[Haskell-cafe] Different forms for RandomT?

[Daniel Gorín]

> Normally, a monad transformer to provide a random number generator 
> would be of the form StateT g, where g is a RandomGen. But I've seen 
> some libraries (like QuickCheck) define their RandomT as:
> 
> newtype RandomT g m a = RandomT { runRandomT :: g -> m a }
> 
> with their monadic bind operation defined as
> 
> (RandomT m) >>= f = RandomT $ \g -> let (ga, gb) = split g in m ga >>= 
> (\a -> runRandomT (f a) gb)
> 
> and return and fail as in ReaderT.
> 
> Can someone describe the advantages and disadvantages of doing RandomT 
> this way? I mean, if your generator has a subpar split operation (and 
> most do), this will obviously exacerbate any problems > with it. Does 
> it give any comparable advantages?
> 

A disadvantage is that it is too easy to end up with a monad that 
doesn’t respect the monad laws. For example, in the following, we expect 
ver_1 and ver_2 to be the same computation and yet their outputs 
differs...

> import System.Random
> 
> newtype RandomT g m a = RandomT { runRandomT :: g -> m a }
> 
> instance (Monad m, RandomGen g) => Monad (RandomT g m) where
>   return = RandomT . const . return
>   (RandomT m) >>= f = RandomT $ \g ->
>     let (ga, gb) = split g
>     in  m ga >>= (\a -> runRandomT (f a) gb)
> 
> sample :: (RandomGen g, Monad m) => RandomT g m Int
> sample = RandomT $ \g -> return (fst $ next g)
> 
> main :: IO ()
> main = do
>   let probe m = runRandomT m (mkStdGen 42)
>   res_1 <- probe ver_1
>   res_2 <- probe ver_2
>   print (res_1,res_2)
> where
>   ver_1 = sample
>   ver_2 = return () >> sample

It is because of this that QuickCheck warns that "Gen is only morally a 
monad: two generators that are supposed to be equal will give the same 
probability distribution, but they might be different as functions from 
random number seeds to values.” [1]. You rarely notice this when using 
quickcheck... except perhaps if you are trying to debug or refactor a 
complex generator, and then good luck with that!


[1] 
https://hackage.haskell.org/package/QuickCheck-2.8.1/docs/Test-QuickCheck-Gen-Unsafe.html