:mod:`functools` --- Higher-order functions and operations on callable objects

.. module:: functools
 :synopsis: Higher-order functions and operations on callable objects.

.. moduleauthor:: Peter Harris <scav@blueyonder.co.uk>

.. moduleauthor:: Raymond Hettinger <python@rcn.com>

.. moduleauthor:: Nick Coghlan <ncoghlan@gmail.com>

.. moduleauthor:: Łukasz Langa <lukasz@langa.pl>

.. sectionauthor:: Peter Harris <scav@blueyonder.co.uk>

Source code: :source:`Lib/functools.py`

The :mod:`functools` module is for higher-order functions: functions that act on or return other functions. In general, any callable object can be treated as a function for the purposes of this module.

The :mod:`functools` module defines the following functions:

.. decorator:: cached_property(func)

 Transform a method of a class into a property whose value is computed once
 and then cached as a normal attribute for the life of the instance. Similar
 to :func:`property`, with the addition of caching. Useful for expensive
 computed properties of instances that are otherwise effectively immutable.

 Example::

 class DataSet:
 def __init__(self, sequence_of_numbers):
 self._data = sequence_of_numbers

 @cached_property
 def stdev(self):
 return statistics.stdev(self._data)

 @cached_property
 def variance(self):
 return statistics.variance(self._data)

 .. versionadded:: 3.8

 .. note::

 This decorator requires that the ``__dict__`` attribute on each instance
 be a mutable mapping. This means it will not work with some types, such as
 metaclasses (since the ``__dict__`` attributes on type instances are
 read-only proxies for the class namespace), and those that specify
 ``__slots__`` without including ``__dict__`` as one of the defined slots
 (as such classes don't provide a ``__dict__`` attribute at all).

.. function:: cmp_to_key(func)

 Transform an old-style comparison function to a :term:`key function`. Used
 with tools that accept key functions (such as :func:`sorted`, :func:`min`,
 :func:`max`, :func:`heapq.nlargest`, :func:`heapq.nsmallest`,
 :func:`itertools.groupby`). This function is primarily used as a transition
 tool for programs being converted from Python 2 which supported the use of
 comparison functions.

 A comparison function is any callable that accept two arguments, compares them,
 and returns a negative number for less-than, zero for equality, or a positive
 number for greater-than. A key function is a callable that accepts one
 argument and returns another value to be used as the sort key.

 Example::

 sorted(iterable, key=cmp_to_key(locale.strcoll)) # locale-aware sort order

 For sorting examples and a brief sorting tutorial, see :ref:`sortinghowto`.

 .. versionadded:: 3.2

.. decorator:: lru_cache(user_function)
 lru_cache(maxsize=128, typed=False)

 Decorator to wrap a function with a memoizing callable that saves up to the
 *maxsize* most recent calls. It can save time when an expensive or I/O bound
 function is periodically called with the same arguments.

 Since a dictionary is used to cache results, the positional and keyword
 arguments to the function must be hashable.

 Distinct argument patterns may be considered to be distinct calls with
 separate cache entries. For example, `f(a=1, b=2)` and `f(b=2, a=1)`
 differ in their keyword argument order and may have two separate cache
 entries.

 If *user_function* is specified, it must be a callable. This allows the
 *lru_cache* decorator to be applied directly to a user function, leaving
 the *maxsize* at its default value of 128::

 @lru_cache
 def count_vowels(sentence):
 sentence = sentence.casefold()
 return sum(sentence.count(vowel) for vowel in 'aeiou')

 If *maxsize* is set to ``None``, the LRU feature is disabled and the cache can
 grow without bound. The LRU feature performs best when *maxsize* is a
 power-of-two.

 If *typed* is set to true, function arguments of different types will be
 cached separately. For example, ``f(3)`` and ``f(3.0)`` will be treated
 as distinct calls with distinct results.

 To help measure the effectiveness of the cache and tune the *maxsize*
 parameter, the wrapped function is instrumented with a :func:`cache_info`
 function that returns a :term:`named tuple` showing *hits*, *misses*,
 *maxsize* and *currsize*. In a multi-threaded environment, the hits
 and misses are approximate.

 The decorator also provides a :func:`cache_clear` function for clearing or
 invalidating the cache.

 The original underlying function is accessible through the
 :attr:`__wrapped__` attribute. This is useful for introspection, for
 bypassing the cache, or for rewrapping the function with a different cache.

 An `LRU (least recently used) cache
 <https://en.wikipedia.org/wiki/Cache_algorithms#Examples>`_ works
 best when the most recent calls are the best predictors of upcoming calls (for
 example, the most popular articles on a news server tend to change each day).
 The cache's size limit assures that the cache does not grow without bound on
 long-running processes such as web servers.

 In general, the LRU cache should only be used when you want to reuse
 previously computed values. Accordingly, it doesn't make sense to cache
 functions with side-effects, functions that need to create distinct mutable
 objects on each call, or impure functions such as time() or random().

 Example of an LRU cache for static web content::

 @lru_cache(maxsize=32)
 def get_pep(num):
 'Retrieve text of a Python Enhancement Proposal'
 resource = 'http://www.python.org/dev/peps/pep-%04d/' % num
 try:
 with urllib.request.urlopen(resource) as s:
 return s.read()
 except urllib.error.HTTPError:
 return 'Not Found'

 >>> for n in 8, 290, 308, 320, 8, 218, 320, 279, 289, 320, 9991:
 ... pep = get_pep(n)
 ... print(n, len(pep))

 >>> get_pep.cache_info()
 CacheInfo(hits=3, misses=8, maxsize=32, currsize=8)

 Example of efficiently computing
 `Fibonacci numbers <https://en.wikipedia.org/wiki/Fibonacci_number>`_
 using a cache to implement a
 `dynamic programming <https://en.wikipedia.org/wiki/Dynamic_programming>`_
 technique::

 @lru_cache(maxsize=None)
 def fib(n):
 if n < 2:
 return n
 return fib(n-1) + fib(n-2)

 >>> [fib(n) for n in range(16)]
 [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610]

 >>> fib.cache_info()
 CacheInfo(hits=28, misses=16, maxsize=None, currsize=16)

 .. versionadded:: 3.2

 .. versionchanged:: 3.3
 Added the *typed* option.

 .. versionchanged:: 3.8
 Added the *user_function* option.

.. decorator:: total_ordering

 Given a class defining one or more rich comparison ordering methods, this
 class decorator supplies the rest. This simplifies the effort involved
 in specifying all of the possible rich comparison operations:

 The class must define one of :meth:`__lt__`, :meth:`__le__`,
 :meth:`__gt__`, or :meth:`__ge__`.
 In addition, the class should supply an :meth:`__eq__` method.

 For example::

 @total_ordering
 class Student:
 def _is_valid_operand(self, other):
 return (hasattr(other, "lastname") and
 hasattr(other, "firstname"))
 def __eq__(self, other):
 if not self._is_valid_operand(other):
 return NotImplemented
 return ((self.lastname.lower(), self.firstname.lower()) ==
 (other.lastname.lower(), other.firstname.lower()))
 def __lt__(self, other):
 if not self._is_valid_operand(other):
 return NotImplemented
 return ((self.lastname.lower(), self.firstname.lower()) <
 (other.lastname.lower(), other.firstname.lower()))

 .. note::

 While this decorator makes it easy to create well behaved totally
 ordered types, it *does* come at the cost of slower execution and
 more complex stack traces for the derived comparison methods. If
 performance benchmarking indicates this is a bottleneck for a given
 application, implementing all six rich comparison methods instead is
 likely to provide an easy speed boost.

 .. versionadded:: 3.2

 .. versionchanged:: 3.4
 Returning NotImplemented from the underlying comparison function for
 unrecognised types is now supported.

.. function:: partial(func, /, *args, **keywords)

 Return a new :ref:`partial object<partial-objects>` which when called
 will behave like *func* called with the positional arguments *args*
 and keyword arguments *keywords*. If more arguments are supplied to the
 call, they are appended to *args*. If additional keyword arguments are
 supplied, they extend and override *keywords*.
 Roughly equivalent to::

 def partial(func, /, *args, **keywords):
 def newfunc(*fargs, **fkeywords):
 newkeywords = {**keywords, **fkeywords}
 return func(*args, *fargs, **newkeywords)
 newfunc.func = func
 newfunc.args = args
 newfunc.keywords = keywords
 return newfunc

 The :func:`partial` is used for partial function application which "freezes"
 some portion of a function's arguments and/or keywords resulting in a new object
 with a simplified signature. For example, :func:`partial` can be used to create
 a callable that behaves like the :func:`int` function where the *base* argument
 defaults to two:

 >>> from functools import partial
 >>> basetwo = partial(int, base=2)
 >>> basetwo.__doc__ = 'Convert base 2 string to an int.'
 >>> basetwo('10010')
 18

.. function:: reduce(function, iterable[, initializer])

 Apply *function* of two arguments cumulatively to the items of *iterable*, from
 left to right, so as to reduce the iterable to a single value. For example,
 ``reduce(lambda x, y: x+y, [1, 2, 3, 4, 5])`` calculates ``((((1+2)+3)+4)+5)``.
 The left argument, *x*, is the accumulated value and the right argument, *y*, is
 the update value from the *iterable*. If the optional *initializer* is present,
 it is placed before the items of the iterable in the calculation, and serves as
 a default when the iterable is empty. If *initializer* is not given and
 *iterable* contains only one item, the first item is returned.

 Roughly equivalent to::

 def reduce(function, iterable, initializer=None):
 it = iter(iterable)
 if initializer is None:
 value = next(it)
 else:
 value = initializer
 for element in it:
 value = function(value, element)
 return value

 See :func:`itertools.accumulate` for an iterator that yields all intermediate
 values.

.. decorator:: singledispatch

 Transform a function into a :term:`single-dispatch <single
 dispatch>` :term:`generic function`.

 To define a generic function, decorate it with the ``@singledispatch``
 decorator. Note that the dispatch happens on the type of the first argument,
 create your function accordingly::

 >>> from functools import singledispatch
 >>> @singledispatch
 ... def fun(arg, verbose=False):
 ... if verbose:
 ... print("Let me just say,", end=" ")
 ... print(arg)

 To add overloaded implementations to the function, use the :func:`register`
 attribute of the generic function. It is a decorator. For functions
 annotated with types, the decorator will infer the type of the first
 argument automatically::

 >>> @fun.register
 ... def _(arg: int, verbose=False):
 ... if verbose:
 ... print("Strength in numbers, eh?", end=" ")
 ... print(arg)
 ...
 >>> @fun.register
 ... def _(arg: list, verbose=False):
 ... if verbose:
 ... print("Enumerate this:")
 ... for i, elem in enumerate(arg):
 ... print(i, elem)

 For code which doesn't use type annotations, the appropriate type
 argument can be passed explicitly to the decorator itself::

 >>> @fun.register(complex)
 ... def _(arg, verbose=False):
 ... if verbose:
 ... print("Better than complicated.", end=" ")
 ... print(arg.real, arg.imag)
 ...


 To enable registering lambdas and pre-existing functions, the
 :func:`register` attribute can be used in a functional form::

 >>> def nothing(arg, verbose=False):
 ... print("Nothing.")
 ...
 >>> fun.register(type(None), nothing)

 The :func:`register` attribute returns the undecorated function which
 enables decorator stacking, pickling, as well as creating unit tests for
 each variant independently::

 >>> @fun.register(float)
 ... @fun.register(Decimal)
 ... def fun_num(arg, verbose=False):
 ... if verbose:
 ... print("Half of your number:", end=" ")
 ... print(arg / 2)
 ...
 >>> fun_num is fun
 False

 When called, the generic function dispatches on the type of the first
 argument::

 >>> fun("Hello, world.")
 Hello, world.
 >>> fun("test.", verbose=True)
 Let me just say, test.
 >>> fun(42, verbose=True)
 Strength in numbers, eh? 42
 >>> fun(['spam', 'spam', 'eggs', 'spam'], verbose=True)
 Enumerate this:
 0 spam
 1 spam
 2 eggs
 3 spam
 >>> fun(None)
 Nothing.
 >>> fun(1.23)
 0.615

 Where there is no registered implementation for a specific type, its
 method resolution order is used to find a more generic implementation.
 The original function decorated with ``@singledispatch`` is registered
 for the base ``object`` type, which means it is used if no better
 implementation is found.

 To check which implementation will the generic function choose for
 a given type, use the ``dispatch()`` attribute::

 >>> fun.dispatch(float)
 <function fun_num at 0x1035a2840>
 >>> fun.dispatch(dict) # note: default implementation
 <function fun at 0x103fe0000>

 To access all registered implementations, use the read-only ``registry``
 attribute::

 >>> fun.registry.keys()
 dict_keys([<class 'NoneType'>, <class 'int'>, <class 'object'>,
 <class 'decimal.Decimal'>, <class 'list'>,
 <class 'float'>])
 >>> fun.registry[float]
 <function fun_num at 0x1035a2840>
 >>> fun.registry[object]
 <function fun at 0x103fe0000>

 .. versionadded:: 3.4

 .. versionchanged:: 3.7
 The :func:`register` attribute supports using type annotations.

Transform a method into a :term:`single-dispatch <single dispatch>` :term:`generic function`.

To define a generic method, decorate it with the @singledispatchmethod decorator. Note that the dispatch happens on the type of the first non-self or non-cls argument, create your function accordingly:

class Negator:
 @singledispatchmethod
 def neg(self, arg):
 raise NotImplementedError("Cannot negate a")

 @neg.register
 def _(self, arg: int):
 return -arg

 @neg.register
 def _(self, arg: bool):
 return not arg

@singledispatchmethod supports nesting with other decorators such as @classmethod. Note that to allow for dispatcher.register, singledispatchmethod must be the outer most decorator. Here is the Negator class with the neg methods being class bound:

class Negator:
 @singledispatchmethod
 @classmethod
 def neg(cls, arg):
 raise NotImplementedError("Cannot negate a")

 @neg.register
 @classmethod
 def _(cls, arg: int):
 return -arg

 @neg.register
 @classmethod
 def _(cls, arg: bool):
 return not arg

The same pattern can be used for other similar decorators: staticmethod, abstractmethod, and others.

.. versionadded:: 3.8

.. function:: update_wrapper(wrapper, wrapped, assigned=WRAPPER_ASSIGNMENTS, updated=WRAPPER_UPDATES)

 Update a *wrapper* function to look like the *wrapped* function. The optional
 arguments are tuples to specify which attributes of the original function are
 assigned directly to the matching attributes on the wrapper function and which
 attributes of the wrapper function are updated with the corresponding attributes
 from the original function. The default values for these arguments are the
 module level constants ``WRAPPER_ASSIGNMENTS`` (which assigns to the wrapper
 function's ``__module__``, ``__name__``, ``__qualname__``, ``__annotations__``
 and ``__doc__``, the documentation string) and ``WRAPPER_UPDATES`` (which
 updates the wrapper function's ``__dict__``, i.e. the instance dictionary).

 To allow access to the original function for introspection and other purposes
 (e.g. bypassing a caching decorator such as :func:`lru_cache`), this function
 automatically adds a ``__wrapped__`` attribute to the wrapper that refers to
 the function being wrapped.

 The main intended use for this function is in :term:`decorator` functions which
 wrap the decorated function and return the wrapper. If the wrapper function is
 not updated, the metadata of the returned function will reflect the wrapper
 definition rather than the original function definition, which is typically less
 than helpful.

 :func:`update_wrapper` may be used with callables other than functions. Any
 attributes named in *assigned* or *updated* that are missing from the object
 being wrapped are ignored (i.e. this function will not attempt to set them
 on the wrapper function). :exc:`AttributeError` is still raised if the
 wrapper function itself is missing any attributes named in *updated*.

 .. versionadded:: 3.2
 Automatic addition of the ``__wrapped__`` attribute.

 .. versionadded:: 3.2
 Copying of the ``__annotations__`` attribute by default.

 .. versionchanged:: 3.2
 Missing attributes no longer trigger an :exc:`AttributeError`.

 .. versionchanged:: 3.4
 The ``__wrapped__`` attribute now always refers to the wrapped
 function, even if that function defined a ``__wrapped__`` attribute.
 (see :issue:`17482`)

.. decorator:: wraps(wrapped, assigned=WRAPPER_ASSIGNMENTS, updated=WRAPPER_UPDATES)

 This is a convenience function for invoking :func:`update_wrapper` as a
 function decorator when defining a wrapper function. It is equivalent to
 ``partial(update_wrapper, wrapped=wrapped, assigned=assigned, updated=updated)``.
 For example::

 >>> from functools import wraps
 >>> def my_decorator(f):
 ... @wraps(f)
 ... def wrapper(*args, **kwds):
 ... print('Calling decorated function')
 ... return f(*args, **kwds)
 ... return wrapper
 ...
 >>> @my_decorator
 ... def example():
 ... """Docstring"""
 ... print('Called example function')
 ...
 >>> example()
 Calling decorated function
 Called example function
 >>> example.__name__
 'example'
 >>> example.__doc__
 'Docstring'

 Without the use of this decorator factory, the name of the example function
 would have been ``'wrapper'``, and the docstring of the original :func:`example`
 would have been lost.

:class:`partial` Objects

:class:`partial` objects are callable objects created by :func:`partial`. They have three read-only attributes:

.. attribute:: partial.func

 A callable object or function. Calls to the :class:`partial` object will be
 forwarded to :attr:`func` with new arguments and keywords.

.. attribute:: partial.args

 The leftmost positional arguments that will be prepended to the positional
 arguments provided to a :class:`partial` object call.

.. attribute:: partial.keywords

 The keyword arguments that will be supplied when the :class:`partial` object is
 called.

:class:`partial` objects are like :class:`function` objects in that they are callable, weak referencable, and can have attributes. There are some important differences. For instance, the :attr:`~definition.__name__` and :attr:`__doc__` attributes are not created automatically. Also, :class:`partial` objects defined in classes behave like static methods and do not transform into bound methods during instance attribute look-up.

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