Control.Monad.State.Lazy

Lazy state monads.

This module is inspired by the paper /Functional Programming with Overloading and Higher-Order Polymorphism/, Mark P Jones (http://www.cse.ogi.edu/~mpj/) Advanced School of Functional Programming, 1995.

See below for examples.

Documentation

module Control.Monad.State.Class

The State Monad

type State s = StateT s Identity

A state monad parameterized by the type s of the state to carry.

The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second.

evalState

Arguments

:: State s a

state-passing computation to execute

-> s

initial value

-> a

return value of the state computation

Evaluate a state computation with the given initial state and return the final value, discarding the final state.

• evalState m s = fst (runState m s)

execState

Arguments

:: State s a

state-passing computation to execute

-> s

initial value

-> s

final state

Evaluate a state computation with the given initial state and return the final state, discarding the final value.

• execState m s = snd (runState m s)

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

Map both the return value and final state of a computation using the given function.

• runState (mapState f m) = f . runState m

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

withState f m executes action m on a state modified by applying f.

• withState f m = modify f >> m

The StateT Monad

newtype StateT s (m :: * -> *) a :: * -> (* -> *) -> * -> *

A state transformer monad parameterized by:

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

The return function leaves the state unchanged, while >>= uses the final state of the first computation as the initial state of the second.

Constructors

StateT

Fields

• runStateT :: s -> m (a, s)

Instances

MonadTrans (StateT s)

Methods

lift :: Monad m => m a -> StateT s m a

Monad m => Monad (StateT s m)

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b

(>>) :: StateT s m a -> StateT s m b -> StateT s m b

return :: a -> StateT s m a

fail :: String -> StateT s m a

Functor m => Functor (StateT s m)

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b

(<$) :: a -> StateT s m b -> StateT s m a

MonadFix m => MonadFix (StateT s m)

Methods

mfix :: (a -> StateT s m a) -> StateT s m a

MonadFail m => MonadFail (StateT s m)

Methods

fail :: String -> StateT s m a

(Functor m, Monad m) => Applicative (StateT s m)

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b

liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c

(*>) :: StateT s m a -> StateT s m b -> StateT s m b

(<*) :: StateT s m a -> StateT s m b -> StateT s m a

MonadIO m => MonadIO (StateT s m)

Methods

liftIO :: IO a -> StateT s m a

(Functor m, MonadPlus m) => Alternative (StateT s m)

Methods

empty :: StateT s m a

(<|>) :: StateT s m a -> StateT s m a -> StateT s m a

some :: StateT s m a -> StateT s m [a]

many :: StateT s m a -> StateT s m [a]

MonadPlus m => MonadPlus (StateT s m)

Methods

mzero :: StateT s m a

mplus :: StateT s m a -> StateT s m a -> StateT s m a

Monad m => MonadState (StateT s m)

Associated Types

type StateType (StateT s m :: * -> *) :: *

Methods

get :: StateT s m (StateType (StateT s m))

put :: StateType (StateT s m) -> StateT s m ()

MonadReader m => MonadReader (StateT s m)

Associated Types

type EnvType (StateT s m :: * -> *) :: *

Methods

ask :: StateT s m (EnvType (StateT s m))

local :: (EnvType (StateT s m) -> EnvType (StateT s m)) -> StateT s m a -> StateT s m a

MonadError m => MonadError (StateT s m)

Associated Types

type ErrorType (StateT s m :: * -> *) :: *

Methods

throwError :: ErrorType (StateT s m) -> StateT s m a

catchError :: StateT s m a -> (ErrorType (StateT s m) -> StateT s m a) -> StateT s m a

MonadCont m => MonadCont (StateT s m)

Methods

callCC :: ((a -> StateT s m b) -> StateT s m a) -> StateT s m a

MonadWriter m => MonadWriter (StateT s m)

Associated Types

type WritType (StateT s m :: * -> *) :: *

Methods

tell :: WritType (StateT s m) -> StateT s m ()

listen :: StateT s m a -> StateT s m (a, WritType (StateT s m))

pass :: StateT s m (a, WritType (StateT s m) -> WritType (StateT s m)) -> StateT s m a

type StateType (StateT s m)

type StateType (StateT s m) = s

type EnvType (StateT s m)

type EnvType (StateT s m) = EnvType m

type ErrorType (StateT s m)

type ErrorType (StateT s m) = ErrorType m

type WritType (StateT s m)

type WritType (StateT s m) = WritType m

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

Evaluate a state computation with the given initial state and return the final value, discarding the final state.

• evalStateT m s = liftM fst (runStateT m s)

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

Evaluate a state computation with the given initial state and return the final state, discarding the final value.

• execStateT m s = liftM snd (runStateT m s)

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

Map both the return value and final state of a computation using the given function.

• runStateT (mapStateT f m) = f . runStateT m

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

withStateT f m executes action m on a state modified by applying f.

• withStateT f m = modify f >> m

module Control.Monad

module Control.Monad.Fix

module Control.Monad.Trans

Examples

A function to increment a counter. Taken from the paper Generalising Monads to Arrows, John Hughes (http://www.math.chalmers.se/~rjmh/), 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 (http://www.cs.kent.ac.uk/people/staff/sjt/), 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)
    where
    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)