diff --git a/torch/_library/simple_registry.py b/torch/_library/simple_registry.py
index bf25cde9cb5..1f11914e8e9 100644
--- a/torch/_library/simple_registry.py
+++ b/torch/_library/simple_registry.py
@@ -1,5 +1,4 @@
-# mypy: allow-untyped-defs
-from typing import Callable, Optional
+from typing import Any, Callable, Optional
 
 from .fake_impl import FakeImplHolder
 from .utils import RegistrationHandle
@@ -24,8 +23,8 @@ class SimpleLibraryRegistry:
     (including the overload) to SimpleOperatorEntry.
     """
 
-    def __init__(self):
-        self._data = {}
+    def __init__(self) -> None:
+        self._data: dict[str, SimpleOperatorEntry] = {}
 
     def find(self, qualname: str) -> "SimpleOperatorEntry":
         res = self._data.get(qualname, None)
@@ -44,7 +43,7 @@ class SimpleOperatorEntry:
     registered to.
     """
 
-    def __init__(self, qualname: str):
+    def __init__(self, qualname: str) -> None:
         self.qualname: str = qualname
         self.fake_impl: FakeImplHolder = FakeImplHolder(qualname)
         self.torch_dispatch_rules: GenericTorchDispatchRuleHolder = (
@@ -53,17 +52,17 @@ class SimpleOperatorEntry:
 
     # For compatibility reasons. We can delete this soon.
     @property
-    def abstract_impl(self):
+    def abstract_impl(self) -> FakeImplHolder:
         return self.fake_impl
 
 
 class GenericTorchDispatchRuleHolder:
-    def __init__(self, qualname):
-        self._data = {}
-        self.qualname = qualname
+    def __init__(self, qualname: str) -> None:
+        self._data: dict[type, Callable[..., Any]] = {}
+        self.qualname: str = qualname
 
     def register(
-        self, torch_dispatch_class: type, func: Callable
+        self, torch_dispatch_class: type, func: Callable[..., Any]
     ) -> RegistrationHandle:
         if self.find(torch_dispatch_class):
             raise RuntimeError(
@@ -71,16 +70,18 @@ class GenericTorchDispatchRuleHolder:
             )
         self._data[torch_dispatch_class] = func
 
-        def deregister():
+        def deregister() -> None:
             del self._data[torch_dispatch_class]
 
         return RegistrationHandle(deregister)
 
-    def find(self, torch_dispatch_class):
+    def find(self, torch_dispatch_class: type) -> Optional[Callable[..., Any]]:
         return self._data.get(torch_dispatch_class, None)
 
 
-def find_torch_dispatch_rule(op, torch_dispatch_class: type) -> Optional[Callable]:
+def find_torch_dispatch_rule(
+    op: Any, torch_dispatch_class: type
+) -> Optional[Callable[..., Any]]:
     return singleton.find(op.__qualname__).torch_dispatch_rules.find(
         torch_dispatch_class
     )