Opaque Type Aliases

Opaque types aliases provide type abstraction without any overhead. Example:

object Logarithms {

  opaque type Logarithm = Double

  object Logarithm {

    // These are the two ways to lift to the Logarithm type

    def apply(d: Double): Logarithm = math.log(d)

    def safe(d: Double): Option[Logarithm] =
      if (d > 0.0) Some(math.log(d)) else None
  }

  // Extension methods define opaque types' public APIs
  extension logarithmOps on (x: Logarithm) {
    def toDouble: Double = math.exp(x)
    def + (y: Logarithm): Logarithm = Logarithm(math.exp(x) + math.exp(y))
    def * (y: Logarithm): Logarithm = x + y
  }
}

This introduces Logarithm as a new abstract type, which is implemented as Double. The fact that Logarithm is the same as Double is only known in the scope where Logarithm is defined which in the above example corresponds to the object Logarithms. Or in other words, within the scope it is treated as type alias, but this is opaque to the outside world where in consequence Logarithm is seen as an abstract type and has nothing to do with Double.

The public API of Logarithm consists of the apply and safe methods defined in the companion object. They convert from Doubles to Logarithm values. Moreover, a collective extension logarithmOps provides the extension methods toDouble that converts the other way, and operations + and * on Logarithm values. The following operations would be valid because they use functionality implemented in the Logarithms object.

import Logarithms.Logarithm

val l = Logarithm(1.0)
val l2 = Logarithm(2.0)
val l3 = l * l2
val l4 = l + l2

But the following operations would lead to type errors:

val d: Double = l       // error: found: Logarithm, required: Double
val l2: Logarithm = 1.0 // error: found: Double, required: Logarithm
l * 2                   // error: found: Int(2), required: Logarithm
l / l2                  // error: `/` is not a member of Logarithm

Bounds For Opaque Type Aliases

Opaque type aliases can also come with bounds. Example:

object Access {

  opaque type Permissions = Int
  opaque type PermissionChoice = Int
  opaque type Permission <: Permissions & PermissionChoice = Int

  def (x: Permissions) & (y: Permissions): Permissions = x | y
  def (x: PermissionChoice) | (y: PermissionChoice): PermissionChoice = x | y
  def (granted: Permissions).is(required: Permissions) = (granted & required) == required
  def (granted: Permissions).isOneOf(required: PermissionChoice) = (granted & required) != 0

  val NoPermission: Permission = 0
  val Read: Permission = 1
  val Write: Permission = 2
  val ReadWrite: Permissions = Read | Write
  val ReadOrWrite: PermissionChoice = Read | Write
}

The Access object defines three opaque type aliases:

• Permission, representing a single permission,
• Permissions, representing a set of permissions with the meaning "all of these permissions granted",
• PermissionChoice, representing a set of permissions with the meaning "at least one of these permissions granted".

Outside the Access object, values of type Permissions may be combined using the & operator, where x & y means "all permissions in x and in y granted". Values of type PermissionChoice may be combined using the | operator, where x | y means "a permission in x or in y granted".

Note that inside the Access object, the & and | operators always resolve to the corresponding methods of Int, because members always take precedence over extension methods. Because of that, the | extension method in Access does not cause infinite recursion. Also, the definition of ReadWrite must use |, even though an equivalent definition outside Access would use &.

All three opaque type aliases have the same underlying representation type Int. The Permission type has an upper bound Permissions & PermissionChoice. This makes it known outside the Access object that Permission is a subtype of the other two types. Hence, the following usage scenario type-checks.

object User {
  import Access._

  case class Item(rights: Permissions)

  val roItem = Item(Read)  // OK, since Permission <: Permissions
  val rwItem = Item(ReadWrite)
  val noItem = Item(NoPermission)

  assert( roItem.rights.is(ReadWrite) == false )
  assert( roItem.rights.isOneOf(ReadOrWrite) == true )

  assert( rwItem.rights.is(ReadWrite) == true )
  assert( rwItem.rights.isOneOf(ReadOrWrite) == true )

  assert( noItem.rights.is(ReadWrite) == false )
  assert( noItem.rights.isOneOf(ReadOrWrite) == false )
}

On the other hand, the call roItem.rights.isOneOf(ReadWrite) would give a type error since Permissions and PermissionChoice are different, unrelated types outside Access.

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