[Haskell-cafe] Stacking State on State.....

[Daniel Fischer]

Am Samstag, 28. Februar 2009 13:23 schrieb Phil:
> Hi,
>
> The problem is ­ HOW DO I WRAP ANOTHER INDEPENDENT STATE AROUND THIS?
>
> After some googling it looked like the answer may be Monad Transformers.
> Specifically we could add a StateT transform for our Box Muller state to
> our VanDerCorput State Monad.
> Google didn¹t yield a direct answer here ­ so I¹m not even sure if my
> thinking is correct, people describe the process of using a transform as
> Œwrapping one monad in another¹ or Œthreading one monad into another¹. 
> What we want to do is have some internal state controlled by an independent
> outer state -  this sounds about right to me?

If you absolutely don't want to have a state describing both, yes.

>
> So I started playing around with the code, and got the below to compile.
>
> test ::  StateT (Bool,Double) (State Int) Double
> test = do (isStored,normal) <- get
>           let (retNorm,storeNorm) = if isStored
>                                     then (normal,0)
>                                     else (n1,n2)
>                                             where
>                                               n1 = 2
>                                               n2 = 3
>           put (not isStored, storeNorm)
>           return retNorm
>
> Now this is incomplete and may be even wrong!  I¹ll Explain my thinking:
>
> (Bool,Double) is equivalent to myState and storedNormal in the C example
> The last Double is the return value of the BoxMuller Monad
> The (State Int) is supposed to represent the VanDerCorput monad ­ but the
> compiler (GHC 6.10) will only let me specify one parameter with it ­ so
> I¹ve put the state and left the return type to the gods!!.... As I said
> this isn¹t quite right ­ any ideas how to specify the type?

You can't, the second argument to StateT must be a Monad, hence a type 
constructor you can pass an arbitrary type which then produces a new type 
from that.
Fortunately, you don't need to.

Say you have

type VDCMonad = State Int

nextVDC :: VDCMonad Double
nextVDC = do
	n <- get
	put $! (n+1)
	return $ calculateVDCFromInt n

Then you could have

boxMullerVDC :: StateT (Maybe Double) VDCMonad Double
boxMullerVDC = StateT $ \s -> case s of
				Just d -> return (d,Nothing)
				Nothing -> do
					d1 <- nextVDC
					d2 <- nextVDC
					let (b1,b2) = boxMullerTransform d1 d2
					return (b1,Just b2)

(I find a state of Maybe a more natural to indicate that *maybe* I have one a 
in store to use directly, than using (Bool,a)).

However, I suspect that you would get better code if you abstracted over the 
sequence of pseudorandom Doubles and had simply

calculation :: Sate [Double] whatever
calculation = ???

result = evalState calculation bmVDC

bmVDC = boxMuller $ map vanDerCorput [1 .. ]
	where
		boxMuller (k:n:more) = u:v:boxMuller more
		    where
			(u,v) = bmTransform k n

>
> The next few lines get and test the BoxMuller state, this seems to work OK
> to me, the problem is when I try to look at the STATE OF THE INTERNAL
> monad. n1 and n2 should evaluate and increment the state of VanDerCorput
> monad ­ but I can¹t get anything to compile here.  2 and 3 are just dummy
> values to make the thing compile so I could debug.
>
> My last gripe is how to actually call this from a pure function ­ do I need
> to use both evalStateT and evalState ­ I can¹t see how to initialize both
> the inner and outer state ?

result = evalState (evalStateT calculation Nothing) 1

>
> OK ­ I think that¹s more than enough typing, apologies for the war&peace
> sized post.
>
> Any help muchly muchly appreciated,
>
> Many Thanks,
>
> Phil.

HTH,
Daniel