- class Monad m => MonadPlus m where
- join :: Monad m => m (m a) -> m a
- guard :: MonadPlus m => Bool -> m ()
- when :: Monad m => Bool -> m () -> m ()
- unless :: Monad m => Bool -> m () -> m ()
- ap :: Monad m => m (a -> b) -> m a -> m b
- 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
- 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
- class Monad m where
- class Functor f where
- fmap :: (a -> b) -> f a -> f b

- 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

# Documentation

class Monad m => MonadPlus m where

Monads that also support choice and failure.

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.

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.

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.

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.

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`

).

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, `Data.Maybe.Maybe`

and `System.IO.IO`

defined in the Prelude satisfy these laws.

(>>=) :: m a -> (a -> m b) -> m b

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: 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 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.

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, `Data.Maybe.Maybe`

and `System.IO.IO`

satisfy these laws.

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

sequence :: Monad m => [m a] -> m [a]

Evaluate each action in the sequence from left to right, and collect the results.