PEP 802: Display Syntax for the Empty Set (#4531)

Author: AA-Turner

.github/CODEOWNERS

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 peps/pep-0800.rst  @JelleZijlstra
 peps/pep-0801.rst  @warsaw
+peps/pep-0802.rst  @AA-Turner
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peps/pep-0802.rst

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+PEP: 802
+Title: Display Syntax for the Empty Set
+Author: Adam Turner <[email protected]>
+Discussions-To: Pending
+Status: Draft
+Type: Standards Track
+Created: 08-Aug-2025
+Python-Version: 3.15
+
+
+Abstract
+========
+
+We propose a new notation, ``{/}``, to construct and represent the empty set.
+This is modelled after the corresponding mathematical symbol ':math:`\emptyset`'.
+
+This complements the existing notation for empty tuples, lists, and
+dictionaries, which use ``()``, ``[]``, and ``{}`` respectively.
+
+
+Motivation
+==========
+
+Sets are currently the only built-in collection type that have a
+:ref:`display syntax <python:comprehensions>`,
+but no notation to express an empty collection.
+The :ref:`Python Language Reference <python:set>` notes this, stating:
+
+   An empty set cannot be constructed with ``{}``;
+   this literal constructs an empty dictionary.
+
+This can be confusing for beginners, especially those coming to the language
+from a scientific or mathematical background, where sets may be in more common
+use than dictionaries or maps.
+
+A syntax notation for the empty set has the important benefit of not requiring
+a name lookup (unlike ``set()``).
+``{/}`` will always have a consistent meaning, improving teachability
+of core concepts to beginners.
+For example, users must be careful not to use ``set`` as a local variable name,
+as doing so prevents constructing new sets.
+This can be frustrating as beginners may not know how to recover the
+:py:class:`set` type if they have overriden the name:
+techniques to do so (e.g. ``type({1}-{1})``) are not immediately obvious.
+
+Finally, this may be helpful for users who do not speak English,
+as it provides a culture-free notation for a common data structure
+that is built into the language.
+
+
+Rationale
+=========
+
+Sets were introduced to Python 2.2 via :pep:`218`, which did not include
+set notation, but discussed the idea of ``{-}`` for the empty set:
+
+    The PEP originally proposed ``{1,2,3}`` as the set notation and ``{-}`` for
+    the empty set.  Experience with Python 2.3's ``sets.py`` showed that
+    the notation was not necessary.  Also, there was some risk of making
+    dictionaries less instantly recognizable.
+
+Python 3.0 introduced set literals (:pep:`3100`), but again chose not to
+introduce notation for the empty set, which was omitted out of pragmatism
+(`python-3000, April 2006`_, `python-3000, May 2006`_).
+
+Since then, the topic has been discussed several times,
+with various proposals, including:
+
+#. Changing ``{}`` to mean an empty set and using ``{:}`` for an empty dictionary
+   (`python-ideas, January 2008`_, `Discourse, March 2023`_)
+#. A Unicode character (e.g. ``∅`` or ``ϕ``)
+   (`python-ideas, April 2021`_)
+#. ``<>``
+   (`python-ideas, November 2010`_, `Discourse, December 2024`_)
+#. ``s{}``
+   (`python-ideas, June 2009`_)
+#. ``{*()}``, perhaps optimising to compile this to the ``BUILD_SET`` opcode
+   (`Discourse, August 2025 (#37)`_)
+#. ``{-}``
+   (`python-ideas, August 2020`_)
+#. ``{,}``
+   (`Discourse, August 2025`_)
+#. ``{/}``
+   (`python-ideas, January 2008`_)
+#. ``set()`` (i.e. doing nothing)
+
+The authors propose ``{/}`` as the notation,
+being in their opinion the best of these options.
+It is simple and concise, with the benefit of resembling the mathematical
+notation for the empty set, :math:`\emptyset`.
+This makes it an easier mnemonic to explain than several in the language,
+such as ``**`` for exponentiation or ``@`` for matrix multiplication.
+
+The ``{/}`` notation was also the most popular in a `recent Discourse poll`_,
+selected by 41% of respondents overall and 60% of those voting for a new syntax.
+
+Brief summaries for the other proposals may be found in `Rejected Ideas`_.
+
+
+Specification
+=============
+
+The grammar for set displays will become:
+
+.. productionlist:: python-grammar
+   set_display: "{" ("/" | flexible_expression_list | comprehension) "}"
+
+``{/}`` will become the default syntax for the empty set.
+
+.. code-block:: python
+
+   >>> type({/})
+   <class 'set'>
+   >>> {/} == set()
+   True
+
+The representation and string forms of the empty set will change to ``'{/}'``.
+
+.. code-block:: python
+
+   >>> repr({/})
+   '{/}'
+   >>> str({/})
+   '{/}'
+
+There will be no behavioural changes to :py:class:`set` objects.
+
+
+Backwards Compatibility
+=======================
+
+Code that relies on the ``repr()`` or ``str()`` of the empty set
+will no longer work, because the representation will change.
+
+There will be no other backwards incompatibile changes,
+all current constructors for the empty set will continue to work,
+and the behaviour of the :py:class:`set` type will remain unchanged.
+
+
+Security Implications
+=====================
+
+None.
+
+
+How to Teach This
+=================
+
+All users can be taught that ``{/}`` is the new spelling for ``set()``,
+and that it is equivalent in all other ways.
+To help reinforce this, we will update the documentation to use ``{/}``
+instead of ``set()``, including the tutorial, standard libary modules,
+and the Python Language Reference.
+
+For new users, sets can be introduced through syntax, noting that the four
+built-in collection types with syntax all have empty forms:
+``()``, ``[]``, ``{/}``, and ``{}``.
+
+The empty set uses a forwards slash to differentiate it from
+an empty dictionary.
+It uses this syntax because it looks like the mathematical symbol
+for the empty set (':math:`\emptyset`').
+This can be used as a helpful mnemonic when teaching beginners,
+especially those that have a maths or science background.
+
+
+Reference Implementation
+========================
+
+Forthcoming.
+
+
+Rejected Ideas
+==============
+
+Change ``{}`` to mean an empty set and use ``{:}`` for an empty dictionary
+--------------------------------------------------------------------------
+
+This would be an entirely backwards incompatible change,
+all current empty :py:class:`dict` objects would become sets.
+
+Use a Unicode character (e.g. ``∅`` or ``ϕ``)
+---------------------------------------------
+
+The Unicode character 'U+2205 ∅ EMPTY SET' is not currently a valid identifier.
+Introducing a Unicode character as syntax would be hard to use,
+as it does not appear on standard keyboards.
+
+Using other characters that look like ∅, such as 'U+03C6 ϕ GREEK SMALL LETTER
+PHI' or 'U+00D8 Ø LATIN CAPITAL LETTER O WITH STROKE', would be more confusing
+with the same drawbacks of using a Unicode character.
+
+Use the ``<>`` syntax
+---------------------
+
+It does not have a resemblance to the syntax for non-empty sets.
+This would be harder to explain than this PEP's proposal.
+
+This syntax further has historic use as the inequality operator,
+which can still be accessed via ``from __future__ import barry_as_FLUFL``.
+Using both the ``barry_as_FLUFL`` future import and ``<>`` for the empty set
+would lead to parser ambiguity: what would ``<> <> <>`` mean?
+
+Use the ``s{}`` syntax
+----------------------
+
+This syntax may cause confusion with ``s`` as a local variable.
+The only current use of prefixes of this kind is for string literals.
+This would be harder to explain than this PEP's proposal.
+
+Use the ``{*()}`` syntax
+------------------------
+
+This relies on unpacking the empty tuple into a set, creating an empty set.
+This has the benefit of support since Python 3.5 (:pep:`448`), but is unwieldy
+and complicated to explain; it was not designed for this purpose.
+
+Use the ``{-}`` syntax
+----------------------
+
+This syntax was originally proposed in :pep:`218`,
+but removed from the PEP before it was accepted.
+The authors prefer ``{/}`` due to the resemblance to :math:`\emptyset`.
+
+Use the ``{,}`` syntax
+----------------------
+
+This is the authors' next preferred option.
+However, if a single comma were to be used to represent an empty collection,
+it may be confusing why this could not be used for empty tuples or lists.
+In time, there might be proposals to add support for ``[,]`` and ``(,)``.
+This conflicts with the general principle that
+'*there should be one-- and preferably only one --obvious way to do it*'.
+Having a visibly different form, in ``{/}``, helps to reinforce the idea
+that the syntax for the empty set is a special case, rather than a general rule
+for all empty collections.
+
+
+Open Issues
+===========
+
+None.
+
+
+Acknowledgements
+================
+
+* Chris Angelico, Dominykas Grigonis, Ben Hsing, James Webber,
+  and other contributors to recent Discourse topics.
+* Hugo van Kemenade, for helpful feedback on a draft of the PEP.
+
+
+Footnotes
+=========
+
+.. _Discourse, August 2025 (#37): https://discuss.python.org/t/101197/37
+.. _Discourse, August 2025: https://discuss.python.org/t/101197
+.. _Discourse, December 2024: https://discuss.python.org/t/73235
+.. _Discourse, March 2023: https://discuss.python.org/t/25213
+.. _explicitly deferred: https://mail.python.org/pipermail/python-3000/2006-May/001599.html
+.. _python-3000, April 2006: https://mail.python.org/pipermail/python-3000/2006-April/001286.html
+.. _python-3000, May 2006: https://mail.python.org/pipermail/python-3000/2006-May/001666.html
+.. _python-ideas, April 2021: https://mail.python.org/archives/list/[email protected]/message/X4TX2HDNKDJ7PVZL3DVI5QD2MIMRHKO4/
+.. _python-ideas, August 2020: https://mail.python.org/archives/list/[email protected]/message/QOBONXUPUMC3ULCGJU6FVHOCIZQDT45W/
+.. _python-ideas, January 2008: https://mail.python.org/archives/list/[email protected]/thread/IBMTTESRSF5755LNMVTUMHHABKOBSPUZ/#IBMTTESRSF5755LNMVTUMHHABKOBSPUZ
+.. _python-ideas, June 2009: https://mail.python.org/archives/list/[email protected]/thread/AMWKPS54ZK6X2FI7NICDM6DG7LERIJFV/#AMWKPS54ZK6X2FI7NICDM6DG7LERIJFV
+.. _python-ideas, November 2010: https://mail.python.org/archives/list/[email protected]/thread/N7CHDYXW2FYHDJ5BTP7CCC5HLAIINOVH/#N7CHDYXW2FYHDJ5BTP7CCC5HLAIINOVH
+.. _recent Discourse poll: https://discuss.python.org/t/101197/15
+
+
+Copyright
+=========
+
+This document is placed in the public domain or under the
+CC0-1.0-Universal license, whichever is more permissive.