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Question:

I finally got a hold on how to use monads (don't know if I understand them...), but my code is never very elegant. I guess is from a lack of grip on how all those functions on `Control.Monad`

can really help. So I'd thought it would be nice to ask for tips on this in a particular piece of code using the state monad.

The goal of the code is to calculate many kinds of random walks, and it's something I'm trying to do before something more complicated. The problem is that I have two stateful computations at the same time, and I'd like to know how to compose them with elegance:

- The function that updates the random number generator is something of type
`Seed -> (DeltaPosition, Seed)`

- The function that updates the position of the random walker is something of type
`DeltaPosition -> Position -> (Log, Position)`

(where`Log`

is just some way for me to report what is the current position of the random walker).

What I've done is this:

I have a function to compose this two stateful computations:

`composing :: (g -> (b, g)) -> (b -> s -> (v,s)) -> (s,g) -> (v, (s, g)) composing generate update (st1, gen1) = let (rnd, gen2) = generate gen1 (val, st2) = update rnd st1 in (val, (st2, gen2)) `

and then I turn it into a function that compose states:

`stateComposed :: State g b -> (b -> State s v) -> State (s,g) v stateComposed rndmizer updater = let generate = runState rndmizer update x = runState $ updater x in State $ composing generate update `

And then I have the simplest thing, for example, a random walker that will just sum a random number to its current position:

`update :: Double -> State Double Double update x = State (\y -> let z = x+y in (z,z)) generate :: State StdGen Double generate = State random rolling1 = stateComposed generate update `

and a function to do this repeatedly:

`rollingN 1 = liftM (:[]) rolling1 rollingN n = liftM2 (:) rolling1 rollings where rollings = rollingN (n-1) `

And then, if I load this in `ghci`

and run:

`*Main> evalState (rollingN 5) (0,mkStdGen 0) [0.9872770354820595,0.9882724161698186,1.9620425108498993,2.0923229488759123,2.296045158010918] `

I get what I want, which is a list of the positions occupied by the random walker. But... I feel there must be a more elegant way to do this. I have two questions:

Can I rewrite those functions in a more "monadic" way, using clever functions from

`Control.Monad`

?Is there a general pattern about combining states like this that can be used? Does this have something to do with monad transformers or something like that?

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Solution:1

Update: I should have mentioned that there's actually a much nicer way to do this that doesn't require `State`

or monads at all:

`takeStep :: (Double, StdGen) -> (Double, StdGen) takeStep (p, g) = let (d, g') = random g in (p + d, g') takeSteps n = take n . tail . map fst $ iterate takeStep (0, mkStdGen 0) `

It works as desired:

`*Main> takeSteps 5 [0.9872770354820595,0.9882724161698186,1.9620425108498993,2.0923229488759123,2.296045158010918] `

If you're not committed to the idea of "composing" two separate stateful computations, you can accomplish the same thing much more straightforwardly:

`takeStep :: State (Double, StdGen) Double takeStep = do (pos, gen) <- get let (delta, gen') = random gen let pos' = pos + delta put (pos', gen') return pos' takeSteps n = evalState (replicateM n takeStep) (0, mkStdGen 0) `

This produces the same output as your example:

`*Main> takeSteps 5 [0.9872770354820595,0.9882724161698186,1.9620425108498993,2.0923229488759123,2.296045158010918] `

This approach (doing all the state manipulation in a single monad instead of trying to compose a `State A`

and `State B`

) seems to me like the most elegant solution.

Update: To answer your question about using monad transformers to stack `State`

monads: it's certainly possible. We can write the following, for example:

`update' :: (Monad m) => Double -> StateT Double m Double update' x = StateT $ \y -> let z = x + y in return (z, z) generate' :: (Monad m) => StateT StdGen m Double generate' = StateT $ return . random takeStep' :: StateT Double (State StdGen) Double takeStep' = update' =<< lift generate' takeSteps' n = evalState (evalStateT (replicateM n takeStep') 0) $ mkStdGen 0 `

We could also do the stacking in the opposite order.

This version again produces the same output, but in my opinion the non-`StateT`

version is a bit clearer.

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Solution:2

The usual way to compose 2 monads (and the only way for most monads) is with monad transformers, but with different `State`

monads you have more options. For example: you could use these functions:

`leftState :: State a r -> State (a,b) r leftState act = state $ \ ~(a,b) -> let (r,a') = runState act a in (r,(a',b)) rightState :: State b r -> State (a,b) r rightState act = state $ \ ~(a,b) -> let (r,b') = runState act b in (r,(a,b')) `

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