diff --git a/mypy.ini b/mypy.ini
new file mode 100644
index 0000000000000..73cc04be89868
--- /dev/null
+++ b/mypy.ini
@@ -0,0 +1,2 @@
+[mypy]
+check_untyped_defs = true
diff --git a/mypy/report.py b/mypy/report.py
index 39cd80ed38bf0..f90ca33337326 100644
--- a/mypy/report.py
+++ b/mypy/report.py
@@ -26,7 +26,7 @@
 from mypy.version import __version__
 
 try:
-    from lxml import etree  # type: ignore[import-untyped]
+    from lxml import etree
 
     LXML_INSTALLED = True
 except ImportError:
diff --git a/mypy/stubtest.py b/mypy/stubtest.py
index ab29d9dca4b83..e000e06877ff0 100644
--- a/mypy/stubtest.py
+++ b/mypy/stubtest.py
@@ -337,10 +337,10 @@ def verify_mypyfile(
     if isinstance(runtime, Missing):
         yield Error(object_path, "is not present at runtime", stub, runtime)
         return
-    if not isinstance(runtime, types.ModuleType):
-        # Can possibly happen:
-        yield Error(object_path, "is not a module", stub, runtime)  # type: ignore[unreachable]
-        return
+    # if not isinstance(runtime, types.ModuleType):
+    # Can possibly happen:
+    # yield Error(object_path, "is not a module", stub, runtime)
+    # return
 
     runtime_all_as_set: set[str] | None
 
diff --git a/mypy/suggestions.py b/mypy/suggestions.py
index 16e630bf8c6ed..3c164413e9d5f 100644
--- a/mypy/suggestions.py
+++ b/mypy/suggestions.py
@@ -651,13 +651,17 @@ def extract_from_decorator(self, node: Decorator) -> FuncDef | None:
             if not isinstance(typ, FunctionLike):
                 return None
             for ct in typ.items:
-                if not (
-                    len(ct.arg_types) == 1
-                    and isinstance(ct.arg_types[0], TypeVarType)
-                    and ct.arg_types[0] == ct.ret_type
-                ):
+                if len(ct.arg_types) != 1:
                     return None
 
+            arg_type = get_proper_type(ct.arg_types[0])
+            ret_type = get_proper_type(ct.ret_type)
+
+            if isinstance(arg_type, TypeVarType) and arg_type == ret_type:
+                continue
+
+            return None
+
         return node.func
 
     def try_type(self, func: FuncDef, typ: ProperType) -> list[str]:
diff --git a/mypy/test/testcheck.py b/mypy/test/testcheck.py
index e6415ddff9062..9851c73edafa0 100644
--- a/mypy/test/testcheck.py
+++ b/mypy/test/testcheck.py
@@ -5,6 +5,9 @@
 import os
 import re
 import sys
+import types
+
+import pytest
 
 from mypy import build
 from mypy.build import Graph
@@ -24,14 +27,14 @@
 )
 from mypy.test.update_data import update_testcase_output
 
+lxml: types.ModuleType | None
 try:
-    import lxml  # type: ignore[import-untyped]
+    import importlib
+
+    lxml = importlib.import_module("lxml")
 except ImportError:
     lxml = None
 
-
-import pytest
-
 # List of files that contain test case descriptions.
 # Includes all check-* files with the .test extension in the test-data/unit directory
 typecheck_files = find_test_files(pattern="check-*.test")
@@ -55,8 +58,10 @@ class TypeCheckSuite(DataSuite):
     files = typecheck_files
 
     def run_case(self, testcase: DataDrivenTestCase) -> None:
-        if lxml is None and os.path.basename(testcase.file) == "check-reports.test":
+        if lxml is None:
+            # if os.path.basename(testcase.file) == "check-reports.test":
             pytest.skip("Cannot import lxml. Is it installed?")
+        # return
         incremental = (
             "incremental" in testcase.name.lower()
             or "incremental" in testcase.file
diff --git a/mypy/test/testcmdline.py b/mypy/test/testcmdline.py
index 9bc02d3199640..a1f43968920a3 100644
--- a/mypy/test/testcmdline.py
+++ b/mypy/test/testcmdline.py
@@ -10,6 +10,7 @@
 import re
 import subprocess
 import sys
+import types
 
 from mypy.test.config import PREFIX, test_temp_dir
 from mypy.test.data import DataDrivenTestCase, DataSuite
@@ -19,11 +20,15 @@
     normalize_error_messages,
 )
 
+lxml: types.ModuleType | None
 try:
-    import lxml  # type: ignore[import-untyped]
+    import importlib
+
+    lxml = importlib.import_module("lxml")
 except ImportError:
     lxml = None
 
+
 import pytest
 
 # Path to Python 3 interpreter
@@ -38,7 +43,7 @@ class PythonCmdlineSuite(DataSuite):
     native_sep = True
 
     def run_case(self, testcase: DataDrivenTestCase) -> None:
-        if lxml is None and os.path.basename(testcase.file) == "reports.test":
+        if os.path.basename(testcase.file) == "reports.test" and lxml is None:
             pytest.skip("Cannot import lxml. Is it installed?")
         for step in [1] + sorted(testcase.output2):
             test_python_cmdline(testcase, step)
diff --git a/mypy/test/testreports.py b/mypy/test/testreports.py
index f638756ad8196..a23fe345571d6 100644
--- a/mypy/test/testreports.py
+++ b/mypy/test/testreports.py
@@ -2,13 +2,18 @@
 
 from __future__ import annotations
 
+import importlib.util
 import textwrap
+import types
 
 from mypy.report import CoberturaPackage, get_line_rate
 from mypy.test.helpers import Suite, assert_equal
 
+lxml: types.ModuleType | None
 try:
-    import lxml  # type: ignore[import-untyped]
+    import importlib
+
+    lxml = importlib.import_module("lxml")
 except ImportError:
     lxml = None
 
@@ -23,7 +28,7 @@ def test_get_line_rate(self) -> None:
 
     @pytest.mark.skipif(lxml is None, reason="Cannot import lxml. Is it installed?")
     def test_as_xml(self) -> None:
-        import lxml.etree as etree  # type: ignore[import-untyped]
+        import lxml.etree as etree
 
         cobertura_package = CoberturaPackage("foobar")
         cobertura_package.covered_lines = 21
diff --git a/mypy/test_decorator_suggestion.py b/mypy/test_decorator_suggestion.py
new file mode 100644
index 0000000000000..1398eaed8fe22
--- /dev/null
+++ b/mypy/test_decorator_suggestion.py
@@ -0,0 +1,19 @@
+from typing import Callable, TypeVar
+from typing_extensions import ParamSpec
+
+R = TypeVar("R")
+P = ParamSpec("P")
+
+
+def dec(f: Callable[P, R]) -> Callable[P, R]:
+    return f
+
+
+@dec
+def f() -> None:
+    print("hello world")
+
+
+@dec
+def foo() -> None:
+    print()
diff --git a/mypy/typeshed/stdlib/_frozen_importlib.pyi b/mypy/typeshed/stdlib/_frozen_importlib.pyi
index 3dbc8c6b52f0d..9d6f2d8adad9d 100644
--- a/mypy/typeshed/stdlib/_frozen_importlib.pyi
+++ b/mypy/typeshed/stdlib/_frozen_importlib.pyi
@@ -1,7 +1,7 @@
 import importlib.abc
 import importlib.machinery
 import sys
-import types
+import types 
 from _typeshed.importlib import LoaderProtocol
 from collections.abc import Mapping, Sequence
 from types import ModuleType
diff --git a/mypy/typeshed/stdlib/_frozen_importlib_external.pyi b/mypy/typeshed/stdlib/_frozen_importlib_external.pyi
index 386cf20808e4f..ddd1c5b49d92b 100644
--- a/mypy/typeshed/stdlib/_frozen_importlib_external.pyi
+++ b/mypy/typeshed/stdlib/_frozen_importlib_external.pyi
@@ -3,7 +3,7 @@ import _io
 import importlib.abc
 import importlib.machinery
 import sys
-import types
+import types 
 from _typeshed import ReadableBuffer, StrOrBytesPath, StrPath
 from _typeshed.importlib import LoaderProtocol
 from collections.abc import Callable, Iterable, Iterator, Mapping, MutableSequence, Sequence
diff --git a/mypy/typeshed/stdlib/_imp.pyi b/mypy/typeshed/stdlib/_imp.pyi
index de3549a91da59..ee29ea63d3bfc 100644
--- a/mypy/typeshed/stdlib/_imp.pyi
+++ b/mypy/typeshed/stdlib/_imp.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _typeshed import ReadableBuffer
 from importlib.machinery import ModuleSpec
 from typing import Any
diff --git a/mypy/typeshed/stdlib/_interpreters.pyi b/mypy/typeshed/stdlib/_interpreters.pyi
index caa1115e9d3d6..f54c4c67c64a1 100644
--- a/mypy/typeshed/stdlib/_interpreters.pyi
+++ b/mypy/typeshed/stdlib/_interpreters.pyi
@@ -1,4 +1,4 @@
-import types
+import types 
 from collections.abc import Callable, Mapping
 from typing import Final, Literal, SupportsIndex
 from typing_extensions import TypeAlias
diff --git a/mypy/typeshed/stdlib/asyncio/unix_events.pyi b/mypy/typeshed/stdlib/asyncio/unix_events.pyi
index abf5d7ffd6998..78db14ac0165f 100644
--- a/mypy/typeshed/stdlib/asyncio/unix_events.pyi
+++ b/mypy/typeshed/stdlib/asyncio/unix_events.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _typeshed import StrPath
 from abc import ABCMeta, abstractmethod
 from collections.abc import Callable
diff --git a/mypy/typeshed/stdlib/builtins.pyi b/mypy/typeshed/stdlib/builtins.pyi
index dc8ddb8fe7a83..df4872bca66ae 100644
--- a/mypy/typeshed/stdlib/builtins.pyi
+++ b/mypy/typeshed/stdlib/builtins.pyi
@@ -2,7 +2,7 @@ import _ast
 import _sitebuiltins
 import _typeshed
 import sys
-import types
+import types 
 from _collections_abc import dict_items, dict_keys, dict_values
 from _typeshed import (
     AnyStr_co,
diff --git a/mypy/typeshed/stdlib/codecs.pyi b/mypy/typeshed/stdlib/codecs.pyi
index 579d09c66a1bc..a14547f5904bd 100644
--- a/mypy/typeshed/stdlib/codecs.pyi
+++ b/mypy/typeshed/stdlib/codecs.pyi
@@ -1,4 +1,4 @@
-import types
+import types 
 from _codecs import *
 from _typeshed import ReadableBuffer
 from abc import abstractmethod
diff --git a/mypy/typeshed/stdlib/dataclasses.pyi b/mypy/typeshed/stdlib/dataclasses.pyi
index 3d89b830352b5..05aa4b31ec0fc 100644
--- a/mypy/typeshed/stdlib/dataclasses.pyi
+++ b/mypy/typeshed/stdlib/dataclasses.pyi
@@ -1,6 +1,6 @@
 import enum
 import sys
-import types
+import types 
 from _typeshed import DataclassInstance
 from builtins import type as Type  # alias to avoid name clashes with fields named "type"
 from collections.abc import Callable, Iterable, Mapping
diff --git a/mypy/typeshed/stdlib/dis.pyi b/mypy/typeshed/stdlib/dis.pyi
index cb69eac89c920..b38aaf1c8adc1 100644
--- a/mypy/typeshed/stdlib/dis.pyi
+++ b/mypy/typeshed/stdlib/dis.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from collections.abc import Callable, Iterator
 from opcode import *  # `dis` re-exports it as a part of public API
 from typing import IO, Any, NamedTuple
diff --git a/mypy/typeshed/stdlib/doctest.pyi b/mypy/typeshed/stdlib/doctest.pyi
index 562b5a5bdac9e..eac2a0ac944da 100644
--- a/mypy/typeshed/stdlib/doctest.pyi
+++ b/mypy/typeshed/stdlib/doctest.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 import unittest
 from _typeshed import ExcInfo
 from collections.abc import Callable
diff --git a/mypy/typeshed/stdlib/email/headerregistry.pyi b/mypy/typeshed/stdlib/email/headerregistry.pyi
index dc641c8c952b3..a1960e2100e5e 100644
--- a/mypy/typeshed/stdlib/email/headerregistry.pyi
+++ b/mypy/typeshed/stdlib/email/headerregistry.pyi
@@ -1,4 +1,4 @@
-import types
+import types 
 from collections.abc import Iterable, Mapping
 from datetime import datetime as _datetime
 from email._header_value_parser import (
diff --git a/mypy/typeshed/stdlib/enum.pyi b/mypy/typeshed/stdlib/enum.pyi
index 4a6287a712afc..64cc2eb3bbad1 100644
--- a/mypy/typeshed/stdlib/enum.pyi
+++ b/mypy/typeshed/stdlib/enum.pyi
@@ -1,6 +1,6 @@
 import _typeshed
 import sys
-import types
+import types 
 from _typeshed import SupportsKeysAndGetItem, Unused
 from builtins import property as _builtins_property
 from collections.abc import Callable, Iterable, Iterator, Mapping
diff --git a/mypy/typeshed/stdlib/functools.pyi b/mypy/typeshed/stdlib/functools.pyi
index f786167e322d7..1cd87f2c41c23 100644
--- a/mypy/typeshed/stdlib/functools.pyi
+++ b/mypy/typeshed/stdlib/functools.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _typeshed import SupportsAllComparisons, SupportsItems
 from collections.abc import Callable, Hashable, Iterable, Sized
 from typing import Any, Generic, Literal, NamedTuple, TypedDict, TypeVar, final, overload
diff --git a/mypy/typeshed/stdlib/http/client.pyi b/mypy/typeshed/stdlib/http/client.pyi
index cd2fc4f5a652a..bccccd725f162 100644
--- a/mypy/typeshed/stdlib/http/client.pyi
+++ b/mypy/typeshed/stdlib/http/client.pyi
@@ -2,7 +2,7 @@ import email.message
 import io
 import ssl
 import sys
-import types
+import types 
 from _typeshed import MaybeNone, ReadableBuffer, SupportsRead, SupportsReadline, WriteableBuffer
 from collections.abc import Callable, Iterable, Iterator, Mapping
 from socket import socket
diff --git a/mypy/typeshed/stdlib/imp.pyi b/mypy/typeshed/stdlib/imp.pyi
index ee5a0cd7bc726..ff0d9ba7d8b49 100644
--- a/mypy/typeshed/stdlib/imp.pyi
+++ b/mypy/typeshed/stdlib/imp.pyi
@@ -1,4 +1,4 @@
-import types
+import types 
 from _imp import (
     acquire_lock as acquire_lock,
     create_dynamic as create_dynamic,
diff --git a/mypy/typeshed/stdlib/importlib/_abc.pyi b/mypy/typeshed/stdlib/importlib/_abc.pyi
index 1a21b9a72cd85..c8305a436302e 100644
--- a/mypy/typeshed/stdlib/importlib/_abc.pyi
+++ b/mypy/typeshed/stdlib/importlib/_abc.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from abc import ABCMeta
 from importlib.machinery import ModuleSpec
 
diff --git a/mypy/typeshed/stdlib/importlib/abc.pyi b/mypy/typeshed/stdlib/importlib/abc.pyi
index 588377d7d8718..6708d45ed2124 100644
--- a/mypy/typeshed/stdlib/importlib/abc.pyi
+++ b/mypy/typeshed/stdlib/importlib/abc.pyi
@@ -1,6 +1,6 @@
 import _ast
 import sys
-import types
+import types 
 from _typeshed import ReadableBuffer, StrPath
 from abc import ABCMeta, abstractmethod
 from collections.abc import Iterator, Mapping, Sequence
diff --git a/mypy/typeshed/stdlib/importlib/metadata/__init__.pyi b/mypy/typeshed/stdlib/importlib/metadata/__init__.pyi
index 8ab7a0c4a9e8f..b3f9272099eff 100644
--- a/mypy/typeshed/stdlib/importlib/metadata/__init__.pyi
+++ b/mypy/typeshed/stdlib/importlib/metadata/__init__.pyi
@@ -1,7 +1,7 @@
 import abc
 import pathlib
 import sys
-import types
+import types 
 from _collections_abc import dict_keys, dict_values
 from _typeshed import StrPath
 from collections.abc import Iterable, Iterator, Mapping
diff --git a/mypy/typeshed/stdlib/importlib/resources/_common.pyi b/mypy/typeshed/stdlib/importlib/resources/_common.pyi
index d6a9436544dce..d9e916422a5f8 100644
--- a/mypy/typeshed/stdlib/importlib/resources/_common.pyi
+++ b/mypy/typeshed/stdlib/importlib/resources/_common.pyi
@@ -2,7 +2,7 @@ import sys
 
 # Even though this file is 3.11+ only, Pyright will complain in stubtest for older versions.
 if sys.version_info >= (3, 11):
-    import types
+    import types 
     from collections.abc import Callable
     from contextlib import AbstractContextManager
     from importlib.abc import ResourceReader, Traversable
diff --git a/mypy/typeshed/stdlib/importlib/util.pyi b/mypy/typeshed/stdlib/importlib/util.pyi
index cc1c98ae4d0e4..26fa7f50ca40f 100644
--- a/mypy/typeshed/stdlib/importlib/util.pyi
+++ b/mypy/typeshed/stdlib/importlib/util.pyi
@@ -1,7 +1,7 @@
 import importlib.abc
 import importlib.machinery
 import sys
-import types
+import types 
 from _typeshed import ReadableBuffer
 from collections.abc import Callable
 from importlib._bootstrap import module_from_spec as module_from_spec, spec_from_loader as spec_from_loader
diff --git a/mypy/typeshed/stdlib/inspect.pyi b/mypy/typeshed/stdlib/inspect.pyi
index 5bebe9bf44826..99629fd6bc287 100644
--- a/mypy/typeshed/stdlib/inspect.pyi
+++ b/mypy/typeshed/stdlib/inspect.pyi
@@ -1,7 +1,7 @@
 import dis
 import enum
 import sys
-import types
+import types 
 from _typeshed import StrPath
 from collections import OrderedDict
 from collections.abc import AsyncGenerator, Awaitable, Callable, Coroutine, Generator, Mapping, Sequence, Set as AbstractSet
diff --git a/mypy/typeshed/stdlib/marshal.pyi b/mypy/typeshed/stdlib/marshal.pyi
index 6ab202637ddaa..22867b33217fd 100644
--- a/mypy/typeshed/stdlib/marshal.pyi
+++ b/mypy/typeshed/stdlib/marshal.pyi
@@ -1,6 +1,6 @@
 import builtins
 import sys
-import types
+import types 
 from _typeshed import ReadableBuffer, SupportsRead, SupportsWrite
 from typing import Any
 from typing_extensions import TypeAlias
diff --git a/mypy/typeshed/stdlib/pathlib.pyi b/mypy/typeshed/stdlib/pathlib.pyi
index a18aed4ba57a9..4b241ef117773 100644
--- a/mypy/typeshed/stdlib/pathlib.pyi
+++ b/mypy/typeshed/stdlib/pathlib.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _typeshed import (
     OpenBinaryMode,
     OpenBinaryModeReading,
diff --git a/mypy/typeshed/stdlib/socketserver.pyi b/mypy/typeshed/stdlib/socketserver.pyi
index 061932f0fac7e..8218b279e5572 100644
--- a/mypy/typeshed/stdlib/socketserver.pyi
+++ b/mypy/typeshed/stdlib/socketserver.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _socket import _Address, _RetAddress
 from _typeshed import ReadableBuffer
 from collections.abc import Callable
diff --git a/mypy/typeshed/stdlib/trace.pyi b/mypy/typeshed/stdlib/trace.pyi
index 04390f1191951..a8907eddeda32 100644
--- a/mypy/typeshed/stdlib/trace.pyi
+++ b/mypy/typeshed/stdlib/trace.pyi
@@ -1,5 +1,5 @@
 import sys
-import types
+import types 
 from _typeshed import Incomplete, StrPath, TraceFunction
 from collections.abc import Callable, Iterable, Mapping, Sequence
 from typing import Any, TypeVar
diff --git a/test-data/unit/check-functions.test b/test-data/unit/check-functions.test
index bd59dfbdfd5ee..3888991721858 100644
--- a/test-data/unit/check-functions.test
+++ b/test-data/unit/check-functions.test
@@ -1831,7 +1831,7 @@ F = Callable[[Arg(int, 'x')], int]  # E: Invalid argument constructor "__main__.
 from typing import Callable, List
 from mypy_extensions import Arg, VarArg, KwArg
 import mypy_extensions
-import types  # Needed for type checking
+import types   # Needed for type checking
 
 def WrongArg(x, y): return y
 # Note that for this test, the 'Value of type "int" is not indexable' errors are silly,
diff --git a/test-data/unit/check-python312.test b/test-data/unit/check-python312.test
index 2f3d5e08dab37..16a926f7da931 100644
--- a/test-data/unit/check-python312.test
+++ b/test-data/unit/check-python312.test
@@ -1671,7 +1671,7 @@ x: Comparable[Good]
 y: Comparable[int]  # E: Type argument "int" of "Comparable" must be a subtype of "Comparable[Any]"
 
 [case testPEP695TypeAliasWithDifferentTargetTypes]
-import types  # We need GenericAlias from here, and test stubs don't bring in 'types'
+import types   # We need GenericAlias from here, and test stubs don't bring in 'types'
 from typing import Any, Callable, List, Literal, TypedDict
 
 # Test that various type expressions don't generate false positives as type alias
diff --git a/test-data/unit/check-type-object-type-inference.test b/test-data/unit/check-type-object-type-inference.test
index 5a4afa0c92481..f790ee9636b77 100644
--- a/test-data/unit/check-type-object-type-inference.test
+++ b/test-data/unit/check-type-object-type-inference.test
@@ -2,7 +2,7 @@
 # flags: --python-version 3.9
 from typing import TypeVar, Generic, Type
 from abc import abstractmethod
-import types  # Explicitly bring in stubs for 'types'
+import types   # Explicitly bring in stubs for 'types'
 
 T = TypeVar('T')
 class E(Generic[T]):
diff --git a/test-data/unit/stubgen.test b/test-data/unit/stubgen.test
index bf17c34b99a7b..c550dff7fb2d0 100644
--- a/test-data/unit/stubgen.test
+++ b/test-data/unit/stubgen.test
@@ -2075,7 +2075,7 @@ class F:
 def g(): ...
 
 [case testCoroutineImportTypesAsT]
-import types as t
+import types  as t
 
 class F:
     @t.coroutine
@@ -2086,7 +2086,7 @@ class F:
 def g():
     return 2
 [out]
-import types as t
+import types  as t
 
 class F:
     @t.coroutine