diff --git a/src/TypeChecker/TypeChecker.hs b/src/TypeChecker/TypeChecker.hs
index 9cc37ee..8b7625e 100644
--- a/src/TypeChecker/TypeChecker.hs
+++ b/src/TypeChecker/TypeChecker.hs
@@ -12,6 +12,7 @@ import Control.Monad.State
 import Data.Bifunctor (second)
 import Data.Coerce (coerce)
 import Data.Foldable (traverse_)
+import Data.Function (on)
 import Data.List (foldl')
 import Data.List.Extra (unsnoc)
 import Data.Map (Map)
@@ -149,6 +150,12 @@ typeEq t1 (T.TAll _ t2) = t1 `typeEq` t2
 typeEq (T.TVar _) (T.TVar _) = True
 typeEq _ _ = False
 
+skolem :: T.Type -> T.Type
+skolem (T.TVar (T.MkTVar a)) = T.TLit a
+skolem (T.TAll x t) = T.TAll x (skolem t)
+skolem (T.TFun t1 t2) = (T.TFun `on` skolem) t1 t2
+skolem t = t
+
 isMoreSpecificOrEq :: T.Type -> T.Type -> Bool
 isMoreSpecificOrEq t1 (T.TAll _ t2) = isMoreSpecificOrEq t1 t2
 isMoreSpecificOrEq (T.TFun a b) (T.TFun c d) =
@@ -181,7 +188,7 @@ instance CollectTVars Exp where
 instance CollectTVars Type where
     collectTypeVars (TVar (MkTVar i)) = S.singleton (coerce i)
     collectTypeVars (TAll _ t) = collectTypeVars t
-    collectTypeVars (TFun t1 t2) = collectTypeVars t1 `S.union` collectTypeVars t2
+    collectTypeVars (TFun t1 t2) = (S.union `on` collectTypeVars) t1 t2
     collectTypeVars (TData _ ts) = foldl' (\acc x -> acc `S.union` collectTypeVars x) S.empty ts
     collectTypeVars _ = S.empty
 
@@ -195,7 +202,7 @@ instance NewType Type T.Type where
     toNew = \case
         TLit i -> T.TLit $ coerce i
         TVar v -> T.TVar $ toNew v
-        TFun t1 t2 -> T.TFun (toNew t1) (toNew t2)
+        TFun t1 t2 -> (T.TFun `on` toNew) t1 t2
         TAll b t -> T.TAll (toNew b) (toNew t)
         TData i ts -> T.TData (coerce i) (map toNew ts)
         TEVar _ -> error "Should not exist after typechecker"
@@ -414,10 +421,8 @@ occurs i t =
 
 -- | Generalize a type over all free variables in the substitution set
 generalize :: Map T.Ident T.Type -> T.Type -> T.Type
-generalize env t = go freeVars $ removeForalls t
+generalize env t = go (S.toList $ free t S.\\ free env) (removeForalls t)
   where
-    freeVars :: [T.Ident]
-    freeVars = S.toList $ free t S.\\ free env
     go :: [T.Ident] -> T.Type -> T.Type
     go [] t = t
     go (x : xs) t = T.TAll (T.MkTVar x) (go xs t)