does kotlin have a way to turn a function into one which is evaluated only once? Something like

fun <R> (() -> R).evalOnce(): () -> R {
    val v by lazy { this() }
    return { v }
}

but which works also for functions with one or more parameters?

Do you mean memoization?

kind of yes

Well part of the memoization would involve making sure that the parameters matched a previous call. You'd probably have to roll your own on this one.

It seems you want a cache

ok, thanks for the information

If you want to make this generic, I'd suggest that you make your memoization function, a simple way to get around the multi-argument problem is just make a version of the function that takes one arg and when you need more args, throw those into a data class.