Copyright | (c) Andy Gill 2001, (c) Oregon Graduate Institute of Science and Technology, 2001 |
---|---|

License | BSD-style (see the file LICENSE) |

Maintainer | ross@soi.city.ac.uk |

Stability | experimental |

Portability | portable |

Safe Haskell | Safe-Inferred |

Language | Haskell98 |

Lazy state monads, passing an updatable state through a computation. See below for examples.

In this version, sequencing of computations is lazy. For a strict version, see Control.Monad.Trans.State.Strict, which has the same interface.

Some computations may not require the full power of state transformers:

- For a read-only 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 :: Monad m => (s -> (a, s)) -> StateT s m 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 Identity Source

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.

:: Monad m | |

=> (s -> (a, s)) | pure state transformer |

-> StateT s m a | equivalent state-passing computation |

Construct a state monad computation from a function.
(The inverse of `runState`

.)

:: State s a | state-passing 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 | state-passing computation to execute |

-> s | initial value |

-> a | return value of the state computation |

:: State s a | state-passing 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 a Source

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 Source

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 Source

executes action `withStateT`

f m`m`

on a state modified by
applying `f`

.

`withStateT`

f m =`modify`

f >> m

# State operations

# 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 a Source

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 a Source

In-situ 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 a Source

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 a Source

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.cse.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/),
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)