Thursday 10 November 2011

Implicit Conversions in Scala

Following on from the previous post on operator overloading I'm going to be looking at Implicit Conversions, and how we can combine them to with operator overloading to do some really neat things, including one way of creating a multi-parameter conversion.

So what's an "Implicit Conversion" when it's at home?

So lets start with some basic Scala syntax, if you've spent any time with Scala you've probably noticed it allows you to do things like:

   (1 to 4).foreach(println) // print out 1 2 3 4 

Ever wondered how it does this? Lets make things more explicit, you could rewrite the above code as:

    val a : Int = 1
    val b : Int = 4
    val myRange : Range = a to b
    myRange.foreach(println)

Scala is creating a Range object directly from two Ints, and a method called to.

So what's going on here? Is this just a sprinkling of syntactic sugar to make writing loops easier? Is to just a keyword in like def or val?

The answers to all this is no, there's nothing special going on here. to is simply a method defined in the RichInt class, which takes a parameter and returns a Range object (specifically a subclass of Range called Inclusive). You could rewrite it as the following if you really wanted to:

   val myRange : Range = a.to(b)

Hang on though, RichInt may have a "to" method but Int certainly doesn't, in your example you're even explicitly casting your numbers to Ints

Which brings me nicely on to the subject of this post, Implicit Conversions. This is how Scala does this. Implicit Conversions are a set of methods that Scala tries to apply when it encounters an object of the wrong type being used. In the case of the to example there's a method defined and included by default that will convert Ints into RichInts.

So when Scala sees 1 to 4 it first runs the implicit conversion on the 1 converting it from an Int primitive into a RichInt. It can then call the to method on the new RichInt object, passing in the second Int (4) as the parameter.

Hmm, think I understand, how's about another example?

Certainly. Lets try to improve our Complex number class we created in the previous post.

Using operator overloading we were able to support adding two complex numbers together using the + operator. eg.

class Complex(val real : Double, val imag : Double) {
  
  def +(that: Complex) = 
            new Complex(this.real + that.real, this.imag + that.imag)
  
  def -(that: Complex) = 
            new Complex(this.real - that.real, this.imag - that.imag)

  override def toString = real + " + " + imag + "i"
  
}

object Complex {
  def main(args : Array[String]) : Unit = {
       var a = new Complex(4.0,5.0)
       var b = new Complex(2.0,3.0)
       println(a)  // 4.0 + 5.0i
       println(a + b)  // 6.0 + 8.0i
       println(a - b)  // 2.0 + 2.0i
  }
}

But what if we want to support adding a normal number to a complex number, how would we do that? We could certainly overload our "+" method to take a Double argument, ie something like...

    def +(n: Double) = new Complex(this.real + n, this.imag)

Which would allow us to do...

    val sum = myComplexNumber + 8.5

...but it'll break if we try...

    val sum = 8.5 + myComplexNumber

To get around this we could use an Implicit Conversion. Here's how we create one.

  object ComplexImplicits {
    implicit def Double2Complex(value : Double) = 
                                     new Complex(value,0.0) 
 }

Simple! Although you do need to be careful to import the ComplexImplicits methods before they can be used. You need to make sure you add the following to the top of your file (even if your Implicits object is in the same file)...

   import ComplexImplicits._

And that's the problem solved, you can now write val sum = 8.5 + myComplexNumber and it'll do what you expect!

Nice. Is there anything else I can do with them?

One other thing I've found them good for is creating easy ways of instantiating objects. Wouldn't it be nice if there were a simpler way of creating one of our complex numbers other than with new Complex(3.0,5.0). Sure you could get rid of the new by making it a case class, or implementing an apply method. But we can do better, how's about just (3.0,5.0)

Awesome, but I'd need some sort of multi parameter implicit conversion, and I don't really see how that's possible!?

The thing is, ordinarily (3.0,5.0) would create a Tuple. So we can just use that tuple as the parameter for our implicit conversion and convert it into a Complex. how we might go about doing this...

  implicit def Tuple2Complex(value : Tuple2[Double,Double]) = 
                               new Complex(value._1,value._2);

And there we have it, a simple way to instantiate our Complex objects, for reference here's what the entire Complex code looks like now.

import ComplexImplicits._

object ComplexImplicits {
  implicit def Double2Complex(value : Double) = new Complex(value,0.0) 

  implicit def Tuple2Complex(value : Tuple2[Double,Double]) = new Complex(value._1,value._2);

}

class Complex(val real : Double, val imag : Double) {
  
  def +(that: Complex) : Complex = (this.real + that.real, this.imag + that.imag)
  
  def -(that: Complex) : Complex = (this.real - that.real, this.imag + that.imag)
      
  def unary_~ = Math.sqrt(real * real + imag * imag)
         
  override def toString = real + " + " + imag + "i"
  
}

object Complex {
  
  val i = new Complex(0,1);
  
  def main(args : Array[String]) : Unit = {
       var a : Complex = (4.0,5.0)
       var b : Complex = (2.0,3.0)
       println(a)  // 4.0 + 5.0i
       println(a + b)  // 6.0 + 8.0i
       println(a - b)  // 2.0 + 8.0i
       println(~b)  // 3.60555
      
       var c = 4 + b
       println(c)  // 6.0 + 3.0i
       var d = (1.0,1.0) + c  
       println(d)  // 7.0 + 4.0i
       
  }

}

"Operator Overloading" in Scala

So, I've been teaching myself Scala recently, and it's a very interesting language.

One of the nice things I like about it, is it's support for creating DSLs, domain specific languages. A domain specific language - or at least my understanding of it - is a language that is written specifically for one problem domain. One example would be SQL, great for querying relational databases, useless for creating first person shooters.

Of course Scala itself is not a DSL, it's a general purpose language. However it does offer several features that allow you to simulate a DSL, in particular operator overloading, and implicit conversions. In this post I'm going to focus on the first of these...

Operator Overloading

So what's operator overloading?

Well operators are typically things such as +, -, and !. You know those things you use to do arithmetic on numbers, or occasionally for manipulating Strings. Well, operator overloading - just like method overloading - allows you to redefine their behaviour for a particular type, and give them meaning for your own custom classes.

Hang on a minute! I'm sure someone once told me operator overloading was evil?

Indeed, this is quite a controversial topic. It's considered far too open for abuse by some, and was so maligned in C++ that the creators of Java deliberately disallowed it (excepting "+" for String concatenation).

I'm of a slightly different opinion, used responsibly it can be very useful. For example lots of different objects support a concept of addition, so why not just use an addition operator?

Lets say you were developing a complex number class, and you want to support addition. Wouldn't it be nicer to write...

Complex result = complex1 + complex2;

...rather than...

Complex result = complex1.add(complex2);

The first example is much more natural don't you think?

So Scala allows you to overload operators then?

Well, not really. In fact, technically not at all.

So all this is just a tease? This is the most stupid blog post I've ever read. Scala's rubbish. I'm going back to Algol 68.

Wait a second, I've not finished. You see Scala doesn't support operator overloading, because it doesn't have operators!

Scala doesn't have operators? You've gone mad, I write stuff like "sum = 2 + 3" all the time, and what about all those funny list operations? "::", and ":/". They look like operators to me!

Well they're not. The thing is, Scala has a rather relaxed attitude to what you can name a method.

When you write...

sum = 2 + 3,

...you're actually calling a method called + on a RichInt type with a value of 2. You could even rewrite it as...

sum = 2.+(3)

...if you really really wanted to.

Aha, I got it. So how do you go about overloading an operator then?

Simple, it's exactly the same as writing a normal method. Here's an example.

class Complex(val real : Double, val imag : Double) {
  
  def +(that: Complex) = 
            new Complex(this.real + that.real, this.imag + that.imag)
  
  def -(that: Complex) = 
            new Complex(this.real - that.real, this.imag - that.imag)

  override def toString = real + " + " + imag + "i"
  
}

object Complex {
  def main(args : Array[String]) : Unit = {
       var a = new Complex(4.0,5.0)
       var b = new Complex(2.0,3.0)
       println(a)  // 4.0 + 5.0i
       println(a + b)  // 6.0 + 8.0i
       println(a - b)  // 2.0 + 2.0i
  }
}
Ok that's nice, what if I wanted a "not" operator though, ie something like a "!"

That's a unary prefix operator, and yes scala can support these, although in a more limited fashion than an infix operator like "+"

Only four operators can be supported in this fashion, +, -, !, and ~. You simply need to call your methods unary_! or unary_~, etc. Here's how you might add a "~" to calculate the magnitude of a Complex number to our complex number class

class Complex(val real : Double, val imag : Double) {
    // ...
    def unary_~ = Math.sqrt(real * real + imag * imag)
}

object Complex {
  def main(args : Array[String]) : Unit = {
     var b = new Complex(2.0,3.0)
     prinln(~b) //  3.60555
   }
}

So that's all pretty simple, but please use responsibly. Don't create methods called "+" unless your class really does something that could be interpreted as addition. And never ever redefine the binary shift left operator "<<" as some sort of substitute for println. It's not clever and you'll make the Scala gods angry.

Hope you found that useful. Next up I'll cover implicit conversions. Another nice feature of Scala that really allows you to write your code in a more natural way