If a function receives immutable state, returns immutable state, and does not depend or modify outside mutable state, then that function has no side effects. Mutating state within the function itself will not affect anything outside it and so mutations are not side effects, at least by default.

About your two situations, I am guessing you mean that the functions rely on state not being passed in, but rather on state referenced from the outer scope? I agree that that complicates both reasoning and testing, and so it should be avoided. In C/C++ this type of design (i.e. relying on static scope state) is practically always avoided as there's rarely any need for it.

If instead you mean that mutable references are being passed in as parameters then logic wise isn't this similar to assignment/binding in a functional language as long as you avoid propagating the side effect to other functions?

I am personally a great fan of immutability, just not functional languages. I can see the justification for limiting the tools at your disposable to guarantee certain things, it's just that in this case I think they are not sufficient.

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For those downvoting, gee thanks. I see how trying to have a discussion is hurting your feelings.