Functions vs. methods in Scala

Here's a question that often comes up while teaching Scala: what's the difference between functions and methods. If you look this up on the web, you'll find many different answers, some of which are mathematically grounded but hardly helpful, others which are just plain confusing.

Here's how I like to explain it: a function is an object, just like any other expression: it has a type (which will be a subclass of FunctionN[T] where T is the type of the result and N is 0... according to the number of parameters the function requires). But note that the type is not a T but a function which must be invoked to yield a value of T. In Scala, this means that to get an actual T, you need to follow the function with a "(...)" where the number of parameters between the parentheses is N.

In Scala (or any other functional language for that matter), we can label expressions and functions by writing a statement like the following:

val a = 42

val f = { x: Int => x*x }

In the first case, our expression is quite simple: the constant 42 ("The answer to life, the universe and everything"). In the second case, it's a bit more complex (it's a function literal or "lamda"). But there's essentially no difference between the intent of the two statements. In each case, we have asserted that, from here on, whenever we write the variable "a", we mean 42 and wherever we write "f", we mean { x: Int => x*x }.

So much for functions. What about methods?

Methods aren't objects like functions. They are properties of a class or object. In an object-oriented language, if they are properties of a class, that implies that they are "instance methods", if of an object then they are just plain "methods".  A method is really just like a variable that is a property of a class/object. But it has a special syntax for its declaration which is more human-friendly than the syntax used above for the variable "f".

If we wanted to use the same function as a method in an object, then we could write it like this:

def m(x: Int) = x*x

This has exactly the same effect as with "f" above, except this time its label is "m" and it belongs to an object--it doesn't exist beyond the scope of that object. You can think of this form as syntactic sugar for "val m = { x: Int => x*x }".

So, what about instance methods? Instance methods are special to object-oriented programming because there is an implicit parameter which is generally written as this. It refers to the instance that is the "receiver" (class, owner, etc..) of the method.

Therefore we might define the following class:

class MyClass(x: Int) {
  def sqr = x*x
}

This time, we don't need to provide our own parameter to satisfy the need for "x" in the function (remember that this is essentially syntactic sugar for something that really looks like the definition of f above). The compiler supplies the parameter "this" and so "x" is now syntactic sugar for "this.x".

I do hope that I haven't made things even more confusing! And, I further hope that I haven't said anything that is clearly incorrect. But I don't believe so. However, if you consider yourself a Scala expert or are closely related to Martin Odersky, then feel free to add a clarifying or disputational comment.