This is only my subjective point of view.
I use require whenever I want a constraint on parameters.
As an example we can take the factorial for natural numbers. As we do not want to address negative numbers, we want to throw an IllegalArgumentException.
I would use assert, whenever you want to make sure some conditions (like invariants) are always true during execution. I see it as a way of testing.
Here is an example implementation of factorial with require and assert
def fac(i: Int) = {
require(i >= 0, "i must be non negative") //this is for correct input
@tailrec def loop(k: Int, result: Long = 1): Long = {
assert(result == 1 || result >= k) //this is only for verification
if(k > 0) loop(k - 1, result * k) else result
}
loop(i)
}
When result > 1 is true, then the loop was executed at least once. So the result has to be bigger or equal to k. That would be a loop invariant.
When you are sure that your code is correct, you can remove the assert, but the require would stay.