base-4.8.2.0: Basic libraries

Description

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

Synopsis

class Functor f where Source

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 Source

Instances

class Applicative m => Monad m where Source

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.

Instances of `Monad` should satisfy the following laws:

• ``return` a `>>=` k  =  k a`
• `m `>>=` `return`  =  m`
• `m `>>=` (x -> k x `>>=` h)  =  (m `>>=` k) `>>=` h`

Furthermore, the `Monad` and `Applicative` operations should relate as follows:

• ``pure` = `return``
• `(`<*>`) = `ap``

The above laws imply:

• ``fmap` f xs  =  xs `>>=` `return` . f`
• `(`>>`) = (`*>`)`

and that `pure` and (`<*>`) satisfy the applicative functor laws.

The instances of `Monad` for lists, `Maybe` and `IO` defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

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

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 Source

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 Source

Inject a value into the monadic type.

fail :: String -> m a Source

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.

Minimal complete definition

Nothing

Methods

mzero :: m a Source

the identity of `mplus`. It should also satisfy the equations

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

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

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 :: (Traversable t, Monad m) => (a -> m b) -> t a -> m (t b) Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see `mapM_`.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see `mapM`.

As of base 4.8.0.0, `mapM_` is just `traverse_`, specialized to `Monad`.

forM :: (Traversable t, Monad m) => t a -> (a -> m b) -> m (t b) Source

`forM` is `mapM` with its arguments flipped. For a version that ignores the results see `forM_`.

forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m () Source

`forM_` is `mapM_` with its arguments flipped. For a version that doesn't ignore the results see `forM`.

As of base 4.8.0.0, `forM_` is just `for_`, specialized to `Monad`.

sequence :: (Traversable t, Monad m) => t (m a) -> m (t a) Source

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see `sequence_`.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see `sequence`.

As of base 4.8.0.0, `sequence_` is just `sequenceA_`, specialized to `Monad`.

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

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

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

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

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

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

`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.

#### Examples

Replace the contents of a `Maybe Int` with unit:

````>>> ````void Nothing
```Nothing
`>>> ````void (Just 3)
```Just ()
```

Replace the contents of an `Either Int Int` with unit, resulting in an `Either Int '()'`:

````>>> ````void (Left 8675309)
```Left 8675309
`>>> ````void (Right 8675309)
```Right ()
```

Replace every element of a list with unit:

````>>> ````void [1,2,3]
```[(),(),()]
```

Replace the second element of a pair with unit:

````>>> ````void (1,2)
```(1,())
```

Discard the result of an `IO` action:

````>>> ````mapM print [1,2]
```1
2
[(),()]
`>>> ````void \$ mapM print [1,2]
```1
2
```

## Generalisations of list functions

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

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 :: (Foldable t, MonadPlus m) => t (m a) -> m a Source

The sum of a collection of actions, generalizing `concat`. As of base 4.8.0.0, `msum` is just `asum`, specialized to `MonadPlus`.

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

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 :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b Source

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.

Note: `foldM` is the same as `foldlM`

foldM_ :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> 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 :: Alternative f => Bool -> f () Source

`guard b` is `pure ()` if `b` is `True`, and `empty` if `b` is `False`.

when :: Applicative f => Bool -> f () -> f () Source

Conditional execution of `Applicative` expressions. For example,

`when debug (putStrLn "Debugging")`

will output the string `Debugging` if the Boolean value `debug` is `True`, and otherwise do nothing.

unless :: Applicative f => Bool -> f () -> f () Source

The reverse of `when`.

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

Promote a function to a monad.

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

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 Source

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 Source

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 Source

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 Source

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`

Strict version of `<\$>`.