PEP: 635
Title: Structural Pattern Matching: Motivation and Rationale
Version: $Revision$
Last-Modified: $Date$
Author: Tobias Kohn <kohnt@tobiaskohn.ch>,
        Guido van Rossum <guido@python.org>
BDFL-Delegate:
Discussions-To: Python-Dev <python-dev@python.org>
Status: Draft
Type: Informational
Content-Type: text/x-rst
Created: 12-Sep-2020
Python-Version: 3.10
Post-History: 22-Oct-2020
Resolution:


Abstract
========

This PEP provides the motivation and rationale for PEP 634
("Structural Pattern Matching: Specification").  First-time readers
are encouraged to start with PEP 636, which provides a gentler
introduction to the concepts, syntax and semantics of patterns.


Motivation
==========

(Structural) pattern matching syntax is found in many languages, from
Haskell, Erlang and Scala to Elixir and Ruby.  (A proposal for
JavaScript is also under consideration.)

Python already supports a limited form of this through sequence
unpacking assignments, which the new proposal leverages.

Several other common Python idioms are also relevant:

- The ``if ... elif ... elif ... else`` idiom is often used to find
  out the type or shape of an object in an ad-hoc fashion, using one
  or more checks like ``isinstance(x, cls)``, ``hasattr(x, "attr")``,
  ``len(x) == n`` or ``"key" in x`` as guards to select an applicable
  block.  The block can then assume ``x`` supports the interface
  checked by the guard.  For example::

    if isinstance(x, tuple) and len(x) == 2:
        host, port = x
        mode = "http"
    elif isinstance(x, tuple) and len(x) == 3:
        host, port, mode = x
    # Etc.

  Code like this is more elegantly rendered using ``match``::

    match x:
        case host, port:
            mode = "http"
        case host, port, mode:
            pass
        # Etc.

- AST traversal code often looks for nodes matching a given pattern,
  for example the code to detect a node of the shape "A + B * C" might
  look like this::

    if (isinstance(node, BinOp) and node.op == "+"
            and isinstance(node.right, BinOp) and node.right.op == "*"):
        a, b, c = node.left, node.right.left, node.right.right
        # Handle a + b*c

  Using ``match`` this becomes more readable::

    match node:
        case BinOp("+", a, BinOp("*", b, c)):
            # Handle a + b*c

We believe that adding pattern matching to Python will enable Python
users to write cleaner, more readable code for examples like those
above, and many others.

For a more academic discussion to this proposal, see [1]_.


Pattern Matching and OO
-----------------------

Pattern matching is complimentary to the object-oriented paradigm.
Using OO and inheritance we can easily define a method on a base class
that defines default behavior for a specific operation on that class,
and we can override this default behavior in subclasses.  We can also
use the Visitor pattern to separate actions from data.

But this is not sufficient for all situations.  For example, a code
generator may consume an AST, and have many operations where the
generated code needs to vary based not just on the class of a node,
but also on the value of some class attributes, like the ``BinOp``
example above.  The Visitor pattern is insufficiently flexible for
this: it can only select based on the class.

For a complete example, see
https://github.com/gvanrossum/patma/blob/master/examples/expr.py#L231

Like the Visitor pattern, pattern matching allows for a strict separation
of concerns: specific actions or data processing is independent of the
class hierarchy or manipulated objects.  When dealing with predefined or
even built-in classes, in particular, it is often impossible to add further
methods to the individual classes.  Pattern matching not only relieves the
programmer or class designer from the burden of the boilerplate code needed
for the Visitor pattern, but is also flexible enough to directly work with
built-in types.  It naturally distinguishes between sequences of different
lengths, which might all share the same class despite obviously differing
structures.  Moreover, pattern matching automatically takes inheritance
into account: a class *D* inheriting from *C* will be handled by a pattern
that targets *C* by default.

Object oriented programming is geared towards single-dispatch: it is a
single instance (or the type thereof) that determines which method is to
be called.  This leads to a somewhat artificial situation in case of binary
operators where both objects might play an equal role in deciding which
implementation to use (Python addresses this through the use of reversed
binary methods).  Pattern matching is structurally better suited to handle
such situations of multi-dispatch, where the action to be taken depends on
the types of several objects to equal parts.


Patterns and Functional Style
-----------------------------

Many Python applications and libraries are not written in a consistent
OO style -- unlike Java, Python encourages defining functions at the
top-level of a module, and for simple data structures, tuples (or
named tuples or lists) and dictionaries are often used exclusively or
mixed with classes or data classes.

Pattern matching is particularly suitable for picking apart such data
structures.  As an extreme example, it's easy to write code that picks
a JSON data structure using ``match``::

  match json_pet:
      case {"type": "cat", "name": name, "pattern": pattern}:
          return Cat(name, pattern)
      case {"type": "dog", "name": name, "breed": breed):
          return Dog(name, breed)
      case _:
          raise ValueError("Not an suitable pet")

Functional programming generally prefers a declarative style with a focus
on relationships in data.  Side effects are avoided whenever possible.
Pattern matching thus naturally fits and highly supports functional
programming style.


Rationale
=========

This section provides the rationale for individual design decisions.
It takes the place of "Rejected ideas" in the standard PEP format.
It is organized in sections corresponding to the specification (PEP 634).


Overview and Terminology
------------------------

Much of the power of pattern matching comes from the nesting of subpatterns.
That the success of a pattern match depends directly on the success of
subpattern is thus a cornerstone of the design.  However, although a
pattern like ``P(Q(), R())`` succeeds only if both subpatterns ``Q()``
and ``R()`` succeed (i.e. the success of pattern ``P`` depends on ``Q``
and ``R``), the pattern ``P`` is checked first.  If ``P`` fails, neither
``Q()`` nor ``R()`` will be tried (this is a direct consequence of the
fact that if ``P`` fails, there are no subjects to match against ``Q()``
and ``R()`` in the first place).

Also note that patterns bind names to values rather than performing an
assignment.  This reflects the fact that patterns aim to not have side
effects, which also means that Capture or AS patterns cannot assign a
value to an attribute or subscript.  We thus consistently use the term
'bind' instead of 'assign' to emphasise this subtle difference between
traditional assignments and name binding in patterns.


The Match Statement
-------------------

The match statement evaluates an expression to produce a subject, finds the
first pattern that matches the subject, and executes the associated block
of code.  Syntactically, the match statement thus takes an expression and
a sequence of case clauses, where each case clause comprises a pattern and
a block of code.

Since case clauses comprise a block of code, they adhere to the existing
indentation scheme with the syntactic structure of
``<keyword> ...: <(indented) block>``, which resembles a compound
statement.  The keyword ``case`` reflects its widespread use in
pattern matching languages, ignoring those languages that use other
syntactic means such as a symbol like ``|``, because it would not fit
established Python structures.  The syntax of patterns following the
keyword is discussed below.

Given that the case clauses follow the structure of a compound statement,
the match statement itself naturally becomes a compound statement itself
as well, following the same syntactic structure.  This naturally leads to
``match <expr>: <case_clause>+``.  Note that the match statement determines
a quasi-scope in which the evaluated subject is kept alive (although not in
a local variable), similar to how a with statement might keep a resource
alive during execution of its block.  Furthermore, control flows from the
match statement to a case clause and then leaves the block of the match
statement.  The block of the match statement thus has both syntactic and
semantic meaning.

Various suggestions have sought to eliminate or avoid the naturally arising
"double indentation" of a case clause's code block.  Unfortunately, all such
proposals of *flat indentation schemes* come at the expense of violating
Python's established structural paradigm, leading to additional syntactic
rules:

- *Unindented case clauses.*
  The idea is to align case clauses with the ``match``, i.e.::

    match expression:
    case pattern_1:
        ...
    case pattern_2:
        ...

  This may look awkward to the eye of a Python programmer, because
  everywhere else a colon is followed by an indent.  The ``match`` would
  neither follow the syntactic scheme of simple nor composite statements
  but rather establish a category of its own.

- *Putting the expression on a separate line after "match".*
  The idea is to use the expression yielding the subject as a statement
  to avoid the singularity of ``match`` having no actual block despite
  the colons::

    match:
        expression
    case pattern_1:
        ...
    case pattern_2:
        ...

  This was ultimately rejected because the first block would be another
  novelty in Python's grammar: a block whose only content is a single
  expression rather than a sequence of statements.  Attempts to amend this
  issue by adding or repurposing yet another keyword along the lines of
  ``match: return expression`` did not yield any satisfactory solution.

Although flat indentation would save some horizontal space, the cost of
increased complexity or unusual rules is too high.  It would also complicate
life for simple-minded code editors. Finally, the horizontal space issue can
be alleviated by allowing "half-indent" (i.e. two spaces instead of four)
for match statements (though we do not recommend this).

In sample programs using ``match``, written as part of the development of this
PEP, a noticeable improvement in code brevity is observed, more than making
up for the additional indentation level.


*Statement vs. Expression.*  Some suggestions centered around the idea of
making ``match`` an expression rather than a statement.  However, this
would fit poorly with Python's statement-oriented nature and lead to
unusually long and complex expressions and the need to invent new
syntactic constructs or break well established syntactic rules.  An
obvious consequence of ``match`` as an expression would be that case
clauses could no longer have arbitrary blocks of code attached, but only
a single expression.  Overall, the strong limitations could in no way
offset the slight simplification in some special use cases.


*Hard vs. Soft Keyword.*  There were options to make match a hard keyword,
or choose a different keyword. Although using a hard keyword would simplify
life for simple-minded syntax highlighters, we decided not to use hard
keyword for several reasons:

- Most importantly, the new parser doesn't require us to do this. Unlike
  with ``async`` that caused hardships with being a soft keyword for few
  releases, here we can make ``match`` a permanent soft keyword.

- ``match`` is so commonly used in existing code, that it would break
  almost every existing program and will put a burden to fix code on many
  people who may not even benefit from the new syntax.

- It is hard to find an alternative keyword that would not be commonly used
  in existing programs as an identifier, and would still clearly reflect the
  meaning of the statement.


**Use "as" or "|" instead of "case" for case clauses.**
The pattern matching proposed here is a combination of multi-branch control
flow (in line with ``switch`` in Algol-derived languages or ``cond`` in Lisp)
and object-deconstruction as found in functional languages.  While the proposed
keyword ``case`` highlights the multi-branch aspect, alternative keywords such
as ``as`` would equally be possible, highlighting the deconstruction aspect.
``as`` or ``with``, for instance, also have the advantage of already being
keywords in Python.  However, since ``case`` as a keyword can only occur as a
leading keyword inside  a ``match`` statement, it is easy for a parser to
distinguish between its use as a keyword or as a variable.

Other variants would use a symbol like ``|`` or ``=>``, or go entirely without
special marker.

Since Python is a statement-oriented language in the tradition of Algol, and as
each composite statement starts with an identifying keyword, ``case`` seemed to
be most in line with Python's style and traditions.


Match Semantics
~~~~~~~~~~~~~~~

The patterns of different case clauses might overlap in that more than
one case clause would match a given subject.  The first-to-match rule
ensures that the selection of a case clause for a given subject is
unambiguous.  Furthermore, case clauses can have increasingly general
patterns matching wider sets of subjects.  The first-to-match rule
then ensures that the most precise pattern can be chosen (although it
is the programmer's responsibility to order the case clauses correctly).

In a statically typed language, the match statement would be compiled to
a decision tree to select a matching pattern quickly and very efficiently.
This would, however, require that all patterns be purely declarative and
static, running against the established dynamic semantics of Python.  The
proposed semantics thus represent a path incorporating the best of both
worlds: patterns are tried in a strictly sequential order so that each
case clause constitutes an actual statement.  At the same time, we allow
the interpreter to cache any information about the subject or change the
order in which subpatterns are tried.  In other words: if the interpreter
has found that the subject is not an instance of a class ``C``, it can
directly skip case clauses testing for this again, without having to
perform repeated instance-checks.  If a guard stipulates that a variable
``x`` must be positive, say (i.e. ``if x > 0``), the interpreter might
check this directly after binding ``x`` and before any further
subpatterns are considered.


*Binding and scoping.*  In many pattern matching implementations, each
case clause would establish a separate scope of its own.  Variables bound
by a pattern would then only be visible inside the corresponding case block.
In Python, however, this does not make sense.  Establishing separate scopes
would essentially mean that each case clause is a separate function without
direct access to the variables in the surrounding scope (without having to
resort to ``nonlocal`` that is).  Moreover, a case clause could no longer
influence any surrounding control flow through standard statement such as
``return`` or ``break``.  Hence, such strict scoping would lead to
unintuitive and surprising behavior.

A direct consequence of this is that any variable bindings outlive the
respective case or match statements.  Even patterns that only match a
subject partially might bind local variables (this is, in fact, necessary
for guards to function properly).  However, these semantics for variable
binding are in line with existing Python structures such as for loops and
with statements.


Guards
~~~~~~

Some constraints cannot be adequately expressed through patterns alone.
For instance, a 'less' or 'greater than' relationship defies the usual
'equal' semantics of patterns.  Moreover, different subpatterns are
independent and cannot refer to each other.  The addition of *guards*
addresses these restrictions: a guard is an arbitrary expression attached
to a pattern and that must evaluate to a "truthy" value for the pattern to succeed.

For example, ``case [x, y] if x < y:`` uses a guard (``if x < y``) to
express a 'less than' relationship between two otherwise disjoint capture
patterns ``x`` and ``y``.

From a conceptual point of view, patterns describe structural constraints
on the subject in a declarative style, ideally without any side-effects.
Recall, in particular, that patterns are clearly distinct from expressions,
following different objectives and semantics.  Guards then enhance case
blocks in a highly controlled way with arbitrary expressions (that might
have side effects).  Splitting the overall functionality into a static structural
and a dynamically evaluated part not only helps with readability, but can
also introduce dramatic potential for compiler optimizations.  To keep this
clear separation, guards are only supported on the level of case clauses
and not for individual patterns.

**Example** using guards::

  def sort(seq):
      match seq:
          case [] | [_]:
              return seq
          case [x, y] if x <= y:
              return seq
          case [x, y]:
              return [y, x]
          case [x, y, z] if x <= y <= z:
              return seq
          case [x, y, z] if x >= y >= z:
              return [z, y, x]
          case [p, *rest]:
              a = sort([x for x in rest if x <= p])
              b = sort([x for x in rest if p < x])
              return a + [p] + b


.. _patterns:

Patterns
--------

Patterns fulfill two purposes: they impose (structural) constraints on
the subject and they specify which data values should be extracted from
the subject and bound to variables.  In iterable unpacking, which can be
seen as a prototype to pattern matching in Python, there is only one
*structural pattern* to express sequences while there is a rich set of
*binding patterns* to assign a value to a specific variable or field.
Full pattern matching differs from this in that there is more variety
in structural patterns but only a minimum of binding patterns.

Patterns differ from assignment targets (as in iterable unpacking) in two ways:
they impose additional constraints on the structure of the subject, and
a subject may safely fail to match a specific pattern at any point
(in iterable unpacking, this constitutes an error).  The latter means that
pattern should avoid side effects wherever possible.

This desire to avoid side effects is one reason why capture patterns
don't allow binding values to attributes or subscripts: if the
containing pattern were to fail in a later step, it would be hard to
revert such bindings.

A cornerstone of pattern matching is the possibility of arbitrarily
*nesting patterns*.  The nesting allows expressing deep
tree structures (for an example of nested class patterns, see the motivation
section above) as well as alternatives.

Although patterns might superficially look like expressions,
it is important to keep in mind that there is a clear distinction.  In fact,
no pattern is or contains an expression.  It is more productive to think of
patterns as declarative elements similar to the formal parameters in a
function definition.


AS Patterns
~~~~~~~~~~~

Patterns fall into two categories: most patterns impose a (structural)
constraint that the subject needs to fulfill, whereas the capture pattern
binds the subject to a name without regard for the subject's structure or
actual value.  Consequently, a pattern can either express a constraint or
bind a value, but not both.  AS patterns fill this gap in that they
allow the user to specify a general pattern as well as capture the subject
in a variable.

Typical use cases for the AS pattern include OR and Class patterns
together with a binding name as in, e.g., ``case BinOp('+'|'-' as op, ...):``
or ``case [int() as first, int() as second]:``.  The latter could be
understood as saying that the subject must fulfil two distinct pattern:
``[first, second]`` as well as ``[int(), int()]``.  The AS pattern
can thus be seen as a special case of an 'and' pattern (see OR patterns
below for an additional discussion of 'and' patterns).

In an earlier version, the AS pattern was devised as a 'Walrus pattern',
written as ``case [first:=int(), second:=int()]``.  However, using ``as``
offers some advantages over ``:=``:

- The walrus operator ``:=`` is used to capture the result of an expression
  on the right hand side, whereas ``as`` generally indicates some form of
  'processing' as in ``import foo as bar`` or ``except E as err:``.  Indeed,
  the pattern ``P as x`` does not assign the pattern ``P`` to ``x``, but
  rather the subject that successfully matches ``P``.

- ``as`` allows for a more consistent data flow from left to right (the
  attributes in Class patterns also follow a left-to-right data flow).

- The walrus operator looks very similar to the syntax for matching attributes in the Class pattern,
  potentially leading to some confusion.

**Example** using the AS pattern::

  def simplify_expr(tokens):
      match tokens:
          case [('('|'[') as l, *expr, (')'|']') as r] if (l+r) in ('()', '[]'):
              return simplify_expr(expr)
          case [0, ('+'|'-') as op, right]:
              return UnaryOp(op, right)
          case [(int() | float() as left) | Num(left), '+', (int() | float() as right) | Num(right)]:
              return Num(left + right)
          case [(int() | float()) as value]:
              return Num(value)


OR Patterns
~~~~~~~~~~~

The OR pattern allows you to combine 'structurally equivalent' alternatives
into a new pattern, i.e. several patterns can share a common handler.  If any
of an OR pattern's subpatterns matches the subject, the entire OR
pattern succeeds.

Statically typed languages prohibit the binding of names (capture patterns)
inside an OR pattern because of potential conflicts concerning the types of
variables.  As a dynamically typed language, Python can be less restrictive
here and allow capture patterns inside OR patterns.  However, each subpattern
must bind the same set of variables so as not to leave potentially undefined
names.  With two alternatives ``P | Q``, this means that if *P* binds the
variables *u* and *v*, *Q* must bind exactly the same variables *u* and *v*.

There was some discussion on whether to use the bar symbol ``|`` or the ``or``
keyword to separate alternatives.  The OR pattern does not fully fit
the existing semantics and usage of either of these two symbols.  However,
``|`` is the symbol of choice in all programming languages with support of
the OR pattern and is used in that capacity for regular expressions in
Python as well.  It is also the traditional separator between alternatives
in formal grammars (including Python's).
Moreover, ``|`` is not only used for bitwise OR, but also
for set unions and dict merging (:pep:`584`).

Other alternatives were considered as well, but none of these would allow
OR-patterns to be nested inside other patterns:

- *Using a comma*::

    case 401, 403, 404:
        print("Some HTTP error")

  This looks too much like a tuple -- we would have to find a different way
  to spell tuples, and the construct would have to be parenthesized inside
  the argument list of a class pattern. In general, commas already have many
  different meanings in Python, we shouldn't add more.

- *Using stacked cases*::

    case 401:
    case 403:
    case 404:
        print("Some HTTP error")

  This is how this would be done in *C*, using its fall-through semantics
  for cases. However, we don't want to mislead people into thinking that
  match/case uses fall-through semantics (which are a common source of bugs
  in *C*). Also, this would be a novel indentation pattern, which might make
  it harder to support in IDEs and such (it would break the simple rule "add
  an indentation level after a line ending in a colon").  Finally, this
  would not support OR patterns nested inside other patterns, either.

- *Using "case in" followed by a comma-separated list*::

    case in 401, 403, 404:
        print("Some HTTP error")

  This would not work for OR patterns nested inside other patterns, like::

    case Point(0|1, 0|1):
        print("A corner of the unit square")


**AND and NOT Patterns**

Since this proposal defines an OR-pattern (``|``) to match one of several alternates,
why not also an AND-pattern (``&``) or even a NOT-pattern (``!``)?
Especially given that some other languages (``F#`` for example) support
AND-patterns.

However, it is not clear how useful this would be. The semantics for matching
dictionaries, objects and sequences already incorporates an implicit 'and':
all attributes and elements mentioned must be present for the match to
succeed. Guard conditions can also support many of the use cases that a
hypothetical 'and' operator would be used for.

A negation of a match pattern using the operator ``!`` as a prefix
would match exactly if the pattern itself does not match.  For
instance, ``!(3 | 4)`` would match anything except ``3`` or ``4``.
However, there is `evidence from other languages
<https://dl.acm.org/doi/abs/10.1145/2480360.2384582>`_ that this is
rarely useful, and primarily used as double negation ``!!`` to control
variable scopes and prevent variable bindings (which does not apply to
Python).  Other use cases are better expressed using guards.

In the end, it was decided that this would make the syntax more complex
without adding a significant benefit.  It can always be added later.

**Example** using the OR pattern::

  def simplify(expr):
      match expr:
          case ('/', 0, 0):
              return expr
          case ('*'|'/', 0, _):
              return 0
          case ('+'|'-', x, 0) | ('+', 0, x) | ('*', 1, x) | ('*'|'/', x, 1):
              return x
      return expr


.. _literal_pattern:

Literal Patterns
~~~~~~~~~~~~~~~~

Literal patterns are a convenient way for imposing constraints on the
value of a subject, rather than its type or structure.  They also
allow you to emulate a switch statement using pattern matching.

Generally, the subject is compared to a literal pattern by means of standard
equality (``x == y`` in Python syntax).  Consequently, the literal patterns
``1.0`` and ``1`` match exactly the same set of objects, i.e. ``case 1.0:``
and ``case 1:`` are fully interchangeable.  In principle, ``True`` would also
match the same set of objects because ``True == 1`` holds.  However, we
believe that many users would be surprised finding that ``case True:``
matched the subject ``1.0``, resulting in some subtle bugs and convoluted
workarounds.  We therefore adopted the rule that the three singleton
patterns ``None``, ``False`` and ``True`` match by identity (``x is y`` in
Python syntax) rather than equality.  Hence, ``case True:`` will match only
``True`` and nothing else.  Note that ``case 1:`` would still match ``True``,
though, because the literal pattern ``1`` works by equality and not identity.

Early ideas to induce a hierarchy on numbers so that ``case 1.0`` would
match both the integer ``1`` and the floating point number ``1.0``, whereas
``case 1:`` would only match the integer ``1`` were eventually dropped in
favor of the simpler and more consistent rule based on equality.  Moreover, any
additional checks whether the subject is an instance of ``numbers.Integral``
would come at a high runtime cost to introduce what would essentially be
a novel idea in Python.  When needed, the explicit syntax ``case int(1):`` can
be used.

Recall that literal patterns are *not* expressions, but directly
denote a specific value.  From a pragmatic point of view, we want to
allow using negative and even complex values as literal patterns, but
they are not atomic literals (only unsigned real and imaginary numbers
are).  E.g., ``-3+4j`` is syntactically an expression of the form
``BinOp(UnaryOp('-', 3), '+', 4j)``.  Since expressions are not part
of patterns, we had to add explicit syntactic support for such values
without having to resort to full expressions.

Interpolated *f*-strings, on the
other hand, are not literal values, despite their appearance and can
therefore not be used as literal patterns (string concatenation, however,
is supported).

Literal patterns not only occur as patterns in their own right, but also
as keys in *mapping patterns*.


**Range matching patterns.**
This would allow patterns such as ``1...6``. However, there are a host of
ambiguities:

* Is the range open, half-open, or closed? (I.e. is ``6`` included in the
  above example or not?)
* Does the range match a single number, or a range object?
* Range matching is often used for character ranges ('a'...'z') but that
  won't work in Python since there's no character data type, just strings.
* Range matching can be a significant performance optimization if you can
  pre-build a jump table, but that's not generally possible in Python due
  to the fact that names can be dynamically rebound.

Rather than creating a special-case syntax for ranges, it was decided
that allowing custom pattern objects (``InRange(0, 6)``) would be more flexible
and less ambiguous; however those ideas have been postponed for the time
being.


**Example** using Literal patterns::

  def simplify(expr):
      match expr:
          case ('+', 0, x):
              return x
          case ('+' | '-', x, 0):
              return x
          case ('and', True, x):
              return x
          case ('and', False, x):
              return False
          case ('or', False, x):
              return x
          case ('or', True, x):
              return True
          case ('not', ('not', x)):
              return x
      return expr


.. _capture_pattern:

Capture Patterns
~~~~~~~~~~~~~~~~

Capture patterns take on the form of a name that accepts any value and binds
it to a (local) variable (unless the name is declared as ``nonlocal`` or
``global``).  In that sense, a capture pattern is similar
to a parameter in a function definition (when the function is called, each
parameter binds the respective argument to a local variable in the function's
scope).

A name used for a capture pattern must not coincide with another capture
pattern in the same pattern.  This, again, is similar to parameters, which
equally require each parameter name to be unique within the list of
parameters.  It differs, however, from iterable unpacking assignment, where
the repeated use of a variable name as target is permissible (e.g.,
``x, x = 1, 2``).  The rationale for not supporting ``(x, x)`` in patterns
is its ambiguous reading: it could be seen as in iterable unpacking where
only the second binding to ``x`` survives.  But it could be equally seen as
expressing a tuple with two equal elements (which comes with its own issues).
Should the need arise, then it is still possible to introduce support for
repeated use of names later on.

There were calls to explicitly mark capture patterns and thus identify them
as binding targets.  According to that idea, a capture pattern would be
written as, e.g. ``?x``, ``$x`` or ``=x``.  The aim of such explicit capture
markers is to let an unmarked name be a value pattern (see below).
However, this is based on the misconception that pattern matching was an
extension of *switch* statements, placing the emphasis on fast switching based
on (ordinal) values.  Such a *switch* statement has indeed been proposed for
Python before (see :pep:`275` and :pep:`3103`).  Pattern matching, on the other
hand, builds a generalized concept of iterable unpacking.  Binding values
extracted from a data structure is at the very core of the concept and hence
the most common use case.  Explicit markers for capture patterns would thus
betray the objective of the proposed pattern matching syntax and simplify
a secondary use case at the expense of additional syntactic clutter for
core cases.

It has been proposed that capture patterns are not needed at all,
since the equivalent effect can be obtained by combining a AS
pattern with a wildcard pattern (e.g., ``case _ as x`` is equivalent
to ``case x``).  However, this would be unpleasantly verbose,
especially given that we expect capture patterns to be very common.

**Example** using Capture patterns::

  def average(*args):
      match args:
          case [x, y]:           # captures the two elements of a sequence
              return (x + y) / 2
          case [x]:              # captures the only element of a sequence
              return x
          case []:
              return 0
          case a:                # captures the entire sequence
              return sum(a) / len(a)


.. _wildcard_pattern:

Wildcard Pattern
~~~~~~~~~~~~~~~~

The wildcard pattern is a special case of a 'capture' pattern: it accepts
any value, but does not bind it to a variable.  The idea behind this rule
is to support repeated use of the wildcard in patterns.  While ``(x, x)``
is an error, ``(_, _)`` is legal.

Particularly in larger (sequence) patterns, it is important to allow the
pattern to concentrate on values with actual significance while ignoring
anything else.  Without a wildcard, it would become necessary to 'invent'
a number of local variables, which would be bound but never used.  Even
when sticking to naming conventions and using e.g. ``_1, _2, _3`` to name
irrelevant values, say, this still introduces visual clutter and can hurt
performance (compare the sequence pattern ``(x, y, *z)`` to ``(_, y, *_)``,
where the ``*z`` forces the interpreter to copy a potentially very long
sequence, whereas the second version simply compiles to code along the
lines of ``y = seq[1]``).

There has been much discussion about the choice of the underscore as ``_``
as a wildcard pattern, i.e. making this one name non-binding.  However, the
underscore is already heavily used as an 'ignore value' marker in iterable
unpacking.  Since the wildcard pattern ``_`` never binds, this use of the
underscore does not interfere with other uses such as inside the REPL or
the ``gettext`` module.

It has been proposed to use ``...`` (i.e., the ellipsis token) or ``*``
(star) as a wildcard.  However, both these look as if an arbitrary number
of items is omitted::

  case [a, ..., z]: ...
  case [a, *, z]: ...

Either example looks like it would match a sequence of two or more
items, capturing the first and last values.  While that may be the
ultimate "wildcard", it does not convey the desired semantics.

An alternative that does not suggest an arbitrary number of items
would be ``?``.  This is even being proposed independently from
pattern matching in PEP 640.  We feel however that using ``?`` as a
special "assignment" target is likely more confusing to Python users
than using ``_``.  It violates Python's (admittedly vague) principle
of using punctuation characters only in ways similar to how they are
used in common English usage or in high school math, unless the usage
is *very* well established in other programming languages (like, e.g.,
using a dot for member access).

The question mark fails on both counts: its use in other programming
languages is a grab-bag of usages only vaguely suggested by the idea
of a "question".  For example, it means "any character" in shell
globbing, "maybe" in regular expressions, "conditional expression" in
C and many C-derived languages, "predicate function" in Scheme,
"modify error handling" in Rust, "optional argument" and "optional
chaining" in TypeScript (the latter meaning has also been proposed for
Python by PEP 505).  An as yet unnamed PEP proposes it to mark
optional types, e.g. ``int?``.

Another common use of ``?`` in programming systems is "help", for
example, in IPython and Jupyter Notebooks and many interactive
command-line utilities.

In addition, this would put Python in a rather unique position:
The underscore is as a wildcard pattern in *every*
programming language with pattern matching that we could find
(including *C#*, *Elixir*, *Erlang*, *F#*, *Grace*, *Haskell*,
*Mathematica*, *OCaml*, *Ruby*, *Rust*, *Scala*, *Swift*, and *Thorn*).
Keeping in mind that many users of Python also work with other programming
languages, have prior experience when learning Python, and may move on to
other languages after having learned Python, we find that such
well-established standards are important and relevant with respect to
readability and learnability.  In our view, concerns that this wildcard
means that a regular name received special treatment are not strong
enough to introduce syntax that would make Python special.

*Else blocks.*  A case block without a guard whose pattern is a single
wildcard (i.e., ``case _:``) accepts any subject without binding it to
a variable or performing any other operation.  It is thus semantically
equivalent to ``else:``, if it were supported.  However, adding such
an else block to the match statement syntax would not remove the need
for the wildcard pattern in other contexts.  Another argument against
this is that there would be two plausible indentation levels for an
else block: aligned with ``case`` or aligned with ``match``.  The
authors have found it quite contentious which indentation level to
prefer.

**Example** using the Wildcard pattern::

  def is_closed(sequence):
      match sequence:
          case [_]:               # any sequence with a single element
              return True
          case [start, *_, end]:  # a sequence with at least two elements
              return start == end
          case _:                 # anything
              return False


.. _value_pattern:

Value Patterns
~~~~~~~~~~~~~~

It is good programming style to use named constants for parametric values or
to clarify the meaning of particular values.  Clearly, it would be preferable
to write ``case (HttpStatus.OK, body):`` over
``case (200, body):``, for example.  The main issue that arises here is how to
distinguish capture patterns (variable bindings) from value patterns.  The
general discussion surrounding this issue has brought forward a plethora of
options, which we cannot all fully list here.

Strictly speaking, value patterns are not really necessary, but
could be implemented using guards, i.e.
``case (status, body) if status == HttpStatus.OK:``.  Nonetheless, the
convenience of value patterns is unquestioned and obvious.

The observation that constants tend to be written in uppercase letters or
collected in enumeration-like namespaces suggests possible rules to discern
constants syntactically.  However, the idea of using upper- vs. lowercase as
a marker has been met with scepticism since there is no similar precedence
in core Python (although it is common in other languages).  We therefore only
adopted the rule that any dotted name (i.e., attribute access) is to be
interpreted as a value pattern, for example ``HttpStatus.OK``
above.  This precludes, in particular, local variables and global
variables defined in the current module from acting as constants.

A proposed rule to use a leading dot (e.g.
``.CONSTANT``) for that purpose was criticised because it was felt that the
dot would not be a visible-enough marker for that purpose.  Partly inspired
by forms found in other programming languages, a number of different
markers/sigils were proposed (such as ``^CONSTANT``, ``$CONSTANT``,
``==CONSTANT``, ``CONSTANT?``, or the word enclosed in backticks), although
there was no obvious or natural choice.  The current proposal therefore
leaves the discussion and possible introduction of such a 'constant' marker
for a future PEP.

Distinguishing the semantics of names based on whether it is a global
variable (i.e. the compiler would treat global variables as constants rather
than capture patterns) leads to various issues.  The addition or alteration
of a global variable in the module could have unintended side effects on
patterns.  Moreover, pattern matching could not be used directly inside a
module's scope because all variables would be global, making capture
patterns impossible.

**Example** using the Value pattern::

  def handle_reply(reply):
      match reply:
          case (HttpStatus.OK, MimeType.TEXT, body):
              process_text(body)
          case (HttpStatus.OK, MimeType.APPL_ZIP, body):
              text = deflate(body)
              process_text(text)
          case (HttpStatus.MOVED_PERMANENTLY, new_URI):
              resend_request(new_URI)
          case (HttpStatus.NOT_FOUND):
              raise ResourceNotFound()

:pep:`642` proposes using ``?`` as a prefix for *constraint patterns*: arbitrary
expressions that replace the value and literal patterns defined here.  The PEP
is motivated by a desire to "treat match patterns as a variation on assignment
targets".

We believe that attempting to unify the grammars of assignment targets and
patterns is attractive, but misguided.  Evidence of this is PEP 642's need to
introduce new syntax (which *neither* assignments nor our proposal requires) as
a best attempt to unify them.  In contrast, consider function parameters and
iterable unpacking: while they are certainly similar, they each have key
syntactic incompatibilities that reflect their different purposes.

It is also not clear from our research that there is need for value patterns to
contain arbitrary expressions.  Any such dynamic elements can be easily
expressed using one or more capture patterns together with a guard.  Having a
clear separation between static and dynamic elements of patterns is a benefit,
not a drawback [1]_.

There are deeper issues as well.  Even if the grammars for both assignments and
patterns are made "consistent" with one another, strings, byte-strings,
mappings, sequences, and iterators will all behave differently in both contexts.
This leaves us in a worse situation: one where the *grammar* is consistent, but
the *behavior* differs in meaningful ways.

The proposed syntax (prefixing arbitrary expressions with ``?``) is also quite
ugly and distracting, harming readability.  (Our issues with using ``?`` as a
wildcard symbol here have already been enumerated above.)


Group Patterns
~~~~~~~~~~~~~~

Allowing users to explicitly specify the grouping is particularly helpful
in case of OR patterns.


.. _sequence_pattern:

Sequence Patterns
~~~~~~~~~~~~~~~~~

Sequence patterns follow as closely as possible the already established
syntax and semantics of iterable unpacking.  Of course, subpatterns take
the place of assignment targets (variables, attributes and subscript).
Moreover, the sequence pattern only matches a carefully selected set of
possible subjects, whereas iterable unpacking can be applied to any
iterable.

- As in iterable unpacking, we do not distinguish between 'tuple' and
  'list' notation.  ``[a, b, c]``, ``(a, b, c)`` and ``a, b, c`` are all
  equivalent.  While this means we have a redundant notation and checking
  specifically for lists or tuples requires more effort (e.g.
  ``case list([a, b, c])``), we mimic iterable unpacking as much as
  possible.

- A starred pattern will capture a sub-sequence of arbitrary length,
  again mirroring iterable unpacking.  Only one starred item may be
  present in any sequence pattern.  In theory, patterns such as ``(*_, 3, *_)``
  could be understood as expressing any sequence containing the value ``3``.
  In practice, however, this would only work for a very narrow set of use
  cases and lead to inefficient backtracking or even ambiguities otherwise.

- The sequence pattern does *not* iterate through an iterable subject.  All
  elements are accessed through subscripting and slicing, and the subject must
  be an instance of ``collections.abc.Sequence``.  This includes, of course,
  lists and tuples, but excludes e.g. sets and dictionaries.  While it would
  include strings and bytes, we make an exception for these (see below).

A sequence pattern cannot just iterate through any iterable object.  The
consumption of elements from the iteration would have to be undone if the
overall pattern fails, which is not feasible.

To identify sequences we cannot rely on ``len()`` and subscripting and
slicing alone, because sequences share these protocols with mappings
(e.g. `dict`) in this regard.  It would be surprising if a sequence
pattern also matched a dictionaries or other objects implementing
the mapping protocol (i.e. ``__getitem__``).  The interpreter therefore
performs an instance check to ensure that the subject in question really
is a sequence (of known type).  (As an optimization of the most common
case, if the subject is exactly a list or a tuple, the instance check
can be skipped.)

String and bytes objects have a dual nature: they are both 'atomic' objects
in their own right, as well as sequences (with a strongly recursive nature
in that a string is a sequence of strings).  The typical behavior and use
cases for strings and bytes are different enough from those of tuples and
lists to warrant a clear distinction.  It is in fact often unintuitive and
unintended that strings pass for sequences, as evidenced by regular questions
and complaints.  Strings and bytes are therefore not matched by a sequence
pattern, limiting the sequence pattern to a very specific understanding of
'sequence'.  The built-in ``bytearray`` type, being a mutable version of
``bytes``, also deserves an exception; but we don't intend to
enumerate all other types that may be used to represent bytes
(e.g. some, but not all, instances of ``memoryview`` and ``array.array``).


.. _mapping_pattern:

Mapping Patterns
~~~~~~~~~~~~~~~~

Dictionaries or mappings in general are one of the most important and most
widely used data structures in Python.  In contrast to sequences, mappings
are built for fast direct access to arbitrary elements identified by a key.
In most cases an element is retrieved from a dictionary by a known key
without regard for any ordering or other key-value pairs stored in the same
dictionary.  Particularly common are string keys.

The mapping pattern reflects the common usage of dictionary lookup: it allows
the user to extract some values from a mapping by means of constant/known
keys and have the values match given subpatterns.  Moreover, the mapping
pattern does not check for the presence of additional keys.  Should it be
necessary to impose an upper bound on the mapping and ensure that no
additional keys are present, then the usual double-star-pattern ``**rest``
can be used.  The special case ``**_`` with a wildcard, however, is not
supported as it would not have any effect, but might lead to an incorrect
understanding of the mapping pattern's semantics.

To avoid overly expensive matching algorithms, keys must be literals or
value patterns.

There is a subtle reason for using ``get(key, default)`` instead of
``__getitem__(key)`` followed by a check for ``AttributeError``: if
the subject happens to be a ``defaultdict``, calling ``__getitem__``
for a non-existent key would add the key.  Using ``get()`` avoids this
unexpected side effect.

**Example** using the Mapping pattern::

  def change_red_to_blue(json_obj):
      match json_obj:
          case { 'color': ('red' | '#FF0000') }:
              json_obj['color'] = 'blue'
          case { 'children': children }:
              for child in children:
                  change_red_to_blue(child)


.. _class_pattern:

Class Patterns
~~~~~~~~~~~~~~

Class patterns fulfill two purposes: checking whether a given subject is
indeed an instance of a specific class, and extracting data from specific
attributes of the subject.  Anecdotal evidence revealed that ``isinstance()``
is one of the most often used functions in Python in terms of
static occurrences in programs.  Such instance checks typically precede
a subsequent access to information stored in the object, or a possible
manipulation thereof.  A typical pattern might be along the lines of::

  def traverse_tree(node):
      if isinstance(node, Node):
          traverse_tree(node.left)
          traverse_tree(node.right)
      elif isinstance(node, Leaf):
          print(node.value)

In many cases class patterns occur nested, as in the example
given in the motivation::

  if (isinstance(node, BinOp) and node.op == "+"
          and isinstance(node.right, BinOp) and node.right.op == "*"):
      a, b, c = node.left, node.right.left, node.right.right
      # Handle a + b*c

The class pattern lets you concisely specify both an instance check
and relevant attributes (with possible further constraints).  It is
thereby very tempting to write, e.g., ``case Node(left, right):`` in the
first case above and ``case Leaf(value):`` in the second.  While this
indeed works well for languages with strict algebraic data types, it is
problematic with the structure of Python objects.

When dealing with general Python objects, we face a potentially very large
number of unordered attributes: an instance of ``Node`` contains a large
number of attributes (most of which are 'special methods' such as
``__repr__``).  Moreover, the interpreter cannot reliably deduce the
ordering of attributes.  For an object that
represents a circle, say, there is no inherently obvious ordering of the
attributes ``x``, ``y`` and ``radius``.

We envision two possibilities for dealing with this issue: either explicitly
name the attributes of interest, or provide an additional mapping that tells
the interpreter which attributes to extract and in which order.  Both
approaches are supported.  Moreover, explicitly naming the attributes of
interest lets you further specify the required structure of an object; if
an object lacks an attribute specified by the pattern, the match fails.

- Attributes that are explicitly named pick up the syntax of named arguments.
  If an object of class ``Node`` has two attributes ``left`` and ``right``
  as above, the pattern ``Node(left=x, right=y)`` will extract the values of
  both attributes and assign them to ``x`` and ``y``, respectively.  The data
  flow from left to right seems unusual, but is in line with mapping patterns
  and has precedents such as assignments via ``as`` in *with*- or
  *import*-statements (and indeed AS patterns).

  Naming the attributes in question explicitly will be mostly used for more
  complex cases where the positional form (below) is insufficient.

- The class field ``__match_args__`` specifies a number of attributes
  together with their ordering, allowing class patterns to rely on positional
  sub-patterns without having to explicitly name the attributes in question.
  This is particularly handy for smaller objects or instances of data classes,
  where the attributes of interest are rather obvious and often have a
  well-defined ordering.  In a way, ``__match_args__`` is similar to the
  declaration of formal parameters, which allows calling functions with
  positional arguments rather than naming all the parameters.

  This is a class attribute, because it needs to be looked up on the class
  named in the class pattern, not on the subject instance.


The syntax of class patterns is based on the idea that de-construction
mirrors the syntax of construction.  This is already the case in virtually
any Python construct, be assignment targets, function definitions or
iterable unpacking.  In all these cases, we find that the syntax for
sending and that for receiving 'data' are virtually identical.

- Assignment targets such as variables, attributes and subscripts:
  ``foo.bar[2] = foo.bar[3]``;

- Function definitions: a function defined with ``def foo(x, y, z=6)``
  is called as, e.g., ``foo(123, y=45)``, where the actual arguments
  provided at the call site are matched against the formal parameters
  at the definition site;

- Iterable unpacking: ``a, b = b, a`` or ``[a, b] = [b, a]`` or
  ``(a, b) = (b, a)``, just to name a few equivalent possibilities.

Using the same syntax for reading and writing, l- and r-values, or
construction and de-construction is widely accepted for its benefits in
thinking about data, its flow and manipulation.  This equally extends to
the explicit construction of instances, where class patterns ``C(p, q)``
deliberately mirror the syntax of creating instances.

The special case for the built-in classes ``bool``, ``bytearray``
etc. (where e.g. ``str(x)`` captures the subject value in ``x``) can
be emulated by a user-defined class as follows::

  class MyClass:
      __match_args__ = ["__myself__"]
      __myself__ = property(lambda self: self)


**Type annotations for pattern variables.**
The proposal was to combine patterns with type annotations::

  match x:
      case [a: int, b: str]: print(f"An int {a} and a string {b}:)
      case [a: int, b: int, c: int]: print("Three ints", a, b, c)
      ...

This idea has a lot of problems.  For one, the colon can only
be used inside of brackets or parentheses, otherwise the syntax becomes
ambiguous.  And because Python disallows ``isinstance()`` checks
on generic types, type annotations containing generics will not
work as expected.


History and Context
===================

Pattern matching emerged in the late 1970s in the form of tuple unpacking
and as a means to handle recursive data structures such as linked lists or
trees (object-oriented languages usually use the visitor pattern for handling
recursive data structures).  The early proponents of pattern matching
organised structured data in 'tagged tuples' rather than ``struct`` as in
*C* or the objects introduced later.  A node in a binary tree would, for
instance, be a tuple with two elements for the left and right branches,
respectively, and a ``Node`` tag, written as ``Node(left, right)``.  In
Python we would probably put the tag inside the tuple as
``('Node', left, right)`` or define a data class `Node` to achieve the
same effect.

Using modern syntax, a depth-first tree traversal would then be written as
follows::

  def traverse(node):
      node match:
          case Node(left, right):
              traverse(left)
              traverse(right)
          case Leaf(value):
              handle(value)

The notion of handling recursive data structures with pattern matching
immediately gave rise to the idea of handling more general recursive
'patterns' (i.e. recursion beyond recursive data structures)
with pattern matching.  Pattern matching would thus also be used to define
recursive functions such as::

  def fib(arg):
      match arg:
          case 0:
              return 1
          case 1:
              return 1
          case n:
              return fib(n-1) + fib(n-2)

As pattern matching was repeatedly integrated into new and emerging
programming languages, its syntax slightly evolved and expanded.  The two
first cases in the ``fib`` example above could be written more succinctly
as ``case 0 | 1:`` with ``|`` denoting alternative patterns.  Moreover, the
underscore ``_`` was widely adopted as a wildcard, a filler where neither
the structure nor value of parts of a pattern were of substance.  Since the
underscore is already frequently used in equivalent capacity in Python's
iterable unpacking (e.g., ``_, _, third, _* = something``) we kept these
universal standards.

It is noteworthy that the concept of pattern matching has always been
closely linked to the concept of functions.  The different case clauses
have always been considered as something like semi-independent functions
where pattern variables take on the role of parameters.  This becomes
most apparent when pattern matching is written as an overloaded function,
along the lines of (Standard ML)::

  fun fib 0 = 1
    | fib 1 = 1
    | fib n = fib (n-1) + fib (n-2)

Even though such a strict separation of case clauses into independent
functions does not apply in Python, we find that patterns share many
syntactic rules with parameters, such as binding arguments to unqualified
names only or that variable/parameter names must not be repeated for
a particular pattern/function.

With its emphasis on abstraction and encapsulation, object-oriented
programming posed a serious challenge to pattern matching.  In short: in
object-oriented programming, we can no longer view objects as tagged tuples.
The arguments passed into the constructor do not necessarily specify the
attributes or fields of the objects.  Moreover, there is no longer a strict
ordering of an object's fields and some of the fields might be private and
thus inaccessible.  And on top of this, the given object might actually be
an instance of a subclass with slightly different structure.

To address this challenge, patterns became increasingly independent of the
original tuple constructors.  In a pattern like ``Node(left, right)``,
``Node`` is no longer a passive tag, but rather a function that can actively
check for any given object whether it has the right structure and extract a
``left`` and ``right`` field.  In other words: the ``Node``-tag becomes a
function that transforms an object into a tuple or returns some failure
indicator if it is not possible.

In Python, we simply use ``isinstance()`` together with the ``__match_args__``
field of a class to check whether an object has the correct structure and
then transform some of its attributes into a tuple.  For the `Node` example
above, for instance, we would have ``__match_args__ = ('left', 'right')`` to
indicate that these two attributes should be extracted to form the tuple.
That is, ``case Node(x, y)`` would first check whether a given object is an
instance of ``Node`` and then assign ``left`` to ``x`` and ``right`` to ``y``,
respectively.

Paying tribute to Python's dynamic nature with 'duck typing', however, we
also added a more direct way to specify the presence of, or constraints on
specific attributes.  Instead of ``Node(x, y)`` you could also write
``object(left=x, right=y)``, effectively eliminating the ``isinstance()``
check and thus supporting any object with ``left`` and ``right`` attributes.
Or you would combine these ideas to write ``Node(right=y)`` so as to require
an instance of ``Node`` but only extract the value of the `right` attribute.


Backwards Compatibility
=======================

Through its use of "soft keywords" and the new PEG parser (PEP 617),
the proposal remains fully backwards compatible.  However, 3rd party
tooling that uses a LL(1) parser to parse Python source code may be
forced to switch parser technology to be able to support those same
features.


Security Implications
=====================

We do not expect any security implications from this language feature.


Reference Implementation
========================

A `feature-complete CPython implementation
<https://github.com/brandtbucher/cpython/tree/patma>`_ is available on
GitHub.

An `interactive playground
<https://mybinder.org/v2/gh/gvanrossum/patma/master?urlpath=lab/tree/playground-622.ipynb>`_
based on the above implementation was created using Binder [2]_ and Jupyter [3]_.


References
==========

.. [1] Kohn et al., Dynamic Pattern Matching with Python
   https://doi.org/10.1145/3426422.3426983
   (Accepted by DLS 2020.  The link will go live after Nov. 17;
   a preview PDF can be obtained from the first author.)

.. [2] Binder
   https://mybinder.org

.. [3] Jupyter
   https://jupyter.org


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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