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Parameterized State Transformer Monad in F#?

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I have have been playing around with F# and I decided to create a state monad.  This worked out really well since I was able to leverage the F# computation expressions.  I then decided to try to extend this and make it more general by creating a parameterized state transformer monad.  This is a state monad which encapsulates another monad.  What this allow you to do is turn any computation into a statefull one.

 

This concept exists in Haskell which you can see here. However, my attempts at replicating this in F# failed.  Unlike in Haskell, the computation expressions in F# don't share a common interface (or type class).  This prevents a computation from being able to generically take another computation as a parameter.  The reason is that an operation on the parameterized state transformer monad such as bind will result in a bind called on its encapsulated monad.  But since there is no interface for computations there is no bind method to call. 

I attempted to fix this by creating my own monad interface but this didn't work:

    1: type Monad =

    2:     abstract Bind : 'm * ('a -> 'm) -> 'm

    3:     abstract Delay : (unit ->'m) -> 'm

    4:     abstract Let : 'a * ('a -> 'm) -> 'm

    5:     abstract Return : 'a -> 'm

    6:     abstract Zero : unit -> 'm

    7:     abstract Combine : 'm -> 'm2 -> 'm3

    8:     abstract Run : (unit ->'m) -> 'm

 

After playing with that and failing I ended up with a less than ideal solution.  Given a Maybe monad like below:

    1: // Maybe Monad    

    2: type MaybeBuilder() =

    3:     member b.Return(x) = Some x

    4:     member b.Run(f) = f()

    5:     member b.Delay(f) = f

    6:     member b.Let(p,rest) = rest p

    7:     member b.Zero () = None

    8:     member b.Combine(m1,dm2) = match m1 with

    9:                                  | None -> dm2()

   10:                                  | x -> x

   11:  

   12:     member b.Bind(p,rest) = match p with 

   13:                             | None -> None

   14:                             | Some r -> rest r

 

I created a state transformer monad which take an argument of type m:MaybeBuilder

    1: type StateMBuilder(m:MaybeBuilder) = 

    2:     member b.Return(x) = fun s -> m.Return (x,s)

    3:     member b.Run(f) = fun inp -> (f inp)()

    4:     member b.Delay(f) = fun inp -> fun () -> f() inp

    5:     member b.Let(p,rest) = rest p

    6:     member b.Zero () = fun s -> m.Zero()

    7:     member b.Bind(p,rest) = fun s -> m.Bind(p s,fun (v,s2) -> rest v s2)

    8:     member b.Combine(p1,dp2) = fun s -> m.Combine(p1 s, dp2 s)

    9:  

   10:     // State specific functions

   11:     member b.Update f = fun s -> try m.Return (s, f s) with e -> m.Zero()

   12:     member b.Read () = b.Update id

   13:     member b.Set t = b.Update (fun _ -> t)

 

Now although this type is technically parameterized ;) it isn't really the idea since its not generic, it has to be a MaybeBuilder.  To use this with a different monad I would need to change m:MaybeBuild to m:SomeOtherMonad. 

I am still going to play with this but this is as far as I have gotten.

After all of that here is how you create a state transformer monad parameterized over the maybe monad:

    1: let maybe = MaybeBuilder()

    2: let state = StateMBuilder(maybe)

 

If anyone has an idea how I can make this work I would love to hear it.

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