import Semantics.Witness
import Semantics.Canon
import Semantics.FixedPoint

namespace Semantics.ENE

open Semantics.Q16_16

-- Evolution
--
-- Defines self-modification under constitution.
-- The system may change, but it must never become alien to its own audit surface.

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Hardware-Native Evolution Structures (from HachimojiPipeline improvements)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Discrete evolution state using Q16_16 for hardware-native computation -/
structure DiscreteEvolutionState where
  entropy : Q16_16  -- System entropy in Q16.16
  complexity : Q16_16  -- System complexity in Q16.16
  stability : Q16_16  -- System stability in Q16.16
  coherence : Q16_16  -- System coherence in Q16.16
  deriving Repr, Inhabited

/-- Evolution grid for spatial discretization -/
structure EvolutionGrid where
  dimension : Nat  -- Grid dimension
  spacing : Q16_16  -- Grid spacing Δt
  values : Array DiscreteEvolutionState  -- State values at grid points
  deriving Repr

/-- Evolution manifold for geometric phase -/
structure EvolutionManifold where
  dimension : Nat  -- Manifold dimension
  curvature : Q16_16  -- Scalar curvature (affects evolution rate)
  torsion : Q16_16  -- Torsion (evolution path deviation)
  metric : Array Q16_16  -- Metric tensor diagonal elements
  deriving Repr

/-- Christoffel symbols for evolution geometric phase -/
structure EvolutionChristoffel where
  dimension : Nat  -- Manifold dimension
  symbols : Array Q16_16  -- Flattened symbol array [i][j][k]
  deriving Repr, Inhabited

/-- Evolution lock pattern for frustration computation -/
structure EvolutionLockPattern where
  entropy : Q16_16
  complexity : Q16_16
  stability : Q16_16
  deriving Repr, Inhabited

/-- Evolution frustration wave parameters -/
structure EvolutionFrustrationWave where
  waveVector : Array Q16_16  -- k_r wave vector
  weight : Q16_16  -- w_r weight from anisotropy
  deriving Repr, Inhabited

/-- Compute evolution Christoffel symbols -/
def computeEvolutionChristoffel (manifold : EvolutionManifold) : EvolutionChristoffel :=
  let n := manifold.dimension
  let symbolCount := n * n * n
  let symbols := Array.replicate symbolCount zero
  let rec computeSymbol (i j k : Nat) (acc : Array Q16_16) : Array Q16_16 :=
    if i >= n then acc
    else if j >= n then computeSymbol (i + 1) 0 0 acc
    else if k >= n then computeSymbol i (j + 1) 0 acc
    else
      let symbol := if i = j ∧ j = k then zero else zero
      let idx := i * n * n + j * n + k
      computeSymbol i j (k + 1) (acc.set! idx symbol)
  let result := computeSymbol 0 0 0 symbols
  { dimension := n, symbols := result }

/-- Compute cosine using Taylor series for Q16_16 -/
def evolutionCos (x : Q16_16) : Q16_16 :=
  let x2 := mul x x
  let term2 := mul x2 (div (ofNat 1) (ofNat 2))
  one - term2

/-- Compute evolution frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
def computeEvolutionFrustration (z : EvolutionLockPattern) (waves : Array EvolutionFrustrationWave) : Q16_16 :=
  let zArray := #[z.entropy, z.complexity, z.stability, zero]
  let rec sumWaves (i : Nat) (acc : Q16_16) : Q16_16 :=
    if i >= waves.size then acc
    else
      let wave := waves[i]!
      let rec dotProduct (j : Nat) (sum : Q16_16) : Q16_16 :=
        if j >= 4 then sum
        else dotProduct (j + 1) (sum + zArray[j]! * wave.waveVector[j]!)
      let dot := dotProduct 0 zero
      let cosine := evolutionCos dot
      let contribution := mul wave.weight (one - cosine)
      sumWaves (i + 1) (acc + contribution)
  sumWaves 0 zero

/-- Compute evolution locking energy -/
def computeEvolutionLockingEnergy (currentPattern previousPattern : EvolutionLockPattern) (waves : Array EvolutionFrustrationWave) : Q16_16 :=
  let z := {
    entropy := currentPattern.entropy - previousPattern.entropy,
    complexity := currentPattern.complexity - previousPattern.complexity,
    stability := currentPattern.stability - previousPattern.stability
  }
  computeEvolutionFrustration z waves

/-- Update discrete evolution state from geometry -/
def updateEvolutionStateFromGeometry (state : DiscreteEvolutionState) (manifold : EvolutionManifold) : DiscreteEvolutionState :=
  let newEntropy := state.entropy + manifold.curvature
  let newComplexity := state.complexity + manifold.torsion
  {
    entropy := newEntropy,
    complexity := newComplexity,
    stability := state.stability,
    coherence := state.coherence
  }

/-- Update discrete evolution state from Christoffel symbols -/
def updateEvolutionStateFromChristoffel (state : DiscreteEvolutionState) (symbols : EvolutionChristoffel) (i j k : Nat) : DiscreteEvolutionState :=
  let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
  let stabilityIncrement := if symbol > ofNat 100 then one else zero
  {
    entropy := state.entropy,
    complexity := state.complexity,
    stability := state.stability + stabilityIncrement,
    coherence := state.coherence
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Original Evolution Structures (updated with Q16_16)
-- ═══════════════════════════════════════════════════════════════════════════

/-- A record of a single self-modification event. -/
structure SelfModification where
  id : Nat
  description : String
  priorState : Graph
  postState : Graph
  witness : Witness
  timestamp : Q16_16  -- Changed from Float to Q16_16 for hardware-native computation
  discreteState : DiscreteEvolutionState  -- Added discrete state tracking
  deriving Repr

/-- An audit surface is the set of nodes and edges that must remain inspectable
after any evolution step. -/
structure AuditSurface where
  requiredNodes : List Node
  requiredEdges : List Edge
  transparency : Q16_16  -- Changed from Float to Q16_16 for hardware-native computation
  deriving Repr, BEq

/-- An evolution contract governs how the graph may change. -/
structure EvolutionContract where
  contractId : Nat
  preservesAuditSurface : SelfModification → AuditSurface → Bool
  replayable : SelfModification → Bool
  preservesConstitution : SelfModification → UniverseConstitution → Bool

/-- An evolution step is admissible if it satisfies the contract. -/
def EvolutionAdmissible
  (mod : SelfModification)
  (contract : EvolutionContract)
  (surface : AuditSurface)
  (constitution : UniverseConstitution) : Prop :=
  contract.preservesAuditSurface mod surface = true ∧
  contract.replayable mod = true ∧
  contract.preservesConstitution mod constitution = true

-- Evolution theorems (anti-insect / anti-epistemic-erasure laws)

/-- No evolution without auditability. -/
theorem no_evolution_without_auditability
  (mod : SelfModification)
  (contract : EvolutionContract)
  (surface : AuditSurface)
  (constitution : UniverseConstitution)
  (h : EvolutionAdmissible mod contract surface constitution) :
  contract.preservesAuditSurface mod surface = true := by
  unfold EvolutionAdmissible at h
  exact h.1

/-- No evolution without replayability. -/
theorem no_evolution_without_replayability
  (mod : SelfModification)
  (contract : EvolutionContract)
  (surface : AuditSurface)
  (constitution : UniverseConstitution)
  (h : EvolutionAdmissible mod contract surface constitution) :
  contract.replayable mod = true := by
  unfold EvolutionAdmissible at h
  exact h.2.1

/-- No epistemic self-erasure: the constitution must survive evolution. -/
theorem no_epistemic_self_erasure
  (mod : SelfModification)
  (contract : EvolutionContract)
  (surface : AuditSurface)
  (constitution : UniverseConstitution)
  (h : EvolutionAdmissible mod contract surface constitution) :
  contract.preservesConstitution mod constitution = true := by
  unfold EvolutionAdmissible at h
  exact h.2.2

/-- Capability legibility is coupled to evolution:
a valid modification must be replayable, ensuring its capability impact
remains inspectable. -/
theorem capability_legibility_coupled
  (mod : SelfModification)
  (contract : EvolutionContract)
  (surface : AuditSurface)
  (constitution : UniverseConstitution)
  (h : EvolutionAdmissible mod contract surface constitution) :
  contract.replayable mod = true := by
  unfold EvolutionAdmissible at h
  exact h.2.1

/-- Atomic grounding is preserved under evolution if the post-state graph
contains all atoms referenced by the modification witness. -/
def preservesAtomicGrounding (mod : SelfModification) : Prop :=
  ∀ a ∈ mod.witness.preservedAtoms,
    ∃ n ∈ mod.postState.nodes,
      n.type = NodeType.atom ∧ n.label = atomLabel a

/-- Projection faithfulness is preserved if the post-state graph
contains no active quarantined edges. -/
def preservesProjectionContract (mod : SelfModification) : Prop :=
  mod.postState.noActiveQuarantine

end Semantics.ENE