You can keep reading here or jump to my blog to get the full experience, including the wonderful pink, blue and white palette.

A good way to metabolize new concepts is to copy ideas from other people and try to make them compile. This is exactly what we are going to do today.

In case you wanted to read the (better) original, please check out "A Gentle Introduction to Monad Transformers".

## The Problem

Let's write a function to extract the domain from an email:

```
getDomain :: Text -> Either LoginError Text
getDomain email =
case T.splitOn "@" email of
[_, domain] -> Right domain
_ -> Left InvalidEmail
```

Then let's say we want to ask the user for their email and use the domain as a token for authentication:

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

Besides the token, the user need to input a password. The database of users is the following:

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

For our authentication system three possible errors are possible:

```
data LoginError
= InvalidEmail
| NoSuchUser
| WrongPassword
deriving (Show)
```

Finally, we can put all together:

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

And we are done!

Nope, it's a joke. That piece of code really is ugly. We need to do something about it.

There's one secret to clean up `userLogin`

: the indentation comes from the fact that we are dealing with two different monads (i.e. `IO`

and `Either`

).

Let's see if merging the two into one solves our issue.

## The Solution

We first wrap the two monads into `EitherIO`

:

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

Then we define instances for `Functor`

, `Applicative`

and `Monad`

:

```
instance Functor (EitherIO e) where
-- fmap :: Functor f => (a -> b) -> f a -> f b
-- fmap g f = EitherIO $ fmap (fmap g) (runEitherIO f)
fmap g = EitherIO . fmap (fmap g) . runEitherIO
-- THIS IS NOT LAWFUL. DO NOT USE FOR SERIOUS STUFF!
instance Applicative (EitherIO e) where
-- pure :: a -> f a
pure = EitherIO . pure . Right
-- (<*>) :: f (a -> b) -> f a -> f b
fg <*> f = EitherIO $ liftA2 (<*>) (runEitherIO fg) (runEitherIO f)
instance Monad (EitherIO e) where
-- (>>=) :: forall a b. m a -> (a -> m b) -> m b
m >>= mg = EitherIO $ (runEitherIO m >>= either (pure . Left) (runEitherIO . mg))
```

We can define `getToken`

in terms of our new monad:

```
getToken' :: EitherIO LoginError Text
getToken' = do
EitherIO $ fmap Right (T.putStrLn "Enter email address:")
email <- EitherIO $ fmap Right T.getLine
EitherIO $ pure $ getDomain email
```

Even better, we can create a couple of helpers to make it cleaner

```
liftEither :: Either e a -> EitherIO e a
liftEither = EitherIO . pure
liftIO :: IO a -> EitherIO e a
liftIO = EitherIO . fmap Right
getToken'' :: EitherIO LoginError Text
getToken'' = do
liftIO $ T.putStrLn "Enter email address:"
email <- liftIO T.getLine
liftEither $ getDomain email
```

Now, `userLogin`

can be rewritten as:

```
userLogin' :: EitherIO LoginError Text
userLogin' = do
domain <- getToken''
case Map.lookup domain users of
Just password -> do
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
liftEither $ Left WrongPassword
Nothing ->
liftEither $ Left NoSuchUser
```

We have removed one level of nesting. That is because with the Monad instance of `EitherIO`

, we "extract" the domain with `<- getToken''`

and not the `Either _ domain`

as before. But we can do even better:

```
userLogin'' :: EitherIO LoginError Text
userLogin'' = do
domain <- getToken''
password <- maybe (liftEither $ Left NoSuchUser) pure $ Map.lookup domain users
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
liftEither $ Left WrongPassword
```

With all of that in place we can run the login with:

```
main :: IO ()
main = do
result <- runEitherIO getToken''
print result
```

## But wait, there's more!

We could refactor `userLogin`

to:

```
throwE :: e -> EitherIO e a
throwE = liftEither . Left
userLogin''' :: EitherIO LoginError Text
userLogin''' = do
domain <- getToken''
password <- maybe (throwE NoSuchUser) pure $ Map.lookup domain users
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
throwE WrongPassword
```

But if we can throw, we can also catch:

```
catchE :: EitherIO e a -> (e -> EitherIO e a) -> EitherIO e a
catchE throwing handler = EitherIO $ do
result <- runEitherIO throwing
case result of
Left e -> runEitherIO $ handler e
success -> pure success
```

And have a handler that allows the user to retry the login in case of `WrongPassword`

error:

```
wrongPasswordHandler :: LoginError -> EitherIO LoginError Text
wrongPasswordHandler WrongPassword = do
liftIO $ T.putStrLn "Wrong password, one more chance."
userLogin'''
wrongPasswordHandler e = throwE e
```

With that we can:

```
main :: IO ()
main = do
result <- runEitherIO $ userLogin''' `catchE` wrongPasswordHandler
print result
```

## The whole code

```
{-# LANGUAGE OverloadedStrings #-}
module Main where
import Data.Text as T
import Data.Text.IO as T
import Data.Map as Map
import Data.Either (either)
import Data.Maybe (maybe)
import Control.Applicative (liftA2)
data LoginError
= InvalidEmail
| NoSuchUser
| WrongPassword
deriving (Show)
getDomain :: Text -> Either LoginError Text
getDomain email =
case T.splitOn "@" email of
[_, domain] -> Right domain
_ -> Left InvalidEmail
getToken :: IO (Either LoginError Text)
getToken = do
T.putStrLn "Enter email address:"
email <- T.getLine
pure $ getDomain email
users :: Map Text Text
users = Map.fromList
[ ("example.com", "qwerty123")
, ("localhost", "password")
]
userLogin :: IO (Either LoginError Text)
userLogin = do
token <- getToken
case token of
Right domain ->
case Map.lookup domain users of
Just password -> do
T.putStrLn "Enter password:"
pw <- T.getLine
if pw == password then
pure $ Right domain
else
pure $ Left WrongPassword
Nothing ->
pure $ Left NoSuchUser
left ->
pure $ left
data EitherIO e a = EitherIO {
runEitherIO :: IO (Either e a)
}
instance Functor (EitherIO e) where
-- fmap :: Functor f => (a -> b) -> f a -> f b
-- fmap g f = EitherIO $ fmap (fmap g) (runEitherIO f)
fmap g = EitherIO . fmap (fmap g) . runEitherIO
instance Applicative (EitherIO e) where
-- pure :: a -> f a
pure = EitherIO . pure . Right
-- (<*>) :: f (a -> b) -> f a -> f b
fg <*> f = EitherIO $ liftA2 (<*>) (runEitherIO fg) (runEitherIO f)
instance Monad (EitherIO e) where
-- (>>=) :: forall a b. m a -> (a -> m b) -> m b
m >>= mg = EitherIO $ (runEitherIO m >>= either (pure . Left) (runEitherIO . mg))
getToken' :: EitherIO LoginError Text
getToken' = do
EitherIO $ fmap Right (T.putStrLn "Enter email address:")
email <- EitherIO $ fmap Right T.getLine
EitherIO $ pure $ getDomain email
liftEither :: Either e a -> EitherIO e a
liftEither = EitherIO . pure
liftIO :: IO a -> EitherIO e a
liftIO = EitherIO . fmap Right
getToken'' :: EitherIO LoginError Text
getToken'' = do
liftIO $ T.putStrLn "Enter email address:"
email <- liftIO T.getLine
liftEither $ getDomain email
userLogin' :: EitherIO LoginError Text
userLogin' = do
domain <- getToken''
case Map.lookup domain users of
Just password -> do
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
liftEither $ Left WrongPassword
Nothing ->
liftEither $ Left NoSuchUser
userLogin'' :: EitherIO LoginError Text
userLogin'' = do
domain <- getToken''
password <- maybe (liftEither $ Left NoSuchUser) pure $ Map.lookup domain users
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
liftEither $ Left WrongPassword
throwE :: e -> EitherIO e a
throwE = liftEither . Left
userLogin''' :: EitherIO LoginError Text
userLogin''' = do
domain <- getToken''
password <- maybe (throwE NoSuchUser) pure $ Map.lookup domain users
liftIO $ T.putStrLn "Enter password:"
pw <- liftIO T.getLine
if pw == password then
liftEither $ Right domain
else
throwE WrongPassword
catchE :: EitherIO e a -> (e -> EitherIO e a) -> EitherIO e a
catchE throwing handler = EitherIO $ do
result <- runEitherIO throwing
case result of
Left e -> runEitherIO $ handler e
success -> pure success
wrongPasswordHandler :: LoginError -> EitherIO LoginError Text
wrongPasswordHandler WrongPassword = do
liftIO $ T.putStrLn "Wrong password, one more chance."
userLogin'''
wrongPasswordHandler e = throwE e
main :: IO ()
main = do
print $ getDomain "a"
print $ getDomain "a@b"
t <- getToken
print t
result <- userLogin
print result
t' <- runEitherIO getToken''
print t'
t'' <- runEitherIO $ userLogin''' `catchE` wrongPasswordHandler
print t''
```

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Posted on by:

### Riccardo Odone

🏳️🌈 Pronoun.is/he 💣 Maverick & Leader @Lunar_Logic 🧑💻 Functional Programming Rambler 🔥 Sometimes failing 🚀 Sometimes succeeding 💡Always learning

## Discussion