Partial Functions in Scala

Question

I just wanted to clarify something about partially defined functions in Scala. I looked at the docs and it said the type of a partial function is PartialFunction[A,B]

Answer 1

In the set theoretic view of a function, if a function can map every value in the domain to a value in the range, we say that this function is a total function. There can be situations where a function cannot map some element(s) in the domain to the range; such functions are called partial functions.

Taking the example from the Scala docs for partial functions:

val isEven: PartialFunction[Int, String] = {
  case x if x % 2 == 0 => x+" is even"
}

Here a partial function is defined since it is defined to only map an even integer to a string. So the input to the partial function is an integer and the output is a string.

val isOdd: PartialFunction[Int, String] = {
  case x if x % 2 == 1 => x+" is odd"
}

isOdd is another partial function similarly defined as isEven but for odd numbers. Again, the input to the partial function is an integer and the output is a string.

If you have a list of numbers such as:

List(1,2,3,4,5)

and apply the isEven partial function on this list you will get as output

List(2 is even, 4 is even)

Notice that not all the elements in the original list have been mapped by the partial function. However, there may be situations where you want to apply another function in those cases where a partial function cannot map an element from the domain to the range. In this case we use orElse:

val numbers = sample map (isEven orElse isOdd)

And now you will get as output:

List(1 is odd, 2 is even, 3 is odd, 4 is even, 5 is odd)