From b5d1f4e2f375e697ad99897ee452e2539208950e Mon Sep 17 00:00:00 2001
From: DualFroz <me@dualfroz.com>
Date: Mon, 24 Aug 2026 22:40:00 +0200
Subject: [PATCH] feat(cdcl): add cdcl search with 1-uip analysis and restarts

---
 src/Sift/Cdcl/Search.hs | 393 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 393 insertions(+)
 create mode 100644 src/Sift/Cdcl/Search.hs

diff --git a/src/Sift/Cdcl/Search.hs b/src/Sift/Cdcl/Search.hs
new file mode 100644
index 0000000..aa302a3
--- /dev/null
+++ b/src/Sift/Cdcl/Search.hs
@@ -0,0 +1,393 @@
+{-# LANGUAGE FlexibleContexts #-}
+module Sift.Cdcl.Search
+  ( solveInternal
+  , luby
+  , propagate
+  , analyze
+  , analyzeFinal
+  , pickBranchVar
+  , maybeReduce
+  , installLearnt
+  , extractModel
+  , collectStats
+  ) where
+
+import Control.Monad (when, forM_, foldM, filterM)
+import Control.Monad.ST (ST)
+import Data.STRef
+import Data.Array.ST
+import qualified Data.IntSet as IntSet
+import Sift.Cdcl.State
+import Sift.Cdcl.Heap
+import Sift.Stats
+
+luby :: Int -> Int
+luby x0 = descend size0 seq0 x0
+  where
+    (size0, seq0) = ascend 1 0
+    ascend :: Int -> Int -> (Int, Int)
+    ascend size sq
+      | size < x0 + 1 = ascend (2 * size + 1) (sq + 1)
+      | otherwise     = (size, sq)
+    descend :: Int -> Int -> Int -> Int
+    descend size sq x
+      | size - 1 == x = 2 ^ sq
+      | otherwise =
+          let size' = (size - 1) `div` 2
+          in descend size' (sq - 1) (x `mod` size')
+
+propagate :: Solver s -> ST s Cid
+propagate s = loop
+  where
+    loop = do
+      qh <- readSTRef (qhead s)
+      n  <- readSTRef (trailN s)
+      if qh >= n
+        then pure (-1)
+        else do
+          p <- readArray (trail s) qh
+          writeSTRef (qhead s) (qh + 1)
+          modifySTRef' (statProp s) (+ 1)
+          confl <- propagateLit s p
+          if confl >= 0 then pure confl else loop
+
+propagateLit :: Solver s -> Int -> ST s Cid
+propagateLit s p = do
+  ws <- readArray (watches s) p
+  writeArray (watches s) p []
+  go ws []
+  where
+    falseLit = litNeg p
+    go [] kept = do
+      writeArray (watches s) p kept
+      pure (-1)
+    go (w@(Watcher cid blocker) : rest) kept = do
+      bv <- litValueInt s blocker
+      if bv == 1
+        then go rest (w : kept)
+        else do
+          cl <- getClause s cid
+          dead <- readSTRef (clsDead cl)
+          if dead
+            then go rest kept
+            else do
+              let lits = clsLits cl
+                  sz = clsSize cl
+              l0 <- readArray lits 0
+              when (l0 == falseLit) $ do
+                l1 <- readArray lits 1
+                writeArray lits 0 l1
+                writeArray lits 1 l0
+              first <- readArray lits 0
+              fv <- litValueInt s first
+              if fv == 1
+                then go rest (Watcher cid first : kept)
+                else do
+                  mNew <- findNewWatch s lits sz 2
+                  case mNew of
+                    Just k -> do
+                      lk <- readArray lits k
+                      writeArray lits 1 lk
+                      writeArray lits k falseLit
+                      modifyWatch s (litNeg lk) (Watcher cid first)
+                      go rest kept
+                    Nothing ->
+                      if fv == -1
+                        then do
+                          writeArray (watches s) p (reverse kept ++ (w : rest))
+                          pure cid
+                        else do
+                          _ <- enqueue s first cid
+                          go rest (Watcher cid first : kept)
+
+findNewWatch :: Solver s -> STUArray s Int Int -> Int -> Int -> ST s (Maybe Int)
+findNewWatch s lits sz i
+  | i >= sz = pure Nothing
+  | otherwise = do
+      l <- readArray lits i
+      lv <- litValueInt s l
+      if lv /= -1 then pure (Just i) else findNewWatch s lits sz (i + 1)
+
+analyze :: Solver s -> Cid -> ST s ([Int], Int, Int)
+analyze s conflict0 = do
+  dl <- currentLevel s
+  othersRef <- newSTRef []
+  counterRef <- newSTRef (0 :: Int)
+  pathRef <- newSTRef conflict0
+  pivotRef <- newSTRef (-1 :: Int)
+  idxRef <- newSTRef =<< (subtract 1 <$> readSTRef (trailN s))
+  let step = do
+        cid <- readSTRef pathRef
+        cl <- getClause s cid
+        when (clsLearnt cl) $ claBumpActivity s cl
+        let lits = clsLits cl
+            sz = clsSize cl
+        pivot <- readSTRef pivotRef
+        forM_ [0 .. sz - 1] $ \j -> do
+          q <- readArray lits j
+          when (q /= pivot) $ do
+            let v = litVar q
+            sv <- readArray (seen s) v
+            lev <- readArray (varLevel s) v
+            when (not sv && lev > 0) $ do
+              varBumpActivity s v
+              writeArray (seen s) v True
+              if lev >= dl
+                then modifySTRef' counterRef (+ 1)
+                else modifySTRef' othersRef (q :)
+        let selectNext = do
+              i <- readSTRef idxRef
+              l <- readArray (trail s) i
+              sv <- readArray (seen s) (litVar l)
+              if sv then pure (i, l) else do writeSTRef idxRef (i - 1); selectNext
+        (i, l) <- selectNext
+        writeSTRef idxRef (i - 1)
+        let v = litVar l
+        writeArray (seen s) v False
+        writeSTRef pivotRef l
+        writeSTRef pathRef =<< readArray (varReason s) v
+        modifySTRef' counterRef (subtract 1)
+        c <- readSTRef counterRef
+        when (c > 0) step
+  step
+  pivot <- readSTRef pivotRef
+  let asserting = litNeg pivot
+  othersRaw <- readSTRef othersRef
+  minimized <- minimize s othersRaw
+  let learnt = orderLearnt asserting minimized
+  btLevel <- computeBtLevel s minimized
+  lbd <- computeLbd s learnt
+  forM_ (litVar asserting : map litVar othersRaw) $ \v -> writeArray (seen s) v False
+  pure (learnt, btLevel, lbd)
+
+installLearnt :: Solver s -> [Int] -> Int -> ST s ()
+installLearnt s learnt lbd = do
+  case learnt of
+    [u] -> do
+      _ <- enqueue s u (-1)
+      pure ()
+    _ -> do
+      cid <- newClause s learnt True
+      cl <- getClause s cid
+      writeSTRef (clsLbd cl) lbd
+      claBumpActivity s cl
+      attachClause s cid
+      l0 <- readArray (clsLits cl) 0
+      _ <- enqueue s l0 cid
+      pure ()
+  modifySTRef' (statLearn s) (+ 1)
+  modifySTRef' (varInc s) (/ varDecayConst)
+  modifySTRef' (claInc s) (/ claDecayConst)
+
+analyzeFinal :: Solver s -> Int -> ST s [Int]
+analyzeFinal s p = do
+  dl <- currentLevel s
+  if dl == 0
+    then pure [p]
+    else do
+      writeArray (seen s) (litVar p) True
+      lim <- readSTRef (trailLim s)
+      n <- readSTRef (trailN s)
+      let bottom = last lim
+      outRef <- newSTRef [p]
+      forM_ [n - 1, n - 2 .. bottom] $ \i -> do
+        l <- readArray (trail s) i
+        let x = litVar l
+        sv <- readArray (seen s) x
+        when sv $ do
+          r <- readArray (varReason s) x
+          if r < 0
+            then modifySTRef' outRef (litNeg l :)
+            else do
+              cl <- getClause s r
+              let lits = clsLits cl
+                  sz = clsSize cl
+              forM_ [1 .. sz - 1] $ \j -> do
+                q <- readArray lits j
+                lev <- readArray (varLevel s) (litVar q)
+                when (lev > 0) $ writeArray (seen s) (litVar q) True
+          writeArray (seen s) x False
+      writeArray (seen s) (litVar p) False
+      readSTRef outRef
+
+minimize :: Solver s -> [Int] -> ST s [Int]
+minimize s others = filterM (fmap not . redundant s) others
+
+redundant :: Solver s -> Int -> ST s Bool
+redundant s l = do
+  r <- readArray (varReason s) (litVar l)
+  if r < 0
+    then pure False
+    else do
+      cl <- getClause s r
+      let lits = clsLits cl
+          sz = clsSize cl
+      let chk j
+            | j >= sz = pure True
+            | otherwise = do
+                q <- readArray lits j
+                let v = litVar q
+                sv <- readArray (seen s) v
+                lev <- readArray (varLevel s) v
+                if sv || lev == 0 then chk (j + 1) else pure False
+      chk 1
+
+orderLearnt :: Int -> [Int] -> [Int]
+orderLearnt asserting [] = [asserting]
+orderLearnt asserting others = asserting : others
+
+computeBtLevel :: Solver s -> [Int] -> ST s Int
+computeBtLevel s others =
+  foldM (\acc l -> do
+            lev <- readArray (varLevel s) (litVar l)
+            pure (max acc lev)) 0 others
+
+computeLbd :: Solver s -> [Int] -> ST s Int
+computeLbd s learnt = do
+  levels <- foldM (\acc l -> do
+                      lev <- readArray (varLevel s) (litVar l)
+                      pure (IntSet.insert lev acc)) IntSet.empty learnt
+  pure (IntSet.size levels)
+
+pickBranchVar :: Solver s -> ST s Int
+pickBranchVar s = go
+  where
+    go = do
+      empty <- heapIsEmpty (heapH s)
+      if empty
+        then pure (-1)
+        else do
+          v <- heapRemoveMax (heapH s)
+          val <- varValue s v
+          if val == 0 then pure v else go
+
+search :: Solver s -> Int -> ST s (Maybe Bool)
+search s confBudget = loop 0
+  where
+    loop confSoFar = do
+      confl <- propagate s
+      if confl >= 0
+        then do
+          modifySTRef' (statConf s) (+ 1)
+          lvl <- currentLevel s
+          if lvl == 0
+            then do
+              writeSTRef (okFlag s) False
+              pure (Just False)
+            else do
+              (learnt, btLevel, lbd) <- analyze s confl
+              cancelUntil s btLevel
+              installLearnt s learnt lbd
+              loop (confSoFar + 1)
+        else do
+          if confSoFar >= confBudget
+            then do
+              cancelUntil s 0
+              pure Nothing
+            else do
+              maybeReduce s
+              v <- pickBranchVar s
+              if v < 0
+                then pure (Just True)
+                else do
+                  modifySTRef' (statDec s) (+ 1)
+                  pol <- readArray (polarity s) v
+                  let l = if pol then posLit v else negLit v
+                  newDecisionLevel s
+                  _ <- enqueue s l (-1)
+                  loop confSoFar
+
+maybeReduce :: Solver s -> ST s ()
+maybeReduce s = do
+  nl <- readSTRef (nLearnts s)
+  when (nl >= 2000) $ reduceDB s
+
+reduceDB :: Solver s -> ST s ()
+reduceDB s = do
+  cids <- readSTRef (learnts s)
+  alive <- filterM (\cid -> do cl <- getClause s cid; not <$> readSTRef (clsDead cl)) cids
+  scored <- mapM (\cid -> do
+                     cl <- getClause s cid
+                     a <- readSTRef (clsAct cl)
+                     lbd <- readSTRef (clsLbd cl)
+                     locked <- isLocked s cid cl
+                     pure (cid, cl, a, lbd, locked)) alive
+  let removable = [ t | t@(_, _, _, lbd, locked) <- scored, not locked, lbd > 2 ]
+      keepFixed = [ (cid, cl) | (cid, cl, _, lbd, locked) <- scored, locked || lbd <= 2 ]
+      sortedByAct = sortByActAsc removable
+      half = length sortedByAct `div` 2
+      (toRemove, toKeepRest) = splitAt half sortedByAct
+  forM_ toRemove $ \(_, cl, _, _, _) -> writeSTRef (clsDead cl) True
+  let survivors = map (\(cid, cl) -> (cid, cl)) keepFixed
+                  ++ map (\(cid, cl, _, _, _) -> (cid, cl)) toKeepRest
+  writeSTRef (learnts s) (map fst survivors)
+  writeSTRef (nLearnts s) (length survivors)
+  modifySTRef' (statRemove s) (+ length toRemove)
+
+sortByActAsc :: [(Cid, Clause s, Double, Int, Bool)] -> [(Cid, Clause s, Double, Int, Bool)]
+sortByActAsc = sortByKey (\(_, _, a, _, _) -> a)
+
+sortByKey :: Ord k => (a -> k) -> [a] -> [a]
+sortByKey f = foldr insertBy []
+  where
+    insertBy x [] = [x]
+    insertBy x (y : ys)
+      | f x <= f y = x : y : ys
+      | otherwise  = y : insertBy x ys
+
+isLocked :: Solver s -> Cid -> Clause s -> ST s Bool
+isLocked s cid cl = do
+  l0 <- readArray (clsLits cl) 0
+  let v = litVar l0
+  vv <- varValue s v
+  if vv == 0
+    then pure False
+    else do
+      r <- readArray (varReason s) v
+      pure (r == cid)
+
+solveInternal :: Int -> [[Int]] -> ST s (Maybe [Bool], Stats)
+solveInternal nv clausesIn = do
+  s <- newSolver nv
+  forM_ clausesIn (addClause s)
+  ok0 <- readSTRef (okFlag s)
+  result <-
+    if not ok0
+      then pure False
+      else do
+        confl0 <- propagate s
+        if confl0 >= 0
+          then do writeSTRef (okFlag s) False; pure False
+          else runRestarts s 0
+  model <-
+    if result
+      then Just <$> extractModel s
+      else pure Nothing
+  st <- collectStats s
+  pure (model, st)
+
+runRestarts :: Solver s -> Int -> ST s Bool
+runRestarts s restartNo = do
+  let budget = luby restartNo * 100
+  outcome <- search s budget
+  case outcome of
+    Just verdict -> pure verdict
+    Nothing -> do
+      modifySTRef' (statRest s) (+ 1)
+      runRestarts s (restartNo + 1)
+
+extractModel :: Solver s -> ST s [Bool]
+extractModel s =
+  mapM (\v -> do
+          vv <- varValue s v
+          pure (vv /= -1)) [0 .. numVars s - 1]
+
+collectStats :: Solver s -> ST s Stats
+collectStats s = do
+  d <- readSTRef (statDec s)
+  c <- readSTRef (statConf s)
+  p <- readSTRef (statProp s)
+  r <- readSTRef (statRest s)
+  l <- readSTRef (statLearn s)
+  rm <- readSTRef (statRemove s)
+  pure (Stats d c p r l rm)