Scala has support of algebraic data types out of the box but often it is not enough for complex cases. In this article I will try to show its limits and how to bypass them using shapeless library by the example of sum data types.


What is ADT?

ADT - is acronym for Algebraic Data Type which is a type that is composed from other types by using operations like “sum” or “product”, where:

  • “sum” is the tagged union. sealed trait is a common way to describe it in Scala:
sealed trait Option[T]
case class  Some[T](value: T) extends Option[T]
case object None extends Option[Nothing]
  • “product” is a combination of types. In Scala it can be described using tuples or case classes:
type Product = (Int, String, Long, Seq[Int])
case class Product(i: Int, s: String, l: Long, seq: Seq[Int])

Sealed trait as a sum type

In scala a sum time can be represented as a sealed trait:

sealed trait Request
case class CreateUser(name: String)                   extends Request
case class ReadUserInfo(userId: Int)                  extends Request
case class UpdateUserInfo(userId: Int, name: String)  extends Request
case class DeleteUser(userId: Int)                    extends Request

This means that a value of request: Request can be equal only to an instance of one of classes mentioned above. And the compile can check exhaustiveness of pattern matching for such a type.

// the compiler throws a warning/error if there is no `case ... => ...` for all possible subtypes:
// Error: match may not be exhaustive.
def exhaustivePatternMatch(request: Request) = {
  request match {
    case CreateUser(name)         => ???
    case ReadUserInfo(id)         => ???
    case UpdateUserInfo(id, name) => ???
    case DeleteUser(id)           => ???

Extending ADTs using Wrapper + Evidence

This approach works fine for simple cases but it fails in case if it is necessary to extend a predefined type which we can’t control. For example, sealed trait Request is defined in a library but we want to add new types of requests to the protocol:

sealed trait AdvancedRequest
case object  GetAllUsers     extends AdvancedRequest
case object  DeleteAllUsers  extends AdvancedRequest

In this case we have to introduce additional abstractions to make it possible:

case class Wrapper[T: Evidence](value: T)
object Wrapper {
  sealed trait Evidence[-T]
  implicit object RequestEvidence extends Evidence[Request]
  implicit object AdvancedRequestEvidence extends Evidence[AdvancedRequest]

// can be compiled without problems
val withBasicRequest = Wrapper(CreateUser("test-user"))
val withAdvancedRequest = Wrapper(GetAllUsers)

// throw an error:
// Error: could not find implicit value for evidence parameter of type Evidence[DeletedUsers]
val withInvalidValue = Wrapper(DeletedUsers(Seq(1, 2)))

Using Wrapper + Evidence we can’t make a mistake and wrap a value of an invalid type - the compiler will find a problem and throw the error. But we can make a mistake in pattern matching and the compiler won’t help us:

private def patternMatch[T](wrapper: Wrapper[T]) = {
  // compiles with several matches missed - no warns or errors :(
  wrapper.value match {
    case CreateUser(name) => ???
    case ReadUserInfo(id) => ???
    //UpdateUserInfo, DeleteUser, GetAllUsers and DeleteAllUsers are missed here

In order to deal with this problem we can use Coproduct types and Poly1 functions from shapeless library.

Coproduct as a sum type

Coproduct is a way of representing sum types in shapeless library. It can be used like this:

type Shape = Rectangle :+: Circle :+: Triangle :+: CNil

It means that value: Shape can be either Rectangle or Circle or Triangle. More information about how to work with Coproduct in shapeless is available here.

Coproduct in contrast to sealed trait makes possible to combine an arbitrary set of predefined types in a sum type. For example, we can use it to recombine types from above like this:

type ReadRequests   = ReadUserInfo :+: GetAllUsers.type :+: CNil
type WriteRequests  = CreateUser :+: UpdateUserInfo :+: DeleteUser :+: DeleteAllUsers.type :+: CNil

Poly1 as pattern matching

Having our sum types defined we can implement pattern matching for them. For that we will use Poly1 function.

object read extends Poly1 {
  implicit val readUserInfo = at[ReadUserInfo]    (_ => true)
  implicit val getAllUsers  = at[GetAllUsers.type](_ => 1)

object write extends Poly1 {
  implicit val createUser     = at[CreateUser]          (_ => true)
  implicit val updateUserInfo = at[UpdateUserInfo]      (_ => 1)
  implicit val deleteUser     = at[DeleteUser]          (_ => "2")
  implicit val deleteAllUsers = at[DeleteAllUsers.type] (_ => List(3))

object function extends Poly1 {...} is a definition of a polymorphic function - a function that is defined for an arbitrary set of types. There are a lot of use cases for such functions but we are interested in the fact that these functions can work as exhaustive pattern matching being applied to Coproduct values.

In the example above we can see that read function is defined for ReadUserInfo and GetAllUsers requests, write - for CreateUser, UpdateUserInfo, DeleteUser and DeleteAllUsers. Inasmuch as read is defined for all types in ReadRequests and write for all types in WriteRequests we can use it for pattern matching of values of these types:

private def readPatternMatch(request: ReadRequests): Unit = {
  val result =

private def writePatternMatch(request: WriteRequests): Unit = {
  val result =

Check of exhaustiveness of such functions during compilation is implemented in shapeless. The compiler will throw an error if a poly function does not have handlers for all types in Coproduct.

object read extends Poly1 {
  implicit val readUserInfo = at[ReadUserInfo](_ => true)
// Assume we forgot to add a handler for `GetAllUsers` request
// implicit val getAllUsers  = at[GetAllUsers.type](_ => 1)

private def readPatternMatch(request: ReadRequests): Unit = {
  val result =

The code above will generate:

Error: could not find implicit value for parameter mapper: shapeless.ops.coproduct.Mapper[,io.koff.shapeless_algebraic.UsingPolys.ReadRequests]
    val result =

Though this error does not provide information about a specific type that does not have a handler, it makes impossible to omit it without notice.

Merging sum types with Shapeless

Using shapeless you get another cool feature - ability to join sum types together keeping compile time checks.

// joined coproducts
val joined = Adjoin[WriteRequests :+: ReadRequests]
type AllRequests = joined.Out

Such a definition of AllRequests is an equivalent to:

type AllRequests2 = CreateUser :+: UpdateUserInfo :+: DeleteUser :+: DeleteAllUsers.type :+: ReadUserInfo :+: GetAllUsers.type :+: CNil

val value1: AllRequests2 = Coproduct[AllRequests] (GetAllUsers)
val value2: AllRequests  = Coproduct[AllRequests2](DeleteAllUsers)

The next step is to join different sealed traits together. In order to do it we need shapeless.Generic.

/* It is possible to extract Coproducts from sealed traits */
val genRequest    = Generic[Request]
val genAdvRequest = Generic[AdvancedRequest]
val joinedTraits  = Adjoin [genRequest.Repr :+: genAdvRequest.Repr]
/* And join them together */
type JoinedTraits = joinedTraits.Out

It is also possible to “merge” poly functions if they are defined as traits:

trait read { self: Poly1 =>
  implicit val readUserInfo = at[ReadUserInfo]    (_ => true)
  implicit val getAllUsers  = at[GetAllUsers.type](_ => 1)

trait write { self: Poly1 =>
  implicit val createUser     = at[CreateUser]          (_ => 2.0F)
  implicit val updateUserInfo = at[UpdateUserInfo]      (_ => 3.0D)
  implicit val deleteUser     = at[DeleteUser]          (_ => "4")
  implicit val deleteAllUsers = at[DeleteAllUsers.type] (_ => List(5))

//Ad Hoc definition of a merged poly function
object polyFunc extends Poly1 with read with write

private def patternMatchForAllRequests(all: AllRequests) = {


So it is possible to use shapeless.Coproduct to define sum types on the analogy of sealed traits. But when to use what?

Use sealed traits for:

  1. simple well-defined types like Option[_]
  2. sum types you control
  3. defining basic pieces that might be composed later(using Generic)

Use shapeless when you need:

  1. to create a sum type from arbitrary set of types - Coproduct
  2. to compose and use sealed traits you don’t control - Generic
  3. to have compile time checks for exhaustiveness of pattern-matching for composed sum types - Poly functions

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