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Control.Monad.State.Lazy | Portability | non-portable (multi-param classes, functional dependencies) | Stability | experimental | Maintainer | libraries@haskell.org |
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Description |
Lazy 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.
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Synopsis |
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MonadState class
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get returns the state from the internals of the monad.
put replaces the state inside the monad.
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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.
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Gets specific component of the state, using a projection function
supplied.
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The State monad
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A parameterizable state monad where s is the type of the state
to carry and a is the type of the return value.
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:: | | => State s a | An initial value
| -> s | The return value of the state application
| -> a | | Evaluate this state monad with the given initial state,throwing
away the final state. Very much like fst composed with
runstate.
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:: | | => State s a | An initial value
| -> s | The new state
| -> s | | Execute this state and return the new state, throwing away the
return value. Very much like snd composed with
runstate.
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Map a stateful computation from one (return value, state) pair to
another. For instance, to convert numberTree from a function that
returns a tree to a function that returns the sum of the numbered
tree (see the Examples section for numberTree and sumTree) you may
write:
sumNumberedTree :: (Eq a) => Tree a -> State (Table a) Int
sumNumberedTree = mapState (\ (t, tab) -> (sumTree t, tab)) . numberTree
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Apply this function to this state and return the resulting state.
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The StateT monad transformer
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A parameterizable state monad for encapsulating an inner
monad.
The StateT Monad structure is parameterized over two things:
- s - The state.
- m - The inner monad.
Here are some examples of use:
(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))
| Constructors | StateT | | runStateT :: s -> m (a, s) | |
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Similar to evalState
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Similar to execState
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Similar to mapState
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Similar to withState
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module Control.Monad |
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module Control.Monad.Fix |
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module Control.Monad.Trans |
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Examples
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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)
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