Bardur Arantsson:
Random streams are not referentially transparent, though, AFAICT...?
Either way this thread has gone on long enough, let's not prolong it needlessly with this side discussion.
but why should we forget about them? The usual approach(*) is to gather entropy from a truly(**) random source and use that to seed (and perhaps periodically re-seed) a PRNG. So, sorry, I didn't mean really "forget", only to change the subject which was irrelevant for the purity (but somehow has shown once more
Sure. But the discussion on randomness is /per se/ interesting, especially in a functional setting. Anyway, nobody can convince Steve Horne. Perhaps as an "unintentional" side-effect... But random streams, or rather pseudo-random streals (infinite lazy lists, as the example I gave, the `iterate` of `next`) are as referentially transparent as any Haskell data. Really. What I find really amazing, since I converted my soul from physics to computer since (many, many years ago...) is that most comments about random number generators come from people who don't need them, don't use them, and usually don't care about them... I taught random numbers, and I did some Monte-Carlo calculation in High Energy Physics, when many people here were not born. I *NEVER* used "true" random numbers, even to initialize a generator, since in the simulation business it is essential that you can repeat the sequence on some other platform, with some other parameters, etc. Of course, they are useful (don't need to convince an ancien physicist... And I lied. I used them, e.g. when I programmed some games for my children.) -- that Steve Horne had strange ideas about random generators). The generator of L'Ecuyer, or Mersenne Twister, or anything, don't care about the entropy. For a typical user, the only interesting thing is that the "random" streams pass the usual statistical tests : moments, correlation, spectrum... Otherwise it is as deterministic as 1 2 3 4. (For a typical user from my mafia. The mafia of cryptographists has different criteria ; from time to time we shoot ourselves in the coffee-machine corner of our dept.) Thank you for the discussion. You are right, I brake. Jerzy