functools — Higher-order functions and operations on callable objects

Source code: Lib/functools.py

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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.cache(user_function)

Simple lightweight unbounded function cache. Sometimes called “memoize”.

Returns the same as lru_cache(maxsize=None), creating a thin wrapper around a dictionary lookup for the function arguments. Because it never needs to evict old values, this is smaller and faster than lru_cache() with a size limit.

For example:

@cache
def factorial(n):
    return n * factorial(n-1) if n else 1

>>> factorial(10)      # no previously cached result, makes 11 recursive calls
3628800
>>> factorial(5)       # just looks up cached value result
120
>>> factorial(12)      # makes two new recursive calls, the other 10 are cached
479001600

New in version 3.9.

@functools.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 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 = tuple(sequence_of_numbers)

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

The mechanics of cached_property() are somewhat different from property(). A regular property blocks attribute writes unless a setter is defined. In contrast, a cached_property allows writes.

The cached_property decorator only runs on lookups and only when an attribute of the same name doesn’t exist. When it does run, the cached_property writes to the attribute with the same name. Subsequent attribute reads and writes take precedence over the cached_property method and it works like a normal attribute.

The cached value can be cleared by deleting the attribute. This allows the cached_property method to run again.

Note, this decorator interferes with the operation of PEP 412 key-sharing dictionaries. This means that instance dictionaries can take more space than usual.

Also, 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).

If a mutable mapping is not available or if space-efficient key sharing is desired, an effect similar to cached_property() can be achieved by a stacking property() on top of cache():

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

    @property
    @cache
    def stdev(self):
        return statistics.stdev(self._data)

New in version 3.8.

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 accepts 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 Sorting HOW TO.

New in version 3.2.

@functools.lru_cache(user_function)

@functools.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):
    return sum(sentence.count(vowel) for vowel in 'AEIOUaeiou')

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

If typed is set to true, function arguments of different types will be cached separately. If typed is false, the implementation will usually regard them as equivalent calls and only cache a single result. (Some types such as str and int may be cached separately even when typed is false.)

Note, type specificity applies only to the function’s immediate arguments rather than their contents. The scalar arguments, Decimal(42) and Fraction(42) are be treated as distinct calls with distinct results. In contrast, the tuple arguments ('answer', Decimal(42)) and ('answer', Fraction(42)) are treated as equivalent.

The wrapped function is instrumented with a cache_parameters() function that returns a new dict showing the values for maxsize and typed. This is for information purposes only. Mutating the values has no effect.

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.

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.

The cache keeps references to the arguments and return values until they age out of the cache or until the cache is cleared.

An LRU (least recently used) cache 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 = 'https://python.domainunion.de/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 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)

>>> [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)

New in version 3.2.

Changed in version 3.3: Added the typed option.

Changed in version 3.8: Added the user_function option.

New in version 3.9: Added the function cache_parameters()

@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 _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.

Note

This decorator makes no attempt to override methods that have been declared in the class or its superclasses. Meaning that if a superclass defines a comparison operator, total_ordering will not implement it again, even if the original method is abstract.

New in version 3.2.

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

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, **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

class functools.partialmethod(func, /, *args, **keywords)

Return a new partialmethod descriptor which behaves like partial except that it is designed to be used as a method definition rather than being directly callable.

func must be a descriptor or a callable (objects which are both, like normal functions, are handled as descriptors).

When func is a descriptor (such as a normal Python function, classmethod(), staticmethod(), abstractmethod() or another instance of partialmethod), calls to __get__ are delegated to the underlying descriptor, and an appropriate partial object returned as the result.

When func is a non-descriptor callable, an appropriate bound method is created dynamically. This behaves like a normal Python function when used as a method: the self argument will be inserted as the first positional argument, even before the args and keywords supplied to the partialmethod constructor.

Example:

>>> class Cell:
...     def __init__(self):
...         self._alive = False
...     @property
...     def alive(self):
...         return self._alive
...     def set_state(self, state):
...         self._alive = bool(state)
...     set_alive = partialmethod(set_state, True)
...     set_dead = partialmethod(set_state, False)
...
>>> c = Cell()
>>> c.alive
False
>>> c.set_alive()
>>> c.alive
True

New in version 3.4.

functools.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 itertools.accumulate() for an iterator that yields all intermediate values.

@functools.singledispatch

Transform a function into a single-dispatch generic function.

To define a generic function, decorate it with the @singledispatch decorator. When defining a function using @singledispatch, note that the dispatch happens on the type of the first argument:

>>> 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 register() attribute of the generic function, which can be used as 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 register() attribute can also be used in a functional form:

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

The register() attribute returns the undecorated function. This enables decorator stacking, pickling, and the creation of 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.

If an implementation is registered to an abstract base class, virtual subclasses of the base class will be dispatched to that implementation:

>>> from collections.abc import Mapping
>>> @fun.register
... def _(arg: Mapping, verbose=False):
...     if verbose:
...         print("Keys & Values")
...     for key, value in arg.items():
...         print(key, "=>", value)
...
>>> fun({"a": "b"})
a => b

To check which implementation the generic function will 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>

New in version 3.4.

Changed in version 3.7: The register() attribute now supports using type annotations.

class functools.singledispatchmethod(func)

Transform a method into a single-dispatch generic function.

To define a generic method, decorate it with the @singledispatchmethod decorator. When defining a function using @singledispatchmethod, note that the dispatch happens on the type of the first non-self or non-cls argument:

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 bound to the class, rather than an instance of the class:

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.

New in version 3.8.

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 __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 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 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.

Changed in version 3.4: The __wrapped__ attribute now always refers to the wrapped function, even if that function defined a __wrapped__ attribute. (see bpo-17482)

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

This is a convenience function for invoking 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 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.