Monad

haskell98-2.0.0.3: Compatibility with Haskell 98

Safe Haskell | Safe
Language | Haskell98

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 Source

Monads that also support choice and failure.

Methods

mzero :: m a Source

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

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

mplus :: m a -> m a -> m a Source

an associative operation

Instances

MonadPlus [] |
MonadPlus P |
MonadPlus ReadPrec |
MonadPlus ReadP |
MonadPlus Maybe |

join :: Monad m => m (m a) -> m a Source

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 () Source

``guard` b` is ``return` ()` if `b` is `True`, and `mzero` if `b` is `False`.

when :: Monad m => Bool -> m () -> m () Source

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 () Source

The reverse of `when`.

ap :: Monad m => m (a -> b) -> m a -> m b Source

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 Source

This generalizes the list-based `concat` function.

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

This generalizes the list-based `filter` function.

mapAndUnzipM :: Monad m => (a -> m (b, c)) -> [a] -> m ([b], [c]) Source

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] Source

The `zipWithM` function generalizes `zipWith` to arbitrary monads.

zipWithM_ :: Monad m => (a -> b -> m c) -> [a] -> [b] -> m () Source

`zipWithM_` is the extension of `zipWithM` which ignores the final result.

foldM :: Monad m => (a -> b -> m a) -> a -> [b] -> m a Source

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 Source

Promote a function to a monad.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source

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 Source

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 Source

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 Source

Promote a function to a monad, scanning the monadic arguments from left to right (cf. `liftM2`).

class Monad m where Source

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.

Minimal complete definition

(>>=), return

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source

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

(>>) :: m a -> m b -> m b infixl 1 Source

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 Source

Inject a value into the monadic type.

fail :: String -> m a Source

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 P |
Monad ReadPrec |
Monad ReadP |
Monad Maybe |
Monad ((->) r) |
Monad (Either e) |
Monad m => Monad (WrappedMonad m) |

class Functor f where Source

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` satisfy these laws.

Methods

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

Instances

Functor [] |
Functor IO |
Functor ZipList |
Functor ReadPrec |
Functor ReadP |
Functor Maybe |
Functor ((->) r) |
Functor (Either a) |
Functor ((,) a) |
Ix i => Functor (Array i) |
Functor (Const m) |
Monad m => Functor (WrappedMonad m) |
Arrow a => Functor (WrappedArrow a b) |

mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source

``mapM` f` is equivalent to ``sequence` . `map` f`.

mapM_ :: Monad m => (a -> m b) -> [a] -> m () Source

``mapM_` f` is equivalent to ``sequence_` . `map` f`.

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

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

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

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

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source

Same as `>>=`, but with the arguments interchanged.