diff --git a/src/Control/Monad/Errorful.hs b/src/Control/Monad/Errorful.hs
index 175d39b..9f78471 100644
--- a/src/Control/Monad/Errorful.hs
+++ b/src/Control/Monad/Errorful.hs
@@ -16,6 +16,7 @@ module Control.Monad.Errorful
 import Control.Monad.State.Strict
 import Control.Monad.Writer
 import Control.Monad.Reader
+import Control.Monad.Accum
 import Control.Monad.Trans
 import Data.Functor.Identity
 import Data.Coerce
@@ -95,3 +96,7 @@ instance (Monoid w, Monad m, MonadWriter w m) => MonadWriter w (ErrorfulT e m) w
         ((,w) <$> ma, es)
     pass (ErrorfulT m) = undefined
 
+instance (Monoid w, Monad m, MonadAccum w m)
+      => MonadAccum w (ErrorfulT e m) where
+    accum = lift . accum
+
diff --git a/src/Rlp/AltParse.y b/src/Rlp/AltParse.y
index fd4f1e5..abc33fe 100644
--- a/src/Rlp/AltParse.y
+++ b/src/Rlp/AltParse.y
@@ -128,7 +128,6 @@ Expr                :: { RlpExpr PsName }
                     : AppE                  { $1 }
                     | LetE                  { $1 }
                     | CaseE                 { $1 }
-                    | Expr1                 { $1 }
                     | LamE                  { $1 }
 
 LamE                :: { RlpExpr PsName }
@@ -155,6 +154,7 @@ Expr1               :: { RlpExpr PsName }
                     | litint                { $1 ^. to extract
                                                   . singular _TokenLitInt
                                                   . to (Finl . Core.LitF . Core.IntL) }
+                    | '(' Expr ')'          { $2 }
 
 AppE                :: { RlpExpr PsName }
                     : AppE Expr1            { Finl $ Core.AppF $1 $2 }
diff --git a/src/Rlp/HindleyMilner.hs b/src/Rlp/HindleyMilner.hs
index 4b3035e..53e4454 100644
--- a/src/Rlp/HindleyMilner.hs
+++ b/src/Rlp/HindleyMilner.hs
@@ -13,7 +13,9 @@ module Rlp.HindleyMilner
 import Control.Lens             hiding (Context', Context, (:<), para)
 import Control.Monad.Errorful
 import Control.Monad.State
+import Control.Monad.Accum
 import Control.Monad
+import Control.Arrow            ((>>>))
 import Control.Monad.Writer.Strict
 import Data.Text                qualified as T
 import Data.Pretty
@@ -40,10 +42,6 @@ import Core.Syntax              (ExprF(..), Lit(..))
 import Rlp.HindleyMilner.Types
 --------------------------------------------------------------------------------
 
--- | Synonym for @Errorful [TypeError]@. This means an @HMError@ action may
--- throw any number of fatal or nonfatal errors. Run with @runErrorful@.
-type HMError = Errorful TypeError
-
 fixCofree :: (Functor f, Functor g)
           => Iso (Fix f) (Fix g) (Cofree f ()) (Cofree g b)
 fixCofree = iso sa bt where
@@ -55,53 +53,80 @@ lookupVar n g = case g ^. contextVars . at n of
     Just t -> pure t
     Nothing -> addFatal $ TyErrUntypedVariable n
 
-gather :: Context -> RlpExpr PsName -> HM (Type PsName)
-gather g = \case
+gather :: RlpExpr PsName -> HM (Type PsName, PartialJudgement)
+gather e = look >>= (H.lookup e >>> maybe memoise pure)
+    where
+        memoise = do
+            r <- gather' e
+            add (H.singleton e r)
+            pure r
 
-    Finl (LitF (IntL _)) -> pure IntT
+gather' :: RlpExpr PsName -> HM (Type PsName, PartialJudgement)
+gather' = \case
+    Finl (LitF (IntL _)) -> pure (IntT, mempty)
+
+    Finl (VarF n) -> do
+        t <- freshTv
+        let j = mempty & assumptions .~ H.singleton n [t]
+        pure (t,j)
 
     Finl (AppF f x) -> do
-        tf <- gather g f
-        tx <- gather g x
         tfx <- freshTv
-        addConstraint $ Equality tf (tx :-> tfx)
-        pure tfx
+        (tf,jf) <- gather f
+        (tx,jx) <- gather x
+        let jtfx = mempty & constraints .~ [Equality tf (tx :-> tfx)]
+        pure (tfx, jf <> jx <> jtfx)
 
-    Finl (VarF n) -> lookupVar n g
+    Finl (LamF [b] e) -> do
+        tb <- freshTv
+        (te,je) <- gather e
+        let cs = maybe [] (fmap $ Equality tb) (je ^. assumptions . at b)
+            as = je ^. assumptions & at b .~ Nothing
+            j = mempty & constraints .~ cs & assumptions .~ as
+            t = tb :-> te
+        pure (t,j)
 
-    Finl (LamF bs e) -> do
-        tbs <- for bs $ \b -> (b,) <$> freshTv
-        te <- gather (supplement tbs g) e
-        pure $ foldrOf (each . _2) (:->) te tbs
+unify :: [Constraint] -> HM Context
 
-unify :: Context -> [Constraint] -> HM Context
+unify [] = pure mempty
 
-unify g [] = pure g
-
-unify g (Equality (sx :-> sy) (tx :-> ty) : cs) =
-    unify g $ Equality sx tx : Equality sy ty : cs
+unify (Equality (sx :-> sy) (tx :-> ty) : cs) =
+    unify $ Equality sx tx : Equality sy ty : cs
 
 -- elim
-unify g (Equality (ConT s) (ConT t) : cs) | s == t = unify g cs
-unify g (Equality (VarT s) (VarT t) : cs) | s == t = unify g cs
+unify (Equality (ConT s) (ConT t) : cs) | s == t = unify cs
+unify (Equality (VarT s) (VarT t) : cs) | s == t = unify cs
 
-unify g (Equality (VarT s) t : cs)
+unify (Equality (VarT s) t : cs)
     | occurs s t = addFatal $ TyErrRecursiveType s t
-    | otherwise  = unify g' cs'
+    | otherwise  = unify cs' <&> contextVars . at s ?~ t
   where
-    g' = supplement [(s,t)] g
     cs' = cs & each . constraintTypes %~ subst s t
 
 -- swap
-unify g (Equality s (VarT t) : cs) = unify g (Equality (VarT t) s : cs)
+unify (Equality s (VarT t) : cs) = unify (Equality (VarT t) s : cs)
 
-unify _ (Equality s t : _) = addFatal $ TyErrCouldNotUnify s t
+unify (Equality s t : _) = addFatal $ TyErrCouldNotUnify s t
 
-solve :: Context -> RlpExpr PsName -> HM (Type PsName)
-solve g e = do
-    (t,cs) <- listen $ gather g e
-    g' <- unify g cs
-    pure $ ifoldrOf (contextVars . itraversed) subst t g'
+annotate :: RlpExpr PsName
+         -> HM (Cofree (RlpExprF PsName) (Type PsName, PartialJudgement))
+annotate = sequenceA . fixtend (gather . wrapFix)
+
+solveTree :: Cofree (RlpExprF PsName) (Type PsName, PartialJudgement)
+          -> HM (Type PsName)
+solveTree e = undefined
+
+infer1 :: RlpExpr PsName -> HM (Type PsName)
+infer1 e = do
+    ((t,j) :< _) <- annotate e
+    g <- unify (j ^. constraints)
+    pure $ ifoldrOf (contextVars . itraversed) subst t g
+
+solve = undefined
+-- solve g e = do
+--     (t,j) <- gather e
+--     g' <- unify cs
+--     pure $ ifoldrOf (contextVars . itraversed) subst t g'
 
 occurs :: PsName -> Type PsName -> Bool
 occurs n = cata \case
@@ -122,11 +147,11 @@ prettyHM :: (Pretty a)
 prettyHM = over (mapped . _1) rpretty
          . over (mapped . _2 . each) rpretty
 
-fixtend :: (f (Fix f) -> b) -> Fix f -> Cofree f b
-fixtend = undefined
+fixtend :: Functor f => (f (Fix f) -> b) -> Fix f -> Cofree f b
+fixtend c (Fix f) = c f :< fmap (fixtend c) f
 
 infer :: RlpExpr PsName -> HM (Cofree (RlpExprF PsName) (Type PsName))
-infer = _ . fixtend (solve _ . wrapFix)
+infer = undefined
 
 typeCheckRlpProgR :: (Monad m)
                   => Program PsName (RlpExpr PsName)
diff --git a/src/Rlp/HindleyMilner/Types.hs b/src/Rlp/HindleyMilner/Types.hs
index dee81d5..d3604c6 100644
--- a/src/Rlp/HindleyMilner/Types.hs
+++ b/src/Rlp/HindleyMilner/Types.hs
@@ -12,10 +12,13 @@ import GHC.Generics             (Generic(..), Generically(..))
 import Data.Kind                qualified
 import Data.Text                qualified as T
 import Control.Monad.Writer
+import Control.Monad.Accum
+import Control.Monad.Trans.Accum
 import Control.Monad.Errorful
 import Control.Monad.State
 import Text.Printf
 import Data.Pretty
+import Data.Function
 
 import Control.Lens             hiding (Context', Context)
 
@@ -26,22 +29,32 @@ import Rlp.AltSyntax
 newtype Context = Context
     { _contextVars      :: HashMap PsName (Type PsName)
     }
-    deriving (Generic)
+    deriving (Show, Generic)
     deriving (Semigroup, Monoid)
         via Generically Context
 
 data Constraint = Equality (Type PsName) (Type PsName)
     deriving (Eq, Generic, Show)
 
-data PartialJudgement = PartialJudgement [Constraint]
-                                         (HashMap PsName [Type PsName])
+data PartialJudgement = PartialJudgement
+    { _constraints :: [Constraint]
+    , _assumptions :: HashMap PsName [Type PsName]
+    }
     deriving (Generic, Show)
-    deriving (Semigroup, Monoid)
+    deriving (Monoid)
         via Generically PartialJudgement
 
+instance Semigroup PartialJudgement where
+    a <> b = PartialJudgement
+        { _constraints = ((<>) `on` _constraints) a b
+        , _assumptions = (H.unionWith (<>) `on` _assumptions) a b
+        }
+
 instance Hashable Constraint
 
-type HM = ErrorfulT TypeError (StateT Int (Writer [Constraint]))
+type Memo = HashMap (RlpExpr PsName) (Type PsName, PartialJudgement)
+
+type HM = ErrorfulT TypeError (StateT Int (Accum Memo))
 
 -- | Type error enum.
 data TypeError
@@ -116,16 +129,16 @@ freshTv = do
     modify succ
     pure . VarT $ "$a" <> T.pack (show n)
 
-runHM' :: HM a -> Either [TypeError] (a, [Constraint])
-runHM' e = maybe (Left es) (Right . (,cs)) ma
+runHM' :: HM a -> Either [TypeError] a
+runHM' e = maybe (Left es) Right ma
     where
-        ((ma,es),cs) = runWriter . (`evalStateT` 0) . runErrorfulT $ e
+        ((ma,es),m) = (`runAccum` mempty) . (`evalStateT` 0) . runErrorfulT $ e
 
-addConstraint :: Constraint -> HM ()
-addConstraint = tell . pure
-
--- makePrisms ''PartialJudgement
+-- addConstraint :: Constraint -> HM ()
+-- addConstraint = tell . pure
 
+makePrisms ''PartialJudgement
+makeLenses ''PartialJudgement
 makeLenses ''Context
 makePrisms ''Constraint
 makePrisms ''TypeError