What does the `#` operator mean in Scala?

Question

I see this code in this blog: Type-Level Programming in Scala:

// define the abstract types and bounds
trait Recurse {
  type Next <: Recurse
  // this is the recursive function definition
  type X[R <: Recurse] <: Int
}
// implementation
trait RecurseA extends Recurse {
  type Next = RecurseA
  // this is the implementation
  type X[R <: Recurse] = R#X[R#Next]
}
object Recurse {
  // infinite loop
  type C = RecurseA#X[RecurseA]
}

There is an operator # in the code R#X[R#Next] which I've never seen. Since it's difficult to search it(ignored by search engines), who can tell me what does it mean?

Deanedeaner

the "pound sign" is sometimes referred to as "octathrop" (that google search brought me to this page). – Cheekpiece

Make that octothorpe or octothorp – Tuneless

Whatabout other operators like #+ and #- (see github.com/tpolecat/doobie/blob/series/0.4.x/yax/h2/src/main/…)? Is there a comprehensive list? – Roe

Answer 1

To explain it, we first have to explain nested classes in Scala. Consider this simple example:

class A {
  class B

  def f(b: B) = println("Got my B!")
}

Now let's try something with it:

scala> val a1 = new A
a1: A = A@2fa8ecf4

scala> val a2 = new A
a2: A = A@4bed4c8

scala> a2.f(new a1.B)
<console>:11: error: type mismatch;
 found   : a1.B
 required: a2.B
              a2.f(new a1.B)
                   ^

When you declare a class inside another class in Scala, you are saying that each instance of that class has such a subclass. In other words, there's no A.B class, but there are a1.B and a2.B classes, and they are different classes, as the error message is telling us above.

If you did not understand that, look up path dependent types.

Now, # makes it possible for you to refer to such nested classes without restricting it to a particular instance. In other words, there's no A.B, but there's A#B, which means a B nested class of any instance of A.

We can see this in work by changing the code above:

class A {
  class B

  def f(b: B) = println("Got my B!")
  def g(b: A#B) = println("Got a B.")
}

And trying it out:

scala> val a1 = new A
a1: A = A@1497b7b1

scala> val a2 = new A
a2: A = A@2607c28c

scala> a2.f(new a1.B)
<console>:11: error: type mismatch;
 found   : a1.B
 required: a2.B
              a2.f(new a1.B)
                   ^

scala> a2.g(new a1.B)
Got a B.

Larcener

Excellent example. I totally accept that it works that way but hard to understand this: scala> classOf[A#B] res7: Class[A#B] = class A$B scala> classOf[a.B] res8: Class[a.B] = class A$B . which means, they have the same type actually? – Cipher

Their values have the same string representation -- and they might even be equal. Class is a runtime representation of Java classes, and it's limited even in Java. For example, List<String> and List<Integer> have the same runtime Class. If Class is not rich enough to represent Java types, it's almost useless when representing Scala types. Again, res7: Class[A#B] = class A$B, left of the equals sign is a type, right of the equals type if a value which is the Java runtime representation of a class. – Larcener

Answer 2

It's known as type projection, and is used to access type members.

scala> trait R {
     |   type A = Int
     | }
defined trait R

scala> val x = null.asInstanceOf[R#A]
x: Int = 0

Incertitude

This is a non-answer. It basically shows the same code as the question, just slightly shortened. What is, for example the difference to point notation? Where would I use this # in real code? – Subcontract

@Subcontract maybe it's a non-answer to what you meant to ask. But what you asked is "... which I've never seen. Since it's difficult to search it(ignored by search engines), who can tell me what does it mean?" – Flint

Answer 3

Basically, it's a way of referring to classes within other classes.

http://jim-mcbeath.blogspot.com/2008/09/scala-syntax-primer.html (search for "pound")

Korean

Answer 4

Here's a resource for searching on "symbolic operators" (which are really methods), but I haven't figured out how to escape "#" to search on in scalex)

http://www.artima.com/pins1ed/book-index.html#indexanchor

Jordaens