Inner Classes

In Scala it is possible to let classes have other classes as members. As opposed to Java-like languages where such inner classes are members of the enclosing class, in Scala such inner classes are bound to the outer object. Suppose we want the compiler to prevent us, at compile time, from mixing up which nodes belong to what graph. Path-dependent types provide a solution.

To illustrate the difference, we quickly sketch the implementation of a graph datatype:

class Graph {
  class Node {
    var connectedNodes: List[Node] = Nil
    def connectTo(node: Node) {
      if (connectedNodes.find(node.equals).isEmpty) {
        connectedNodes = node :: connectedNodes
      }
    }
  }
  var nodes: List[Node] = Nil
  def newNode: Node = {
    val res = new Node
    nodes = res :: nodes
    res
  }
}

This program represents a graph as a list of nodes (List[Node]). Each node has a list of other nodes it’s connected to (connectedNodes). The class Node is a path-dependent type because it is nested in the class Graph. Therefore, all nodes in the connectedNodes must be created using the newNode from the same instance of Graph.

val graph1: Graph = new Graph
val node1: graph1.Node = graph1.newNode
val node2: graph1.Node = graph1.newNode
val node3: graph1.Node = graph1.newNode
node1.connectTo(node2)
node3.connectTo(node1)

We have explicitly declared the type of node1, node2, and node3 as graph1.Node for clarity but the compiler could have inferred it. This is because when we call graph1.newNode which calls new Node, the method is using the instance of Node specific to the instance graph1.

If we now have two graphs, the type system of Scala does not allow us to mix nodes defined within one graph with the nodes of another graph, since the nodes of the other graph have a different type. Here is an illegal program:

val graph1: Graph = new Graph
val node1: graph1.Node = graph1.newNode
val node2: graph1.Node = graph1.newNode
node1.connectTo(node2)      // legal
val graph2: Graph = new Graph
val node3: graph2.Node = graph2.newNode
node1.connectTo(node3)      // illegal!

The type graph1.Node is distinct from the type graph2.Node. In Java, the last line in the previous example program would have been correct. For nodes of both graphs, Java would assign the same type Graph.Node; i.e. Node is prefixed with class Graph. In Scala such a type can be expressed as well, it is written Graph#Node. If we want to be able to connect nodes of different graphs, we have to change the definition of our initial graph implementation in the following way:

class Graph {
  class Node {
    var connectedNodes: List[Graph#Node] = Nil
    def connectTo(node: Graph#Node) {
      if (connectedNodes.find(node.equals).isEmpty) {
        connectedNodes = node :: connectedNodes
      }
    }
  }
  var nodes: List[Node] = Nil
  def newNode: Node = {
    val res = new Node
    nodes = res :: nodes
    res
  }
}

Note that this program doesn’t allow us to attach a node to two different graphs. If we want to remove this restriction as well, we have to change the type of variable nodes to Graph#Node.

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