& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

Left-to-right composition

Flipped version of <$>.

(<&>) = flip fmap

Examples

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0

List of elements of a structure, from left to right. If the entire list is intended to be reduced via a fold, just fold the structure directly bypassing the list.

Examples

>>> toList Nothing
[]

>>> toList (Just 42)
[42]

>>> toList (Left "foo")
[]

>>> toList (Node (Leaf 5) 17 (Node Empty 12 (Leaf 8)))
[5,17,12,8]

>>> toList [1, 2, 3]
[1,2,3]

Since: base-4.8.0.0

Map covariantly over the first argument.

first f ≡ bimap f id

Examples

>>> first toUpper ('j', 3)
('J',3)

>>> first toUpper (Left 'j')
Left 'J'

Map covariantly over the second argument.

second ≡ bimap id

Examples

>>> second (+1) ('j', 3)
('j',4)

>>> second (+1) (Right 3)
Right 4

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

((+) `on` f) x y = f x + f y

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

• (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g . f)

The isNothing function returns True iff its argument is Nothing.

Examples

>>> isNothing (Just 3)
False

>>> isNothing (Just ())
False

>>> isNothing Nothing
True

>>> isNothing (Just Nothing)
False

The isJust function returns True iff its argument is of the form Just _.

Examples

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

>>> isJust (Just Nothing)
True

The fromMaybe function takes a default value and a Maybe value. If the Maybe is Nothing, it returns the default value; otherwise, it returns the value contained in the Maybe.

Examples

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"

>>> fromMaybe "" Nothing
""

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

>>> safeDiv 4 0
Nothing

>>> safeDiv 4 2
Just 2

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0    = Just (x `div` y)
            | otherwise = Nothing

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y = do
  guard (y /= 0)
  return (x `div` y)

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to Weak Head Normal Form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single strict result (e.g. sum).

For a general Foldable structure this should be semantically identical to,

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for. This is forM_ generalised to Applicative actions.

for_ is just like forM_, but generalised to Applicative actions.

Examples

>>> for_ [1..4] print
1
2
3
4

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

traverse_ is just like mapM_, but generalised to Applicative actions.

Examples

>>> traverse_ print ["Hello", "world", "!"]
"Hello"
"world"
"!"

Given a structure with elements whose type is a Monoid, combine them via the monoid's (<>) operator. This fold is right-associative and lazy in the accumulator. When you need a strict left-associative fold, use foldMap' instead, with id as the map.

Examples

>>> fold [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

>>> fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))
Sum {getSum = 9}

>>> fold (repeat Nothing)
* Hangs forever *

>>> take 12 $ fold $ map (\i -> [i..i+2]) [0..]
[0,1,2,1,2,3,2,3,4,3,4,5]
>>> sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]
2666668666666

for is traverse with its arguments flipped. For a version that ignores the results see for_.

Throw an exception. Exceptions may be thrown from purely functional code, but may only be caught within the IO monad.

WARNING: You may want to use throwIO instead so that your pure code stays exception-free.

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.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

atomically :: STM a -> IO a

atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

join . atomically :: STM (IO b) -> IO b

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

Note how this operator resembles function composition (.):

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

Left-to-right composition of Kleisli arrows.

'(bs >=> cs) a' can be understood as the do expression

do b <- bs a
   cs b

Flipped version of <$.

Examples

>>> Nothing $> "foo"
Nothing
>>> Just 90210 $> "foo"
Just "foo"

>>> Left 8675309 $> "foo"
Left 8675309
>>> Right 8675309 $> "foo"
Right "foo"

>>> [1,2,3] $> "foo"
["foo","foo","foo"]

>>> (1,2) $> "foo"
(1,"foo")

Since: base-4.7.0.0

Return the contents of a Right-value or a default value otherwise.

Examples

>>> fromRight 1 (Right 3)
3
>>> fromRight 1 (Left "foo")
1

Since: base-4.10.0.0

Return True if the given value is a Right-value, False otherwise.

Examples

>>> isRight (Left "foo")
False
>>> isRight (Right 3)
True

>>> import Control.Monad ( when )
>>> let report e = when (isRight e) $ putStrLn "SUCCESS"
>>> report (Left "parse error")
>>> report (Right 1)
SUCCESS

Since: base-4.7.0.0

Return True if the given value is a Left-value, False otherwise.

Examples

>>> isLeft (Left "foo")
True
>>> isLeft (Right 3)
False

>>> import Control.Monad ( when )
>>> let report e = when (isLeft e) $ putStrLn "ERROR"
>>> report (Right 1)
>>> report (Left "parse error")
ERROR

Since: base-4.7.0.0

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

Examples

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

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

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

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

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

Makes an effectful function ignore its result value and return its input value.

The function coerce allows you to safely convert between values of types that have the same representation with no run-time overhead. In the simplest case you can use it instead of a newtype constructor, to go from the newtype's concrete type to the abstract type. But it also works in more complicated settings, e.g. converting a list of newtypes to a list of concrete types.

When used in conversions involving a newtype wrapper, make sure the newtype constructor is in scope.

This function is representation-polymorphic, but the RuntimeRep type argument is marked as Inferred, meaning that it is not available for visible type application. This means the typechecker will accept coerce @Int @Age 42.

Examples

>>> newtype TTL = TTL Int deriving (Eq, Ord, Show)
>>> newtype Age = Age Int deriving (Eq, Ord, Show)
>>> coerce (Age 42) :: TTL
TTL 42
>>> coerce (+ (1 :: Int)) (Age 42) :: TTL
TTL 43
>>> coerce (map (+ (1 :: Int))) [Age 42, Age 24] :: [TTL]
[TTL 43,TTL 25]

Coerce the second argument to the result type of the first one. The motivation for this function is that it's often more annoying to explicitly specify a target type for coerce than to construct an explicit coercion function, so this combinator can be used in cases like that. Plus the code reads better, as it becomes clear what and where gets wrapped/unwrapped.

Same as f -> f . coerce, but does not create any closures and so is completely free.

Same as f -> coerce . f, but does not create any closures and so is completely free.

Same as (.), but ignores the first argument and uses a no-op coerction instead.

Representable types of kind *. This class is derivable in GHC with the DeriveGeneric flag on.

A Generic instance must satisfy the following laws:

from . to ≡ id
to . from ≡ id