Relax strictness on `Middleware` type (#3059)

diff --git a/starlette/middleware/__init__.py b/starlette/middleware/__init__.py
index b99538a272d985e5288faff04d2e7971b938d613..8c3f287e9cf3eb128d26655cf49984ec9820d67e 100644 (file)
--- a/starlette/middleware/__init__.py
+++ b/starlette/middleware/__init__.py
@@ -1,30 +1,32 @@
 from __future__ import annotations
 
 import sys
-from collections.abc import Iterator
-from typing import Any, Protocol
+from collections.abc import Awaitable, Iterator
+from typing import Any, Callable, Protocol
 
 if sys.version_info >= (3, 10):  # pragma: no cover
     from typing import ParamSpec
 else:  # pragma: no cover
     from typing_extensions import ParamSpec
 
-from starlette.types import ASGIApp
 
 P = ParamSpec("P")
 
 
+_Scope = Any
+_Receive = Callable[[], Awaitable[Any]]
+_Send = Callable[[Any], Awaitable[None]]
+# Since `starlette.types.ASGIApp` type differs from `ASGIApplication` from `asgiref`
+# we need to define a more permissive version of ASGIApp that doesn't cause type errors.
+_ASGIApp = Callable[[_Scope, _Receive, _Send], Awaitable[None]]
+
+
 class _MiddlewareFactory(Protocol[P]):
-    def __call__(self, app: ASGIApp, /, *args: P.args, **kwargs: P.kwargs) -> ASGIApp: ...  # pragma: no cover
+    def __call__(self, app: _ASGIApp, /, *args: P.args, **kwargs: P.kwargs) -> _ASGIApp: ...  # pragma: no cover
 
 
 class Middleware:
-    def __init__(
-        self,
-        cls: _MiddlewareFactory[P],
-        *args: P.args,
-        **kwargs: P.kwargs,
-    ) -> None:
+    def __init__(self, cls: _MiddlewareFactory[P], *args: P.args, **kwargs: P.kwargs) -> None:
         self.cls = cls
         self.args = args
         self.kwargs = kwargs