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PEP 653 -- Precise Semantics for Pattern Matching

PEP:653
Title:Precise Semantics for Pattern Matching
Author:Mark Shannon <mark at hotpy.org>
Status:Draft
Type:Standards Track
Created:09-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 two special (dunder) attributes, __match_container__ and __match_class__, in addition to the __match_args__ attribute from PEP 634, to support pattern matching. Both of these new attributes must be integers and __match_args__ is required to be a tuple of unique strings.

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 some 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 delegates the decision over whether a class is a sequence or mapping to collections.abc. Not all classes that could be considered sequences are registered as subclasses of collections.abc.Sequence. This PEP allows them to match sequence patterns, without the full collections.abc.Sequence machinery.

PEP 634 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.

For example, using sympy, we might want to write:

# a*a == a**2
case Mul(args=[Symbol(a), Symbol(b)]) if a == b:
    return Pow(a, 2)

Which requires the sympy class Symbol to "self" match. For sympy to support this pattern with PEP 634 is possible, but a bit tricky. With this PEP it can be implemented very easily [1].

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 more 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_container__ and __match_class__ attributes. This allows the kind of a value to be determined in a efficient fashion.

Specification

Additions to the object model

The __match_container__ ``and ``__match_class__ attributes will be added to object. __match_container__ should be overridden by classes that want to match mapping or sequence patterns. __match_class__ should be overridden by classes that want to change the default behavior when matching class patterns.

__match_container__ must be an integer and should be exactly one of these:

0
MATCH_SEQUENCE = 1
MATCH_MAPPING = 2

MATCH_SEQUENCE is used to indicate that instances of the class can match sequence patterns.

MATCH_MAPPING is used to indicate that instances of the class can match mapping patterns.

__match_class__ must be an integer and should be exactly one of these:

0
MATCH_SELF = 8

MATCH_SELF is used to indicate that for a single positional argument class pattern, the subject will be used and not deconstructed.

Note

In the rest of this document, we will refer to the above values by name only. Symbolic constants will be provided both for Python and C, and the values will never be changed.

object will have the following values for the special attributes:

__match_container__ = 0
__match_class__= 0
__match_args__ = ()

These special attributes will be inherited as normal.

If __match_args__ is overridden, then it is required to hold a tuple of unique strings. It may be empty.

Note

__match_args__ will be automatically generated for dataclasses and named tuples, as specified in PEP 634.

The pattern matching implementation is not required to check that any of these attributes behave as specified. If the value of __match_container__, __match_class__ or __match_args__ 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 FAIL is used to signify that matching failed for this pattern and that matching should move to the next pattern. If control reaches the end of the translation without reaching a FAIL, then it has matched, and following patterns are ignored.

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:

match expr:

translates to:

$value = expr

Capture patterns

Capture patterns always match, so the irrefutable match:

case capture_var:

translates to:

capture_var = $value

Wildcard patterns

Wildcard patterns always match, so:

case _:

translates to:

# No code -- Automatically matches

Literal Patterns

The literal pattern:

case LITERAL:

translates to:

if $value != LITERAL:
    FAIL

except when the literal is one of None, True or False , when it translates to:

if $value is not LITERAL:
    FAIL

Value Patterns

The value pattern:

case value.pattern:

translates to:

if $value != value.pattern:
    FAIL

Sequence Patterns

A pattern not including a star pattern:

case [$VARS]:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_SEQUENCE:
    FAIL
if len($value) != len($VARS):
    FAIL
$VARS = $value

Example: [2]

A pattern including a star pattern:

case [$VARS]

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_SEQUENCE:
    FAIL
if len($value) < len($VARS):
    FAIL
$VARS = $value # Note that $VARS includes a star expression.

Example: [3]

Mapping Patterns

A pattern not including a double-star pattern:

case {$KEYWORD_PATTERNS}:

translates to:

$sentinel = object()
$kind = type($value).__match_container__
if $kind != MATCH_MAPPING:
    FAIL
# $KEYWORD_PATTERNS is a meta-variable mapping names to variables.
for $KEYWORD in $KEYWORD_PATTERNS:
    $tmp = $value.get(QUOTE($KEYWORD), $sentinel)
    if $tmp is $sentinel:
        FAIL
    $KEYWORD_PATTERNS[$KEYWORD] = $tmp

Example: [4]

A pattern including a double-star pattern:

case {$KEYWORD_PATTERNS, **$DOUBLE_STARRED_PATTERN}:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_MAPPING:
    FAIL
# $KEYWORD_PATTERNS is a meta-variable mapping names to variables.
$tmp = dict($value)
if not $tmp.keys() >= $KEYWORD_PATTERNS.keys():
    FAIL:
for $KEYWORD in $KEYWORD_PATTERNS:
    $KEYWORD_PATTERNS[$KEYWORD] = $tmp.pop(QUOTE($KEYWORD))
$DOUBLE_STARRED_PATTERN = $tmp

Example: [5]

Class Patterns

Class pattern with no arguments:

case ClsName():

translates to:

if not isinstance($value, ClsName):
    FAIL

Class pattern with a single positional pattern:

case ClsName($VAR):

translates to:

$kind = type($value).__match_class__
if $kind == MATCH_SELF:
    if not isinstance($value, ClsName):
        FAIL
    $VAR = $value
else:
    As other positional-only class pattern

Positional-only class pattern:

case ClsName($VARS):

translates to:

if not isinstance($value, ClsName):
    FAIL
$attrs = ClsName.__match_args__
if len($attr) < len($VARS):
    raise TypeError(...)
try:
    for i, $VAR in enumerate($VARS):
        $VAR = getattr($value, $attrs[i])
except AttributeError:
    FAIL

Example: [6]

Class patterns with all keyword patterns:

case ClsName($KEYWORD_PATTERNS):

translates to:

if not isinstance($value, ClsName):
    FAIL
try:
    for $KEYWORD in $KEYWORD_PATTERNS:
        $tmp = getattr($value, QUOTE($KEYWORD))
        $KEYWORD_PATTERNS[$KEYWORD] = $tmp
except AttributeError:
    FAIL

Example: [7]

Class patterns with positional and keyword patterns:

case ClsName($VARS, $KEYWORD_PATTERNS):

translates to:

if not isinstance($value, ClsName):
    FAIL
$attrs = ClsName.__match_args__
if len($attr) < len($VARS):
    raise TypeError(...)
$pos_attrs = $attrs[:len($VARS)]
try:
    for i, $VAR in enumerate($VARS):
        $VAR = getattr($value, $attrs[i])
    for $KEYWORD in $KEYWORD_PATTERNS:
        $name = QUOTE($KEYWORD)
        if $name in pos_attrs:
            raise TypeError(...)
        $KEYWORD_PATTERNS[$KEYWORD] = getattr($value, $name)
except AttributeError:
    FAIL

Example: [8]

Nested patterns

The above specification assumes that patterns are not nested. For nested patterns the above translations are applied recursively by introducing temporary capture patterns.

For example, the pattern:

case [int(), str()]:

translates to:

$kind = type($value).__match_class__
if $kind != MATCH_SEQUENCE:
    FAIL
if len($value) != 2:
    FAIL
$value_0, $value_1 = $value
#Now match on temporary values
if not isinstance($value_0, int):
    FAIL
if not isinstance($value_1, str):
    FAIL

Guards

Guards translate to a test following the rest of the translation:

case pattern if guard:

translates to:

[translation for pattern]
if not guard:
    FAIL

Non-conforming special attributes

All classes should ensure that the the values of __match_container__, __match_class__ and __match_args__ follow the specification. Therefore, implementations can assume, without checking, that the following are true:

__match_container__ == 0 or __match_container__ == MATCH_SEQUENCE or __match_container__ == MATCH_MAPPING
__match_class__ == 0 or __match_class__ == MATCH_SELF

and that __match_args__ is a tuple of unique strings.

Values of the special attributes for classes in the standard library

For the core builtin container classes __match_container__ will be:

  • list: MATCH_SEQUENCE
  • tuple: MATCH_SEQUENCE
  • dict: MATCH_MAPPING
  • bytearray: 0
  • bytes: 0
  • str: 0

Named tuples will have __match_container__ set to MATCH_SEQUENCE.

  • All other standard library classes for which issubclass(cls, collections.abc.Mapping) is true will have __match_container__ set to MATCH_MAPPING.
  • All other standard library classes for which issubclass(cls, collections.abc.Sequence) is true will have __match_container__ set to MATCH_SEQUENCE.

For the following builtin classes __match_class__ will be set to MATCH_SELF:

  • bool
  • bytearray
  • bytes
  • float
  • frozenset
  • int
  • set
  • str
  • list
  • tuple
  • dict

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($value) == 2:
    if "a" in $value:
        if "b" in $value:
            x = $value["a"]
            y = $value["b"]
            goto W
        if "c" in $value:
            x = $value["a"]
            y = $value["c"]
            goto X
elif len($value) == 3:
    if "a" in $value and "b" in $value:
        x = $value["a"]
        y = $value["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:

  • Requires __match_args__ to be a tuple of strings, not just a sequence. This make pattern matching a bit more robust and optimizable as __match_args__ can be assumed to be immutable.
  • Selecting the kind of container patterns that can be matched uses cls.__match_container__ instead of issubclass(cls, collections.abc.Mapping) and issubclass(cls, collections.abc.Sequence).
  • Allows classes to opt out of deconstruction altogether, if neccessary, but setting __match_class__ = 0.
  • The behavior when matching patterns is more precisely defined, but is otherwise unchanged.

There are no changes to syntax. All examples given in the PEP 636 tutorial should continue to work as they do now.

Rejected Ideas

Using attributes from the instance's dictionary

An earlier version of this PEP only used attributes from the instance's dictionary when matching a class pattern with __match_class__ was the default value. The intent was to avoid capturing bound-methods and other synthetic attributes. However, this also mean that properties were ignored.

For the class:

class C:
    def __init__(self):
        self.a = "a"
    @property
    def p(self):
        ...
    def m(self):
        ...

Ideally we would match the attributes "a" and "p", but not "m". However, there is no general way to do that, so this PEP now follows the semantics of PEP 634.

Lookup of __match_args__ on the subject not the pattern

An earlier version of this PEP looked up __match_args__ on the class of the subject and not the class specified in the pattern. This has been rejected for a few reasons:

* Using the class specified in the pattern is more amenable to optimization and can offer better performance.
* Using the class specified in the pattern has the potential to provide better error reporting is some cases.
* Neither approach is perfect, both have odd corner cases. Keeping the status quo minimizes disruption.

Combining __match_class__ and __match_container__ into a single value

An earlier version of this PEP combined __match_class__ and __match_container__ into a single value, __match_kind__. Using a single value has a small advantage in terms of performance, but is likely to result in unintended changes to container matching when overriding class matching behavior, and vice versa.

Deferred Ideas

The original version of this PEP included the match kind MATCH_POSITIONAL and special method __deconstruct__ which would allow classes full control over their matching. This is important for libraries like sympy.

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 the positional patterns with current pattern matching is possible, but is tricky. With these additional features it can be implemented easily [9].

This idea will feature in a future PEP for 3.11. However, it is too late in the 3.10 development cycle for such a change.

Having a separate value to reject all class matches

In an earlier version of this PEP, there was a distinct value for __match_class__ that allowed classes to not match any class pattern that would have required deconstruction. However, this would become redundant once MATCH_POSITIONAL is introduced, and complicates the specification for an extremely rare case.

Code examples

[1]
class Symbol:
    __match_class__ = MATCH_SELF
[2]

This:

case [a, b] if a is b:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_SEQUENCE:
    FAIL
if len($value) != 2:
    FAIL
a, b = $value
if not a is b:
    FAIL
[3]

This:

case [a, *b, c]:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_SEQUENCE:
    FAIL
if len($value) < 2:
    FAIL
a, *b, c = $value
[4]

This:

case {"x": x, "y": y} if x > 2:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_MAPPING:
    FAIL
$tmp = $value.get("x", $sentinel)
if $tmp is $sentinel:
    FAIL
x = $tmp
$tmp = $value.get("y", $sentinel)
if $tmp is $sentinel:
    FAIL
y = $tmp
if not x > 2:
    FAIL
[5]

This:

case {"x": x, "y": y, **z}:

translates to:

$kind = type($value).__match_container__
if $kind != MATCH_MAPPING:
    FAIL
$tmp = dict($value)
if not $tmp.keys() >= {"x", "y"}:
    FAIL
x = $tmp.pop("x")
y = $tmp.pop("y")
z = $tmp
[6]

This:

match ClsName(x, y):

translates to:

if not isinstance($value, ClsName):
    FAIL
$attrs = ClsName.__match_args__
if len($attr) < 2:
    FAIL
try:
    x = getattr($value, $attrs[0])
    y = getattr($value, $attrs[1])
except AttributeError:
    FAIL
[7]

This:

match ClsName(a=x, b=y):

translates to:

if not isinstance($value, ClsName):
    FAIL
try:
    x = $value.a
    y = $value.b
except AttributeError:
    FAIL
[8]

This:

match ClsName(x, a=y):

translates to:

if not isinstance($value, ClsName):
    FAIL
$attrs = ClsName.__match_args__
if len($attr) < 1:
    raise TypeError(...)
$positional_names = $attrs[:1]
try:
    x = getattr($value, $attrs[0])
    if "a" in $positional_names:
        raise TypeError(...)
    y = $value.a
except AttributeError:
    FAIL
[9]
class Basic:
    __match_class__ = MATCH_POSITIONAL
    def __deconstruct__(self):
        return self._args
Source: https://github.com/python/peps/blob/master/pep-0653.rst