1 files changed, 28 insertions, 7 deletions
diff --git a/Lib/functools.py b/Lib/functools.py
index 77ec852..ccac6f8 100644
--- a/Lib/functools.py
+++ b/Lib/functools.py
@@ -837,6 +837,14 @@ def singledispatch(func):
             dispatch_cache[cls] = impl
         return impl
 
+    def _is_union_type(cls):
+        from typing import get_origin, Union
+        return get_origin(cls) in {Union, types.UnionType}
+
+    def _is_valid_union_type(cls):
+        from typing import get_args
+        return _is_union_type(cls) and all(isinstance(arg, type) for arg in get_args(cls))
+
     def register(cls, func=None):
         """generic_func.register(cls, func) -> func
 
@@ -845,7 +853,7 @@ def singledispatch(func):
         """
         nonlocal cache_token
         if func is None:
-            if isinstance(cls, type):
+            if isinstance(cls, type) or _is_valid_union_type(cls):
                 return lambda f: register(cls, f)
             ann = getattr(cls, '__annotations__', {})
             if not ann:
@@ -859,12 +867,25 @@ def singledispatch(func):
             # only import typing if annotation parsing is necessary
             from typing import get_type_hints
             argname, cls = next(iter(get_type_hints(func).items()))
-            if not isinstance(cls, type):
-                raise TypeError(
-                    f"Invalid annotation for {argname!r}. "
-                    f"{cls!r} is not a class."
-                )
-        registry[cls] = func
+            if not isinstance(cls, type) and not _is_valid_union_type(cls):
+                if _is_union_type(cls):
+                    raise TypeError(
+                        f"Invalid annotation for {argname!r}. "
+                        f"{cls!r} not all arguments are classes."
+                    )
+                else:
+                    raise TypeError(
+                        f"Invalid annotation for {argname!r}. "
+                        f"{cls!r} is not a class."
+                    )
+
+        if _is_union_type(cls):
+            from typing import get_args
+
+            for arg in get_args(cls):
+                registry[arg] = func
+        else:
+            registry[cls] = func
         if cache_token is None and hasattr(cls, '__abstractmethods__'):
             cache_token = get_cache_token()
         dispatch_cache.clear()