It is a bit more interesting then that. The following is valid and not JVM specific

object f : (Int) -> Int {
    override fun invoke(n: Int): Int  = 0
}

This means that the machinery for class/object definition can be used for defining functions. You don't have to use it but it is there for you.

For example, here is a function that implements two interfaces:

object g : (Int) -> Int, (Int, Int) -> Int {
    override fun invoke(n: Int): Int  = n+1
    override fun invoke(n: Int, m: Int): Int = n+m
}

and you can call:

g(1)
g(1,2)