Monad

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 ()

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

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

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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 ()

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The reverse of when.

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

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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

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This generalizes the list-based concat function.

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

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This generalizes the list-based filter function.

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

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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]

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The zipWithM function generalizes zipWith to arbitrary monads.

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

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

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

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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

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Promote a function to a monad.

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

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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

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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

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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

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

class Monad m where

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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

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

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

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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

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Inject a value into the monadic type.

fail :: String -> m a

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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

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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

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