When developing macros enable -Xcheck-macros scalac option flag to have extra runtime checks.

Macros: Quotes and Splices

Macros are built on two well-known fundamental operations: quotation and splicing. Quotation is expressed as '{...} for expressions and splicing is expressed as ${ ... }. Additionally, within a quote or a splice we can quote or splice identifiers directly (i.e. 'e and $e). Readers may notice the resemblance of the two aforementioned syntactic schemes with the familiar string interpolation syntax.

println(s"Hello, $name, here is the result of 1 + 1 = ${1 + 1}")

In string interpolation we quoted a string and then we spliced into it, two others. The first, name, is a reference to a value of type String, and the second is an arithmetic expression that will be evaluated followed by the splicing of its string representation.

Quotes and splices in this section allow us to treat code in a similar way, effectively supporting macros. The entry point for macros is an inline method with a top-level splice. We call it a top-level because it is the only occasion where we encounter a splice outside a quote (consider as a quote the compilation-unit at the call-site). For example, the code below presents an inline method assert which calls at compile-time a method assertImpl with a boolean expression tree as argument. assertImpl evaluates the expression and prints it again in an error message if it evaluates to false.

import scala.quoted.*

inline def assert(inline expr: Boolean): Unit =
   ${ assertImpl('expr) }

def assertImpl(expr: Expr[Boolean])(using Quotes) = '{
   if !$expr then
      throw AssertionError(s"failed assertion: ${${ showExpr(expr) }}")

def showExpr(expr: Expr[Boolean])(using Quotes): Expr[String] =
   '{ "<some source code>" } // Better implementation later in this document

If e is an expression, then '{e} represents the typed abstract syntax tree representing e. If T is a type, then Type.of[T] represents the type structure representing T. The precise definitions of "typed abstract syntax tree" or "type-structure" do not matter for now, the terms are used only to give some intuition. Conversely, ${e} evaluates the expression e, which must yield a typed abstract syntax tree or type structure, and embeds the result as an expression (respectively, type) in the enclosing program.

Quotations can have spliced parts in them; in this case the embedded splices are evaluated and embedded as part of the formation of the quotation.

Quotes and splices can also be applied directly to identifiers. An identifier $x starting with a $ that appears inside a quoted expression or type is treated as a splice ${x}. Analogously, an quoted identifier 'x that appears inside a splice is treated as a quote '{x}. See the Syntax section below for details.

Quotes and splices are duals of each other. For arbitrary expressions e we have:

${'{e}} = e
'{${e}} = e

Types for Quotations

The type signatures of quotes and splices can be described using two fundamental types:

  • Expr[T]: abstract syntax trees representing expressions of type T
  • Type[T]: non erased representation of type T.

Quoting takes expressions of type T to expressions of type Expr[T] and it takes types T to expressions of type Type[T]. Splicing takes expressions of type Expr[T] to expressions of type T and it takes expressions of type Type[T] to types T.

The two types can be defined in package scala.quoted as follows:

package scala.quoted

sealed trait Expr[+T]
sealed trait Type[T]

Both Expr and Type are abstract and sealed, so all constructors for these types are provided by the system. One way to construct values of these types is by quoting, the other is by type-specific lifting operations that will be discussed later on.

The Phase Consistency Principle

A fundamental phase consistency principle (PCP) regulates accesses to free variables in quoted and spliced code:

  • For any free variable reference x, the number of quoted scopes and the number of spliced scopes between the reference to x and the definition of x must be equal.

Here, this-references count as free variables. On the other hand, we assume that all imports are fully expanded and that _root_ is not a free variable. So references to global definitions are allowed everywhere.

The phase consistency principle can be motivated as follows: First, suppose the result of a program P is some quoted text '{ ... x ... } that refers to a free variable x in P. This can be represented only by referring to the original variable x. Hence, the result of the program will need to persist the program state itself as one of its parts. We don’t want to do this, hence this situation should be made illegal. Dually, suppose a top-level part of a program is a spliced text ${ ... x ... } that refers to a free variable x in P. This would mean that we refer during construction of P to a value that is available only during execution of P. This is of course impossible and therefore needs to be ruled out. Now, the small-step evaluation of a program will reduce quotes and splices in equal measure using the cancellation rules above. But it will neither create nor remove quotes or splices individually. So the PCP ensures that program elaboration will lead to neither of the two unwanted situations described above.

In what concerns the range of features it covers, this form of macros introduces a principled metaprogramming framework that is quite close to the MetaML family of languages. One difference is that MetaML does not have an equivalent of the PCP - quoted code in MetaML can access variables in its immediately enclosing environment, with some restrictions and caveats since such accesses involve serialization. However, this does not constitute a fundamental gain in expressiveness.

From Exprs to Functions and Back

It is possible to convert any Expr[T => R] into Expr[T] => Expr[R] and back. These conversions can be implemented as follows:

def to[T: Type, R: Type](f: Expr[T] => Expr[R])(using Quotes): Expr[T => R] =
   '{ (x: T) => ${ f('x) } }

def from[T: Type, R: Type](f: Expr[T => R])(using Quotes): Expr[T] => Expr[R] =
   (x: Expr[T]) => '{ $f($x) }

Note how the fundamental phase consistency principle works in two different directions here for f and x. In the method to, the reference to f is legal because it is quoted, then spliced, whereas the reference to x is legal because it is spliced, then quoted.

They can be used as follows:

val f1: Expr[Int => String] =
   to((x: Expr[Int]) => '{ $x.toString }) // '{ (x: Int) => x.toString }

val f2: Expr[Int] => Expr[String] =
   from('{ (x: Int) => x.toString }) // (x: Expr[Int]) => '{ ((x: Int) => x.toString)($x) }
f2('{2}) // '{ ((x: Int) => x.toString)(2) }

One limitation of from is that it does not β-reduce when a lambda is called immediately, as evidenced in the code { ((x: Int) => x.toString)(2) }. In some cases we want to remove the lambda from the code, for this we provide the method Expr.betaReduce that turns a tree describing a function into a function mapping trees to trees.

object Expr:
   def betaReduce[...](...)(...): ... = ...

The definition of Expr.betaReduce(f)(x) is assumed to be functionally the same as '{($f)($x)}, however it should optimize this call by returning the result of beta-reducing f(x) if f is a known lambda expression. Expr.betaReduce distributes applications of Expr over function arrows:

Expr.betaReduce(_): Expr[(T1, ..., Tn) => R] => ((Expr[T1], ..., Expr[Tn]) => Expr[R])

Lifting Types

Types are not directly affected by the phase consistency principle. It is possible to use types defined at any level in any other level. But, if a type is used in a subsequent stage it will need to be lifted to a Type. The resulting value of Type will be subject to PCP. Indeed, the definition of to above uses T in the next stage, there is a quote but no splice between the parameter binding of T and its usage. But the code can be rewritten by adding a binding of a Type[T] tag:

def to[T, R](f: Expr[T] => Expr[R])(using Type[T], Type[R], Quotes): Expr[T => R] =
   '{ (x: T) => ${ f('x) } }

In this version of to, the type of x is now the result of splicing the Type value t. This operation is splice correct -- there is one quote and one splice between the use of t and its definition.

To avoid clutter, the Scala implementation tries to convert any type reference to a type T in subsequent phases to a type-splice, by rewriting T to summon[Type[T]].Underlying. For instance, the user-level definition of to:

def to[T, R](f: Expr[T] => Expr[R])(using t: Type[T], r: Type[R])(using Quotes): Expr[T => R] =
   '{ (x: T) => ${ f('x) } }

would be rewritten to

def to[T, R](f: Expr[T] => Expr[R])(using t: Type[T], r: Type[R])(using Quotes): Expr[T => R] =
   '{ (x: t.Underlying) => ${ f('x) } }

The summon query succeeds because there is a given instance of type Type[T] available (namely the given parameter corresponding to the context bound : Type), and the reference to that value is phase-correct. If that was not the case, the phase inconsistency for T would be reported as an error.

Lifting Expressions

Consider the following implementation of a staged interpreter that implements a compiler through staging.

import scala.quoted.*

enum Exp:
   case Num(n: Int)
   case Plus(e1: Exp, e2: Exp)
   case Var(x: String)
   case Let(x: String, e: Exp, in: Exp)

import Exp.*

The interpreted language consists of numbers Num, addition Plus, and variables Var which are bound by Let. Here are two sample expressions in the language:

val exp = Plus(Plus(Num(2), Var("x")), Num(4))
val letExp = Let("x", Num(3), exp)

Here’s a compiler that maps an expression given in the interpreted language to quoted Scala code of type Expr[Int]. The compiler takes an environment that maps variable names to Scala Exprs.

import scala.quoted.*

def compile(e: Exp, env: Map[String, Expr[Int]])(using Quotes): Expr[Int] =
   e match
      case Num(n) =>
      case Plus(e1, e2) =>
         '{ ${ compile(e1, env) } + ${ compile(e2, env) } }
      case Var(x) =>
      case Let(x, e, body) =>
         '{ val y = ${ compile(e, env) }; ${ compile(body, env + (x -> 'y)) } }

Running compile(letExp, Map()) would yield the following Scala code:

'{ val y = 3; (2 + y) + 4 }

The body of the first clause, case Num(n) => Expr(n), looks suspicious. n is declared as an Int, yet it is converted to an Expr[Int] with Expr(). Shouldn’t n be quoted? In fact this would not work since replacing n by 'n in the clause would not be phase correct.

The Expr.apply method is defined in package quoted:

package quoted

object Expr:
   def apply[T: ToExpr](x: T)(using Quotes): Expr[T] =

This method says that values of types implementing the ToExpr type class can be converted to Expr values using Expr.apply.

Scala 3 comes with given instances of ToExpr for several types including Boolean, String, and all primitive number types. For example, Int values can be converted to Expr[Int] values by wrapping the value in a Literal tree node. This makes use of the underlying tree representation in the compiler for efficiency. But the ToExpr instances are nevertheless not magic in the sense that they could all be defined in a user program without knowing anything about the representation of Expr trees. For instance, here is a possible instance of ToExpr[Boolean]:

given ToExpr[Boolean] with
   def toExpr(b: Boolean) =
      if b then '{ true } else '{ false }

Once we can lift bits, we can work our way up. For instance, here is a possible implementation of ToExpr[Int] that does not use the underlying tree machinery:

given ToExpr[Int] with
   def toExpr(n: Int) = n match
      case Int.MinValue    => '{ Int.MinValue }
      case _ if n < 0      => '{ - ${ toExpr(-n) } }
      case 0               => '{ 0 }
      case _ if n % 2 == 0 => '{ ${ toExpr(n / 2) } * 2 }
      case _               => '{ ${ toExpr(n / 2) } * 2 + 1 }

Since ToExpr is a type class, its instances can be conditional. For example, a List is liftable if its element type is:

given [T: ToExpr : Type]: ToExpr[List[T]] with
   def toExpr(xs: List[T]) = xs match
      case head :: tail => '{ ${ Expr(head) } :: ${ toExpr(tail) } }
      case Nil          => '{ Nil: List[T] }

In the end, ToExpr resembles very much a serialization framework. Like the latter it can be derived systematically for all collections, case classes and enums. Note also that the synthesis of type-tag values of type Type[T] is essentially the type-level analogue of lifting.

Using lifting, we can now give the missing definition of showExpr in the introductory example:

def showExpr[T](expr: Expr[T])(using Quotes): Expr[String] =
   val code: String =

That is, the showExpr method converts its Expr argument to a string (code), and lifts the result back to an Expr[String] using Expr.apply.

Lifting Types

The previous section has shown that the metaprogramming framework has to be able to take a type T and convert it to a type tree of type Type[T] that can be reified. This means that all free variables of the type tree refer to types and values defined in the current stage.

For a reference to a global class, this is easy: Just issue the fully qualified name of the class. Members of reifiable types are handled by just reifying the containing type together with the member name. But what to do for references to type parameters or local type definitions that are not defined in the current stage? Here, we cannot construct the Type[T] tree directly, so we need to get it from a recursive implicit search. For instance, to implement


where T is not defined in the current stage, we construct the type constructor of List applied to the splice of the result of searching for a given instance for Type[T]:

Type.of[ List[ summon[Type[T]].Underlying ] ]

This is exactly the algorithm that Scala 2 uses to search for type tags. In fact Scala 2's type tag feature can be understood as a more ad-hoc version of quoted.Type. As was the case for type tags, the implicit search for a quoted.Type is handled by the compiler, using the algorithm sketched above.

Relationship with inline

Seen by itself, principled metaprogramming looks more like a framework for runtime metaprogramming than one for compile-time metaprogramming with macros. But combined with Scala 3’s inline feature it can be turned into a compile-time system. The idea is that macro elaboration can be understood as a combination of a macro library and a quoted program. For instance, here’s the assert macro again together with a program that calls assert.

object Macros:

   inline def assert(inline expr: Boolean): Unit =
      ${ assertImpl('expr) }

   def assertImpl(expr: Expr[Boolean])(using Quotes) =
      val failMsg: Expr[String] = Expr("failed assertion: " +
      '{ if !($expr) then throw new AssertionError($failMsg) }

@main def program =
   val x = 1
   Macros.assert(x != 0)

Inlining the assert function would give the following program:

@main def program =
   val x = 1
   ${ Macros.assertImpl('{ x != 0) } }

The example is only phase correct because Macros is a global value and as such not subject to phase consistency checking. Conceptually that’s a bit unsatisfactory. If the PCP is so fundamental, it should be applicable without the global value exception. But in the example as given this does not hold since both assert and program call assertImpl with a splice but no quote.

However, one could argue that the example is really missing an important aspect: The macro library has to be compiled in a phase prior to the program using it, but in the code above, macro and program are defined together. A more accurate view of macros would be to have the user program be in a phase after the macro definitions, reflecting the fact that macros have to be defined and compiled before they are used. Hence, conceptually the program part should be treated by the compiler as if it was quoted:

@main def program = '{
   val x = 1
   ${ Macros.assertImpl('{ x != 0 }) }

If program is treated as a quoted expression, the call to Macro.assertImpl becomes phase correct even if macro library and program are conceptualized as local definitions.

But what about the call from assert to assertImpl? Here, we need a tweak of the typing rules. An inline function such as assert that contains a splice operation outside an enclosing quote is called a macro. Macros are supposed to be expanded in a subsequent phase, i.e. in a quoted context. Therefore, they are also type checked as if they were in a quoted context. For instance, the definition of assert is typechecked as if it appeared inside quotes. This makes the call from assert to assertImpl phase-correct, even if we assume that both definitions are local.

The inline modifier is used to declare a val that is either a constant or is a parameter that will be a constant when instantiated. This aspect is also important for macro expansion.

To get values out of expressions containing constants Expr provides the method value (or valueOrError). This will convert the Expr[T] into a Some[T] (or T) when the expression contains value. Otherwise it will retrun None (or emit an error). To avoid having incidental val bindings generated by the inlining of the def it is recommended to use an inline parameter. To illustrate this, consider an implementation of the power function that makes use of a statically known exponent:

inline def power(x: Double, inline n: Int) = ${ powerCode('x, 'n) }

private def powerCode(x: Expr[Double], n: Expr[Int])(using Quotes): Expr[Double] =
   n.value match
      case Some(m) => powerCode(x, m)
      case None => '{ Math.pow($x, $n.toDouble) }

private def powerCode(x: Expr[Double], n: Int)(using Quotes): Expr[Double] =
   if n == 0 then '{ 1.0 }
   else if n == 1 then x
   else if n % 2 == 0 then '{ val y = $x * $x; ${ powerCode('y, n / 2) } }
   else '{ $x * ${ powerCode(x, n - 1) } }

Scope Extrusion

Quotes and splices are duals as far as the PCP is concerned. But there is an additional restriction that needs to be imposed on splices to guarantee soundness: code in splices must be free of side effects. The restriction prevents code like this:

var x: Expr[T] = ...
'{ (y: T) => ${ x = 'y; 1 } }

This code, if it was accepted, would extrude a reference to a quoted variable y from its scope. This would subsequently allow access to a variable outside the scope where it is defined, which is likely problematic. The code is clearly phase consistent, so we cannot use PCP to rule it out. Instead, we postulate a future effect system that can guarantee that splices are pure. In the absence of such a system we simply demand that spliced expressions are pure by convention, and allow for undefined compiler behavior if they are not. This is analogous to the status of pattern guards in Scala, which are also required, but not verified, to be pure.

Multi-Stage Programming introduces one additional method where you can expand code at runtime with a method run. There is also a problem with that invocation of run in splices. Consider the following expression:

'{ (x: Int) => ${ run('x); 1 } }

This is again phase correct, but will lead us into trouble. Indeed, evaluating the splice will reduce the expression run('x) to x. But then the result

'{ (x: Int) => ${ x; 1 } }

is no longer phase correct. To prevent this soundness hole it seems easiest to classify run as a side-effecting operation. It would thus be prevented from appearing in splices. In a base language with side effects we would have to do this anyway: Since run runs arbitrary code it can always produce a side effect if the code it runs produces one.

Example Expansion

Assume we have two methods, one map that takes an Expr[Array[T]] and a function f and one sum that performs a sum by delegating to map.

object Macros:

   def map[T](arr: Expr[Array[T]], f: Expr[T] => Expr[Unit])
             (using Type[T], Quotes): Expr[Unit] = '{
      var i: Int = 0
      while i < ($arr).length do
         val element: T = ($arr)(i)
         i += 1

   def sum(arr: Expr[Array[Int]])(using Quotes): Expr[Int] = '{
      var sum = 0
      ${ map(arr, x => '{sum += $x}) }

   inline def sum_m(arr: Array[Int]): Int = ${sum('arr)}

end Macros

A call to sum_m(Array(1,2,3)) will first inline sum_m:

val arr: Array[Int] = Array.apply(1, [2,3 : Int]:Int*)

then it will splice sum:

val arr: Array[Int] = Array.apply(1, [2,3 : Int]:Int*)

var sum = 0
${ map('arr, x => '{sum += $x}) }

then it will inline map:

val arr: Array[Int] = Array.apply(1, [2,3 : Int]:Int*)

var sum = 0
val f = x => '{sum += $x}
${'arr, 'f)(Type.of[Int])}

then it will expand and splice inside quotes map:

val arr: Array[Int] = Array.apply(1, [2,3 : Int]:Int*)

var sum = 0
val f = x => '{sum += $x}
var i: Int = 0
while i < arr.length do
   val element: Int = (arr)(i)
   sum += element
   i += 1

Finally cleanups and dead code elimination:

val arr: Array[Int] = Array.apply(1, [2,3 : Int]:Int*)
var sum = 0
var i: Int = 0
while i < arr.length do
   val element: Int = arr(i)
   sum += element
   i += 1

Find implicits within a macro

Similarly to the summonFrom construct, it is possible to make implicit search available in a quote context. For this we simply provide scala.quoted.Expr.summon:

import scala.collection.immutable.{ TreeSet, HashSet }
inline def setFor[T]: Set[T] = ${ setForExpr[T] }

def setForExpr[T: Type](using Quotes): Expr[Set[T]] =
   Expr.summon[Ordering[T]] match
      case Some(ord) => '{ new TreeSet[T]()($ord) }
      case _ => '{ new HashSet[T] }

Relationship with Transparent Inline

Inline documents inlining. The code below introduces a transparent inline method that can calculate either a value of type Int or a value of type String.

transparent inline def defaultOf(inline str: String) =
   ${ defaultOfImpl('str) }

def defaultOfImpl(strExpr: Expr[String])(using Quotes): Expr[Any] =
   strExpr.valueOrError match
      case "int" => '{1}
      case "string" => '{"a"}

// in a separate file
val a: Int = defaultOf("int")
val b: String = defaultOf("string")

Defining a macro and using it in a single project

It is possible to define macros and use them in the same project as long as the implementation of the macros does not have run-time dependencies on code in the file where it is used. It might still have compile-time dependencies on types and quoted code that refers to the use-site file.

To provide this functionality Scala 3 provides a transparent compilation mode where files that try to expand a macro but fail because the macro has not been compiled yet are suspended. If there are any suspended files when the compilation ends, the compiler will automatically restart compilation of the suspended files using the output of the previous (partial) compilation as macro classpath. In case all files are suspended due to cyclic dependencies the compilation will fail with an error.

Pattern matching on quoted expressions

It is possible to deconstruct or extract values out of Expr using pattern matching.

scala.quoted contains objects that can help extracting values from Expr.

  • scala.quoted.Expr/scala.quoted.Exprs: matches an expression of a value (or list of values) and returns the value (or list of values).
  • scala.quoted.Const/scala.quoted.Consts: Same as Expr/Exprs but only works on primitive values.
  • scala.quoted.Varargs: matches an explicit sequence of expressions and returns them. These sequences are useful to get individual Expr[T] out of a varargs expression of type Expr[Seq[T]].

These could be used in the following way to optimize any call to sum that has statically known values.

inline def sum(inline args: Int*): Int = ${ sumExpr('args) }
private def sumExpr(argsExpr: Expr[Seq[Int]])(using Quotes): Expr[Int] =
   argsExpr match
      case Varargs(args @ Exprs(argValues)) =>
         // args is of type Seq[Expr[Int]]
         // argValues is of type Seq[Int]
         Expr(argValues.sum) // precompute result of sum
      case Varargs(argExprs) => // argExprs is of type Seq[Expr[Int]]
         val staticSum: Int =
         val dynamicSum: Seq[Expr[Int]] = argExprs.filter(_.value.isEmpty)
         dynamicSum.foldLeft(Expr(staticSum))((acc, arg) => '{ $acc + $arg })
      case _ =>
         '{ $argsExpr.sum }

Quoted patterns

Quoted pattens allow deconstructing complex code that contains a precise structure, types or methods. Patterns '{ ... } can be placed in any location where Scala expects a pattern.

For example

optimize {
   sum(sum(1, a, 2), 3, b)
} // should be optimized to 6 + a + b
def sum(args: Int*): Int = args.sum
inline def optimize(inline arg: Int): Int = ${ optimizeExpr('arg) }
private def optimizeExpr(body: Expr[Int])(using Quotes): Expr[Int] =
   body match
      // Match a call to sum without any arguments
      case '{ sum() } => Expr(0)
      // Match a call to sum with an argument $n of type Int.
      // n will be the Expr[Int] representing the argument.
      case '{ sum($n) } => n
      // Match a call to sum and extracts all its args in an `Expr[Seq[Int]]`
      case '{ sum(${Varargs(args)}: _*) } => sumExpr(args)
      case body => body

private def sumExpr(args1: Seq[Expr[Int]])(using Quotes): Expr[Int] =
   def flatSumArgs(arg: Expr[Int]): Seq[Expr[Int]] = arg match
      case '{ sum(${Varargs(subArgs)}: _*) } => subArgs.flatMap(flatSumArgs)
      case arg => Seq(arg)
   val args2 = args1.flatMap(flatSumArgs)
   val staticSum: Int =
   val dynamicSum: Seq[Expr[Int]] = args2.filter(_.value.isEmpty)
   dynamicSum.foldLeft(Expr(staticSum))((acc, arg) => '{ $acc + $arg })

Recovering precise types using patterns

Sometimes it is necessary to get a more precise type for an expression. This can be achieved using the following pattern match.

def f(expr: Expr[Any])(using Quotes) = expr match
   case '{ $x: t } =>
      // If the pattern match succeeds, then there is
      // some type `t` such that
      // - `x` is bound to a variable of type `Expr[t]`
      // - `t` is bound to a new type `t` and a given
      //   instance `Type[t]` is provided for it
      // That is, we have `x: Expr[t]` and `given Type[t]`,
      // for some (unknown) type `t`.

This might be used to then perform an implicit search as in:

extension (inline sc: StringContext)
   inline def showMe(inline args: Any*): String = ${ showMeExpr('sc, 'args) }

private def showMeExpr(sc: Expr[StringContext], argsExpr: Expr[Seq[Any]])(using Quotes): Expr[String] =
   argsExpr match
      case Varargs(argExprs) =>
         val argShowedExprs = {
            case '{ $arg: tp } =>
               Expr.summon[Show[tp]] match
                  case Some(showExpr) =>
                     '{ $$arg) }
                  case None =>
                     report.error(s"could not find implicit for ${[Show[tp]]}", arg); '{???}
         val newArgsExpr = Varargs(argShowedExprs)
         '{ $sc.s($newArgsExpr: _*) }
      case _ =>
         // `new StringContext(...).showMeExpr(args: _*)` not an explicit `showMeExpr"..."`
         report.error(s"Args must be explicit", argsExpr)

trait Show[-T]:
   def show(x: T): String

// in a different file
given Show[Boolean] with
   def show(b: Boolean) = "boolean!"


Open code patterns

Quoted pattern matching also provides higher-order patterns to match open terms. If a quoted term contains a definition, then the rest of the quote can refer to this definition.

   val x: Int = 4
   x * x

To match such a term we need to match the definition and the rest of the code, but we need to explicitly state that the rest of the code may refer to this definition.

case '{ val y: Int = $x; $body(y): Int } =>

Here $x will match any closed expression while $body(y) will match an expression that is closed under y. Then the subexpression of type Expr[Int] is bound to body as an Expr[Int => Int]. The extra argument represents the references to y. Usually this expression is used in combination with Expr.betaReduce to replace the extra argument.

inline def eval(inline e: Int): Int = ${ evalExpr('e) }

private def evalExpr(e: Expr[Int])(using Quotes): Expr[Int] = e match
   case '{ val y: Int = $x; $body(y): Int } =>
      // body: Expr[Int => Int] where the argument represents
      // references to y
   case '{ ($x: Int) * ($y: Int) } =>
      (x.value, y.value) match
         case (Some(a), Some(b)) => Expr(a * b)
         case _ => e
   case _ => e
eval { // expands to the code: (16: Int)
   val x: Int = 4
   x * x

We can also close over several bindings using $b(a1, a2, ..., an). To match an actual application we can use braces on the function part ${b}(a1, a2, ..., an).

More details

More details