
``functools`` --- Higher-order functions and operations on callable objects
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**Source code:** Lib/functools.py

======================================================================

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

functools.cmp_to_key(func)

   Transform an old-style comparison function to a key function.  Used
   with tools that accept key functions (such as ``sorted()``,
   ``min()``, ``max()``, ``heapq.nlargest()``, ``heapq.nsmallest()``,
   ``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 indicating the position in the desired collation
   sequence.

   Example:

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

   New in version 3.2.

@functools.lru_cache(maxsize=100)

   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.

   If *maxsize* is set to None, the LRU feature is disabled and the
   cache can grow without bound.

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

   The decorator also provides a ``cache_clear()`` function for
   clearing or invalidating the cache.

   The original underlying function is accessible through the
   ``__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 works best when more recent
   calls are the best predictors of upcoming calls (for example, the
   most popular articles on a news server tend to change daily). The
   cache's size limit assures that the cache does not grow without
   bound on long-running processes such as web servers.

   Example of an LRU cache for static web content:

      @lru_cache(maxsize=20)
      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))

      >>> print(get_pep.cache_info())
      CacheInfo(hits=3, misses=8, maxsize=20, currsize=8)

   Example of efficiently computing Fibonacci numbers using a cache to
   implement a dynamic programming technique:

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

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

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

   New in version 3.2.

@functools.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 ``__lt__()``, ``__le__()``,
   ``__gt__()``, or ``__ge__()``. In addition, the class should supply
   an ``__eq__()`` method.

   For example:

      @total_ordering
      class Student:
          def __eq__(self, other):
              return ((self.lastname.lower(), self.firstname.lower()) ==
                      (other.lastname.lower(), other.firstname.lower()))
          def __lt__(self, other):
              return ((self.lastname.lower(), self.firstname.lower()) <
                      (other.lastname.lower(), other.firstname.lower()))

   New in version 3.2.

functools.partial(func, *args, **keywords)

   Return a new ``partial`` object 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.copy()
              newkeywords.update(fkeywords)
              return func(*(args + fargs), **newkeywords)
          newfunc.func = func
          newfunc.args = args
          newfunc.keywords = keywords
          return newfunc

   The ``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, ``partial()`` can be used to create a callable that
   behaves like the ``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

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

   Apply *function* of two arguments cumulatively to the items of
   *sequence*, from left to right, so as to reduce the sequence 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 *sequence*.  If the optional *initializer* is
   present, it is placed before the items of the sequence in the
   calculation, and serves as a default when the sequence is empty.
   If *initializer* is not given and *sequence* contains only one
   item, the first item is returned.

functools.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 *__name__*, *__module__*, *__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
   ``lru_cache()``), this function automatically adds a __wrapped__
   attribute to the wrapper that refers to the original function.

   The main intended use for this function is in *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.

   ``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).
   ``AttributeError`` is still raised if the wrapper function itself
   is missing any attributes named in *updated*.

   New in version 3.2: Automatic addition of the ``__wrapped__``
   attribute.

   New in version 3.2: Copying of the ``__annotations__`` attribute by
   default.

   Changed in version 3.2: Missing attributes no longer trigger an
   ``AttributeError``.

@functools.wraps(wrapped, assigned=WRAPPER_ASSIGNMENTS, updated=WRAPPER_UPDATES)

   This is a convenience function for invoking
   ``partial(update_wrapper, wrapped=wrapped, assigned=assigned,
   updated=updated)`` as a function decorator when defining a wrapper
   function. 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 ``example()`` would have been lost.


``partial`` Objects
===================

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

partial.func

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

partial.args

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

partial.keywords

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

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