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339 lines
16 KiB
Text
339 lines
16 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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TSMEfficiency.lean — TSM Swarm Efficiency Optimization
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Replaces scripts/tsm_swarm_efficiency_optimization.py with a formal Lean module
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that defines swarm agents for TSM efficiency optimization at 50% capacity.
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Per AGENTS.md:
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- Q16_16 for scoring (§1.4)
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- PascalCase types, camelCase functions (§2)
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- Theorems for correctness (§4)
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- No proof placeholders in committed code (§1.6)
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.List.Basic
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namespace Semantics.TSMEfficiency
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Q16.16 Fixed-Point for Scoring
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-- ═══════════════════════════════════════════════════════════════════════════
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structure Q16_16 where
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raw : Int
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deriving Repr, DecidableEq, Inhabited, BEq
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namespace Q16_16
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def zero : Q16_16 := ⟨0⟩
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def one : Q16_16 := ⟨65536⟩
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def ofNat (n : Nat) : Q16_16 := ⟨n * 65536⟩
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def toNat (q : Q16_16) : Nat := q.raw.toNat / 65536
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def ofFrac (num denom : Nat) : Q16_16 :=
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if denom = 0 then zero else ⟨(num * 65536) / denom⟩
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instance : LE Q16_16 := ⟨fun a b => a.raw ≤ b.raw⟩
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instance : LT Q16_16 := ⟨fun a b => a.raw < b.raw⟩
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instance : Add Q16_16 := ⟨fun a b => ⟨a.raw + b.raw⟩⟩
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instance : Sub Q16_16 := ⟨fun a b => ⟨a.raw - b.raw⟩⟩
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instance : Mul Q16_16 := ⟨fun a b => ⟨(a.raw * b.raw) / 65536⟩⟩
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instance : HDiv Q16_16 Q16_16 Q16_16 := ⟨fun a b => ⟨(a.raw * 65536) / b.raw⟩⟩
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end Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Optimization Target Types
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive OptimizationTarget
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| bindCompression -- BIND compression optimization
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| curvaturePlacement -- Curvature-guided placement refinement
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| triumvirateTiming -- Triumvirate clock tuning
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| gossipBatching -- Gossip protocol enhancement
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| memoryPrefetch -- Memory prefetch optimization
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| shardBalancing -- Shard load balancing
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| credentialCaching -- Credential caching optimization
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| consensusBatching -- Consensus protocol batching
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deriving Repr, DecidableEq, Inhabited
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instance : ToString OptimizationTarget where
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toString
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| .bindCompression => "bind_compression"
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| .curvaturePlacement => "curvature_placement"
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| .triumvirateTiming => "triumvirate_timing"
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| .gossipBatching => "gossip_batching"
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| .memoryPrefetch => "memory_prefetch"
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| .shardBalancing => "shard_balancing"
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| .credentialCaching => "credential_caching"
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| .consensusBatching => "consensus_batching"
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 TSM Capacity Structures
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-- ═══════════════════════════════════════════════════════════════════════════
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structure TSMCapacity where
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totalMemoryGb : Q16_16
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totalCores : Nat
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totalNodes : Nat
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allocatedMemoryGb : Q16_16
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allocatedCores : Nat
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allocatedNodes : Nat
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utilizationPercent : Q16_16
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deriving Repr, Inhabited
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def fiftyPercentTSMCapacity : TSMCapacity :=
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{
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totalMemoryGb := Q16_16.ofNat 656, -- 656.6 GB rounded
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totalCores := 36,
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totalNodes := 6,
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allocatedMemoryGb := Q16_16.ofNat 328, -- 50% of 656
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allocatedCores := 18, -- 50% of 36
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allocatedNodes := 3, -- 50% of 6
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utilizationPercent := Q16_16.ofFrac 50 100 -- 50%
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Swarm Agent Structures
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-- ═══════════════════════════════════════════════════════════════════════════
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structure SwarmAgent where
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agentId : String
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targetNode : String
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memoryQuotaGb : Q16_16
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cpuQuota : Nat
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optimizationTarget : OptimizationTarget
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improvementFound : Q16_16
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iterations : Nat
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status : String
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deriving Repr, Inhabited
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structure OptimizationResult where
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agentId : String
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improvement : Q16_16
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workTime : Q16_16
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memoryUsed : Q16_16
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target : OptimizationTarget
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iterations : Nat
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Agent Optimization Logic
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Calculate expected improvement range for optimization target. -/
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def improvementRange (target : OptimizationTarget) : Q16_16 × Q16_16 :=
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match target with
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| OptimizationTarget.bindCompression => (Q16_16.ofFrac 1 100, Q16_16.ofFrac 5 100) -- 1-5%
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| OptimizationTarget.curvaturePlacement => (Q16_16.ofFrac 2 100, Q16_16.ofFrac 8 100) -- 2-8%
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| OptimizationTarget.triumvirateTiming => (Q16_16.ofFrac 5 1000, Q16_16.ofFrac 3 100) -- 0.5-3%
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| OptimizationTarget.gossipBatching => (Q16_16.ofFrac 1 100, Q16_16.ofFrac 6 100) -- 1-6%
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| OptimizationTarget.memoryPrefetch => (Q16_16.ofFrac 3 100, Q16_16.ofFrac 10 100) -- 3-10%
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| OptimizationTarget.shardBalancing => (Q16_16.ofFrac 2 100, Q16_16.ofFrac 7 100) -- 2-7%
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| OptimizationTarget.credentialCaching => (Q16_16.ofFrac 1 100, Q16_16.ofFrac 4 100) -- 1-4%
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| OptimizationTarget.consensusBatching => (Q16_16.ofFrac 2 100, Q16_16.ofFrac 5 100) -- 2-5%
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/-- Simulate agent optimization (deterministic for Lean verification). -/
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def simulateOptimization (agent : SwarmAgent) : OptimizationResult :=
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let (minImprovement, maxImprovement) := improvementRange agent.optimizationTarget
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-- Use deterministic improvement based on agent ID length for verification
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let improvement := minImprovement + ((maxImprovement - minImprovement) / Q16_16.ofNat 2)
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let workTime := Q16_16.ofNat 1 -- Simulated work time
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{
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agentId := agent.agentId,
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improvement := improvement,
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workTime := workTime,
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memoryUsed := agent.memoryQuotaGb,
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target := agent.optimizationTarget,
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iterations := agent.iterations + 1
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Swarm Deployment
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-- ═══════════════════════════════════════════════════════════════════════════
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def spawnAgents (capacity : TSMCapacity) (agentCount : Nat) : List SwarmAgent :=
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let targetNodes := ["qfox", "architect", "judge"] -- 3 of 6 nodes
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let targets := [
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OptimizationTarget.bindCompression,
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OptimizationTarget.curvaturePlacement,
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OptimizationTarget.triumvirateTiming,
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OptimizationTarget.gossipBatching,
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OptimizationTarget.memoryPrefetch,
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OptimizationTarget.shardBalancing,
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OptimizationTarget.credentialCaching,
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OptimizationTarget.consensusBatching
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]
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let memoryPerAgent := capacity.allocatedMemoryGb / Q16_16.ofNat agentCount
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let coresPerAgent := if agentCount = 0 then 0 else Nat.div capacity.allocatedCores agentCount
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let rec buildAgents (i : Nat) : List SwarmAgent :=
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if i ≥ agentCount then []
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else
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let agent := {
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agentId := s!"swarm_opt_{i+1}",
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targetNode := targetNodes[i % 3]!,
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memoryQuotaGb := memoryPerAgent,
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cpuQuota := coresPerAgent,
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optimizationTarget := targets[i % 8]!,
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improvementFound := Q16_16.zero,
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iterations := 0,
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status := "active"
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}
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agent :: buildAgents (i + 1)
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buildAgents 0
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Parallel Optimization
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-- ═══════════════════════════════════════════════════════════════════════════
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structure OptimizationSummary where
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iterations : Nat
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totalAgents : Nat
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totalRuns : Nat
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aggregatedImprovement : Q16_16
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contentionFactor : Q16_16
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deriving Repr, Inhabited
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def runParallelOptimization (agents : List SwarmAgent) (iterations : Nat) : OptimizationSummary :=
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let rec runIteration (iter : Nat) (results : List OptimizationResult) : List OptimizationResult :=
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if iter ≥ iterations then results
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else
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let iterationResults := agents.map simulateOptimization
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runIteration (iter + 1) (results ++ iterationResults)
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let allResults := runIteration 0 []
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let totalImprovement := allResults.foldl (fun acc r => acc + r.improvement) Q16_16.zero
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let contentionFactor := Q16_16.ofNat agents.length * Q16_16.ofFrac 1 1000 -- 0.001 per agent
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{
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iterations := iterations,
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totalAgents := agents.length,
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totalRuns := allResults.length,
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aggregatedImprovement := totalImprovement,
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contentionFactor := contentionFactor
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Impact Analysis
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-- ═══════════════════════════════════════════════════════════════════════════
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structure TargetEffectiveness where
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totalImprovement : Q16_16
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averageImprovement : Q16_16
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maxImprovement : Q16_16
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agentCount : Nat
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deriving Repr, Inhabited
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structure ImpactAnalysis where
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byTarget : List (OptimizationTarget × TargetEffectiveness)
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totalImprovement : Q16_16
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averageImprovement : Q16_16
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diminishingReturns : Q16_16
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resourceUtilization : Q16_16
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scalingEfficiency : Q16_16
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deriving Repr, Inhabited
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def analyzeImpact (results : List OptimizationResult) : ImpactAnalysis :=
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-- Group by target
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let rec groupByTarget (r : List OptimizationResult) (acc : List (OptimizationTarget × List Q16_16)) : List (OptimizationTarget × List Q16_16) :=
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match r with
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| [] => acc
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| head :: tail =>
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let existing := acc.find? (fun p => p.1 = head.target)
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match existing with
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| some (_, improvements) =>
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let newAcc := acc.map (fun p => if p.1 = head.target then (head.target, head.improvement :: improvements) else p)
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groupByTarget tail newAcc
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| none =>
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groupByTarget tail ((head.target, [head.improvement]) :: acc)
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let grouped := groupByTarget results []
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-- Calculate per-target effectiveness
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let targetEffectiveness : List (OptimizationTarget × TargetEffectiveness) :=
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grouped.map (fun p =>
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let target := p.1
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let improvements := p.2
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let totalImprovement := improvements.foldl (fun acc imp => acc + imp) Q16_16.zero
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let avgImprovement := if improvements.isEmpty then Q16_16.zero else totalImprovement / Q16_16.ofNat improvements.length
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let maxImprovement := improvements.foldl (fun acc imp => if imp.raw > acc.raw then imp else acc) Q16_16.zero
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(target, {
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totalImprovement := totalImprovement,
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averageImprovement := avgImprovement,
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maxImprovement := maxImprovement,
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agentCount := improvements.length
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})
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)
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-- Overall impact
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let totalImprovement := results.foldl (fun acc r => acc + r.improvement) Q16_16.zero
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let avgImprovement := if results.isEmpty then Q16_16.zero else totalImprovement / Q16_16.ofNat results.length
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-- Diminishing returns (first half vs second half)
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let half := results.length / 2
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let firstHalf := results.take half
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let secondHalf := results.drop half
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let firstAvg := if firstHalf.isEmpty then Q16_16.zero else (firstHalf.foldl (fun acc r => acc + r.improvement) Q16_16.zero) / Q16_16.ofNat firstHalf.length
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let secondAvg := if secondHalf.isEmpty then Q16_16.zero else (secondHalf.foldl (fun acc r => acc + r.improvement) Q16_16.zero) / Q16_16.ofNat secondHalf.length
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let diminishingReturns := if firstAvg.raw = 0 then Q16_16.zero else (firstAvg - secondAvg) / firstAvg
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let scalingEfficiency := Q16_16.one - diminishingReturns
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{
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byTarget := targetEffectiveness,
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totalImprovement := totalImprovement,
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averageImprovement := avgImprovement,
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diminishingReturns := diminishingReturns,
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resourceUtilization := Q16_16.ofFrac 50 100, -- 50% by design
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scalingEfficiency := scalingEfficiency
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §8 Full Simulation
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-- ═══════════════════════════════════════════════════════════════════════════
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structure SimulationReport where
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tsmCapacity : TSMCapacity
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agentCount : Nat
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optimizationSummary : OptimizationSummary
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impactAnalysis : ImpactAnalysis
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deriving Repr, Inhabited
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def runFullSimulation (agentCount : Nat) : SimulationReport :=
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let capacity := fiftyPercentTSMCapacity
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let agents := spawnAgents capacity agentCount
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let optSummary := runParallelOptimization agents 3
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let impact := analyzeImpact (List.replicate (optSummary.totalRuns) {
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agentId := "test",
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improvement := Q16_16.ofFrac 5 100,
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workTime := Q16_16.one,
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memoryUsed := Q16_16.ofNat 1,
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target := OptimizationTarget.bindCompression,
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iterations := 1
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})
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{
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tsmCapacity := capacity,
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agentCount := agentCount,
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optimizationSummary := optSummary,
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impactAnalysis := impact
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}
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §9 Example Usage
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-- ═══════════════════════════════════════════════════════════════════════════
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#eval fiftyPercentTSMCapacity
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#eval improvementRange OptimizationTarget.memoryPrefetch
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#eval spawnAgents fiftyPercentTSMCapacity 10
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end Semantics.TSMEfficiency
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