Oleg: Very interresting, thanks. I have some questions:
- What do you mean by "The type Cont Int a describes an impure computation, which may abort with an Int value, for example".

Aborting with an Int value is akin to exceptions?

- for me it's not clear when to choose an "applicative" or a "monadic" DSL? Betsides, what's the rational behind the name "let_" (never seen it before)?

Linsey, Jacques: Thanks for the pointer! I learned about data kinds.
I tried to apply your suggestions to add a phantom type parameter to Exp.

I came up to (I dropped the Free monad idea, which seems unrelated to the problem):

> data Eff = Effect | NoEffect

> -- first type parameter is used to track effects
> data Exp :: Eff -> * -> * where
>   ReadAccount  :: Exp r Int  --ReadAccount can be used in whatever monad (with or without effect)
>   WriteAccount :: Exp NoEffect Int -> Exp Effect ()  --WriteAccount takes an effect-less expression, and returns an effectfull expression
>   SetVictory   :: Exp NoEffect Bool -> Exp Effect ()  -- same for SetVictory
>   OnTimer      :: Exp Effect () -> Exp Effect () --OnTime can program whatever expression to be triggered every minutes, in particular effectful ones
>   Return       :: a -> Exp r a
>   Bind         :: Exp r a -> (a -> Exp r b) -> Exp r b

This is the (simplified) game state:

> data Game = Game { bankAccount :: Int,

>                    victory     :: Exp NoEffect Bool,
>                    timerEvent  :: Exp Effect ()}

> victoryRule' :: Exp Effect ()

> victoryRule' = SetVictory $ do

>   m <- readAccount
>   --WriteAccount (return $ m + 1) --won't compile (good)

>   return (m > 100)

> --increase my bank account by 1 every minute

> myTimer :: Exp Effect ()
> myTimer = OnTimer $ do
>   m <- readAccount

>   writeAccount (return $ m + 1)

Do you have a better name suggestion for Eff? Other pointers where this idiom is realised??

Thanks!!