2/3/08

Playing with Scala 4: Abstract types and Self-types

Thanks to the scala mailing list, and to Eric, I have a satisfying enough model of a graph to be used by the Dijkstra's algorithm.
(well, there already was a generic graph and directed graph written in Scala... talking about reinventing the wheel!. The solution in Eric's comment works great too... is almost the same, but he was faster than me on coming up with it :D )
http://www.scala-lang.org/intro/abstracttypes.html
http://www.scala-lang.org/intro/selfrefs.html
I just used the same code, and changed the nodes and edges to use sets instead of lists (really, we don't care about the order)
The Scala example of Graph uses abstract types: it declares type Node and type Edge as type "parameters" to be defined by concrete implementation. Even more, by declaring type Node <: NodeIntf, we're restricting Node to be subtypes of NodeIntf. The declaration "self: Node =>" tells "I'll use self as Node type"
Then I declared the trait Weighted and extended the class DirectedGraph adding my extensions to NodeImpl and EdgeImpl to use weighted trait and add the node label and the previous property. I had to add a collection of the adjacent arcs, because they weren't in the original Graph and is easier for the algorithm. I overrode the connectWith method to keep track of the adjacent arcs as they're added, also I defined our --> operator to call the connectWith method.

class DfsNode extends NodeImpl with Weighted {
var previous: DfsNode = _
var label:String = _
var nodeEdges: Set[Edge] = Set()

override def connectWith(node: Node): Edge = {
val newEdge=super.connectWith(node)
nodeEdges = nodeEdges + newEdge
newEdge
}

def -->(n2:Node):DfsEdge =connectWith(n2)

override def toString()= label+ " w:"+weight
}

Edges are simpler, just add the weight and override toString:
class DfsEdge(origin:Node, dest:Node) extends EdgeImpl(origin, dest) with Weighted {
override def toString()= from.label+"-->"+to.label+" w:"+weight
}

All are enclosed in the DfsGraph class extending the DirectedGraph class, now I can assign the concrete types for Node and Edge:
type Node= DfsNode
type Edge= DfsEdge

The DirectedGraph class has a addNode method. To keep the DSL-ish quality of the construction of the graph, I added the method addNewNode to take the node label as parameter
def addNewNode(l:String):Node={
val newNode=super.addNode
newNode.label=l
newNode
}

So we can write: graph addNewNode "nodeLabel".

The example looks like this:

object Example extends Application {

val graph = new DfsGraph

val n1=graph addNewNode "start"
val n2=graph addNewNode "n2"
val n3=graph addNewNode "n3"
val n4=graph addNewNode "n4"
val n5=graph addNewNode "n5"
val n6=graph addNewNode "end"

n1-->n2 weight=2
n1-->n3 weight=1
n2-->n4 weight=1
n3-->n4 weight=3
n2-->n5 weight=1
n4-->n6 weight=1
n5-->n6 weight=3

graph.shortestPath(n1,n6)
println("Path")
graph.pathToStart(n6).reverse.map(println(_))

}

Pretty easy to read, don't you think?
In the next post, I'll show you how we can use this algorithm to solve the "Abbott's revenge" type of maze. Ideally, I want to create an interpreter for the input, exploring Scala's features for creating language interpreters.
Here is the complete code:

package dfs2;

abstract class Graph {
type Edge
type Node <: NodeIntf
abstract class NodeIntf {
def connectWith(node: Node): Edge
}
def nodes: Set[Node]
def edges: Set[Edge]
def addNode: Node
}

abstract class DirectedGraph extends Graph {
type Edge <: EdgeImpl
class EdgeImpl(origin: Node, dest: Node) {
def from = origin
def to = dest
}

class NodeImpl extends NodeIntf {
self: Node =>
def connectWith(node: Node): Edge = {
val edge = newEdge(this, node)
edges = edges + edge
edge
}
}

protected def newNode: Node
protected def newEdge(from: Node, to: Node): Edge

var nodes: Set[Node] =Set()
var edges: Set[Edge] =Set()
def addNode: Node = {
val node = newNode
nodes = nodes + node
node
}
}

trait Weighted {
var weight= Float.PositiveInfinity
}
class DfsGraph extends DirectedGraph {
class DfsNode extends NodeImpl with Weighted {
var previous: DfsNode = _
var label:String = _
var nodeEdges: Set[Edge] = Set()

override def connectWith(node: Node): Edge = {
val newEdge=super.connectWith(node)
nodeEdges = nodeEdges + newEdge
newEdge
}

def -->(n2:Node):DfsEdge =connectWith(n2)

override def toString()= label+ " w:"+weight
}

class DfsEdge(origin:Node, dest:Node) extends EdgeImpl(origin, dest) with Weighted {
override def toString()= from.label+"-->"+to.label+" w:"+weight
}

def addNewNode(l:String):Node={
val newNode=super.addNode
newNode.label=l
newNode
}

type Node= DfsNode
type Edge= DfsEdge

protected def newEdge(from: Node, to: Node): Edge = new DfsEdge(from,to)
protected def newNode: Node = new DfsNode

def shortestPath(start: DfsNode, end: DfsNode) = {
var unvisited=nodes
start.weight=0
while (!unvisited.isEmpty) {
val vertx=min(unvisited)
vertx.nodeEdges.map(improveDistance(_))
unvisited=unvisited-vertx
}
}

def improveDistance(a:Edge) ={
if (a.from.weight+a.weight< a.to.weight) {
a.to.weight=a.from.weight+a.weight
a.to.previous=a.from
}
}

def min(nodes: Set[DfsNode]): DfsNode = {
nodes.reduceLeft((a:DfsNode,b:DfsNode)=>if (a.weight<b.weight) a else b )
}

def pathToStart(end:DfsNode):List[DfsNode] = {
if (end == null)
Nil
else
end :: pathToStart(end.previous)
}
}

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