[Haskell-cafe] Stacking State on State.....
Andrew Wagner
wagner.andrew at gmail.com
Sat Feb 28 09:36:44 EST 2009
Ok, so this question of stacking state on top of state has come up several
times lately. So I decided to whip up a small example. So here's a goofy
little example of an abstract representation of a computer that can compute
a value of type 'a'. The two states here are a value of type 'a', and a
stack of functions of type (a->a) which can be applied to that value.
Disclaimer: this code is only type-checked, not tested!
import Control.Monad.State
-- first, we'll rename the type, for convenience
type Programmable a = StateT [a->a] (State a)
-- add a function to the stack of functions that can be applied
-- notice that we just use the normal State functions when dealing
-- with the first type of state
add :: (a -> a) -> Programmable a ()
add f = modify (f:)
-- add a bunch of functions to the stack
-- this time, notice that Programmable a is just a monad
addAll :: [a -> a] -> Programmable a ()
addAll = mapM_ add
-- this applies a function directly to the stored state, bypassing the
function stack
-- notice that, to use State functions on the second type of state, we must
use
-- lift to get to that layer
modify' :: (a -> a) -> Programmable a ()
modify' f = lift (modify f)
-- pop one function off the stack and apply it
-- notice again the difference between modify' and modify. we use modify' to
modify the value
-- and modify to modify the function stack. This is again because of the
order in which we wrapped
-- the two states. If we were dealing with StateT a (State [a->a]), it would
be the opposite.
step :: Programmable a ()
step = do
fs <- get
let f = if (null fs) then id else (head fs)
modify' f
modify $ if (null fs) then id else (const (tail fs))
-- run the whole 'program'
runAll :: Programmable a ()
runAll = do
fs <- get
if (null fs) then (return ()) else (step >> runAll)
On Sat, Feb 28, 2009 at 8:31 AM, Daniel Fischer <daniel.is.fischer at web.de>wrote:
> 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
>
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