diff --git a/prompt_toolkit/application/application.py b/prompt_toolkit/application/application.py
index 11afcc205..a1ea4f01f 100644
--- a/prompt_toolkit/application/application.py
+++ b/prompt_toolkit/application/application.py
@@ -103,6 +103,9 @@
 _AppResult = TypeVar("_AppResult")
 ApplicationEventHandler = Callable[["Application[_AppResult]"], None]
 
+_SIGWINCH = getattr(signal, "SIGWINCH", None)
+_SIGTSTP = getattr(signal, "SIGTSTP", None)
+
 
 class Application(Generic[_AppResult]):
     """
@@ -686,10 +689,9 @@ def flush_input() -> None:
                     self._redraw()
                     self._start_auto_refresh_task()
 
-                    has_sigwinch = hasattr(signal, "SIGWINCH") and in_main_thread()
-                    if has_sigwinch:
-                        previous_winch_handler = signal.getsignal(signal.SIGWINCH)
-                        loop.add_signal_handler(signal.SIGWINCH, self._on_resize)
+                    if _SIGWINCH is not None and in_main_thread():
+                        previous_winch_handler = signal.getsignal(_SIGWINCH)
+                        loop.add_signal_handler(_SIGWINCH, self._on_resize)
                         if previous_winch_handler is None:
                             # In some situations we receive `None`. This is
                             # however not a valid value for passing to
@@ -727,9 +729,9 @@ def flush_input() -> None:
                             if self.input.responds_to_cpr:
                                 await self.renderer.wait_for_cpr_responses()
 
-                            if has_sigwinch:
-                                loop.remove_signal_handler(signal.SIGWINCH)
-                                signal.signal(signal.SIGWINCH, previous_winch_handler)
+                            if _SIGWINCH is not None:
+                                loop.remove_signal_handler(_SIGWINCH)
+                                signal.signal(_SIGWINCH, previous_winch_handler)
 
                             # Wait for the run-in-terminals to terminate.
                             previous_run_in_terminal_f = self._running_in_terminal_f
@@ -995,18 +997,18 @@ def suspend_to_background(self, suspend_group: bool = True) -> None:
         """
         # Only suspend when the operating system supports it.
         # (Not on Windows.)
-        if hasattr(signal, "SIGTSTP"):
+        if _SIGTSTP is not None:
 
             def run() -> None:
-                # Send `SIGSTP` to own process.
+                # Send `SIGTSTP` to own process.
                 # This will cause it to suspend.
 
                 # Usually we want the whole process group to be suspended. This
                 # handles the case when input is piped from another process.
                 if suspend_group:
-                    os.kill(0, signal.SIGTSTP)
+                    os.kill(0, _SIGTSTP)
                 else:
-                    os.kill(os.getpid(), signal.SIGTSTP)
+                    os.kill(os.getpid(), _SIGTSTP)
 
             run_in_terminal(run)
 
diff --git a/prompt_toolkit/document.py b/prompt_toolkit/document.py
index 6051c92e7..ce88bb726 100644
--- a/prompt_toolkit/document.py
+++ b/prompt_toolkit/document.py
@@ -825,7 +825,9 @@ def find_matching_bracket_position(
         """
 
         # Look for a match.
-        for A, B in "()", "[]", "{}", "<>":
+        for pair in "()", "[]", "{}", "<>":
+            A = pair[0]
+            B = pair[1]
             if self.current_char == A:
                 return self.find_enclosing_bracket_right(A, B, end_pos=end_pos) or 0
             elif self.current_char == B:
diff --git a/prompt_toolkit/shortcuts/progress_bar/base.py b/prompt_toolkit/shortcuts/progress_bar/base.py
index 6ca73c57d..2e89fd7a4 100644
--- a/prompt_toolkit/shortcuts/progress_bar/base.py
+++ b/prompt_toolkit/shortcuts/progress_bar/base.py
@@ -15,6 +15,7 @@
 import traceback
 from asyncio import get_event_loop, new_event_loop, set_event_loop
 from typing import (
+    TYPE_CHECKING,
     Generic,
     Iterable,
     List,
@@ -65,6 +66,8 @@
 
 E = KeyPressEvent
 
+_SIGWINCH = getattr(signal, "SIGWINCH", None)
+
 
 def create_key_bindings() -> KeyBindings:
     """
@@ -142,11 +145,15 @@ def __init__(
 
         self._loop = get_event_loop()
         self._app_loop = new_event_loop()
-        self._previous_winch_handler = (
-            signal.getsignal(signal.SIGWINCH) if hasattr(signal, "SIGWINCH") else None
-        )
+
+        self._previous_winch_handler = None
         self._has_sigwinch = False
 
+        if TYPE_CHECKING:
+            # Infer type from getsignal result, as defined in typeshed. Too
+            # complex to repeat here.
+            self._previous_winch_handler = signal.getsignal(_SIGWINCH)
+
     def __enter__(self) -> "ProgressBar":
         # Create UI Application.
         title_toolbar = ConditionalContainer(
@@ -225,10 +232,10 @@ def run() -> None:
 
         # Attach WINCH signal handler in main thread.
         # (Interrupt that we receive during resize events.)
-        self._has_sigwinch = hasattr(signal, "SIGWINCH") and in_main_thread()
+        self._has_sigwinch = _SIGWINCH is not None and in_main_thread()
         if self._has_sigwinch:
-            self._previous_winch_handler = signal.getsignal(signal.SIGWINCH)
-            self._loop.add_signal_handler(signal.SIGWINCH, self.invalidate)
+            self._previous_winch_handler = signal.getsignal(_SIGWINCH)
+            self._loop.add_signal_handler(_SIGWINCH, self.invalidate)
 
         return self
 
@@ -239,8 +246,8 @@ def __exit__(self, *a: object) -> None:
 
         # Remove WINCH handler.
         if self._has_sigwinch:
-            self._loop.remove_signal_handler(signal.SIGWINCH)
-            signal.signal(signal.SIGWINCH, self._previous_winch_handler)
+            self._loop.remove_signal_handler(_SIGWINCH)
+            signal.signal(_SIGWINCH, self._previous_winch_handler)
 
         if self._thread is not None:
             self._thread.join()