base-4.7.0.2: Basic libraries

Copyright | (c) The University of Glasgow 2001
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | provisional
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Control.Monad

Contents

- Functor and monad classes
- Functions
  - Naming conventions
  - Basic `Monad` functions
  - Generalisations of list functions
  - Conditional execution of monadic expressions
  - Monadic lifting operators

Description

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

Synopsis

- class Functor f where
  - fmap :: (a -> b) -> f a -> f b
- class Monad m where
  - (>>=) :: forall a b. m a -> (a -> m b) -> m b
  - (>>) :: forall a b. m a -> m b -> m b
  - return :: a -> m a
  - fail :: String -> m a
- class Monad m => MonadPlus m where
  - mzero :: m a
  - mplus :: m a -> m a -> m a
- mapM :: Monad m => (a -> m b) -> [a] -> m [b]
- mapM_ :: Monad m => (a -> m b) -> [a] -> m ()
- forM :: Monad m => [a] -> (a -> m b) -> m [b]
- forM_ :: Monad m => [a] -> (a -> m b) -> m ()
- sequence :: Monad m => [m a] -> m [a]
- sequence_ :: Monad m => [m a] -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- (>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c
- (<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c
- forever :: Monad m => m a -> m b
- void :: Functor f => f a -> f ()
- join :: Monad m => m (m a) -> m a
- msum :: MonadPlus m => [m a] -> m a
- mfilter :: MonadPlus m => (a -> Bool) -> 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
- foldM_ :: Monad m => (a -> b -> m a) -> a -> [b] -> m ()
- replicateM :: Monad m => Int -> m a -> m [a]
- replicateM_ :: Monad m => Int -> m a -> m ()
- guard :: MonadPlus m => Bool -> m ()
- when :: Monad m => Bool -> m () -> m ()
- unless :: Monad m => Bool -> m () -> m ()
- 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
- ap :: Monad m => m (a -> b) -> m a -> m b

# Functor and monad classes

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, `Maybe` and `IO` satisfy these laws.

Methods

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

Instances

Functor [] |
Functor IO |
Functor Maybe |
Functor ReadP |
Functor ReadPrec |
Functor STM |
Functor Handler |
Functor ZipList |
Functor ArgDescr |
Functor OptDescr |
Functor ArgOrder |
Functor ((->) r) |
Functor (Either a) |
Functor ((,) a) |
Functor (ST s) |
Functor (Proxy *) |
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 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, `Maybe` and `IO` defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=), return

Methods

(>>=) :: forall a b. m a -> (a -> m b) -> m b infixl 1

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 b infixl 1

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 |
Monad ReadP |
Monad ReadPrec |
Monad STM |
Monad ((->) r) |
Monad (Either e) |
Monad (ST s) |
Monad (Proxy *) |
ArrowApply a => Monad (ArrowMonad a) |
Monad (ST s) |
Monad m => Monad (WrappedMonad m) |

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

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

an associative operation

Instances

MonadPlus [] |
MonadPlus Maybe |
MonadPlus ReadP |
MonadPlus ReadPrec |
MonadPlus STM |
(ArrowApply a, ArrowPlus a) => MonadPlus (ArrowMonad a) |

# 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]

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

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

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

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

`forM` is `mapM` with its arguments flipped

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

`forM_` is `mapM_` with its arguments flipped

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 infixr 1

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

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

Left-to-right Kleisli composition of monads.

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

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

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

``forever` act` repeats the action infinitely.

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

``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 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.

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

This generalizes the list-based `concat` function.

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

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]

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.

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

Like `foldM`, but discards the result.

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

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

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

Like `replicateM`, but discards the result.

## Conditional execution of monadic expressions

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`.

## Monadic lifting operators

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`).

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