diff --git a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck.hs b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck.hs
index a2fff947..506277ef 100644
--- a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck.hs
+++ b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck.hs
@@ -19,11 +19,12 @@ import Control.Monad.Freer.TH (makeEffect)
 import Data.Default (Default (def))
 import Data.Foldable (Foldable (toList), traverse_)
 import Data.Map qualified as M
-import LambdaBuffers.Compiler.KindCheck.Derivation (Context, constraintContext, context)
+import LambdaBuffers.Compiler.KindCheck.Derivation (Context, classContext, context)
 import LambdaBuffers.Compiler.KindCheck.Inference (protoKind2Kind)
 import LambdaBuffers.Compiler.KindCheck.Inference qualified as I
 import LambdaBuffers.Compiler.KindCheck.Kind (Kind (KConstraint, KType, KVar, (:->:)))
 import LambdaBuffers.Compiler.KindCheck.Type (
+  QualifiedTyClassRefName (QualifiedTyClassRefName),
   Variable (QualifiedTyClassRef, QualifiedTyRef, TyVar),
   fcrISOqtcr,
   ftrISOqtr,
@@ -302,11 +303,13 @@ kind2ProtoKind = \case
 --------------------------------------------------------------------------------
 -- Class Definition Based Context Building.
 
-classDef2Context :: forall effs. PC.ClassDef -> Eff effs Context
+classDef2Context :: forall effs. Member (Reader PC.ModuleName) effs => PC.ClassDef -> Eff effs Context
 classDef2Context cDef = do
-  let className = mkInfoLess . view #className $ cDef
+  modName <- ask
+  let className = cDef ^. #className
+  let qtcn = mkInfoLess . QualifiedTyClassRef $ QualifiedTyClassRefName className modName def
   let classArg = tyArg2Kind . view #classArgs $ cDef
-  pure $ mempty & constraintContext .~ M.singleton className classArg
+  pure $ mempty & classContext .~ M.singleton qtcn (classArg :->: KConstraint)
 
 --------------------------------------------------------------------------------
 -- utilities
diff --git a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Derivation.hs b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Derivation.hs
index f496ab43..b86a27e4 100644
--- a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Derivation.hs
+++ b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Derivation.hs
@@ -1,3 +1,5 @@
+{-# OPTIONS_GHC -Wno-unused-imports #-}
+
 module LambdaBuffers.Compiler.KindCheck.Derivation (
   Derivation (Axiom, Abstraction, Application, Implication),
   QClassName (QClassName),
@@ -11,15 +13,14 @@ module LambdaBuffers.Compiler.KindCheck.Derivation (
   context,
   addContext,
   getAllContext,
-  constraintContext,
+  classContext,
 ) where
 
 import Control.Lens (Lens', lens, makeLenses, (&), (.~), (^.))
 import Control.Lens.Operators ((%~))
 import Data.Map qualified as M
 import LambdaBuffers.Compiler.KindCheck.Kind (Kind)
-import LambdaBuffers.Compiler.KindCheck.Type (Type, Variable)
-import LambdaBuffers.Compiler.ProtoCompat qualified as PC
+import LambdaBuffers.Compiler.KindCheck.Type (Type, Variable (QualifiedTyClassRef))
 import LambdaBuffers.Compiler.ProtoCompat.InfoLess (InfoLess)
 import Prettyprinter (
   Doc,
@@ -43,7 +44,7 @@ data QClassName = QClassName
 data Context = Context
   { _context :: M.Map (InfoLess Variable) Kind
   , _addContext :: M.Map (InfoLess Variable) Kind
-  , _constraintContext :: M.Map (InfoLess PC.ClassName) Kind
+  , _classContext :: M.Map (InfoLess Variable) Kind
   }
   deriving stock (Show, Eq)
 
@@ -62,14 +63,14 @@ instance Semigroup Context where
     c1
       & context %~ (<> c2 ^. context)
       & addContext %~ (<> c2 ^. addContext)
-      & constraintContext %~ (<> c2 ^. constraintContext)
+      & classContext %~ (<> c2 ^. classContext)
 
 instance Monoid Context where
   mempty = Context mempty mempty mempty
 
 -- | Utility to unify the two T.
 getAllContext :: Context -> M.Map (InfoLess Variable) Kind
-getAllContext c = c ^. context <> c ^. addContext
+getAllContext c = c ^. context <> c ^. addContext <> c ^. classContext
 
 data Judgement = Judgement
   { _j'ctx :: Context
diff --git a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Inference.hs b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Inference.hs
index d07954f6..4c46219c 100644
--- a/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Inference.hs
+++ b/lambda-buffers-compiler/src/LambdaBuffers/Compiler/KindCheck/Inference.hs
@@ -21,6 +21,7 @@ module LambdaBuffers.Compiler.KindCheck.Inference (
 ) where
 
 import Control.Lens ((%~), (&), (.~), (^.))
+import Control.Lens.Combinators (to)
 import Control.Lens.Iso (withIso)
 import Control.Monad (void)
 import Control.Monad.Freer (Eff, Member, Members, run)
@@ -47,7 +48,6 @@ import LambdaBuffers.Compiler.KindCheck.Type (
   Variable (QualifiedTyClassRef, QualifiedTyRef, TyVar),
   fcrISOqtcr,
   ftrISOqtr,
-  lcrISOftcr,
   lcrISOqtcr,
   ltrISOqtr,
  )
@@ -250,8 +250,17 @@ runClassDefCheck ctx modName classDef = do
 
 -- | Checks the class definition for correct typedness.
 deriveClassDef :: PC.ClassDef -> Derive ()
-deriveClassDef classDef =
-  traverse_ deriveConstraint (classDef ^. #supers)
+deriveClassDef classDef = do
+  vars <- createLocalConstraintContext classDef
+  traverse_ (local (<> vars) . deriveConstraint) (classDef ^. #supers)
+
+-- | Adds the kind of the variable to the local context.
+createLocalConstraintContext :: PC.ClassDef -> Derive Context
+createLocalConstraintContext cd = do
+  let arg = cd ^. #classArgs
+  let n = mkInfoLess $ TyVar $ arg ^. #argName
+  let k = arg ^. #argKind . to protoKind2Kind
+  return $ mempty & addContext .~ M.singleton n k
 
 deriveConstraint :: PC.Constraint -> Derive Derivation
 deriveConstraint constraint = do
@@ -397,5 +406,5 @@ protoKind2Kind = \case
   PC.Kind k -> case k of
     PC.KindArrow k1 k2 -> protoKind2Kind k1 :->: protoKind2Kind k2
     PC.KindRef PC.KType -> KType
-    PC.KindRef PC.KUnspecified -> KType
     PC.KindRef PC.KConstraint -> KConstraint
+    PC.KindRef PC.KUnspecified -> KType
diff --git a/lambda-buffers-compiler/test/Test/Utils/Module.hs b/lambda-buffers-compiler/test/Test/Utils/Module.hs
index dca4a077..1021c5f6 100644
--- a/lambda-buffers-compiler/test/Test/Utils/Module.hs
+++ b/lambda-buffers-compiler/test/Test/Utils/Module.hs
@@ -82,4 +82,4 @@ module'classEq = _Module (_ModuleName ["Module"]) mempty [classDef'Eq] mempty
   class Eq a => Ord a.
 -}
 module'classOrd :: PC.Module
-module'classOrd = _Module (_ModuleName ["Module"]) mempty [classDef'Ord] mempty
+module'classOrd = _Module (_ModuleName ["Module"]) mempty [classDef'Eq, classDef'Ord] mempty