Description

The Control.Monad module provides the `Functor`, `Monad` and `MonadPlus` classes, together with some useful operations on monads.

Synopsis

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 Handler Functor ReadP Functor Maybe Functor ((->) r) Functor (Either a) Functor ((,) a) Ix i => Functor (Array i)

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

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

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

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

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

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

# 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

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

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

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

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.

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`.

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
```