[Haskell-cafe] Building Monads from Monads

Cale Gibbard cgibbard at gmail.com
Thu Mar 23 23:42:17 EST 2006

On 23/03/06, Daniel McAllansmith <dagda at xtra.co.nz> wrote:
> Hi, I've got a few (9) random questions, mainly about monads and building
> monads from existing monads, partly trying to confirm conclusions I've come
> to through experimentation.
> Any, and all, attempts to enlighten me will be much appreciated.
> Thanks
> Daniel
> First, terminology.  In
> StateT s (ReaderT r IO) ()
> Q. 1) StateT is referred to as the outermost monad, and IO as the innermost
> monad, correct?
Yeah, that's the somewhat informal terminology. Probably better would
be that StateT is the outermost monad transformer, and IO is the
transformed monad, or base monad.
> Using a monadic function, eg MonadReader.ask, in a monadic expression will
> access the outermost monad of the appropriate class.
> Q. 2) Does this work for all monad classes in all expressions?
No, basically, applying ask will use the version of ask for your
particular monad. (Including all transformers.) Various instances of
MonadReader are used to automatically get reader instances on
transformed monads in various cases involving the MTL transformers,
but not in all cases. (Read the list of instances for MonadReader to
find out exactly which monad transformers preserve it.) If there's no
instance, you have to write one yourself. Also, when you're newtyping
a monad which is an instance of MonadReader, you can use newtype
deriving to get an instance for the newtype automatically.
> How does Control.Monad.Trans.lift work?  It seems that a single application of
> lift will find the next outermost monad of the appropriate class, but if you
> want to dig deeper into the nest you need to apply lift according to the
> monads actual depth in the nest.
> Q. 3) Why the different behaviour?

Lift is best understood via its type:

lift :: (MonadTrans t, Monad m) => m a -> t m a

it simply takes a value in the base monad, and lifts it into the
transformed monad. When you have a stack of transformers, you may have
to apply it multiple times if you want to lift something up from one
monad, through a stack of transformations of that monad. For example,
I might be working in the
StateT Integer (ReaderT String IO)
monad, and want to get an analogue of (print "Hello") which is of type
IO () in my monad. First I apply lift to it, to get a value in
(ReaderT String IO ()), then again to get something of type StateT
Integer (ReaderT String IO) ().

That's all it does - there's no magic with locating applications of
transformers or anything like that, it just goes one level each time.
However, there's also liftIO, which is a special case for when the
base monad is IO -- this lifts an IO action into any monad which is an
instance of MonadIO. This class is preserved by most monad
transformers, and is satisfied by IO, so the end result is like
applying lift enough times to bring an IO action up through as many
transformers as necessary, but without having to know how many

> Q. 4) Is it possible to give a type to the lifted function so that the monad
> of the correct class _and_ type is used?  E.g. dig into a String Reader
> rather than an Int Reader.

I'm not completely sure what you're after here -- basically, you just
lift things into whichever monad you're using. If you want to be
polymorphic, but insist on a particular instance of MonadReader,
that's easy enough, just put a constraint like (MonadReader String m)
or something similar on your type.

> Defining an instance of MonadTrans for a monad instance seems universally
> useful.
> Q. 5) Are there obvious situations where it's not useful or possible?

MonadTrans is only for monad transformers. Actual monads can't be
turned into transformers into any automatic way. However, in a lot of
cases, it's quite natural and obvious how to write a monad
transformer, such that applying that transformer to the identity monad
gives the monad you were thinking of (for example, writing code for
StateT instead of State), and when this is the case, you usually
should, since it's usually not much extra trouble, and it buys you a
lot of extra flexibility later.

> Carrying out IO in a nested monadic expression requires liftIO.  Apart from
> having to type an extra 7-9 characters it seems good to use liftIO even in
> plain IO monad expressions so they can become nested expressions with no
> trouble later on.
> Q. 6) Is it safe to always use liftIO, even in plain IO monad?

It's safe, sure, though a little awkward. It's easy enough to lift
whole IO computations later on anyway. The only benefit would be if
you wanted to later intersperse actions into the code which came from
a transformed version.

> Q. 7) If it's safe to do, why aren't functions in the IO monad just typed in
> the MonadIO class instead?

First of all, historical reasons -- the MTL is newer than the IO monad
by a good bit, and it doesn't exist in Haskell 98. While it would be
nice to have automatically lifted IO actions, it's actually fairly
rare that this actually gets in your way. The biggest problem is when
you have to deal with functions like bracket which take IO actions as
parameters -- in that case, it would be especially nice for it to take
something in a MonadIO instead.

> It looks to me like types with class constraints are better than types
> specifying nests of monad instances.  So
> g :: (MonadReader String m, MonadState Int m, Monad m) => m ()
> is better than
> g :: StateT Int (Reader String) ()
> because you can change the instance of the monadic class at will.  Also you
> can change the nesting order of the monads, though maybe that's not useful in
> practice.
> The disadvantage seems to be that you can't use lift to access nested monads.
> Q. 8) Is it possible to get access to nested monads when using class
> constraint types?

There's no nesting there: m () isn't a transformed monad -- while it
might be implemented as such, you just don't know that. You can use
polymorphic types with lift (just look at the type of lift itself),
but usually that's not what you want anyway.

Really, you don't want to do a whole lot of explicit lifting outside
of the definitions of core functionality in your new monad. Sometimes
it's necessary to do more than that, but I find it's usually much
nicer if you can find some basic set of actions that you want in your
new monad and pre-lift them all. Better yet, write a class for them,
newtype your monad transformer stack to give it a pretty name, and
then don't export the newtype constructor from your module. (Just the
class and the type.) You then write an instance of your class which
uses the newtype constructor. It's also possible that you might want
to use newtype-deriving to get instances for MTL classes like
MonadReader or MonadState, though quite often your own interface will

> In the following code, the test2 function is not valid because there is no
> instance for (MonadCounter (ReaderT [Char] (StateT Word IO))), which is a
> fair enough complaint.
> Q. 9) What allows ReaderT and StateT to be nested in arbitrary order but not
> ReaderT and CounterT?  Especially given CounterT is actually a StateT.
> [snip code]

The reason is that you don't have lifting instances to lift an
instance of MonadCounter through the application of ReaderT or StateT.

Here's a version of your code which I've cleaned up a bit. I turned
your Counter and CounterT into newtypes (type synonyms will eventually
cause you problems with defining overlapping instances), with Counter
defined using CounterT with the Identity monad, and illustrated how
you can get the behaviour I think you want:

{-# OPTIONS_GHC -fglasgow-exts #-}
module MonadCounter (
    MonadCounter, increment, decrement,
    CounterT, runCounterT,
    Counter, runCounter
  ) where

import Control.Monad
import Control.Monad.Reader
import Control.Monad.State
import Control.Monad.Identity
import Data.Word

class (Monad m) => MonadCounter m where
   increment :: m Word
   decrement :: Word -> m ()

newtype CounterT m a = CounterT (StateT Word m a)
    deriving (Functor, Monad, MonadIO, MonadTrans,
              MonadReader r) -- etc...

instance (Monad m) => MonadCounter (CounterT m) where
   increment = CounterT increment_
   decrement = CounterT . decrement_

increment_ :: (MonadState Word m) => m Word
increment_ = do
   w <- get
   put (w + 5)
   return w

decrement_ :: (MonadState Word m) => Word -> m ()
decrement_ w = do
   curW <- get
   if w > curW
       then put 0
       else put (curW - w)
   return ()

instance MonadCounter m => MonadCounter (ReaderT r m) where
    increment = lift increment
    decrement n = lift (decrement n)

runCounterT :: (Monad m) => CounterT m a -> m a
runCounterT (CounterT c) = evalStateT c 0

newtype Counter a = Counter (CounterT Identity a)
    deriving (Functor, Monad, MonadCounter)

runCounter (Counter x) = runIdentity (runCounterT x)

test1 :: IO ()
test1 = runReaderT (runCounterT bar) "blah"

test2 :: IO ()
test2 = runCounterT (runReaderT bar "blah")

bar :: (MonadReader String m, MonadCounter m, MonadIO m) => m ()
bar = do
   w <- increment
   s <- ask
   liftIO $ putStrLn $ (show w) ++ s
   return ()

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