Portability  nonportable (multiparam classes, functional dependencies) 

Stability  experimental 
Maintainer  ross@soi.city.ac.uk 
Strict state monads.
This module is inspired by the paper /Functional Programming with Overloading and HigherOrder Polymorphism/, Mark P Jones (http://web.cecs.pdx.edu/~mpj/) Advanced School of Functional Programming, 1995.
 class Monad m => MonadState s m  m > s where
 modify :: MonadState s m => (s > s) > m ()
 gets :: MonadState s m => (s > a) > m a
 type State s = StateT s Identity
 runState :: State s a > s > (a, s)
 evalState :: State s a > s > a
 execState :: State s a > s > s
 mapState :: ((a, s) > (b, s)) > State s a > State s b
 withState :: (s > s) > State s a > State s a
 newtype StateT s m a = StateT {
 runStateT :: s > m (a, s)
 evalStateT :: Monad m => StateT s m a > s > m a
 execStateT :: Monad m => StateT s m a > s > m s
 mapStateT :: (m (a, s) > n (b, s)) > StateT s m a > StateT s n b
 withStateT :: (s > s) > StateT s m a > StateT s m a
 module Control.Monad
 module Control.Monad.Fix
 module Control.Monad.Trans
MonadState class
class Monad m => MonadState s m  m > s where
get :: m s
Return the state from the internals of the monad.
put :: s > m ()
Replace the state inside the monad.
MonadState s m => MonadState s (MaybeT m)  
MonadState s m => MonadState s (ListT m)  
MonadState s m => MonadState s (IdentityT m)  
(Monoid w, MonadState s m) => MonadState s (WriterT w m)  
(Monoid w, MonadState s m) => MonadState s (WriterT w m)  
Monad m => MonadState s (StateT s m)  
Monad m => MonadState s (StateT s m)  
MonadState s m => MonadState s (ReaderT r m)  
(Error e, MonadState s m) => MonadState s (ErrorT e m)  
MonadState s m => MonadState s (ContT r m)  
(Monad m, Monoid w) => MonadState s (RWST r w s m)  
(Monad m, Monoid w) => MonadState s (RWST r w s m) 
modify :: MonadState s m => (s > s) > m ()
Monadic state transformer.
Maps an old state to a new state inside a state monad. The old state is thrown away.
Main> :t modify ((+1) :: Int > Int) modify (...) :: (MonadState Int a) => a ()
This says that modify (+1)
acts over any
Monad that is a member of the MonadState
class,
with an Int
state.
gets :: MonadState s m => (s > a) > m a
Gets specific component of the state, using a projection function supplied.
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.
:: State s a  statepassing computation to execute 
> s  initial state 
> (a, s)  return value and final state 
Unwrap a state monad computation as a function.
(The inverse of state
.)
:: State s a  statepassing computation to execute 
> s  initial value 
> a  return value of the state computation 
:: State s a  statepassing computation to execute 
> s  initial value 
> s  final state 
The StateT monad transformer
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.
MonadError e m => MonadError e (StateT s m)  
MonadReader r m => MonadReader r (StateT s m)  
Monad m => MonadState s (StateT s m)  
MonadWriter w m => MonadWriter w (StateT s m)  
MonadTrans (StateT s)  
Monad m => Monad (StateT s m)  
Functor m => Functor (StateT s m)  
MonadFix m => MonadFix (StateT s m)  
MonadPlus m => MonadPlus (StateT s m)  
(Functor m, Monad m) => Applicative (StateT s m)  
(Functor m, MonadPlus m) => Alternative (StateT s m)  
MonadIO m => MonadIO (StateT s m)  
MonadCont m => MonadCont (StateT s 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)
withStateT :: (s > s) > StateT s m a > StateT s m a
executes action withStateT
f mm
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/), AddisonWesley 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 asyetunvisited 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)