[Haskell-cafe] Random number example

[michael rice]

How do I define type Random [Int] for rollNDice in Exercise 1, given the code below?

Michael

============

Exercises

   1. Implement rollNDice :: Int -> Random [Int] from the previous subsection with >>= and return.

NOTE: Since >>= and return are already present in the Prelude, you may want to use import Prelude hiding ((>>=),return) to avoid compilation errors.

=================

{-# LANGUAGE NoImplicitPrelude #-}

import Prelude hiding ((>>), (>>=), return)

type Seed = Int
type Random a = Seed -> (a, Seed)

randomNext :: Seed -> Seed
randomNext rand = if newRand > 0 then newRand else newRand + 2147483647
    where newRand = 16807 * lo - 2836 * hi
          (hi,lo) = rand `divMod` 127773

rollDie :: Random Int
rollDie seed = ((seed `mod` 6) + 1, randomNext seed)

(>>) :: Random a -> Random b -> Random b
(>>) m n = \seed0 ->
  let (result1, seed1) = m seed0
      (result2, seed2) = n seed1
  in (result2, seed2)

(>>=) :: Random a -> (a -> Random b) -> Random b
(>>=) m g = \seed0 -> 
  let (result1, seed1) = m seed0
      (result2, seed2) = (g result1) seed1
  in (result2, seed2)

return :: a -> Random a
return x = \seed0 -> (x, seed0)

sumTwoDice :: Random Int
sumTwoDice = rollDie >>= (\die1 -> rollDie >>= (\die2 -> return (die1 + die2)))

rollNDice :: Int -> Random [Int]


--- On Thu, 4/23/09, michael rice <nowgate at yahoo.com> wrote:

From: michael rice <nowgate at yahoo.com>
Subject: Re: [Haskell-cafe] Random number example
To: "Ross Mellgren" <rmm-haskell at z.odi.ac>
Cc: haskell-cafe at haskell.org
Date: Thursday, April 23, 2009, 5:49 PM

Hi Ross,

Thanks for going the extra mile. A lot of what you did I haven't seen before, so it's going to take me some time to go through it. But I'll be back.

Michael

--- On Thu, 4/23/09, Ross Mellgren <rmm-haskell at z.odi.ac> wrote:

From: Ross Mellgren <rmm-haskell at z.odi.ac>
Subject: Re: [Haskell-cafe] Random number example
To: "michael rice" <nowgate at yahoo.com>
Cc: haskell-cafe at haskell.org
Date: Thursday, April 23, 2009, 11:51 AM

So there are a couple problems. First is you are trying to rebind prelude functions, when instead you should be creating an instance of Monad. This requires a bit of shuffling because without language extensions you can't instance Monad
 Random for your type of Random, as it is a type synonym. So, changing the type synonym to a newtype and instancing monad, you get:
module Rand9b where
import Control.Applicative (Applicative(..), (<$>), (<*>))import Control.Monad (ap, liftM)
type Seed = Intnewtype Random a = Rand { unRand :: (Seed -> (a, Seed)) }
randomNext :: Seed -> SeedrandomNext rand = if newRand > 0 then newRand else newRand + 2147483647    where newRand = 16807 * lo - 2836 * hi          (hi,lo) = rand `divMod` 127773
rollDie :: Random IntrollDie = Rand $ \ seed -> ((seed `mod` 6) + 1, randomNext seed)
instance Monad Random where    (>>=) =
 randomBind    return = randomReturn
instance Functor Random where    fmap = liftM
instance Applicative Random where    pure = return    (<*>) = ap
randomBind :: Random a -> (a -> Random b) -> Random bm `randomBind` g = Rand $ \seed0 ->   let (result1, seed1) = unRand m $ seed0      (result2, seed2) = unRand (g result1) $ seed1  in (result2, seed2)
randomReturn :: a -> Random arandomReturn x = Rand $ \ seed0 -> (x, seed0)
sumTwoDice :: Random IntsumTwoDice = (+) <$> rollDie <*> rollDie

I also threw in instances of Functor and Applicative,
 so that I could simplify sumTwoDice using applicative form (much nicer, no? Applicative is totally rockin')
Now you need one more thing, a way to convert a series of Random actions into a pure function:

runRandom :: Seed -> Random a -> arunRandom s f = fst . unRand f $ s 
which now makes what you want to do in GHCi easy and well wrapped:
Prelude> :reload[1 of 1] Compiling Rand9b           ( rand9b.hs, interpreted )Ok, modules loaded: Rand9b.*Rand9b> runRandom 0 sumTwoDice3

Hope this helps,-Ross

On Apr 23, 2009, at 11:28 AM, michael rice wrote:
I pretty much followed the sequence of steps that led to this final code (see below), but will be looking it over for a while to make sure it sinks in. In the meantime, I get this when I try to use it (sumTwoDice) at the command line:

[michael at localhost ~]$ ghci rand9
GHCi, version 6.10.1: http://www.haskell.org/ghc/  :? for help
Loading package ghc-prim ... linking ... done.
Loading package integer ... linking ... done.
Loading package base ... linking ... done.
[1 of 1] Compiling Main             ( rand9.hs, interpreted )
Ok,
 modules loaded: Main.
*Main> sumTwoDice

<interactive>:1:0:
    No instance for (Show (Seed -> (Int, Seed)))
      arising from a use of `print' at <interactive>:1:0-9
    Possible fix:
      add an instance declaration for (Show (Seed -> (Int, Seed)))
    In a stmt of a 'do' expression: print it
*Main> 


Can I employ a 'do' expression from the command line?

Also, can I now use functions (>>) (>>=) and 'return' defined in the Prelude and still have this code work?

Michael

==================

{-# LANGUAGE NoImplicitPrelude #-}

import Prelude hiding ((>>), (>>=), return)

type Seed = Int
type Random a = Seed -> (a, Seed)

randomNext :: Seed -> Seed
randomNext rand = if newRand > 0 then newRand else newRand +
 2147483647
    where newRand = 16807 * lo - 2836 * hi
          (hi,lo) = rand `divMod` 127773

rollDie :: Random Int
rollDie seed = ((seed `mod` 6) + 1, randomNext seed)

(>>) :: Random a -> Random b -> Random b
(>>) m n = \seed0 ->
  let (result1, seed1) = m seed0
      (result2, seed2) = n seed1
  in (result2, seed2)

(>>=) :: Random a -> (a -> Random b) -> Random b
(>>=) m g = \seed0 -> 
  let (result1, seed1) = m seed0
      (result2, seed2) = (g result1) seed1
  in (result2, seed2)

return :: a -> Random a
return x = \seed0 -> (x, seed0)

sumTwoDice :: Random Int
sumTwoDice = rollDie >>= (\die1 -> rollDie >>= (\die2 -> return (die1 + die2)))


      
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