One use case, as requested...
Imagine you have a list of things, could be integers, floating point numbers, matrices, strings, waveforms, etc. Given this list, you want to add the contents.
One way to do this would be to have some Addable trait that must be inherited by every single type that can be added together, or an implicit conversion to an Addable if dealing with objects from a third party library that you can't retrofit interfaces to.
This approach becomes quickly overwhelming when you also want to begin adding other such operations that can be done to a list of objects. It also doesn't work well if you need alternatives (for example; does adding two waveforms concatenate them, or overlay them?) The solution is ad-hoc polymorphism, where you can pick and chose behaviour to be retrofitted to existing types.
For the original problem then, you could implement an Addable type class:
trait Addable[T] {
def zero: T
def append(a: T, b: T): T
}
//yup, it's our friend the monoid, with a different name!
You can then create implicit subclassed instances of this, corresponding to each type that you wish to make addable:
implicit object IntIsAddable extends Addable[Int] {
def zero = 0
def append(a: Int, b: Int) = a + b
}
implicit object StringIsAddable extends Addable[String] {
def zero = ""
def append(a: String, b: String) = a + b
}
//etc...
The method to sum a list then becomes trivial to write...
def sum[T](xs: List[T])(implicit addable: Addable[T]) =
xs.FoldLeft(addable.zero)(addable.append)
//or the same thing, using context bounds:
def sum[T : Addable](xs: List[T]) = {
val addable = implicitly[Addable[T]]
xs.FoldLeft(addable.zero)(addable.append)
}
The beauty of this approach is that you can supply an alternative definition of some typeclass, either controlling the implicit you want in scope via imports, or by explicitly providing the otherwise implicit argument. So it becomes possible to provide different ways of adding waveforms, or to specify modulo arithmetic for integer addition. It's also fairly painless to add a type from some 3rd-party library to your typeclass.
Incidentally, this is exactly the approach taken by the 2.8 collections API. Though the sum method is defined on TraversableLike instead of on List, and the type class is Numeric (it also contains a few more operations than just zero and append)
