : Cool, reliable
| Rising   -- 01 : Warming, monitor
| Unstable -- 10 : Overheating
| Reset    -- 11 : Snapped
deriving Repr, DecidableEq, Inhabited

inductive CMYK
| K
| C
| M
| Y
deriving Repr, DecidableEq, Inhabited

structure SluqNode where
  acc : UInt16
  phi : UInt8
  selectionCount : UInt32
deriving Repr, DecidableEq, Inhabited

def evaluateState (acc : UInt16) : SLUQState :=
  if acc.toNat < 0x4000 then .Stable
  else if acc.toNat < 0x8000 then .Rising
  else if acc.toNat < 0xC000 then .Unstable
  else .Reset

def evaluateStateInt (acc : UInt16) : UInt8 :=
  if acc.toNat < 0x4000 then 0
  else if acc.toNat < 0x8000 then 1
  else if acc.toNat < 0xC000 then 2
  else 3

def updateNode (node : SluqNode) (value : UInt8) : SluqNode :=
  let increase := value.toUInt16 * node.phi.toUInt16
  let newAcc := node.acc + increase
  let state := evaluateState newAcc
  if state == .Reset then
    { node with acc := 0, selectionCount := node.selectionCount + 1 }
  else
    { node with acc := newAcc, selectionCount := node.selectionCount + 1 }

def tempQ16 (acc : UInt16) : UInt32 :=
  -- Normalize to Q16.16 (65536 is 1.0)
  -- Since max acc is 65535, we can just use acc directly as the fractional part
  -- 0xFFFF -> ~1.0 in Q16.16
  acc.toUInt32

def sluqCost (nodeA nodeB : SluqNode) (_metric : Metric) : UInt32 :=
  let diff := if nodeB.acc > nodeA.acc then nodeB.acc - nodeA.acc else nodeA.acc - nodeB.acc
  diff.toUInt32

def sluqInvariant (node : SluqNode) : String :=
  let st := evaluateStateInt node.acc
  s!"state={st},acc={node.acc}"

def sluqBind (nodeA nodeB : SluqNode) (metric : Metric) : Bind SluqNode SluqNode :=
  thermodynamicBind nodeA nodeB metric sluqCost sluqInvariant sluqInvariant

#eval updateNode { acc := 0x3FFF, phi := 10, selectionCount := 5 } 1

end Semantics.SLUQ
