From: Daniel Fischer <daniel.is.fischer@googlemail.com>
Subject: Re: [Haskell-cafe] Reader monad wrapping State monad
To: "michael rice" <nowgate@yahoo.com>
Cc: haskell-cafe@haskell.org
Date: Thursday, February 3, 2011, 4:15 PM

On Thursday 03 February 2011 21:40:13, michael rice wrote:
> Hi Daniel,
>
> Ok, but what I was looking for was ReaderT on top, State on the bottom.

No problem, just change the definition of the Heron type synonym and swap
the applcations of runReader[T] and evalState[T] in mySqrt, the monadic
sqrtH can remain unchanged :)

> This is very confusing material, with no apparent conceptual commonality
> (ad hoc comes to mind) among the many examples I've looked at. Sometimes
> lift is used, other times a lift helper function, and in this case no
> use of lift at all.

That's because only methods of the MonadState and the MonadReader class are
used and instances of MonadState are propagated/lifted through ReaderT,
instance of MonadReader are propagated/lifted through StateT.

(
instance MonadReader r m => MonadReader r (StateT s m) where
    ask = lift ask
    local = ...
instance MonadState s m => MonadState (ReaderT r m) where
    get = lift get
    put = ...
)

If you use a function on the inner monad which is not propagated to the
entire transformer stack via class instances, you have to use lift (if you
have a MonadTrans instance) or something similar.