diff --git a/midas/checker/python.py b/midas/checker/python.py
index 63a076e..a920990 100644
--- a/midas/checker/python.py
+++ b/midas/checker/python.py
@@ -534,7 +534,11 @@ class PythonTyper(
         return self.types.apply_generic(list_type, [UnknownType()])
 
     def visit_base_type(self, node: p.BaseType) -> Type:
-        return self.types.get_type(node.base)
+        base: Type = self.types.get_type(node.base)
+        if node.param is not None:
+            param: Type = node.param.accept(self)
+            return self.types.apply_generic(base, [param])
+        return base
 
     def visit_constraint_type(self, node: p.ConstraintType) -> Type: ...
 
diff --git a/midas/checker/registry.py b/midas/checker/registry.py
index 1324bbd..da5a7ee 100644
--- a/midas/checker/registry.py
+++ b/midas/checker/registry.py
@@ -3,6 +3,7 @@ from typing import Optional
 from midas.checker.builtins import BUILTIN_SUBTYPES
 from midas.checker.types import (
     AliasType,
+    AppliedType,
     BaseType,
     ComplexType,
     Function,
@@ -254,7 +255,7 @@ class TypesRegistry:
             case AliasType(name=name, type=base):
                 return AliasType(name=name, type=self.apply_generic(base, params))
 
-            case GenericType(params=type_vars, body=body):
+            case GenericType(name=name, params=type_vars, body=body):
                 n_params: int = len(params)
                 n_type_vars: int = len(type_vars)
                 if n_params < n_type_vars:
@@ -274,7 +275,11 @@ class TypesRegistry:
                             f"Type parameter {param} is not a subtype of {type_var.bound}"
                         )
                     substitutions[type_var.name] = param
-                return substitute_typevars(body, substitutions)
+                return AppliedType(
+                    name=name,
+                    args=params,
+                    body=substitute_typevars(body, substitutions),
+                )
 
             case _:
                 raise ValueError(f"{type} is not a generic type")
diff --git a/midas/checker/types.py b/midas/checker/types.py
index 8c95134..9081a95 100644
--- a/midas/checker/types.py
+++ b/midas/checker/types.py
@@ -71,6 +71,13 @@ class GenericType:
     body: Type
 
 
+@dataclass(frozen=True, kw_only=True)
+class AppliedType:
+    name: str
+    args: list[Type]
+    body: Type
+
+
 def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
     def sub_argument(arg: Function.Argument):
         return Function.Argument(
@@ -138,4 +145,5 @@ Type = (
     | ComplexType
     | TypeVar
     | GenericType
+    | AppliedType
 )