Opaque Type Aliases

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

object MyMath:

  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 then Some(math.log(d)) else None

  end Logarithm

  // Extension methods define opaque types' public APIs
  extension (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

end MyMath

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 MyMath. Or in other words, within the scope, it is treated as a type alias, but this is opaque to the outside world where, in consequence, Logarithm is seen as an abstract type that 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, an operation toDouble that converts the other way, and operations + and * are defined as extension methods on Logarithm values. The following operations would be valid because they use functionality implemented in the MyMath object.

import MyMath.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

  extension (x: PermissionChoice)
    def | (y: PermissionChoice): PermissionChoice = x | y
  extension (x: Permissions)
    def & (y: Permissions): Permissions = x | y
  extension (granted: Permissions)
    def is(required: Permissions) = (granted & required) == required
    def 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

end Access

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. For that reason, the | extension method in Access does not cause infinite recursion.

In particular, the definition of ReadWrite must use |, the bitwise operator for Int, even though client code outside Access would use &, the extension method on Permissions. The internal representations of ReadWrite and ReadOrWrite are identical, but this is not visible to the client, which is interested only in the semantics of Permissions, as in the example below.

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)
  extension (item: Item)
    def +(other: Item): Item = Item(item.rights & other.rights)

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

  assert(!roItem.rights.is(ReadWrite))
  assert(roItem.rights.isOneOf(ReadOrWrite))

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

  assert(!noItem.rights.is(ReadWrite))
  assert(!noItem.rights.isOneOf(ReadOrWrite))

  assert((roItem + woItem).rights.is(ReadWrite))
end User

On the other hand, the call roItem.rights.isOneOf(ReadWrite) would give a type error:

assert(roItem.rights.isOneOf(ReadWrite))
                               ^^^^^^^^^
                               Found:    (Access.ReadWrite : Access.Permissions)
                               Required: Access.PermissionChoice

Permissions and PermissionChoice are different, unrelated types outside Access.

Opaque Type Members on Classes

While typically, opaque types are used together with objects to hide implementation details of a module, they can also be used with classes.

For example, we can redefine the above example of Logarithms as a class.

class Logarithms:

  opaque type Logarithm = Double

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

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

  def mul(x: Logarithm, y: Logarithm) = x + y

Opaque type members of different instances are treated as different:

val l1 = new Logarithms
val l2 = new Logarithms
val x = l1(1.5)
val y = l1(2.6)
val z = l2(3.1)
l1.mul(x, y) // type checks
l1.mul(x, z) // error: found l2.Logarithm, required l1.Logarithm

In general, one can think of an opaque type as being only transparent in the scope of private[this].

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