[Python-ideas] PEP 505: None-aware operators

Steve Dower steve.dower at python.org
Wed Jul 18 13:43:36 EDT 2018


Possibly this is exactly the wrong time to propose the next big syntax 
change, since we currently have nobody to declare on it, but since we're 
likely to argue for a while anyway it probably can't hurt (and maybe 
this will become the test PEP for whoever takes the reins?).

FWIW, Guido had previously indicated that he was generally favourable 
towards most of this proposal, provided we could figure out coherent 
semantics. Last time we tried, that didn't happen, so this time I've 
made the semantics much more precise, have implemented and verified 
them, and made much stronger statements about why we are proposing these.

Additional thanks to Mark Haase for writing most of the PEP. All the 
fair and balanced parts are his - all the overly strong opinions are mine.

Also thanks to Nick Coghlan for writing PEPs 531 and 532 last time we 
went through this - if you're unhappy with "None" being treated as a 
special kind of value, I recommend reading those before you start 
repeating them.

There is a formatted version of this PEP at 
https://www.python.org/dev/peps/pep-0505/

My current implementation is at 
https://github.com/zooba/cpython/tree/pep-505 (though I'm considering 
removing some of the new opcodes I added and just generating more 
complex code - in any case, let's get hung up on the proposal rather 
than the implementation :) )

Let the discussions begin!

---

PEP: 505
Title: None-aware operators
Version: $Revision$
Last-Modified: $Date$
Author: Mark E. Haase <mehaase at gmail.com>, Steve Dower 
<steve.dower at python.org>
Status: Draft
Type: Standards Track
Content-Type: text/x-rst
Created: 18-Sep-2015
Python-Version: 3.8

Abstract
========

Several modern programming languages have so-called "``null``-coalescing" or
"``null``- aware" operators, including C# [1]_, Dart [2]_, Perl, Swift, 
and PHP
(starting in version 7). These operators provide syntactic sugar for common
patterns involving null references.

* The "``null``-coalescing" operator is a binary operator that returns 
its left
   operand if it is not ``null``. Otherwise it returns its right operand.
* The "``null``-aware member access" operator accesses an instance 
member only
   if that instance is non-``null``. Otherwise it returns ``null``. 
(This is also
   called a "safe navigation" operator.)
* The "``null``-aware index access" operator accesses an element of a 
collection
   only if that collection is non-``null``. Otherwise it returns 
``null``. (This
   is another type of "safe navigation" operator.)

This PEP proposes three ``None``-aware operators for Python, based on the
definitions and other language's implementations of those above. 
Specifically:

* The "``None`` coalescing`` binary operator ``??`` returns the left 
hand side
   if it evaluates to a value that is not ``None``, or else it evaluates and
   returns the right hand side. A coalescing ``??=`` augmented assignment
   operator is included.
* The "``None``-aware attribute access" operator ``?.`` evaluates the 
complete
   expression if the left hand side evaluates to a value that is not 
``None``
* The "``None``-aware indexing" operator ``?[]`` evaluates the complete
   expression if the left hand site evaluates to a value that is not 
``None``

Syntax and Semantics
====================

Specialness of ``None``
-----------------------

The ``None`` object denotes the lack of a value. For the purposes of these
operators, the lack of a value indicates that the remainder of the 
expression
also lacks a value and should not be evaluated.

A rejected proposal was to treat any value that evaluates to false in a
Boolean context as not having a value. However, the purpose of these 
operators
is to propagate the "lack of value" state, rather that the "false" state.

Some argue that this makes ``None`` special. We contend that ``None`` is
already special, and that using it as both the test and the result of these
operators does not change the existing semantics in any way.

See the `Rejected Ideas`_ section for discussion on the rejected approaches.

Grammar changes
---------------

The following rules of the Python grammar are updated to read::

     augassign: ('+=' | '-=' | '*=' | '@=' | '/=' | '%=' | '&=' | '|=' | 
'^=' |
                 '<<=' | '>>=' | '**=' | '//=' | '??=')

     power: coalesce ['**' factor]
     coalesce: atom_expr ['??' factor]
     atom_expr: ['await'] atom trailer*
     trailer: ('(' [arglist] ')' |
               '[' subscriptlist ']' |
               '?[' subscriptlist ']' |
               '.' NAME |
               '?.' NAME)

Inserting the ``coalesce`` rule in this location ensures that expressions
resulting in ``None`` are natuarlly coalesced before they are used in
operations that would typically raise ``TypeError``. Like ``and`` and ``or``
the right-hand expression is not evaluated until the left-hand side is
determined to be ``None``. For example::

     a, b = None, None
     def c(): return None
     def ex(): raise Exception()

     (a ?? 2 ** b ?? 3) == a ?? (2 ** (b ?? 3))
     (a * b ?? c // d) == a * (b ?? c) // d
     (a ?? True and b ?? False) == (a ?? True) and (b ?? False)
     (c() ?? c() ?? True) == True
     (True ?? ex()) == True
     (c ?? ex)() == c()

Augmented coalescing assignment only rebinds the name if its current 
value is
``None``. If the target name already has a value, the right-hand side is not
evaluated. For example::

     a = None
     b = ''
     c = 0

     a ??= 'value'
     b ??= undefined_name
     c ??= shutil.rmtree('/')    # don't try this at home, kids

     assert a == 'value'
     assert b == ''
     assert c == '0' and any(os.scandir('/'))

Adding new trailers for the other ``None``-aware operators ensures that they
may be used in all valid locations for the existing equivalent operators,
including as part of an assignment target (more details below). As the 
existing
evaluation rules are not directly embedded in the grammar, we specify the
required changes here.

Assume that the ``atom`` is always successfully evaluated. Each 
``trailer`` is
then evaluated from left to right, applying its own parameter (either its
arguments, subscripts or attribute name) to produce the value for the next
``trailer``. Finally, if present, ``await`` is applied.

For example, ``await a.b(c).d[e]`` is currently parsed as
``['await', 'a', '.b', '(c)', '.d', '[e]']`` and evaluated::

     _v = a
     _v = _v.b
     _v = _v(c)
     _v = _v.d
     _v = _v[e]
     await _v

When a ``None``-aware operator is present, the left-to-right evaluation 
may be
short-circuited. For example, ``await a?.b(c).d?[e]`` is evaluated::

     _v = a
     if _v is not None:
         _v = _v.b
         _v = _v(c)
         _v = _v.d
         if _v is not None:
             _v = _v[e]
     await _v

.. note::
     ``await`` will almost certainly fail in this context, as it would in
     the case where code attempts ``await None``. We are not proposing 
to add a
     ``None``-aware ``await`` keyword here, and merely include it in this
     example for completeness of the specification, since the ``atom_expr``
     grammar rule includes the keyword. If it were in its own rule, we 
would have
     never mentioned it.

Parenthesised expressions are handled by the ``atom`` rule (not shown 
above),
which will implicitly terminate the short-circuiting behaviour of the above
transformation. For example, ``(a?.b ?? c).d?.e`` is evaluated as::

     # a?.b
     _v = a
     if _v is not None:
         _v = _v.b

     # ... ?? c
     if _v is None:
         _v = c

     # (...).d?.e
     _v = _v.d
     if _v is not None:
         _v = _v.e

When used as an assignment target, the ``None``-aware operations may only be
used in a "load" context. That is, ``a?.b = 1`` and ``a?[b] = 1`` will raise
``SyntaxError``. Use earlier in the expression (``a?.b.c = 1``) is 
permitted,
though unlikely to be useful unless combined with a coalescing operation::

     (a?.b ?? d).c = 1


Examples
========

This section presents some examples of common ``None`` patterns and 
shows what
conversion to use ``None``-aware operators may look like.

Standard Library
----------------

Using the ``find-pep505.py`` script[3]_ an analysis of the Python 3.7 
standard
library discovered up to 678 code snippets that could be replaced with 
use of
one of the ``None``-aware operators::

     $ find /usr/lib/python3.7 -name '*.py' | xargs python3.7 find-pep505.py
     <snip>
     Total None-coalescing `if` blocks: 449
     Total [possible] None-coalescing `or`: 120
     Total None-coalescing ternaries: 27
     Total Safe navigation `and`: 13
     Total Safe navigation `if` blocks: 61
     Total Safe navigation ternaries: 8

Some of these are shown below as examples before and after converting to 
use the
new operators.

 From ``bisect.py``::

     def insort_right(a, x, lo=0, hi=None):
         # ...
         if hi is None:
             hi = len(a)
         # ...

After updating to use the ``??=`` augmented assignment statement::

     def insort_right(a, x, lo=0, hi=None):
         # ...
         hi ??= len(a)
         # ...

 From ``calendar.py``::

     encoding = options.encoding
     if encoding is None:
         encoding = sys.getdefaultencoding()
     optdict = dict(encoding=encoding, css=options.css)

After updating to use the ``??`` operator::

     optdict = dict(encoding=encoding ?? sys.getdefaultencoding(),
                    css=options.css)

 From ``dis.py``::

     def _get_const_info(const_index, const_list):
         argval = const_index
         if const_list is not None:
             argval = const_list[const_index]
         return argval, repr(argval)

After updating to use the ``?[]`` and ``??`` operators::

     def _get_const_info(const_index, const_list):
         argval = const_list?[const_index] ?? const_index
         return argval, repr(argval)

 From ``inspect.py``::

     for base in object.__bases__:
         for name in getattr(base, "__abstractmethods__", ()):
             value = getattr(object, name, None)
             if getattr(value, "__isabstractmethod__", False):
                 return True

After updating to use the ``?.`` operator (and deliberately not 
converting to
use ``any()``)::

     for base in object.__bases__:
         for name in base?.__abstractmethods__ ?? ():
             if object?.name?.__isabstractmethod__:
                 return True

 From ``os.py``::

     if entry.is_dir():
         dirs.append(name)
         if entries is not None:
             entries.append(entry)
     else:
         nondirs.append(name)

After updating to use the ``?.`` operator::

     if entry.is_dir():
         dirs.append(name)
         entries?.append(entry)
     else:
         nondirs.append(name)


jsonify
-------

This example is from a Python web crawler that uses the Flask framework 
as its
front-end. This function retrieves information about a web site from a SQL
database and formats it as JSON to send to an HTTP client::

     class SiteView(FlaskView):
         @route('/site/<id_>', methods=['GET'])
         def get_site(self, id_):
             site = db.query('site_table').find(id_)

             return jsonify(
                 first_seen=site.first_seen.isoformat() if 
site.first_seen is not None else None,
                 id=site.id,
                 is_active=site.is_active,
                 last_seen=site.last_seen.isoformat() if site.last_seen 
is not None else None,
                 url=site.url.rstrip('/')
             )

Both ``first_seen`` and ``last_seen`` are allowed to be ``null`` in the
database, and they are also allowed to be ``null`` in the JSON response. 
JSON
does not have a native way to represent a ``datetime``, so the server's 
contract
states that any non-``null`` date is represented as an ISO-8601 string.

Without knowing the exact semantics of the ``first_seen`` and ``last_seen``
attributes, it is impossible to know whether the attribute can be safely or
performantly accessed multiple times.

One way to fix this code is to replace each conditional expression with an
explicit value assignment and a full ``if``/``else`` block::

     class SiteView(FlaskView):
         @route('/site/<id_>', methods=['GET'])
         def get_site(self, id_):
             site = db.query('site_table').find(id_)

             first_seen_dt = site.first_seen
             if first_seen_dt is None:
                 first_seen = None
             else:
                 first_seen = first_seen_dt.isoformat()

             last_seen_dt = site.last_seen
             if last_seen_dt is None:
                 last_seen = None
             else:
                 last_seen = last_seen_dt.isoformat()

             return jsonify(
                 first_seen=first_seen,
                 id=site.id,
                 is_active=site.is_active,
                 last_seen=last_seen,
                 url=site.url.rstrip('/')
             )

This adds ten lines of code and four new code paths to the function,
dramatically increasing the apparent complexity. Rewriting using the
``None``-aware attribute operator results in shorter code with more clear
intent::

     class SiteView(FlaskView):
         @route('/site/<id_>', methods=['GET'])
         def get_site(self, id_):
             site = db.query('site_table').find(id_)

             return jsonify(
                 first_seen=site.first_seen?.isoformat(),
                 id=site.id,
                 is_active=site.is_active,
                 last_seen=site.last_seen?.isoformat(),
                 url=site.url.rstrip('/')
             )

Grab
----

The next example is from a Python scraping library called `Grab
<https://github.com/lorien/grab/blob/4c95b18dcb0fa88eeca81f5643c0ebfb114bf728/gr
ab/upload.py>`_::

     class BaseUploadObject(object):
         def find_content_type(self, filename):
             ctype, encoding = mimetypes.guess_type(filename)
             if ctype is None:
                 return 'application/octet-stream'
             else:
                 return ctype

     class UploadContent(BaseUploadObject):
         def __init__(self, content, filename=None, content_type=None):
             self.content = content
             if filename is None:
                 self.filename = self.get_random_filename()
             else:
                 self.filename = filename
             if content_type is None:
                 self.content_type = self.find_content_type(self.filename)
             else:
                 self.content_type = content_type

     class UploadFile(BaseUploadObject):
         def __init__(self, path, filename=None, content_type=None):
             self.path = path
             if filename is None:
                 self.filename = os.path.split(path)[1]
             else:
                 self.filename = filename
             if content_type is None:
                 self.content_type = self.find_content_type(self.filename)
             else:
                 self.content_type = content_type

This example contains several good examples of needing to provide default
values. Rewriting to use conditional expressions reduces the overall 
lines of
code, but does not necessarily improve readability::

     class BaseUploadObject(object):
         def find_content_type(self, filename):
             ctype, encoding = mimetypes.guess_type(filename)
             return 'application/octet-stream' if ctype is None else ctype

     class UploadContent(BaseUploadObject):
         def __init__(self, content, filename=None, content_type=None):
             self.content = content
             self.filename = (self.get_random_filename() if filename
                 is None else filename)
             self.content_type = (self.find_content_type(self.filename)
                 if content_type is None else content_type)

     class UploadFile(BaseUploadObject):
         def __init__(self, path, filename=None, content_type=None):
             self.path = path
             self.filename = (os.path.split(path)[1] if filename is
                 None else filename)
             self.content_type = (self.find_content_type(self.filename)
                 if content_type is None else content_type)

The first ternary expression is tidy, but it reverses the intuitive order of
the operands: it should return ``ctype`` if it has a value and use the 
string
literal as fallback. The other ternary expressions are unintuitive and so
long that they must be wrapped. The overall readability is worsened, not
improved.

Rewriting using the ``None`` coalescing operator::

     class BaseUploadObject(object):
         def find_content_type(self, filename):
             ctype, encoding = mimetypes.guess_type(filename)
             return ctype ?? 'application/octet-stream'

     class UploadContent(BaseUploadObject):
         def __init__(self, content, filename=None, content_type=None):
             self.content = content
             self.filename = filename ?? self.get_random_filename()
             self.content_type = content_type ?? 
self.find_content_type(self.filename)

     class UploadFile(BaseUploadObject):
         def __init__(self, path, filename=None, content_type=None):
             self.path = path
             self.filename = filename ?? os.path.split(path)[1]
             self.content_type = content_type ?? 
self.find_content_type(self.filename)

This syntax has an intuitive ordering of the operands. In 
``find_content_type``,
for example, the preferred value ``ctype`` appears before the fallback 
value.
The terseness of the syntax also makes for fewer lines of code and less 
code to
visually parse, and reading from left-to-right and top-to-bottom more 
accurately
follows the execution flow.


Rejected Ideas
==============

The first three ideas in this section are oft-proposed alternatives to 
treating
``None`` as special. For further background on why these are rejected, 
see their
treatment in `PEP 531 <https://www.python.org/dev/peps/pep-0531/>`_ and
`PEP 532 <https://www.python.org/dev/peps/pep-0532/>`_ and the associated
discussions.

No-Value Protocol
-----------------

The operators could be generalised to user-defined types by defining a 
protocol
to indicate when a value represents "no value". Such a protocol may be a 
dunder
method ``__has_value__(self)` that returns ``True`` if the value should be
treated as having a value, and ``False`` if the value should be treated 
as no
value.

With this generalization, ``object`` would implement a dunder method 
equivalent
to this::

     def __has_value__(self):
         return True

``NoneType`` would implement a dunder method equivalent to this::

     def __has_value__(self):
         return False

In the specification section, all uses of ``x is None`` would be 
replaced with
``not x.__has_value__()``.

This generalization would allow for domain-specific "no-value" objects to be
coalesced just like ``None``. For example the ``pyasn1`` package has a type
called ``Null`` that represents an ASN.1 ``null``::

     >>> from pyasn1.type import univ
     >>> univ.Null() ?? univ.Integer(123)
     Integer(123)

Similarly, values such as ``math.nan`` and ``NotImplemented`` could be 
treated
as representing no value.

However, the "no-value" nature of these values is domain-specific, which 
means
they *should* be treated as a value by the language. For example,
``math.nan.imag`` is well defined (it's ``0.0``), and so short-circuiting
``math.nan?.imag`` to return ``math.nan`` would be incorrect.

As ``None`` is already defined by the language as being the value that
represents "no value", and the current specification would not preclude
switching to a protocol in the future (though changes to built-in 
objects would
not be compatible), this idea is rejected for now.

Boolean-aware operators
-----------------------

This suggestion is fundamentally the same as adding a no-value protocol, 
and so
the discussion above also applies.

Similar behavior to the ``??`` operator can be achieved with an ``or``
expression, however ``or`` checks whether its left operand is false-y 
and not
specifically ``None``. This approach is attractive, as it requires fewer 
changes
to the language, but ultimately does not solve the underlying problem 
correctly.

Assuming the check is for truthiness rather than ``None``, there is no 
longer a
need for the ``??`` operator. However, applying this check to the ``?.`` and
``?[]`` operators prevents perfectly valid operations applying

Consider the following example, where ``get_log_list()`` may return either a
list containing current log messages (potentially empty), or ``None`` if 
logging
is not enabled::

     lst = get_log_list()
     lst?.append('A log message')

If ``?.`` is checking for true values rather than specifically ``None`` 
and the
log has not been initialized with any items, no item will ever be 
appended. This
violates the obvious intent of the code, which is to append an item. The
``append`` method is available on an empty list, as are all other list 
methods,
and there is no reason to assume that these members should not be used 
because
the list is presently empty.

Further, there is no sensible result to use in place of the expression. A
normal ``lst.append`` returns ``None``, but under this idea 
``lst?.append`` may
result in either ``[]`` or ``None``, depending on the value of ``lst``. 
As with
the examples in the previous section, this makes no sense.

As checking for truthiness rather than ``None`` results in apparently valid
expressions no longer executing as intended, this idea is rejected.

Exception-aware operators
-------------------------

Arguably, the reason to short-circuit an expression when ``None`` is 
encountered
is to avoid the ``AttributeError`` or ``TypeError`` that would be raised 
under
normal circumstances. As an alternative to testing for ``None``, the 
``?.`` and
``?[]`` operators could instead handle ``AttributeError`` and ``TypeError``
raised by the operation and skip the remainder of the expression.

This produces a transformation for ``a?.b.c?.d.e`` similar to this::

     _v = a
     try:
         _v = _v.b
     except AttributeError:
         pass
     else:
         _v = _v.c
         try:
             _v = _v.d
         except AttributeError:
             pass
         else:
             _v = _v.e

One open question is which value should be returned as the expression 
when an
exception is handled. The above example simply leaves the partial 
result, but
this is not helpful for replacing with a default value. An alternative 
would be
to force the result to ``None``, which then raises the question as to why
``None`` is special enough to be the result but not special enough to be the
test.

Secondly, this approach masks errors within code executed implicitly as 
part of
the expression. For ``?.``, any ``AttributeError`` within a property or
``__getattr__`` implementation would be hidden, and similarly for 
``?[]`` and
``__getitem__`` implementations.

Similarly, simple typing errors such as ``{}?.ietms()`` could go unnoticed.

Existing conventions for handling these kinds of errors in the form of the
``getattr`` builtin and the ``.get(key, default)`` method pattern 
established by
``dict`` show that it is already possible to explicitly use this behaviour.

As this approach would hide errors in code, it is rejected.

``None``-aware Function Call
----------------------------

The ``None``-aware syntax applies to attribute and index access, so it seems
natural to ask if it should also apply to function invocation syntax. It 
might
be written as ``foo?()``, where ``foo`` is only called if it is not None.

This has been deferred on the basis of the proposed operators being intended
to aid traversal of partially populated hierarchical data structures, *not*
for traversal of arbitrary class hierarchies. This is reflected in the fact
that none of the other mainstream languages that already offer this syntax
have found it worthwhile to support a similar syntax for optional function
invocations.

A workaround similar to that used by C# would be to write
``maybe_none?.__call__(arguments)``. If the callable is ``None``, the
expression will not be evaluated. (The C# equivalent uses ``?.Invoke()`` 
on its
callable type.)

``?`` Unary Postfix Operator
----------------------------

To generalize the ``None``-aware behavior and limit the number of new 
operators
introduced, a unary, postfix operator spelled ``?`` was suggested. The 
idea is
that ``?`` might return a special object that could would override dunder
methods that return ``self``. For example, ``foo?`` would evaluate to 
``foo`` if
it is not ``None``, otherwise it would evaluate to an instance of
``NoneQuestion``::

     class NoneQuestion():
         def __call__(self, *args, **kwargs):
             return self

         def __getattr__(self, name):
             return self

         def __getitem__(self, key):
             return self


With this new operator and new type, an expression like ``foo?.bar[baz]``
evaluates to ``NoneQuestion`` if ``foo`` is None. This is a nifty
generalization, but it's difficult to use in practice since most 
existing code
won't know what ``NoneQuestion`` is.

Going back to one of the motivating examples above, consider the following::

     >>> import json
     >>> created = None
     >>> json.dumps({'created': created?.isoformat()})``

The JSON serializer does not know how to serialize ``NoneQuestion``, nor 
will
any other API. This proposal actually requires *lots of specialized logic*
throughout the standard library and any third party library.

At the same time, the ``?`` operator may also be **too general**, in the 
sense
that it can be combined with any other operator. What should the following
expressions mean?::

     >>> x? + 1
     >>> x? -= 1
     >>> x? == 1
     >>> ~x?

This degree of generalization is not useful. The operators actually proposed
herein are intentionally limited to a few operators that are expected to 
make it
easier to write common code patterns.

Built-in ``maybe``
------------------

Haskell has a concept called `Maybe <https://wiki.haskell.org/Maybe>`_ that
encapsulates the idea of an optional value without relying on any special
keyword (e.g. ``null``) or any special instance (e.g. ``None``). In 
Haskell, the
purpose of ``Maybe`` is to avoid separate handling of "something" and 
nothing".

A Python package called `pymaybe <https://pypi.org/p/pymaybe/>`_ provides a
rough approximation. The documentation shows the following example::

     >>> maybe('VALUE').lower()
     'value'

     >>> maybe(None).invalid().method().or_else('unknown')
     'unknown'

The function ``maybe()`` returns either a ``Something`` instance or a
``Nothing`` instance. Similar to the unary postfix operator described in the
previous section, ``Nothing`` overrides dunder methods in order to allow
chaining on a missing value.

Note that ``or_else()`` is eventually required to retrieve the 
underlying value
from ``pymaybe``'s wrappers. Furthermore, ``pymaybe`` does not short 
circuit any
evaluation. Although ``pymaybe`` has some strengths and may be useful in 
its own
right, it also demonstrates why a pure Python implementation of 
coalescing is
not nearly as powerful as support built into the language.

The idea of adding a builtin ``maybe`` type to enable this scenario is 
rejected.

Just use a conditional expression
---------------------------------

Another common way to initialize default values is to use the ternary 
operator.
Here is an excerpt from the popular `Requests package
<https://github.com/kennethreitz/requests/blob/14a555ac716866678bf17e43e23230d81
a8149f5/requests/models.py#L212>`_::

     data = [] if data is None else data
     files = [] if files is None else files
     headers = {} if headers is None else headers
     params = {} if params is None else params
     hooks = {} if hooks is None else hooks

This particular formulation has the undesirable effect of putting the 
operands
in an unintuitive order: the brain thinks, "use ``data`` if possible and use
``[]`` as a fallback," but the code puts the fallback *before* the preferred
value.

The author of this package could have written it like this instead::

     data = data if data is not None else []
     files = files if files is not None else []
     headers = headers if headers is not None else {}
     params = params if params is not None else {}
     hooks = hooks if hooks is not None else {}

This ordering of the operands is more intuitive, but it requires 4 extra
characters (for "not "). It also highlights the repetition of identifiers:
``data if data``, ``files if files``, etc.

When written using the ``None`` coalescing operator, the sample reads::

     data = data ?? []
     files = files ?? []
     headers = headers ?? {}
     params = params ?? {}
     hooks = hooks ?? {}


References
==========

.. [1] C# Reference: Operators
    (https://msdn.microsoft.com/en-us/library/6a71f45d.aspx)

.. [2] A Tour of the Dart Language: Operators
    (https://www.dartlang.org/docs/dart-up-and-running/ch02.html#operators)

.. [3] Associated scripts
    (https://github.com/python/peps/tree/master/pep-0505/)

Copyright
=========

This document has been placed in the public domain.


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