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PEP 653: Precise Semantics for Pattern Matching (#1819)

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PEP: 653
Title: Precise Semantics for Pattern Matching
Author: Mark Shannon <mark@hotpy.org>
Status: Draft
Type: Standards Track
Content-Type: text/x-rst
Created: 9-Feb-2021
Post-History: 18-Feb-2021
Abstract
========
This PEP proposes a semantics for pattern matching that respects the general concept of PEP 634,
but is more precise, easier to reason about, and should be faster.
The object model will be extended with three special (dunder) attributes to support pattern matching:
* A ``__match_kind__`` attribute. Must be an integer.
* An ``__attributes__`` attribute. Only needed for those classes wanting to customize matching the class pattern.
If present, it must be a tuple of strings.
* A ``__deconstruct__()`` method. Only needed if ``__attributes__`` is present.
Returns an iterable over the components of the deconstructed object.
With this PEP:
* The semantics of pattern matching will be clearer, so that patterns are easier to reason about.
* It will be possible to implement pattern matching in a more efficient fashion.
* Pattern matching will be more usable for complex classes, by allowing classes more control over which patterns they match.
Motivation
==========
Pattern matching in Python, as described in PEP 634, is to be added to Python 3.10.
Unfortunately, PEP 634 is not as precise about the semantics as it could be,
nor does it allow classes sufficient control over how they match patterns.
Precise semantics
-----------------
PEP 634 explicitly includes a section on undefined behavior.
Large amounts of undefined behavior may be acceptable in a language like C,
but in Python it should be kept to a minimum.
Pattern matching in Python can be defined more precisely without loosing expressiveness or performance.
Improved control over class matching
------------------------------------
PEP 634 assumes that class instances are simply a collection of their attributes,
and that deconstruction by attribute access is the dual of construction. That is not true, as
many classes have a more complex relation between their constructor and internal attributes.
Those classes need to be able to define their own deconstruction.
For example, using ``sympy``, we might want to write::
# sin(x)**2 + cos(x)**2 == 1
case Add(Pow(sin(a), 2), Pow(cos(b), 2)) if a == b:
return 1
For ``sympy`` to support this pattern for PEP 634 would be possible, but tricky and cumbersome.
With this PEP it can be implemented easily [1]_.
PEP 634 also privileges some builtin classes with a special form of matching, the "self" match.
For example the pattern ``list(x)`` matches a list and assigns the list to ``x``.
By allowing classes to choose which kinds of pattern they match, other classes can use this form as well.
Robustness
----------
With this PEP, access to attributes during pattern matching becomes well defined and deterministic.
This makes pattern matching less error prone when matching objects with hidden side effects, such as object-relational mappers.
Objects will have control over their own deconstruction, which can help prevent unintended consequences should attribute access have side-effects.
PEP 634 relies on the ``collections.abc`` module when determining which patterns a value can match, implicitly importing it if necessary.
This PEP will eliminate surprising import errors and misleading audit events from those imports.
Efficient implementation
------------------------
The semantics proposed in this PEP will allow efficient implementation, partly as a result of having precise semantics
and partly from using the object model.
With precise semantics, it is possible to reason about what code transformations are correct,
and thus apply optimizations effectively.
Because the object model is a core part of Python, implementations already handle special attribute lookup efficiently.
Looking up a special attribute is much faster than performing a subclass test on an abstract base class.
Rationale
=========
The object model and special methods are at the core of the Python language. Consequently,
implementations support them well.
Using special attributes for pattern matching allows pattern matching to be implemented in a way that
integrates well with the rest of the implementation, and is thus easier to maintain and is likely to perform better.
A match statement performs a sequence of pattern matches. In general, matching a pattern has three parts:
1. Can the value match this kind of pattern?
2. When deconstructed, does the value match this particular pattern?
3. Is the guard true?
To determine whether a value can match a particular kind of pattern, we add the ``__match_kind__`` attribute.
This allows the kind of a value to be determined once and in a efficient fashion.
To deconstruct an object, pre-existing special methods can be used for sequence and mapping patterns, but something new is needed for class patterns.
PEP 634 proposes using ad-hoc attribute access, disregarding the possibility of side-effects.
This could be problematic should the attributes of the object be dynamically created or consume resources.
By adding the ``__attributes__`` attribute and ``__deconstruct__()`` method, objects can control how they are deconstructed,
and patterns with a different set of attributes can be efficiently rejected.
Should deconstruction of an object make no sense, then classes can define ``__match_kind__`` to reject class patterns completely.
Specification
=============
Additions to the object model
-----------------------------
A ``__match_kind__`` attribute will be added to ``object``.
It should be overridden by classes that want to match class, mapping or sequence patterns.
It must be an integer and should be exactly one of these::
0
MATCH_SEQUENCE
MATCH_MAPPING
bitwise ``or``\ ed with exactly one of these::
0
MATCH_DEFAULT
MATCH_CLASS
MATCH_SELF
.. note::
It does not matter what the actual values are. We will refer to them by name only.
Symbolic constants will be provided both for Python and C, and once defined they will
never be changed.
Classes which define ``__match_kind__ & MATCH_CLASS`` to be non-zero must
implement one additional special attribute, and one special method:
* ``__attributes__``: should hold a tuple of strings indicating the names of attributes that are to be considered for matching; it may be empty for postional-only matches.
* ``__deconstruct__()``: should return a sequence which contains the parts of the deconstructed object.
.. note::
``__attributes__`` and ``__deconstruct__`` will be automatically generated for dataclasses and named tuples.
The pattern matching implementation is *not* required to check that ``__attributes__`` and ``__deconstruct__`` behave as specified.
If the value of ``__attributes__`` or the result of ``__deconstruct__()`` is not as specified, then
the implementation may raise any exception, or match the wrong pattern.
Of course, implementations are free to check these properties and provide meaningful error messages if they can do so efficiently.
Semantics of the matching process
---------------------------------
In the following, all variables of the form ``$var`` are temporary variables and are not visible to the Python program.
They may be visible via introspection, but that is an implementation detail and should not be relied on.
The psuedo-statement ``DONE`` is used to signify that matching is complete and that following patterns should be ignored.
All the translations below include guards. If no guard is present, simply substitute the guard ``if True`` when translating.
Variables of the form ``$ALL_CAPS`` are meta-variables holding a syntactic element, they are not normal variables.
So, ``$VARS = $items`` is not an assignment of ``$items`` to ``$VARS``,
but an unpacking of ``$items`` into the variables that ``$VARS`` holds.
For example, with the abstract syntax ``case [$VARS]:``, and the concrete syntax ``case[a, b]:`` then ``$VARS`` would hold the variables ``(a, b)``,
not the values of those variables.
The psuedo-function ``QUOTE`` takes a variable and returns the name of that variable.
For example, if the meta-variable ``$VAR`` held the variable ``foo`` then ``QUOTE($VAR) == "foo"``.
All additional code listed below that is not present in the original source will not trigger line events, conforming to PEP 626.
Preamble
''''''''
Before any patterns are matched, the expression being matched is evaluated and its kind is determined::
match expr:
translates to::
$value = expr
$kind = type($value).__match_kind__
In addition some helper variables are initialized::
$list = None
$dict = None
$attrs = None
$items = None
Capture patterns
''''''''''''''''
Capture patterns always match, so::
case capture_var if guard:
translates to::
capture_var = $value
if guard:
DONE
Wildcard patterns
'''''''''''''''''
Wildcard patterns always match, so::
case _ if guard:
translates to::
if guard:
DONE
Literal Patterns
''''''''''''''''
The literal pattern::
case LITERAL if guard:
translates to::
if $value == LITERAL and guard:
DONE
except when the literal is one of ``None``, ``True`` or ``False`` ,
when it translates to::
if $value is LITERAL and guard:
DONE
Value Patterns
''''''''''''''
The value pattern::
case value.pattern if guard:
translates to::
if $value == value.pattern and guard:
DONE
Sequence Patterns
'''''''''''''''''
Before matching the first sequence pattern, but after checking that ``$value`` is a sequence,
``$value`` is converted to a list.
A pattern not including a star pattern::
case [$VARS] if guard:
translates to::
if $kind & MATCH_SEQUENCE:
if $list is None:
$list = list($value)
if len($list) == len($VARS):
$VARS = $list
if guard:
DONE
Example: [2]_
A pattern including a star pattern::
case [$VARS] if guard
translates to::
if $kind & MATCH_SEQUENCE:
if $list is None:
$list = list($value)
if len($list) >= len($VARS):
$VARS = $list # Note that $VARS includes a star expression.
if guard:
DONE
Example: [3]_
Mapping Patterns
''''''''''''''''
Before matching the first mapping pattern, but after checking that ``$value`` is a mapping,
``$value`` is converted to a ``dict``.
A pattern not including a double-star pattern::
case {$KEYWORD_PATTERNS} if guard:
translates to::
if $kind & MATCH_MAPPING:
if $dict is None:
$dict = dict($value)
if $dict.keys() == $KEYWORD_PATTERNS.keys():
# $KEYWORD_PATTERNS is a meta-variable mapping names to variables.
for $KEYWORD in $KEYWORD_PATTERNS:
$KEYWORD_PATTERNS[$KEYWORD] = $dict[QUOTE($KEYWORD)]
if guard:
DONE
Example: [4]_
A pattern including a double-star pattern::
case {$KEYWORD_PATTERNS, **$DOUBLE_STARRED_PATTERN} if guard::
translates to::
if $kind & MATCH_MAPPING:
if $dict is None:
$dict = dict($value)
if $dict.keys() >= $KEYWORD_PATTERNS.keys():
# $KEYWORD_PATTERNS is a meta-variable mapping names to variables.
$tmp = dict($dict)
for $KEYWORD in $KEYWORD_PATTERNS:
$KEYWORD_PATTERNS[$KEYWORD] = $tmp.pop(QUOTE($KEYWORD))
$DOUBLE_STARRED_PATTERN = $tmp
DONE
Example: [5]_
Class Patterns
''''''''''''''
Class pattern with no arguments::
match ClsName() if guard:
translates to::
if $kind & MATCH_CLASS:
if isinstance($value, ClsName):
if guard:
DONE
Class pattern with a single positional pattern::
match ClsName($PATTERN) if guard:
translates to::
if $kind & MATCH_SELF:
if isinstance($value, ClsName):
x = $value
if guard:
DONE
else:
As other positional-only class pattern
Positional-only class pattern::
match ClsName($VARS) if guard:
translates to::
if $kind & MATCH_CLASS:
if isinstance($value, ClsName):
if $items is None:
$items = type($value).__deconstruct__($value)
# $VARS is a meta-variable.
if len($items) == len($VARS):
$VARS = $items
if guard:
DONE
.. note::
``__attributes__`` is not checked when matching positional-only class patterns,
this allows classes to match only positional-only patterns by setting ``__attributes__`` to ``()``.
Class patterns with keyword patterns::
match ClsName($VARS, $KEYWORD_PATTERNS) if guard:
translates to::
if $kind & MATCH_CLASS:
if isinstance($value, ClsName):
if $attrs is None:
$attrs = type($value).__attributes__
if $items is None:
$items = type($value).__deconstruct__($value)
$right_attrs = attrs[len($VARS):]
if set($right_attrs) >= set($KEYWORD_PATTERNS):
$VARS = items[:len($VARS)]
for $KEYWORD in $KEYWORD_PATTERNS:
$index = $attrs.index(QUOTE($KEYWORD))
$KEYWORD_PATTERNS[$KEYWORD] = $items[$index]
if guard:
DONE
Example: [6]_
Class patterns with all keyword patterns::
match ClsName($KEYWORD_PATTERNS) if guard:
translates to::
if $kind & MATCH_CLASS:
As above with $VARS == ()
elif $kind & MATCH_DEFAULT:
if isinstance($value, ClsName) and hasattr($value, "__dict__"):
if $value.__dict__.keys() >= set($KEYWORD_PATTERNS):
for $KEYWORD in $KEYWORD_PATTERNS:
$KEYWORD_PATTERNS[$KEYWORD] = $value.__dict__[QUOTE($KEYWORD)]
if guard:
DONE
Example: [7]_
Non-conforming ``__match_kind__``
'''''''''''''''''''''''''''''''''
All classes should ensure that the the value of ``__match_kind__`` follows the specification.
Therefore, implementations can assume, without checking, that all the following are *false*::
(__match_kind__ & (MATCH_SEQUENCE | MATCH_MAPPING)) == (MATCH_SEQUENCE | MATCH_MAPPING)
(__match_kind__ & (MATCH_SELF | MATCH_CLASS)) == (MATCH_SELF | MATCH_CLASS)
(__match_kind__ & (MATCH_SELF | MATCH_DEFAULT)) == (MATCH_SELF | MATCH_DEFAULT)
(__match_kind__ & (MATCH_DEFAULT | MATCH_CLASS)) == (MATCH_DEFAULT | MATCH_CLASS)
Thus, implementations can assume that ``__match_kind__ & MATCH_SEQUENCE`` implies ``(__match_kind__ & MATCH_MAPPING) == 0``, and vice-versa.
Likewise for ``MATCH_SELF``, ``MATCH_CLASS`` and ``MATCH_DEFAULT``.
If ``__match_kind__`` does not follow the specification,
then implementations may treat any of the expressions of the form ``$kind & MATCH_...`` above as having any value.
Implementation of ``__match_kind__`` in the standard library
------------------------------------------------------------
``object.__match_kind__`` will be ``MATCH_DEFAULT``.
For common builtin classes ``__match_kind__`` will be:
* ``bool``: ``MATCH_SELF``
* ``bytearray``: ``MATCH_SELF``
* ``bytes``: ``MATCH_SELF``
* ``float``: ``MATCH_SELF``
* ``frozenset``: ``MATCH_SELF``
* ``int``: ``MATCH_SELF``
* ``set``: ``MATCH_SELF``
* ``str``: ``MATCH_SELF``
* ``list``: ``MATCH_SEQUENCE | MATCH_SELF``
* ``tuple``: ``MATCH_SEQUENCE | MATCH_SELF``
* ``dict``: ``MATCH_MAPPING | MATCH_SELF``
Named tuples will have ``__match_kind__`` set to ``MATCH_SEQUENCE | MATCH_CLASS``.
* All other standard library classes for which ``issubclass(cls, collections.abc.Mapping)`` is true will have ``__match_kind__`` set to ``MATCH_MAPPING``.
* All other standard library classes for which ``issubclass(cls, collections.abc.Sequence)`` is true will have ``__match_kind__`` set to ``MATCH_SEQUENCE``.
Legal optimizations
-------------------
The above semantics implies a lot of redundant effort and copying in the implementation.
However, it is possible to implement the above semantics efficiently by employing semantic preserving transformations
on the naive implementation.
When performing matching, implementations are allowed
to treat the following functions and methods as pure:
* ``cls.__len__()`` for any class supporting ``MATCH_SEQUENCE``
* ``dict.keys()``
* ``dict.__contains__()``
* ``dict.__getitem__()``
Implementations are also allowed to freely replace ``isinstance(obj, cls)`` with ``issubclass(type(obj), cls)`` and vice-versa.
Security Implications
=====================
Preventing the possible registering or unregistering of classes as sequences or a mappings, that PEP 634 allows,
should improve security. However, the advantage is slight and is not a motivation for this PEP.
Implementation
==============
The naive implementation that follows from the specification will not be very efficient.
Fortunately, there are some reasonably straightforward transformations that can be used to improve performance.
Performance should be comparable to the implementation of PEP 634 (at time of writing) by the release of 3.10.
Further performance improvements may have to wait for the 3.11 release.
Possible optimizations
----------------------
The following is not part of the specification,
but guidelines to help developers create an efficient implementation.
Splitting evaluation into lanes
'''''''''''''''''''''''''''''''
Since the first step in matching each pattern is check to against the kind, it is possible to combine all the checks against kind into a single multi-way branch at the beginning
of the match. The list of cases can then be duplicated into several "lanes" each corresponding to one kind.
It is then trivial to remove unmatchable cases from each lane.
Depending on the kind, different optimization strategies are possible for each lane.
Note that the body of the match clause does not need to be duplicated, just the pattern.
Sequence patterns
'''''''''''''''''
This is probably the most complex to optimize and the most profitable in terms of performance.
Since each pattern can only match a range of lengths, often only a single length,
the sequence of tests can be rewitten in as an explicit iteration over the sequence,
attempting to match only those patterns that apply to that sequence length.
For example:
::
case []:
A
case [x]:
B
case [x, y]:
C
case other:
D
Can be compiled roughly as:
::
# Choose lane
$i = iter($value)
for $0 in $i:
break
else:
A
goto done
for $1 in $i:
break
else:
x = $0
B
goto done
for $2 in $i:
del $0, $1, $2
break
else:
x = $0
y = $1
C
goto done
other = $value
D
done:
Mapping patterns
''''''''''''''''
The best stategy here is probably to form a decision tree based on the size of the mapping and which keys are present.
There is no point repeatedly testing for the presence of a key.
For example::
match obj:
case {a:x, b:y}:
W
case {a:x, c:y}:
X
case {a:x, b:_, c:y}:
Y
case other:
Z
If the key ``"a"`` is not present when checking for case X, there is no need to check it again for Y.
The mapping lane can be implemented, roughly as:
::
# Choose lane
if len($dict) == 2:
if "a" in $dict:
if "b" in $dict:
x = $dict["a"]
y = $dict["b"]
goto W
if "c" in $dict:
x = $dict["a"]
y = $dict["c"]
goto X
elif len(dict) == 3:
if "a" in $dict and "b" in $dict:
x = $dict["a"]
y = $dict["c"]
goto Y
other = $value
goto Z
Summary of differences between this PEP and PEP 634
===================================================
The changes to the semantics can be summarized as:
* Selecting the kind of pattern uses ``cls.__match_kind__`` instead of
``issubclass(cls, collections.abc.Mapping)`` and ``issubclass(cls, collections.abc.Sequence)``
and allows classes control over which kinds of pattern they match.
* Class matching is via the ``__attributes__`` attribute and ``__deconstruct__`` method,
rather than the ``__match_args__`` method, and allows classes more control over how
they are deconstructed.
There are no changes to syntax.
Rejected Ideas
==============
None, as yet.
Open Issues
===========
None, as yet.
References
==========
PEP 634
https://www.python.org/dev/peps/pep-0634
Code examples
=============
.. [1]
::
class Basic:
__match_kind__ = MATCH_CLASS
__attributes__ = ()
def __deconstruct__(self):
return self._args
.. [2]
This::
case [a, b] if a is b:
translates to::
if $kind & MATCH_SEQUENCE:
if $list is None:
$list = list($value)
if len($list) == 2:
a, b = $list
if a is b:
DONE
.. [3]
This::
case [a, *b, c]:
translates to::
if $kind & MATCH_SEQUENCE:
if $list is None:
$list = list($value)
if len($list) >= 2:
a, *b, c = $list
DONE
.. [4]
This::
case {"x": x, "y": y} if x > 2:
translates to::
if $kind & MATCH_MAPPING:
if $dict is None:
$dict = dict($value)
if $dict.keys() == {"x", "y"}:
x = $dict["x"]
y = $dict["y"]
if x > 2:
DONE
.. [5]
This::
case {"x": x, "y": y, **: z}:
translates to::
if $kind & MATCH_MAPPING:
if $dict is None:
$dict = dict($value)
if $dict.keys() >= {"x", "y"}:
$tmp = dict($dict)
x = $tmp.pop("x")
y = $tmp.pop("y")
z = $tmp
DONE
.. [6]
This::
match ClsName(x, a=y):
translates to::
if $kind & MATCH_CLASS:
if isinstance($value, ClsName):
if $attrs is None:
$attrs = type($value).__attributes__
if $items is None:
$items = type($value).__deconstruct__($value)
$right_attrs = $attrs[1:]
if "a" in $right_attrs:
$y_index = $attrs.index("a")
x = $items[0]
y = $items[$y_index]
DONE
.. [7]
This::
match ClsName(a=x, b=y):
translates to::
if $kind & MATCH_CLASS:
if isinstance($value, ClsName):
if $attrs is None:
$attrs = type($value).__attributes__
if $items is None:
$items = type($value).__deconstruct__($value)
if "a" in $attrs and "b" in $attrs:
$x_index = $attrs.index("a")
x = $items[$x_index]
$y_index = $attrs.index("b")
y = $items[$y_index]
DONE
elif $kind & MATCH_DEFAULT:
if isinstance($value, ClsName) and hasattr($value, "__dict__"):
$obj_dict = $value.__dict__
if "a" in $obj_dict and "b" in $obj_dict:
x = $obj_dict["a"]
y = $obj_dict["b"]
DONE
Copyright
=========
This document is placed in the public domain or under the
CC0-1.0-Universal license, whichever is more permissive.
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