:mod:`threading` --- Higher-level threading interface
=====================================================
.. module:: threading
:synopsis: Higher-level threading interface.
**Source code:** :source:`Lib/threading.py`
--------------
This module constructs higher-level threading interfaces on top of the lower
level :mod:`thread` module.
See also the :mod:`mutex` and :mod:`Queue` modules.
The :mod:`dummy_threading` module is provided for situations where
:mod:`threading` cannot be used because :mod:`thread` is missing.
.. note::
Starting with Python 2.6, this module provides :pep:`8` compliant aliases and
properties to replace the ``camelCase`` names that were inspired by Java's
threading API. This updated API is compatible with that of the
:mod:`multiprocessing` module. However, no schedule has been set for the
deprecation of the ``camelCase`` names and they remain fully supported in
both Python 2.x and 3.x.
.. note::
Starting with Python 2.5, several Thread methods raise :exc:`RuntimeError`
instead of :exc:`AssertionError` if called erroneously.
.. impl-detail::
In CPython, due to the :term:`Global Interpreter Lock`, only one thread
can execute Python code at once (even though certain performance-oriented
libraries might overcome this limitation).
If you want your application to make better use of the computational
resources of multi-core machines, you are advised to use
:mod:`multiprocessing`. However, threading is still an appropriate model
if you want to run multiple I/O-bound tasks simultaneously.
This module defines the following functions and objects:
.. function:: active_count()
activeCount()
Return the number of :class:`Thread` objects currently alive. The returned
count is equal to the length of the list returned by :func:`.enumerate`.
.. function:: Condition()
:noindex:
A factory function that returns a new condition variable object. A condition
variable allows one or more threads to wait until they are notified by another
thread.
See :ref:`condition-objects`.
.. function:: current_thread()
currentThread()
Return the current :class:`Thread` object, corresponding to the caller's thread
of control. If the caller's thread of control was not created through the
:mod:`threading` module, a dummy thread object with limited functionality is
returned.
.. function:: enumerate()
Return a list of all :class:`Thread` objects currently alive. The list
includes daemonic threads, dummy thread objects created by
:func:`current_thread`, and the main thread. It excludes terminated threads
and threads that have not yet been started.
.. function:: Event()
:noindex:
A factory function that returns a new event object. An event manages a flag
that can be set to true with the :meth:`~Event.set` method and reset to false
with the :meth:`clear` method. The :meth:`wait` method blocks until the flag
is true.
See :ref:`event-objects`.
.. class:: local
A class that represents thread-local data. Thread-local data are data whose
values are thread specific. To manage thread-local data, just create an
instance of :class:`local` (or a subclass) and store attributes on it::
mydata = threading.local()
mydata.x = 1
The instance's values will be different for separate threads.
For more details and extensive examples, see the documentation string of the
:mod:`_threading_local` module.
.. versionadded:: 2.4
.. function:: Lock()
A factory function that returns a new primitive lock object. Once a thread has
acquired it, subsequent attempts to acquire it block, until it is released; any
thread may release it.
See :ref:`lock-objects`.
.. function:: RLock()
A factory function that returns a new reentrant lock object. A reentrant lock
must be released by the thread that acquired it. Once a thread has acquired a
reentrant lock, the same thread may acquire it again without blocking; the
thread must release it once for each time it has acquired it.
See :ref:`rlock-objects`.
.. function:: Semaphore([value])
:noindex:
A factory function that returns a new semaphore object. A semaphore manages a
counter representing the number of :meth:`release` calls minus the number of
:meth:`acquire` calls, plus an initial value. The :meth:`acquire` method blocks
if necessary until it can return without making the counter negative. If not
given, *value* defaults to 1.
See :ref:`semaphore-objects`.
.. function:: BoundedSemaphore([value])
A factory function that returns a new bounded semaphore object. A bounded
semaphore checks to make sure its current value doesn't exceed its initial
value. If it does, :exc:`ValueError` is raised. In most situations semaphores
are used to guard resources with limited capacity. If the semaphore is released
too many times it's a sign of a bug. If not given, *value* defaults to 1.
.. class:: Thread
:noindex:
A class that represents a thread of control. This class can be safely
subclassed in a limited fashion.
See :ref:`thread-objects`.
.. class:: Timer
:noindex:
A thread that executes a function after a specified interval has passed.
See :ref:`timer-objects`.
.. function:: settrace(func)
.. index:: single: trace function
Set a trace function for all threads started from the :mod:`threading` module.
The *func* will be passed to :func:`sys.settrace` for each thread, before its
:meth:`run` method is called.
.. versionadded:: 2.3
.. function:: setprofile(func)
.. index:: single: profile function
Set a profile function for all threads started from the :mod:`threading` module.
The *func* will be passed to :func:`sys.setprofile` for each thread, before its
:meth:`run` method is called.
.. versionadded:: 2.3
.. function:: stack_size([size])
Return the thread stack size used when creating new threads. The optional
*size* argument specifies the stack size to be used for subsequently created
threads, and must be 0 (use platform or configured default) or a positive
integer value of at least 32,768 (32kB). If changing the thread stack size is
unsupported, a :exc:`ThreadError` is raised. If the specified stack size is
invalid, a :exc:`ValueError` is raised and the stack size is unmodified. 32kB
is currently the minimum supported stack size value to guarantee sufficient
stack space for the interpreter itself. Note that some platforms may have
particular restrictions on values for the stack size, such as requiring a
minimum stack size > 32kB or requiring allocation in multiples of the system
memory page size - platform documentation should be referred to for more
information (4kB pages are common; using multiples of 4096 for the stack size is
the suggested approach in the absence of more specific information).
Availability: Windows, systems with POSIX threads.
.. versionadded:: 2.5
Detailed interfaces for the objects are documented below.
The design of this module is loosely based on Java's threading model. However,
where Java makes locks and condition variables basic behavior of every object,
they are separate objects in Python. Python's :class:`Thread` class supports a
subset of the behavior of Java's Thread class; currently, there are no
priorities, no thread groups, and threads cannot be destroyed, stopped,
suspended, resumed, or interrupted. The static methods of Java's Thread class,
when implemented, are mapped to module-level functions.
All of the methods described below are executed atomically.
.. _thread-objects:
Thread Objects
--------------
This class represents an activity that is run in a separate thread of control.
There are two ways to specify the activity: by passing a callable object to the
constructor, or by overriding the :meth:`run` method in a subclass. No other
methods (except for the constructor) should be overridden in a subclass. In
other words, *only* override the :meth:`__init__` and :meth:`run` methods of
this class.
Once a thread object is created, its activity must be started by calling the
thread's :meth:`start` method. This invokes the :meth:`run` method in a
separate thread of control.
Once the thread's activity is started, the thread is considered 'alive'. It
stops being alive when its :meth:`run` method terminates -- either normally, or
by raising an unhandled exception. The :meth:`is_alive` method tests whether the
thread is alive.
Other threads can call a thread's :meth:`join` method. This blocks the calling
thread until the thread whose :meth:`join` method is called is terminated.
A thread has a name. The name can be passed to the constructor, and read or
changed through the :attr:`name` attribute.
A thread can be flagged as a "daemon thread". The significance of this flag is
that the entire Python program exits when only daemon threads are left. The
initial value is inherited from the creating thread. The flag can be set
through the :attr:`daemon` property.
.. note::
Daemon threads are abruptly stopped at shutdown. Their resources (such
as open files, database transactions, etc.) may not be released properly.
If you want your threads to stop gracefully, make them non-daemonic and
use a suitable signalling mechanism such as an :class:`Event`.
There is a "main thread" object; this corresponds to the initial thread of
control in the Python program. It is not a daemon thread.
There is the possibility that "dummy thread objects" are created. These are
thread objects corresponding to "alien threads", which are threads of control
started outside the threading module, such as directly from C code. Dummy
thread objects have limited functionality; they are always considered alive and
daemonic, and cannot be :meth:`join`\ ed. They are never deleted, since it is
impossible to detect the termination of alien threads.
.. class:: Thread(group=None, target=None, name=None, args=(), kwargs={})
This constructor should always be called with keyword arguments. Arguments
are:
*group* should be ``None``; reserved for future extension when a
:class:`ThreadGroup` class is implemented.
*target* is the callable object to be invoked by the :meth:`run` method.
Defaults to ``None``, meaning nothing is called.
*name* is the thread name. By default, a unique name is constructed of the
form "Thread-*N*" where *N* is a small decimal number.
*args* is the argument tuple for the target invocation. Defaults to ``()``.
*kwargs* is a dictionary of keyword arguments for the target invocation.
Defaults to ``{}``.
If the subclass overrides the constructor, it must make sure to invoke the
base class constructor (``Thread.__init__()``) before doing anything else to
the thread.
.. method:: start()
Start the thread's activity.
It must be called at most once per thread object. It arranges for the
object's :meth:`run` method to be invoked in a separate thread of control.
This method will raise a :exc:`RuntimeError` if called more than once
on the same thread object.
.. method:: run()
Method representing the thread's activity.
You may override this method in a subclass. The standard :meth:`run`
method invokes the callable object passed to the object's constructor as
the *target* argument, if any, with sequential and keyword arguments taken
from the *args* and *kwargs* arguments, respectively.
.. method:: join([timeout])
Wait until the thread terminates. This blocks the calling thread until the
thread whose :meth:`join` method is called terminates -- either normally
or through an unhandled exception -- or until the optional timeout occurs.
When the *timeout* argument is present and not ``None``, it should be a
floating point number specifying a timeout for the operation in seconds
(or fractions thereof). As :meth:`join` always returns ``None``, you must
call :meth:`isAlive` after :meth:`join` to decide whether a timeout
happened -- if the thread is still alive, the :meth:`join` call timed out.
When the *timeout* argument is not present or ``None``, the operation will
block until the thread terminates.
A thread can be :meth:`join`\ ed many times.
:meth:`join` raises a :exc:`RuntimeError` if an attempt is made to join
the current thread as that would cause a deadlock. It is also an error to
:meth:`join` a thread before it has been started and attempts to do so
raises the same exception.
.. method:: getName()
setName()
Old API for :attr:`~Thread.name`.
.. attribute:: name
A string used for identification purposes only. It has no semantics.
Multiple threads may be given the same name. The initial name is set by
the constructor.
.. attribute:: ident
The 'thread identifier' of this thread or ``None`` if the thread has not
been started. This is a nonzero integer. See the
:func:`thread.get_ident()` function. Thread identifiers may be recycled
when a thread exits and another thread is created. The identifier is
available even after the thread has exited.
.. versionadded:: 2.6
.. method:: is_alive()
isAlive()
Return whether the thread is alive.
This method returns ``True`` just before the :meth:`run` method starts
until just after the :meth:`run` method terminates. The module function
:func:`.enumerate` returns a list of all alive threads.
.. method:: isDaemon()
setDaemon()
Old API for :attr:`~Thread.daemon`.
.. attribute:: daemon
A boolean value indicating whether this thread is a daemon thread (True)
or not (False). This must be set before :meth:`start` is called,
otherwise :exc:`RuntimeError` is raised. Its initial value is inherited
from the creating thread; the main thread is not a daemon thread and
therefore all threads created in the main thread default to :attr:`daemon`
= ``False``.
The entire Python program exits when no alive non-daemon threads are left.
.. _lock-objects:
Lock Objects
------------
A primitive lock is a synchronization primitive that is not owned by a
particular thread when locked. In Python, it is currently the lowest level
synchronization primitive available, implemented directly by the :mod:`thread`
extension module.
A primitive lock is in one of two states, "locked" or "unlocked". It is created
in the unlocked state. It has two basic methods, :meth:`acquire` and
:meth:`release`. When the state is unlocked, :meth:`acquire` changes the state
to locked and returns immediately. When the state is locked, :meth:`acquire`
blocks until a call to :meth:`release` in another thread changes it to unlocked,
then the :meth:`acquire` call resets it to locked and returns. The
:meth:`release` method should only be called in the locked state; it changes the
state to unlocked and returns immediately. If an attempt is made to release an
unlocked lock, a :exc:`RuntimeError` will be raised.
When more than one thread is blocked in :meth:`acquire` waiting for the state to
turn to unlocked, only one thread proceeds when a :meth:`release` call resets
the state to unlocked; which one of the waiting threads proceeds is not defined,
and may vary across implementations.
All methods are executed atomically.
.. method:: Lock.acquire([blocking])
Acquire a lock, blocking or non-blocking.
When invoked with the *blocking* argument set to ``True`` (the default),
block until the lock is unlocked, then set it to locked and return ``True``.
When invoked with the *blocking* argument set to ``False``, do not block.
If a call with *blocking* set to ``True`` would block, return ``False``
immediately; otherwise, set the lock to locked and return ``True``.
.. method:: Lock.release()
Release a lock.
When the lock is locked, reset it to unlocked, and return. If any other threads
are blocked waiting for the lock to become unlocked, allow exactly one of them
to proceed.
When invoked on an unlocked lock, a :exc:`ThreadError` is raised.
There is no return value.
.. _rlock-objects:
RLock Objects
-------------
A reentrant lock is a synchronization primitive that may be acquired multiple
times by the same thread. Internally, it uses the concepts of "owning thread"
and "recursion level" in addition to the locked/unlocked state used by primitive
locks. In the locked state, some thread owns the lock; in the unlocked state,
no thread owns it.
To lock the lock, a thread calls its :meth:`acquire` method; this returns once
the thread owns the lock. To unlock the lock, a thread calls its
:meth:`release` method. :meth:`acquire`/:meth:`release` call pairs may be
nested; only the final :meth:`release` (the :meth:`release` of the outermost
pair) resets the lock to unlocked and allows another thread blocked in
:meth:`acquire` to proceed.
.. method:: RLock.acquire([blocking=1])
Acquire a lock, blocking or non-blocking.
When invoked without arguments: if this thread already owns the lock, increment
the recursion level by one, and return immediately. Otherwise, if another
thread owns the lock, block until the lock is unlocked. Once the lock is
unlocked (not owned by any thread), then grab ownership, set the recursion level
to one, and return. If more than one thread is blocked waiting until the lock
is unlocked, only one at a time will be able to grab ownership of the lock.
There is no return value in this case.
When invoked with the *blocking* argument set to true, do the same thing as when
called without arguments, and return true.
When invoked with the *blocking* argument set to false, do not block. If a call
without an argument would block, return false immediately; otherwise, do the
same thing as when called without arguments, and return true.
.. method:: RLock.release()
Release a lock, decrementing the recursion level. If after the decrement it is
zero, reset the lock to unlocked (not owned by any thread), and if any other
threads are blocked waiting for the lock to become unlocked, allow exactly one
of them to proceed. If after the decrement the recursion level is still
nonzero, the lock remains locked and owned by the calling thread.
Only call this method when the calling thread owns the lock. A
:exc:`RuntimeError` is raised if this method is called when the lock is
unlocked.
There is no return value.
.. _condition-objects:
Condition Objects
-----------------
A condition variable is always associated with some kind of lock; this can be
passed in or one will be created by default. (Passing one in is useful when
several condition variables must share the same lock.)
A condition variable has :meth:`acquire` and :meth:`release` methods that call
the corresponding methods of the associated lock. It also has a :meth:`wait`
method, and :meth:`notify` and :meth:`notifyAll` methods. These three must only
be called when the calling thread has acquired the lock, otherwise a
:exc:`RuntimeError` is raised.
The :meth:`wait` method releases the lock, and then blocks until it is awakened
by a :meth:`notify` or :meth:`notifyAll` call for the same condition variable in
another thread. Once awakened, it re-acquires the lock and returns. It is also
possible to specify a timeout.
The :meth:`notify` method wakes up one of the threads waiting for the condition
variable, if any are waiting. The :meth:`notifyAll` method wakes up all threads
waiting for the condition variable.
Note: the :meth:`notify` and :meth:`notifyAll` methods don't release the lock;
this means that the thread or threads awakened will not return from their
:meth:`wait` call immediately, but only when the thread that called
:meth:`notify` or :meth:`notifyAll` finally relinquishes ownership of the lock.
Tip: the typical programming style using condition variables uses the lock to
synchronize access to some shared state; threads that are interested in a
particular change of state call :meth:`wait` repeatedly until they see the
desired state, while threads that modify the state call :meth:`notify` or
:meth:`notifyAll` when they change the state in such a way that it could
possibly be a desired state for one of the waiters. For example, the following
code is a generic producer-consumer situation with unlimited buffer capacity::
# Consume one item
cv.acquire()
while not an_item_is_available():
cv.wait()
get_an_available_item()
cv.release()
# Produce one item
cv.acquire()
make_an_item_available()
cv.notify()
cv.release()
To choose between :meth:`notify` and :meth:`notifyAll`, consider whether one
state change can be interesting for only one or several waiting threads. E.g.
in a typical producer-consumer situation, adding one item to the buffer only
needs to wake up one consumer thread.
.. class:: Condition([lock])
If the *lock* argument is given and not ``None``, it must be a :class:`Lock`
or :class:`RLock` object, and it is used as the underlying lock. Otherwise,
a new :class:`RLock` object is created and used as the underlying lock.
.. method:: acquire(*args)
Acquire the underlying lock. This method calls the corresponding method on
the underlying lock; the return value is whatever that method returns.
.. method:: release()
Release the underlying lock. This method calls the corresponding method on
the underlying lock; there is no return value.
.. method:: wait([timeout])
Wait until notified or until a timeout occurs. If the calling thread has not
acquired the lock when this method is called, a :exc:`RuntimeError` is raised.
This method releases the underlying lock, and then blocks until it is
awakened by a :meth:`notify` or :meth:`notifyAll` call for the same
condition variable in another thread, or until the optional timeout
occurs. Once awakened or timed out, it re-acquires the lock and returns.
When the *timeout* argument is present and not ``None``, it should be a
floating point number specifying a timeout for the operation in seconds
(or fractions thereof).
When the underlying lock is an :class:`RLock`, it is not released using
its :meth:`release` method, since this may not actually unlock the lock
when it was acquired multiple times recursively. Instead, an internal
interface of the :class:`RLock` class is used, which really unlocks it
even when it has been recursively acquired several times. Another internal
interface is then used to restore the recursion level when the lock is
reacquired.
.. method:: notify(n=1)
By default, wake up one thread waiting on this condition, if any. If the
calling thread has not acquired the lock when this method is called, a
:exc:`RuntimeError` is raised.
This method wakes up at most *n* of the threads waiting for the condition
variable; it is a no-op if no threads are waiting.
The current implementation wakes up exactly *n* threads, if at least *n*
threads are waiting. However, it's not safe to rely on this behavior.
A future, optimized implementation may occasionally wake up more than
*n* threads.
Note: an awakened thread does not actually return from its :meth:`wait`
call until it can reacquire the lock. Since :meth:`notify` does not
release the lock, its caller should.
.. method:: notify_all()
notifyAll()
Wake up all threads waiting on this condition. This method acts like
:meth:`notify`, but wakes up all waiting threads instead of one. If the
calling thread has not acquired the lock when this method is called, a
:exc:`RuntimeError` is raised.
.. _semaphore-objects:
Semaphore Objects
-----------------
This is one of the oldest synchronization primitives in the history of computer
science, invented by the early Dutch computer scientist Edsger W. Dijkstra (he
used :meth:`P` and :meth:`V` instead of :meth:`acquire` and :meth:`release`).
A semaphore manages an internal counter which is decremented by each
:meth:`acquire` call and incremented by each :meth:`release` call. The counter
can never go below zero; when :meth:`acquire` finds that it is zero, it blocks,
waiting until some other thread calls :meth:`release`.
.. class:: Semaphore([value])
The optional argument gives the initial *value* for the internal counter; it
defaults to ``1``. If the *value* given is less than 0, :exc:`ValueError` is
raised.
.. method:: acquire([blocking])
Acquire a semaphore.
When invoked without arguments: if the internal counter is larger than
zero on entry, decrement it by one and return immediately. If it is zero
on entry, block, waiting until some other thread has called
:meth:`release` to make it larger than zero. This is done with proper
interlocking so that if multiple :meth:`acquire` calls are blocked,
:meth:`release` will wake exactly one of them up. The implementation may
pick one at random, so the order in which blocked threads are awakened
should not be relied on. There is no return value in this case.
When invoked with *blocking* set to true, do the same thing as when called
without arguments, and return true.
When invoked with *blocking* set to false, do not block. If a call
without an argument would block, return false immediately; otherwise, do
the same thing as when called without arguments, and return true.
.. method:: release()
Release a semaphore, incrementing the internal counter by one. When it
was zero on entry and another thread is waiting for it to become larger
than zero again, wake up that thread.
.. _semaphore-examples:
:class:`Semaphore` Example
^^^^^^^^^^^^^^^^^^^^^^^^^^
Semaphores are often used to guard resources with limited capacity, for example,
a database server. In any situation where the size of the resource is fixed,
you should use a bounded semaphore. Before spawning any worker threads, your
main thread would initialize the semaphore::
maxconnections = 5
...
pool_sema = BoundedSemaphore(value=maxconnections)
Once spawned, worker threads call the semaphore's acquire and release methods
when they need to connect to the server::
pool_sema.acquire()
conn = connectdb()
... use connection ...
conn.close()
pool_sema.release()
The use of a bounded semaphore reduces the chance that a programming error which
causes the semaphore to be released more than it's acquired will go undetected.
.. _event-objects:
Event Objects
-------------
This is one of the simplest mechanisms for communication between threads: one
thread signals an event and other threads wait for it.
An event object manages an internal flag that can be set to true with the
:meth:`~Event.set` method and reset to false with the :meth:`clear` method. The
:meth:`wait` method blocks until the flag is true.
.. class:: Event()
The internal flag is initially false.
.. method:: is_set()
isSet()
Return true if and only if the internal flag is true.
.. versionchanged:: 2.6
The ``is_set()`` syntax is new.
.. method:: set()
Set the internal flag to true. All threads waiting for it to become true
are awakened. Threads that call :meth:`wait` once the flag is true will
not block at all.
.. method:: clear()
Reset the internal flag to false. Subsequently, threads calling
:meth:`wait` will block until :meth:`.set` is called to set the internal
flag to true again.
.. method:: wait([timeout])
Block until the internal flag is true. If the internal flag is true on
entry, return immediately. Otherwise, block until another thread calls
:meth:`.set` to set the flag to true, or until the optional timeout
occurs.
When the timeout argument is present and not ``None``, it should be a
floating point number specifying a timeout for the operation in seconds
(or fractions thereof).
This method returns the internal flag on exit, so it will always return
``True`` except if a timeout is given and the operation times out.
.. versionchanged:: 2.7
Previously, the method always returned ``None``.
.. _timer-objects:
Timer Objects
-------------
This class represents an action that should be run only after a certain amount
of time has passed --- a timer. :class:`Timer` is a subclass of :class:`Thread`
and as such also functions as an example of creating custom threads.
Timers are started, as with threads, by calling their :meth:`start` method. The
timer can be stopped (before its action has begun) by calling the :meth:`cancel`
method. The interval the timer will wait before executing its action may not be
exactly the same as the interval specified by the user.
For example::
def hello():
print "hello, world"
t = Timer(30.0, hello)
t.start() # after 30 seconds, "hello, world" will be printed
.. class:: Timer(interval, function, args=[], kwargs={})
Create a timer that will run *function* with arguments *args* and keyword
arguments *kwargs*, after *interval* seconds have passed.
.. method:: cancel()
Stop the timer, and cancel the execution of the timer's action. This will
only work if the timer is still in its waiting stage.
.. _with-locks:
Using locks, conditions, and semaphores in the :keyword:`with` statement
------------------------------------------------------------------------
All of the objects provided by this module that have :meth:`acquire` and
:meth:`release` methods can be used as context managers for a :keyword:`with`
statement. The :meth:`acquire` method will be called when the block is entered,
and :meth:`release` will be called when the block is exited.
Currently, :class:`Lock`, :class:`RLock`, :class:`Condition`,
:class:`Semaphore`, and :class:`BoundedSemaphore` objects may be used as
:keyword:`with` statement context managers. For example::
import threading
some_rlock = threading.RLock()
with some_rlock:
print "some_rlock is locked while this executes"
.. _threaded-imports:
Importing in threaded code
--------------------------
While the import machinery is thread-safe, there are two key restrictions on
threaded imports due to inherent limitations in the way that thread-safety is
provided:
* Firstly, other than in the main module, an import should not have the
side effect of spawning a new thread and then waiting for that thread in
any way. Failing to abide by this restriction can lead to a deadlock if
the spawned thread directly or indirectly attempts to import a module.
* Secondly, all import attempts must be completed before the interpreter
starts shutting itself down. This can be most easily achieved by only
performing imports from non-daemon threads created through the threading
module. Daemon threads and threads created directly with the thread
module will require some other form of synchronization to ensure they do
not attempt imports after system shutdown has commenced. Failure to
abide by this restriction will lead to intermittent exceptions and
crashes during interpreter shutdown (as the late imports attempt to
access machinery which is no longer in a valid state).
|
