diff --git a/midas/checker/types.py b/midas/checker/types.py
index 83707b6..15079e0 100644
--- a/midas/checker/types.py
+++ b/midas/checker/types.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 from dataclasses import dataclass
+from typing import Optional
 
 
 @dataclass(frozen=True, kw_only=True)
@@ -57,4 +58,75 @@ class Operation:
         right: Type
 
 
-Type = BaseType | AliasType | UnknownType | UnitType | Function | ComplexType
+@dataclass(frozen=True, kw_only=True)
+class TypeVar:
+    name: str
+    bound: Optional[Type]
+
+
+@dataclass(frozen=True, kw_only=True)
+class GenericType:
+    params: list[TypeVar]
+    body: Type
+
+
+def substitute_typevars(type: Type, substitutions: dict[str, Type]) -> Type:
+    def sub_argument(arg: Function.Argument):
+        return Function.Argument(
+            pos=arg.pos,
+            name=arg.name,
+            type=substitute_typevars(arg.type, substitutions),
+            required=arg.required,
+        )
+
+    match type:
+        case BaseType(name=name) if name in substitutions:
+            return substitutions[name]
+
+        case AliasType(name=name, type=type2):
+            return AliasType(name=name, type=substitute_typevars(type2, substitutions))
+
+        case Function(
+            name=name,
+            pos_args=pos_args,
+            args=args,
+            kw_args=kw_args,
+            returns=returns,
+        ):
+            return Function(
+                name=name,
+                pos_args=list(map(sub_argument, pos_args)),
+                args=list(map(sub_argument, args)),
+                kw_args=list(map(sub_argument, kw_args)),
+                returns=substitute_typevars(returns, substitutions),
+            )
+
+        case ComplexType(properties=properties):
+            properties2: dict[str, Type] = {
+                name: substitute_typevars(prop, substitutions)
+                for name, prop in properties.items()
+            }
+            return ComplexType(properties=properties2)
+
+        case TypeVar(name=name):
+            if name in substitutions:
+                return substitutions[name]
+            raise ValueError(f"Missing TypeVar substitution for {name}")
+
+        case UnknownType() | UnitType():
+            return type
+
+        case _:
+            raise NotImplementedError(f"Unsupported type {type}")
+
+
+Type = (
+    BaseType
+    | AliasType
+    | UnknownType
+    | UnitType
+    | Function
+    | ComplexType
+    | TypeVar
+    | GenericType
+)