Functions vs methods in Scala

I am watching Runar Bjarnason present Functional Programming for Beginners, and at 14:45 he defines a method:

def isDivisibleBy(k: Int): Int => Boolean = i => i % k == 0

and a function:

val isEven = isDivisibleBy(2)

What are the pros and cons of defining isEven as a function rather than a method?

I have read Scala Functions vs Methods as well as Difference between method and function in Scala, and I understand the semantic differences, but I wonder if there's some deeper reason in this case why a function might or might not be preferable to using a method:

def isEven = isDivisibleBy(2)

Under the hood, there are other differences between functions and methods. Generally, a plain method generated less overhead than a function (which technically is an object with an apply method).

However, if you try not to care about those differences and think of def, val and var as fields with different semantics, then it’s simply that def evaluates every time it gets called while val evaluates only once.

So, a val isEven = isDivisibleBy(2) should call isDivisibleBy(2) during its definition and assign the result of isDivisibleBy(2). E.g. it replaces the k in

def isDivisibleBy(k: Int): Int => Boolean = i => i % k == 0

with 2 and assigns the result of the final expression (in this case there is only one expression):

val isEven: Int => Boolean = i => i % 2 == 0

def isEven on the other hand does no such evaluation and results in a call to isDivisibleBy(2) every time.

That means, later, when you execute the code, isEven(11) generates in case of a val

11 % 2 == 0

and in case of a def, you’ll have

isDivisibleBy(2)(11)

and only after evaluating isDivisibleBy you’ll get the result.

You can add some debug code to isDivisibleBy to see the difference:

def isDivisibleBy(k: Int): Int => Boolean = {
  println("evaluating isDivisibleBy")
  i => i % k == 0
}

I'd like to address another point here. This defines isEven as a method:

def isEven = isDivisibleBy(2)

And this defines isEven as a method as well:

val isEven = isDivisibleBy(2)

In both cases, isEven is a method which, when called, return a function.

In the first case, isDivisible(2) is called every time isEven is called. For example, this calls isDivisible(2) three times:

def isEven = isDivisibleBy(2)
List(1,2,3).filter(isEven)

In the second case, isDivisible(2) is called once (at construction time, or when that line in a definition is executed), and that value is retrieved every time isEven is called. The following example calls isDivisible(2) one time only:

val isEven = isDivisibleBy(2)
List(1,2,3).filter(isEven)

I think that the main pro of defining the function isEven as val is to show to audience that the function can be defined this way. Then it's clear, that a function is just an object like everything else in scala. But in the world of non-demonstrating programming, there's no need to write functions as vals.

The method def isDivisibleBy(k: Int): Int => Boolean returns a function which takes an Int (i) as parameter and returns a Boolean (i % k == 0).

val isEven = isDivisibleBy(2) on the other hand is a field into which the function returned by isDivisibleBy(2) is stored. If you use def instead of val then the isDivisibleBy method would be called every time the isEven method is called, but now it's called only once and the result is stored in the field.

You could achieve the same result by writing def isEven(i: Int): Boolean = i % 2 == 0

I think the point of the example is that you can have functions which return other functions, and you can store the functions as objects, and then call them as if they were traditionally defined methods. The above code is also quite similar to currying, so that might also be one thing demonstrated by the example (although it doesn't use Scala's syntax for currying).