Reader and Writer Monads

In part 3 of this series, we finally tackled the conceptual idea of monads. We learned what they are, and saw how some common types like IO and Maybe work as monads. Now in this part, we’ll start looking at some other useful monads. In particular, we’ll consider the Reader and Writer monads.

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Global Variables (or a lack thereof)

In Haskell, our code is generally “pure”, meaning functions can only interact with the arguments passed to them. This effectively means we cannot have global variables. We can have global expressions, but these are fixed at compile time. If user behavior might change them, we have to wrap them in the IO monad, which means they can’t be used from pure code.

Consider this example. Here, we want to have an Environment containing different parameters as a global variable. However, we might have to load these from a config file or a command line interface, which requires the IO monad.

main :: IO ()
main = do
  env <- loadEnv
  let str = func1 env
  print str

data Environment = Environment
  { param1 :: String
  , param2 :: String
  , param3 :: String }

loadEnv :: IO Environment
loadEnv = …

func1 :: Environment -> String
func1 env = “Result: “ ++ (show (func2 env))

func2 :: Environment -> Int
func2 env = 2 + floor (func3 env)

func3 :: Environment -> Float
func3 env = … -- Some calculation based on the environment

The only function actually using the environment is func3. However func3 is an impure function. This means it cannot directly call loadEnv, an impure function. This means the environment has to be passed through as a variable to the other functions, just so they can ultimately pass it to func3. In a language with global variables, we could save env as a global value in main. Then func3 could access it directly. There would be no need to have it as a parameter to func1 and func2. In larger programs, these “pass-through” variables can cause a lot of headaches.

The Reader Solution

The Reader monad solves this problem. It effectively creates a global read-only value of a specified type. All functions within the monad can “read” the type. Let’s look at how the Reader monad changes the shape of our code. Our functions no longer need the Environment as an explicit parameter, as they can access it through the monad.

main :: IO ()
main = do
  env <- loadEnv
  let str = runReader func1 env
  print str

data Environment = Environment
  { param1 :: String
  , param2 :: String
  , param3 :: String }

loadEnv :: IO Environment
loadEnv = …

func1 :: Reader Environment String
func1 = do
  res <- func2
  return (“Result: “ ++ (show res))

func2 :: Reader Environment Int
func2 = do
  env <- ask
  let res3 = func3 env
  return (2 + (floor res3))

func3 :: Environment -> Float

The ask function unwraps the environment so we can use it. The monad’s bind action allows us to glue different Reader actions together together. In order to call a reader action from pure code, all we need to do is call the runReader function and supply the environment as a parameter. All functions within the action will be able to treat it like a global variable.

It might not seem like we’ve accomplished much, but our code is much more intuitive now. We keep func3 as it was. It makes sense to describe it as a function from an Environment to a value. However, our other two functions no longer take the environment as an explicit parameter. They simply exist in a context where the environment is a global variable.

Accumulating Values

Now, to motivate the Writer monad, let’s talk about the accumulation problem. Suppose we have a few different functions. Each will perform some string operations we’ve assigned an arbitrary “cost” to. We want to keep track of how “expensive” it was to run the full computation. We can do this by using accumulator arguments to keep track of the cost we’ve seen so far. We then keep passing the accumulated value along.

-- Calls func2 if even length, func3 and func4 if odd
func1 :: String -> (Int, String)
func1 input = if length input `mod` 2 == 0
  then func2 (0, input)
  else (i1 + i2, str1 ++ str2)
      (i1, str1) = func3 (0, tail input)
      (i2, str2) = func4 (0, take 1 input)

-- Calls func4 on truncated version
func2 :: (Int, String) -> (Int, String)
func2 (prev, input) = if (length input) > 10
  then func4 (prev + 1, take 9 input)
  else (10, input)

-- Calls func2 on expanded version if a multiple of 3
func3 :: (Int, String) -> (Int, String)
func3 (prev, input) = if (length input) `mod` 3 == 0
  then (prev + f2resI + 3, f2resStr)
  else (prev + 1, tail input)
    (f2resI, f2resStr) = func2 (prev, input ++ "ab")

func4 :: (Int, String) -> (Int, String)
func4 (prev, input) = if (length input) < 10
  then (prev + length input, input ++ input)
  else (prev + 5, take 5 input)

However, an Int isn’t the only type of value we could accumulate. We could instead be accumulating a list of strings to print as log messages so we know what computations were run. There is a generalization of this behavior: the Monoid typeclass.

The Monoid Typeclass

In this example, Int is a simple example of a Monoid. Let’s look at the monoid typeclass definition:

class Monoid a where
  mempty :: a
  mappend :: a -> a -> a

This is effectively an accumulation class. It defines two functions. The mempty function is an initial value for our monoid. Then with mappend, we can combine two values of this type into a result. It is quite easy to how we can make a monoid instance for Int:

instance Monoid Int where
  memty = 0
  mappend a b = a + b

Our accumulator starts at 0, and we combine values by adding them.

Using Writer to Track the Accumulator

The Writer monad is parameterized by some monoidal type. Its main job is to keep track of an accumulated value of this type. So it’s operations live in the context of having a global value that they can modify in this particular way. We can change our code examples above to use the Writer monad as follows:

func1 :: String -> (String, Int)
func1 input = if length input `mod` 2 == 0
  then runWriter (func2 input)
  else runWriter $ do
    str1 <- func3 input
    str2 <- func4 (take 1 input)
    return (str1 ++ str2)

func2 :: String -> Writer Int String
func2 input = if (length input) > 10
  then do
    tell 1
    func4 (take 9 input)
  else do
    tell 10
    return input

func3 :: String -> Writer Int String
func3 input = if (length input) `mod` 3 == 0
  then do
    tell 3
    func2 (input ++ “ab”)
  else do
    tell 1
    return $ tail input

func4 :: String -> Writer Int String
func4 input = if (length input) < 10
  then do
    tell (length input)
    return (input ++ input)
  else do
    tell 5
    return (take 5 input)

Notice we no longer need to actually explicitly keep track of the accumulator. It is now wrapped by the Writer monad. We can increase it in any of our functions by calling “tell”. Now our code is much simpler and our types are cleaner.


Now that we know about the Reader and Writer monads, it’s time to move on to part 5. There, we’ll discuss the State monad. This monad combines these two concepts into a read/write state, essentially allowing the full privilege of a global variable. If these concepts were still a little confusing, don’t be afraid to take another look at part 3 to solidify your understanding of monads.

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