Re: [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 Cobeņa
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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