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

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

Maintainer | libraries@haskell.org |

Stability | experimental |

Portability | non-portable (multi-param classes, functional dependencies) |

Safe Haskell | Safe-Inferred |

Language | Haskell98 |

Strict state monads.

This module is inspired by the paper
*Functional Programming with Overloading and Higher-Order 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
- 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
- module Control.Monad
- module Control.Monad.Fix
- module Control.Monad.Trans

# MonadState class

class Monad m => MonadState s m | m -> s where Source

Return the state from the internals of the monad.

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) | |

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 => MonadState s (StateT s m) | |

Monad m => MonadState s (StateT s 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 () Source

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 Source

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.

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

-> State s 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

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.

MonadWriter w m => MonadWriter w (StateT s m) | |

Monad m => MonadState s (StateT s m) | |

MonadReader r m => MonadReader r (StateT s m) | |

MonadError e m => MonadError e (StateT s m) | |

MonadTrans (StateT s) | |

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

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) | |

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 m`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)