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approaches","anchor":"alternative-approaches","htmlText":"Alternative 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class=\"markdown-body entry-content container-lg\" itemprop=\"text\"\u003e\u003cp dir=\"auto\"\u003ePEP: 443\nTitle: Single-dispatch generic functions\nAuthor: Łukasz Langa \u0026lt;\u003ca href=\"mailto:lukasz@python.org\"\u003elukasz@python.org\u003c/a\u003e\u0026gt;\nDiscussions-To: \u003ca href=\"mailto:python-dev@python.org\"\u003epython-dev@python.org\u003c/a\u003e\nStatus: Final\nType: Standards Track\nCreated: 22-May-2013\nPython-Version: 3.4\nPost-History: 22-May-2013, 25-May-2013, 31-May-2013\nReplaces: 245, 246, 3124\u003c/p\u003e\n\u003ca name=\"user-content-abstract\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAbstract\u003c/h2\u003e\u003ca id=\"user-content-abstract\" class=\"anchor\" aria-label=\"Permalink: Abstract\" href=\"#abstract\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis PEP proposes a new mechanism in the \u003ccode\u003efunctools\u003c/code\u003e standard library\nmodule that provides a simple form of generic programming known as\nsingle-dispatch generic functions.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eA \u003cstrong\u003egeneric function\u003c/strong\u003e is composed of multiple functions implementing\nthe same operation for different types. Which implementation should be\nused during a call is determined by the dispatch algorithm. When the\nimplementation is chosen based on the type of a single argument, this is\nknown as \u003cstrong\u003esingle dispatch\u003c/strong\u003e.\u003c/p\u003e\n\u003ca name=\"user-content-rationale-and-goals\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eRationale and Goals\u003c/h2\u003e\u003ca id=\"user-content-rationale-and-goals\" class=\"anchor\" aria-label=\"Permalink: Rationale and Goals\" href=\"#rationale-and-goals\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003ePython has always provided a variety of built-in and standard-library\ngeneric functions, such as \u003ccode\u003elen()\u003c/code\u003e, \u003ccode\u003eiter()\u003c/code\u003e, \u003ccode\u003epprint.pprint()\u003c/code\u003e,\n\u003ccode\u003ecopy.copy()\u003c/code\u003e, and most of the functions in the \u003ccode\u003eoperator\u003c/code\u003e module.\nHowever, it currently:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003edoes not have a simple or straightforward way for developers to\ncreate new generic functions,\u003c/li\u003e\n\u003cli\u003edoes not have a standard way for methods to be added to existing\ngeneric functions (i.e., some are added using registration\nfunctions, others require defining \u003ccode\u003e__special__\u003c/code\u003e methods, possibly\nby monkeypatching).\u003c/li\u003e\n\u003c/ol\u003e\n\u003cp dir=\"auto\"\u003eIn addition, it is currently a common anti-pattern for Python code to\ninspect the types of received arguments, in order to decide what to do\nwith the objects.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eFor example, code may wish to accept either an object\nof some type, or a sequence of objects of that type.\nCurrently, the \"obvious way\" to do this is by type inspection, but this\nis brittle and closed to extension.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAbstract Base Classes make it easier\nto discover present behaviour, but don't help adding new behaviour.\nA developer using an already-written library may be unable to change how\ntheir objects are treated by such code, especially if the objects they\nare using were created by a third party.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTherefore, this PEP proposes a uniform API to address dynamic\noverloading using decorators.\u003c/p\u003e\n\u003ca name=\"user-content-user-api\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUser API\u003c/h2\u003e\u003ca id=\"user-content-user-api\" class=\"anchor\" aria-label=\"Permalink: User API\" href=\"#user-api\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eTo define a generic function, decorate it with the \u003ccode\u003e@singledispatch\u003c/code\u003e\ndecorator. Note that the dispatch happens on the type of the first\nargument. Create your function accordingly:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; from functools import singledispatch\n\u0026gt;\u0026gt;\u0026gt; @singledispatch\n... def fun(arg, verbose=False):\n... if verbose:\n... print(\"Let me just say,\", end=\" \")\n... print(arg)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eTo add overloaded implementations to the function, use the\n\u003ccode\u003eregister()\u003c/code\u003e attribute of the generic function. This is a decorator,\ntaking a type parameter and decorating a function implementing the\noperation for that type:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; @fun.register(int)\n... def _(arg, verbose=False):\n... if verbose:\n... print(\"Strength in numbers, eh?\", end=\" \")\n... print(arg)\n...\n\u0026gt;\u0026gt;\u0026gt; @fun.register(list)\n... def _(arg, verbose=False):\n... if verbose:\n... print(\"Enumerate this:\")\n... for i, elem in enumerate(arg):\n... print(i, elem)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eTo enable registering lambdas and pre-existing functions, the\n\u003ccode\u003eregister()\u003c/code\u003e attribute can be used in a functional form:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; def nothing(arg, verbose=False):\n... print(\"Nothing.\")\n...\n\u0026gt;\u0026gt;\u0026gt; fun.register(type(None), nothing)\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eThe \u003ccode\u003eregister()\u003c/code\u003e attribute returns the undecorated function. This\nenables decorator stacking, pickling, as well as creating unit tests for\neach variant independently:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; @fun.register(float)\n... @fun.register(Decimal)\n... def fun_num(arg, verbose=False):\n... if verbose:\n... print(\"Half of your number:\", end=\" \")\n... print(arg / 2)\n...\n\u0026gt;\u0026gt;\u0026gt; fun_num is fun\nFalse\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eWhen called, the generic function dispatches on the type of the first\nargument:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; fun(\"Hello, world.\")\nHello, world.\n\u0026gt;\u0026gt;\u0026gt; fun(\"test.\", verbose=True)\nLet me just say, test.\n\u0026gt;\u0026gt;\u0026gt; fun(42, verbose=True)\nStrength in numbers, eh? 42\n\u0026gt;\u0026gt;\u0026gt; fun(['spam', 'spam', 'eggs', 'spam'], verbose=True)\nEnumerate this:\n0 spam\n1 spam\n2 eggs\n3 spam\n\u0026gt;\u0026gt;\u0026gt; fun(None)\nNothing.\n\u0026gt;\u0026gt;\u0026gt; fun(1.23)\n0.615\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eWhere there is no registered implementation for a specific type, its\nmethod resolution order is used to find a more generic implementation.\nThe original function decorated with \u003ccode\u003e@singledispatch\u003c/code\u003e is registered\nfor the base \u003ccode\u003eobject\u003c/code\u003e type, which means it is used if no better\nimplementation is found.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eTo check which implementation will the generic function choose for\na given type, use the \u003ccode\u003edispatch()\u003c/code\u003e attribute:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; fun.dispatch(float)\n\u0026lt;function fun_num at 0x104319058\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; fun.dispatch(dict) # note: default implementation\n\u0026lt;function fun at 0x103fe0000\u0026gt;\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eTo access all registered implementations, use the read-only \u003ccode\u003eregistry\u003c/code\u003e\nattribute:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; fun.registry.keys()\ndict_keys([\u0026lt;class 'NoneType'\u0026gt;, \u0026lt;class 'int'\u0026gt;, \u0026lt;class 'object'\u0026gt;,\n \u0026lt;class 'decimal.Decimal'\u0026gt;, \u0026lt;class 'list'\u0026gt;,\n \u0026lt;class 'float'\u0026gt;])\n\u0026gt;\u0026gt;\u0026gt; fun.registry[float]\n\u0026lt;function fun_num at 0x1035a2840\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; fun.registry[object]\n\u0026lt;function fun at 0x103fe0000\u0026gt;\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eThe proposed API is intentionally limited and opinionated, as to ensure\nit is easy to explain and use, as well as to maintain consistency with\nexisting members in the \u003ccode\u003efunctools\u003c/code\u003e module.\u003c/p\u003e\n\u003ca name=\"user-content-implementation-notes\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eImplementation Notes\u003c/h2\u003e\u003ca id=\"user-content-implementation-notes\" class=\"anchor\" aria-label=\"Permalink: Implementation Notes\" href=\"#implementation-notes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe functionality described in this PEP is already implemented in the\n\u003ccode\u003epkgutil\u003c/code\u003e standard library module as \u003ccode\u003esimplegeneric\u003c/code\u003e. Because this\nimplementation is mature, the goal is to move it largely as-is. The\nreference implementation is available on hg.python.org \u003ca href=\"#ref-impl\" id=\"user-content-id1\"\u003e[1]\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe dispatch type is specified as a decorator argument. An alternative\nform using function annotations was considered but its inclusion\nhas been rejected. As of May 2013, this usage pattern is out of scope\nfor the standard library \u003ca href=\"#pep-0008\" id=\"user-content-id2\"\u003e[2]\u003c/a\u003e, and the best practices for\nannotation usage are still debated.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBased on the current \u003ccode\u003epkgutil.simplegeneric\u003c/code\u003e implementation, and\nfollowing the convention on registering virtual subclasses on Abstract\nBase Classes, the dispatch registry will not be thread-safe.\u003c/p\u003e\n\u003ca name=\"user-content-abstract-base-classes\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch3 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAbstract Base Classes\u003c/h3\u003e\u003ca id=\"user-content-abstract-base-classes\" class=\"anchor\" aria-label=\"Permalink: Abstract Base Classes\" href=\"#abstract-base-classes\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe \u003ccode\u003epkgutil.simplegeneric\u003c/code\u003e implementation relied on several forms of\nmethod resolution order (MRO). \u003ccode\u003e@singledispatch\u003c/code\u003e removes special\nhandling of old-style classes and Zope's ExtensionClasses. More\nimportantly, it introduces support for Abstract Base Classes (ABC).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWhen a generic function implementation is registered for an ABC, the\ndispatch algorithm switches to an extended form of C3 linearization,\nwhich includes the relevant ABCs in the MRO of the provided argument.\nThe algorithm inserts ABCs where their functionality is introduced, i.e.\n\u003ccode\u003eissubclass(cls, abc)\u003c/code\u003e returns \u003ccode\u003eTrue\u003c/code\u003e for the class itself but\nreturns \u003ccode\u003eFalse\u003c/code\u003e for all its direct base classes. Implicit ABCs for\na given class (either registered or inferred from the presence of\na special method like \u003ccode\u003e__len__()\u003c/code\u003e) are inserted directly after the\nlast ABC explicitly listed in the MRO of said class.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn its most basic form, this linearization returns the MRO for the given\ntype:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; _compose_mro(dict, [])\n[\u0026lt;class 'dict'\u0026gt;, \u0026lt;class 'object'\u0026gt;]\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eWhen the second argument contains ABCs that the specified type is\na subclass of, they are inserted in a predictable order:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; _compose_mro(dict, [Sized, MutableMapping, str,\n... Sequence, Iterable])\n[\u0026lt;class 'dict'\u0026gt;, \u0026lt;class 'collections.abc.MutableMapping'\u0026gt;,\n \u0026lt;class 'collections.abc.Mapping'\u0026gt;, \u0026lt;class 'collections.abc.Sized'\u0026gt;,\n \u0026lt;class 'collections.abc.Iterable'\u0026gt;, \u0026lt;class 'collections.abc.Container'\u0026gt;,\n \u0026lt;class 'object'\u0026gt;]\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eWhile this mode of operation is significantly slower, all dispatch\ndecisions are cached. The cache is invalidated on registering new\nimplementations on the generic function or when user code calls\n\u003ccode\u003eregister()\u003c/code\u003e on an ABC to implicitly subclass it. In the latter case,\nit is possible to create a situation with ambiguous dispatch, for\ninstance:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; from collections.abc import Iterable, Container\n\u0026gt;\u0026gt;\u0026gt; class P:\n... pass\n\u0026gt;\u0026gt;\u0026gt; Iterable.register(P)\n\u0026lt;class '__main__.P'\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; Container.register(P)\n\u0026lt;class '__main__.P'\u0026gt;\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eFaced with ambiguity, \u003ccode\u003e@singledispatch\u003c/code\u003e refuses the temptation to\nguess:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; @singledispatch\n... def g(arg):\n... return \"base\"\n...\n\u0026gt;\u0026gt;\u0026gt; g.register(Iterable, lambda arg: \"iterable\")\n\u0026lt;function \u0026lt;lambda\u0026gt; at 0x108b49110\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; g.register(Container, lambda arg: \"container\")\n\u0026lt;function \u0026lt;lambda\u0026gt; at 0x108b491c8\u0026gt;\n\u0026gt;\u0026gt;\u0026gt; g(P())\nTraceback (most recent call last):\n...\nRuntimeError: Ambiguous dispatch: \u0026lt;class 'collections.abc.Container'\u0026gt;\nor \u0026lt;class 'collections.abc.Iterable'\u0026gt;\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eNote that this exception would not be raised if one or more ABCs had\nbeen provided explicitly as base classes during class definition. In\nthis case dispatch happens in the MRO order:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; class Ten(Iterable, Container):\n... def __iter__(self):\n... for i in range(10):\n... yield i\n... def __contains__(self, value):\n... return value in range(10)\n...\n\u0026gt;\u0026gt;\u0026gt; g(Ten())\n'iterable'\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eA similar conflict arises when subclassing an ABC is inferred from the\npresence of a special method like \u003ccode\u003e__len__()\u003c/code\u003e or \u003ccode\u003e__contains__()\u003c/code\u003e:\u003c/p\u003e\n\u003cpre\u003e\u0026gt;\u0026gt;\u0026gt; class Q:\n... def __contains__(self, value):\n... return False\n...\n\u0026gt;\u0026gt;\u0026gt; issubclass(Q, Container)\nTrue\n\u0026gt;\u0026gt;\u0026gt; Iterable.register(Q)\n\u0026gt;\u0026gt;\u0026gt; g(Q())\nTraceback (most recent call last):\n...\nRuntimeError: Ambiguous dispatch: \u0026lt;class 'collections.abc.Container'\u0026gt;\nor \u0026lt;class 'collections.abc.Iterable'\u0026gt;\n\u003c/pre\u003e\n\u003cp dir=\"auto\"\u003eAn early version of the PEP contained a custom approach that was simpler\nbut created a number of edge cases with surprising results \u003ca href=\"#why-c3\" id=\"user-content-id3\"\u003e[3]\u003c/a\u003e.\u003c/p\u003e\n\u003ca name=\"user-content-usage-patterns\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage Patterns\u003c/h2\u003e\u003ca id=\"user-content-usage-patterns\" class=\"anchor\" aria-label=\"Permalink: Usage Patterns\" href=\"#usage-patterns\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis PEP proposes extending behaviour only of functions specifically\nmarked as generic. Just as a base class method may be overridden by\na subclass, so too a function may be overloaded to provide custom\nfunctionality for a given type.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eUniversal overloading does not equal \u003cem\u003earbitrary\u003c/em\u003e overloading, in the\nsense that we need not expect people to randomly redefine the behavior\nof existing functions in unpredictable ways. To the contrary, generic\nfunction usage in actual programs tends to follow very predictable\npatterns and registered implementations are highly-discoverable in the\ncommon case.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIf a module is defining a new generic operation, it will usually also\ndefine any required implementations for existing types in the same\nplace. Likewise, if a module is defining a new type, then it will\nusually define implementations there for any generic functions that it\nknows or cares about. As a result, the vast majority of registered\nimplementations can be found adjacent to either the function being\noverloaded, or to a newly-defined type for which the implementation is\nadding support.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIt is only in rather infrequent cases that one will have implementations\nregistered in a module that contains neither the function nor the\ntype(s) for which the implementation is added. In the absence of\nincompetence or deliberate intention to be obscure, the few\nimplementations that are not registered adjacent to the relevant type(s)\nor function(s), will generally not need to be understood or known about\noutside the scope where those implementations are defined. (Except in\nthe \"support modules\" case, where best practice suggests naming them\naccordingly.)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAs mentioned earlier, single-dispatch generics are already prolific\nthroughout the standard library. A clean, standard way of doing them\nprovides a way forward to refactor those custom implementations to use\na common one, opening them up for user extensibility at the same time.\u003c/p\u003e\n\u003ca name=\"user-content-alternative-approaches\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAlternative approaches\u003c/h2\u003e\u003ca id=\"user-content-alternative-approaches\" class=\"anchor\" aria-label=\"Permalink: Alternative approaches\" href=\"#alternative-approaches\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIn \u003ca href=\"http://www.python.org/dev/peps/pep-3124\" rel=\"nofollow\"\u003ePEP 3124\u003c/a\u003e Phillip J. Eby proposes a full-grown solution\nwith overloading based on arbitrary rule sets (with the default\nimplementation dispatching on argument types), as well as interfaces,\nadaptation and method combining. PEAK-Rules \u003ca href=\"#peak-rules\" id=\"user-content-id4\"\u003e[4]\u003c/a\u003e is\na reference implementation of the concepts described in PJE's PEP.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eSuch a broad approach is inherently complex, which makes reaching\na consensus hard. In contrast, this PEP focuses on a single piece of\nfunctionality that is simple to reason about. It's important to note\nthis does not preclude the use of other approaches now or in the future.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eIn a 2005 article on Artima \u003ca href=\"#artima2005\" id=\"user-content-id5\"\u003e[5]\u003c/a\u003e Guido van Rossum presents\na generic function implementation that dispatches on types of all\narguments on a function. The same approach was chosen in Andrey Popp's\n\u003ccode\u003egeneric\u003c/code\u003e package available on PyPI \u003ca href=\"#pypi-generic\" id=\"user-content-id6\"\u003e[6]\u003c/a\u003e, as well as David\nMertz's \u003ccode\u003egnosis.magic.multimethods\u003c/code\u003e \u003ca href=\"#gnosis-multimethods\" id=\"user-content-id7\"\u003e[7]\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eWhile this seems desirable at first, I agree with Fredrik Lundh's\ncomment that \"if you design APIs with pages of logic just to sort out\nwhat code a function should execute, you should probably hand over the\nAPI design to someone else\". In other words, the single argument\napproach proposed in this PEP is not only easier to implement but also\nclearly communicates that dispatching on a more complex state is an\nanti-pattern. It also has the virtue of corresponding directly with the\nfamiliar method dispatch mechanism in object oriented programming. The\nonly difference is whether the custom implementation is associated more\nclosely with the data (object-oriented methods) or the algorithm\n(single-dispatch overloading).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003ePyPy's RPython offers \u003ccode\u003eextendabletype\u003c/code\u003e \u003ca href=\"#pairtype\" id=\"user-content-id8\"\u003e[8]\u003c/a\u003e, a metaclass which\nenables classes to be externally extended. In combination with\n\u003ccode\u003epairtype()\u003c/code\u003e and \u003ccode\u003epair()\u003c/code\u003e factories, this offers a form of\nsingle-dispatch generics.\u003c/p\u003e\n\u003ca name=\"user-content-acknowledgements\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAcknowledgements\u003c/h2\u003e\u003ca id=\"user-content-acknowledgements\" class=\"anchor\" aria-label=\"Permalink: Acknowledgements\" href=\"#acknowledgements\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eApart from Phillip J. Eby's work on \u003ca href=\"http://www.python.org/dev/peps/pep-3124\" rel=\"nofollow\"\u003ePEP 3124\u003c/a\u003e and\nPEAK-Rules, influences include Paul Moore's original issue\n\u003ca href=\"#issue-5135\" id=\"user-content-id9\"\u003e[9]\u003c/a\u003e that proposed exposing \u003ccode\u003epkgutil.simplegeneric\u003c/code\u003e as part\nof the \u003ccode\u003efunctools\u003c/code\u003e API, Guido van Rossum's article on multimethods\n\u003ca href=\"#artima2005\" id=\"user-content-id10\"\u003e[5]\u003c/a\u003e, and discussions with Raymond Hettinger on a general\npprint rewrite. Huge thanks to Alyssa Coghlan for encouraging me to create\nthis PEP and providing initial feedback.\u003c/p\u003e\n\u003ca name=\"user-content-references\"\u003e\u003c/a\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eReferences\u003c/h2\u003e\u003ca id=\"user-content-references\" class=\"anchor\" aria-label=\"Permalink: References\" href=\"#references\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-ref-impl\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id1\"\u003e[1]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://hg.python.org/features/pep-443/file/tip/Lib/functools.py#l359\" rel=\"nofollow\"\u003ehttp://hg.python.org/features/pep-443/file/tip/Lib/functools.py#l359\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-pep-0008\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id2\"\u003e[2]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://www.python.org/dev/peps/pep-0008\" rel=\"nofollow\"\u003ePEP 8\u003c/a\u003e states in the \"Programming Recommendations\"\nsection that \"the Python standard library will not use function\nannotations as that would result in a premature commitment to\na particular annotation style\".\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-why-c3\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id3\"\u003e[3]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://bugs.python.org/issue18244\" rel=\"nofollow\"\u003ehttp://bugs.python.org/issue18244\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-peak-rules\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id4\"\u003e[4]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://peak.telecommunity.com/DevCenter/PEAK_2dRules\" rel=\"nofollow\"\u003ehttp://peak.telecommunity.com/DevCenter/PEAK_2dRules\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-artima2005\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e[5]\u003c/td\u003e\u003ctd\u003e\u003cem\u003e(\u003ca href=\"#id5\"\u003e1\u003c/a\u003e, \u003ca href=\"#id10\"\u003e2\u003c/a\u003e)\u003c/em\u003e \u003ca href=\"http://www.artima.com/weblogs/viewpost.jsp?thread=101605\" rel=\"nofollow\"\u003ehttp://www.artima.com/weblogs/viewpost.jsp?thread=101605\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-pypi-generic\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id6\"\u003e[6]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://pypi.python.org/pypi/generic\" rel=\"nofollow\"\u003ehttp://pypi.python.org/pypi/generic\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-gnosis-multimethods\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id7\"\u003e[7]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"http://gnosis.cx/publish/programming/charming_python_b12.html\" rel=\"nofollow\"\u003ehttp://gnosis.cx/publish/programming/charming_python_b12.html\u003c/a\u003e\u003c/td\u003e\u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\u003c/markdown-accessiblity-table\u003e\n\u003cmarkdown-accessiblity-table\u003e\u003ctable frame=\"void\" id=\"user-content-pairtype\" rules=\"none\"\u003e\n\n\u003ctbody valign=\"top\"\u003e\n\u003ctr\u003e\u003ctd\u003e\u003ca href=\"#id8\"\u003e[8]\u003c/a\u003e\u003c/td\u003e\u003ctd\u003e\u003ca href=\"https://bitbucket.org/pypy/pypy/raw/default/rpython/tool/pairtype.py\" 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3Z"></path></svg></button></div></div></div></div><div></div></div><div class="Box-sc-g0xbh4-0 hGyMdv"><section aria-labelledby="file-name-id-wide file-name-id-mobile" class="Box-sc-g0xbh4-0 fGqKFv"><div class="Box-sc-g0xbh4-0 eoaCFS js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><p dir="auto">PEP: 443 Title: Single-dispatch generic functions Author: Łukasz Langa <<a href="mailto:lukasz@python.org">lukasz@python.org</a>> Discussions-To: <a href="mailto:python-dev@python.org">python-dev@python.org</a> Status: Final Type: Standards Track Created: 22-May-2013 Python-Version: 3.4 Post-History: 22-May-2013, 25-May-2013, 31-May-2013 Replaces: 245, 246, 3124</p> <a name="user-content-abstract"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Abstract</h2><a id="user-content-abstract" class="anchor" aria-label="Permalink: Abstract" href="#abstract"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This PEP proposes a new mechanism in the <code>functools</code> standard library module that provides a simple form of generic programming known as single-dispatch generic functions.</p> <p dir="auto">A <strong>generic function</strong> is composed of multiple functions implementing the same operation for different types. Which implementation should be used during a call is determined by the dispatch algorithm. When the implementation is chosen based on the type of a single argument, this is known as <strong>single dispatch</strong>.</p> <a name="user-content-rationale-and-goals"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Rationale and Goals</h2><a id="user-content-rationale-and-goals" class="anchor" aria-label="Permalink: Rationale and Goals" href="#rationale-and-goals"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Python has always provided a variety of built-in and standard-library generic functions, such as <code>len()</code>, <code>iter()</code>, <code>pprint.pprint()</code>, <code>copy.copy()</code>, and most of the functions in the <code>operator</code> module. However, it currently:</p> <ol dir="auto"> <li>does not have a simple or straightforward way for developers to create new generic functions,</li> <li>does not have a standard way for methods to be added to existing generic functions (i.e., some are added using registration functions, others require defining <code>__special__</code> methods, possibly by monkeypatching).</li> </ol> <p dir="auto">In addition, it is currently a common anti-pattern for Python code to inspect the types of received arguments, in order to decide what to do with the objects.</p> <p dir="auto">For example, code may wish to accept either an object of some type, or a sequence of objects of that type. Currently, the "obvious way" to do this is by type inspection, but this is brittle and closed to extension.</p> <p dir="auto">Abstract Base Classes make it easier to discover present behaviour, but don't help adding new behaviour. A developer using an already-written library may be unable to change how their objects are treated by such code, especially if the objects they are using were created by a third party.</p> <p dir="auto">Therefore, this PEP proposes a uniform API to address dynamic overloading using decorators.</p> <a name="user-content-user-api"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">User API</h2><a id="user-content-user-api" class="anchor" aria-label="Permalink: User API" href="#user-api"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">To define a generic function, decorate it with the <code>@singledispatch</code> decorator. Note that the dispatch happens on the type of the first argument. Create your function accordingly:</p> <pre>>>> from functools import singledispatch >>> @singledispatch ... def fun(arg, verbose=False): ... if verbose: ... print("Let me just say,", end=" ") ... print(arg) </pre> <p dir="auto">To add overloaded implementations to the function, use the <code>register()</code> attribute of the generic function. This is a decorator, taking a type parameter and decorating a function implementing the operation for that type:</p> <pre>>>> @fun.register(int) ... def _(arg, verbose=False): ... if verbose: ... print("Strength in numbers, eh?", end=" ") ... print(arg) ... >>> @fun.register(list) ... def _(arg, verbose=False): ... if verbose: ... print("Enumerate this:") ... for i, elem in enumerate(arg): ... print(i, elem) </pre> <p dir="auto">To enable registering lambdas and pre-existing functions, the <code>register()</code> attribute can be used in a functional form:</p> <pre>>>> def nothing(arg, verbose=False): ... print("Nothing.") ... >>> fun.register(type(None), nothing) </pre> <p dir="auto">The <code>register()</code> attribute returns the undecorated function. This enables decorator stacking, pickling, as well as creating unit tests for each variant independently:</p> <pre>>>> @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 </pre> <p dir="auto">When called, the generic function dispatches on the type of the first argument:</p> <pre>>>> 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 </pre> <p dir="auto">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 <code>@singledispatch</code> is registered for the base <code>object</code> type, which means it is used if no better implementation is found.</p> <p dir="auto">To check which implementation will the generic function choose for a given type, use the <code>dispatch()</code> attribute:</p> <pre>>>> fun.dispatch(float) <function fun_num at 0x104319058> >>> fun.dispatch(dict) # note: default implementation <function fun at 0x103fe0000> </pre> <p dir="auto">To access all registered implementations, use the read-only <code>registry</code> attribute:</p> <pre>>>> 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> </pre> <p dir="auto">The proposed API is intentionally limited and opinionated, as to ensure it is easy to explain and use, as well as to maintain consistency with existing members in the <code>functools</code> module.</p> <a name="user-content-implementation-notes"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Implementation Notes</h2><a id="user-content-implementation-notes" class="anchor" aria-label="Permalink: Implementation Notes" href="#implementation-notes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The functionality described in this PEP is already implemented in the <code>pkgutil</code> standard library module as <code>simplegeneric</code>. Because this implementation is mature, the goal is to move it largely as-is. The reference implementation is available on hg.python.org <a href="#ref-impl" id="user-content-id1">[1]</a>.</p> <p dir="auto">The dispatch type is specified as a decorator argument. An alternative form using function annotations was considered but its inclusion has been rejected. As of May 2013, this usage pattern is out of scope for the standard library <a href="#pep-0008" id="user-content-id2">[2]</a>, and the best practices for annotation usage are still debated.</p> <p dir="auto">Based on the current <code>pkgutil.simplegeneric</code> implementation, and following the convention on registering virtual subclasses on Abstract Base Classes, the dispatch registry will not be thread-safe.</p> <a name="user-content-abstract-base-classes"></a> <div class="markdown-heading" dir="auto"><h3 tabindex="-1" class="heading-element" dir="auto">Abstract Base Classes</h3><a id="user-content-abstract-base-classes" class="anchor" aria-label="Permalink: Abstract Base Classes" href="#abstract-base-classes"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The <code>pkgutil.simplegeneric</code> implementation relied on several forms of method resolution order (MRO). <code>@singledispatch</code> removes special handling of old-style classes and Zope's ExtensionClasses. More importantly, it introduces support for Abstract Base Classes (ABC).</p> <p dir="auto">When a generic function implementation is registered for an ABC, the dispatch algorithm switches to an extended form of C3 linearization, which includes the relevant ABCs in the MRO of the provided argument. The algorithm inserts ABCs where their functionality is introduced, i.e. <code>issubclass(cls, abc)</code> returns <code>True</code> for the class itself but returns <code>False</code> for all its direct base classes. Implicit ABCs for a given class (either registered or inferred from the presence of a special method like <code>__len__()</code>) are inserted directly after the last ABC explicitly listed in the MRO of said class.</p> <p dir="auto">In its most basic form, this linearization returns the MRO for the given type:</p> <pre>>>> _compose_mro(dict, []) [<class 'dict'>, <class 'object'>] </pre> <p dir="auto">When the second argument contains ABCs that the specified type is a subclass of, they are inserted in a predictable order:</p> <pre>>>> _compose_mro(dict, [Sized, MutableMapping, str, ... Sequence, Iterable]) [<class 'dict'>, <class 'collections.abc.MutableMapping'>, <class 'collections.abc.Mapping'>, <class 'collections.abc.Sized'>, <class 'collections.abc.Iterable'>, <class 'collections.abc.Container'>, <class 'object'>] </pre> <p dir="auto">While this mode of operation is significantly slower, all dispatch decisions are cached. The cache is invalidated on registering new implementations on the generic function or when user code calls <code>register()</code> on an ABC to implicitly subclass it. In the latter case, it is possible to create a situation with ambiguous dispatch, for instance:</p> <pre>>>> from collections.abc import Iterable, Container >>> class P: ... pass >>> Iterable.register(P) <class '__main__.P'> >>> Container.register(P) <class '__main__.P'> </pre> <p dir="auto">Faced with ambiguity, <code>@singledispatch</code> refuses the temptation to guess:</p> <pre>>>> @singledispatch ... def g(arg): ... return "base" ... >>> g.register(Iterable, lambda arg: "iterable") <function <lambda> at 0x108b49110> >>> g.register(Container, lambda arg: "container") <function <lambda> at 0x108b491c8> >>> g(P()) Traceback (most recent call last): ... RuntimeError: Ambiguous dispatch: <class 'collections.abc.Container'> or <class 'collections.abc.Iterable'> </pre> <p dir="auto">Note that this exception would not be raised if one or more ABCs had been provided explicitly as base classes during class definition. In this case dispatch happens in the MRO order:</p> <pre>>>> class Ten(Iterable, Container): ... def __iter__(self): ... for i in range(10): ... yield i ... def __contains__(self, value): ... return value in range(10) ... >>> g(Ten()) 'iterable' </pre> <p dir="auto">A similar conflict arises when subclassing an ABC is inferred from the presence of a special method like <code>__len__()</code> or <code>__contains__()</code>:</p> <pre>>>> class Q: ... def __contains__(self, value): ... return False ... >>> issubclass(Q, Container) True >>> Iterable.register(Q) >>> g(Q()) Traceback (most recent call last): ... RuntimeError: Ambiguous dispatch: <class 'collections.abc.Container'> or <class 'collections.abc.Iterable'> </pre> <p dir="auto">An early version of the PEP contained a custom approach that was simpler but created a number of edge cases with surprising results <a href="#why-c3" id="user-content-id3">[3]</a>.</p> <a name="user-content-usage-patterns"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage Patterns</h2><a id="user-content-usage-patterns" class="anchor" aria-label="Permalink: Usage Patterns" href="#usage-patterns"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This PEP proposes extending behaviour only of functions specifically marked as generic. Just as a base class method may be overridden by a subclass, so too a function may be overloaded to provide custom functionality for a given type.</p> <p dir="auto">Universal overloading does not equal <em>arbitrary</em> overloading, in the sense that we need not expect people to randomly redefine the behavior of existing functions in unpredictable ways. To the contrary, generic function usage in actual programs tends to follow very predictable patterns and registered implementations are highly-discoverable in the common case.</p> <p dir="auto">If a module is defining a new generic operation, it will usually also define any required implementations for existing types in the same place. Likewise, if a module is defining a new type, then it will usually define implementations there for any generic functions that it knows or cares about. As a result, the vast majority of registered implementations can be found adjacent to either the function being overloaded, or to a newly-defined type for which the implementation is adding support.</p> <p dir="auto">It is only in rather infrequent cases that one will have implementations registered in a module that contains neither the function nor the type(s) for which the implementation is added. In the absence of incompetence or deliberate intention to be obscure, the few implementations that are not registered adjacent to the relevant type(s) or function(s), will generally not need to be understood or known about outside the scope where those implementations are defined. (Except in the "support modules" case, where best practice suggests naming them accordingly.)</p> <p dir="auto">As mentioned earlier, single-dispatch generics are already prolific throughout the standard library. A clean, standard way of doing them provides a way forward to refactor those custom implementations to use a common one, opening them up for user extensibility at the same time.</p> <a name="user-content-alternative-approaches"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Alternative approaches</h2><a id="user-content-alternative-approaches" class="anchor" aria-label="Permalink: Alternative approaches" href="#alternative-approaches"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">In <a href="http://www.python.org/dev/peps/pep-3124" rel="nofollow">PEP 3124</a> Phillip J. Eby proposes a full-grown solution with overloading based on arbitrary rule sets (with the default implementation dispatching on argument types), as well as interfaces, adaptation and method combining. PEAK-Rules <a href="#peak-rules" id="user-content-id4">[4]</a> is a reference implementation of the concepts described in PJE's PEP.</p> <p dir="auto">Such a broad approach is inherently complex, which makes reaching a consensus hard. In contrast, this PEP focuses on a single piece of functionality that is simple to reason about. It's important to note this does not preclude the use of other approaches now or in the future.</p> <p dir="auto">In a 2005 article on Artima <a href="#artima2005" id="user-content-id5">[5]</a> Guido van Rossum presents a generic function implementation that dispatches on types of all arguments on a function. The same approach was chosen in Andrey Popp's <code>generic</code> package available on PyPI <a href="#pypi-generic" id="user-content-id6">[6]</a>, as well as David Mertz's <code>gnosis.magic.multimethods</code> <a href="#gnosis-multimethods" id="user-content-id7">[7]</a>.</p> <p dir="auto">While this seems desirable at first, I agree with Fredrik Lundh's comment that "if you design APIs with pages of logic just to sort out what code a function should execute, you should probably hand over the API design to someone else". In other words, the single argument approach proposed in this PEP is not only easier to implement but also clearly communicates that dispatching on a more complex state is an anti-pattern. It also has the virtue of corresponding directly with the familiar method dispatch mechanism in object oriented programming. The only difference is whether the custom implementation is associated more closely with the data (object-oriented methods) or the algorithm (single-dispatch overloading).</p> <p dir="auto">PyPy's RPython offers <code>extendabletype</code> <a href="#pairtype" id="user-content-id8">[8]</a>, a metaclass which enables classes to be externally extended. In combination with <code>pairtype()</code> and <code>pair()</code> factories, this offers a form of single-dispatch generics.</p> <a name="user-content-acknowledgements"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Acknowledgements</h2><a id="user-content-acknowledgements" class="anchor" aria-label="Permalink: Acknowledgements" href="#acknowledgements"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Apart from Phillip J. Eby's work on <a href="http://www.python.org/dev/peps/pep-3124" rel="nofollow">PEP 3124</a> and PEAK-Rules, influences include Paul Moore's original issue <a href="#issue-5135" id="user-content-id9">[9]</a> that proposed exposing <code>pkgutil.simplegeneric</code> as part of the <code>functools</code> API, Guido van Rossum's article on multimethods <a href="#artima2005" id="user-content-id10">[5]</a>, and discussions with Raymond Hettinger on a general pprint rewrite. Huge thanks to Alyssa Coghlan for encouraging me to create this PEP and providing initial feedback.</p> <a name="user-content-references"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">References</h2><a id="user-content-references" class="anchor" aria-label="Permalink: References" href="#references"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <markdown-accessiblity-table><table frame="void" id="user-content-ref-impl" rules="none"> <tbody valign="top"> <tr><td><a href="#id1">[1]</a></td><td><a href="http://hg.python.org/features/pep-443/file/tip/Lib/functools.py#l359" rel="nofollow">http://hg.python.org/features/pep-443/file/tip/Lib/functools.py#l359</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-pep-0008" rules="none"> <tbody valign="top"> <tr><td><a href="#id2">[2]</a></td><td><a href="http://www.python.org/dev/peps/pep-0008" rel="nofollow">PEP 8</a> states in the "Programming Recommendations" section that "the Python standard library will not use function annotations as that would result in a premature commitment to a particular annotation style".</td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-why-c3" rules="none"> <tbody valign="top"> <tr><td><a href="#id3">[3]</a></td><td><a href="http://bugs.python.org/issue18244" rel="nofollow">http://bugs.python.org/issue18244</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-peak-rules" rules="none"> <tbody valign="top"> <tr><td><a href="#id4">[4]</a></td><td><a href="http://peak.telecommunity.com/DevCenter/PEAK_2dRules" rel="nofollow">http://peak.telecommunity.com/DevCenter/PEAK_2dRules</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-artima2005" rules="none"> <tbody valign="top"> <tr><td>[5]</td><td><em>(<a href="#id5">1</a>, <a href="#id10">2</a>)</em> <a href="http://www.artima.com/weblogs/viewpost.jsp?thread=101605" rel="nofollow">http://www.artima.com/weblogs/viewpost.jsp?thread=101605</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-pypi-generic" rules="none"> <tbody valign="top"> <tr><td><a href="#id6">[6]</a></td><td><a href="http://pypi.python.org/pypi/generic" rel="nofollow">http://pypi.python.org/pypi/generic</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-gnosis-multimethods" rules="none"> <tbody valign="top"> <tr><td><a href="#id7">[7]</a></td><td><a href="http://gnosis.cx/publish/programming/charming_python_b12.html" rel="nofollow">http://gnosis.cx/publish/programming/charming_python_b12.html</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-pairtype" rules="none"> <tbody valign="top"> <tr><td><a href="#id8">[8]</a></td><td><a href="https://bitbucket.org/pypy/pypy/raw/default/rpython/tool/pairtype.py" rel="nofollow">https://bitbucket.org/pypy/pypy/raw/default/rpython/tool/pairtype.py</a></td></tr> </tbody> </table></markdown-accessiblity-table> <markdown-accessiblity-table><table frame="void" id="user-content-issue-5135" rules="none"> <tbody valign="top"> <tr><td><a href="#id9">[9]</a></td><td><a href="http://bugs.python.org/issue5135" rel="nofollow">http://bugs.python.org/issue5135</a></td></tr> </tbody> </table></markdown-accessiblity-table> <a name="user-content-copyright"></a> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Copyright</h2><a id="user-content-copyright" class="anchor" aria-label="Permalink: Copyright" href="#copyright"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This document has been placed in the public domain.</p> </article></div><button hidden=""></button></section></div></div></div> <!-- --> <!-- --> </div></div></div><div class="Box-sc-g0xbh4-0"></div></div></div></div></div><div id="find-result-marks-container" class="Box-sc-g0xbh4-0 cCoXib"></div><button hidden="" data-testid="" data-hotkey-scope="read-only-cursor-text-area"></button><button hidden=""></button></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-app> </turbo-frame> </div> </turbo-frame> </main> </div> </div> <footer class="footer pt-8 pb-6 f6 color-fg-muted p-responsive" role="contentinfo" > <h2 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width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon m-2"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none m-2"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> <template id="snippet-clipboard-copy-button-unpositioned"> <div class="zeroclipboard-container"> <clipboard-copy aria-label="Copy" class="ClipboardButton btn btn-invisible js-clipboard-copy m-2 p-0 d-flex flex-justify-center flex-items-center" data-copy-feedback="Copied!" data-tooltip-direction="w"> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-copy js-clipboard-copy-icon"> <path d="M0 6.75C0 5.784.784 5 1.75 5h1.5a.75.75 0 0 1 0 1.5h-1.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-1.5a.75.75 0 0 1 1.5 0v1.5A1.75 1.75 0 0 1 9.25 16h-7.5A1.75 1.75 0 0 1 0 14.25Z"></path><path d="M5 1.75C5 .784 5.784 0 6.75 0h7.5C15.216 0 16 .784 16 1.75v7.5A1.75 1.75 0 0 1 14.25 11h-7.5A1.75 1.75 0 0 1 5 9.25Zm1.75-.25a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h7.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Z"></path> </svg> <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-check js-clipboard-check-icon color-fg-success d-none"> <path d="M13.78 4.22a.75.75 0 0 1 0 1.06l-7.25 7.25a.75.75 0 0 1-1.06 0L2.22 9.28a.751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018L6 10.94l6.72-6.72a.75.75 0 0 1 1.06 0Z"></path> </svg> </clipboard-copy> </div> </template> </div> <div id="js-global-screen-reader-notice" class="sr-only mt-n1" aria-live="polite" aria-atomic="true" ></div> <div id="js-global-screen-reader-notice-assertive" class="sr-only mt-n1" aria-live="assertive" aria-atomic="true"></div> </body> </html>