haskell2010-1.1.0.0: Compatibility with Haskell 2010

Control.Monad

Contents

Description

The Control.Monad module provides the Functor, Monad and MonadPlus classes, together 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, Data.Maybe.Maybe and System.IO.IO satisfy these laws.

Methods

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

Instances

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, Data.Maybe.Maybe and System.IO.IO defined in the Prelude satisfy these laws.

Methods

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

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

(>>) :: 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.

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