Hi mate, working in intelli J following a pdf tute on case classes, just can't work out why the compiler is complaining about where I've done my type definition?

/**
 * Created by jim on 31/10/2014.
 */
abstract class Tree
case class Sum(l: Tree, r: Tree) extends Tree
case class Var(n: String) extends Tree
case class Const(v: Int) extends Tree

type Environment = String => Int

def eval(t: Tree, env: Environment): Int = t match {
  case Sum(l, r)  => eval(l, env) + eval(r, env)
  case Var(n)     => env(n)
  case Const(v)   => v
}

def derive(t: Tree, v: String): Tree = t match {
  case Sum(l, r) => Sum(derive(l, v), derive(r,v))
  case Var(n) if (v == n) => Const(1)
  case _ => Const (0)
}

def main(args: Array[String]): Unit = {
  val exp: Tree = Sum(Sum(Var("x"), Var("x")), Sum(Const(7), Var("y")))
  val env: Environment = { case "x" => 5 case "y" => 7 }
  println("Expression: " + exp)
  println("Evaluation with x=5, y=7: " + eval(exp, env))
  println("Derivative relative to x:\n " + derive(exp, "x"))
  println("Derivative relative to y:\n" + derive(exp, "y"))
}


Compiler errors are:

Error:(8, 1) expected class or object definition
type Environment = String => Int
^
Error:(10, 1) expected class or object definition
def eval(t: Tree, env: Environment): Int = t match {
^
Error:(16, 1) expected class or object definition
def derive(t: Tree, v: String): Tree = t match {
^
Error:(22, 1) expected class or object definition
def main(args: Array[String]): Unit = {
^