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:

classGraph{classNode{varconnectedNodes:List[Node]=NildefconnectTo(node:Node):Unit={if(!connectedNodes.exists(node.equals)){connectedNodes=node::connectedNodes}}}varnodes:List[Node]=NildefnewNode:Node={valres=newNodenodes=res::nodesres}}

classGraph:classNode:varconnectedNodes:List[Node]=NildefconnectTo(node:Node):Unit=if!connectedNodes.exists(node.equals)thenconnectedNodes=node::connectedNodesvarnodes:List[Node]=NildefnewNode:Node=valres=Node()nodes=res::nodesres

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.

valgraph1:Graph=newGraphvalnode1:graph1.Node=graph1.newNodevalnode2:graph1.Node=graph1.newNodevalnode3:graph1.Node=graph1.newNodenode1.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:

valgraph1:Graph=newGraphvalnode1:graph1.Node=graph1.newNodevalnode2:graph1.Node=graph1.newNodenode1.connectTo(node2)// legalvalgraph2:Graph=newGraphvalnode3:graph2.Node=graph2.newNodenode1.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:

classGraph{classNode{varconnectedNodes:List[Graph#Node]=NildefconnectTo(node:Graph#Node):Unit={if(!connectedNodes.exists(node.equals)){connectedNodes=node::connectedNodes}}}varnodes:List[Node]=NildefnewNode:Node={valres=newNodenodes=res::nodesres}}

classGraph:classNode:varconnectedNodes:List[Graph#Node]=NildefconnectTo(node:Graph#Node):Unit=if!connectedNodes.exists(node.equals)thenconnectedNodes=node::connectedNodesvarnodes:List[Node]=NildefnewNode:Node=valres=Node()nodes=res::nodesres