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154 lines
6 KiB
Text
154 lines
6 KiB
Text
import Semantics.FixedPoint
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namespace Semantics
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Hardware-Native Semantic Atom Structures (from HachimojiPipeline improvements)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Discrete semantic state using Q16_16 for hardware-native computation -/
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structure DiscreteSemanticState where
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activation : Q16_16 -- Semantic activation level
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salience : Q16_16 -- Semantic salience
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coherence : Q16_16 -- Semantic coherence
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entropy : Q16_16 -- Semantic entropy
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deriving Repr, Inhabited
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/-- Semantic grid for spatial discretization -/
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structure SemanticGrid where
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dimension : Nat -- Grid dimension
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spacing : Q16_16 -- Grid spacing
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values : Array DiscreteSemanticState -- State values at grid points
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deriving Repr
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/-- Semantic manifold for geometric phase evolution -/
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structure SemanticManifold where
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dimension : Nat -- Manifold dimension
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curvature : Q16_16 -- Scalar curvature (affects semantic field)
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torsion : Q16_16 -- Torsion (semantic deviation)
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metric : Array Q16_16 -- Metric tensor diagonal elements
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deriving Repr
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/-- Christoffel symbols for semantic geometric phase -/
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structure SemanticChristoffel where
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dimension : Nat -- Manifold dimension
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symbols : Array Q16_16 -- Flattened symbol array [i][j][k]
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deriving Repr, Inhabited
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/-- Semantic lock pattern for frustration computation -/
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structure SemanticLockPattern where
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activation : Q16_16
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salience : Q16_16
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coherence : Q16_16
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deriving Repr, Inhabited
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/-- Semantic frustration wave parameters -/
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structure SemanticFrustrationWave where
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waveVector : Array Q16_16 -- k_r wave vector
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weight : Q16_16 -- w_r weight from anisotropy
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deriving Repr, Inhabited
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/-- Compute semantic Christoffel symbols -/
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def computeSemanticChristoffel (manifold : SemanticManifold) : SemanticChristoffel :=
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let n := manifold.dimension
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let symbolCount := n * n * n
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let symbols := Array.replicate symbolCount zero
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let rec computeSymbol (i j k : Nat) (acc : Array Q16_16) : Array Q16_16 :=
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if i >= n then acc
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else if j >= n then computeSymbol (i + 1) 0 0 acc
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else if k >= n then computeSymbol i (j + 1) 0 acc
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else
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let symbol := if i = j ∧ j = k then zero else zero
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let idx := i * n * n + j * n + k
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computeSymbol i j (k + 1) (acc.set! idx symbol)
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let result := computeSymbol 0 0 0 symbols
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{ dimension := n, symbols := result }
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/-- Compute cosine using Taylor series for Q16_16 -/
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def semanticCos (x : Q16_16) : Q16_16 :=
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let x2 := mul x x
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let term2 := mul x2 (div (ofNat 1) (ofNat 2))
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one - term2
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/-- Compute semantic frustration W(z;A) = Σ_r w_r(A)(1 - cos(k_r·z)) -/
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def computeSemanticFrustration (z : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
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let zArray := #[z.activation, z.salience, z.coherence, zero]
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let rec sumWaves (i : Nat) (acc : Q16_16) : Q16_16 :=
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if i >= waves.size then acc
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else
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let wave := waves[i]!
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let rec dotProduct (j : Nat) (sum : Q16_16) : Q16_16 :=
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if j >= 4 then sum
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else dotProduct (j + 1) (sum + zArray[j]! * wave.waveVector[j]!)
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let dot := dotProduct 0 zero
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let cosine := semanticCos dot
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let contribution := mul wave.weight (one - cosine)
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sumWaves (i + 1) (acc + contribution)
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sumWaves 0 zero
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/-- Compute semantic locking energy for stability -/
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def computeSemanticLockingEnergy (currentPattern previousPattern : SemanticLockPattern) (waves : Array SemanticFrustrationWave) : Q16_16 :=
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let z := {
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activation := currentPattern.activation - previousPattern.activation,
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salience := currentPattern.salience - previousPattern.salience,
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coherence := currentPattern.coherence - previousPattern.coherence
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}
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computeSemanticFrustration z waves
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/-- Update discrete semantic state from geometry -/
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def updateSemanticStateFromGeometry (state : DiscreteSemanticState) (manifold : SemanticManifold) : DiscreteSemanticState :=
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let newActivation := state.activation + manifold.curvature
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let newSalience := state.salience + manifold.torsion
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{
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activation := newActivation,
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salience := newSalience,
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coherence := state.coherence,
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entropy := state.entropy
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}
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/-- Update discrete semantic state from Christoffel symbols -/
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def updateSemanticStateFromChristoffel (state : DiscreteSemanticState) (symbols : SemanticChristoffel) (i j k : Nat) : DiscreteSemanticState :=
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let symbol := symbols.symbols[i * symbols.dimension * symbols.dimension + j * symbols.dimension + k]!
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let entropyIncrement := if symbol > ofNat 100 then one else zero
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{
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activation := state.activation,
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salience := state.salience,
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coherence := state.coherence,
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entropy := state.entropy + entropyIncrement
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Original Semantic Atoms (NSM theory primitives)
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-- ═══════════════════════════════════════════════════════════════════════════
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/--
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Universal Semantic Primes (Atoms).
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These are the irreducible primitives of human thought according to NSM theory.
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-/
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inductive Atom : Type
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| someone
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| something
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| do_
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| happen
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| move
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| cause
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| die
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| want
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| know
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| feel
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| think
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| good
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| bad
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| because
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| not
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deriving Repr, DecidableEq
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/-- Enhanced atom with discrete semantic state tracking -/
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structure AtomWithState where
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atom : Atom
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semanticState : DiscreteSemanticState
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deriving Repr
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end Semantics
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