mtl-2.2.2: Monad classes, using functional dependencies

Description

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.

Synopsis

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

Minimal definition is either both of get and put or just state

Minimal complete definition

Methods

get :: m s Source #

Return the state from the internals of the monad.

put :: s -> m () Source #

Replace the state inside the monad.

state :: (s -> (a, s)) -> m a Source #

Embed a simple state action into the monad.

Instances

modify :: MonadState s m => (s -> s) -> m () Source #

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.

modify' :: MonadState s m => (s -> s) -> m () Source #

A variant of modify in which the computation is strict in the new state.

Since: 2.2

gets :: MonadState s m => (s -> a) -> m a Source #

Gets specific component of the state, using a projection function supplied.

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.

Arguments

 :: 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.)

Arguments

 :: State s a state-passing computation to execute -> s initial value -> a return value of the state computation

Evaluate a state computation with the given initial state and return the final value, discarding the final state.

• evalState m s = fst (runState m s)

Arguments

 :: State s a state-passing computation to execute -> s initial value -> s final state

Evaluate a state computation with the given initial state and return the final state, discarding the final value.

• execState m s = snd (runState m s)

mapState :: ((a, s) -> (b, s)) -> State s a -> State s b #

Map both the return value and final state of a computation using the given function.

• runState (mapState f m) = f . runState m

withState :: (s -> s) -> State s a -> State s a #

withState f m executes action m on a state modified by applying f.

• withState f m = modify f >> m

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.

Constructors

 StateT (s -> m (a, s))
Instances
 MonadError e m => MonadError e (StateT s m) Source # Instance detailsMethodsthrowError :: e -> StateT s m a Source #catchError :: StateT s m a -> (e -> StateT s m a) -> StateT s m a Source # MonadReader r m => MonadReader r (StateT s m) Source # Instance detailsMethodsask :: StateT s m r Source #local :: (r -> r) -> StateT s m a -> StateT s m a Source #reader :: (r -> a) -> StateT s m a Source # Monad m => MonadState s (StateT s m) Source # Instance detailsMethodsget :: StateT s m s Source #put :: s -> StateT s m () Source #state :: (s -> (a, s)) -> StateT s m a Source # MonadWriter w m => MonadWriter w (StateT s m) Source # Instance detailsMethodswriter :: (a, w) -> StateT s m a Source #tell :: w -> StateT s m () Source #listen :: StateT s m a -> StateT s m (a, w) Source #pass :: StateT s m (a, w -> w) -> StateT s m a Source # Instance detailsMethodslift :: Monad m => m a -> StateT s m a # Monad m => Monad (StateT s m) Instance detailsMethods(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b #(>>) :: StateT s m a -> StateT s m b -> StateT s m b #return :: a -> StateT s m a #fail :: String -> StateT s m a # Functor m => Functor (StateT s m) Instance detailsMethodsfmap :: (a -> b) -> StateT s m a -> StateT s m b #(<$) :: a -> StateT s m b -> StateT s m a # MonadFix m => MonadFix (StateT s m) Instance detailsMethodsmfix :: (a -> StateT s m a) -> StateT s m a # MonadFail m => MonadFail (StateT s m) Instance detailsMethodsfail :: String -> StateT s m a # (Functor m, Monad m) => Applicative (StateT s m) Instance detailsMethodspure :: a -> StateT s m a #(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b #liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c #(*>) :: StateT s m a -> StateT s m b -> StateT s m b #(<*) :: StateT s m a -> StateT s m b -> StateT s m a # MonadIO m => MonadIO (StateT s m) Instance detailsMethodsliftIO :: IO a -> StateT s m a # (Functor m, MonadPlus m) => Alternative (StateT s m) Instance detailsMethodsempty :: StateT s m a #(<|>) :: StateT s m a -> StateT s m a -> StateT s m a #some :: StateT s m a -> StateT s m [a] #many :: StateT s m a -> StateT s m [a] # MonadPlus m => MonadPlus (StateT s m) Instance detailsMethodsmzero :: StateT s m a #mplus :: StateT s m a -> StateT s m a -> StateT s m a # MonadCont m => MonadCont (StateT s m) Source # Instance detailsMethodscallCC :: ((a -> StateT s m b) -> StateT s m a) -> StateT s m a Source # runStateT :: StateT s m a -> s -> m (a, s) # 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) mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b # Map both the return value and final state of a computation using the given function. • runStateT (mapStateT f m) = f . runStateT m withStateT :: (s -> s) -> StateT s m a -> StateT s m a # withStateT f m executes action m on a state modified by applying f. • withStateT f m = modify f >> m # 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)