diff --git a/src/Sift/Preprocess.hs b/src/Sift/Preprocess.hs
new file mode 100644
index 0000000..26ceae4
--- /dev/null
+++ b/src/Sift/Preprocess.hs
@@ -0,0 +1,120 @@
+module Sift.Preprocess
+  ( PreResult(..)
+  , unitPropagate
+  , pureLiteralElim
+  , subsume
+  , selfSubsume
+  , preprocess
+  , reconstruct
+  ) where
+
+import Sift.Types
+import Data.List (foldl')
+import Data.Set (Set)
+import qualified Data.Set as Set
+import qualified Data.Map.Strict as Map
+
+data PreResult
+  = Unsatisfiable
+  | Simplified [Lit] CNF
+  deriving (Eq, Show)
+
+toSets :: CNF -> [Set Lit]
+toSets (CNF cs) = map Set.fromList cs
+
+fromSets :: [Set Lit] -> CNF
+fromSets = CNF . map Set.toList
+
+unitPropagate :: CNF -> Maybe ([Lit], CNF)
+unitPropagate cnf = go [] (toSets cnf)
+  where
+    go assigned clauses
+      | any Set.null clauses = Nothing
+      | otherwise =
+          case [ Set.findMin c | c <- clauses, Set.size c == 1 ] of
+            []      -> Just (reverse assigned, fromSets clauses)
+            (l : _) ->
+              let clauses' = propagateOne l clauses
+              in go (l : assigned) clauses'
+
+propagateOne :: Lit -> [Set Lit] -> [Set Lit]
+propagateOne l = foldr step []
+  where
+    step c acc
+      | l `Set.member` c        = acc
+      | neg l `Set.member` c    = Set.delete (neg l) c : acc
+      | otherwise               = c : acc
+
+pureLiteralElim :: CNF -> ([Lit], CNF)
+pureLiteralElim cnf = go [] (toSets cnf)
+  where
+    go assigned clauses =
+      case pureLiterals clauses of
+        []   -> (reverse assigned, fromSets clauses)
+        pures ->
+          let clauses' = foldl' (flip removeSatisfied) clauses pures
+          in go (reverse pures ++ assigned) clauses'
+
+pureLiterals :: [Set Lit] -> [Lit]
+pureLiterals clauses =
+  [ l
+  | l <- Set.toList allLits
+  , not (neg l `Set.member` allLits)
+  ]
+  where
+    allLits = Set.unions clauses
+
+removeSatisfied :: Lit -> [Set Lit] -> [Set Lit]
+removeSatisfied l = filter (not . Set.member l)
+
+subsume :: CNF -> CNF
+subsume cnf = fromSets (dropSubsumed (dedupe (toSets cnf)))
+
+dedupe :: [Set Lit] -> [Set Lit]
+dedupe = Set.toList . Set.fromList
+
+dropSubsumed :: [Set Lit] -> [Set Lit]
+dropSubsumed clauses =
+  [ c | c <- clauses, not (any (subsumedBy c) clauses) ]
+  where
+    subsumedBy c d = d /= c && d `Set.isSubsetOf` c
+
+selfSubsume :: CNF -> CNF
+selfSubsume cnf = fromSets (fixSelf (toSets cnf))
+
+fixSelf :: [Set Lit] -> [Set Lit]
+fixSelf clauses =
+  let stepped = map (strengthen clauses) clauses
+  in if stepped == clauses then clauses else fixSelf stepped
+
+strengthen :: [Set Lit] -> Set Lit -> Set Lit
+strengthen clauses c = foldl' tryLit c (Set.toList c)
+  where
+    tryLit acc l
+      | any (resolvesAway l acc) clauses = Set.delete l acc
+      | otherwise                        = acc
+    resolvesAway l acc d =
+      neg l `Set.member` d
+        && Set.delete (neg l) d `Set.isSubsetOf` Set.delete l acc
+
+preprocess :: CNF -> PreResult
+preprocess cnf = loop [] cnf
+  where
+    loop fixed current =
+      case unitPropagate current of
+        Nothing -> Unsatisfiable
+        Just (units, afterUnits) ->
+          let (pures, afterPures) = pureLiteralElim afterUnits
+              afterSub  = subsume afterPures
+              afterSelf = subsume (selfSubsume afterSub)
+              fixed'    = fixed ++ units ++ pures
+          in if clauseSetEq afterSelf current && null units && null pures
+               then Simplified fixed' afterSelf
+               else loop fixed' afterSelf
+
+clauseSetEq :: CNF -> CNF -> Bool
+clauseSetEq a b = Set.fromList (toSets a) == Set.fromList (toSets b)
+
+reconstruct :: [Lit] -> Assignment -> Assignment
+reconstruct fixed asn =
+  foldl' (\m l -> Map.insert (litVar l) (litSign l) m) asn fixed