mtl- Monad transformer library

Portabilitynon-portable (multi-param classes, functional dependencies)




Lazy state monads.

This module is inspired by the paper /Functional Programming with Overloading and Higher-Order Polymorphism/, Mark P Jones ( Advanced School of Functional Programming, 1995.

See below for examples.



The State Monad

newtype State s a Source

A parameterizable state monad where s is the type of the state to carry and a is the type of the return value.




runState :: s -> (a, s)




:: State s a

The state to evaluate

-> s

An initial value

-> a

The return value of the state application

Evaluate this state monad with the given initial state,throwing away the final state. Very much like fst composed with runstate.



:: State s a

The state to evaluate

-> s

An initial value

-> s

The new state

Execute this state and return the new state, throwing away the return value. Very much like snd composed with runstate.

mapState :: ((a, s) -> (b, s)) -> State s a -> State s bSource

Map a stateful computation from one (return value, state) pair to another. For instance, to convert numberTree from a function that returns a tree to a function that returns the sum of the numbered tree (see the Examples section for numberTree and sumTree) you may write:

 sumNumberedTree :: (Eq a) => Tree a -> State (Table a) Int
 sumNumberedTree = mapState (\ (t, tab) -> (sumTree t, tab))  . numberTree

withState :: (s -> s) -> State s a -> State s aSource

Apply this function to this state and return the resulting state.

The StateT Monad

newtype StateT s m a Source

A parameterizable state monad for encapsulating an inner monad.

The StateT Monad structure is parameterized over two things:

  • s - The state.
  • m - The inner monad.

Here are some examples of use:

(Parser from ParseLib with Hugs)

  type Parser a = StateT String [] a
     ==> StateT (String -> [(a,String)])

For example, item can be written as:

   item = do (x:xs) <- get
          put xs
          return x

   type BoringState s a = StateT s Indentity a
        ==> StateT (s -> Identity (a,s))

   type StateWithIO s a = StateT s IO a
        ==> StateT (s -> IO (a,s))

   type StateWithErr s a = StateT s Maybe a
        ==> StateT (s -> Maybe (a,s))




runStateT :: s -> m (a, s)


MonadWriter w m => MonadWriter w (StateT s m) 
MonadError e m => MonadError e (StateT s m) 
Monad m => MonadState s (StateT s m) 
MonadReader r m => MonadReader r (StateT s m) 
MonadTrans (StateT s) 
Monad m => Monad (StateT s m) 
Monad m => Functor (StateT s m) 
MonadFix m => MonadFix (StateT s m) 
MonadPlus m => MonadPlus (StateT s m) 
MonadIO m => MonadIO (StateT s m) 
MonadCont m => MonadCont (StateT s m) 

evalStateT :: Monad m => StateT s m a -> s -> m aSource

Similar to evalState

execStateT :: Monad m => StateT s m a -> s -> m sSource

Similar to execState

mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n bSource

Similar to mapState

withStateT :: (s -> s) -> StateT s m a -> StateT s m aSource

Similar to withState


A function to increment a counter. Taken from the paper Generalising Monads to Arrows, John Hughes (, November 1998:

 tick :: State Int Int
 tick = do n <- get
           put (n+1)
           return n

Add one to the given number using the state monad:

 plusOne :: Int -> Int
 plusOne n = execState tick n

A contrived addition example. Works only with positive numbers:

 plus :: Int -> Int -> Int
 plus n x = execState (sequence $ replicate n tick) x

An example from The Craft of Functional Programming, Simon Thompson (, Addison-Wesley 1999: "Given an arbitrary tree, transform it to a tree of integers in which the original elements are replaced by natural numbers, starting from 0. The same element has to be replaced by the same number at every occurrence, and when we meet an as-yet-unvisited element we have to find a 'new' number to match it with:"

 data Tree a = Nil | Node a (Tree a) (Tree a) deriving (Show, Eq)
 type Table a = [a]
 numberTree :: Eq a => Tree a -> State (Table a) (Tree Int)
 numberTree Nil = return Nil
 numberTree (Node x t1 t2)
        =  do num <- numberNode x
              nt1 <- numberTree t1
              nt2 <- numberTree t2
              return (Node num nt1 nt2)
     numberNode :: Eq a => a -> State (Table a) Int
     numberNode x
        = do table <- get
             (newTable, newPos) <- return (nNode x table)
             put newTable
             return newPos
     nNode::  (Eq a) => a -> Table a -> (Table a, Int)
     nNode x table
        = case (findIndexInList (== x) table) of
          Nothing -> (table ++ [x], length table)
          Just i  -> (table, i)
     findIndexInList :: (a -> Bool) -> [a] -> Maybe Int
     findIndexInList = findIndexInListHelp 0
     findIndexInListHelp _ _ [] = Nothing
     findIndexInListHelp count f (h:t)
        = if (f h)
          then Just count
          else findIndexInListHelp (count+1) f t

numTree applies numberTree with an initial state:

 numTree :: (Eq a) => Tree a -> Tree Int
 numTree t = evalState (numberTree t) []
 testTree = Node "Zero" (Node "One" (Node "Two" Nil Nil) (Node "One" (Node "Zero" Nil Nil) Nil)) Nil
 numTree testTree => Node 0 (Node 1 (Node 2 Nil Nil) (Node 1 (Node 0 Nil Nil) Nil)) Nil

sumTree is a little helper function that does not use the State monad:

 sumTree :: (Num a) => Tree a -> a
 sumTree Nil = 0
 sumTree (Node e t1 t2) = e + (sumTree t1) + (sumTree t2)