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Control.Monad

Portability | portable
Stability | provisional
Maintainer | libraries@haskell.org

Contents

Functor and monad classes
Functions
  Naming conventions
  Basic functions from the Prelude
  Generalisations of list functions
  Conditional execution of monadic expressions
  Monadic lifting operators

Description
The `Functor`, `Monad` and `MonadPlus` classes, with some useful operations on monads.
Synopsis

class Functor f where

fmap :: (a -> b) -> f a -> f b

class Monad m where

(>>=) :: forall a b . m a -> (a -> m b) -> m b
(>>) :: forall a b . m a -> m b -> m b
return :: a -> m a
fail :: String -> m a

class Monad m => MonadPlus m where

mzero :: m a
mplus :: m a -> m a -> m a

mapM :: Monad m => (a -> m b) -> [a] -> m [b]
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
sequence :: Monad m => [m a] -> m [a]
sequence_ :: Monad m => [m a] -> m ()
(=<<) :: Monad m => (a -> m b) -> m a -> m b
join :: Monad m => m (m a) -> m a
msum :: MonadPlus m => [m a] -> m a
filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])
zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a
foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
replicateM :: Monad m => Int -> m a -> m [a]
replicateM_ :: Monad m => Int -> m a -> m ()
guard :: MonadPlus m => Bool -> m ()
when :: Monad m => Bool -> m () -> m ()
unless :: Monad m => Bool -> m () -> m ()
liftM :: Monad m => (a1 -> r) -> m a1 -> m r
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
ap :: Monad m => m (a -> b) -> m a -> m b

Functor and monad classes
class Functor f where

The `Functor` class is used for types that can be mapped over. Instances of `Functor` should satisfy the following laws:

     fmap id  ==  id
     fmap (f . g)  ==  fmap f . fmap g

The instances of `Functor` for lists, `Maybe` and `IO` defined in the Prelude satisfy these laws.

Methods

fmap :: (a -> b) -> f a -> f b

Instances

Functor IO
Functor IntMap
Functor Maybe
Functor Queue
Functor ReadP
Functor ReadPrec
Functor STM
Functor Tree
Functor []
Ix i => Functor (Array i)
Functor (FiniteMap k)
Functor (Map k)
Functor (ST s)
Functor (ST s)

class Monad m where

The `Monad` class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's `do` expressions provide a convenient syntax for writing monadic expressions.

Minimal complete definition: `>>=` and `return`.

Instances of `Monad` should satisfy the following laws:

     return a >>= k  ==  k a
     m >>= return  ==  m
     m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Instances of both `Monad` and `Functor` should additionally satisfy the law:

     fmap f xs  ==  xs >>= return . f

The instances of `Monad` for lists, `Maybe` and `IO` defined in the Prelude satisfy these laws.

Methods

(>>=) :: forall a b . m a -> (a -> m b) -> m b
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
(>>) :: forall a b . m a -> m b -> m b
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
return :: a -> m a
Inject a value into the monadic type.
fail :: String -> m a
Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a `do` expression.

Instances

Monad IO
Monad Maybe
Monad P
Monad ReadP
Monad ReadPrec
Monad STM
Monad []
ArrowApply a => Monad (ArrowMonad a)
Monad (ST s)
Monad (ST s)

class Monad m => MonadPlus m where

Monads that also support choice and failure.
Methods

mzero :: m a

the identity of `mplus`. It should also satisfy the equations

     mzero >>= f  =  mzero
     v >> mzero   =  mzero

(but the instance for `IO` defined in Control.Monad.Error does not satisfy the second one).

mplus :: m a -> m a -> m a
an associative operation

Instances

MonadPlus Maybe
MonadPlus P
MonadPlus ReadP
MonadPlus ReadPrec
MonadPlus []

Functions
Naming conventions

The functions in this library use the following naming conventions:

- A postfix '`M`' always stands for a function in the Kleisli category: The monad type constructor `m` is added to function results (modulo currying) and nowhere else. So, for example,

      filter  ::              (a ->   Bool) -> [a] ->   [a]
      filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]

- A postfix '`_`' changes the result type from `(m a)` to `(m ())`. Thus, for example:

      sequence  :: Monad m => [m a] -> m [a]
      sequence_ :: Monad m => [m a] -> m ()

- A prefix '`m`' generalizes an existing function to a monadic form. Thus, for example:

      sum  :: Num a       => [a]   -> a
      msum :: MonadPlus m => [m a] -> m a

Basic functions from the Prelude
mapM :: Monad m => (a -> m b) -> [a] -> m [b]
``mapM` f` is equivalent to ``sequence` . `map` f`.
mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
``mapM_` f` is equivalent to ``sequence_` . `map` f`.
sequence :: Monad m => [m a] -> m [a]
Evaluate each action in the sequence from left to right, and collect the results.
sequence_ :: Monad m => [m a] -> m ()
Evaluate each action in the sequence from left to right, and ignore the results.
(=<<) :: Monad m => (a -> m b) -> m a -> m b
Same as `>>=`, but with the arguments interchanged.
Generalisations of list functions
join :: Monad m => m (m a) -> m a
The `join` function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.
msum :: MonadPlus m => [m a] -> m a
This generalizes the list-based `concat` function.
filterM :: Monad m => (a -> m Bool) -> [a] -> m [a]
This generalizes the list-based `filter` function.
mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c])
The `mapAndUnzipM` function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state-transforming monad.
zipWithM :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m [c]
The `zipWithM` function generalizes `zipWith` to arbitrary monads.
zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m ()
`zipWithM_` is the extension of `zipWithM` which ignores the final result.
foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a

The `foldM` function is analogous to `foldl`, except that its result is encapsulated in a monad. Note that `foldM` works from left-to-right over the list arguments. This could be an issue where '(>>)' and the `folded function' are not commutative.

    	foldM f a1 [x1, x2, ..., xm ]

==

    	do
    	  a2 <- f a1 x1
    	  a3 <- f a2 x2
    	  ...
    	  f am xm

If right-to-left evaluation is required, the input list should be reversed.

foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
Like `foldM`, but discards the result.
replicateM :: Monad m => Int -> m a -> m [a]
``replicateM` n act` performs the action `n` times, gathering the results.
replicateM_ :: Monad m => Int -> m a -> m ()
Like `replicateM`, but discards the result.
Conditional execution of monadic expressions
guard :: MonadPlus m => Bool -> m ()
``guard` b` is ``return` ()` if `b` is `True`, and `mzero` if `b` is `False`.
when :: Monad m => Bool -> m () -> m ()

Conditional execution of monadic expressions. For example,

    	when debug (putStr "Debugging\n")

will output the string `Debugging\n` if the Boolean value `debug` is `True`, and otherwise do nothing.

unless :: Monad m => Bool -> m () -> m ()
The reverse of `when`.
Monadic lifting operators
liftM :: Monad m => (a1 -> r) -> m a1 -> m r
Promote a function to a monad.
liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r

Promote a function to a monad, scanning the monadic arguments from left to right. For example,

    	liftM2 (+) [0,1] [0,2] = [0,2,1,3]
    	liftM2 (+) (Just 1) Nothing = Nothing

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).
liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).
liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r
Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).
ap :: Monad m => m (a -> b) -> m a -> m b

In many situations, the `liftM` operations can be replaced by uses of `ap`, which promotes function application.

    	return f `ap` x1 `ap` ... `ap` xn

is equivalent to

    	liftMn f x1 x2 ... xn

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