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

/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

MoECache.lean — MoE Cache Data Structures and Eviction Policy

Replaces infra/moe_ene_cache.py cache logic with a formal Lean module.
Defines MoE (Mixture-of-Experts) cache structures and eviction policies.

Per AGENTS.md:
  - Q16_16 for scoring (§1.4)
  - PascalCase types, camelCase functions (§2)
  - Theorems for correctness (§4)
  - No proof placeholders in committed code (§1.6)
-/

import Mathlib.Data.Nat.Basic
import Mathlib.Data.List.Basic
import Std

namespace Semantics.MoECache

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Q16_16 Fixed-Point Arithmetic
-- ═══════════════════════════════════════════════════════════════════════════

structure Q16_16 where
  raw : Int
  deriving Repr, DecidableEq, Inhabited, BEq

namespace Q16_16
  def zero : Q16_16 := ⟨0⟩
  def one : Q16_16 := ⟨65536⟩
  def ofFrac (num denom : Nat) : Q16_16 :=
    if denom = 0 then zero else ⟨(num * 65536) / denom⟩
end Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Expert Configuration Structure
-- ═══════════════════════════════════════════════════════════════════════════

structure ExpertConfiguration where
  expertId : Nat
  gatingWeight : Q16_16  -- g
  qualityWeight : Q16_16  -- w
  coherence : Q16_16  -- h
  penaltyWeight : Q16_16  -- v
  distortion : Q16_16  -- p
  arity : Q16_16  -- N
  costCoefficient : Q16_16  -- a
  overhead : Q16_16  -- c
  domain : String
  version : String
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Cache Entry Structure
-- ═══════════════════════════════════════════════════════════════════════════

structure MoECacheEntry where
  cacheKey : String
  expertIds : List Nat
  etaMoEResult : Q16_16
  iDiscarded : Q16_16
  timestamp : Nat
  confidence : Q16_16
  hitCount : Nat
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Cache Statistics
-- ═══════════════════════════════════════════════════════════════════════════

structure CacheStatistics where
  expertCacheEntries : Nat
  expertCacheHits : Nat
  computationCacheEntries : Nat
  computationCacheHits : Nat
  rewiringProposals : Nat
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  LRU Eviction Policy
-- ═══════════════════════════════════════════════════════════════════════════

structure LRUEntry where
  key : String
  accessTime : Nat
  deriving Repr, Inhabited

/-- LRU cache with maximum size -/
structure LRUCache where
  entries : List LRUEntry
  maxSize : Nat
  currentTime : Nat
  deriving Repr, Inhabited

/-- Initialize empty LRU cache -/
def initLRUCache (maxSize : Nat) : LRUCache :=
  { entries := [], maxSize := maxSize, currentTime := 0 }

/-- Update access time for a key -/
def lruAccess (cache : LRUCache) (key : String) : LRUCache :=
  let newTime := cache.currentTime + 1
  let updatedEntries := cache.entries.map (fun e =>
    if e.key = key then { key := e.key, accessTime := newTime } else e
  )
  let keyExists := cache.entries.any (fun e => e.key = key)
  let finalEntries :=
    if keyExists then
      updatedEntries
    else
      { key := key, accessTime := newTime } :: updatedEntries
  let trimmedEntries := List.take cache.maxSize finalEntries
  { entries := trimmedEntries, maxSize := cache.maxSize, currentTime := newTime }

/-- Get least recently used key for eviction -/
def getLRUEvictionKey (cache : LRUCache) : Option String :=
  if cache.entries.isEmpty then
    none
  else
    let minEntry := cache.entries.foldl (fun min e =>
      if e.accessTime < min.accessTime then e else min
    ) cache.entries.head!
    some minEntry.key

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Cache Operations
-- ═══════════════════════════════════════════════════════════════════════════

/-- Increment hit count for cache entry -/
def incrementHitCount (entry : MoECacheEntry) : MoECacheEntry :=
  { entry with hitCount := entry.hitCount + 1 }

/-- Compute cache hit rate -/
def computeHitRate (hits total : Nat) : Q16_16 :=
  if total = 0 then Q16_16.zero else Q16_16.ofFrac hits total

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

/-- Hit count always increases after increment -/
theorem hitCountIncreases (entry : MoECacheEntry) :
    (incrementHitCount entry).hitCount = entry.hitCount + 1 := by
  simp [incrementHitCount]

/-- LRU cache size is bounded by max size after initialization -/
theorem lruInitBounded (maxSize : Nat) :
    (initLRUCache maxSize).entries.length ≤ maxSize := by
  simp [initLRUCache]

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  Example Usage
-- ═══════════════════════════════════════════════════════════════════════════

#eval let cache := initLRUCache 10
      let cache1 := lruAccess cache "key1"
      let cache2 := lruAccess cache1 "key2"
      let cache3 := lruAccess cache2 "key1"
      getLRUEvictionKey cache3

#eval computeHitRate 85 100

#eval incrementHitCount {
    cacheKey := "test",
    expertIds := [1, 2, 3],
    etaMoEResult := Q16_16.ofFrac 85 100,
    iDiscarded := Q16_16.ofFrac 10 100,
    timestamp := 12345,
    confidence := Q16_16.ofFrac 95 100,
    hitCount := 5
  }

end Semantics.MoECache