Combining distinct-thread state monads?

[Wolfgang Jeltsch]

Hello,

your problem can be solved with StateT:

(warning: untested code)

First we want to execute two independent state threads:
    start1 :: Monad m => StateT Int m startOutput1
    start1 = <definition as with State>

    start2 :: Monad m => StateT Bool m startOutput2
    start2 = <definition as with State>

After this there is a part where we want to use both states togeter:
    intermediate ::
        Monad m =>
        startOutput1 -> startOutput2 ->
        StateT Int (StateT Bool m) intermediateOutput
    intermediate = ...
In the definition of intermediate, the state monad functions like put and get 
act on the Int state.  To access the Bool state, you have to lift the state 
monad functions, like in lift (put s) and lift get.

Last but not least, we want both states to be processed independently again:
    end1 :: Monad m => intermediateOutput -> StateT Int m endOutput1
    end1 = <definition as with State>

    end2 :: Monad m => intermediateOutput -> StateT Int m endOutput2
    end2 = <definition as with State>

Now we combine these transformers:
    whole :: Monad m => StateT Int (StateT Bool m) (endOutput1,endOutput2)
    whole
        = do
            startOutput1 <- start1
            startOutput2 <- lift start2
            intermediateOutput <- intermediate startOutput1 startOutput2
            endOutput1 <- end1 intermediateOutput
            endOutput2 <- lift end2 intermediateOutput
            return endOutput1 endOutput2

We can run this state transformer by using the following utility function:
    runWhole ::
        Monad m => Int -> Bool -> m (((endOutput1,endOutput2),Int),Bool)
    runWhole initInt initBool = runStateT (runStateT whole initInt) initBool

We can get the resulting outputs and states with the definition:
    Identity (((endOutput1,endOutput2),finalInt),finalBool)
        = runWhole initInt initBool

Wolfgang

Am Dienstag, 6. Januar 2004 08:49 schrieb Dr Mark H Phillips:
> Hi,
>
> I am still learning about monads.  I have a problem
> in mind and am wondering whether state monads are
> able to solve it.  The difficulty is that it would
> necessitate the interaction of two state threads
> and I'm not sure whether Haskell state monads
> allow this.  Let me explain what I'm getting at.
>
> Consider two state threads.  The first has each state
> being a non-negative int, thought of as a string of
> binary digits.  The second thread has each state
> being a bool.
>
> Now I want to have a state monad which modifies
> both threads as follows.  Consider input states i (the
> int thought of as binary string) and b (the bool),
> and output states i' and b'.
>
>   b' = not (b && (i `mod` 2))
>   i' = i `div` 2
>
> As you can see, both of these should be able to do
> update-in-place provided the above order is adhered to.
> We could achieve this using state monads where state
> is an (Int, Bool) pair.  We would have one monad
> which did the first line, leaving i unchanged and
> a second monad which did the second line, leaving
> b' unchanged.
>
> But... what if before this interaction, the int
> thread and the bool thread were separate monads
> doing their own thing, and we just wanted to
> combine these threads briefly (using the above
> interaction) before letting the threads do their
> own thing again?  Is this possible?
>
> Also, suppose we have previously defined an int thread
> monad which takes i, returns a value of i `mod` 2,
> and changes the state to i' = i `div` 2.  Suppose
> also we have previously defined a bool thread
> monad which takes b, returns a nothing value, and
> changes the state to b' = not b.  Can we use
> these two monads (each acting on different
> threads), to form a combined-interaction monad
> that does (same as before):
>
>   b' = not (b && (i `mod` 2))
>   i' = i `div` 2
>
> I hope this is possible.  It would facilitate
> both code reuse and readability.  However I
> fear that it is not, requiring one to instead
> explicitly rewrite the two separate thread monads
> into (Int, Bool) pair acting ones.
>
> Cheers,
>
> Mark.