python-peps/pep-0484.txt

PEP: 484
Title: Type Hints
Version: $Revision$
Last-Modified: $Date$
Author: Guido van Rossum <guido@python.org>, Jukka Lehtosalo <jukka.lehtosalo@iki.fi>, Łukasz Langa <lukasz@langa.pl>
BDFL-Delegate: Mark Shannon
Discussions-To: Python-Dev <python-dev@python.org>
Status: Accepted
Type: Standards Track
Content-Type: text/x-rst
Created: 29-Sep-2014
Python-Version: 3.5
Post-History: 16-Jan-2015,20-Mar-2015,17-Apr-2015,20-May-2015,22-May-2015
Resolution: https://mail.python.org/pipermail/python-dev/2015-May/140104.html


Abstract
========

PEP 3107 introduced syntax for function annotations, but the semantics
were deliberately left undefined.  There has now been enough 3rd party
usage for static type analysis that the community would benefit from
a standard vocabulary and baseline tools within the standard library.

This PEP introduces a provisional module to provide these standard
definitions and tools, along with some conventions for situations
where annotations are not available.

Note that this PEP still explicitly does NOT prevent other uses of
annotations, nor does it require (or forbid) any particular processing
of annotations, even when they conform to this specification.  It
simply enables better coordination, as PEP 333 did for web frameworks.

For example, here is a simple function whose argument and return type
are declared in the annotations::

  def greeting(name: str) -> str:
      return 'Hello ' + name

While these annotations are available at runtime through the usual
``__annotations__`` attribute, *no type checking happens at runtime*.
Instead, the proposal assumes the existence of a separate off-line
type checker which users can run over their source code voluntarily.
Essentially, such a type checker acts as a very powerful linter.
(While it would of course be possible for individual users to employ
a similar checker at run time for Design By Contract enforcement or
JIT optimization, those tools are not yet as mature.)

The proposal is strongly inspired by mypy [mypy]_.  For example, the
type "sequence of integers" can be written as ``Sequence[int]``.  The
square brackets mean that no new syntax needs to be added to the
language.  The example here uses a custom type ``Sequence``, imported
from a pure-Python module ``typing``.  The ``Sequence[int]`` notation
works at runtime by implementing ``__getitem__()`` in the metaclass
(but its significance is primarily to an offline type checker).

The type system supports unions, generic types, and a special type
named ``Any`` which is consistent with (i.e. assignable to and from) all
types.  This latter feature is taken from the idea of gradual typing.
Gradual typing and the full type system are explained in PEP 483.

Other approaches from which we have borrowed or to which ours can be
compared and contrasted are described in PEP 482.


Rationale and Goals
===================

PEP 3107 added support for arbitrary annotations on parts of a
function definition.  Although no meaning was assigned to annotations
then, there has always been an implicit goal to use them for type
hinting [gvr-artima]_, which is listed as the first possible use case
in said PEP.

This PEP aims to provide a standard syntax for type annotations,
opening up Python code to easier static analysis and refactoring,
potential runtime type checking, and (perhaps, in some contexts)
code generation utilizing type information.

Of these goals, static analysis is the most important.  This includes
support for off-line type checkers such as mypy, as well as providing
a standard notation that can be used by IDEs for code completion and
refactoring.

Non-goals
---------

While the proposed typing module will contain some building blocks for
runtime type checking -- in particular the ``get_type_hints()``
function -- third party packages would have to be developed to
implement specific runtime type checking functionality, for example
using decorators or metaclasses.  Using type hints for performance
optimizations is left as an exercise for the reader.

It should also be emphasized that **Python will remain a dynamically
typed language, and the authors have no desire to ever make type hints
mandatory, even by convention.**


The meaning of annotations
==========================

Any function without annotations should be treated as having the most
general type possible, or ignored, by any type checker.  Functions
with the ``@no_type_check`` decorator or with a ``# type: ignore``
comment should be treated as having no annotations.

It is recommended but not required that checked functions have
annotations for all arguments and the return type.  For a checked
function, the default annotation for arguments and for the return type
is ``Any``.  An exception is that the first argument of instance and
class methods does not need to be annotated; it is assumed to have the
type of the containing class for instance methods, and a type object
type corresponding to the containing class object for class methods.
For example, in class ``A`` the first argument of an instance method
has the implicit type ``A``. In a class method, the precise type of
the first argument cannot be represented using the available type
notation.

(Note that the return type of ``__init__`` ought to be annotated with
``-> None``.  The reason for this is subtle.  If ``__init__`` assumed
a return annotation of ``-> None``, would that mean that an
argument-less, un-annotated ``__init__`` method should still be
type-checked?  Rather than leaving this ambiguous or introducing an
exception to the exception, we simply say that ``__init__`` ought to
have a return annotation; the default behavior is thus the same as for
other methods.)

A type checker is expected to check the body of a checked function for
consistency with the given annotations.  The annotations may also used
to check correctness of calls appearing in other checked functions.

Type checkers are expected to attempt to infer as much information as
necessary.  The minimum requirement is to handle the builtin
decorators ``@property``, ``@staticmethod`` and ``@classmethod``.


Type Definition Syntax
======================

The syntax leverages PEP 3107-style annotations with a number of
extensions described in sections below.  In its basic form, type
hinting is used by filling function annotation slots with classes::

  def greeting(name: str) -> str:
      return 'Hello ' + name

This states that the expected type of the ``name`` argument is
``str``.  Analogically, the expected return type is ``str``.

Expressions whose type is a subtype of a specific argument type are
also accepted for that argument.


Acceptable type hints
---------------------

Type hints may be built-in classes (including those defined in
standard library or third-party extension modules), abstract base
classes, types available in the ``types`` module, and user-defined
classes (including those defined in the standard library or
third-party modules).

While annotations are normally the best format for type hints,
there are times when it is more appropriate to represent them
by a special comment, or in a separately distributed stub
file.  (See below for examples.)

Annotations must be valid expressions that evaluate without raising
exceptions at the time the function is defined (but see below for
forward references).

Annotations should be kept simple or static analysis tools may not be
able to interpret the values. For example, dynamically computed types
are unlikely to be understood.  (This is an
intentionally somewhat vague requirement, specific inclusions and
exclusions may be added to future versions of this PEP as warranted by
the discussion.)

In addition to the above, the following special constructs defined
below may be used: ``None``, ``Any``, ``Union``, ``Tuple``,
``Callable``, all ABCs and stand-ins for concrete classes exported
from ``typing`` (e.g. ``Sequence`` and ``Dict``), type variables, and
type aliases.

All newly introduced names used to support features described in
following sections (such as ``Any`` and ``Union``) are available in
the ``typing`` module.


Using None
----------

When used in a type hint, the expression ``None`` is considered
equivalent to ``type(None)``.


Type aliases
------------

Type aliases are defined by simple variable assignments::

  Url = str

  def retry(url: Url, retry_count: int) -> None: ...

Note that we recommend capitalizing alias names, since they represent
user-defined types, which (like user-defined classes) are typically
spelled that way.

Type aliases may be as complex as type hints in annotations --
anything that is acceptable as a type hint is acceptable in a type
alias::

    from typing import TypeVar, Iterable, Tuple

    T = TypeVar('T', int, float, complex)
    Vector = Iterable[Tuple[T, T]]

    def inproduct(v: Vector) -> T:
        return sum(x*y for x, y in v)

This is equivalent to::

    from typing import TypeVar, Iterable, Tuple

    T = TypeVar('T', int, float, complex)

    def inproduct(v: Iterable[Tuple[T, T]]) -> T:
        return sum(x*y for x, y in v)


Callable
--------

Frameworks expecting callback functions of specific signatures might be
type hinted using ``Callable[[Arg1Type, Arg2Type], ReturnType]``.
Examples::

  from typing import Callable

  def feeder(get_next_item: Callable[[], str]) -> None:
      # Body

  def async_query(on_success: Callable[[int], None],
                  on_error: Callable[[int, Exception], None]) -> None:
      # Body

It is possible to declare the return type of a callable without
specifying the call signature by substituting a literal ellipsis
(three dots) for the list of arguments::

  def partial(func: Callable[..., str], *args) -> Callable[..., str]:
      # Body

Note that there are no square brackets around the ellipsis.  The
arguments of the callback are completely unconstrained in this case
(and keyword arguments are acceptable).

Since using callbacks with keyword arguments is not perceived as a
common use case, there is currently no support for specifying keyword
arguments with ``Callable``.  Similarly, there is no support for
specifying callback signatures with a variable number of argument of a
specific type.

Because ``typing.Callable`` does double-duty as a replacement for
``collections.abc.Callable``, ``isinstance(x, typing.Callable)`` is
implemented by deferring to ```isinstance(x, collections.abc.Callable)``.
However, ``isinstance(x, typing.Callable[...])`` is not supported.


Generics
--------

Since type information about objects kept in containers cannot be
statically inferred in a generic way, abstract base classes have been
extended to support subscription to denote expected types for container
elements.  Example::

  from typing import Mapping, Set

  def notify_by_email(employees: Set[Employee], overrides: Mapping[str, str]) -> None: ...

Generics can be parametrized by using a new factory available in
``typing`` called ``TypeVar``.  Example::

  from typing import Sequence, TypeVar

  T = TypeVar('T')      # Declare type variable

  def first(l: Sequence[T]) -> T:   # Generic function
      return l[0]

In this case the contract is that the returned value is consistent with
the elements held by the collection.

A ``TypeVar()`` expression must always directly be assigned to a
variable (it should not be used as part of a larger expression).  The
argument to ``TypeVar()`` must be a string equal to the variable name
to which it is assigned.  Type variables must not be redefined.

``TypeVar`` supports constraining parametric types to a fixed set of
possible types.  For example, we can define a type variable that ranges
over just ``str`` and ``bytes``.  By default, a type variable ranges
over all possible types.  Example of constraining a type variable::

  from typing import TypeVar

  AnyStr = TypeVar('AnyStr', str, bytes)

  def concat(x: AnyStr, y: AnyStr) -> AnyStr:
      return x + y

The function ``concat`` can be called with either two ``str`` arguments
or two ``bytes`` arguments, but not with a mix of ``str`` and ``bytes``
arguments.

There should be at least two constraints, if any; specifying a single
constraint is disallowed.

Subtypes of types constrained by a type variable should be treated
as their respective explicitly listed base types in the context of the
type variable.  Consider this example::

  class MyStr(str): ...

  x = concat(MyStr('apple'), MyStr('pie'))

The call is valid but the type variable ``AnyStr`` will be set to
``str`` and not ``MyStr``. In effect, the inferred type of the return
value assigned to ``x`` will also be ``str``.

Additionally, ``Any`` is a valid value for every type variable.
Consider the following::

  def count_truthy(elements: List[Any]) -> int:
      return sum(1 for elem in elements if element)

This is equivalent to omitting the generic notation and just saying
``elements: List``.


User-defined generic types
--------------------------

You can include a ``Generic`` base class to define a user-defined class
as generic.  Example::

  from typing import TypeVar, Generic

  T = TypeVar('T')

  class LoggedVar(Generic[T]):
      def __init__(self, value: T, name: str, logger: Logger) -> None:
          self.name = name
          self.logger = logger
          self.value = value

      def set(self, new: T) -> None:
          self.log('Set ' + repr(self.value))
          self.value = new

      def get(self) -> T:
          self.log('Get ' + repr(self.value))
          return self.value

      def log(self, message: str) -> None:
          self.logger.info('{}: {}'.format(self.name message))

``Generic[T]`` as a base class defines that the class ``LoggedVar``
takes a single type parameter ``T``. This also makes ``T`` valid as
a type within the class body.

The ``Generic`` base class uses a metaclass that defines ``__getitem__``
so that ``LoggedVar[t]`` is valid as a type::

  from typing import Iterable

  def zero_all_vars(vars: Iterable[LoggedVar[int]]) -> None:
      for var in vars:
          var.set(0)

A generic type can have any number of type variables, and type variables
may be constrained. This is valid::

  from typing import TypeVar, Generic
  ...

  T = TypeVar('T')
  S = TypeVar('S')

  class Pair(Generic[T, S]):
      ...

Each type variable argument to ``Generic`` must be distinct. This is
thus invalid::

  from typing import TypeVar, Generic
  ...

  T = TypeVar('T')

  class Pair(Generic[T, T]):   # INVALID
      ...

You can use multiple inheritance with ``Generic``::

  from typing import TypeVar, Generic, Sized

  T = TypeVar('T')

  class LinkedList(Sized, Generic[T]):
      ...

Subclassing a generic class without specifying type parameters assumes
``Any`` for each position.  In the following example, ``MyIterable``
is not generic but implicitly inherits from ``Iterable[Any]``::

  from typing import Iterable

  class MyIterable(Iterable):  # Same as Iterable[Any]
      ...

Generic metaclasses are not supported.


Instantiating generic classes and type erasure
----------------------------------------------

Generic types like ``List`` or ``Sequence`` cannot be instantiated.
However, user-defined classes derived from them can be instantiated.
Suppose we write a ``Node`` class inheriting from ``Generic[T]``::

  from typing import TypeVar, Generic

  T = TypeVar('T')

  class Node(Generic[T]):
      ...

Now there are two ways we can instantiate this class; the type
inferred by a type checker may be different depending on the form we
use.  The first way is to give the value of the type parameter
explicitly -- this overrides whatever type inference the type
checker would otherwise perform::

  x = Node[T]()  # The type inferred for x is Node[T].

  y = Node[int]()  # The type inferred for y is Node[int].

If no explicit types are given, the type checker is given some
freedom. Consider this code::

  x = Node()

The inferred type could be ``Node[Any]``, as there isn't enough
context to infer a more precise type.  Alternatively, a type checker
may reject the line and require an explicit annotation, like this::

  x = Node()  # type: Node[int]  # Inferred type is Node[int].

A type checker with more powerful type inference could look at how
``x`` is used elsewhere in the file and try to infer a more precise
type such as ``Node[int]`` even without an explicit type annotation.
However, it is probably impossible to make such type inference work
well in all cases, since Python programs can be very dynamic.

This PEP doesn't specify the details of how type inference should
work.  We allow different tools to experiment with various approaches.
We may give more explicit rules in future revisions.

At runtime the type is not preserved, and the class of ``x`` is just
``Node`` in all cases.  This behavior is called "type erasure"; it is
common practice in languages with generics (e.g. Java, TypeScript).


Arbitrary generic types as base classes
---------------------------------------

``Generic[T]`` is only valid as a base class -- it's not a proper type.
However, user-defined generic types such as ``LinkedList[T]`` from the
above example and built-in generic types and ABCs such as ``List[T]``
and ``Iterable[T]`` are valid both as types and as base classes. For
example, we can define a subclass of ``Dict`` that specializes type
arguments::

  from typing import Dict, List, Optional

  class Node:
      ...

  class SymbolTable(Dict[str, List[Node]]):
      def push(self, name: str, node: Node) -> None:
          self.setdefault(name, []).append(node)

      def pop(self, name: str) -> Node:
          return self[name].pop()

      def lookup(self, name: str) -> Optional[Node]:
          nodes = self.get(name)
          if nodes:
              return nodes[-1]
          return None

``SymbolTable`` is a subclass of ``dict`` and a subtype of ``Dict[str,
List[Node]]``.

If a generic base class has a type variable as a type argument, this
makes the defined class generic. For example, we can define a generic
``LinkedList`` class that is iterable and a container::

  from typing import TypeVar, Iterable, Container

  T = TypeVar('T')

  class LinkedList(Iterable[T], Container[T]):
      ...

Now ``LinkedList[int]`` is a valid type. Note that we can use ``T``
multiple times in the base class list, as long as we don't use the
same type variable ``T`` multiple times within ``Generic[...]``.

Also consider the following example::

  from typing import TypeVar, Mapping

  T = TypeVar('T')

  class MyDict(Mapping[str, T]):
      ...

In this case MyDict has a single parameter, T.


Abstract generic types
----------------------

The metaclass used by ``Generic`` is a subclass of ``abc.ABCMeta``.
A generic class can be an ABC by including abstract methods
or properties, and generic classes can also have ABCs as base
classes without a metaclass conflict.


Type variables with an upper bound
----------------------------------

A type variable may specify an upper bound using ``bound=<type>``.
This means that an actual type substituted (explicitly or implictly)
for the type variable must be a subclass of the boundary type.  A
common example is the definition of a Comparable type that works well
enough to catch the most common errors::

  from typing import TypeVar

  class Comparable(metaclass=ABCMeta):
      @abstractmethod
      def __lt__(self, other: Any) -> bool: ...
      ... # __gt__ etc. as well

  CT = TypeVar('CT', bound=Comparable)

  def min(x: CT, y: CT) -> CT:
      if x < y:
          return x
      else:
          return y

  min(1, 2) # ok, return type int
  min('x', 'y') # ok, return type str

(Note that this is not ideal -- for example ``min('x', 1)`` is invalid
at runtime but a type checker would simply infer the return type
``Comparable``.  Unfortunately, addressing this would require
introducing a much more powerful and also much more complicated
concept, F-bounded polymorphism.  We may revisit this in the future.)

An upper bound cannot be combined with type constraints (as in used
``AnyStr``, see the example earlier); type constraints cause the
inferred type to be _exactly_ one of the constraint types, while an
upper bound just requires that the actual type is a subclass of the
boundary type.


Covariance and contravariance
-----------------------------

Consider a class ``Employee`` with a subclass ``Manager``.  Now
suppose we have a function with an argument annotated with
``List[Employee]``.  Should we be allowed to call this function with a
variable of type ``List[Manager]`` as its argument?  Many people would
answer "yes, of course" without even considering the consequences.
But unless we know more about the function, a type checker should
reject such a call: the function might append an ``Employee`` instance
to the list, which would violate the variable's type in the caller.

It turns out such an argument acts _contravariantly_, whereas the
intuitive answer (which is correct in case the function doesn't mutate
its argument!) requires the argument to act _covariantly_.  A longer
introduction to these concepts can be found on Wikipedia
[wiki-variance]_; here we just show how to control a type checker's
behavior.

By default type variables are considered _invariant_, which means that
arguments for arguments annotated with types like ``List[Employee]``
must exactly match the type annotation -- no subclasses or
superclasses of the type parameter (in this example ``Employee``) are
allowed.

To facilitate the declaration of container types where covariant type
checking is acceptable, a type variable can be declared using
``covariant=True``.  For the (rare) case where contravariant behavior
is desirable, pass ``contravariant=True``.  At most one of these may
be passed.

A typical example involves defining an immutable (or read-only)
container class::

  from typing import TypeVar, Generic, Iterable, Iterator

  T = TypeVar('T', covariant=True)

  class ImmutableList(Generic[T]):
      def __init__(self, items: Iterable[T]) -> None: ...
      def __iter__(self) -> Iterator[T]: ...
      ...

  class Employee: ...

  class Manager(Employee): ...

  def dump_employees(emps: ImmutableList[Employee]) -> None:
      for emp in emps:
          ...

  mgrs = ImmutableList([Manager()])  # type: ImmutableList[Manager]
  dump_employees(mgrs)  # OK

The read-only collection classes in ``typing`` are all defined using a
covariant type variable (e.g. ``Mapping`` and ``Sequence``).  The
mutable collection classes (e.g. ``MutableMapping`` and
``MutableSequence``) are defined using regular invariant type
variables.  The one example of a contravariant type variable is the
``Generator`` type, which is contravariant in the ``send()`` argument
type (see below).

Note: variance affects type parameters for generic types -- it does
not affect regular parameters.  For example, the following example is
fine::

  from typing import TypeVar

  class Employee: ...

  class Manager(Employee): ...

  E = TypeVar('E', bound=Employee)  # Invariant

  def dump_employee(e: E) -> None: ...

  dump_employee(Manager())  # OK


The numeric tower
-----------------

PEP 3141 defines Python's numeric tower, and the stdlib module
``numbers`` implements the corresponding ABCs (``Number``,
``Complex``, ``Real``, ``Rational`` and ``Integral``).  There are some
issues with these ABCs, but the built-in concrete numeric classes
``complex``, ``float`` and ``int`` are ubiquitous (especially the
latter two :-).

Rather than requiring that users write ``import numbers`` and then use
``numbers.Float`` etc., this PEP proposes a straightforward shortcut
that is almost as effective: when an argument is annotated as having
type ``float``, an argument of type ``int`` is acceptable; similar,
for an argument annotated as having type ``complex``, arguments of
type ``float`` or ``int`` are acceptable.  This does not handle
classes implementing the corresponding ABCs or the
``fractions.Fraction`` class, but we believe those use cases are
exceedingly rare.


The bytes types
---------------

There are three different builtin classes used for arrays of bytes
(not counting the classes available in the ``array`` module):
``bytes``, ``bytearray`` and ``memoryview``.  Of these, ``bytes`` and
``bytearray`` have many behaviors in common (though not all --
``bytearray`` is mutable).

While there is an ABC ``ByteString`` defined in ``collections.abc``
and a corresponding type in ``typing``, functions accepting bytes (of
some form) are so common that it would be cumbersome to have to write
``typing.ByteString`` everywhere.  So, as a shortcut similar to that
for the builtin numeric classes, when an argument is annotated as
having type ``bytes``, arguments of type ``bytearray`` or
``memoryview`` are acceptable.  (Again, there are situations where
this isn't sound, but we believe those are exceedingly rare in
practice.)


Forward references
------------------

When a type hint contains names that have not been defined yet, that
definition may be expressed as a string literal, to be resolved later.

A situation where this occurs commonly is the definition of a
container class, where the class being defined occurs in the signature
of some of the methods.  For example, the following code (the start of
a simple binary tree implementation) does not work::

  class Tree:
      def __init__(self, left: Tree, right: Tree):
          self.left = left
          self.right = right

To address this, we write::

  class Tree:
      def __init__(self, left: 'Tree', right: 'Tree'):
          self.left = left
          self.right = right

The string literal should contain a valid Python expression (i.e.,
``compile(lit, '', 'eval')`` should be a valid code object) and it
should evaluate without errors once the module has been fully loaded.
The local and global namespace in which it is evaluated should be the
same namespaces in which default arguments to the same function would
be evaluated.

Moreover, the expression should be parseable as a valid type hint, i.e.,
it is constrained by the rules from the section `Acceptable type hints`_
above.

It is allowable to use string literals as *part* of a type hint, for
example::

    class Tree:
        ...
        def leaves(self) -> List['Tree']:
            ...

A common use for forward references is when e.g. Django models are
needed in the signatures.  Typically, each model is in a separate
file, and has methods that arguments whose type involves other models.
Because of the way circular imports work in Python, it is often not
possible to import all the needed models directly::

    # File models/a.py
    from models.b import B
    class A(Model):
        def foo(self, b: B): ...

    # File models/b.py
    from models.a import A
    class B(Model):
        def bar(self, a: A): ...

    # File main.py
    from models.a import A
    from models.b import B

Assuming main is imported first, this will fail with an ImportError at
the line ``from models.a import A`` in models/b.py, which is being
imported from models/a.py before a has defined class A.  The solution
is to switch to module-only imports and reference the models by their
_module_._class_ name::

    # File models/a.py
    from models import b
    class A(Model):
        def foo(self, b: 'b.B'): ...

    # File models/b.py
    from models import a
    class B(Model):
        def bar(self, a: 'a.A'): ...

    # File main.py
    from models.a import A
    from models.b import B


Union types
-----------

Since accepting a small, limited set of expected types for a single
argument is common, there is a new special factory called ``Union``.
Example::

  from typing import Union

  def handle_employees(e: Union[Employee, Sequence[Employee]]) -> None:
      if isinstance(e, Employee):
          e = [e]
      ...

A type factored by ``Union[T1, T2, ...]`` responds ``True`` to
``issubclass`` checks for ``T1`` and any of its subtypes, ``T2`` and
any of its subtypes, and so on.

One common case of union types are *optional* types.  By default,
``None`` is an invalid value for any type, unless a default value of
``None`` has been provided in the function definition.  Examples::

  def handle_employee(e: Union[Employee, None]) -> None: ...

As a shorthand for ``Union[T1, None]`` you can write ``Optional[T1]``;
for example, the above is equivalent to::

  from typing import Optional

  def handle_employee(e: Optional[Employee]) -> None: ...

An optional type is also automatically assumed when the default value is
``None``, for example::

  def handle_employee(e: Employee = None): ...

This is equivalent to::

  def handle_employee(e: Optional[Employee] = None) -> None: ...

The ``Any`` type
----------------

A special kind of type is ``Any``.  Every type is a subtype of
``Any``.  This is also true for the builtin type ``object``.
However, to the static type checker these are completely different.

When the type of a value is ``object``, the type checker will reject
almost all operations on it, and assigning it to a variable (or using
it as a return value) of a more specialized type is a type error.  On
the other hand, when a value has type ``Any``, the type checker will
allow all operations on it, and a value of type ``Any`` can be assigned
to a variable (or used as a return value) of a more constrained type.


Version and platform checking
-----------------------------

Type checkers are expected to understand simple version and platform
checks, e.g.::

  import sys

  if sys.version_info[0] >= 3:
      # Python 3 specific definitions
  else:
      # Python 2 specific definitions

  if sys.platform == 'win32':
      # Windows specific definitions
  else:
      # Posix specific definitions

Don't expect a checker to understand obfuscations like
``"".join(reversed(sys.platform)) == "xunil"``.


Default argument values
-----------------------

In stubs it may be useful to declare an argument as having a default
without specifying the actual default value.  For example::

  def foo(x: AnyStr, y: AnyStr = ...) -> AnyStr: ...

What should the default value look like?  Any of the options ``""``,
``b""`` or ``None`` fails to satisfy the type constraint (actually,
``None`` will *modify* the type to become ``Optional[AnyStr]``).

In such cases the default value may be specified as a literal
ellipsis, i.e. the above example is literally what you would write.


Compatibility with other uses of function annotations
=====================================================

A number of existing or potential use cases for function annotations
exist, which are incompatible with type hinting.  These may confuse
a static type checker.  However, since type hinting annotations have no
runtime behavior (other than evaluation of the annotation expression and
storing annotations in the ``__annotations__`` attribute of the function
object), this does not make the program incorrect -- it just may cause
a type checker to emit spurious warnings or errors.

To mark portions of the program that should not be covered by type
hinting, you can use one or more of the following:

* a ``# type: ignore`` comment;

* a ``@no_type_check`` decorator on a class or function;

* a custom class or function decorator marked with
  ``@no_type_check_decorator``.

For more details see later sections.

In order for maximal compatibility with offline type checking it may
eventually be a good idea to change interfaces that rely on annotations
to switch to a different mechanism, for example a decorator.  In Python
3.5 there is no pressure to do this, however.  See also the longer
discussion under `Rejected alternatives`_ below.


Type comments
=============

No first-class syntax support for explicitly marking variables as being
of a specific type is added by this PEP.  To help with type inference in
complex cases, a comment of the following format may be used::

  x = []   # type: List[Employee]
  x, y, z = [], [], []  # type: List[int], List[int], List[str]
  x, y, z = [], [], []  # type: (List[int], List[int], List[str])
  x = [
     1,
     2,
  ]  # type: List[int]

Type comments should be put on the last line of the statement that
contains the variable definition. They can also be placed on
``with`` statements and ``for`` statements, right after the colon.

Examples of type comments on ``with`` and ``for`` statements::

  with frobnicate() as foo:  # type: int
      # Here foo is an int
      ...

  for x, y in points:  # type: float, float
      # Here x and y are floats
      ...

In stubs it may be useful to declare the existence of a variable
without giving it an initial value.  This can be done using a literal
ellipsis::

  from typing import IO

  stream = ...  # type: IO[str]

In non-stub code, there is a similar special case::

  from typing import IO

  stream = None  # type: IO[str]

Type checkers should not complain about this (despite the value
``None`` not matching the given type), nor should they change the
inferred type to ``Optional[...]`` (despite the rule that does this
for annotated arguments with a default value of ``None``).  The
assumption here is that other code will ensure that the variable is
given a value of the proper type, and all uses can assume that the
variable has the given type.

The ``# type: ignore`` comment should be put on the line that the
error refers to::

  import http.client
  errors = {
      'not_found': http.client.NOT_FOUND  # type: ignore
  }

A ``# type: ignore`` comment on a line by itself disables all type
checking for the rest of the file.

If type hinting proves useful in general, a syntax for typing variables
may be provided in a future Python version.

Casts
=====

Occasionally the type checker may need a different kind of hint: the
programmer may know that an expression is of a more constrained type
than a type checker may be able to infer.  For example::

  from typing import List, cast

  def find_first_str(a: List[object]) -> str:
      index = next(i for i, x in enumerate(a) if isinstance(x, str))
      # We only get here if there's at least one string in a
      return cast(str, a[index])

Some type checkers may not be able to infer that the type of
``a[index]`` is ``str`` and only infer ``object`` or ``Any``, but we
know that (if the code gets to that point) it must be a string.  The
``cast(t, x)`` call tells the type checker that we are confident that
the type of ``x`` is ``t``.  At runtime a cast always returns the
expression unchanged -- it does not check the type, and it does not
convert or coerce the value.

Casts differ from type comments (see the previous section).  When using
a type comment, the type checker should still verify that the inferred
type is consistent with the stated type.  When using a cast, the type
checker should blindly believe the programmer.  Also, casts can be used
in expressions, while type comments only apply to assignments.


Stub Files
==========

Stub files are files containing type hints that are only for use by
the type checker, not at runtime.  There are several use cases for
stub files:

* Extension modules

* Third-party modules whose authors have not yet added type hints

* Standard library modules for which type hints have not yet been
  written

* Modules that must be compatible with Python 2 and 3

* Modules that use annotations for other purposes

Stub files have the same syntax as regular Python modules.  There is one
feature of the ``typing`` module that may only be used in stub files:
the ``@overload`` decorator described below.

The type checker should only check function signatures in stub files;
It is recommended that function bodies in stub files just be a single
ellipsis (``...``).

The type checker should have a configurable search path for stub files.
If a stub file is found the type checker should not read the
corresponding "real" module.

While stub files are syntactically valid Python modules, they use the
``.pyi`` extension to make it possible to maintain stub files in the
same directory as the corresponding real module.  This also reinforces
the notion that no runtime behavior should be expected of stub files.

Additional notes on stub files:

* Modules and variables imported into the stub are not considered
  exported from the stub unless the import uses the ``import ... as
  ...`` form or the equivalent ``from ... import ... as ...`` form.

* However, as an exception to the previous bullet, all objects
  imported into a stub using ``from ... import *`` are considered
  exported.  (This makes it easier to re-export all objects from a
  given module that may vary by Python version.)

Function overloading
--------------------

The ``@overload`` decorator allows describing functions that support
multiple different combinations of argument types.  This pattern is
used frequently in builtin modules and types.  For example, the
``__getitem__()`` method of the ``bytes`` type can be described as
follows::

  from typing import overload

  class bytes:
      ...
      @overload
      def __getitem__(self, i: int) -> int: ...
      @overload
      def __getitem__(self, s: slice) -> bytes: ...

This description is more precise than would be possible using unions
(which cannot express the relationship between the argument and return
types)::

  from typing import Union

  class bytes:
      ...
      def __getitem__(self, a: Union[int, slice]) -> Union[int, bytes]: ...

Another example where ``@overload`` comes in handy is the type of the
builtin ``map()`` function, which takes a different number of
arguments depending on the type of the callable::

  from typing import Callable, Iterable, Iterator, Tuple, TypeVar, overload

  T1 = TypeVar('T1')
  T2 = TypeVar('T2)
  S = TypeVar('S')

  @overload
  def map(func: Callable[[T1], S], iter1: Iterable[T1]) -> Iterator[S]: ...
  @overload
  def map(func: Callable[[T1, T2], S],
          iter1: Iterable[T1], iter2: Iterable[T2]) -> Iterator[S]: ...
  # ... and we could add more items to support more than two iterables

Note that we could also easily add items to support ``map(None, ...)``::

  @overload
  def map(func: None, iter1: Iterable[T1]) -> Iterable[T1]: ...
  @overload
  def map(func: None,
          iter1: Iterable[T1],
          iter2: Iterable[T2]) -> Iterable[Tuple[T1, T2]]: ...

The ``@overload`` decorator may only be used in stub files.  While it
would be possible to provide a multiple dispatch implementation using
this syntax, its implementation would require using
``sys._getframe()``, which is frowned upon.  Also, designing and
implementing an efficient multiple dispatch mechanism is hard, which
is why previous attempts were abandoned in favor of
``functools.singledispatch()``.  (See PEP 443, especially its section
"Alternative approaches".)  In the future we may come up with a
satisfactory multiple dispatch design, but we don't want such a design
to be constrained by the overloading syntax defined for type hints in
stub files.  In the meantime, using the ``@overload`` decorator or
calling ``overload()`` directly raises ``RuntimeError``.

A constrained ``TypeVar`` type can often be used instead of using the
``@overload`` decorator.  For example, the definitions of ``concat1``
and ``concat2`` in this stub file are equivalent::

  from typing import TypeVar

  AnyStr = TypeVar('AnyStr', str, bytes)

  def concat1(x: AnyStr, y: AnyStr) -> AnyStr: ...

  @overload
  def concat2(x: str, y: str) -> str: ...
  @overload
  def concat2(x: bytes, y: bytes) -> bytes: ...

Some functions, such as ``map`` or ``bytes.__getitem__`` above, can't
be represented precisely using type variables.  However, unlike
``@overload``, type variables can also be used outside stub files.  We
recommend that ``@overload`` is only used in cases where a type
variable is not sufficient, due to its special stub-only status.

Another important difference between type variables such as ``AnyStr``
and using ``@overload`` is that the prior can also be used to define
constraints for generic class type parameters.  For example, the type
parameter of the generic class ``typing.IO`` is constrained (only
``IO[str]``, ``IO[bytes]`` and ``IO[Any]`` are valid)::

  class IO(Generic[AnyStr]): ...

Storing and distributing stub files
-----------------------------------

The easiest form of stub file storage and distribution is to put them
alongside Python modules in the same directory.  This makes them easy to
find by both programmers and the tools.  However, since package
maintainers are free not to add type hinting to their packages,
third-party stubs installable by ``pip`` from PyPI are also supported.
In this case we have to consider three issues: naming, versioning,
installation path.

This PEP does not provide a recommendation on a naming scheme that
should be used for third-party stub file packages.  Discoverability will
hopefully be based on package popularity, like with Django packages for
example.

Third-party stubs have to be versioned using the lowest version of the
source package that is compatible.  Example: FooPackage has versions
1.0, 1.1, 1.2, 1.3, 2.0, 2.1, 2.2.  There are API changes in versions
1.1, 2.0 and 2.2.  The stub file package maintainer is free to release
stubs for all versions but at least 1.0, 1.1, 2.0 and 2.2 are needed
to enable the end user type check all versions.  This is because the
user knows that the closest *lower or equal* version of stubs is
compatible.  In the provided example, for FooPackage 1.3 the user would
choose stubs version 1.1.

Note that if the user decides to use the "latest" available source
package, using the "latest" stub files should generally also work if
they're updated often.

Third-party stub packages can use any location for stub storage.  Type
checkers should search for them using PYTHONPATH.  A default fallback
directory that is always checked is ``shared/typehints/python3.5/`` (or
3.6, etc.).  Since there can only be one package installed for a given
Python version per environment, no additional versioning is performed
under that directory (just like bare directory installs by ``pip`` in
site-packages).  Stub file package authors might use the following
snippet in ``setup.py``::

  ...
  data_files=[
      (
          'shared/typehints/python{}.{}'.format(*sys.version_info[:2]),
          pathlib.Path(SRC_PATH).glob('**/*.pyi'),
      ),
  ],
  ...

The Typeshed Repo
-----------------

There is a shared repository where useful stubs are being collected
[typeshed]_.  Note that stubs for a given package will not be included
here without the explicit consent of the package owner.  Further
policies regarding the stubs collected here will be decided at a later
time, after discussion on python-dev, and reported in the typeshed
repo's README.


Exceptions
==========

No syntax for listing explicitly raised exceptions is proposed.
Currently the only known use case for this feature is documentational,
in which case the recommendation is to put this information in a
docstring.


The ``typing`` Module
=====================

To open the usage of static type checking to Python 3.5 as well as older
versions, a uniform namespace is required.  For this purpose, a new
module in the standard library is introduced called ``typing``.

It defines the fundamental building blocks for constructing types
(e.g. ``Any``), types representing generic variants of builtin
collections (e.g. ``List``), types representing generic
collection ABCs (e.g. ``Sequence``), and a small collection of
convenience definitions.

Fundamental building blocks:

* Any, used as ``def get(key: str) -> Any: ...``

* Union, used as ``Union[Type1, Type2, Type3]``

* Callable, used as ``Callable[[Arg1Type, Arg2Type], ReturnType]``

* Tuple, used by listing the element types, for example
  ``Tuple[int, int, str]``.
  Arbitrary-length homogeneous tuples can be expressed
  using one type and ellipsis, for example ``Tuple[int, ...]``.
  (The ``...`` here are part of the syntax, a literal ellipsis.)

* TypeVar, used as ``X = TypeVar('X', Type1, Type2, Type3)`` or simply
  ``Y = TypeVar('Y')`` (see above for more details)

* Generic, used to create user-defined generic classes

Generic variants of builtin collections:

* Dict, used as ``Dict[key_type, value_type]``

* List, used as ``List[element_type]``

* Set, used as ``Set[element_type]``. See remark for ``AbstractSet``
  below.

* FrozenSet, used as ``FrozenSet[element_type]``

Note: ``Dict``, ``List``, ``Set`` and ``FrozenSet`` are mainly useful
for annotating return values.  For arguments, prefer the abstract
collection types defined below, e.g.  ``Mapping``, ``Sequence`` or
``AbstractSet``.

Generic variants of container ABCs (and a few non-containers):

* ByteString

* Callable (see above, listed here for completeness)

* Container

* Generator, used as ``Generator[yield_type, send_type,
  return_type]``.  This represents the return value of generator
  functions.  It is a subtype of ``Iterable`` and it has additional
  type variables for the type accepted by the ``send()`` method (which
  is contravariant -- a generator that accepts sending it ``Employee``
  instance is valid in a context where a generator is required that
  accepts sending it ``Manager`` instances) and the return type of the
  generator.

* Hashable (not generic, but present for completeness)

* ItemsView

* Iterable

* Iterator

* KeysView

* Mapping

* MappingView

* MutableMapping

* MutableSequence

* MutableSet

* Sequence

* Set, renamed to ``AbstractSet``. This name change was required
  because ``Set`` in the ``typing`` module means ``set()`` with
  generics.

* Sized (not generic, but present for completeness)

* ValuesView

A few one-off types are defined that test for single special methods
(similar to ``Hashable`` or ``Sized``):

* Reversible, to test for ``__reversed__``

* SupportsAbs, to test for ``__abs__``

* SupportsComplex, to test for ``__complex__``

* SupportsFloat, to test for ``__float__``

* SupportsInt, to test for ``__int__``

* SupportsRound, to test for ``__round__``

* SupportsBytes, to test for ``__bytes__``

Convenience definitions:

* Optional, defined by ``Optional[t] == Union[t, type(None)]``

* AnyStr, defined as ``TypeVar('AnyStr', str, bytes)``

* NamedTuple, used as
  ``NamedTuple(type_name, [(field_name, field_type), ...])``
  and equivalent to
  ``collections.namedtuple(type_name, [field_name, ...])``.
  This is useful to declare the types of the fields of a a named tuple
  type.

* cast(), described earlier

* @no_type_check, a decorator to disable type checking per class or
  function (see below)

* @no_type_check_decorator, a decorator to create your own decorators
  with the same meaning as ``@no_type_check`` (see below)

* @overload, described earlier

* get_type_hints(), a utility function to retrieve the type hints from a
  function or method.  Given a function or method object, it returns
  a dict with the same format as ``__annotations__``, but evaluating
  forward references (which are given as string literals) as expressions
  in the context of the original function or method definition.

Types available in the ``typing.io`` submodule:

* IO (generic over ``AnyStr``)

* BinaryIO (a simple subtype of ``IO[bytes]``)

* TextIO (a simple subtype of ``IO[str]``)

Types available in the ``typing.re`` submodule:

* Match and Pattern, types of ``re.match()`` and ``re.compile()``
  results (generic over ``AnyStr``)


Rejected Alternatives
=====================

During discussion of earlier drafts of this PEP, various objections
were raised and alternatives were proposed.  We discuss some of these
here and explain why we reject them.

Several main objections were raised.

Which brackets for generic type parameters?
-------------------------------------------

Most people are familiar with the use of angular brackets
(e.g. ``List<int>``) in languages like C++, Java, C# and Swift to
express the parametrization of generic types.  The problem with these
is that they are really hard to parse, especially for a simple-minded
parser like Python.  In most languages the ambiguities are usually
dealt with by only allowing angular brackets in specific syntactic
positions, where general expressions aren't allowed.  (And also by
using very powerful parsing techniques that can backtrack over an
arbitrary section of code.)

But in Python, we'd like type expressions to be (syntactically) the
same as other expressions, so that we can use e.g. variable assignment
to create type aliases.  Consider this simple type expression::

    List<int>

From the Python parser's perspective, the expression begins with the
same four tokens (NAME, LESS, NAME, GREATER) as a chained comparison::

    a < b > c  # I.e., (a < b) and (b > c)

We can even make up an example that could be parsed both ways::

    a < b > [ c ]

Assuming we had angular brackets in the language, this could be
interpreted as either of the following two::

    (a<b>)[c]      # I.e., (a<b>).__getitem__(c)
    a < b > ([c])  # I.e., (a < b) and (b > [c])

It would surely be possible to come up with a rule to disambiguate
such cases, but to most users the rules would feel arbitrary and
complex.  It would also require us to dramatically change the CPython
parser (and every other parser for Python).  It should be noted that
Python's current parser is intentionally "dumb" -- a simple grammar is
easier for users to reason about.

For all these reasons, square brackets (e.g. ``List[int]``) are (and
have long been) the preferred syntax for generic type parameters.
They can be implemented by defining the ``__getitem__()`` method on
the metaclass, and no new syntax is required at all.  This option
works in all recent versions of Python (starting with Python 2.2).
Python is not alone in this syntactic choice -- generic classes in
Scala also use square brackets.

What about existing uses of annotations?
----------------------------------------

One line of argument points out that PEP 3107 explicitly supports
the use of arbitrary expressions in function annotations.  The new
proposal is then considered incompatible with the specification of PEP
3107.

Our response to this is that, first of all, the current proposal does
not introduce any direct incompatibilities, so programs using
annotations in Python 3.4 will still work correctly and without
prejudice in Python 3.5.

We do hope that type hints will eventually become the sole use for
annotations, but this will require additional discussion and a
deprecation period after the initial roll-out of the typing module
with Python 3.5.  The current PEP will have provisional status (see
PEP 411) until Python 3.6 is released.  The fastest conceivable scheme
would introduce silent deprecation of non-type-hint annotations in
3.6, full deprecation in 3.7, and declare type hints as the only
allowed use of annotations in Python 3.8.  This should give authors of
packages that use annotations plenty of time to devise another
approach, even if type hints become an overnight success.

Another possible outcome would be that type hints will eventually
become the default meaning for annotations, but that there will always
remain an option to disable them.  For this purpose the current
proposal defines a decorator ``@no_type_check`` which disables the
default interpretation of annotations as type hints in a given class
or function.  It also defines a meta-decorator
``@no_type_check_decorator`` which can be used to decorate a decorator
(!), causing annotations in any function or class decorated with the
latter to be ignored by the type checker.

There are also ``# type: ignore`` comments, and static checkers should
support configuration options to disable type checking in selected
packages.

Despite all these options, proposals have been circulated to allow
type hints and other forms of annotations to coexist for individual
arguments.  One proposal suggests that if an annotation for a given
argument is a dictionary literal, each key represents a different form
of annotation, and the key ``'type'`` would be use for type hints.
The problem with this idea and its variants is that the notation
becomes very "noisy" and hard to read.  Also, in most cases where
existing libraries use annotations, there would be little need to
combine them with type hints.  So the simpler approach of selectively
disabling type hints appears sufficient.

The problem of forward declarations
-----------------------------------

The current proposal is admittedly sub-optimal when type hints must
contain forward references.  Python requires all names to be defined
by the time they are used.  Apart from circular imports this is rarely
a problem: "use" here means "look up at runtime", and with most
"forward" references there is no problem in ensuring that a name is
defined before the function using it is called.

The problem with type hints is that annotations (per PEP 3107, and
similar to default values) are evaluated at the time a function is
defined, and thus any names used in an annotation must be already
defined when the function is being defined.  A common scenario is a
class definition whose methods need to reference the class itself in
their annotations.  (More general, it can also occur with mutually
recursive classes.)  This is natural for container types, for
example::

  class Node:
      """Binary tree node."""

      def __init__(self, left: Node, right: Node):
          self.left = left
          self.right = right

As written this will not work, because of the peculiarity in Python
that class names become defined once the entire body of the class has
been executed.  Our solution, which isn't particularly elegant, but
gets the job done, is to allow using string literals in annotations.
Most of the time you won't have to use this though -- most *uses* of
type hints are expected to reference builtin types or types defined in
other modules.

A counterproposal would change the semantics of type hints so they
aren't evaluated at runtime at all (after all, type checking happens
off-line, so why would type hints need to be evaluated at runtime at
all).  This of course would run afoul of backwards compatibility,
since the Python interpreter doesn't actually know whether a
particular annotation is meant to be a type hint or something else.

A compromise is possible where a ``__future__`` import could enable
turning *all* annotations in a given module into string literals, as
follows::

  from __future__ import annotations

  class ImSet:
      def add(self, a: ImSet) -> List[ImSet]: ...

  assert ImSet.add.__annotations__ == {'a': 'ImSet', 'return': 'List[ImSet]'}

Such a ``__future__`` import statement may be proposed in a separate
PEP.


The double colon
----------------

A few creative souls have tried to invent solutions for this problem.
For example, it was proposed to use a double colon (``::``) for type
hints, solving two problems at once: disambiguating between type hints
and other annotations, and changing the semantics to preclude runtime
evaluation.  There are several things wrong with this idea, however.

* It's ugly.  The single colon in Python has many uses, and all of
  them look familiar because they resemble the use of the colon in
  English text.  This is a general rule of thumb by which Python
  abides for most forms of punctuation; the exceptions are typically
  well known from other programming languages.  But this use of ``::``
  is unheard of in English, and in other languages (e.g. C++) it is
  used as a scoping operator, which is a very different beast.  In
  contrast, the single colon for type hints reads naturally -- and no
  wonder, since it was carefully designed for this purpose (the idea
  long predates PEP 3107 [gvr-artima]_).  It is also used in the same
  fashion in other languages from Pascal to Swift.

* What would you do for return type annotations?

* It's actually a feature that type hints are evaluated at runtime.

  * Making type hints available at runtime allows runtime type
    checkers to be built on top of type hints.

  * It catches mistakes even when the type checker is not run.  Since
    it is a separate program, users may choose not to run it (or even
    install it), but might still want to use type hints as a concise
    form of documentation.  Broken type hints are no use even for
    documentation.

* Because it's new syntax, using the double colon for type hints would
  limit them to code that works with Python 3.5 only.  By using
  existing syntax, the current proposal can easily work for older
  versions of Python 3.  (And in fact mypy supports Python 3.2 and
  newer.)

* If type hints become successful we may well decide to add new syntax
  in the future to declare the type for variables, for example
  ``var age: int = 42``.  If we were to use a double colon for
  argument type hints, for consistency we'd have to use the same
  convention for future syntax, perpetuating the ugliness.

Other forms of new syntax
-------------------------

A few other forms of alternative syntax have been proposed, e.g. the
introduction of a ``where`` keyword [roberge]_, and Cobra-inspired
``requires`` clauses.  But these all share a problem with the double
colon: they won't work for earlier versions of Python 3.  The same
would apply to a new ``__future__`` import.

Other backwards compatible conventions
--------------------------------------

The ideas put forward include:

* A decorator, e.g. ``@typehints(name=str, returns=str)``.  This could
  work, but it's pretty verbose (an extra line, and the argument names
  must be repeated), and a far cry in elegance from the PEP 3107
  notation.

* Stub files.  We do want stub files, but they are primarily useful
  for adding type hints to existing code that doesn't lend itself to
  adding type hints, e.g. 3rd party packages, code that needs to
  support both Python 2 and Python 3, and especially extension
  modules.  For most situations, having the annotations in line with
  the function definitions makes them much more useful.

* Docstrings.  There is an existing convention for docstrings, based
  on the Sphinx notation (``:type arg1: description``).  This is
  pretty verbose (an extra line per parameter), and not very elegant.
  We could also make up something new, but the annotation syntax is
  hard to beat (because it was designed for this very purpose).

It's also been proposed to simply wait another release.  But what
problem would that solve?  It would just be procrastination.


PEP Development Process
=======================

A live draft for this PEP lives on GitHub [github]_.  There is also an
issue tracker [issues]_, where much of the technical discussion takes
place.

The draft on GitHub is updated regularly in small increments.  The
official PEPS repo [peps_] is (usually) only updated when a new draft
is posted to python-dev.


Acknowledgements
================

This document could not be completed without valuable input,
encouragement and advice from Jim Baker, Jeremy Siek, Michael Matson
Vitousek, Andrey Vlasovskikh, Radomir Dopieralski, Peter Ludemann,
and the BDFL-Delegate, Mark Shannon.

Influences include existing languages, libraries and frameworks
mentioned in PEP 482.  Many thanks to their creators, in alphabetical
order: Stefan Behnel, William Edwards, Greg Ewing, Larry Hastings,
Anders Hejlsberg, Alok Menghrajani, Travis E. Oliphant, Joe Pamer,
Raoul-Gabriel Urma, and Julien Verlaguet.


References
==========

.. [mypy]
   http://mypy-lang.org

.. [gvr-artima]
   http://www.artima.com/weblogs/viewpost.jsp?thread=85551

.. [wiki-variance]
   http://en.wikipedia.org/wiki/Covariance_and_contravariance_%28computer_science%29

.. [typeshed]
   https://github.com/python/typeshed/

.. [pyflakes]
   https://github.com/pyflakes/pyflakes/

.. [pylint]
   http://www.pylint.org

.. [roberge]
   http://aroberge.blogspot.com/2015/01/type-hinting-in-python-focus-on.html

.. [github]
   https://github.com/ambv/typehinting

.. [issues]
   https://github.com/ambv/typehinting/issues

.. [peps]
   https://hg.python.org/peps/file/tip/pep-0484.txt


Copyright
=========

This document has been placed in the public domain.



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