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 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 `Double`

s 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: Permissions)
def & (y: Permissions): Permissions = x | y
extension (x: PermissionChoice)
def | (y: PermissionChoice): PermissionChoice = x | y
extension (granted: Permissions)
def is(required: Permissions) = (granted & required) == required
extension (granted: Permissions)
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.
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))
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))
end User
```

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`

.

### 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]`

.