import Semantics.FixedPoint

namespace Semantics

open Semantics.Q16_16

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

/-- Discrete semantic state using Q16_16 for hardware-native computation -/
structure DiscreteSemanticState where
  activation : Q16_16  -- Semantic activation level
  salience : Q16_16  -- Semantic salience
  coherence : Q16_16  -- Semantic coherence
  entropy : Q16_16  -- Semantic entropy
  deriving Repr, Inhabited

/-- Semantic grid for spatial discretization -/
structure SemanticGrid where
  dimension : Nat  -- Grid dimension
  spacing : Q16_16  -- Grid spacing
  values : Array DiscreteSemanticState  -- State values at grid points
  deriving Repr

/-- Semantic manifold for geometric phase evolution -/
structure SemanticManifold where
  dimension : Nat  -- Manifold dimension
  curvature : Q16_16  -- Scalar curvature (affects semantic field)
  torsion : Q16_16  -- Torsion (semantic deviation)
  metric : Array Q16_16  -- Metric tensor diagonal elements
  deriving Repr

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

/-- Semantic lock pattern for frustration computation -/
structure SemanticLockPattern where
  activation : Q16_16
  salience : Q16_16
  coherence : Q16_16
  deriving Repr, Inhabited

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

/-- Compute semantic Christoffel symbols -/
def computeSemanticChristoffel (manifold : SemanticManifold) : SemanticChristoffel :=
  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 semanticCos (x : Q16_16) : Q16_16 :=
  let x2 := mul x x
  let term2 := mul x2 (div (ofNat 1) (ofNat 2))
  one - term2

/-- Compute semantic frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
def computeSemanticFrustration (z : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
  let zArray := #[z.activation, z.salience, z.coherence, 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 := semanticCos dot
      let contribution := mul wave.weight (one - cosine)
      sumWaves (i + 1) (acc + contribution)
  sumWaves 0 zero

/-- Compute semantic locking energy for stability -/
def computeSemanticLockingEnergy (currentPattern previousPattern : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
  let z := {
    activation := currentPattern.activation - previousPattern.activation,
    salience := currentPattern.salience - previousPattern.salience,
    coherence := currentPattern.coherence - previousPattern.coherence
  }
  computeSemanticFrustration z waves

/-- Update discrete semantic state from geometry -/
def updateSemanticStateFromGeometry (state : DiscreteSemanticState) (manifold : SemanticManifold) : DiscreteSemanticState :=
  let newActivation := state.activation + manifold.curvature
  let newSalience := state.salience + manifold.torsion
  {
    activation := newActivation,
    salience := newSalience,
    coherence := state.coherence,
    entropy := state.entropy
  }

/-- Update discrete semantic state from Christoffel symbols -/
def updateSemanticStateFromChristoffel (state : DiscreteSemanticState) (symbols : SemanticChristoffel) (i j k : Nat) : DiscreteSemanticState :=
  let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
  let entropyIncrement := if symbol > ofNat 100 then one else zero
  {
    activation := state.activation,
    salience := state.salience,
    coherence := state.coherence,
    entropy := state.entropy + entropyIncrement
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Original Semantic Atoms (NSM theory primitives)
-- ═══════════════════════════════════════════════════════════════════════════

/-- 
Universal Semantic Primes (Atoms).
These are the irreducible primitives of human thought according to NSM theory.
-/
inductive Atom : Type
| someone
| something
| do_
| happen
| move
| cause
| die
| want
| know
| feel
| think
| good
| bad
| because
| not
deriving Repr, DecidableEq

/-- Enhanced atom with discrete semantic state tracking -/
structure AtomWithState where
  atom : Atom
  semanticState : DiscreteSemanticState
  deriving Repr

end Semantics