Ok, I think I get it. That cleared it up. =).
So, if you have a functioned labelled pure, it's your job to not pass it 
mutable arguments, but the compiler's job to
make sure it doesn't mutate anything not in the arguments. And that's why a 
strongly pure function can call a weakly
pure one - only the first function's internal state can be mutated by a weakly 
pure function.
Thanks!

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