Portability  portable 

Stability  experimental 
Maintainer  ross@soi.city.ac.uk 
Lazy state monads, passing an updateable state through a computation. See below for examples.
In this version, sequencing of computations is lazy in the state. For a strict version, see Control.Monad.Trans.Writer.Strict, which has the same interface.
Some computations may not require the full power of state transformers:
 For a readonly state, see Control.Monad.Trans.Reader.
 To accumulate a value without using it on the way, see Control.Monad.Trans.Writer.
 type State s = StateT s Identity
 state :: (s > (a, s)) > State s a
 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
 get :: Monad m => StateT s m s
 put :: Monad m => s > StateT s m ()
 modify :: Monad m => (s > s) > StateT s m ()
 gets :: Monad m => (s > a) > StateT s m a
 liftCallCC :: ((((a, s) > m (b, s)) > m (a, s)) > m (a, s)) > ((a > StateT s m b) > StateT s m a) > StateT s m a
 liftCallCC' :: ((((a, s) > m (b, s)) > m (a, s)) > m (a, s)) > ((a > StateT s m b) > StateT s m a) > StateT s m a
 liftCatch :: (m (a, s) > (e > m (a, s)) > m (a, s)) > StateT s m a > (e > StateT s m a) > StateT s m a
 liftListen :: Monad m => (m (a, s) > m ((a, s), w)) > StateT s m a > StateT s m (a, w)
 liftPass :: Monad m => (m ((a, s), b) > m (a, s)) > StateT s m (a, b) > StateT s m a
The State monad
type State s = StateT s IdentitySource
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.
:: (s > (a, s))  pure state transformer 
> State s a  equivalent statepassing computation 
Construct a state monad computation from a function.
(The inverse of runState
.)
:: 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
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.
evalStateT :: Monad m => StateT s m a > s > m aSource
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 sSource
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 aSource
executes action withStateT
f mm
on a state modified by
applying f
.
withStateT
f m =modify
f >> m
State operations
modify :: Monad m => (s > s) > StateT s m ()Source
is an action that updates the state to the result of
applying modify
ff
to the current state.
Lifting other operations
liftCallCC :: ((((a, s) > m (b, s)) > m (a, s)) > m (a, s)) > ((a > StateT s m b) > StateT s m a) > StateT s m aSource
Uniform lifting of a callCC
operation to the new monad.
This version rolls back to the original state on entering the
continuation.
liftCallCC' :: ((((a, s) > m (b, s)) > m (a, s)) > m (a, s)) > ((a > StateT s m b) > StateT s m a) > StateT s m aSource
Insitu lifting of a callCC
operation to the new monad.
This version uses the current state on entering the continuation.
It does not satisfy the laws of a monad transformer.
liftCatch :: (m (a, s) > (e > m (a, s)) > m (a, s)) > StateT s m a > (e > StateT s m a) > StateT s m aSource
Lift a catchError
operation to the new monad.
liftListen :: Monad m => (m (a, s) > m ((a, s), w)) > StateT s m a > StateT s m (a, w)Source
Lift a listen
operation to the new monad.
liftPass :: Monad m => (m ((a, s), b) > m (a, s)) > StateT s m (a, b) > StateT s m aSource
Lift a pass
operation to the new monad.
Examples
State monads
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 Identity 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))
Counting
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
Labelling trees
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)