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Monad Transformers Explained

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Below is a short explanation of and motivating example for monad transformers. Comments and aggressive editing welcome.

Thanks to Ryan Ingram and Tommy M McGuire of Haskell-Cafe for their comments on an earlier draft.

Basically it's like making a double, triple, quadruple, ... monad by wrapping around existing monads that provide wanted functionality.

You have an innermost monad (usually
Identity
or
IO
but you can use any monad). You then wrap monad transformers around this monad to make bigger, better monads. Concrete example: Suppose I was writing a server. Each client handling thread must be of type
IO ()
(that's because
forkIO :: IO () -> IO ThreadID
)).

Suppose also that this server has some configuration that (in an imperative program) would be global because client handling threads all need to query it. 

data Config = Config Foo Bar Baz
One way of doing this is to use currying and making all the client threads of type
Config -> IO ()
. Not too nice because any functions they call have to be passed the
Config
parameter manually. The
Reader
monad solves this problem but we've already got one monad. We need to wrap
IO
in a
ReaderT
. The type constructor for
ReaderT
is
ReaderT r m a
, with
r
the shared environment to read from,
m
the inner monad and
a
the return type. Our
client_func
becomes: 
client_func :: ReaderT Config IO ()
We can then use the
ask
,
asks
and
local
functions as if Reader was the only Monad: (these examples are inside
do
blocks) 
p <- asks port
(Assuming some function
port :: Config -> Int
or similar.) To do stuff in an inner monad, there is the function
lift
. Because having big chains of
lift $ lift $ lift $ foo
can get annoying, the libraries in mtl (the Monad Transformer Library) play a trick using the type system. Each monad in the mtl is defined in terms of a type class. For example,
Reader
is actually an instance of
MonadReader
, as is
ReaderT
. Further, anything in the mtl that wraps a
MonadReader
is also set up to be a
MonadReader
, so the
ask
,
asks
and
local
functions will work without any (manual) lifting. Other mtl monads behave in a similar way. To do stuff in
IO
the
liftIO
function is used: (given
h :: Handle
, the client's handle) 
liftIO $ hPutStrLn h "You win"
liftIO $ hFlush h
A type class called
MonadIO
is used to implement a similar trick as above.
IO
is an instance of
MonadIO
, and any mtl transformer that wraps a
MonadIO
instance also is an instance of
MonadIO
. This means that
IO
functions need only use
liftIO
and not a big chain of
lift
s. Note also that
IO
has no transformer and must therefore always be the innermost monad. This is all well and good, but the
client_func
now has type
ReaderT Config IO ()
and
forkIO
needs a function of type
IO ()
. The escape function for
Reader
is
runReader :: Reader r a -> r -> a
and similarly for
ReaderT
the escape function is
runReaderT :: ReaderT r m a -> r -> m a
: (Given some
c :: Config
that's been assembled from config files or the like) 
forkIO (runReaderT client_func c)

Will do the trick.

Monad transformers are like onions. At first, they make you cry but then you learn to appreciate them. Like onions, they're also made of layers. Each layer is the functionality of a new monad, you lift monadic functions to get into the inner monads and you have transformerised functions to unwrap each layer. They're also like a present in that regard: in this example we unwrapped the outer wrapping paper to get to the present: an object of type
IO ()
, which lets us make Haskell do something.
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Category: Monad