Pattern Matching for Java -- Semantics

Gavin Bierman and Brian Goetz, September 2018

This document explores a possible direction for supporting pattern matching in the Java Language. This is an exploratory document only and does not constitute a plan for any specific feature in any specific version of the Java Language. This document also may reference other features under exploration; this is purely for illustrative purposes, and does not constitute any sort of plan or committment to deliver any of these features.

In a companion document, we outline the motivation for adding pattern matching to Java, the sorts of patterns that might be supported (constant patterns, type patterns, deconstruction patterns, etc) and the constructs that could support patterns ( instanceof , switch , and a pattern-bind statement.)

Pattern semantics

We first define what it means for a pattern to match a target, and then we will outline the interaction between pattern matching and pattern-aware language constructs. We define several categories of patterns:

The any pattern, denoted by _ ;

; The var pattern, denoted by var x ;

; Type patterns, denoted by T t ;

; Nullable type patterns, denoted by T? t ;

; Constant patterns, denoted by lexical literals or by names of constant variables (JLS 4.12.4) or enum constants;

Deconstruction patterns for a type T , denoted by T(P*) , where P* is a sequence of nested patterns.

Static type checking

In a pattern match, there is an operand (the thing we are trying to match against the pattern) and a pattern. The operand is an expression, so it has both a static and a dynamic type. Certain pattern matches can be rejected at compile time based on static types, such as:

String s = "Hello"; if (s instanceof Integer i) { ... }

The compiler knows the operand s is a String , and the type pattern Integer i only matches expressions of type Integer , and that both are final classes. So we can conclude the match cannot succeed, and can therefore reject this at compile time on the basis of static type checking (just as we reject an attempt to cast an Integer to a String .)

We define an applicability relation between a pattern and a type, which determines if the pattern is applicable to an operand of (static) type T . We define applicability as follows:

The any pattern and the var pattern are applicable to all types.

pattern are applicable to all types. The null constant pattern is applicable to all reference types.

constant pattern is applicable to all reference types. A numeric literal constant pattern n without a type suffix is applicable to any primitive type P to which n is assignable (within the numeric range of P ), and to P 's box type.

without a type suffix is applicable to any primitive type to which is assignable (within the numeric range of ), and to 's box type. Other constant patterns of primitive type P are applicable to P and to types U which are cast-convertible to P 's box type.

are applicable to and to types which are cast-convertible to 's box type. Constant patterns of reference type T are applicable to types U which are cast-convertible to T .

are applicable to types which are cast-convertible to . The type pattern P p for a primitive type P is applicable to P .

for a primitive type is applicable to . The type pattern T t and the nullable type pattern T? t for a reference type T , are applicable to types U which are cast-convertible to T .

and the nullable type pattern for a reference type , are applicable to types which are cast-convertible to . A deconstruction pattern D(...) , is applicable to types U which are cast convertible to D .

Generic type patterns are permitted (this is a relaxation of the current semantics of the instanceof operator, which requires that the type operand is reifiable.) However, when determining applicability involves cast conversions, the pattern is not applicable if the cast conversion would be unchecked. So it is allowable to say

List<Integer> list = ... if (list instanceof ArrayList<Integer> a) { ... }

but not

List<?> list = ... if (list instanceof ArrayList<String> a) { ... }

as the latter cast conversion would be unchecked.

If a pattern is not applicable to the static type of its operand (including if a cast conversion required for applicability would be unchecked), a compilation error results. For a deconstructor declared D(T*) (where T* are the types of the pattern variables), we further require a deconstruction pattern D(P*) have each Pi be applicable to the corresponding Ti .

It may appear we are being unnecessarily unfriendly to numeric constant patterns here, by not being more liberal about widening and boxing conversions. However, we wish to avoid situations where an Object operand is matched against a literal constant 0 ; one could mistakenly expect this to match all of Integer zero, Short zero, etc. Instead, when matching against broad operand types (which are necessarily reference types), we should be explicit and either use typed constants or use destructuring patterns on the box type, such as Integer(0) or Short(0) . We reserve the numeric literal patterns for matching primitives and their boxes only where there is no possible type ambiguity.

For numeric literal constants without type suffixes, when attempting to match against an operand of primitive type P or the box type for a primitive type P , then the constant is interpreted as being of type P . This means that we can speak of every constant pattern having an unambiguous type.

Matching

We define a matches relation between patterns and expressions as follows.

The any pattern and the var pattern match anything.

pattern match anything. The null constant pattern matches e if e == null .

constant pattern matches if . A primitive constant pattern c of type P matches e : P if c is equal to e , and matches e : T if e is an instance of P 's box type, and c equals unbox(e) . Equality is determined by the appropriate primitive == operator, except for float and double , where equality is determined by the semantics of Float::equals and Double::equals .

of type matches if is equal to , and matches if is an instance of 's box type, and equals . Equality is determined by the appropriate primitive operator, except for and , where equality is determined by the semantics of and . A reference constant pattern c of type T matches e if c.equals(e) .

of type matches if . A type pattern T t matches e if e instanceof T .

matches if . A nullable type pattern T? t matches e if e == null or e instanceof T .

matches if or . A deconstruction pattern D(Pi...) matches e if e instanceof T , and for all i, Pi matches the _i_th component extracted by D .

A pattern is nullable if it can match null; the any pattern, var patterns, the null constant pattern, and nullable type patterns are nullable. We say a pattern is total on a type T if it matches all values of type T .

Pattern variables

Some patterns define variables which will be bound to components extracted from the target if the match succeeds. These variables have types defined as follows:

For a type pattern T t or nullable type pattern T? t , the pattern variable t has type T .

or nullable type pattern , the pattern variable has type . For a pattern var x , the type of the pattern variable x is computed by type inference, where constraints are derived from the match operand, and, in the case of a nested var pattern, from the types declared in the corresponding extractor declaration.

In both cases, the pattern variable is initialized to the match operand (after casting to the appropriate type) when a successful match is made. Pattern variables are always final .

Pattern-aware constructs

Several constructs, such as instanceof , switch , and __let , are pattern-aware.

The syntax of instanceof is extended as follows:

<expression> instanceof <reifiable-type> <expression> instanceof <pattern>

The instanceof operator evaluates to false if the pattern operand is non-nullable and the expression operand is null .

Currently, switch only supports a limited range of operand types; when it becomes pattern aware, it can accept any operand type (but patterns are type checked for applicability with the operand type), and patterns may be used as case labels.

If none of the patterns in a switch is nullable, then a switch throws NullPointerException on entry if the expression operand is null.

A pattern bind statement, which for purposes of exposition we'll call __let , will unconditionally match the expression operand to the pattern.

__let <pattern> = <expression>; __let <pattern> = <expression> else <statement>;

In the simpler form (no else ), the pattern must be total on the type of the expression operand (excluding null for non-nullable patterns.) This allows us to write:

Point p; __let Point(var x, var y) = p; // can use x and y here

without having to explicitly write an else clause.

In the full form, partial patterns are allowed, and if the expression operand does not match the pattern, the else statement is executed. The else statement must terminate abruptly.

Scoping of pattern variables

Unlike traditional locals, which have "rectangular" scopes, the scope of a pattern variable is flow-sensitive. This ensures that it is in scope only where it would be definitely assigned.

To define the scoping semantics, we assign to each expression e a "true set" and a "false set" of bindings, denoted e.T and e.F , which are always disjoint. The following table shows the true and false sets for all expression forms, along with an "include" column, which tells us which bindings are in scope in which contexts.

Expression form T F Include x instanceof P bindings(P) (empty) x && y union(x.T,y.T) intersect(x.F,y.F) x.T in y x || y intersect(x.T,y.T) union(x.F,y.F) x.F in y ( x ) x.T x.F !x x.F x.T x ? y : z union( intersect(y.T,z.T), intersect(x.T,z.T), intersect(x.F,y.T)) union( intersect(y.F,z.F), intersect(x.T,z.F), intersect(x.F,y.F)) x.T in y

x.F in z others empty empty

In this table, union is a disjoint union (it is an error if the sets being unioned contain variables with the same name). For intersection, it is an error if any variables in the sets being intersected contain the same name but have different types.

For example, in the following:

if (x instanceof Foo(int y) && y > 0) { ... } if (!(x instanceof Foo(int y)) || y > 0) { ... }

the pattern variable y is in scope and DA where it is used, but in

if (x instanceof Foo(int y) || y > 0) { ... } if (!(x instanceof Foo(int y)) && y > 0) { ... }

the pattern variable y is not in scope, and hence this is an error. The rule about && is also what allows us to express equals() in terms of a pattern match:

public boolean equals(Object o) { return (o instanceof Point p) && p.x == x // p in scope here && p.y == y; // p in scope here }

Why would we declare a pattern variable to be not in scope where it is not defined, rather than simply defining it to be DU? This is so that binding names can be reused. Consider the following:

if (x instanceof Point p && p.x == 0) { ... } else if (x instanceof Point p && p.x == p.y) { ... }

If p were in scope for the whole of the statement containing the first instanceof , as would be implied by a traditional scope, then the second arm of the if-else chain would have to pick a different name for its pattern variable. With a simple if..else like this one, this might not seem like a big deal, but in a switch statement with dozens of clauses, this would indeed get annoying.

Further, we want to support merging of pattern bindings, as in:

if ((x instanceof BlueBox(int height) || x instanceof RedBox(int height)) && height > 10) { ... }

Since exactly one of the two bindings for height are in scope and DA in the last clause, we can merge these bindings. If we could not, we would have to restructure the code, likely with significant duplication, to achieve the same effect.

Scoping and statements

We have defined which expressions produce bindings, but we have not yet tied their scopes to statements. The obvious extension of the above rules to if statements would yield:

if (x instanceof Foo f) { // f is in scope here } else { // if is not in scope here }

But, what about this:

if (!(x instanceof Foo(var y, var z))) throw new NotFooException(); // Are y and z in scope here?

Because the body of the if always completes abruptly, it is as if the remainder of the scope was an implicit else block, and it would be desirable for y and z to be in scope (and DA) in the remainder of the scope. On the other hand, in this example:

if (!(x instanceof Foo(var y, var z))) System.out.println("not a Foo, saddenz"); // Are y and z in scope here?

If y and z were in scope after the if , they would definitely not be DA. And, as per the argument above about reuse, we only want bindings to be in scope where they are DA, so we can reuse the names elsewhere. We can accomplish this by incorporating additional results from the existing flow analysis into the scoping rules for pattern variables.

We define several additional predicates on statements: AA(x) is true when x always completes abruptly; NB(x) is true when x never completes abruptly because of break ; MF(x) is true when x may "fall through" into the following case label. (These are already computed by existing flow analysis.) We can now add in the effects of nonlocal control flow to our scoping rules:

Statement Include if (x) y else z; s; x.T in y

x.F in z

AA(y) && !AA(z) ? x.F in s

AA(z) && !AA(y) ? x.T in s

while (x) y; s; x.T in y

NB(y) ? x.F in s do { x } while (y); s; NB(x) ? y.F in s for (a; b; c) d; s; b.T in c

b.T in d

NB(d) ? b.F in s switch (e) {

case P: a;

case Q: b;

} bindings(P) in a

MF(a)

? intersection(bindings(P), bindings(Q)) in b

: bindings(Q) in b; let P = e;

else s;

t; e.T in t

With these rules, we are able to get the full desired scoping with awareness of whether we throw out of if blocks, break out of while loops, or fall out of case groups..

As mentioned already, the motivation for flow-sensitive scoping is so we can reuse pattern variable names when they are not in scope:

switch (e) { case RedBox(int height) -> System.out.printf("Red(%d)", height); case BlueBox(int height) -> System.out.printf("Blue(%d)", height); }

And we can even even merge pattern variables in switch fallthrough:

switch (e) { case RedBox(int height): System.out.println("It's red"); // fall through case Box(int height): System.out.println("It's a box of height: " height); }

While these rules may look complicated at first, the rules are derived strictly from the flow analysis rules (such as DA/DU) already in the language. So the result is that a pattern variable is in scope wherever it would be DA, and not in scope wherever it would not be DA. (In informal focus-testing with experienced Java programmers, we asked "is it reasonable to be able to use variable x here" for various examples, and there were no surprises, because they were already familiar with when a variable is guaranteed to have a value, and when not.)

Shadowing

Because the scoping of pattern bindings is not exactly the same as for local variables, we must describe the interaction between pattern bindings and other kinds of variables (locals, fields.)

To avoid confusion, it makes sense to adopt a strict "no shadowing" rule: pattern variables may not shadow local variables, fields, or other pattern variables, and similarly locals cannot shadow pattern variables. This avoids problems like:

class Swiss { String s; void cheese(Object o) { // pattern variable s "declared" here if (!(o instanceof String s)) { // But s not in scope here! // So s here would refer to the field } else { // And s here would refer to the pattern variable } }

Because pattern variable names are strictly local, we can always choose names that do not conflict with locals or fields in scope.

Nullability

Nullability is a complex topic, and one fraught with tradeoffs. We start with existing constraints: switch throws NullPointerException on entry if its operand is null ; instanceof treats null as not an instance of anything but does not throw. Source compatibility prevents us from changing these for code that is currently valid, but we also want to extend the semantics of these constructs in a non-surprising way. Along the way, we will encounter strong and diverse opinions about how null should be handled (ranging from "null is just another value" to "kill it dead, now, dead, now.") Our approach is to avoid picking winners and losers here, and to provide a set of primitives that can equally well support null-avoiding and null-tolerant coding styles.

Constraints

Unfortunately, a more nuanced story for null handling is needed than what we have now, in part because the current story scales poorly to nested patterns. If we have a class:

class Box<T> { private final T t; public Box(T t) { this.t = t; } public extractor Box(T t) { t = this.t; } }

The author of the class has decided that new Box(null) is an entirely reasonable value for this class; the language shouldn't second-guess this design choice. So it would be unreasonable to prevent Box(_) from matching Box(null) , for example; if we're matching "any box", then we should match any box.

We also have some constraints that come from the desire to have unsurprising semantics for control constructs. For example, for a switch that is free of "weird" control flow (i.e., fallthrough):

switch (e) { case P: A; case Q: B; default: C; }

this should be (to the extent possible) equivalent to, and therefore mechanically refactorable back and forth between, an if-else chain:

if (e instanceof P) { A } else if (e instanceof Q) { B } else { C }

Similarly, a switch on nested patterns:

switch (e) { case Foo(P): ... case Foo(Q): ... case Foo(_): ... }

should be "unrollable" to:

switch (e) { case Foo(var x): switch (x) { case P: ... case Q: ... case _: ... } }

Taken together, this means that there are at least some cases where it is reasonable to expect switch to deal with null operands without throwing NPE. (If Foo(_) should match Foo(null) , then unrollability demands _ should match null -- which means a switch containing a _ pattern should not throw on entry when the operand is null .)

Nulls and individual patterns

Our path for determining the semantics of various patterns with respect to null has been a fairly winding one. While its impractical to rehash the entire journey, let's look at some specific examples.

We initially liked the idea that a type pattern T t would match anything that is assignment-compatible to T , including null . But this runs into a few problems.

First, it means that refactoring between switch and instanceof is painful, because instanceof T t would not be consistent with instanceof T ; this was a warning sign. (Some might assume the problem here is that we're trying to generalize instanceof , but having a matches T t that behaves similarly but subtly differently from instanceof T is no better, as it has a similar cognitive load for users to deal with.)

Additionally, if T t were to match nulls, this would likely lead to unexpected NPEs. For example, it would be easy to forget that one can't safely use s in the following example:

if (x instanceof String s) printf("String of length %d%n", s.length());

If the type pattern String s matched null , this code would NPE in the body of the if , since we'd be dereferencing a null String reference. This would be a sharp edge that cuts over and over.

Further, having type patterns match nulls would result in surprising order dependency. If we have:

switch (box) { case Box(String s): ... case Box(Integer i): ... case Box(_): ... }

and type patterns matched null, the nulls would fall into the first case . Not only is this surprising, but its even more surprising that if we reordered the first two cases -- which surely look disjoint -- it would subtly change the behavior of the program, because they both match Box(null) .

So the conclusion is: type patterns T t should be have the same semantics as instanceof T .

On the other hand, there must be some way to match and destructure all boxes; asking users to partition boxes into null-containing and non-null-containing ones would be unworkable.

Intuitively, we'd like Box(var x) to match all boxes, even if the box holds a null , but this also runs afoul of another intuition -- that var patterns should simply be type-inferred type patterns, so that var x is merely a shorthand for writing some other type pattern.

Another candidate, that also is a near-miss, is to treat total patterns specially in a nested context; to have Box(Object o) match all boxes, even those that contain a null. This seems attractive when you look at typical switches over nested patterns; there are often some more specific patterns first, and then we fall into the most general Box pattern, Box(Object o) . But, this falls afoul of desiring that a switch with nested patterns neatly unroll into a nest of switches with non-nested patterns, and creates an "action at a distance" effect.

Nullable type patterns

The root cause of our wanderings here is that sometimes we want Object to mean non-null objects (as in instanceof ), and other times we want to use it as a catch-all that means "everything". The standard move in this situation is to split it into two locutions, so people can say what they mean explicitly.

To accomplish this, we introduce a nullable type pattern, T? t , which matches instances of T as well as null . (This does not mean we're introducing nullable types, but also doesn't foreclose on our ability to do so later.) So our inclusive chain of box-matching is now:

switch (box) { case Box(String s): ... case Box(Integer i): ... case Box(Object? o): ... }

and it is clear from the source that o might be null. We can think of Box(var x) as using type inference to find the maximal type that is permitted based on the pattern signature, and then inferring a nullable type pattern. So if given:

class StringBox { StringBox(String s) { ... } extractor StringBox(String s) { ... } }

then the pattern StringBox(var x) will be equivalent, after inference, to StringBox(String? x) .

Pattern dominance

We can impose a partial ordering on patterns, called dominance, that means that any value matched by a dominated pattern is also matched by the dominating pattern. We can use this ordering to reject dead switch arms (as we reject dead catch arms today.) Dominance is reflexive; P always dominates itself (or patterns equivalent to itself). Any subtyping conditions used in computing dominance is computed on raw types; type patterns for List<?> and List<String> are considered equivalent.

Examples of dominance include:

A constant pattern of type T is dominated by a type pattern for T .

is dominated by a type pattern for . A type pattern for T is dominated by the nullable type pattern for T .

is dominated by the nullable type pattern for . If T <: U , then a type pattern for T is dominated by a type pattern for U .

, then a type pattern for is dominated by a type pattern for . A deconstruction pattern T(P) is dominated by a type pattern for T . If T(P) is total on T , then the type pattern T t is also dominated by T(P) .

is dominated by a type pattern for . If is total on , then the type pattern is also dominated by . If T <: U , then a total deconstruction pattern T(P) is dominated by a total deconstruction pattern U(Q) .

, then a total deconstruction pattern is dominated by a total deconstruction pattern . If P is dominated by Q , then T(P) is dominated by T(Q) .

is dominated by , then is dominated by . null is dominated by any nullable type pattern.

is dominated by any nullable type pattern. All patterns are dominated by the "any" pattern _ and by var patterns.

It is a compile-time error to have a case label in a switch that cannot match any values. This includes patterns that are dominated by prior case labels, as well as case labels that are dominated by combinations of prior case labels -- such as a T? pattern that follows a nullable pattern and a T pattern.

The default case is special. For switches with reference operands, default effectively means case Object , in that it matches everything but null , and for switches with primitive operands, it effectively means case _ . For existing switches, the default clause need not be the last case (in fact, you can even fall out of a default into a labeled case!), but once we start enforcing dominance order, this will be confusing. So for switches that are not "classic" switches (operand is one of the currently supported types, and all cases are constant labels), default will be treated as either case Object or case _ , and the dominance order enforced. (For those who want default to match anything including null , that's easy: have a case null arm that falls into default , which renders the switch nullable, or have an explicit case Object? o or case _ arm.)

Open issues

Some open issues include: