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Understand monads, do-notation, and in particular the State and Except monads in advance will make the content of this page more transparent.

In imperative programming languages, it is straightforward to write code which performs "side effects", like:

  • throwing an error
  • reading from a file
  • reading from an environment variable
  • writing to a log
  • mutating a local variable
  • non-determinism: multiple computation paths are taken

A standard way in Haskell to have these abilities in a pure functional setting is with the use of types like Maybe, State or Reader. Because these have Monad instances, one can write imperative style code like:

{-# LANGUAGE OverloadedStrings #-}
import Control.Monad.State
import Control.Monad.Reader
import Control.Monad.Except
import Data.Text (Text)

example :: State Bool ()
example = do
    flag <- get
    put (not flag) 


Simple monads tend to only express one of the above effects, so a system for combining them is needed. One approach is to build more complex types modularly, like StateT Bool (Except Text) and define the corresponding Monad instances in a library.

This is what the transformers library does, thus called because StateT, ExceptT, ReaderT and so on are known as monad transformers. Here are some of their definitions:

  • data StateT s m a = StateT {runStateT :: s -> m (a, s)}
  • newtype ExceptT e m a = ExceptT {runExceptT :: m (Either e a)}

StateT (like ExceptT) is parametrized by three types:

  • the type of the state s
  • the type of the underlying monad m
  • the return type of the whole monad, a.

It has kind: * -> (* -> *) -> * -> *.

For example, StateT Bool (Except Text) Int is equivalent to:

(Bool -> Either Text (Int, Bool))

so represents an Int value or failure that results from a boolean state (which could change).


Meanwhile, ExceptT Text (State Bool) Int is equivalent to:

(Bool -> (Either Text Int, Bool))

which is similar, except that the new state is obtained whether or not there is a failure.

However, these types (sometimes referred to as monad transformer stacks) tend to be cumbersome to work with, and involve the ungainly use of a lift function to coerce types into the right shapes.

Abstracting the typeclasses

mtl1 is a widely used library designed to make the experience smoother, which supplies typeclasses that work in conjunction with transformers. Here is an example with error throwing and local variable updating:

example2 :: (MonadError Text m, MonadState Bool m) => m Bool
example2 = do
    flag <- get
    if flag
            put (not flag) 
            >> throwError "flag should not have been on!"
        else pure ()
    return flag
example3 :: (MonadError Text m, MonadState Bool m) => m Bool
example3 = do
    flag <- get
    when flag $ 
        put (not flag) 
        >> throwError "flag should not have been on!"
    return flag

The type of example is abstracted over the concrete monad transformer stack, which could either be ExceptT Text (State Bool) or StateT Bool (Except Text).

Depending on how example is called, either of these can end up being the concrete type that is inferred and used:

errorOverState :: Bool -> IO ()
errorOverState flagVal = 
    let (result, state) = flip runState flagVal $ runExceptT example2
    in do
        putStrLn ("Result: " <> show result)
        putStrLn ("State: " <> show state)

main :: IO ()
main = do
    errorOverState True
    errorOverState False

results in:

repl example
> errorOverState False
Result: Right False
State: False
> errorOverState True
Result: Left "flag should not have been on!"
State: False
stateOverError :: Bool -> IO ()
stateOverError flagVal = case runExcept $ flip runStateT flagVal example of
    Left err -> putStrLn ("Error: " <> show err)
    Right (result, state) -> do
        putStrLn ("Result: " <> show result)
        putStrLn ("State: " <> show state) 

results in

repl example
> stateOverError False
Result: False
State: False
> stateOverError True
Error: "flag should not have been on!"
State: False

Except is a type synonym for ExceptT Identity, where Identity is the monad which does nothing whatsoever.


Alternatives to mtl have become popular in recent years, such as Polysemy and cleff. These are often experimental, or require slightly more advanced use of types (e.g. type level lists) and so are recommended for experienced Haskellers only.

  1. Short for: monad transformer library 

Last update: February 10, 2023
Created: January 12, 2023