The definition of pure function says that if the return value of a function is completely dependent on its arguments/parameters, then this function may be referred to as a pure function. So, if we declare a function as fun func1(x:Int):Int, then its return value will be strictly dependent on its argument x; say, if you call func1 with a value of 3 twice, then, for both the times, its return value will be the same. A pure function can be a lambda or a named function as well. In the previous example, the first lambda expression was a pure function but not the second one, as for the second one, its return value can be different at different times with the same value passed to it. Let's look at the following example to understand it better:

    fun square(n:Int):Int {//(1) 
      return n*n 
    } 
 
    fun main(args: Array<String>) { 
      println("named pure func square = ${square(3)}") 
      val qube = {n:Int -> n*n*n}//(2) 
      println("lambda pure func qube = ${qube(3)}") 
    } 

Both the functions, (1) and (2), here are pure functions–one is named, while the other is lambda. If you pass the value 3 to any of the functions n times, their return value will be the same for each time. Pure functions don't have side effects.

It is to note that, as we said earlier, pure functions have nothing to do with lambda expressions, their definitions are completely different.

The following is the output:

named pure func square = 9
lambda pure func qube = 27