[Haskell-cafe] Help defining a Typeable polymorphic-state monad transformer

[Brandon Simmons]

Hi all,

I gave myself until this evening to figure this out on my own, and
time is up! Hopefully this makes for a good discussion, though the
idea could be dumb.

What I'm trying to do is define a state monad in which the passed
state can change type during the computation. The only constraint is
that the state types must always be of the Typeable class (see:
http://hackage.haskell.org/packages/archive/base/latest/doc/html/Data-Typeable.html
).

The idea is that the new monad would be something like 'StateT s Maybe
a', but where the 's' type is not fixed (indeed is hidden in an
existential type) and where any programmer errors in the chaining of
the polymorphic state will be caught in the Maybe type (or really the
'fail' implementation of any monad).

Here is how I imagine a computation might look:

    computation :: TypeableState Maybe String
    computation = do
        (c:cs) <-  getTS
        putTS (length cs)
        return ("c" ++ " was the first letter of the string passed as
initial state.")

So TypeableState is very similar to StateT, except that the state type
is not present as a type argument. In the example above 'Maybe' is the
monad that catches Typeable errors, and String is the return type of
the computation.

getTS and putTS would be get and put functions that constrain their
arguments to the Typeable class.

Here is what I have so far (at least this is my most recent
uncommented attempt):

> {-# LANGUAGE ExistentialQuantification #-}
> module Main
>       where
>
> import Control.Monad.State
> import Data.Typeable
>
> -- we might have restricted our 'm' to MonadPlus and used the explicit
> -- 'mzero', but decided instead to use Monad, with 'fail'. This is
> -- more appropriate since we won't be using 'mplus'. See 'liftMaybe'.
> data TypeableState m a = forall s0 sN. (Typeable s0, Typeable sN)=>
>                            TypeableState (s0 -> m (a,sN))
>
> -- this is probably one of the more non-sensical attempts I've made at
> -- this... but I'm not sure:
> runTypeableState :: (Monad m, Typeable s0, Typeable sN)=> TypeableState m a -> s0 -> m (a,sN)
> runTypeableState (TypeableState st) s0 = (liftMaybe $ cast s0) >>= st
>
> -- copied from Control.Monad.StateT
> instance (Monad m) => Monad (TypeableState m) where
>     return a = TypeableState $ \s -> return (a, s)
>     m >>= k  = TypeableState $ \s -> do
>         ~(a, s') <- runTypeableState m s
>         runTypeableState (k a) s'
>     fail str = TypeableState $ \_ -> fail str
>
> -- I imagine using this with 'cast' to thread the type in our monad
> -- transformer
> liftMaybe :: (Monad m)=> Maybe a -> m a
> liftMaybe = maybe (fail "Monadic failure") return

So is this even feasible? Or do I not grok what we can and can't do
with the Typeable class?

Any thoughts on this are appreciated.

Sincerely,
Brandon Simmons
http://coder.bsimmons.name