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Is (probabilistic) non-determinism pure ?

I am currently designing my own programming language (as many other visitors of this site are doing, too, I guess :-)). I want it to have a purely functional subset. I decided to include "random" and "choice" in this purely functional subset. My reasons why (probabilistic) non-determinism should still be considered (weakly) purely functional are outlined here in my blog. I am very interested in your opinions on this topic!