RIO.Prelude

Documentation

module RIO.Prelude.Types

Bool

Re-exported from Data.Bool:

(||) :: Bool -> Bool -> Bool infixr 2

Boolean "or", lazy in the second argument

(&&) :: Bool -> Bool -> Bool infixr 3

Boolean "and", lazy in the second argument

not :: Bool -> Bool

Boolean "not"

otherwise :: Bool

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

bool :: a -> a -> Bool -> a

Case analysis for the Bool type. bool x y p evaluates to x when p is False, and evaluates to y when p is True.

This is equivalent to if p then y else x; that is, one can think of it as an if-then-else construct with its arguments reordered.

Examples

Basic usage:

>>> bool "foo" "bar" True
"bar"
>>> bool "foo" "bar" False
"foo"

Confirm that bool x y p and if p then y else x are equivalent:

>>> let p = True; x = "bar"; y = "foo"
>>> bool x y p == if p then y else x
True
>>> let p = False
>>> bool x y p == if p then y else x
True

Since: base-4.7.0.0

Maybe

Re-exported from Data.Maybe:

maybe :: b -> (a -> b) -> Maybe a -> b

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Basic usage:

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

fromMaybe :: a -> Maybe a -> a

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

Examples

Basic usage:

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

>>> fromMaybe "" Nothing
""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

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

fromFirst :: a -> First a -> a

Get a First value with a default fallback

isJust :: Maybe a -> Bool

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

Examples

Basic usage:

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)
True

isNothing :: Maybe a -> Bool

The isNothing function returns True iff its argument is Nothing.

Examples

Basic usage:

>>> isNothing (Just 3)
False

>>> isNothing (Just ())
False

>>> isNothing Nothing
True

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)
False

listToMaybe :: [a] -> Maybe a

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

Examples

Basic usage:

>>> listToMaybe []
Nothing

>>> listToMaybe [9]
Just 9

>>> listToMaybe [1,2,3]
Just 1

Composing maybeToList with listToMaybe should be the identity on singleton/empty lists:

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

But not on lists with more than one element:

>>> maybeToList $ listToMaybe [1,2,3]
[1]

maybeToList :: Maybe a -> [a]

The maybeToList function returns an empty list when given Nothing or a singleton list when given Just.

Examples

Basic usage:

>>> maybeToList (Just 7)
[7]

>>> maybeToList Nothing
[]

One can use maybeToList to avoid pattern matching when combined with a function that (safely) works on lists:

>>> import Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

catMaybes :: [Maybe a] -> [a]

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

Examples

Basic usage:

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

When constructing a list of Maybe values, catMaybes can be used to return all of the "success" results (if the list is the result of a map, then mapMaybe would be more appropriate):

>>> import Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

mapMaybe :: (a -> Maybe b) -> [a] -> [b]

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

Examples

Using mapMaybe f x is a shortcut for catMaybes $ map f x in most cases:

>>> import Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

If we map the Just constructor, the entire list should be returned:

>>> mapMaybe Just [1,2,3]
[1,2,3]

mapMaybeA :: Applicative f => (a -> f (Maybe b)) -> [a] -> f [b]

Applicative mapMaybe.

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

Monadic mapMaybe.

forMaybeA :: Applicative f => [a] -> (a -> f (Maybe b)) -> f [b]

forMaybeA == flip mapMaybeA

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

forMaybeM == flip mapMaybeM

Either

Re-exported from Data.Either:

either :: (a -> c) -> (b -> c) -> Either a b -> c

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

fromLeft :: a -> Either a b -> a

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

Examples

Basic usage:

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

Since: base-4.10.0.0

fromRight :: b -> Either a b -> b

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

Examples

Basic usage:

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

Since: base-4.10.0.0

isLeft :: Either a b -> Bool

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

Examples

Basic usage:

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

Assuming a Left value signifies some sort of error, we can use isLeft to write a very simple error-reporting function that does absolutely nothing in the case of success, and outputs "ERROR" if any error occurred.

This example shows how isLeft might be used to avoid pattern matching when one does not care about the value contained in the constructor:

>>> 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

isRight :: Either a b -> Bool

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

Examples

Basic usage:

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

Assuming a Left value signifies some sort of error, we can use isRight to write a very simple reporting function that only outputs "SUCCESS" when a computation has succeeded.

This example shows how isRight might be used to avoid pattern matching when one does not care about the value contained in the constructor:

>>> 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

mapLeft :: (a1 -> a2) -> Either a1 b -> Either a2 b

Apply a function to a Left constructor

lefts :: [Either a b] -> [a]

Extracts from a list of Either all the Left elements. All the Left elements are extracted in order.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> lefts list
["foo","bar","baz"]

partitionEithers :: [Either a b] -> ([a], [b])

Partitions a list of Either into two lists. All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list
(["foo","bar","baz"],[3,7])

The pair returned by partitionEithers x should be the same pair as (lefts x, rights x):

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list == (lefts list, rights list)
True

rights :: [Either a b] -> [b]

Extracts from a list of Either all the Right elements. All the Right elements are extracted in order.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> rights list
[3,7]

Tuples

Re-exported from Data.Tuple:

fst :: (a, b) -> a

Extract the first component of a pair.

snd :: (a, b) -> b

Extract the second component of a pair.

curry :: ((a, b) -> c) -> a -> b -> c

curry converts an uncurried function to a curried function.

Examples

>>> curry fst 1 2
1

uncurry :: (a -> b -> c) -> (a, b) -> c

uncurry converts a curried function to a function on pairs.

Examples

>>> uncurry (+) (1,2)
3

>>> uncurry ($) (show, 1)
"1"

>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

Eq

Re-exported from Data.Eq:

(==) :: Eq a => a -> a -> Bool infix 4

(/=) :: Eq a => a -> a -> Bool infix 4

Ord

Re-exported from Data.Ord:

(<) :: Ord a => a -> a -> Bool infix 4

(<=) :: Ord a => a -> a -> Bool infix 4

(>) :: Ord a => a -> a -> Bool infix 4

(>=) :: Ord a => a -> a -> Bool infix 4

max :: Ord a => a -> a -> a

min :: Ord a => a -> a -> a

compare :: Ord a => a -> a -> Ordering

comparing :: Ord a => (b -> a) -> b -> b -> Ordering

comparing p x y = compare (p x) (p y)

Useful combinator for use in conjunction with the xxxBy family of functions from Data.List, for example:

  ... sortBy (comparing fst) ...

newtype Down a

The Down type allows you to reverse sort order conveniently. A value of type Down a contains a value of type a (represented as Down a). If a has an Ord instance associated with it then comparing two values thus wrapped will give you the opposite of their normal sort order. This is particularly useful when sorting in generalised list comprehensions, as in: then sortWith by Down x

Since: base-4.6.0.0

Constructors

Down

Fields

• getDown :: a

  Since: base-4.14.0.0

Instances

Monad Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

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

(>>) :: Down a -> Down b -> Down b

return :: a -> Down a

Functor Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

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

(<$) :: a -> Down b -> Down a

Applicative Down

Since: base-4.11.0.0

Defined in Data.Ord

Methods

pure :: a -> Down a

(<*>) :: Down (a -> b) -> Down a -> Down b

liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c

(*>) :: Down a -> Down b -> Down b

(<*) :: Down a -> Down b -> Down a

Foldable Down

Since: base-4.12.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Down m -> m

foldMap :: Monoid m => (a -> m) -> Down a -> m

foldMap' :: Monoid m => (a -> m) -> Down a -> m

foldr :: (a -> b -> b) -> b -> Down a -> b

foldr' :: (a -> b -> b) -> b -> Down a -> b

foldl :: (b -> a -> b) -> b -> Down a -> b

foldl' :: (b -> a -> b) -> b -> Down a -> b

foldr1 :: (a -> a -> a) -> Down a -> a

foldl1 :: (a -> a -> a) -> Down a -> a

toList :: Down a -> [a]

null :: Down a -> Bool

length :: Down a -> Int

elem :: Eq a => a -> Down a -> Bool

maximum :: Ord a => Down a -> a

minimum :: Ord a => Down a -> a

sum :: Num a => Down a -> a

product :: Num a => Down a -> a

Traversable Down

Since: base-4.12.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b)

sequenceA :: Applicative f => Down (f a) -> f (Down a)

mapM :: Monad m => (a -> m b) -> Down a -> m (Down b)

sequence :: Monad m => Down (m a) -> m (Down a)

Eq1 Down

Since: base-4.12.0.0

Defined in Data.Functor.Classes

Methods

liftEq :: (a -> b -> Bool) -> Down a -> Down b -> Bool

Ord1 Down

Since: base-4.12.0.0

Defined in Data.Functor.Classes

Methods

liftCompare :: (a -> b -> Ordering) -> Down a -> Down b -> Ordering

Read1 Down

Since: base-4.12.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Down a)

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Down a]

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Down a)

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Down a]

Show1 Down

Since: base-4.12.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Down a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Down a] -> ShowS

NFData1 Down

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Down a -> ()

Unbox a => Vector Vector (Down a)

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> m (Vector (Down a))

basicUnsafeThaw :: PrimMonad m => Vector (Down a) -> m (Mutable Vector (PrimState m) (Down a))

basicLength :: Vector (Down a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Down a) -> Vector (Down a)

basicUnsafeIndexM :: Monad m => Vector (Down a) -> Int -> m (Down a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Down a) -> Vector (Down a) -> m ()

elemseq :: Vector (Down a) -> Down a -> b -> b

Unbox a => MVector MVector (Down a)

Defined in Data.Vector.Unboxed.Base

Methods

basicLength :: MVector s (Down a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Down a) -> MVector s (Down a)

basicOverlaps :: MVector s (Down a) -> MVector s (Down a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Down a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Down a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Down a -> m (MVector (PrimState m) (Down a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> m (Down a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> Down a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Down a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Down a) -> Down a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Down a) -> MVector (PrimState m) (Down a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Down a) -> MVector (PrimState m) (Down a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Down a) -> Int -> m (MVector (PrimState m) (Down a))

Bounded a => Bounded (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

minBound :: Down a

maxBound :: Down a

Enum a => Enum (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

succ :: Down a -> Down a

pred :: Down a -> Down a

toEnum :: Int -> Down a

fromEnum :: Down a -> Int

enumFrom :: Down a -> [Down a]

enumFromThen :: Down a -> Down a -> [Down a]

enumFromTo :: Down a -> Down a -> [Down a]

enumFromThenTo :: Down a -> Down a -> Down a -> [Down a]

Eq a => Eq (Down a)

Since: base-4.6.0.0

Defined in Data.Ord

Methods

(==) :: Down a -> Down a -> Bool

(/=) :: Down a -> Down a -> Bool

Floating a => Floating (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

pi :: Down a

exp :: Down a -> Down a

log :: Down a -> Down a

sqrt :: Down a -> Down a

(**) :: Down a -> Down a -> Down a

logBase :: Down a -> Down a -> Down a

sin :: Down a -> Down a

cos :: Down a -> Down a

tan :: Down a -> Down a

asin :: Down a -> Down a

acos :: Down a -> Down a

atan :: Down a -> Down a

sinh :: Down a -> Down a

cosh :: Down a -> Down a

tanh :: Down a -> Down a

asinh :: Down a -> Down a

acosh :: Down a -> Down a

atanh :: Down a -> Down a

log1p :: Down a -> Down a

expm1 :: Down a -> Down a

log1pexp :: Down a -> Down a

log1mexp :: Down a -> Down a

Fractional a => Fractional (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

(/) :: Down a -> Down a -> Down a

recip :: Down a -> Down a

fromRational :: Rational -> Down a

Integral a => Integral (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

quot :: Down a -> Down a -> Down a

rem :: Down a -> Down a -> Down a

div :: Down a -> Down a -> Down a

mod :: Down a -> Down a -> Down a

quotRem :: Down a -> Down a -> (Down a, Down a)

divMod :: Down a -> Down a -> (Down a, Down a)

toInteger :: Down a -> Integer

Data a => Data (Down a)

Since: base-4.12.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Down a -> c (Down a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Down a)

toConstr :: Down a -> Constr

dataTypeOf :: Down a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Down a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Down a))

gmapT :: (forall b. Data b => b -> b) -> Down a -> Down a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Down a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Down a -> r

gmapQ :: (forall d. Data d => d -> u) -> Down a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Down a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Down a -> m (Down a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Down a -> m (Down a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Down a -> m (Down a)

Num a => Num (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(+) :: Down a -> Down a -> Down a

(-) :: Down a -> Down a -> Down a

(*) :: Down a -> Down a -> Down a

negate :: Down a -> Down a

abs :: Down a -> Down a

signum :: Down a -> Down a

fromInteger :: Integer -> Down a

Ord a => Ord (Down a)

Since: base-4.6.0.0

Defined in Data.Ord

Methods

compare :: Down a -> Down a -> Ordering

(<) :: Down a -> Down a -> Bool

(<=) :: Down a -> Down a -> Bool

(>) :: Down a -> Down a -> Bool

(>=) :: Down a -> Down a -> Bool

max :: Down a -> Down a -> Down a

min :: Down a -> Down a -> Down a

Read a => Read (Down a)

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Defined in Data.Ord

Methods

readsPrec :: Int -> ReadS (Down a)

readList :: ReadS [Down a]

readPrec :: ReadPrec (Down a)

readListPrec :: ReadPrec [Down a]

Real a => Real (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

toRational :: Down a -> Rational

RealFloat a => RealFloat (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

floatRadix :: Down a -> Integer

floatDigits :: Down a -> Int

floatRange :: Down a -> (Int, Int)

decodeFloat :: Down a -> (Integer, Int)

encodeFloat :: Integer -> Int -> Down a

exponent :: Down a -> Int

significand :: Down a -> Down a

scaleFloat :: Int -> Down a -> Down a

isNaN :: Down a -> Bool

isInfinite :: Down a -> Bool

isDenormalized :: Down a -> Bool

isNegativeZero :: Down a -> Bool

isIEEE :: Down a -> Bool

atan2 :: Down a -> Down a -> Down a

RealFrac a => RealFrac (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

properFraction :: Integral b => Down a -> (b, Down a)

truncate :: Integral b => Down a -> b

round :: Integral b => Down a -> b

ceiling :: Integral b => Down a -> b

floor :: Integral b => Down a -> b

Show a => Show (Down a)

This instance would be equivalent to the derived instances of the Down newtype if the getDown field were removed

Since: base-4.7.0.0

Defined in Data.Ord

Methods

showsPrec :: Int -> Down a -> ShowS

show :: Down a -> String

showList :: [Down a] -> ShowS

Ix a => Ix (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

range :: (Down a, Down a) -> [Down a]

index :: (Down a, Down a) -> Down a -> Int

unsafeIndex :: (Down a, Down a) -> Down a -> Int

inRange :: (Down a, Down a) -> Down a -> Bool

rangeSize :: (Down a, Down a) -> Int

unsafeRangeSize :: (Down a, Down a) -> Int

Generic (Down a)

Since: base-4.12.0.0

Defined in GHC.Generics

Associated Types

type Rep (Down a) :: Type -> Type

Methods

from :: Down a -> Rep (Down a) x

to :: Rep (Down a) x -> Down a

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a

sconcat :: NonEmpty (Down a) -> Down a

stimes :: Integral b => b -> Down a -> Down a

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

mempty :: Down a

mappend :: Down a -> Down a -> Down a

mconcat :: [Down a] -> Down a

Storable a => Storable (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

sizeOf :: Down a -> Int

alignment :: Down a -> Int

peekElemOff :: Ptr (Down a) -> Int -> IO (Down a)

pokeElemOff :: Ptr (Down a) -> Int -> Down a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Down a)

pokeByteOff :: Ptr b -> Int -> Down a -> IO ()

peek :: Ptr (Down a) -> IO (Down a)

poke :: Ptr (Down a) -> Down a -> IO ()

Bits a => Bits (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

(.&.) :: Down a -> Down a -> Down a

(.|.) :: Down a -> Down a -> Down a

xor :: Down a -> Down a -> Down a

complement :: Down a -> Down a

shift :: Down a -> Int -> Down a

rotate :: Down a -> Int -> Down a

zeroBits :: Down a

bit :: Int -> Down a

setBit :: Down a -> Int -> Down a

clearBit :: Down a -> Int -> Down a

complementBit :: Down a -> Int -> Down a

testBit :: Down a -> Int -> Bool

bitSizeMaybe :: Down a -> Maybe Int

bitSize :: Down a -> Int

isSigned :: Down a -> Bool

shiftL :: Down a -> Int -> Down a

unsafeShiftL :: Down a -> Int -> Down a

shiftR :: Down a -> Int -> Down a

unsafeShiftR :: Down a -> Int -> Down a

rotateL :: Down a -> Int -> Down a

rotateR :: Down a -> Int -> Down a

popCount :: Down a -> Int

FiniteBits a => FiniteBits (Down a)

Since: base-4.14.0.0

Defined in Data.Ord

Methods

finiteBitSize :: Down a -> Int

countLeadingZeros :: Down a -> Int

countTrailingZeros :: Down a -> Int

NFData a => NFData (Down a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Down a -> ()

Prim a => Prim (Down a)

Since: primitive-0.6.5.0

Defined in Data.Primitive.Types

Methods

sizeOf# :: Down a -> Int#

alignment# :: Down a -> Int#

indexByteArray# :: ByteArray# -> Int# -> Down a

readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Down a #)

writeByteArray# :: MutableByteArray# s -> Int# -> Down a -> State# s -> State# s

setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Down a -> State# s -> State# s

indexOffAddr# :: Addr# -> Int# -> Down a

readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Down a #)

writeOffAddr# :: Addr# -> Int# -> Down a -> State# s -> State# s

setOffAddr# :: Addr# -> Int# -> Int# -> Down a -> State# s -> State# s

Unbox a => Unbox (Down a)

Defined in Data.Vector.Unboxed.Base

Generic1 Down

Since: base-4.12.0.0

Defined in GHC.Generics

Associated Types

type Rep1 Down :: k -> Type

Methods

from1 :: forall (a :: k). Down a -> Rep1 Down a

to1 :: forall (a :: k). Rep1 Down a -> Down a

newtype MVector s (Down a)

Defined in Data.Vector.Unboxed.Base

newtype MVector s (Down a) = MV_Down (MVector s a)

type Rep (Down a)

Defined in GHC.Generics

type Rep (Down a) = D1 ('MetaData "Down" "Data.Ord" "base" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Vector (Down a)

Defined in Data.Vector.Unboxed.Base

newtype Vector (Down a) = V_Down (Vector a)

type Rep1 Down

Defined in GHC.Generics

type Rep1 Down = D1 ('MetaData "Down" "Data.Ord" "base" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Enum

Re-exported from Prelude:

fromEnum :: Enum a => a -> Int

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

Bounded

Re-exported from Prelude:

minBound :: Bounded a => a

maxBound :: Bounded a => a

Num

Re-exported from Prelude:

(+) :: Num a => a -> a -> a infixl 6

(-) :: Num a => a -> a -> a infixl 6

(*) :: Num a => a -> a -> a infixl 7

(^) :: (Num a, Integral b) => a -> b -> a infixr 8

raise a number to a non-negative integral power

negate :: Num a => a -> a

Unary negation.

abs :: Num a => a -> a

Absolute value.

signum :: Num a => a -> a

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Num a => Integer -> a

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

subtract :: Num a => a -> a -> a

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

Real

Re-exported from Prelude:

toRational :: Real a => a -> Rational

the rational equivalent of its real argument with full precision

Integral

Re-exported from Prelude:

quot :: Integral a => a -> a -> a infixl 7

integer division truncated toward zero

rem :: Integral a => a -> a -> a infixl 7

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: Integral a => a -> a -> a infixl 7

integer division truncated toward negative infinity

mod :: Integral a => a -> a -> a infixl 7

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: Integral a => a -> a -> (a, a)

simultaneous quot and rem

divMod :: Integral a => a -> a -> (a, a)

simultaneous div and mod

toInteger :: Integral a => a -> Integer

conversion to Integer

even :: Integral a => a -> Bool

odd :: Integral a => a -> Bool

gcd :: Integral a => a -> a -> a

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm :: Integral a => a -> a -> a

lcm x y is the smallest positive integer that both x and y divide.

fromIntegral :: (Integral a, Num b) => a -> b

general coercion from integral types

Fractional

Re-exported from Prelude:

(/) :: Fractional a => a -> a -> a infixl 7

Fractional division.

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8

raise a number to an integral power

recip :: Fractional a => a -> a

Reciprocal fraction.

fromRational :: Fractional a => Rational -> a

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

realToFrac :: (Real a, Fractional b) => a -> b

general coercion to fractional types

Floating

Re-exported from Prelude:

pi :: Floating a => a

exp :: Floating a => a -> a

log :: Floating a => a -> a

sqrt :: Floating a => a -> a

(**) :: Floating a => a -> a -> a infixr 8

logBase :: Floating a => a -> a -> a

sin :: Floating a => a -> a

cos :: Floating a => a -> a

tan :: Floating a => a -> a

asin :: Floating a => a -> a

acos :: Floating a => a -> a

atan :: Floating a => a -> a

sinh :: Floating a => a -> a

cosh :: Floating a => a -> a

tanh :: Floating a => a -> a

asinh :: Floating a => a -> a

acosh :: Floating a => a -> a

atanh :: Floating a => a -> a

RealFrac

Re-exported from Prelude:

properFraction :: (RealFrac a, Integral b) => a -> (b, a)

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

• n is an integral number with the same sign as x; and
• f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: (RealFrac a, Integral b) => a -> b

truncate x returns the integer nearest x between zero and x

round :: (RealFrac a, Integral b) => a -> b

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: (RealFrac a, Integral b) => a -> b

ceiling x returns the least integer not less than x

floor :: (RealFrac a, Integral b) => a -> b

floor x returns the greatest integer not greater than x

RealFloat

Re-exported from Prelude:

floatRadix :: RealFloat a => a -> Integer

a constant function, returning the radix of the representation (often 2)

floatDigits :: RealFloat a => a -> Int

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: RealFloat a => a -> (Int, Int)

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: RealFloat a => a -> (Integer, Int)

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: RealFloat a => Integer -> Int -> a

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: RealFloat a => a -> Int

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: RealFloat a => a -> a

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: RealFloat a => Int -> a -> a

multiplies a floating-point number by an integer power of the radix

isNaN :: RealFloat a => a -> Bool

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: RealFloat a => a -> Bool

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: RealFloat a => a -> Bool

True if the argument is too small to be represented in normalized format

isNegativeZero :: RealFloat a => a -> Bool

True if the argument is an IEEE negative zero

isIEEE :: RealFloat a => a -> Bool

True if the argument is an IEEE floating point number

atan2 :: RealFloat a => a -> a -> a

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Word

Re-exported from Data.Word:

byteSwap16 :: Word16 -> Word16

Reverse order of bytes in Word16.

Since: base-4.7.0.0

byteSwap32 :: Word32 -> Word32

Reverse order of bytes in Word32.

Since: base-4.7.0.0

byteSwap64 :: Word64 -> Word64

Reverse order of bytes in Word64.

Since: base-4.7.0.0

Semigroup

Re-exported from Data.Semigroup:

(<>) :: Semigroup a => a -> a -> a infixr 6

An associative operation.

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

sappend :: Semigroup s => s -> s -> s

Monoid

Re-exported from Data.Monoid:

mempty :: Monoid a => a

Identity of mappend

>>> "Hello world" <> mempty
"Hello world"

mappend :: Monoid a => a -> a -> a

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: Monoid a => [a] -> a

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Functor

Re-exported from Data.Functor:

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

Using ApplicativeDo: 'fmap f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint.

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

(<$) :: Functor f => a -> f b -> f a infixl 4

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Using ApplicativeDo: 'a <$ bs' can be understood as the do expression

do bs
   pure a

with an inferred Functor constraint.

($>) :: Functor f => f a -> b -> f b infixl 4

Flipped version of <$.

Using ApplicativeDo: 'as $> b' can be understood as the do expression

do as
   pure b

with an inferred Functor constraint.

Examples

Replace the contents of a Maybe Int with a constant String:

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

Replace the contents of an Either Int Int with a constant String, resulting in an Either Int String:

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

Replace each element of a list with a constant String:

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

Replace the second element of a pair with a constant String:

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

Since: base-4.7.0.0

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

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

Using ApplicativeDo: 'void as' can be understood as the do expression

do as
   pure ()

with an inferred Functor constraint.

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

(<&>) :: Functor f => f a -> (a -> b) -> f b infixl 1

Flipped version of <$>.

(<&>) = flip fmap

Examples

Apply (+1) to a list, a Just and a Right:

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

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

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

Since: base-4.11.0.0

Applicative

Re-exported from Control.Applicative:

pure :: Applicative f => a -> f a

Lift a value.

(<*>) :: Applicative f => f (a -> b) -> f a -> f b infixl 4

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Using ApplicativeDo: 'fs <*> as' can be understood as the do expression

do f <- fs
   a <- as
   pure (f a)

(<*) :: Applicative f => f a -> f b -> f a infixl 4

Sequence actions, discarding the value of the second argument.

Using ApplicativeDo: 'as <* bs' can be understood as the do expression

do a <- as
   bs
   pure a

(*>) :: Applicative f => f a -> f b -> f b infixl 4

Sequence actions, discarding the value of the first argument.

'as *> bs' can be understood as the do expression

do as
   bs

This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form

do _ <- as
   b <- bs
   pure b

liftA :: Applicative f => (a -> b) -> f a -> f b

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

| Using ApplicativeDo: 'liftA f as' can be understood as the do expression

do a <- as
   pure (f a)

with an inferred Functor constraint, weaker than Applicative.

liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Using ApplicativeDo: 'liftA2 f as bs' can be understood as the do expression

do a <- as
   b <- bs
   pure (f a b)

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d

Lift a ternary function to actions.

Using ApplicativeDo: 'liftA3 f as bs cs' can be understood as the do expression

do a <- as
   b <- bs
   c <- cs
   pure (f a b c)

forever :: Applicative f => f a -> f b

Repeat an action indefinitely.

Using ApplicativeDo: 'forever as' can be understood as the pseudo-do expression

do as
   as
   ..

with as repeating.

Examples

A common use of forever is to process input from network sockets, Handles, and channels (e.g. MVar and Chan).

For example, here is how we might implement an echo server, using forever both to listen for client connections on a network socket and to echo client input on client connection handles:

echoServer :: Socket -> IO ()
echoServer socket = forever $ do
  client <- accept socket
  forkFinally (echo client) (\_ -> hClose client)
  where
    echo :: Handle -> IO ()
    echo client = forever $
      hGetLine client >>= hPutStrLn client

traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()

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

for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for.

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

sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()

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

filterM :: Applicative m => (a -> m Bool) -> [a] -> m [a]

This generalizes the list-based filter function.

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

Like replicateM, but discards the result.

zipWithM :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m [c]

The zipWithM function generalizes zipWith to arbitrary applicative functors.

zipWithM_ :: Applicative m => (a -> b -> m c) -> [a] -> [b] -> m ()

zipWithM_ is the extension of zipWithM which ignores the final result.

Monad

Re-exported from Control.Monad:

return :: Monad m => a -> m a

Inject a value into the monadic type.

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.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

A common use of join is to run an IO computation returned from an STM transaction, since STM transactions can't perform IO directly. Recall that

atomically :: STM a -> IO a

is used to run STM transactions atomically. So, by specializing the types of atomically and join to

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

we can compose them as

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

to run an STM transaction and the IO action it returns.

fail :: MonadFail m => String -> m a

(>>=) :: Monad m => 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.

'as >>= bs' can be understood as the do expression

do a <- as
   bs a

(>>) :: Monad m => 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.

'as >> bs' can be understood as the do expression

do as
   bs

(=<<) :: 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 composition of Kleisli arrows.

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

do b <- bs a
   cs b

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

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

(<$!>) :: Monad m => (a -> b) -> m a -> m b infixl 4

Strict version of <$>.

Since: base-4.8.0.0

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

whenM :: Monad m => m Bool -> m () -> m ()

Run the second value if the first value returns True

unlessM :: Monad m => m Bool -> m () -> m ()

Run the second value if the first value returns False

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

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

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

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.

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

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 ()

Like foldM, but discards the result.

Foldable

Re-exported from Data.Foldable:

foldr :: Foldable t => (a -> b -> b) -> b -> t a -> b

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

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

foldr f z = foldr f z . toList

foldl' :: Foldable t => (b -> a -> b) -> b -> t a -> b

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 list to a single, monolithic result (e.g. length).

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

foldl' f z = foldl' f z . toList

Since: base-4.6.0.0

fold :: (Foldable t, Monoid m) => t m -> m

Combine the elements of a structure using a monoid.

foldMap :: (Foldable t, Monoid m) => (a -> m) -> t a -> m

Map each element of the structure to a monoid, and combine the results.

foldMapM :: (Monad m, Monoid w, Foldable t) => (a -> m w) -> t a -> m w

Extend foldMap to allow side effects.

Internally, this is implemented using a strict left fold. This is used for performance reasons. It also necessitates that this function has a Monad constraint and not just an Applicative constraint. For more information, see https://github.com/commercialhaskell/rio/pull/99#issuecomment-394179757.

Since: 0.1.3.0

elem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4

Does the element occur in the structure?

Since: base-4.8.0.0

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4

notElem is the negation of elem.

null :: Foldable t => t a -> Bool

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

length :: Foldable t => t a -> Int

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Since: base-4.8.0.0

sum :: (Foldable t, Num a) => t a -> a

The sum function computes the sum of the numbers of a structure.

Since: base-4.8.0.0

product :: (Foldable t, Num a) => t a -> a

The product function computes the product of the numbers of a structure.

Since: base-4.8.0.0

all :: Foldable t => (a -> Bool) -> t a -> Bool

Determines whether all elements of the structure satisfy the predicate.

any :: Foldable t => (a -> Bool) -> t a -> Bool

Determines whether any element of the structure satisfies the predicate.

and :: Foldable t => t Bool -> Bool

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

or :: Foldable t => t Bool -> Bool

or returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

toList :: Foldable t => t a -> [a]

List of elements of a structure, from left to right.

Since: base-4.8.0.0

concat :: Foldable t => t [a] -> [a]

The concatenation of all the elements of a container of lists.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b]

Map a function over all the elements of a container and concatenate the resulting lists.

Traversable

Re-exported from Data.Traversable:

traverse :: (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b)

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

for :: (Traversable t, Applicative f) => t a -> (a -> f b) -> f (t b)

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

sequenceA :: (Traversable t, Applicative f) => t (f a) -> f (t a)

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

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

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_.

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

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

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

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

Alternative

Re-exported from Control.Applicative:

(<|>) :: Alternative f => f a -> f a -> f a infixl 3

An associative binary operation

some :: Alternative f => f a -> f [a]

One or more.

many :: Alternative f => f a -> f [a]

Zero or more.

optional :: Alternative f => f a -> f (Maybe a)

One or none.

asum :: (Foldable t, Alternative f) => t (f a) -> f a

The sum of a collection of actions, generalizing concat.

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"

guard :: Alternative f => Bool -> f ()

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

Common uses of guard include conditionally signaling an error in an error monad and conditionally rejecting the current choice in an Alternative-based parser.

As an example of signaling an error in the error monad Maybe, consider a safe division function safeDiv x y that returns Nothing when the denominator y is zero and Just (x `div` y) otherwise. For example:

>>> safeDiv 4 0
Nothing
>>> safeDiv 4 2
Just 2

A definition of safeDiv using guards, but not guard:

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

A definition of safeDiv using guard and Monad do-notation:

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

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

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 ()

The reverse of when.

Bifunctor

Re-exported from Data.Bifunctor:

bimap :: Bifunctor p => (a -> b) -> (c -> d) -> p a c -> p b d

Map over both arguments at the same time.

bimap f g ≡ first f . second g

Examples

>>> bimap toUpper (+1) ('j', 3)
('J',4)

>>> bimap toUpper (+1) (Left 'j')
Left 'J'

>>> bimap toUpper (+1) (Right 3)
Right 4

first :: Bifunctor p => (a -> b) -> p a c -> p b c

Map covariantly over the first argument.

first f ≡ bimap f id

Examples

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

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

second :: Bifunctor p => (b -> c) -> p a b -> p a c

Map covariantly over the second argument.

second ≡ bimap id

Examples

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

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

Bifoldable

Re-exported from Data.Bifoldable:

bifold :: (Bifoldable p, Monoid m) => p m m -> m

Combines the elements of a structure using a monoid.

bifold ≡ bifoldMap id id

Since: base-4.10.0.0

bifoldMap :: (Bifoldable p, Monoid m) => (a -> m) -> (b -> m) -> p a b -> m

Combines the elements of a structure, given ways of mapping them to a common monoid.

bifoldMap f g
     ≡ bifoldr (mappend . f) (mappend . g) mempty

Since: base-4.10.0.0

bifoldr :: Bifoldable p => (a -> c -> c) -> (b -> c -> c) -> c -> p a b -> c

Combines the elements of a structure in a right associative manner. Given a hypothetical function toEitherList :: p a b -> [Either a b] yielding a list of all elements of a structure in order, the following would hold:

bifoldr f g z ≡ foldr (either f g) z . toEitherList

Since: base-4.10.0.0

bifoldl :: Bifoldable p => (c -> a -> c) -> (c -> b -> c) -> c -> p a b -> c

Combines the elements of a structure in a left associative manner. Given a hypothetical function toEitherList :: p a b -> [Either a b] yielding a list of all elements of a structure in order, the following would hold:

bifoldl f g z
     ≡ foldl (acc -> either (f acc) (g acc)) z . toEitherList

Note that if you want an efficient left-fold, you probably want to use bifoldl' instead of bifoldl. The reason is that the latter does not force the "inner" results, resulting in a thunk chain which then must be evaluated from the outside-in.

Since: base-4.10.0.0

bifoldr' :: Bifoldable t => (a -> c -> c) -> (b -> c -> c) -> c -> t a b -> c

As bifoldr, but strict in the result of the reduction functions at each step.

Since: base-4.10.0.0

bifoldr1 :: Bifoldable t => (a -> a -> a) -> t a a -> a

A variant of bifoldr that has no base case, and thus may only be applied to non-empty structures.

Since: base-4.10.0.0

bifoldrM :: (Bifoldable t, Monad m) => (a -> c -> m c) -> (b -> c -> m c) -> c -> t a b -> m c

Right associative monadic bifold over a structure.

Since: base-4.10.0.0

bifoldl' :: Bifoldable t => (a -> b -> a) -> (a -> c -> a) -> a -> t b c -> a

As bifoldl, but strict in the result of the reduction functions at each step.

This ensures that each step of the bifold 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, monolithic result (e.g., bilength).

Since: base-4.10.0.0

bifoldl1 :: Bifoldable t => (a -> a -> a) -> t a a -> a

A variant of bifoldl that has no base case, and thus may only be applied to non-empty structures.

Since: base-4.10.0.0

bifoldlM :: (Bifoldable t, Monad m) => (a -> b -> m a) -> (a -> c -> m a) -> a -> t b c -> m a

Left associative monadic bifold over a structure.

Since: base-4.10.0.0

bitraverse_ :: (Bifoldable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f ()

Map each element of a structure using one of two actions, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results, see bitraverse.

Since: base-4.10.0.0

bifor_ :: (Bifoldable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f ()

As bitraverse_, but with the structure as the primary argument. For a version that doesn't ignore the results, see bifor.

>>> > bifor_ ('a', "bc") print (print . reverse)
'a'
"cb"

Since: base-4.10.0.0

bisequence_ :: (Bifoldable t, Applicative f) => t (f a) (f b) -> f ()

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

Since: base-4.10.0.0

biasum :: (Bifoldable t, Alternative f) => t (f a) (f a) -> f a

The sum of a collection of actions, generalizing biconcat.

Since: base-4.10.0.0

biList :: Bifoldable t => t a a -> [a]

Collects the list of elements of a structure, from left to right.

Since: base-4.10.0.0

binull :: Bifoldable t => t a b -> Bool

Test whether the structure is empty.

Since: base-4.10.0.0

bilength :: Bifoldable t => t a b -> Int

Returns the size/length of a finite structure as an Int.

Since: base-4.10.0.0

bielem :: (Bifoldable t, Eq a) => a -> t a a -> Bool

Does the element occur in the structure?

Since: base-4.10.0.0

bimaximum :: (Bifoldable t, Ord a) => t a a -> a

The largest element of a non-empty structure.

Since: base-4.10.0.0

biminimum :: (Bifoldable t, Ord a) => t a a -> a

The least element of a non-empty structure.

Since: base-4.10.0.0

bisum :: (Bifoldable t, Num a) => t a a -> a

The bisum function computes the sum of the numbers of a structure.

Since: base-4.10.0.0

biproduct :: (Bifoldable t, Num a) => t a a -> a

The biproduct function computes the product of the numbers of a structure.

Since: base-4.10.0.0

biconcat :: Bifoldable t => t [a] [a] -> [a]

Reduces a structure of lists to the concatenation of those lists.

Since: base-4.10.0.0

biconcatMap :: Bifoldable t => (a -> [c]) -> (b -> [c]) -> t a b -> [c]

Given a means of mapping the elements of a structure to lists, computes the concatenation of all such lists in order.

Since: base-4.10.0.0

biand :: Bifoldable t => t Bool Bool -> Bool

biand returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Since: base-4.10.0.0

bior :: Bifoldable t => t Bool Bool -> Bool

bior returns the disjunction of a container of Bools. For the result to be False, the container must be finite; True, however, results from a True value finitely far from the left end.

Since: base-4.10.0.0

biany :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool

Determines whether any element of the structure satisfies its appropriate predicate argument.

Since: base-4.10.0.0

biall :: Bifoldable t => (a -> Bool) -> (b -> Bool) -> t a b -> Bool

Determines whether all elements of the structure satisfy their appropriate predicate argument.

Since: base-4.10.0.0

bimaximumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a

The largest element of a non-empty structure with respect to the given comparison function.

Since: base-4.10.0.0

biminimumBy :: Bifoldable t => (a -> a -> Ordering) -> t a a -> a

The least element of a non-empty structure with respect to the given comparison function.

Since: base-4.10.0.0

binotElem :: (Bifoldable t, Eq a) => a -> t a a -> Bool

binotElem is the negation of bielem.

Since: base-4.10.0.0

bifind :: Bifoldable t => (a -> Bool) -> t a a -> Maybe a

The bifind function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Since: base-4.10.0.0

Bitraverse

Re-exported from Data.Bitraversable:

bitraverse :: (Bitraversable t, Applicative f) => (a -> f c) -> (b -> f d) -> t a b -> f (t c d)

Evaluates the relevant functions at each element in the structure, running the action, and builds a new structure with the same shape, using the results produced from sequencing the actions.

bitraverse f g ≡ bisequenceA . bimap f g

For a version that ignores the results, see bitraverse_.

Since: base-4.10.0.0

bisequence :: (Bitraversable t, Applicative f) => t (f a) (f b) -> f (t a b)

Sequences all the actions in a structure, building a new structure with the same shape using the results of the actions. For a version that ignores the results, see bisequence_.

bisequence ≡ bitraverse id id

Since: base-4.10.0.0

bifor :: (Bitraversable t, Applicative f) => t a b -> (a -> f c) -> (b -> f d) -> f (t c d)

bifor is bitraverse with the structure as the first argument. For a version that ignores the results, see bifor_.

Since: base-4.10.0.0

bimapAccumL :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)

The bimapAccumL function behaves like a combination of bimap and bifoldl; it traverses a structure from left to right, threading a state of type a and using the given actions to compute new elements for the structure.

Since: base-4.10.0.0

bimapAccumR :: Bitraversable t => (a -> b -> (a, c)) -> (a -> d -> (a, e)) -> a -> t b d -> (a, t c e)

The bimapAccumR function behaves like a combination of bimap and bifoldl; it traverses a structure from right to left, threading a state of type a and using the given actions to compute new elements for the structure.

Since: base-4.10.0.0

MonadPlus

Re-exported from Control.Monad:

mzero :: MonadPlus m => m a

The identity of mplus. It should also satisfy the equations

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

The default definition is

mzero = empty

mplus :: MonadPlus m => m a -> m a -> m a

An associative operation. The default definition is

mplus = (<|>)

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

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

Direct MonadPlus equivalent of filter.

Examples

The filter function is just mfilter specialized to the list monad:

filter = ( mfilter :: (a -> Bool) -> [a] -> [a] )

An example using mfilter with the Maybe monad:

>>> mfilter odd (Just 1)
Just 1
>>> mfilter odd (Just 2)
Nothing

Arrow

Re-exported from Control.Arrow and Control.Category:

(&&&) :: Arrow a => a b c -> a b c' -> a b (c, c') infixr 3

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.

(***) :: Arrow a => a b c -> a b' c' -> a (b, b') (c, c') infixr 3

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

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

(>>>) :: forall k cat (a :: k) (b :: k) (c :: k). Category cat => cat a b -> cat b c -> cat a c infixr 1

Left-to-right composition

Function

Re-exported from Data.Function:

id :: a -> a

Identity function.

id x = x

const :: a -> b -> a

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

Function composition.

($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.

(&) :: a -> (a -> b) -> b infixl 1

& 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

flip :: (a -> b -> c) -> b -> a -> c

flip f takes its (first) two arguments in the reverse order of f.

>>> flip (++) "hello" "world"
"worldhello"

fix :: (a -> a) -> a

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120

This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120

Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix’s argument, hence the recursion is reintroduced.

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0

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)

Miscellaneous functions

($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a

error stops execution and displays an error message.

undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

asTypeOf :: a -> a -> a

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

asIO :: IO a -> IO a

Helper function to force an action to run in IO. Especially useful for overly general contexts, like hspec tests.

Since: 0.1.3.0

List

Re-exported from Data.List:

(++) :: [a] -> [a] -> [a] infixr 5

Append two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

break :: (a -> Bool) -> [a] -> ([a], [a])

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
break (< 9) [1,2,3] == ([],[1,2,3])
break (> 9) [1,2,3] == ([1,2,3],[])

break p is equivalent to span (not . p).

drop :: Int -> [a] -> [a]

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

drop 6 "Hello World!" == "World!"
drop 3 [1,2,3,4,5] == [4,5]
drop 3 [1,2] == []
drop 3 [] == []
drop (-1) [1,2] == [1,2]
drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

dropWhile :: (a -> Bool) -> [a] -> [a]

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

filter :: (a -> Bool) -> [a] -> [a]

\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

>>> filter odd [1, 2, 3]
[1,3]

lookup :: Eq a => a -> [(a, b)] -> Maybe b

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list.

>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")]
Just "second"

map :: (a -> b) -> [a] -> [b]

\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

>>> map (+1) [1, 2, 3]

replicate :: Int -> a -> [a]

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

reverse :: [a] -> [a]

reverse xs returns the elements of xs in reverse order. xs must be finite.

span :: (a -> Bool) -> [a] -> ([a], [a])

span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:

span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
span (< 9) [1,2,3] == ([1,2,3],[])
span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

take :: Int -> [a] -> [a]

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

take 5 "Hello World!" == "Hello"
take 3 [1,2,3,4,5] == [1,2,3]
take 3 [1,2] == [1,2]
take 3 [] == []
take (-1) [1,2] == []
take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

takeWhile :: (a -> Bool) -> [a] -> [a]

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
takeWhile (< 9) [1,2,3] == [1,2,3]
takeWhile (< 0) [1,2,3] == []

zip :: [a] -> [b] -> [(a, b)]

\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]

zipWith is right-lazy:

zipWith f [] _|_ = []

zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.

nubOrd :: Ord a => [a] -> [a]

Strip out duplicates

String

Re-exported from Data.String:

fromString :: IsString a => String -> a

lines :: String -> [String]

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]

>>> lines "\n"
[""]

>>> lines "one"
["one"]

>>> lines "one\n"
["one"]

>>> lines "one\n\n"
["one",""]

>>> lines "one\ntwo"
["one","two"]

>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

unlines :: [String] -> String

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

unwords :: [String] -> String

unwords is an inverse operation to words. It joins words with separating spaces.

>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"

words :: String -> [String]

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

Show

Re-exported from Text.Show:

show :: Show a => a -> String

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

Read

Re-exported from Text.Read:

readMaybe :: Read a => String -> Maybe a

Parse a string using the Read instance. Succeeds if there is exactly one valid result.

>>> readMaybe "123" :: Maybe Int
Just 123

>>> readMaybe "hello" :: Maybe Int
Nothing

Since: base-4.6.0.0

NFData

Re-exported from Control.DeepSeq:

($!!) :: NFData a => (a -> b) -> a -> b infixr 0

the deep analogue of $!. In the expression f $!! x, x is fully evaluated before the function f is applied to it.

Since: deepseq-1.2.0.0

rnf :: NFData a => a -> ()

rnf should reduce its argument to normal form (that is, fully evaluate all sub-components), and then return ().

Generic NFData deriving

Starting with GHC 7.2, you can automatically derive instances for types possessing a Generic instance.

Note: Generic1 can be auto-derived starting with GHC 7.4

{-# LANGUAGE DeriveGeneric #-}

import GHC.Generics (Generic, Generic1)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1)

instance NFData a => NFData (Foo a)
instance NFData1 Foo

data Colour = Red | Green | Blue
              deriving Generic

instance NFData Colour

Starting with GHC 7.10, the example above can be written more concisely by enabling the new DeriveAnyClass extension:

{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}

import GHC.Generics (Generic)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1, NFData, NFData1)

data Colour = Red | Green | Blue
              deriving (Generic, NFData)

Compatibility with previous deepseq versions

Prior to version 1.4.0.0, the default implementation of the rnf method was defined as

rnf a = seq a ()

However, starting with deepseq-1.4.0.0, the default implementation is based on DefaultSignatures allowing for more accurate auto-derived NFData instances. If you need the previously used exact default rnf method implementation semantics, use

instance NFData Colour where rnf x = seq x ()

or alternatively

instance NFData Colour where rnf = rwhnf

or

{-# LANGUAGE BangPatterns #-}
instance NFData Colour where rnf !_ = ()

deepseq :: NFData a => a -> b -> b

deepseq: fully evaluates the first argument, before returning the second.

The name deepseq is used to illustrate the relationship to seq: where seq is shallow in the sense that it only evaluates the top level of its argument, deepseq traverses the entire data structure evaluating it completely.

deepseq can be useful for forcing pending exceptions, eradicating space leaks, or forcing lazy I/O to happen. It is also useful in conjunction with parallel Strategies (see the parallel package).

There is no guarantee about the ordering of evaluation. The implementation may evaluate the components of the structure in any order or in parallel. To impose an actual order on evaluation, use pseq from Control.Parallel in the parallel package.

Since: deepseq-1.1.0.0

force :: NFData a => a -> a

a variant of deepseq that is useful in some circumstances:

force x = x `deepseq` x

force x fully evaluates x, and then returns it. Note that force x only performs evaluation when the value of force x itself is demanded, so essentially it turns shallow evaluation into deep evaluation.

force can be conveniently used in combination with ViewPatterns:

{-# LANGUAGE BangPatterns, ViewPatterns #-}
import Control.DeepSeq

someFun :: ComplexData -> SomeResult
someFun (force -> !arg) = {- 'arg' will be fully evaluated -}

Another useful application is to combine force with evaluate in order to force deep evaluation relative to other IO operations:

import Control.Exception (evaluate)
import Control.DeepSeq

main = do
  result <- evaluate $ force $ pureComputation
  {- 'result' will be fully evaluated at this point -}
  return ()

Finally, here's an exception safe variant of the readFile' example:

readFile' :: FilePath -> IO String
readFile' fn = bracket (openFile fn ReadMode) hClose $ \h ->
                       evaluate . force =<< hGetContents h

Since: deepseq-1.2.0.0

Void

Re-exported from Data.Void:

absurd :: Void -> a

Since Void values logically don't exist, this witnesses the logical reasoning tool of "ex falso quodlibet".

>>> let x :: Either Void Int; x = Right 5
>>> :{
case x of
    Right r -> r
    Left l  -> absurd l
:}
5

Since: base-4.8.0.0

Reader

Re-exported from Control.Monad.Reader:

lift :: (MonadTrans t, Monad m) => m a -> t m a

Lift a computation from the argument monad to the constructed monad.

ask :: MonadReader r m => m r

Retrieves the monad environment.

asks

Arguments

:: MonadReader r m

=> (r -> a)

The selector function to apply to the environment.

-> m a

Retrieves a function of the current environment.

local

Arguments

:: MonadReader r m

=> (r -> r)

The function to modify the environment.

-> m a

Reader to run in the modified environment.

-> m a

Executes a computation in a modified environment.

runReader

Arguments

:: Reader r a

A Reader to run.

-> r

An initial environment.

-> a

Runs a Reader and extracts the final value from it. (The inverse of reader.)

runReaderT :: ReaderT r m a -> r -> m a

ByteString

Helper synonyms for converting bewteen lazy and strict ByteStrings

toStrictBytes :: LByteString -> ByteString

fromStrictBytes :: ByteString -> LByteString

ShortByteString

Re-exported from Data.ByteString.Short:

toShort :: ByteString -> ShortByteString

O(n). Convert a ByteString into a ShortByteString.

This makes a copy, so does not retain the input string.

fromShort :: ShortByteString -> ByteString

O(n). Convert a ShortByteString into a ByteString.

Text

tshow :: Show a => a -> Text

decodeUtf8Lenient :: ByteString -> Text

Re-exported from Data.Text.Encoding:

decodeUtf8' :: ByteString -> Either UnicodeException Text

Decode a ByteString containing UTF-8 encoded text.

If the input contains any invalid UTF-8 data, the relevant exception will be returned, otherwise the decoded text.

decodeUtf8With :: OnDecodeError -> ByteString -> Text

Decode a ByteString containing UTF-8 encoded text.

NOTE: The replacement character returned by OnDecodeError MUST be within the BMP plane; surrogate code points will automatically be remapped to the replacement char U+FFFD (since 0.11.3.0), whereas code points beyond the BMP will throw an error (since 1.2.3.1); For earlier versions of text using those unsupported code points would result in undefined behavior.

encodeUtf8 :: Text -> ByteString

Encode text using UTF-8 encoding.

encodeUtf8Builder :: Text -> Builder

Encode text to a ByteString Builder using UTF-8 encoding.

Since: text-1.1.0.0

lenientDecode :: OnDecodeError

Replace an invalid input byte with the Unicode replacement character U+FFFD.

PrimMonad

Re-exported from Control.Monad.Primitive:

primitive :: PrimMonad m => (State# (PrimState m) -> (# State# (PrimState m), a #)) -> m a

Execute a primitive operation

Re-exported from Control.Monad.ST:

runST :: (forall s. ST s a) -> a

Return the value computed by a state thread. The forall ensures that the internal state used by the ST computation is inaccessible to the rest of the program.