This article was originally posted on the Monday Morning Haskell blog on February 20th, 2017. Check out the blog for more Haskell content!
So last week we discussed what a monad is. It isn’t some scary thing only wizards with arcane knowledge of category theory can understand. It’s just a type class with a couple functions describing a particular context. These functions, when used properly, can dramatically expand what we can do while keeping our code purely functional.
We haven’t gone over all the “laws” these functions need to follow. But if we explore enough examples, we’ll have an intuitive grasp of what should happen. We saw some simple examples last time with the Maybe, Either, and IO monads. In this article, we will look at the Reader and Writer monads.
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 where we might 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 EnvironmentloadEnv = …
func1 :: Environment -> Stringfunc1 env = “Result: “ ++ (show (func2 env))
func2 :: Environment -> Intfunc2 env = 2 + floor (func3 env)
func3 :: Environment -> Floatfunc3 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 EnvironmentloadEnv = …
func1 :: Reader Environment Stringfunc1 = do res <- func2 return (“Result: “ ++ (show res))
func2 :: Reader Environment Intfunc2 = 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 Readeractions 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 oddfunc1 :: String -> (Int, String)func1 input = if length input `mod` 2 == 0 then func2 (0, input) else (i1 + i2, str1 ++ str2) where (i1, str1) = func3 (0, tail input) (i2, str2) = func4 (0, take 1 input)
-- Calls func4 on truncated versionfunc2 :: (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 3func3 :: (Int, String) -> (Int, String)func3 (prev, input) = if (length input) `mod` 3 == 0 then (prev + f2resI + 3, f2resStr) else (prev + 1, tail input) where (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 Stringfunc2 input = if (length input) > 10 then do tell 1 func4 (take 9 input) else do tell 10 return input
func3 :: String -> Writer Int Stringfunc3 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 Stringfunc4 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.
Conclusion
The Reader and Writer monads both offer pure functional ways to deal with common side effects. The Reader monad allows you to keep track of a shared global state. It allows you to avoid passing that state as an explicit parameter to functions that don’t really use it. The Writer monad allows you to keep track of a global accumulated value using a monoid. If you want to see how to combine these ideas together, head over to the Monday Morning Haskell Blog and check out the latest article there on the State Monad!
Hopefully this article has helped convinced you that monads (and Haskell for that matter) aren’t all that scary! If this has inspired you to pick up Haskell and start writing some code, check out our free checklist for getting stated!
Not quite ready for monads but want to try some different Haskell skills? Check out our recursion workbook. It includes 2 chapters of material on recursion and higher order functions, as well as 10 practice problems with a test harness.