Functional programming course at Coursera week 7.

GameDef.scala

package streams

import common._

trait GameDef {

  case class Pos(x: Int, y: Int) {
    def dx(d: Int) = copy(x = x + d, y)

    def dy(d: Int) = copy(x, y = y + d)
  }

  val startPos: Pos

  val goal: Pos

  type Terrain = Pos => Boolean

  val terrain: Terrain


  sealed abstract class Move
  case object Left  extends Move
  case object Right extends Move
  case object Up    extends Move
  case object Down  extends Move

  def startBlock: Block = Block(startPos, startPos)

  case class Block(b1: Pos, b2: Pos) {

    require(b1.x <= b2.x && b1.y <= b2.y, "Invalid block position: b1=" + b1 + ", b2=" + b2)

    def dx(d1: Int, d2: Int) = Block(b1.dx(d1), b2.dx(d2))

    def dy(d1: Int, d2: Int) = Block(b1.dy(d1), b2.dy(d2))


    def left = if (isStanding)         dy(-2, -1)
               else if (b1.x == b2.x)  dy(-1, -2)
               else                    dy(-1, -1)

    def right = if (isStanding)        dy(1, 2)
                else if (b1.x == b2.x) dy(2, 1)
                else                   dy(1, 1)

    def up = if (isStanding)           dx(-2, -1)
             else if (b1.x == b2.x)    dx(-1, -1)
             else                      dx(-1, -2)

    def down = if (isStanding)         dx(1, 2)
               else if (b1.x == b2.x)  dx(1, 1)
               else                    dx(2, 1)


    def neighbors: List[(Block, Move)] = List((left, Left), (right, Right), (up, Up), (down, Down))

    def legalNeighbors: List[(Block, Move)] = neighbors.filter(_._1.isLegal)

    def isStanding: Boolean = b1 == b2

    def isLegal: Boolean = terrain(b1) && terrain(b2)

  }
}

Solver.scala

package streams

import common._

trait Solver extends GameDef {

  def done(b: Block): Boolean = b == Block(goal, goal)

  def neighborsWithHistory(b: Block, history: List[Move]): Stream[(Block, List[Move])] =
    b.legalNeighbors.map(x => x match {case (s,t) => (s, t :: history)}).toStream

  def newNeighborsOnly(neighbors: Stream[(Block, List[Move])],
                       explored: Set[Block]): Stream[(Block, List[Move])] =
    neighbors filterNot (explored contains _._1)

  def from(initial: Stream[(Block, List[Move])],
           explored: Set[Block]): Stream[(Block, List[Move])] = initial match {
    case (b,h) #:: xs => {
      val ys = newNeighborsOnly(neighborsWithHistory(b,h), explored)
      (b,h) #:: from(xs ++ ys, explored + b)
    }
    case _ => Stream.empty
  }

  lazy val pathsFromStart: Stream[(Block, List[Move])] = from(Stream((startBlock, Nil)), Set.empty)

  lazy val pathsToGoal: Stream[(Block, List[Move])] = pathsFromStart.filter(b => done(b._1))

  lazy val solution: List[Move] = pathsToGoal match {
    case x #:: _ => x._2.reverse
    case _ => Nil
  }
}

StringParserTerrain.scala

package streams

import common._

trait StringParserTerrain extends GameDef {

  val level: String

  def terrainFunction(levelVector: Vector[Vector[Char]]): Pos => Boolean =
    p => if (p.x < 0 || p.y < 0) false
         else if (p.x > levelVector.length - 1) false
         else if (p.y > levelVector(0).length - 1) false
         else levelVector(p.x)(p.y) != '-'

  def findChar(c: Char, levelVector: Vector[Vector[Char]]): Pos = {
    def x = levelVector.indexWhere(_.indexWhere(_ == c) > -1)
    def y = levelVector(x).indexWhere(_ == c)
    Pos(x, y)
  }

  private lazy val vector: Vector[Vector[Char]] =
    Vector(level.split("\n").map(str => Vector(str: _*)): _*)

  lazy val terrain: Terrain = terrainFunction(vector)
  lazy val startPos: Pos = findChar('S', vector)
  lazy val goal: Pos = findChar('T', vector)

}

You can also initial.head #:: from(xs ++ ys, explored + b) instead of (b,h) #:: from(xs ++ ys, explored + b). This better captures the fact that we leave first element intact.