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Monad

Synopsis

class Monad m => MonadPlus m where

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

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

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

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.
Methods

mzero :: m a
the identity of `mplus`. It should also satisfy the equations `mzero >>= f = mzero v >> mzero = mzero` (but the instance for System.IO.IO defined in Control.Monad.Error in the mtl package does not satisfy the second one).
mplus :: m a -> m a -> m a
an associative operation

Instances

MonadPlus []
MonadPlus Maybe

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.
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`.
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`
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.

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`).
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.

Methods

(>>=) :: 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 :: 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 []
Monad IO
Monad Maybe

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.
Methods

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

Instances

Functor []
Functor IO
Functor Maybe
Ix i => Functor (Array i)

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.
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