Scala – How does one write the Pythagoras Theorem in Scala

This answer uses the Manifest-API, which is deprecated as of Scala 2.10. Please see answers below for more current solutions.

Scala was defined with Type Erasure because the Java Virtual Machine (JVM), unlike Java, did not get generics. This means that, at run time, only the class exists, not its type parameters. In the example, JVM knows it is handling a scala.collection.immutable.List, but not that this list is parameterized with Int.

Fortunately, there's a feature in Scala that lets you get around that. It’s the Manifest. A Manifest is class whose instances are objects representing types. Since these instances are objects, you can pass them around, store them, and generally call methods on them. With the support of implicit parameters, it becomes a very powerful tool. Take the following example, for instance:

object Registry {
  import scala.reflect.Manifest
  
  private var map= Map.empty[Any,(Manifest[_], Any)] 
  
  def register[T](name: Any, item: T)(implicit m: Manifest[T]) {
    map = map.updated(name, m -> item)
  }
  
  def get[T](key:Any)(implicit m : Manifest[T]): Option[T] = {
    map get key flatMap {
      case (om, s) => if (om <:< m) Some(s.asInstanceOf[T]) else None
    }     
  }
}

scala> Registry.register("a", List(1,2,3))

scala> Registry.get[List[Int]]("a")
res6: Option[List[Int]] = Some(List(1, 2, 3))

scala> Registry.get[List[String]]("a")
res7: Option[List[String]] = None

When storing an element, we store a "Manifest" of it too. A Manifest is a class whose instances represent Scala types. These objects have more information than JVM does, which enable us to test for the full, parameterized type.

Note, however, that a Manifest is still an evolving feature. As an example of its limitations, it presently doesn't know anything about variance, and assumes everything is co-variant. I expect it will get more stable and solid once the Scala reflection library, presently under development, gets finished.

As so many others have said, the object assigned to a val cannot be replaced, and the object assigned to a var can. However, said object can have its internal state modified. For example:

class A(n: Int) {
  var value = n
}

class B(n: Int) {
  val value = new A(n)
}

object Test {
  def main(args: Array[String]) {
    val x = new B(5)
    x = new B(6) // Doesn't work, because I can't replace the object created on the line above with this new one.
    x.value = new A(6) // Doesn't work, because I can't replace the object assigned to B.value for a new one.
    x.value.value = 6 // Works, because A.value can receive a new object.
  }
}

So, even though we can't change the object assigned to x, we could change the state of that object. At the root of it, however, there was a var.

Now, immutability is a good thing for many reasons. First, if an object doesn't change internal state, you don't have to worry if some other part of your code is changing it. For example:

x = new B(0)
f(x)
if (x.value.value == 0)
  println("f didn't do anything to x")
else
  println("f did something to x")

This becomes particularly important with multithreaded systems. In a multithreaded system, the following can happen:

x = new B(1)
f(x)
if (x.value.value == 1) {
  print(x.value.value) // Can be different than 1!
}

If you use val exclusively, and only use immutable data structures (that is, avoid arrays, everything in scala.collection.mutable, etc.), you can rest assured this won't happen. That is, unless there's some code, perhaps even a framework, doing reflection tricks -- reflection can change "immutable" values, unfortunately.

That's one reason, but there is another reason for it. When you use var, you can be tempted into reusing the same var for multiple purposes. This has some problems:

• It will be more difficult for people reading the code to know what is the value of a variable in a certain part of the code.
• You may forget to re-initialize the variable in some code path, and end up passing wrong values downstream in the code.

Simply put, using val is safer and leads to more readable code.

We can, then, go the other direction. If val is that better, why have var at all? Well, some languages did take that route, but there are situations in which mutability improves performance, a lot.

For example, take an immutable Queue. When you either enqueue or dequeue things in it, you get a new Queue object. How then, would you go about processing all items in it?

I'll go through that with an example. Let's say you have a queue of digits, and you want to compose a number out of them. For example, if I have a queue with 2, 1, 3, in that order, I want to get back the number 213. Let's first solve it with a mutable.Queue:

def toNum(q: scala.collection.mutable.Queue[Int]) = {
  var num = 0
  while (!q.isEmpty) {
    num *= 10
    num += q.dequeue
  }
  num
}

This code is fast and easy to understand. Its main drawback is that the queue that is passed is modified by toNum, so you have to make a copy of it beforehand. That's the kind of object management that immutability makes you free from.

Now, let's covert it to an immutable.Queue:

def toNum(q: scala.collection.immutable.Queue[Int]) = {
  def recurse(qr: scala.collection.immutable.Queue[Int], num: Int): Int = {
    if (qr.isEmpty)
      num
    else {
      val (digit, newQ) = qr.dequeue
      recurse(newQ, num * 10 + digit)
    }
  }
  recurse(q, 0)
}

Because I can't reuse some variable to keep track of my num, like in the previous example, I need to resort to recursion. In this case, it is a tail-recursion, which has pretty good performance. But that is not always the case: sometimes there is just no good (readable, simple) tail recursion solution.

Note, however, that I can rewrite that code to use an immutable.Queue and a var at the same time! For example:

def toNum(q: scala.collection.immutable.Queue[Int]) = {
  var qr = q
  var num = 0
  while (!qr.isEmpty) {
    val (digit, newQ) = qr.dequeue
    num *= 10
    num += digit
    qr = newQ
  }
  num
}

This code is still efficient, does not require recursion, and you don't need to worry whether you have to make a copy of your queue or not before calling toNum. Naturally, I avoided reusing variables for other purposes, and no code outside this function sees them, so I don't need to worry about their values changing from one line to the next -- except when I explicitly do so.

Scala opted to let the programmer do that, if the programmer deemed it to be the best solution. Other languages have chosen to make such code difficult. The price Scala (and any language with widespread mutability) pays is that the compiler doesn't have as much leeway in optimizing the code as it could otherwise. Java's answer to that is optimizing the code based on the run-time profile. We could go on and on about pros and cons to each side.

Personally, I think Scala strikes the right balance, for now. It is not perfect, by far. I think both Clojure and Haskell have very interesting notions not adopted by Scala, but Scala has its own strengths as well. We'll see what comes up on the future.