/-
  MechanicalLogic.lean - Formalization of Merkle Molecular Mechanical Logic
  Implements the "Locks and Balances" primitive system.
  Ref: arXiv:1801.03534 & arXiv:2505.05693
-/
import Semantics.FixedPoint
import Semantics.Bind

namespace Semantics.MechanicalLogic

open Q16_16

/-- 
  Mechanical State: A link can be Displaced (1) or Neutral (0).
  In fixed-point, we map 1.0 to Displaced.
-/
structure LinkState where
  displacement : Q16_16
deriving Repr, DecidableEq

/-- 
  A Mechanical Lock: Restricts displacement based on a control link.
  Formalized as a conditional constraint.
-/
def mechanicalLock (control input : LinkState) : LinkState :=
  -- If control is displaced (>= 0.5), input displacement is blocked (forced to 0).
  if control.displacement.val >= 32768 then
    { displacement := zero }
  else
    input

/-- 
  A Mechanical Balance: A reversible gate equivalent to a Fredkin or Toffoli primitive.
  Sums displacements and outputs the residual.
-/
def mechanicalBalance (a b c : LinkState) : LinkState :=
  let total := add a.displacement (add b.displacement c.displacement)
  { displacement := total }

/-- 
  Energy Dissipation: 
  The Landauer Limit at 300K is ~2.8e-21 Joules.
  Merkle 2025 claims 1e-24 Joules.
  
  In our Q16_16 model, we use a normalized 'Entropy Cost' where 1.0 = Landauer Limit.
-/
def landauerLimit : Q16_16 := one
def merkleDissipation : Q16_16 := Q16_16.ofRawInt 65 -- ~0.001 * Landauer Limit (approx 10^-24 vs 10^-21)

/-- 
  Verification: Is the operation 'Ultra-Efficient' (below Landauer)?
-/
def isUltraEfficient (cost : Q16_16) : Bool :=
  cost.val < landauerLimit.val

/-- 
  Mechanical Logic Invariant: 
  Conservation of mechanical work (simplified).
-/
def mechanicalInvariant (links : List LinkState) : String :=
  let sum := links.foldl (fun acc l => add acc l.displacement) zero
  s!"mech_work[{sum.val}]"

/-- #eval Witnesses -/
def neutral : LinkState := { displacement := zero }
def displaced : LinkState := { displacement := one }

-- Lock test: Blocked
#eval (mechanicalLock displaced displaced).displacement.val
-- Lock test: Clear
#eval (mechanicalLock neutral displaced).displacement.val
-- Efficiency check
#eval isUltraEfficient merkleDissipation

end Semantics.MechanicalLogic
