- 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
defined in the Prelude 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.