[Haskell] Re: About Random Integer without IO

[Thomas Davie]

This method unfortunately depends on having a seed first though.  One 
must use a different value every time the program is started, commonly 
time or the first few bytes from /dev/random.  Any one of these is 
going to require a monadic function to generate (i.e. it must come from 
the environment in some way - it must change every time you run the 
program)

So while this eliminates the IO monad from most of the program, it must 
still be initiated using it.

Thanks

Tom Davie

--
Computer Science is as much about computers as astronomy is about 
telescopes -- Edsgar Dijkstra

On 11 Nov 2004, at 20:58, karczma wrote:

> Georg Martius answers the request of:
> Jose Manuel Hernando Cobeña
>>> I need generate random numbers by create polygons with "wxHaskell",
>>> I am searching in the web, but all I only find IO functions like
>>>>> test :: Integer -> IO Integer
> ...
>>> I need this but with types :: Integer -> Integer
>
>> you need to reallise that Haskell is a pure language. That means a 
>> function has the same result if you call it with the same arguments 
>> (deterministic). A function that produces random numbers are not of 
>> such kind in the first place.
>
> All depends on how you organize your computations.
> 1. You may in a purely functional, non-monadic way produce an infinite
>  list, a stream of numbers, and use them as you wish, incrementally.
>  gener seed =(aaa*seed + ccc) `mod` mmm     -- or something alike...
>  strm = st seed0 where
>    st x = x : st (gener x)
>  Eventually, you can directly pass the updated seed from one function 
> to
>  another in your program. In two words, write your programs in CPS, or
>  a little 'monadized' style.
>  Of course, you can transform the result from an integer between 0 and
>  mmm-1 to other thing.
> 2. Despite what G. Martius says, you CAN USE a pure, deterministic 
> function
>  to produce something which looks randomly, it suffices to change the
>  argument. Concretely, Ward in Graphics Gems, and other people in other
>  places propose 'chaotic', *ergodic* functions, which vary wildly from
>  arg to arg, even neighbouring.
>  This is a "kind of hashing function".
>  An example can be found in this tutorial
>  http://freespace.virgin.net/hugo.elias/models/m_perlin.htm
>  You take an integer, and mix its bits by taking xors, modulo,
>  polynomials, etc.
>  Then, such a function sampled for j=0,1,2,3, ... N will look like
>  a genuinely random signal, without any need to 'propagate' anything.
>
> Jerzy Karczmarczuk
> PS. Georg Martius concludes:
>> PS: this question is more appropriate for haskell-cafe.
>
> Well, why not haskell-bratwurst-mit-pils?  The protocol of making/using
> random stuff within Haskell is a specific problem which is not very 
> well
> developed nor taught, but it is not anecdotical, it may be important.
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