Haskell Nomads

So can anybody tell me in a way one can understand it what a fucking monad does?

>>40
There's nothing to it, really. Monads allow you to express a purely functional computation while keeping some aspect of that computation hidden or implicit. For example, if you wanted to write a function that returns a list of n random numbers using the function random :: (RandomGen g, Random a) => g -> (a, g), you'd write something like this:

nRandoms n gen
   | n <= 0 = ([], gen)
   | otherwise = (r:rs, gen'')
   where
      (r, gen') = random gen
      (rs, gen'') = nRandoms (n - 1) gen'

See how you have to explicitly handle the "state changes" of the random generator by passing it around? Well, if you turn the random function into a State monad:

randomS :: (RandomGen g, Random a) => State g a
randomS = State random

then you can write nRandoms like this:

nRandomsS n
   | n <= 0 = return []
   | otherwise = liftM2 (:) randomS (nRandomsS (n - 1))

nRandoms n gen = runState (nRandomsS n) gen

or even like this:

nRandoms n gen = runState (replicateM n randomS) gen

What this particular monad, the State monad, does is handle the state changes implicitly, so you don't have to worry about it. Here's (part of) the definition of that monad, see how simple it is:

newtype State s a = State { runState :: s -> (a, s) }

instance Monad (State s) where
    return a = State $ \s -> (a, s)
    m >>= k  = State $ \s -> let (a, s') = runState m s
                                 in runState (k a) s'

Hope this helps clear things up for you.