# A Gentle Introduction to Monad Transformers

# Table of Contents

This has long been resting in a GitHub repo of mine, but I felt like it was time
to move it to the home where it belongs. It is probably one of my most popular
texts, where I occasionally get emails about it still. I *think* it was one of
the first beginner-level explanations of monad transformers, so that probably
helped its popularity.

However it happened, people appear to like it. So if you haven’t seen it yet, grab a cup of tea, carve out half an hour, and I hope you’ll enjoy it!

# Either Left or Right

Before we break into the mysterious world of monad transformers, I want to start
with reviewing a much simpler concept, namely the `Either`

data type. If you
aren’t familiar with the `Either`

type, you should probably not jump straight
into monad transformers – they do require you to be somewhat comfortable with
the most common monads.

With that out of the way:

Pretend we have a function that extracts the domain from an email address.
Actually checking this properly is a rather complex topic which I will avoid,
and instead I will assume an email address can only contain one `@`

symbol, and
everything after it is the domain.

I’m going to work with `Text`

values rather than `String`

s. This means if you
don’t have the `text`

library, you can either work with `String`

s instead, or
`cabal install text`

. If you have the Haskell platform, you have the `text`

library.

We need to import `Data.Text`

*and* set the `OverloadedStrings`

pragma. The
latter lets us write string literals (such as `"Hello, world!"`

) and have them
become `Text`

values automatically.

λ> :module +Data.Text λ> :set -XOverloadedStrings

Now, figuring out how many `@`

symbols there are in an email address is
fairly simple. We can see that

λ> splitOn "@" "" [""] λ> splitOn "@" "test" ["test"] λ> splitOn "@" "test@example.com" ["test", "example.com"] λ> splitOn "@" "test@example@com" ["test", "example", "com"]

So if the split gives us just two elements back, we know the address
contains just one `@`

symbol, and we also as a bonus know that the second
element of the list is the domain we wanted. We can put this in a file.

{-# LANGUAGE OverloadedStrings #-} import Data.Text -- Imports that will be needed later: import qualified Data.Text.IO as T import Data.Map as Map import Control.Applicative data LoginError = InvalidEmail deriving Show getDomain :: Text -> Either LoginError Text getDomain email = case splitOn "@" email of [name, domain] -> Right domain _ -> Left InvalidEmail

This draws on our previous discoveries and is pretty self-explainatory. The
function returns `Right domain`

if the address is valid, otherwise
`Left InvalidEmail`

, a custom error type we use to make handling the errors
easier later on. (Why this is called `LoginError`

will be apparent soon.)

This function behaves as we expect it to.

λ> getDomain "test@example.com" Right "example.com" λ> getDomain "invalid.email@example@com" Left InvalidEmail

To deal with the result of this function immediately, we have a couple of
alternatives. The basic tool to deal with `Either`

values is pattern matching,
in other words,

printResult' :: Either LoginError Text -> IO () printResult' domain = case domain of Right text -> T.putStrLn (append "Domain: " text) Left InvalidEmail -> T.putStrLn "ERROR: Invalid domain"

Testing in the interpreter shows us that

λ> printResult' (getDomain "test@example.com") Domain: example.com λ> printResult' (getDomain "test#example.com") ERROR: Invalid domain

Another way of dealing with `Either`

values is by using the `either`

function.
`either`

has the type signature

either :: (a -> c) -> (b -> c) -> Either a b -> c

In other words, it “unpacks” the `Either`

value and applies one of the two
functions to get a `c`

value back. In this program, we have an
`Either LoginError Text`

and we want just a `Text`

back, which tells us what
to print. So we can view the signature of `either`

as

either :: (LoginError -> Text) -> (Text -> Text) -> (Either LoginError Text -> Text)

and writing `printResult`

with the help of `either`

yields a pretty neat
function.

printResult :: Either LoginError Text -> IO () printResult = T.putStrLn . either (const "ERROR: Invalid domain") (append "Domain: ")

This function works the same way as the previous one, except with the
pattern matching hidden inside the call to `either`

.

# Introducing Side-Effects

Now we’ll use the domain as some sort of “user token” – a value the user uses to prove they have authenticated. This means we need to ask the user for their email address and return the associated token.

getToken :: IO (Either LoginError Text) getToken = do T.putStrLn "Enter email address:" email <- T.getLine return (getDomain email)

So when `getToken`

runs, it’ll get an email address from the user and
return the domain of the email address.

λ> getToken Enter email address: test@example.com Right "example.com"

and, importantly,

λ> getToken Enter email address: not.an.email.address Left InvalidEmail

Now, let’s complete this with an authentication system. We’ll have two users who both have terrible passwords:

users :: Map Text Text users = Map.fromList [ ("example.com", "qwerty123") , ("localhost", "password") ]

With an authentication system, we can also run into two new kinds of errors,
so let’s change our `LoginError`

data type to reflect that.

data LoginError = InvalidEmail | NoSuchUser | WrongPassword deriving Show

We also need to write the actual authentication function. Here we go…

userLogin :: IO (Either LoginError Text) userLogin = do token <- getToken case token of Right domain -> case Map.lookup domain users of Just userpw -> do T.putStrLn "Enter password:" password <- T.getLine if userpw == password then return token else return (Left WrongPassword) Nothing -> return (Left NoSuchUser) left -> return left

This beast of a function gets the email and password from the user, checks that the email was processed without problems, finds the user in the collection of users, and if the passwords match, it returns the token to show the user is of authenticated.

If anything goes wrong, such as the passwords not matching, there not
being a user with the entered domain, or the `getToken`

function failing to
process, then a `Left`

value will be returned.

This function is *not* something we want to deal with. It’s big, it’s bulky,
it has several layers of nesting… it’s not the Haskell we know and love.

Sure, it’s possible to rewrite it using function calls to `either`

and
`maybe`

, but that wouldn’t help very much. The real reason the code is this
ugly is that we’re trying to mix both `Either`

and `IO`

, and they don’t seem
to blend well.

The core of the problem is that the `IO`

monad is designed for dealing with
`IO`

actions, and it’s terrible at handling errors. On the other hand, the
`Either`

monad is great at handling errors, but it can’t do `IO`

. So let’s
explore what happens if you imagine a monad that is designed to *both*
handle errors *and* `IO`

actions.

Too good to be true? Read on and find out.

# We Can Make Our Own Monads

We keep coming across the `IO (Either e a)`

type, so maybe there is something
special about that. What happens if we make a Haskell data type out of that
combination?

data EitherIO e a = EitherIO { runEitherIO :: IO (Either e a) }

What did we get just by doing this? Let’s see:

λ> :type EitherIO EitherIO :: IO (Either e a) -> EitherIO e a λ> :type runEitherIO runEitherIO :: EitherIO e a -> IO (Either e a)

So already we have a way to go between our own type and the combination
we used previously! That’s *gotta* be useful somehow.

# Implementing Instances for Common Typeclasses

This section might be a little difficult if you’re new to the language and
haven’t had a lot of exposure to the internals of how common typeclasses
work. You don’t *need* to understand this section to continue reading the
article, but I strongly suggest you put on your to-do list to learn enough
to understand this section. It touches on many of the core components of
what makes Haskell Haskell and not just another functional language.

If you want to read more about this kind of thing, The Typeclassopedia by Brent Yorgey is a comprehensive reference of the most common typeclasses used in Haskell code. Learn You a Haskell has a popular introduction to the three typeclasses we use here. Additionally, Adit provides us with a humourous picture guide to the same three typeclasses.

But before we do anything else, let’s make `EitherIO`

a functor, an
applicative and a monad, starting with the functor, of course.

instance Functor (EitherIO e) where fmap f ex = wrapped where unwrapped = runEitherIO ex fmapped = fmap (fmap f) unwrapped wrapped = EitherIO fmapped

This may look a little silly initially, but it does make sense. First, we
“unwrap” the `EitherIO`

type to expose the raw `IO (Either e a)`

value. Then
we `fmap`

over the inner `a`

, by combining two `fmap`

s. Then we wrap the
new value up in `EitherIO`

again, and return the wrapped value. If you are
a more experienced Haskell user, you might prefer the following, equivalent,
definition instead.

instance Functor (EitherIO e) where fmap f = EitherIO . fmap (fmap f) . runEitherIO

In a sense, that definition makes it more clear that you are just unwrapping, running a function on the inner value, and then wrapping it together again.

The two other instances are more of the same, really. Creating them is a
mostly mechanical process of following the types and unwrapping and wrapping
our custom type. I challenge the reader to come up with these instances on
their own before looking below how I did it, because trying to figure these
things out *will* improve your Haskell abilities in the long run.

In any case, explaining them gets boring, so I’ll just show you the instances as an experienced Haskell user might write them.

Warning:A very sharp-sighted reader has pointed out to me that this applicative instance is unlawful. Specifically, it executes the side effects of the right-hand side unconditionally. The expectation of a lawful instance is that it should only execute the side-effects of the right-hand side if the left-hand side was a successful operation.The fix is easy but not trivial from a pedagogical perspective. I’m putting a hold on fixing it at the moment, until I come up with a satisfactory way to describe it.

If you are curious on what it should look like, I recommend checking out the implementation of

`ExceptT`

in`Control.Monad.Trans.Except`

from thetransformerspackage.

-- XXX: Unlawful instance. Don't use for anything serious. instance Applicative (EitherIO e) where pure = EitherIO . return . Right f <*> x = EitherIO $ liftA2 (<*>) (runEitherIO f) (runEitherIO x) instance Monad (EitherIO e) where return = pure x >>= f = EitherIO $ runEitherIO x >>= either (return . Left) (runEitherIO . f)

If your definitions look nothing like these, don’t worry. As long as your definitions give the correct results, they are just as good as mine. There are many ways to write these definitions, and none is better than the other as long as all are correct.

# Using EitherIO

Now that our `EitherIO`

type is a real monad, we’ll try to put it to work!
If we change the type signature of our `getToken`

function, we’ll run into
problems quickly, though.

getToken :: EitherIO LoginError Text getToken = do T.putStrLn "Enter email address: " input <- T.getLine return (getDomain input)

We get three type errors from this function alone, now! In order:

`T.putStrLn "email"`

returns`IO ()`

, but we want`EitherIO LoginError ()`

.`T.getLine`

returns`IO Text`

, we want`EitherIO LoginError Text`

.`getDomain input`

returns`Either LoginError Text`

, we want`EitherIO LoginError Text`

.

Converting `Either e a`

to `EitherIO e a`

isn’t terribly difficult. We have
two functions to help us with that.

return :: Either e a -> IO (Either e a) EitherIO :: IO (Either e a) -> EitherIO e a

With both of those, we can take the `getDomain`

function call and fit it in
the new `getToken`

function, like so:

EitherIO (return (getDomain input))

Remember this line, because we’re going to put it into the function soon
enough. But first, let’s find out how to convert the two `IO a`

values to an
`EitherIO e a`

. Again, we will have use of the `EitherIO`

function. For the
rest, it’s useful to know your functors. If you do, you’ll realise that

fmap Right :: IO a -> IO (Either e a)

so our `IO`

actions would both be

EitherIO (fmap Right (T.putStrLn "email")) EitherIO (fmap Right (T.getLine))

With these three lines, the `getToken`

function is now written as

getToken :: EitherIO LoginError Text getToken = do EitherIO (fmap Right (T.putStrLn "Enter email address:")) input <- EitherIO (fmap Right T.getLine) EitherIO (return (getDomain input))

But this looks even *more* horrible than it was before! Relax. We’ll take a
detour to clean this up slightly.

# Do You Even Lift?

The more general pattern here is that we have two kinds of functions: Those
that return `IO`

something, and those that return `Either`

something. We want
to use both of those in our `EitherIO`

monad. Converting a “lesser” monad to
a “more powerful” one, like we want to do here, is often called *lifting* the
lesser operation *into* the more powerful monad.

We can define two lift operations to do exactly this for our case.

liftEither :: Either e a -> EitherIO e a liftEither x = EitherIO (return x) liftIO :: IO a -> EitherIO e a liftIO x = EitherIO (fmap Right x)

With these two functions, the `getToken`

function in turn is a little more
clean.

getToken :: EitherIO LoginError Text getToken = do liftIO (T.putStrLn "Enter email address:") input <- liftIO T.getLine liftEither (getDomain input)

If you try to run this in the interpreter, you’ll get a nasty type error. The
reason is that the interpreter expects something of type `IO a`

, but
`getToken`

has type `EitherIO e a`

, so we need to convert it back to `IO a`

when we run it in the interpreter. Fortunately, we had a function that does
just that – `runEitherIO`

.

λ> runEitherIO getToken Enter email address: test@example.com Right "example.com"

We’ll also want to do the same conversion for `userLogin`

, of course. First
we change the type signature, and then we fix the values that are of the
wrong type. If you haven’t been paying 100% attention, the new look of
`userLogin`

might surprise you.

userLogin :: EitherIO LoginError Text userLogin = do token <- getToken userpw <- maybe (liftEither (Left NoSuchUser)) return (Map.lookup token users) password <- liftIO ( T.putStrLn "Enter your password:" >> T.getLine ) if userpw == password then return token else liftEither (Left WrongPassword)

Where did all the nesting go? It’s gone. All the nesting was there simply
because we had to handle a bunch of error cases in the `IO`

monad. The IO
monad is not meant to handle error cases, so you have to do it manually.
Our `EitherIO`

monad on the other hand, is built *both* to handle errors
*and* to perform IO actions, so we get the best of both worlds. We just
have to signal when errors occur, and the `EitherIO`

monad takes care of
the rest.

If we want to, say, print the result of this, we’ll need a print function similar to the one we had previously.

printResult :: Either LoginError Text -> IO () printResult res = T.putStrLn $ case res of Right token -> append "Logged in with token: " token Left InvalidEmail -> "Invalid email address entered." Left NoSuchUser -> "No user with that email exists." Left WrongPassword -> "Wrong password."

This function, just like the previous one, takes an `Either`

value, so we’ll
need to “unwrap” our result before we send it over.

λ> runEitherIO userLogin >>= printResult Enter email address: test@example.com Enter your password: qwerty123 Logged in with token: example.com λ> runEitherIO userLogin >>= printResult Enter email address: test@127.0.0.1 No user with that email exists.

As you can see, we’ve got a lot of convenience already, being able to just
signal errors and let our `EitherIO`

monad take care of them just like it
takes care of `IO`

actions.

# Signalling Errors

But how *are* we signalling errors, really? It turns out that to signal
something like `WrongPassword`

, we have to return

liftEither (Left WrongPassword)

and that’s not very tidy. We can easily make a function

throwE :: e -> EitherIO e a throwE x = liftEither (Left x)

When we have this function, `userLogin`

gets even better.

userLogin :: EitherIO LoginError Text userLogin = do token <- getToken userpw <- maybe (throwE NoSuchUser) return (Map.lookup token users) password <- liftIO $ T.putStrLn "Enter your password:" >> T.getLine if userpw == password then return token else throwE WrongPassword

`throwE`

? What Is This, Java?

No, of course not. But I did choose that name deliberately. What we have with
our `EitherIO`

monad is looking more and more like exceptions in languages like
Java, Python, C++ and so on. And that’s not a bad way to view it.

However, there are some differences. One big difference is that our “exceptions” are just normal values that are being returned from the function, while more traditional (Java, Python) exceptions are interruptions of normal control flow. Another difference is that our “exceptions” are checked by the type system, so we can’t forget to catch our exceptions.

`ExceptIO`

But let’s entertain that idea further. What happens if we just say goodbye to
`Either`

and talk about exceptions instead? First, we’ll need to rename our
`EitherIO`

monad:

data ExceptIO e a = ExceptIO { runExceptIO :: IO (Either e a) }

It still works the same as before, it’s just been renamed. The names need to be changed throughout the code, but other than that, the code still works.

# Gotta Catch ’Em All

So if we can *throw* what basically amounts to exceptions…

Yes! Keep going!

Can we also…

Yes?

…catch them?

Oh, I’m so happy you asked! Of course we can. And it’s real simple too! We
need to define a function that does the catching. Call it `catchE`

, so it
looks similar to `throwE`

.

catchE :: ExceptIO e a -> (e -> ExceptIO e a) -> ExceptIO e a catchE throwing handler = ExceptIO $ do result <- runExceptIO throwing case result of Left failure -> runExceptIO (handler failure) success -> return success

This unwraps the `throwing`

computation and inspects its result, if it was
successful, it just returns it right back without doing anything. If it was
a failure, it runs the `handler`

with the error as an argument, and returns
the result of that instead.

We can use this to spice up our application a little. We’ll start by writing two exception handlers – one that catches just a single exception, and one that catches all exceptions.

wrongPasswordHandler :: LoginError -> ExceptIO LoginError Text wrongPasswordHandler WrongPassword = do liftIO (T.putStrLn "Wrong password, one more chance.") userLogin wrongPasswordHandler err = throwE err

The `wrongPasswordHandler`

handles only the `WrongPassword`

exception, and
rethrows everything else. It responds to a `WrongPassword`

exception by
running the `userLogin`

function again to give the user a second chance.

The other exception handler will respond to exceptions by printing an error message and then re-throwing the exception to abort the current execution.

printError :: LoginError -> ExceptIO LoginError a printError err = do liftIO . T.putStrLn $ case err of WrongPassword -> "Wrong password. No more chances." NoSuchUser -> "No user with that email exists." InvalidEmail -> "Invalid email address entered." throwE err

We’ll create a third function where we use these exceptions.

loginDialogue :: ExceptIO LoginError () loginDialogue = do let retry = userLogin `catchE` wrongPasswordHandler token <- retry `catchE` printError liftIO $ T.putStrLn (append "Logged in with token: " token)

Note in particular how we “wrap” exception handlers around each other. In
the innermost layer is the `userLogin`

computation, which gets wrapped by
the `wrongPasswordHandler`

handler, and then that entire package gets wrapped
by the `printError`

handler. You need to wrap your handlers in the order you
expect them to catch exceptions from underneath each other.

# Going General

There is just one, tiny, little thing I want to change in our `ExceptIO`

type.
Currently, we’re stuck with only being able to combine `IO`

and exceptions.
What if we wanted to combine exceptions with database transactions, or lists,
or some other kind of monad? We can make the other monad an argument to our
exception monad.

Then we’ll also have to change the name from `ExceptIO`

to `ExceptT`

. Why
the `T`

, you ask? Because it’s a monad transformer. Congratulations! You made
it all the way. You’ve created and used your first monad transformer. That’s
no small feat.

The following is our entire program after that change. Most of the functions we
defined manually already exist in the `transformers`

library, in
the `Control.Monad.Trans.Except`

module. Use that when you can instead of creating
your own types, but feel free to reference our program here when you are curious
how something works!

# Appendix A: Complete Program

{-# LANGUAGE OverloadedStrings #-} import Data.Text import Data.Text.IO as T import Data.Map as Map import Control.Applicative data ExceptT e m a = ExceptT { runExceptT :: m (Either e a) } instance Functor m => Functor (ExceptT e m) where fmap f = ExceptT . fmap (fmap f) . runExceptT -- XXX: Unlawful instance. Don't use for anything serious. instance Applicative m => Applicative (ExceptT e m) where pure = ExceptT . pure . Right f <*> x = ExceptT $ liftA2 (<*>) (runExceptT f) (runExceptT x) instance Monad m => Monad (ExceptT e m) where return = ExceptT . return . Right x >>= f = ExceptT $ runExceptT x >>= either (return . Left) (runExceptT . f) liftEither :: Monad m => Either e a -> ExceptT e m a liftEither x = ExceptT (return x) lift :: Functor m => m a -> ExceptT e m a lift x = ExceptT (fmap Right x) throwE :: Monad m => e -> ExceptT e m a throwE x = liftEither (Left x) catchE :: Monad m => ExceptT e m a -> (e -> ExceptT c m a) -> ExceptT c m a catchE throwing handler = ExceptT $ do x <- runExceptT throwing case x of Left failure -> runExceptT (handler failure) Right success -> return (Right success) data LoginError = InvalidEmail | NoSuchUser | WrongPassword users :: Map Text Text users = Map.fromList [("example.com", "qwerty123"), ("localhost", "password")] main :: IO () main = do runExceptT loginDialogue return () loginDialogue :: ExceptT LoginError IO () loginDialogue = do let retry = userLogin ~catchE~ wrongPasswordHandler token <- retry ~catchE~ printError lift $ T.putStrLn (append "Logged in with token: " token) wrongPasswordHandler :: LoginError -> ExceptT LoginError IO Text wrongPasswordHandler WrongPassword = do lift (T.putStrLn "Wrong password, one more chance.") userLogin wrongPasswordHandler err = throwE err printError :: LoginError -> ExceptT LoginError IO a printError err = do lift . T.putStrLn $ case err of WrongPassword -> "Wrong password. No more chances." NoSuchUser -> "No user with that email exists." InvalidEmail -> "Invalid email address entered." throwE err userLogin :: ExceptT LoginError IO Text userLogin = do token <- getToken userpw <- maybe (throwE NoSuchUser) return (Map.lookup token users) password <- lift (T.putStrLn "Enter your password:" >> T.getLine) if userpw == password then return token else throwE WrongPassword getToken :: ExceptT LoginError IO Text getToken = do lift (T.putStrLn "Enter email address:") input <- lift T.getLine liftEither (getDomain input) getDomain :: Text -> Either LoginError Text getDomain email = case splitOn "@" email of [name, domain] -> Right domain _ -> Left InvalidEmail