KDB+/Q: how to understand the definitions in the language reference?

Question

I am trying to understand the definition of an atomic function quoted here: .[f;x]~.[f';x]

Now I believe the . is function application as documented here, but what is f' in the above ?

Answer 1

The statement is saying that the two are equivalent and that using each is not required in an atomic function i.e. .[f;x] is essentially .[f';x]

You can see this in the example given here where + is f and (2;(3 4;5)) x https://code.kx.com/q/basics/atomic/

q).[+;(2;(3 4;5))]
5 6
7
q).[+';(2;(3 4;5))]   / the iterator is unnecessary
5 6
7

where the function + is applied to each item in the nested list using the atomic function