diff --git a/src/TypeChecker/Bugs.md b/src/TypeChecker/Bugs.md
index 8dad339..fb986a5 100644
--- a/src/TypeChecker/Bugs.md
+++ b/src/TypeChecker/Bugs.md
@@ -27,38 +27,12 @@ Program below should not type check
 main : a -> b ;
 main x = x;
 ```
+## Pattern match on functions
+
+Program below should not type check
 
-## Bugged error message
 ```hs
-data Maybe () where {
-    Nothing : Maybe
-    Just : Int -> Maybe
-    };
-
-fmap : (Int -> Int) -> Maybe -> Maybe ;
-fmap f ma = case ma of {
-    Nothing => Nothing ;
-    Just a => Just (f a) ;
-};
-
-pure : Int -> Maybe ;
-pure x = Just x ;
-
-ap mf ma = case mf of {
-    Just f => case ma of {
-        Nothing => Nothing;
-        Just a => Just (f a);
-    };
-    Nothing => Nothing;
-};
-    
-return = pure;
-
-bind ma f = case ma of {
-    Nothing => Nothing ;
-    Just a => f a ;
+main = case \x. x of {
+    _ => 0;
 };
 ```
-```
-TYPECHECKER ERROR
-Inferred type '("c" -> "Int") -> "Maybe" -> "Maybe" does not match specified type '("Int" -> "Int") -> "Maybe" -> "Maybe"'
diff --git a/src/TypeChecker/TypeCheckerHm.hs b/src/TypeChecker/TypeCheckerHm.hs
index 1fc0ee4..2edd1f2 100644
--- a/src/TypeChecker/TypeCheckerHm.hs
+++ b/src/TypeChecker/TypeCheckerHm.hs
@@ -12,7 +12,6 @@ import Control.Monad.Except
 import Control.Monad.Identity (Identity, runIdentity)
 import Control.Monad.Reader
 import Control.Monad.State
-import Data.Bifunctor (second)
 import Data.Coerce (coerce)
 import Data.Function (on)
 import Data.List (foldl')
@@ -30,16 +29,17 @@ initCtx = Ctx mempty
 initEnv = Env 0 'a' mempty mempty mempty
 
 run :: Infer a -> Either Error a
-run = runC initEnv initCtx
+run = run' initEnv initCtx
 
-runC :: Env -> Ctx -> Infer a -> Either Error a
-runC e c =
+run' :: Env -> Ctx -> Infer a -> Either Error a
+run' e c =
     runIdentity
         . runExceptT
         . flip runReaderT c
         . flip evalStateT e
         . runInfer
 
+-- | Type check a program
 typecheck :: Program -> Either String (T.Program' Type)
 typecheck = onLeft msg . run . checkPrg
   where
@@ -47,20 +47,87 @@ typecheck = onLeft msg . run . checkPrg
     onLeft f (Left x) = Left $ f x
     onLeft _ (Right x) = Right x
 
+checkPrg :: Program -> Infer (T.Program' Type)
+checkPrg (Program bs) = do
+    preRun bs
+    bs' <- checkDef bs
+    return $ T.Program bs'
+
+preRun :: [Def] -> Infer ()
+preRun [] = return ()
+preRun (x : xs) = case x of
+    DSig (Sig n t) -> do
+        collect (collectTVars t)
+        gets (M.member (coerce n) . sigs)
+            >>= flip
+                when
+                ( uncatchableErr $ Aux.do
+                    "Duplicate signatures for function"
+                    quote $ printTree n
+                )
+        insertSig (coerce n) (Just t) >> preRun xs
+    DBind (Bind n _ e) -> do
+        collect (collectTVars e)
+        s <- gets sigs
+        case M.lookup (coerce n) s of
+            Nothing -> insertSig (coerce n) Nothing >> preRun xs
+            Just _ -> preRun xs
+    DData d@(Data t _) -> collect (collectTVars t) >> checkData d >> preRun xs
+
+checkDef :: [Def] -> Infer [T.Def' Type]
+checkDef [] = return []
+checkDef (x : xs) = case x of
+    (DBind b) -> do
+        b' <- checkBind b
+        xs' <- checkDef xs
+        return $ T.DBind b' : xs'
+    (DData d) -> do
+        xs' <- checkDef xs
+        return $ T.DData (coerceData d) : xs'
+    (DSig _) -> checkDef xs
+  where
+    coerceData (Data t injs) =
+        T.Data t $ map (\(Inj name typ) -> T.Inj (coerce name) typ) injs
+
+checkBind :: Bind -> Infer (T.Bind' Type)
+checkBind (Bind name args e) = do
+    let lambda = makeLambda e (reverse (coerce args))
+    (sub0, (e, lambda_t)) <- inferExp lambda
+    s <- gets sigs
+    case M.lookup (coerce name) s of
+        Just (Just t') -> do
+            let fsig = apply sub0 t'
+            sub1 <- liftEither $ runIdentity $ runExceptT $ execStateT (typeEq fsig lambda_t) mempty
+            sub2 <- liftEither $ runIdentity $ runExceptT $ execStateT (typeEq lambda_t fsig) mempty
+            unless
+                (lambda_t == apply sub1 fsig && apply sub2 lambda_t == fsig)
+                ( uncatchableErr $ Aux.do
+                    "Inferred type"
+                    quote $ printTree lambda_t
+                    "does not match specified type"
+                    quote $ printTree t'
+                )
+            return $ T.Bind (coerce name, lambda_t) [] (e, lambda_t)
+        _ -> do
+            insertSig (coerce name) (Just lambda_t)
+            return (T.Bind (coerce name, lambda_t) [] (e, lambda_t))
+
 checkData :: Data -> Infer ()
 checkData err@(Data typ injs) = do
     (name, tvars) <- go typ
-    dataErr (mapM_ (\i -> typecheckInj i name tvars) injs) err
+    dataErr (mapM_ (\i -> checkInj i name tvars) injs) err
   where
     go = \case
         TData name typs
             | Right tvars' <- mapM toTVar typs ->
                 pure (name, tvars')
         TAll _ _ -> uncatchableErr "Explicit foralls not allowed, for now"
-        _ -> uncatchableErr $ unwords ["Bad data type definition: ", printTree typ]
+        _ ->
+            uncatchableErr $
+                unwords ["Bad data type definition: ", printTree typ]
 
-typecheckInj :: Inj -> UIdent -> [TVar] -> Infer ()
-typecheckInj (Inj c inj_typ) name tvars
+checkInj :: Inj -> UIdent -> [TVar] -> Infer ()
+checkInj (Inj c inj_typ) name tvars
     | Right False <- boundTVars tvars inj_typ =
         catchableErr "Unbound type variables"
     | TData name' typs <- returnType inj_typ
@@ -108,109 +175,11 @@ returnType :: Type -> Type
 returnType (TFun _ t2) = returnType t2
 returnType a = a
 
-checkPrg :: Program -> Infer (T.Program' Type)
-checkPrg (Program bs) = do
-    preRun bs
-    bs' <- checkDef bs
-    return $ T.Program bs'
-
-preRun :: [Def] -> Infer ()
-preRun [] = return ()
-preRun (x : xs) = case x of
-    DSig (Sig n t) -> do
-        collect (collectTVars t)
-        gets (M.member (coerce n) . sigs)
-            >>= flip
-                when
-                ( uncatchableErr $ Aux.do
-                    "Duplicate signatures for function"
-                    quote $ printTree n
-                )
-        insertSig (coerce n) (Just t) >> preRun xs
-    DBind (Bind n _ e) -> do
-        collect (collectTVars e)
-        s <- gets sigs
-        case M.lookup (coerce n) s of
-            Nothing -> insertSig (coerce n) Nothing >> preRun xs
-            Just _ -> preRun xs
-    DData d@(Data t _) -> collect (collectTVars t) >> checkData d >> preRun xs
-
-checkDef :: [Def] -> Infer [T.Def' Type]
-checkDef [] = return []
-checkDef (x : xs) = case x of
-    (DBind b) -> do
-        b' <- checkBind b
-        xs' <- checkDef xs
-        return $ T.DBind b' : xs'
-    (DData d) -> do
-        xs' <- checkDef xs
-        return $ T.DData (coerceData d) : xs'
-    (DSig _) -> checkDef xs
-  where
-    coerceData (Data t injs) =
-        T.Data t $ map (\(Inj name typ) -> T.Inj (coerce name) typ) injs
-
-checkBind :: Bind -> Infer (T.Bind' Type)
-checkBind (Bind name args e) = do
-    let lambda = makeLambda e (reverse (coerce args))
-    (e, lambda_t) <- inferExp lambda
-    s <- gets sigs
-    case M.lookup (coerce name) s of
-        Just (Just t') -> do
-            sub1 <- unify lambda_t t'
-            sub2 <- unify t' lambda_t
-            unless
-                (apply sub1 lambda_t == t' && lambda_t == apply sub2 t')
-                ( uncatchableErr $ Aux.do
-                    "Inferred type"
-                    quote $ printTree lambda_t
-                    "does not match specified type"
-                    quote $ printTree t'
-                )
-            return $ T.Bind (coerce name, t') [] (e, lambda_t)
-        _ -> do
-            insertSig (coerce name) (Just lambda_t)
-            return (T.Bind (coerce name, lambda_t) [] (e, lambda_t))
-
-typeEq :: Type -> Type -> Bool
-typeEq (TFun l r) (TFun l' r') = typeEq l l' && typeEq r r'
-typeEq (TLit a) (TLit b) = a == b
-typeEq (TData name a) (TData name' b) =
-    length a == length b
-        && name == name'
-        && and (zipWith typeEq a b)
-typeEq (TAll _ t1) t2 = t1 `typeEq` t2
-typeEq t1 (TAll _ t2) = t1 `typeEq` t2
-typeEq (TVar _) (TVar _) = True
-typeEq _ _ = False
-
-skolemize :: Type -> Type
-skolemize (TVar (MkTVar a)) = TEVar (MkTEVar $ coerce a)
-skolemize (TAll x t) = TAll x (skolemize t)
-skolemize (TFun t1 t2) = (TFun `on` skolemize) t1 t2
-skolemize t = t
-
-isMoreSpecificOrEq :: Type -> Type -> Bool
-isMoreSpecificOrEq t1 (TAll _ t2) = isMoreSpecificOrEq t1 t2
-isMoreSpecificOrEq (TFun a b) (TFun c d) =
-    isMoreSpecificOrEq a c && isMoreSpecificOrEq b d
-isMoreSpecificOrEq (TData n1 ts1) (TData n2 ts2) =
-    n1 == n2
-        && length ts1 == length ts2
-        && and (zipWith isMoreSpecificOrEq ts1 ts2)
-isMoreSpecificOrEq _ (TVar _) = True
-isMoreSpecificOrEq a b = a == b
-
-isPoly :: Type -> Bool
-isPoly (TAll _ _) = True
-isPoly (TVar _) = True
-isPoly _ = False
-
-inferExp :: Exp -> Infer (T.ExpT' Type)
+inferExp :: Exp -> Infer (Subst, T.ExpT' Type)
 inferExp e = do
     (s, (e', t)) <- algoW e
     let subbed = apply s t
-    return $ second (const subbed) (e', t)
+    return (s, (e', subbed))
 
 class CollectTVars a where
     collectTVars :: a -> Set T.Ident
@@ -223,7 +192,8 @@ instance CollectTVars Type where
     collectTVars (TVar (MkTVar i)) = S.singleton (coerce i)
     collectTVars (TAll _ t) = collectTVars t
     collectTVars (TFun t1 t2) = (S.union `on` collectTVars) t1 t2
-    collectTVars (TData _ ts) = foldl' (\acc x -> acc `S.union` collectTVars x) S.empty ts
+    collectTVars (TData _ ts) =
+        foldl' (\acc x -> acc `S.union` collectTVars x) S.empty ts
     collectTVars _ = S.empty
 
 collect :: Set T.Ident -> Infer ()
@@ -232,7 +202,7 @@ collect s = modify (\st -> st{takenTypeVars = s `S.union` takenTypeVars st})
 algoW :: Exp -> Infer (Subst, T.ExpT' Type)
 algoW = \case
     err@(EAnn e t) -> do
-        (s1, (e', t')) <- exprErr (algoW e) err
+        (sub0, (e', t')) <- exprErr (algoW e) err
         sub1 <- unify t t'
         sub2 <- unify t' t
         unless
@@ -243,8 +213,7 @@ algoW = \case
                 "does not match inferred type"
                 quote $ printTree t'
             )
-        s2 <- exprErr (unify t t') err
-        let comp = s2 `compose` s1
+        let comp = sub2 `compose` sub1 `compose` sub0
         return (comp, apply comp (e', t))
 
     -- \| ------------------
@@ -257,7 +226,9 @@ algoW = \case
     EVar i -> do
         var <- asks vars
         case M.lookup (coerce i) var of
-            Just t -> inst t >>= \x -> return (nullSubst, (T.EVar $ coerce i, x))
+            Just t ->
+                inst t >>= \x ->
+                    return (nullSubst, (T.EVar $ coerce i, x))
             Nothing -> do
                 sig <- gets sigs
                 case M.lookup (coerce i) sig of
@@ -266,7 +237,10 @@ algoW = \case
                         fr <- fresh
                         insertSig (coerce i) (Just fr)
                         return (nullSubst, (T.EVar $ coerce i, fr))
-                    Nothing -> uncatchableErr $ "Unbound variable: " <> printTree i
+                    Nothing ->
+                        uncatchableErr $
+                            "Unbound variable: "
+                                <> printTree i
     EInj i -> do
         constr <- gets injections
         case M.lookup (coerce i) constr of
@@ -283,14 +257,11 @@ algoW = \case
 
     err@(EAbs name e) -> do
         fr <- fresh
-        exprErr
-            ( withBinding (coerce name) fr $ do
-                (s1, (e', t')) <- exprErr (algoW e) err
-                let varType = apply s1 fr
-                let newArr = TFun varType t'
-                return (s1, apply s1 (T.EAbs (coerce name) (e', t'), newArr))
-            )
-            err
+        withBinding (coerce name) fr $ do
+            (s1, (e', t')) <- exprErr (algoW e) err
+            let varType = apply s1 fr
+            let newArr = TFun varType t'
+            return (s1, apply s1 (T.EAbs (coerce name) (e', t'), newArr))
 
     -- \| Γ ⊢ e₀ : τ₀, S₀    S₀Γ ⊢ e₁ : τ₁, S₁
     -- \| s₂ = mgu(s₁τ₀, Int)    s₃ = mgu(s₂τ₁, Int)
@@ -338,29 +309,120 @@ algoW = \case
             (s2, (e1', t2)) <- algoW e1
             let comp = s2 `compose` s1
             return (comp, apply comp (T.ELet bind' (e1', t2), t2))
-
-    -- \| TODO: Add judgement
     ECase caseExpr injs -> do
         (sub, (e', t)) <- algoW caseExpr
         (subst, injs, ret_t) <- checkCase t injs
         let comp = subst `compose` sub
         return (comp, apply comp (T.ECase (e', t) injs, ret_t))
 
-makeLambda :: Exp -> [T.Ident] -> Exp
-makeLambda = foldl (flip (EAbs . coerce))
+checkCase :: Type -> [Branch] -> Infer (Subst, [T.Branch' Type], Type)
+checkCase _ [] = catchableErr "Atleast one case required"
+checkCase expT brnchs = do
+    (subs, branchTs, injs, returns) <- unzip4 <$> mapM inferBranch brnchs
+    let sub0 = composeAll subs
+    (sub1, _) <-
+        foldM
+            ( \(sub, acc) x ->
+                (\a -> (a `compose` sub, a `apply` acc)) <$> unify x acc
+            )
+            (nullSubst, expT)
+            branchTs
+    (sub2, returns_type) <-
+        foldM
+            ( \(sub, acc) x ->
+                (\a -> (a `compose` sub, a `apply` acc)) <$> unify x acc
+            )
+            (nullSubst, head returns)
+            (tail returns)
+    let comp = sub2 `compose` sub1 `compose` sub0
+    return (comp, apply comp injs, apply comp returns_type)
+
+inferBranch :: Branch -> Infer (Subst, Type, T.Branch' Type, Type)
+inferBranch (Branch pat expr) = do
+    newPat@(pat, branchT) <- inferPattern pat
+    (sub, newExp@(_, exprT)) <- withPattern pat (algoW expr)
+    return
+        ( sub
+        , apply sub branchT
+        , T.Branch (apply sub newPat) (apply sub newExp)
+        , apply sub exprT
+        )
+
+inferPattern :: Pattern -> Infer (T.Pattern' Type, Type)
+inferPattern = \case
+    PLit lit -> let lt = litType lit in return (T.PLit (lit, lt), lt)
+    PInj constr patterns -> do
+        t <- gets (M.lookup (coerce constr) . injections)
+        t <-
+            maybeToRightM
+                ( Error
+                    ( Aux.do
+                        "Constructor:"
+                        quote $ printTree constr
+                        "does not exist"
+                    )
+                    True
+                )
+                t
+        let numArgs = typeLength t - 1
+        let (vs, ret) = fromJust (unsnoc $ flattenType t)
+        patterns <- mapM inferPattern patterns
+        unless
+            (length patterns == numArgs)
+            ( catchableErr $ Aux.do
+                "The constructor"
+                quote $ printTree constr
+                " should have "
+                show numArgs
+                " arguments but has been given "
+                show (length patterns)
+            )
+        sub <- composeAll <$> zipWithM unify vs (map snd patterns)
+        return
+            ( T.PInj (coerce constr) (apply sub (map fst patterns))
+            , apply sub ret
+            )
+    PCatch -> (T.PCatch,) <$> fresh
+    PEnum p -> do
+        t <- gets (M.lookup (coerce p) . injections)
+        t <-
+            maybeToRightM
+                ( Error
+                    ( Aux.do
+                        "Constructor:"
+                        quote $ printTree p
+                        "does not exist"
+                    )
+                    True
+                )
+                t
+        unless
+            (typeLength t == 1)
+            ( catchableErr $ Aux.do
+                "The constructor"
+                quote $ printTree p
+                " should have "
+                show (typeLength t - 1)
+                " arguments but has been given 0"
+            )
+        let (TData _data _ts) = t -- nasty nasty
+        frs <- mapM (const fresh) _ts
+        return (T.PEnum $ coerce p, TData _data frs)
+    PVar x -> do
+        fr <- fresh
+        let pvar = T.PVar (coerce x, fr)
+        return (pvar, fr)
 
 -- | Unify two types producing a new substitution
 unify :: Type -> Type -> Infer Subst
-unify t0 t1 = do
+unify t0 t1 =
     case (t0, t1) of
         (TFun a b, TFun c d) -> do
             s1 <- unify a c
             s2 <- unify (apply s1 b) (apply s1 d)
             return $ s1 `compose` s2
-        ----------- TODO: BE CAREFUL!!!! THIS IS PROBABLY WRONG!!! -----------
         (TVar (T.MkTVar a), t@(TData _ _)) -> return $ M.singleton (coerce a) t
         (t@(TData _ _), TVar (T.MkTVar b)) -> return $ M.singleton (coerce b) t
-        -------------------------------------------------------------------
         (TVar (T.MkTVar a), t) -> occurs (coerce a) t
         (t, TVar (T.MkTVar b)) -> occurs (coerce b) t
         (TAll _ t, b) -> unify t b
@@ -422,7 +484,12 @@ occurs i t =
                 )
         else return $ M.singleton i t
 
--- | Generalize a type over all free variables in the substitution set
+{- | Generalize a type over all free variables in the substitution set
+     Used for let bindings to allow expression that do not type check in
+     equivalent lambda expressions:
+        Type checks: let f = \x. x in (f True, f 'a')
+        Does not type check: (\f. (f True, f 'a')) (\x. x)
+-}
 generalize :: Map T.Ident Type -> Type -> Type
 generalize env t = go (S.toList $ free t S.\\ free env) (removeForalls t)
   where
@@ -446,15 +513,27 @@ inst = \case
     TFun t1 t2 -> TFun <$> inst t1 <*> inst t2
     rest -> return rest
 
--- | Compose two substitution sets
-compose :: Subst -> Subst -> Subst
-compose m1 m2 = M.map (apply m1) m2 `M.union` m1
-
-composeAll :: [Subst] -> Subst
-composeAll = foldl' compose nullSubst
-
--- TODO: Split this class into two separate classes, one for free variables
---       and one for applying substitutions
+-- | Generate a new fresh variable
+fresh :: Infer Type
+fresh = do
+    c <- gets nextChar
+    n <- gets count
+    taken <- gets takenTypeVars
+    if c == 'z'
+        then do
+            modify (\st -> st{count = succ (count st), nextChar = 'a'})
+        else modify (\st -> st{nextChar = next (nextChar st)})
+    if coerce [c] `S.member` taken
+        then do
+            fresh
+        else
+            if n == 0
+                then return . TVar . T.MkTVar $ LIdent [c]
+                else return . TVar . T.MkTVar . LIdent $ c : show n
+  where
+    next :: Char -> Char
+    next 'z' = 'a'
+    next a = succ a
 
 -- | A class for substitutions
 class SubstType t where
@@ -468,7 +547,8 @@ class FreeVars t where
 instance FreeVars Type where
     free :: Type -> Set T.Ident
     free (TVar (T.MkTVar a)) = S.singleton (coerce a)
-    free (TAll (T.MkTVar bound) t) = S.singleton (coerce bound) `S.intersection` free t
+    free (TAll (T.MkTVar bound) t) =
+        S.singleton (coerce bound) `S.intersection` free t
     free (TLit _) = mempty
     free (TFun a b) = free a `S.union` free b
     free (TData _ a) = free a
@@ -540,27 +620,19 @@ instance SubstType (T.Id' Type) where
 nullSubst :: Subst
 nullSubst = M.empty
 
--- | Generate a new fresh variable and increment the state counter
-fresh :: Infer Type
-fresh = do
-    c <- gets nextChar
-    n <- gets count
-    taken <- gets takenTypeVars
-    if c == 'z'
-        then do
-            modify (\st -> st{count = succ (count st), nextChar = 'a'})
-        else modify (\st -> st{nextChar = next (nextChar st)})
-    if coerce [c] `S.member` taken
-        then do
-            fresh
-        else
-            if n == 0
-                then return . TVar . T.MkTVar $ LIdent [c]
-                else return . TVar . T.MkTVar . LIdent $ c : show n
-  where
-    next :: Char -> Char
-    next 'z' = 'a'
-    next a = succ a
+-- | Compose two substitution sets
+compose :: Subst -> Subst -> Subst
+compose m1 m2 = M.map (apply m1) m2 `M.union` m1
+
+-- | Compose a list of substitution sets into one
+composeAll :: [Subst] -> Subst
+composeAll = foldl' compose nullSubst
+
+{- | Convert a function with arguments to its pointfree version
+> makeLambda (add x y = x + y) = add = \x. \y. x + y
+-}
+makeLambda :: Exp -> [T.Ident] -> Exp
+makeLambda = foldl (flip (EAbs . coerce))
 
 -- | Run the monadic action with an additional binding
 withBinding :: (Monad m, MonadReader Ctx m) => T.Ident -> Type -> m a -> m a
@@ -571,49 +643,8 @@ withBindings :: (Monad m, MonadReader Ctx m) => [(T.Ident, Type)] -> m a -> m a
 withBindings xs =
     local (\st -> st{vars = foldl' (flip (uncurry M.insert)) (vars st) xs})
 
--- | Insert a function signature into the environment
-insertSig :: T.Ident -> Maybe Type -> Infer ()
-insertSig i t = modify (\st -> st{sigs = M.insert i t (sigs st)})
-
--- | Insert a constructor with its data type
-insertInj :: T.Ident -> Type -> Infer ()
-insertInj i t =
-    modify (\st -> st{injections = M.insert i t (injections st)})
-
-existInj :: T.Ident -> Infer (Maybe Type)
-existInj n = gets (M.lookup n . injections)
-
--------- PATTERN MATCHING ---------
-
-checkCase :: Type -> [Branch] -> Infer (Subst, [T.Branch' Type], Type)
-checkCase _ [] = catchableErr "Atleast one case required"
-checkCase expT brnchs = do
-    (subs, injTs, injs, returns) <- unzip4 <$> mapM inferBranch brnchs
-    let sub0 = composeAll subs
-    (sub1, _) <-
-        foldM
-            ( \(sub, acc) x ->
-                (\a -> (a `compose` sub, a `apply` acc)) <$> unify x acc
-            )
-            (nullSubst, expT)
-            injTs
-    (sub2, returns_type) <-
-        foldM
-            ( \(sub, acc) x ->
-                (\a -> (a `compose` sub, a `apply` acc)) <$> unify x acc
-            )
-            (nullSubst, head returns)
-            (tail returns)
-    let comp = sub2 `compose` sub1 `compose` sub0
-    return (comp, apply comp injs, apply comp returns_type)
-
-inferBranch :: Branch -> Infer (Subst, Type, T.Branch' Type, Type)
-inferBranch (Branch pat expr) = do
-    newPat@(pat, branchT) <- inferPattern pat
-    (sub, newExp@(_, exprT)) <- withPattern pat (algoW expr)
-    return (sub, apply sub branchT, T.Branch (apply sub newPat) (apply sub newExp), apply sub exprT)
-
-withPattern :: T.Pattern' Type -> Infer a -> Infer a
+-- | Run the monadic action with a pattern
+withPattern :: (Monad m, MonadReader Ctx m) => T.Pattern' Type -> m a -> m a
 withPattern p ma = case p of
     T.PVar (x, t) -> withBinding x t ma
     T.PInj _ ps -> foldl' (flip withPattern) ma ps
@@ -621,74 +652,27 @@ withPattern p ma = case p of
     T.PCatch -> ma
     T.PEnum _ -> ma
 
-inferPattern :: Pattern -> Infer (T.Pattern' Type, Type)
-inferPattern = \case
-    PLit lit -> let lt = litType lit in return (T.PLit (lit, lt), lt)
-    PInj constr patterns -> do
-        t <- gets (M.lookup (coerce constr) . injections)
-        t <-
-            maybeToRightM
-                ( Error
-                    ( Aux.do
-                        "Constructor:"
-                        quote $ printTree constr
-                        "does not exist"
-                    )
-                    True
-                )
-                t
-        let numArgs = typeLength t - 1
-        let (vs, ret) = fromJust (unsnoc $ flattenType t)
-        patterns <- mapM inferPattern patterns
-        unless
-            (length patterns == numArgs)
-            ( catchableErr $ Aux.do
-                "The constructor"
-                quote $ printTree constr
-                " should have "
-                show numArgs
-                " arguments but has been given "
-                show (length patterns)
-            )
-        sub <- composeAll <$> zipWithM unify vs (map snd patterns)
-        return (T.PInj (coerce constr) (apply sub (map fst patterns)), apply sub ret)
-    PCatch -> (T.PCatch,) <$> fresh
-    PEnum p -> do
-        t <- gets (M.lookup (coerce p) . injections)
-        t <-
-            maybeToRightM
-                ( Error
-                    ( Aux.do
-                        "Constructor:"
-                        quote $ printTree p
-                        "does not exist"
-                    )
-                    True
-                )
-                t
-        unless
-            (typeLength t == 1)
-            ( catchableErr $ Aux.do
-                "The constructor"
-                quote $ printTree p
-                " should have "
-                show (typeLength t - 1)
-                " arguments but has been given 0"
-            )
-        let (TData _data _ts) = t -- nasty nasty
-        frs <- mapM (const fresh) _ts
-        return (T.PEnum $ coerce p, TData _data frs)
-    PVar x -> do
-        fr <- fresh
-        let pvar = T.PVar (coerce x, fr)
-        return (pvar, fr)
+-- | Insert a function signature into the environment
+insertSig :: T.Ident -> Maybe Type -> Infer ()
+insertSig i t = modify (\st -> st{sigs = M.insert i t (sigs st)})
+
+-- | Insert a constructor into the start with its type
+insertInj :: T.Ident -> Type -> Infer ()
+insertInj i t =
+    modify (\st -> st{injections = M.insert i t (injections st)})
+
+{- | Check if an injection (constructor of data type)
+with an equivalent name has been declared already
+-}
+existInj :: T.Ident -> Infer (Maybe Type)
+existInj n = gets (M.lookup n . injections)
 
 flattenType :: Type -> [Type]
 flattenType (TFun a b) = flattenType a <> flattenType b
 flattenType a = [a]
 
 typeLength :: Type -> Int
-typeLength (TFun a b) = typeLength a + typeLength b
+typeLength (TFun _ b) = 1 + typeLength b
 typeLength _ = 1
 
 litType :: Lit -> Type
@@ -698,23 +682,63 @@ litType (LChar _) = char
 int = TLit "Int"
 char = TLit "Char"
 
-partitionType ::
-    Int -> -- Number of parameters to apply
-    Type ->
-    ([Type], Type)
-partitionType = go []
-  where
-    go acc 0 t = (acc, t)
-    go acc i t = case t of
-        TAll tvar t' -> second (TAll tvar) $ go acc i t'
-        TFun t1 t2 -> go (acc <> [t1]) (i - 1) t2
-        _ -> error "Number of parameters and type doesn't match"
+typeEq :: Type -> Type -> StateT Subst (ExceptT Error Identity) ()
+typeEq (TVar (T.MkTVar a)) t@(TVar _) = do
+    st <- get
+    case M.lookup (coerce a) st of
+        Nothing -> put $ M.insert (coerce a) t st
+        Just t' -> unless (t == t') (catchableErr "TYPE MISMATCH")
+typeEq (TFun l r) (TFun l' r') = typeEq l l' *> typeEq r r'
+typeEq (TAll _ l) (TAll _ r) = typeEq l r
+typeEq (TLit a) (TLit b) = unless (a == b) (catchableErr "TYPE MISMATCH")
+typeEq (TData nameL tL) (TData nameR tR) = do
+    unless (nameL == nameR) (catchableErr "TYPE MISMATCH")
+    zipWithM_ typeEq tL tR
+typeEq (TEVar _) (TEVar _) = catchableErr "TYPE MISMATCH"
+typeEq _ _ = catchableErr "TYPE MISMATCH"
 
-exprErr :: Infer a -> Exp -> Infer a
-exprErr ma exp = catchError ma (\x -> if x.catchable then throwError (x{msg = x.msg <> " in expression: \n" <> printTree exp, catchable = False}) else throwError x)
+{- | Catch an error if possible and add the given
+expression as addition to the error message
+-}
+exprErr :: (Monad m, MonadError Error m) => m a -> Exp -> m a
+exprErr ma exp =
+    catchError
+        ma
+        ( \x ->
+            if x.catchable
+                then
+                    throwError
+                        ( x
+                            { msg =
+                                x.msg
+                                    <> " in expression: \n"
+                                    <> printTree exp
+                            , catchable = False
+                            }
+                        )
+                else throwError x
+        )
 
+{- | Catch an error if possible and add the given
+data as addition to the error message
+-}
 dataErr :: Infer a -> Data -> Infer a
-dataErr ma d = catchError ma (\x -> if x.catchable then throwError (x{msg = x.msg <> " in data: \n" <> printTree d}) else throwError (x{catchable = False}))
+dataErr ma d =
+    catchError
+        ma
+        ( \x ->
+            if x.catchable
+                then
+                    throwError
+                        ( x
+                            { msg =
+                                x.msg
+                                    <> " in data: \n"
+                                    <> printTree d
+                            }
+                        )
+                else throwError (x{catchable = False})
+        )
 
 unzip4 :: [(a, b, c, d)] -> ([a], [b], [c], [d])
 unzip4 =
@@ -737,6 +761,7 @@ data Env = Env
     deriving (Show)
 
 data Error = Error {msg :: String, catchable :: Bool}
+    deriving (Show)
 type Subst = Map T.Ident Type
 
 newtype Infer a = Infer {runInfer :: StateT Env (ReaderT Ctx (ExceptT Error Identity)) a}
diff --git a/tests/TestTypeCheckerHm.hs b/tests/TestTypeCheckerHm.hs
index 5f600ed..bf51a29 100644
--- a/tests/TestTypeCheckerHm.hs
+++ b/tests/TestTypeCheckerHm.hs
@@ -187,6 +187,31 @@ bes =
             "    Nil => 0 ;"
             " };"
         )
+    , testBe
+        "length function on int list infers correct signature"
+        ( D.do
+            "data List () where {"
+            "    Nil : List ()"
+            "    Cons : Int -> List () -> List ()"
+            "};"
+
+            "length xs = case xs of {"
+            "    Nil => 0 ;"
+            "    Cons _ xs => 1 + length xs ;"
+            "};"
+        )
+        ( D.do
+            "data List () where {"
+            "    Nil : List ()"
+            "    Cons : Int -> List () -> List ()"
+            "};"
+
+            "length : List () -> Int ;"
+            "length xs = case xs of {"
+            "    Nil => 0 ;"
+            "    Cons _ xs => 1 + length xs ;"
+            "};"
+        )
     ]
 
 testSatisfy desc test satisfaction = specify desc $ run test `shouldSatisfy` satisfaction