Intersection Types

Used on types, the & operator creates an intersection type.

Type Checking

The type S & T represents values that are of the type S and T at the same time.

trait Resettable:
  def reset(): Unit

trait Growable[T]:
  def add(t: T): Unit

def f(x: Resettable & Growable[String]) =
  x.reset()
  x.add("first")

The parameter x is required to be both a Resettable and a Growable[String].

The members of an intersection type A & B are all the members of A and all the members of B. For instance Resettable & Growable[String] has member methods reset and add.

& is commutative: A & B is the same type as B & A.

If a member appears in both A and B, its type in A & B is the intersection of its type in A and its type in B. For instance, assume the definitions:

trait A:
  def children: List[A]

trait B:
  def children: List[B]

val x: A & B = new C
val ys: List[A & B] = x.children

The type of children in A & B is the intersection of children's type in A and its type in B, which is List[A] & List[B]. This can be further simplified to List[A & B] because List is covariant.

One might wonder how the compiler could come up with a definition for children of type List[A & B] since what is given are children definitions of type List[A] and List[B]. The answer is the compiler does not need to. A & B is just a type that represents a set of requirements for values of the type. At the point where a value is constructed, one must make sure that all inherited members are correctly defined. So if one defines a class C that inherits A and B, one needs to give at that point a definition of a children method with the required type.

class C extends A, B:
  def children: List[A & B] = ???

More details