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