diff --git a/toy-impl/top_level.py b/toy-impl/top_level.py
index 9afa138..615dd9b 100644
--- a/toy-impl/top_level.py
+++ b/toy-impl/top_level.py
@@ -18,6 +18,7 @@ def parse_type(ctx: Context, ty):
     if ty is None:
         return None, set()
     elif isinstance(ty, ast.Name):
+        # we should support string either, but no need for toy implementaiton
         if ty.id in ctx.types:
             return ctx.types[ty.id], set()
         elif ty.id in ctx.variables:
diff --git a/toy-impl/type_def.py b/toy-impl/type_def.py
index 21c981e..a2196de 100644
--- a/toy-impl/type_def.py
+++ b/toy-impl/type_def.py
@@ -1,9 +1,11 @@
 class Type:
-    pass
+    def __eq__(self, other):
+        return False
 
 
 class BotType:
-    pass
+    def __eq__(self, other):
+        return isinstance(other, BotType)
 
 
 class PrimitiveType(Type):
@@ -15,9 +17,15 @@ class PrimitiveType(Type):
     def __str__(self):
         return self.name
 
+    def __eq__(self, other):
+        return isinstance(other, PrimitiveType) and self.name == other.name
+
 
 class TypeVariable(Type):
     name: str
+    # this may be a list of str, Type may not be determined when type variables
+    # are instantiated...
+    # and they cannot contain other type variables
     constraints: list[Type]
 
     def __init__(self, name: str, constraints: list[Type]):
@@ -27,6 +35,9 @@ class TypeVariable(Type):
     def __str__(self):
         return self.name
 
+    def __eq__(self, other):
+        return isinstance(other, TypeVariable) and self.name == other.name
+
 
 class ClassType(Type):
     name: str
@@ -43,6 +54,8 @@ class ClassType(Type):
     def __str__(self):
         return self.name
 
+    def __eq__(self, other):
+        return isinstance(other, ClassType) and self.name == other.name
 
 class VirtualClassType(Type):
     base: ClassType
@@ -53,22 +66,36 @@ class VirtualClassType(Type):
     def __str__(self):
         return f"virtual[{self.base}]"
 
-class ListType(Type):
-    elements: Type
+    def __eq__(self, other):
+        return isinstance(other, VirtualClassType) and self.base== other.base
 
-    def __init__(self, elements: Type):
-        self.elements = elements
+class ParametricType(Type):
+    params: list[Type]
+
+    def __init__(self, params: list[Type]):
+        self.params = params
+
+    def __eq__(self, other):
+        if type(self) != type(other) or len(self.params) != len(other.params):
+            return False
+        for x, y in zip(self.params, other.params):
+            if x != y:
+                return False
+        return True
+
+class ListType(ParametricType):
+    def __init__(self, param: Type):
+        super().__init__([param])
 
     def __str__(self):
-        return f"list[{self.elements}]"
+        return f"list[{self.params[0]}]"
 
-class TupleType(Type):
-    elements: list[Type]
 
-    def __init__(self, elements: Type):
-        self.elements = elements
+class TupleType(ParametricType):
+    def __init__(self, params: list[Type]):
+        super().__init__(params)
 
     def __str__(self):
-        return f"tuple[{', '.join([str(v) for v in self.elements])}]"
+        return f"tuple[{', '.join([str(v) for v in self.params])}]"
 
 
diff --git a/type_check.py b/type_check.py
deleted file mode 100644
index cb9d172..0000000
--- a/type_check.py
+++ /dev/null
@@ -1,51 +0,0 @@
-def is_variable(b):
-    return isinstance(b, str) and b.isupper()
-
-def unify(ctx, a, b):
-    """
-    a is the more specific type
-    b is the type with parameter
-    lower case means primitive type
-    upper case means type variable
-    list and tuples are just list and tuples
-    """
-    if isinstance(ctx, str):
-        return ctx
-
-    if is_variable(b):
-        if b in ctx:
-            b = ctx[b]
-        else:
-            ctx[b] = a
-            return ctx
-    else:
-        if is_variable(a):
-            return f"{a} is less specific then {b}"
-
-    if isinstance(a, list) and isinstance(b, list):
-        return unify(ctx, a[0], b[0])
-    elif isinstance(a, tuple) and isinstance(b, tuple) and len(a) == len(b):
-        old = ctx
-        for x, y in zip(a, b):
-            old = unify(old, x, y)
-        return old
-    else:
-        if a == b:
-            return ctx
-        else:
-            return f"{a} != {b}"
-
-def check_eq(a, b):
-    unifier = unify({}, a, b)
-    print(f"{a} <- {b}\n{unifier}\n")
-
-check_eq('a', 'A')
-check_eq('A', 'B')
-check_eq('A', 'a')
-check_eq(['a'], 'A')
-check_eq(['a'], ['A'])
-check_eq(['a'], ['b'])
-check_eq([('a', 'a', 'b')], ['A'])
-check_eq([('a', 'a', 'b')], [('A', 'A', 'B')])
-check_eq([('a', 'a', 'b')], [('A', 'A', 'A')])
-