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PEP 635 -- Structural Pattern Matching: Motivation and Rationale

PEP:635
Title: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 <python-dev at python.org>
Status:Draft
Type:Informational
Created:12-Sep-2020
Python-Version:3.10
Post-History:
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 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 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 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

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()

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 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 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 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 is available on GitHub.

An interactive playground based on the above implementation was created using Binder [2] and Jupyter [3].

References

[1](1, 2) 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
Source: https://github.com/python/peps/blob/master/pep-0635.rst