# Algebraic Data Types

The enum concept is general enough to also support algebraic data types (ADTs) and their generalized version (GADTs). Here is an example how an Option type can be represented as an ADT:

enum Option[+T] {
case Some(x: T)
case None
}

This example introduces an Option enum with a covariant type parameter T consisting of two cases, Some and None. Some is parameterized with a value parameter x. It is a shorthand for writing a case class that extends Option. Since None is not parameterized, it is treated as a normal enum value.

The extends clauses that were omitted in the example above can also be given explicitly:

enum Option[+T] {
case Some(x: T) extends Option[T]
case None       extends Option[Nothing]
}

Note that the parent type of the None value is inferred as Option[Nothing]. Generally, all covariant type parameters of the enum class are minimized in a compiler-generated extends clause whereas all contravariant type parameters are maximized. If Option was non-variant, you would need to give the extends clause of None explicitly.

As for normal enum values, the cases of an enum are all defined in the enums companion object. So it's Option.Some and Option.None unless the definitions are "pulled out" with an import:

scala> Option.Some("hello")
val res1: t2.Option[String] = Some(hello)

scala> Option.None
val res2: t2.Option[Nothing] = None

Note that the type of the expressions above is always Option. That is, the implementation case classes are not visible in the result types of their apply methods. This is a subtle difference with respect to normal case classes. The classes making up the cases do exist, and can be unveiled by constructing them directly with a new.

scala> new Option.Some(2)
val res3: t2.Option.Some[Int] = Some(2)

As all other enums, ADTs can define methods. For instance, here is Option again, with an isDefined method and an Option(...) constructor in its companion object.

enum Option[+T] {
case Some(x: T)
case None

def isDefined: Boolean = this match {
case None => false
case some => true
}
}
object Option {
def apply[T >: Null](x: T): Option[T] =
if (x == null) None else Some(x)
}

Enumerations and ADTs have been presented as two different concepts. But since they share the same syntactic construct, they can be seen simply as two ends of a spectrum and it is perfectly possible to construct hybrids. For instance, the code below gives an implementation of Color either with three enum values or with a parameterized case that takes an RGB value.

enum Color(val rgb: Int) {
case Red   extends Color(0xFF0000)
case Green extends Color(0x00FF00)
case Blue  extends Color(0x0000FF)
case Mix(mix: Int) extends Color(mix)
}

### Syntax of Enums

Changes to the syntax fall in two categories: enum definitions and cases inside enums. The changes are specified below as deltas with respect to the Scala syntax given here

1. Enum definitions are defined as follows:
TmplDef   ::=  `enum' EnumDef
EnumDef   ::=  id ClassConstr [`extends' [ConstrApps]] EnumBody
EnumBody  ::=  [nl] ‘{’ [SelfType] EnumStat {semi EnumStat} ‘}’
EnumStat  ::=  TemplateStat
|  {Annotation [nl]} {Modifier} EnumCase

2. Cases of enums are defined as follows:
EnumCase  ::=  `case' (id ClassConstr [`extends' ConstrApps]] | ids)