[Haskell-cafe] Re: Fwd: Re: Simple game: a monad for each player

[Heinrich Apfelmus]

Limestraël wrote:
> Okay, I start to understand better...
> 
> Just, Heinrich, how would implement the mapMonad function in terms of the
> operational package?
> You just shown the signature.

Ah, that has to be implemented by the library, the user cannot implement
this. Internally, the code would be as Bertram suggests:

    mapMonad :: (Monad m1, Monad m2)
             => (forall a . m1 a -> m2 a)
             -> ProgramT instr m1 a -> ProgramT instr m2 a
    mapMonad f (Lift m1)  = Lift (f m1)
    mapMonad f (Bind m k) = Bind (mapMonad f m) (mapMonad f . k)
    mapMonad f (Instr i)  = Instr i

I was musing that every instance of  MonadTrans  should implement this
function.

Also note that there's a precondition on  f  , namely it has to respect
the monad laws:

    f (m >>= k) = f m >>= f . k
    f return    = return

For instance,

    f :: Identity a -> IO a
    f x = launchMissiles >> return (runIdentity x)

violates this condition.


Regards,
Heinrich Apfelmus

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