Identity and constant are straightforward functions. The identity function returns the same value provided as parameter; similar to additive and multiplicative identity property, adding 0 to any number is still the same number.

The constant<T, R>(t: T) function returns a new function that will always return the t value:

fun main(args: Array<String>) {

   val oneToFour = 1..4

   println("With identity: ${oneToFour.map(::identity).joinToString()}") //1, 2, 3, 4

   println("With constant: ${oneToFour.map(constant(1)).joinToString()}") //1, 1, 1, 1
   
}

We can rewrite our fizzBuzz value using constant:

fun main(args: Array<String>) {
   val fizz = PartialFunction({ n: Int -> n % 3 == 0 }, constant("FIZZ"))
   val buzz = PartialFunction({ n: Int -> n % 5 == 0 }, constant("BUZZ"))
   val fizzBuzz = PartialFunction({ n: Int -> fizz.isDefinedAt(n) && buzz.isDefinedAt(n) }, constant("FIZZBUZZ"))
   val pass = PartialFunction<Int, String>(constant(true)) { n -> n.toString() }

   (1..50).map(fizzBuzz orElse buzz orElse fizz orElse pass).forEach(::println)
}

Identity and constant functions are useful in functional programming or in implementations of math algorithms, for example, constant is K in SKI combinator calculus.