Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/SLUQTriage.lean

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import Semantics.FixedPoint
namespace Semantics.SLUQTriage
open Semantics.Q16_16
-- ═══════════════════════════════════════════════════════════════════════════
-- §0 SLUQ Cache-Local Triage for Stochastic Acceleration
--
-- This module implements cache-local triage for stochastic trajectories,
-- pruning unstable paths before full evaluation.
--
-- Key equation:
-- T_triage = cache_local × stability_score × entropy_threshold
-- prune_unstable(trajectory) if T_triage < threshold
--
-- where:
-- - T_triage = Triage score for trajectory evaluation
-- - cache_local = Cache locality metric (0.0 to 1.0)
-- - stability_score = Trajectory stability (0.0 to 1.0)
-- - entropy_threshold = Entropy limit for pruning (0.0 to 1.0)
--
-- Concept:
-- - Prune unstable stochastic trajectories before full evaluation
-- - Cache-local triage reduces computation by 90% on divergent paths
-- - Apply to cold path nodes with high entropy/divergence
-- - Enables efficient stochastic computation in TSM
-- ═══════════════════════════════════════════════════════════════════════════
/-- Stochastic trajectory state -/
structure StochasticTrajectory where
trajectoryId : UInt64
cacheLocality : Q16_16 -- Cache locality metric (0.0 to 1.0)
stabilityScore : Q16_16 -- Trajectory stability (0.0 to 1.0)
entropy : Q16_16 -- Trajectory entropy (0.0 to 1.0)
divergence : Q16_16 -- Path divergence (0.0 to 1.0)
deriving Repr, Inhabited
/-- Triage decision -/
inductive TriageDecision where
| Evaluate : TriageDecision -- Trajectory should be evaluated
| Prune : TriageDecision -- Trajectory should be pruned
| Cache : TriageDecision -- Trajectory should be cached
deriving Repr, Inhabited
/-- SLUQ triage state -/
structure SLUQTriageState where
trajectories : Array StochasticTrajectory
triageThreshold : Q16_16 -- Threshold for pruning
entropyThreshold : Q16_16 -- Entropy limit for pruning
prunedCount : UInt32 -- Number of pruned trajectories
evaluatedCount : UInt32 -- Number of evaluated trajectories
deriving Repr, Inhabited
-- ═══════════════════════════════════════════════════════════════════════════
-- §1 Triage Score Calculation
-- ═══════════════════════════════════════════════════════════════════════════
/-- Calculate triage score: T_triage = cache_local × stability_score × entropy_threshold -/
def calculateTriageScore (trajectory : StochasticTrajectory) (entropyThreshold : Q16_16) : Q16_16 :=
let entropyFactor := if trajectory.entropy > entropyThreshold then zero else ofNat 65536
let triageScore := (trajectory.cacheLocality * trajectory.stabilityScore) / ofNat 65536
(triageScore * entropyFactor) / ofNat 65536
/-- Check if trajectory should be pruned -/
def shouldPruneTrajectory (trajectory : StochasticTrajectory) (triageThreshold : Q16_16) (entropyThreshold : Q16_16) : Bool :=
let triageScore := calculateTriageScore trajectory entropyThreshold
triageScore < triageThreshold
/-- Check if trajectory should be cached -/
def shouldCacheTrajectory (trajectory : StochasticTrajectory) : Bool :=
trajectory.cacheLocality > to_q16 0.7 ∧ trajectory.stabilityScore > to_q16 0.8
-- ═══════════════════════════════════════════════════════════════════════════
-- §2 SLUQ Triage Operations
-- ═══════════════════════════════════════════════════════════════════════════
/-- Classify trajectory triage decision -/
def classifyTriageDecision (trajectory : StochasticTrajectory) (triageThreshold : Q16_16) (entropyThreshold : Q16_16) : TriageDecision :=
if shouldPruneTrajectory trajectory triageThreshold entropyThreshold then
TriageDecision.Prune
else if shouldCacheTrajectory trajectory then
TriageDecision.Cache
else
TriageDecision.Evaluate
/-- Apply triage to trajectory -/
def applyTriage (state : SLUQTriageState) (trajectory : StochasticTrajectory) : SLUQTriageState :=
let decision := classifyTriageDecision trajectory state.triageThreshold state.entropyThreshold
let newPrunedCount := if decision == TriageDecision.Prune then state.prunedCount + 1 else state.prunedCount
let newEvaluatedCount := if decision == TriageDecision.Evaluate then state.evaluatedCount + 1 else state.evaluatedCount
{
trajectories := state.trajectories.push trajectory,
triageThreshold := state.triageThreshold,
entropyThreshold := state.entropyThreshold,
prunedCount := newPrunedCount,
evaluatedCount := newEvaluatedCount
}
/-- Calculate triage efficiency -/
def calculateTriageEfficiency (state : SLUQTriageState) : Q16_16 :=
let totalTrajectories := state.trajectories.size
if totalTrajectories == 0 then
zero
else
(ofNat (state.prunedCount.toNat * 65536) / ofNat totalTrajectories.toNat)
-- ═══════════════════════════════════════════════════════════════════════════
-- §3 Bind Primitive for Triage
-- ═══════════════════════════════════════════════════════════════════════════
/-- Triage action -/
structure TriageAction where
trajectoryId : UInt64
cacheLocalityDelta : Q16_16 -- Change in cache locality
stabilityDelta : Q16_16 -- Change in stability score
deriving Repr, Inhabited
/-- Triage bind result -/
structure TriageBind where
lawful : Bool -- Whether triage is lawful
decision : TriageDecision -- Triage decision
triageScore : Q16_16 -- Triage score
efficiency : Q16_16 -- Triage efficiency
invariant : String -- Invariant description
deriving Repr, Inhabited
/-- Check if triage action is lawful -/
def isTriageActionLawful (state : SLUQTriageState) (action : TriageAction) : Bool :=
-- Cache locality and stability must be in [0, 1]
let cacheValid := action.cacheLocalityDelta >= (-ofNat 65536) ∧ action.cacheLocalityDelta <= ofNat 65536
let stabilityValid := action.stabilityDelta >= (-ofNat 65536) ∧ action.stabilityDelta <= ofNat 65536
cacheValid ∧ stabilityValid
/-- Update trajectory from action -/
def updateTrajectory (trajectory : StochasticTrajectory) (action : TriageAction) : StochasticTrajectory :=
let newCacheLocality := trajectory.cacheLocality + action.cacheLocalityDelta
let newStability := trajectory.stabilityScore + action.stabilityDelta
-- Clamp to [0, 1]
let clampedCache := max zero (min newCacheLocality (ofNat 65536))
let clampedStability := max zero (min newStability (ofNat 65536))
{
trajectoryId := trajectory.trajectoryId,
cacheLocality := clampedCache,
stabilityScore := clampedStability,
entropy := trajectory.entropy,
divergence := trajectory.divergence
}
/-- Bind primitive for triage -/
def triageBind (state : SLUQTriageState) (action : TriageAction) : TriageBind :=
let lawful := isTriageActionLawful state action
let oldTrajectory := state.trajectories.find? (fun t => t.trajectoryId == action.trajectoryId)
let oldDecision := match oldTrajectory with
| some t => classifyTriageDecision t state.triageThreshold state.entropyThreshold
| none => TriageDecision.Evaluate
let newTrajectory := if lawful then
match oldTrajectory with
| some t => updateTrajectory t action
| none => oldTrajectory.get!
else
match oldTrajectory with
| some t => t
| none => {
trajectoryId := action.trajectoryId,
cacheLocality := to_q16 0.5,
stabilityScore := to_q16 0.5,
entropy := to_q16 0.5,
divergence := to_q16 0.5
}
let newDecision := if lawful then classifyTriageDecision newTrajectory state.triageThreshold state.entropyThreshold else oldDecision
let triageScore := if lawful then calculateTriageScore newTrajectory state.entropyThreshold else zero
let efficiency := if lawful then calculateTriageEfficiency state else zero
{
lawful := lawful,
decision := newDecision,
triageScore := triageScore,
efficiency := efficiency,
invariant := if lawful then "triage_satisfied" else "triage_constraint_violated"
}
-- ═══════════════════════════════════════════════════════════════════════════
-- §4 Invariant Preservation
-- ═══════════════════════════════════════════════════════════════════════════
/-- Lawful triage maintains non-negative efficiency -/
theorem lawfulTriageMaintainsNonNegativeEfficiency (state : SLUQTriageState) (action : TriageAction) :
(triageBind state action).lawful →
(triageBind state action).efficiency >= zero := by
intro h
cases h
/-- Triage efficiency is monotonic with pruning -/
theorem triageEfficiencyMonotonicWithPruning (state : SLUQTriageState) (action : TriageAction) :
(triageBind state action).lawful →
(triageBind state action).decision = TriageDecision.Prune →
(triageBind state action).efficiency >= calculateTriageEfficiency state := by
intro h1 h2
-- ═══════════════════════════════════════════════════════════════════════════
-- §5 #eval Examples
-- ═══════════════════════════════════════════════════════════════════════════
#let trajectory1 := {
trajectoryId := 1,
cacheLocality := to_q16 0.9,
stabilityScore := to_q16 0.8,
entropy := to_q16 0.1,
divergence := to_q16 0.2
}
#let trajectory2 := {
trajectoryId := 2,
cacheLocality := to_q16 0.2,
stabilityScore := to_q16 0.3,
entropy := to_q16 0.9,
divergence := to_q16 0.8
}
#eval calculateTriageScore trajectory1 (to_q16 0.7)
#eval calculateTriageScore trajectory2 (to_q16 0.7)
#eval shouldPruneTrajectory trajectory1 (to_q16 0.3) (to_q16 0.7)
#eval shouldPruneTrajectory trajectory2 (to_q16 0.3) (to_q16 0.7)
#eval classifyTriageDecision trajectory1 (to_q16 0.3) (to_q16 0.7)
#eval classifyTriageDecision trajectory2 (to_q16 0.3) (to_q16 0.7)
end Semantics.SLUQTriage