base-4.6.0.1: Basic libraries

Portability portable provisional [email protected] Trustworthy

Description

The Functor, Monad and MonadPlus classes, with some useful operations on monads.

Synopsis

# Functor and monad classes

class Functor f whereSource

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 bSource

Instances

 Functor [] Functor IO Functor Maybe Functor ReadP Functor ReadPrec Functor STM Functor Handler Functor ZipList Functor ((->) r) Functor (Either a) Functor ((,) a) Functor (ST s) Arrow a => Functor (ArrowMonad a) Functor (ST s) Monad m => Functor (WrappedMonad m) Functor (Const m) Arrow a => Functor (WrappedArrow a b)

class Monad m whereSource

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.

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m bSource

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

(>>) :: forall a b. m a -> m b -> m bSource

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m aSource

Inject a value into the monadic type.

fail :: String -> m aSource

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

class Monad m => MonadPlus m whereSource

Monads that also support choice and failure.

Methods

mzero :: m aSource

the identity of mplus. It should also satisfy the equations

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

mplus :: m a -> m a -> m aSource

an associative operation

Instances

# Functions

## Naming conventions

The functions in this library use the following naming conventions:

• A postfix 'M' always stands for a function in the Kleisli category: The monad type constructor m is added to function results (modulo currying) and nowhere else. So, for example,
filter  ::              (a ->   Bool) -> [a] ->   [a]
filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]
• A postfix '_' changes the result type from (m a) to (m ()). Thus, for example:
sequence  :: Monad m => [m a] -> m [a]
sequence_ :: Monad m => [m a] -> m ()
• A prefix 'm' generalizes an existing function to a monadic form. Thus, for example:
sum  :: Num a       => [a]   -> a
msum :: MonadPlus m => [m a] -> m a

## Basic Monad functions

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.

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

forM is mapM with its arguments flipped

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

forM_ is mapM_ with its arguments flipped

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 bSource

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

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m cSource

Left-to-right Kleisli composition of monads.

(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m cSource

Right-to-left Kleisli composition of monads. (>=>), with the arguments flipped

forever :: Monad m => m a -> m bSource

forever act repeats the action infinitely.

void :: Functor f => f a -> f ()Source

void value discards or ignores the result of evaluation, such as the return value of an IO action.

## Generalisations of list functions

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

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.

msum :: MonadPlus m => [m a] -> m aSource

This generalizes the list-based concat function.

mfilter :: MonadPlus m => (a -> Bool) -> m a -> m aSource

Direct MonadPlus equivalent of filter filter = (mfilter:: (a -> Bool) -> [a] -> [a] applicable to any MonadPlus, for example mfilter odd (Just 1) == Just 1 mfilter odd (Just 2) == Nothing

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 aSource

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.

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

Like foldM, but discards the result.

replicateM :: Monad m => Int -> m a -> m [a]Source

replicateM n act performs the action n times, gathering the results.

replicateM_ :: Monad m => Int -> m a -> m ()Source

Like replicateM, but discards the result.

## Conditional execution of monadic expressions

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.

## Monadic lifting operators

liftM :: Monad m => (a1 -> r) -> m a1 -> m rSource

Promote a function to a monad.

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

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 rSource

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 rSource

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 rSource

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

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

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