Type Class Derivation

Exact mechanism

In the following, when type arguments are enumerated and the first index evaluates to a larger value than the last, then there are actually no arguments, for example: A[T_2, ..., T_1] means A.

For a class/trait/object/enum DerivingType[T_1, ..., T_N] derives TC, a derived instance is created in DerivingType's companion object (or DerivingType itself if it is an object).

The general "shape" of the derived instance is as follows:

given [...](using ...): TC[ ... DerivingType[...] ... ] = TC.derived

TC.derived should be an expression that conforms to the expected type on the left, potentially elaborated using term and/or type inference.

Note: TC.derived is a normal access, therefore if there are multiple definitions of TC.derived, overloading resolution applies.

What the derived instance precisely looks like depends on the specifics of DerivingType and TC, we first examine TC:

TC takes 1 parameter F

Therefore TC is defined as TC[F[A_1, ..., A_K]] (TC[F] if K == 0) for some F. There are two further cases depending on the kinds of arguments:

F and all arguments of DerivingType have kind *

Note: K == 0 in this case.

The generated instance is then:

given [T_1: TC, ..., T_N: TC]: TC[DerivingType[T_1, ..., T_N]] = TC.derived

This is the most common case, and is the one that was highlighted in the introduction.

Note: The [T_i: TC, ...] introduces a (using TC[T_i], ...), more information in Context Bounds. This allows the derived member to access these evidences.

Note: If N == 0 the above means:

given TC[DerivingType] = TC.derived

For example, the class

case class Point(x: Int, y: Int) derives Ordering

generates the instance

object Point:
  ...
  given Ordering[Point] = Ordering.derived

F and DerivingType have parameters of matching kind on the right

This section covers cases where you can pair arguments of F and DerivingType starting from the right such that they have the same kinds pairwise, and all arguments of F or DerivingType (or both) are used up. F must also have at least one parameter.

The general shape will then be:

given [...]: TC[ [...] =>> DerivingType[...] ] = TC.derived

Where of course TC and DerivingType are applied to types of the correct kind.

To make this work, we split it into 3 cases:

If F and DerivingType take the same number of arguments (N == K):

given TC[DerivingType] = TC.derived
// simplified form of:
given TC[ [A_1, ..., A_K] =>> DerivingType[A_1, ..., A_K] ] = TC.derived

If DerivingType takes less arguments than F (N < K), we use only the rightmost parameters from the type lambda:

given TC[ [A_1, ..., A_K] =>> DerivingType[A_(K-N+1), ..., A_K] ] = TC.derived

// if DerivingType takes no arguments (N == 0), the above simplifies to:
given TC[ [A_1, ..., A_K] =>> DerivingType ] = TC.derived

If F takes less arguments than DerivingType (K < N), we fill in the remaining leftmost slots with type parameters of the given:

given [T_1, ... T_(N-K)]: TC[[A_1, ..., A_K] =>> DerivingType[T_1, ... T_(N-K), A_1, ..., A_K]] = TC.derived

TC is the CanEqual type class

We have therefore: DerivingType[T_1, ..., T_N] derives CanEqual.

Let U_1, ..., U_M be the parameters of DerivingType of kind *. (These are a subset of the T_is)

The generated instance is then:

given [T_1L, T_1R, ..., T_NL, T_NR]                            // every parameter of DerivingType twice
      (using CanEqual[U_1L, U_1R], ..., CanEqual[U_ML, U_MR]): // only parameters of DerivingType with kind *
        CanEqual[DerivingType[T_1L, ..., T_NL], DerivingType[T_1R, ..., T_NR]] = // again, every parameter
          CanEqual.derived

The bounds of T_is are handled correctly, for example: T_2 <: T_1 becomes T_2L <: T_1L.

For example, the class

class MyClass[A, G[_]](a: A, b: G[B]) derives CanEqual

generates the following given instance:

object MyClass:
  ...
  given [A_L, A_R, G_L[_], G_R[_]](using CanEqual[A_L, A_R]): CanEqual[MyClass[A_L, G_L], MyClass[A_R, G_R]] = CanEqual.derived

TC is not valid for automatic derivation

Throw an error.

The exact error depends on which of the above conditions failed. As an example, if TC takes more than 1 parameter and is not CanEqual, the error is DerivingType cannot be unified with the type argument of TC.

All data types can have a derives clause. The rest of this document focuses primarily on data types which also have a given instance of the Mirror type class available.

Mirror

scala.deriving.Mirror type class instances provide information at the type level about the components and labelling of the type. They also provide minimal term level infrastructure to allow higher level libraries to provide comprehensive derivation support.

Instances of the Mirror type class are generated automatically by the compiler unconditionally for:

• enums and enum cases,
• case objects.

Instances for Mirror are also generated conditionally for:

• case classes where the constructor is visible at the callsite (always true if the companion is not a case object)
• sealed classes and sealed traits where:
  • there exists at least one child case,
  • each child case is reachable from the parent's definition,
  • if the sealed trait/class has no companion, then each child case is reachable from the callsite through the prefix of the type being mirrored,
  • and where the compiler can generate a Mirror type class instance for each child case.

The scala.deriving.Mirror type class definition is as follows:

sealed trait Mirror:

  /** the type being mirrored */
  type MirroredType

  /** the type of the elements of the mirrored type */
  type MirroredElemTypes

  /** The mirrored *-type */
  type MirroredMonoType

  /** The name of the type */
  type MirroredLabel <: String

  /** The names of the elements of the type */
  type MirroredElemLabels <: Tuple

object Mirror:

  /** The Mirror for a product type */
  trait Product extends Mirror:

    /** Create a new instance of type `T` with elements
     *  taken from product `p`.
     */
    def fromProduct(p: scala.Product): MirroredMonoType

  trait Sum extends Mirror:

    /** The ordinal number of the case class of `x`.
     *  For enums, `ordinal(x) == x.ordinal`
     */
    def ordinal(x: MirroredMonoType): Int

end Mirror

Product types (i.e. case classes and objects, and enum cases) have mirrors which are subtypes of Mirror.Product. Sum types (i.e. sealed class or traits with product children, and enums) have mirrors which are subtypes of Mirror.Sum.

For the Tree ADT from above the following Mirror instances will be automatically provided by the compiler,

// Mirror for Tree
new Mirror.Sum:
  type MirroredType = Tree
  type MirroredElemTypes[T] = (Branch[T], Leaf[T])
  type MirroredMonoType = Tree[_]
  type MirroredLabel = "Tree"
  type MirroredElemLabels = ("Branch", "Leaf")

  def ordinal(x: MirroredMonoType): Int = x match
    case _: Branch[_] => 0
    case _: Leaf[_] => 1

// Mirror for Branch
new Mirror.Product:
  type MirroredType = Branch
  type MirroredElemTypes[T] = (Tree[T], Tree[T])
  type MirroredMonoType = Branch[_]
  type MirroredLabel = "Branch"
  type MirroredElemLabels = ("left", "right")

  def fromProduct(p: Product): MirroredMonoType =
    new Branch(...)

// Mirror for Leaf
new Mirror.Product:
  type MirroredType = Leaf
  type MirroredElemTypes[T] = Tuple1[T]
  type MirroredMonoType = Leaf[_]
  type MirroredLabel = "Leaf"
  type MirroredElemLabels = Tuple1["elem"]

  def fromProduct(p: Product): MirroredMonoType =
    new Leaf(...)

If a Mirror cannot be generated automatically for a given type, an error will appear explaining why it is neither a supported sum type nor a product type. For example, if A is a trait that is not sealed,

No given instance of type deriving.Mirror.Of[A] was found for parameter x of method summon in object Predef. Failed to synthesize an instance of type deriving.Mirror.Of[A]:
     * trait A is not a generic product because it is not a case class
     * trait A is not a generic sum because it is not a sealed trait

Note the following properties of Mirror types,

• Properties are encoded using types rather than terms. This means that they have no runtime footprint unless used and also that they are a compile time feature for use with Scala 3's metaprogramming facilities.
• There is no restriction against the mirrored type being a local or inner class.
• The kinds of MirroredType and MirroredElemTypes match the kind of the data type the mirror is an instance for. This allows Mirrors to support ADTs of all kinds.
• There is no distinct representation type for sums or products (ie. there is no HList or Coproduct type as in Scala 2 versions of Shapeless). Instead the collection of child types of a data type is represented by an ordinary, possibly parameterized, tuple type. Scala 3's metaprogramming facilities can be used to work with these tuple types as-is, and higher level libraries can be built on top of them.
• For both product and sum types, the elements of MirroredElemTypes are arranged in definition order (i.e. Branch[T] precedes Leaf[T] in MirroredElemTypes for Tree because Branch is defined before Leaf in the source file). This means that Mirror.Sum differs in this respect from Shapeless's generic representation for ADTs in Scala 2, where the constructors are ordered alphabetically by name.
• The methods ordinal and fromProduct are defined in terms of MirroredMonoType which is the type of kind-* which is obtained from MirroredType by wildcarding its type parameters.

Implementing derived with Mirror

As seen before, the signature and implementation of a derived method for a type class TC[_] are arbitrary, but we expect it to typically be of the following form:

import scala.deriving.Mirror

inline def derived[T](using Mirror.Of[T]): TC[T] = ...

That is, the derived method takes a context parameter of (some subtype of) type Mirror which defines the shape of the deriving type T, and computes the type class implementation according to that shape. This is all that the provider of an ADT with a derives clause has to know about the derivation of a type class instance.

Note that derived methods may have context Mirror parameters indirectly (e.g. by having a context argument which in turn has a context Mirror parameter, or not at all (e.g. they might use some completely different user-provided mechanism, for instance using Scala 3 macros or runtime reflection). We expect that (direct or indirect) Mirror based implementations will be the most common and that is what this document emphasises.

Type class authors will most likely use higher level derivation or generic programming libraries to implement derived methods. An example of how a derived method might be implemented using only the low level facilities described above and Scala 3's general metaprogramming features is provided below. It is not anticipated that type class authors would normally implement a derived method in this way, however this walkthrough can be taken as a guide for authors of the higher level derivation libraries that we expect typical type class authors will use (for a fully worked out example of such a library, see Shapeless 3).

How to write a type class derived method using low level mechanisms

The low-level method we will use to implement a type class derived method in this example exploits three new type-level constructs in Scala 3: inline methods, inline matches, and implicit searches via summonInline or summonFrom. Given this definition of the Eq type class,

trait Eq[T]:
  def eqv(x: T, y: T): Boolean

we need to implement a method Eq.derived on the companion object of Eq that produces a given instance for Eq[T] given a Mirror[T]. Here is a possible implementation,

import scala.deriving.Mirror

inline given derived[T](using m: Mirror.Of[T]): Eq[T] =
  val elemInstances = summonAll[m.MirroredElemTypes]           // (1)
  inline m match                                               // (2)
    case s: Mirror.SumOf[T]     => eqSum(s, elemInstances)
    case p: Mirror.ProductOf[T] => eqProduct(p, elemInstances)

Note that derived is defined as an inline given. This means that the method will be expanded at call sites (for instance the compiler generated instance definitions in the companion objects of ADTs which have a derived Eq clause), and also that it can be used recursively if necessary, to compute instances for children.

The body of this method (1) first materializes the Eq instances for all the child types of type the instance is being derived for. This is either all the branches of a sum type or all the fields of a product type. The implementation of summonAll is inline and uses Scala 3's summonInline construct to collect the instances as a List,

inline def summonAll[T <: Tuple]: List[Eq[_]] =
  inline erasedValue[T] match
    case _: EmptyTuple => Nil
    case _: (t *: ts) => summonInline[Eq[t]] :: summonAll[ts]

with the instances for children in hand the derived method uses an inline match to dispatch to methods which can construct instances for either sums or products (2). Note that because derived is inline the match will be resolved at compile-time and only the left-hand side of the matching case will be inlined into the generated code with types refined as revealed by the match.

In the sum case, eqSum, we use the runtime ordinal values of the arguments to eqv to first check if the two values are of the same subtype of the ADT (3) and then, if they are, to further test for equality based on the Eq instance for the appropriate ADT subtype using the auxiliary method check (4).

import scala.deriving.Mirror

def eqSum[T](s: Mirror.SumOf[T], elems: List[Eq[_]]): Eq[T] =
  new Eq[T]:
    def eqv(x: T, y: T): Boolean =
      val ordx = s.ordinal(x)                            // (3)
      (s.ordinal(y) == ordx) && check(elems(ordx))(x, y) // (4)

In the product case, eqProduct we test the runtime values of the arguments to eqv for equality as products based on the Eq instances for the fields of the data type (5),

import scala.deriving.Mirror

def eqProduct[T](p: Mirror.ProductOf[T], elems: List[Eq[_]]): Eq[T] =
  new Eq[T]:
    def eqv(x: T, y: T): Boolean =
      iterator(x).zip(iterator(y)).zip(elems.iterator).forall {  // (5)
        case ((x, y), elem) => check(elem)(x, y)
      }

Pulling this all together we have the following complete implementation,

import scala.deriving.*
import scala.compiletime.{erasedValue, summonInline}

inline def summonAll[T <: Tuple]: List[Eq[_]] =
  inline erasedValue[T] match
    case _: EmptyTuple => Nil
    case _: (t *: ts) => summonInline[Eq[t]] :: summonAll[ts]

trait Eq[T]:
  def eqv(x: T, y: T): Boolean

object Eq:
  given Eq[Int] with
    def eqv(x: Int, y: Int) = x == y

  def check(elem: Eq[_])(x: Any, y: Any): Boolean =
    elem.asInstanceOf[Eq[Any]].eqv(x, y)

  def iterator[T](p: T) = p.asInstanceOf[Product].productIterator

  def eqSum[T](s: Mirror.SumOf[T], elems: => List[Eq[_]]): Eq[T] =
    new Eq[T]:
      def eqv(x: T, y: T): Boolean =
        val ordx = s.ordinal(x)
        (s.ordinal(y) == ordx) && check(elems(ordx))(x, y)

  def eqProduct[T](p: Mirror.ProductOf[T], elems: => List[Eq[_]]): Eq[T] =
    new Eq[T]:
      def eqv(x: T, y: T): Boolean =
        iterator(x).zip(iterator(y)).zip(elems.iterator).forall {
          case ((x, y), elem) => check(elem)(x, y)
        }

  inline given derived[T](using m: Mirror.Of[T]): Eq[T] =
    lazy val elemInstances = summonAll[m.MirroredElemTypes]
    inline m match
      case s: Mirror.SumOf[T]     => eqSum(s, elemInstances)
      case p: Mirror.ProductOf[T] => eqProduct(p, elemInstances)
end Eq

we can test this relative to a simple ADT like so,

enum Opt[+T] derives Eq:
  case Sm(t: T)
  case Nn

@main def test(): Unit =
  import Opt.*
  val eqoi = summon[Eq[Opt[Int]]]
  assert(eqoi.eqv(Sm(23), Sm(23)))
  assert(!eqoi.eqv(Sm(23), Sm(13)))
  assert(!eqoi.eqv(Sm(23), Nn))

In this case the code that is generated by the inline expansion for the derived Eq instance for Opt looks like the following, after a little polishing,

given derived$Eq[T](using eqT: Eq[T]): Eq[Opt[T]] =
  eqSum(
    summon[Mirror[Opt[T]]],
    List(
      eqProduct(summon[Mirror[Sm[T]]], List(summon[Eq[T]])),
      eqProduct(summon[Mirror[Nn.type]], Nil)
    )
  )

Alternative approaches can be taken to the way that derived methods can be defined. For example, more aggressively inlined variants using Scala 3 macros, whilst being more involved for type class authors to write than the example above, can produce code for type classes like Eq which eliminate all the abstraction artefacts (eg. the Lists of child instances in the above) and generate code which is indistinguishable from what a programmer might write by hand. As a third example, using a higher level library such as Shapeless the type class author could define an equivalent derived method as,

given eqSum[A](using inst: => K0.CoproductInstances[Eq, A]): Eq[A] with
  def eqv(x: A, y: A): Boolean = inst.fold2(x, y)(false)(
    [t] => (eqt: Eq[t], t0: t, t1: t) => eqt.eqv(t0, t1)
  )

given eqProduct[A](using inst: K0.ProductInstances[Eq, A]): Eq[A] with
  def eqv(x: A, y: A): Boolean = inst.foldLeft2(x, y)(true: Boolean)(
    [t] => (acc: Boolean, eqt: Eq[t], t0: t, t1: t) =>
      Complete(!eqt.eqv(t0, t1))(false)(true)
  )

inline def derived[A](using gen: K0.Generic[A]): Eq[A] =
  gen.derive(eqProduct, eqSum)

The framework described here enables all three of these approaches without mandating any of them.

For a brief discussion on how to use macros to write a type class derived method please read more at How to write a type class derived method using macros.

Syntax

Template          ::=  InheritClauses [TemplateBody]
EnumDef           ::=  id ClassConstr InheritClauses EnumBody
InheritClauses    ::=  [‘extends’ ConstrApps] [‘derives’ QualId {‘,’ QualId}]
ConstrApps        ::=  ConstrApp {‘with’ ConstrApp}
                    |  ConstrApp {‘,’ ConstrApp}

Note: To align extends clauses and derives clauses, Scala 3 also allows multiple extended types to be separated by commas. So the following is now legal:

class A extends B, C { ... }

It is equivalent to the old form

class A extends B with C { ... }

Discussion

This type class derivation framework is intentionally very small and low-level. There are essentially two pieces of infrastructure in compiler-generated Mirror instances,

• type members encoding properties of the mirrored types.
• a minimal value level mechanism for working generically with terms of the mirrored types.

The Mirror infrastructure can be seen as an extension of the existing Product infrastructure for case classes: typically Mirror types will be implemented by the ADTs companion object, hence the type members and the ordinal or fromProduct methods will be members of that object. The primary motivation for this design decision, and the decision to encode properties via types rather than terms was to keep the bytecode and runtime footprint of the feature small enough to make it possible to provide Mirror instances unconditionally.

Whilst Mirrors encode properties precisely via type members, the value level ordinal and fromProduct are somewhat weakly typed (because they are defined in terms of MirroredMonoType) just like the members of Product. This means that code for generic type classes has to ensure that type exploration and value selection proceed in lockstep and it has to assert this conformance in some places using casts. If generic type classes are correctly written these casts will never fail.

As mentioned, however, the compiler-provided mechanism is intentionally very low level and it is anticipated that higher level type class derivation and generic programming libraries will build on this and Scala 3's other metaprogramming facilities to hide these low-level details from type class authors and general users. Type class derivation in the style of both Shapeless and Magnolia are possible (a prototype of Shapeless 3, which combines aspects of both Shapeless 2 and Magnolia has been developed alongside this language feature) as is a more aggressively inlined style, supported by Scala 3's new quote/splice macro and inlining facilities.