PEP 635 – Structural Pattern Matching: Motivation and Rationale
- Author:
- Tobias Kohn <kohnt at tobiaskohn.ch>, Guido van Rossum <guido at python.org>
- BDFL-Delegate:
- Discussions-To:
- Python-Dev list
- Status:
- Final
- Type:
- Informational
- Created:
- 12-Sep-2020
- Python-Version:
- 3.10
- Post-History:
- 22-Oct-2020, 08-Feb-2021
- Resolution:
- Python-Committers message
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 likeisinstance(x, cls)
,hasattr(x, "attr")
,len(x) == n
or"key" in x
as guards to select an applicable block. The block can then assumex
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.
See a complete example.
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 a 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 makematch
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 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, whereasas
generally indicates some form of ‘processing’ as inimport foo as bar
orexcept E as err:
. Indeed, the patternP as x
does not assign the patternP
tox
, but rather the subject that successfully matchesP
. 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 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 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 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 an 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
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 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()
Group Patterns
Allowing users to explicitly specify the grouping is particularly helpful in case of OR patterns.
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)
anda, 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 value3
. 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 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.
Extra keys in the subject are ignored even if **rest
is not present.
This is different from sequence patterns, where extra items will cause a
match to fail. But mappings are actually different from sequences: they
have natural structural sub-typing behavior, i.e., passing a dictionary
with extra keys somewhere will likely just work.
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 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 attributesleft
andright
as above, the patternNode(left=x, right=y)
will extract the values of both attributes and assign them tox
andy
, respectively. The data flow from left to right seems unusual, but is in line with mapping patterns and has precedents such as assignments viaas
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):
match node:
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 is available on GitHub.
An interactive playground based on the above implementation was created using Binder [2] and Jupyter [3].
References
Copyright
This document is placed in the public domain or under the CC0-1.0-Universal license, whichever is more permissive.
Source: https://github.com/python/peps/blob/main/peps/pep-0635.rst
Last modified: 2024-07-24 22:56:04 GMT