import Semantics.FixedPoint
import Semantics.Canon

namespace Semantics.Transition

/-- 
The Regime type represents the operational mode of the substrate.
-/
inductive Regime
  | GROUNDED  -- Steady state, phonon stratum
  | SEISMIC   -- Entropic harvesting, exploration
  | FLAME     -- Structural emergency, silicon stratum
deriving Repr, BEq, DecidableEq

/--
Signature: 4-bit nibble summary from the Hutter extraction.
-/
structure Signature where
  s1 : UInt8
  s2 : UInt8
  s3 : UInt8
  s4 : UInt8

/--
Telemetry: Hardware/environmental feedback fields.
-/
structure Telemetry where
  drift     : Q16_16
  curvature : Q16_16
  entropy   : Q16_16

/--
Priority: Task-layer weights (e.g. from Linear/Notion).
-/
structure Priority where
  weight : Q16_16

/--
The Route Function: $route(sig(S_t), telemetry, priority)$
Selects the target regime based on cellular signal and substrate feedback.
-/
def route (sig : Signature) (tel : Telemetry) (prio : Priority) : Regime :=
  -- If entropy is extremely high, promote to FLAME (Emergency)
  if Q16_16.ge tel.entropy (Q16_16.mk 0x00050000) then .FLAME -- 5.0 entropy
  -- If curvature is high or priority is elevated, enter SEISMIC (Exploration)
  else if Q16_16.ge tel.curvature (Q16_16.mk 0x00010000) || Q16_16.ge prio.weight (Q16_16.mk 0x00020000) then .SEISMIC
  -- Default to GROUNDED (Steady state)
  else .GROUNDED

/--
The Apply Function: $apply(regime)$
Executes the state transition and generates the next canonical state.
-/
def apply (regime : Regime) (prev : CanonicalState) : CanonicalState :=
  match regime with
  | .GROUNDED => { prev with mode := .commit, tau := Q16_16.mk 0x00001000 } -- Low tension
  | .SEISMIC  => { prev with mode := .hold,   tau := Q16_16.mk 0x00008000 } -- Medium tension
  | .FLAME    => { prev with mode := .flame,  tau := Q16_16.mk 0x00020000 } -- High tension

/--
The Dynamic Transition Law: $S_{t+1} = apply(route(sig(S_t), telemetry, priority))$
-/
def step (sig : Signature) (tel : Telemetry) (prio : Priority) (curr : CanonicalState) : CanonicalState :=
  apply (route sig tel prio) curr

end Semantics.Transition