rio-0.1.22.0: A standard library for Haskell
Safe HaskellNone
LanguageHaskell2010

RIO.Prelude

Synopsis

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 f t p evaluates to f when p is False, and evaluates to t when p is True.

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

@since base-4.7.0.0

Examples

Expand

Basic usage:

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

Confirm that bool f t p and if p then t else f are equivalent:

>>> let p = True; f = "bar"; t = "foo"
>>> bool f t p == if p then t else f
True
>>> let p = False
>>> bool f t p == if p then t else f
True

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

Expand

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 GHC.Internal.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 a Maybe value. If the Maybe is Nothing, it returns the default value; otherwise, it returns the value contained in the Maybe.

Examples

Expand

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 GHC.Internal.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

Expand

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

Expand

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

Expand

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

Expand

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 GHC.Internal.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

Expand

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 GHC.Internal.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

Expand

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

>>> import GHC.Internal.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] #

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

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

Expand

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.

@since base-4.10.0.0

Examples

Expand

Basic usage:

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

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

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

@since base-4.10.0.0

Examples

Expand

Basic usage:

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

isLeft :: Either a b -> Bool #

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

@since base-4.7.0.0

Examples

Expand

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

isRight :: Either a b -> Bool #

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

@since base-4.7.0.0

Examples

Expand

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

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

Expand

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

Expand

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

Expand

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 #

Convert an uncurried function to a curried function.

Examples

Expand
>>> curry fst 1 2
1

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

uncurry converts a curried function to a function on pairs.

Examples

Expand
>>> 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.

>>> compare True False
GT
>>> compare (Down True) (Down False)
LT

If a has a Bounded instance then the wrapped instance also respects the reversed ordering by exchanging the values of minBound and maxBound.

>>> minBound :: Int
-9223372036854775808
>>> minBound :: Down Int
Down 9223372036854775807

All other instances of Down a behave as they do for a.

@since base-4.6.0.0

Constructors

Down 

Fields

Instances

Instances details
MonadZip Down

Since: base-4.12.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Down a -> Down b -> Down (a, b) #

mzipWith :: (a -> b -> c) -> Down a -> Down b -> Down c #

munzip :: Down (a, b) -> (Down a, Down b) #

Foldable1 Down

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Down m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Down a -> m #

foldMap1' :: Semigroup m => (a -> m) -> Down a -> m #

toNonEmpty :: Down a -> NonEmpty a #

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

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

head :: Down a -> a #

last :: Down a -> a #

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Down a -> b #

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Down a -> b #

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Down a -> b #

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Down a -> b #

Eq1 Down

Since: base-4.12.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Ord1 Down

Since: base-4.12.0.0

Instance details

Defined in Data.Functor.Classes

Methods

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

Read1 Down

Since: base-4.12.0.0

Instance details

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

Instance details

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

Instance details

Defined in Control.DeepSeq

Methods

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

Applicative Down

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.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 #

Functor Down

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

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

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

Monad Down

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

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

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

return :: a -> Down a #

Foldable Down

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.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

Instance details

Defined in GHC.Internal.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) #

Generic1 Down 
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep1 Down

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

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

Methods

from1 :: Down a -> Rep1 Down a #

to1 :: Rep1 Down a -> Down a #

Unbox a => Vector Vector (Down a) 
Instance details

Defined in Data.Vector.Unboxed.Base

Methods

basicUnsafeFreeze :: Mutable Vector s (Down a) -> ST s (Vector (Down a)) #

basicUnsafeThaw :: Vector (Down a) -> ST s (Mutable Vector s (Down a)) #

basicLength :: Vector (Down a) -> Int #

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

basicUnsafeIndexM :: Vector (Down a) -> Int -> Box (Down a) #

basicUnsafeCopy :: Mutable Vector s (Down a) -> Vector (Down a) -> ST s () #

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

Unbox a => MVector MVector (Down a) 
Instance details

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

basicInitialize :: MVector s (Down a) -> ST s ()

basicUnsafeReplicate :: Int -> Down a -> ST s (MVector s (Down a))

basicUnsafeRead :: MVector s (Down a) -> Int -> ST s (Down a)

basicUnsafeWrite :: MVector s (Down a) -> Int -> Down a -> ST s ()

basicClear :: MVector s (Down a) -> ST s ()

basicSet :: MVector s (Down a) -> Down a -> ST s ()

basicUnsafeCopy :: MVector s (Down a) -> MVector s (Down a) -> ST s ()

basicUnsafeMove :: MVector s (Down a) -> MVector s (Down a) -> ST s ()

basicUnsafeGrow :: MVector s (Down a) -> Int -> ST s (MVector s (Down a))

NFData a => NFData (Down a)

Since: deepseq-1.4.0.0

Instance details

Defined in Control.DeepSeq

Methods

rnf :: Down a -> () #

Monoid a => Monoid (Down a)

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

mempty :: Down a #

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

mconcat :: [Down a] -> Down a #

Semigroup a => Semigroup (Down a)

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

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

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

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

Bits a => Bits (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.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

Instance details

Defined in GHC.Internal.Data.Ord

Data a => Data (Down a)

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.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) #

Bounded a => Bounded (Down a)

Swaps minBound and maxBound of the underlying type.

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

minBound :: Down a #

maxBound :: Down a #

(Enum a, Bounded a, Eq a) => Enum (Down a)

Swaps succ and pred of the underlying type.

@since base-4.18.0.0

Instance details

Defined in GHC.Internal.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] #

Floating a => Floating (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.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 #

RealFloat a => RealFloat (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Storable a => Storable (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.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 () #

Generic (Down a) 
Instance details

Defined in GHC.Internal.Generics

Associated Types

type Rep (Down a)

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

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

Methods

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

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

Ix a => Ix (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.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 #

Num a => Num (Down a)

@since base-4.11.0.0

Instance details

Defined in GHC.Internal.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 #

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

Instance details

Defined in GHC.Internal.Data.Ord

Fractional a => Fractional (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

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

recip :: Down a -> Down a #

fromRational :: Rational -> Down a #

Real a => Real (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

toRational :: Down a -> Rational #

RealFrac a => RealFrac (Down a)

@since base-4.14.0.0

Instance details

Defined in GHC.Internal.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

Instance details

Defined in GHC.Internal.Data.Ord

Methods

showsPrec :: Int -> Down a -> ShowS #

show :: Down a -> String #

showList :: [Down a] -> ShowS #

Eq a => Eq (Down a)

@since base-4.6.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

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

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

Ord a => Ord (Down a)

@since base-4.6.0.0

Instance details

Defined in GHC.Internal.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 #

Prim a => Prim (Down a)

Since: primitive-0.6.5.0

Instance details

Defined in Data.Primitive.Types

Unbox a => Unbox (Down a) 
Instance details

Defined in Data.Vector.Unboxed.Base

type Rep1 Down

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep1 Down = D1 ('MetaData "Down" "GHC.Internal.Data.Ord" "ghc-internal" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))
newtype MVector s (Down a) 
Instance details

Defined in Data.Vector.Unboxed.Base

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

@since base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

type Rep (Down a) = D1 ('MetaData "Down" "GHC.Internal.Data.Ord" "ghc-internal" 'True) (C1 ('MetaCons "Down" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDown") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))
newtype Vector (Down a) 
Instance details

Defined in Data.Vector.Unboxed.Base

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

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 #

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.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

Integer remainder, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

Integer division truncated toward negative infinity.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

Integer modulus, satisfying

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

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

Simultaneous quot and rem.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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

simultaneous div and mod.

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

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.

WARNING: This function performs silent truncation if the result type is not at least as big as the argument's type.

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.

WARNING: This function goes through the Rational type, which does not have values for NaN for example. This means it does not round-trip.

For Double it also behaves differently with or without -O0:

Prelude> realToFrac nan -- With -O0
-Infinity
Prelude> realToFrac nan
NaN

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.

Examples

Expand
>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]
>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

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

Monoid

Re-exported from Data.Monoid:

mempty :: Monoid a => a #

Identity of mappend

Examples

Expand
>>> "Hello world" <> mempty
"Hello world"
>>> mempty <> [1, 2, 3]
[1,2,3]

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 #

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.

Examples

Expand

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

>>> fmap show Nothing
Nothing
>>> fmap show (Just 3)
Just "3"

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

>>> fmap show (Left 17)
Left 17
>>> fmap show (Right 17)
Right "17"

Double each element of a list:

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

Apply even to the second element of a pair:

>>> fmap even (2,2)
(2,True)

It may seem surprising that the function is only applied to the last element of the tuple compared to the list example above which applies it to every element in the list. To understand, remember that tuples are type constructors with multiple type parameters: a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over with fmap).

It explains why fmap can be used with tuples containing values of different types as in the following example:

>>> fmap even ("hello", 1.0, 4)
("hello",1.0,True)

(<$>) :: 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

Expand

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.

Examples

Expand

Perform a computation with Maybe and replace the result with a constant value if it is Just:

>>> 'a' <$ Just 2
Just 'a'
>>> 'a' <$ Nothing
Nothing

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

Flipped version of <$.

@since base-4.7.0.0

Examples

Expand

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")

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

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

Examples

Expand

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

@since base-4.11.0.0

Examples

Expand

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

Applicative

Re-exported from Control.Applicative:

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

Lift a value into the Structure.

Examples

Expand
>>> pure 1 :: Maybe Int
Just 1
>>> pure 'z' :: [Char]
"z"
>>> pure (pure ":D") :: Maybe [String]
Just [":D"]

(<*>) :: 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.

Example

Expand

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>> produceFoo :: Applicative f => f Foo
>>> produceBar :: Applicative f => f Bar
>>> produceBaz :: Applicative f => f Baz
>>> mkState :: Applicative f => f MyState
>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

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

Sequence actions, discarding the value of the second argument.

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

Sequence actions, discarding the value of the first argument.

Examples

Expand

If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing.

>>> Just 2 *> Just 3
Just 3
>>> Nothing *> Just 3
Nothing

Of course a more interesting use case would be to have effectful computations instead of just returning pure values.

>>> import Data.Char
>>> import GHC.Internal.Text.ParserCombinators.ReadP
>>> let p = string "my name is " *> munch1 isAlpha <* eof
>>> readP_to_S p "my name is Simon"
[("Simon","")]

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

Lift a function to actions. Equivalent to Functor's fmap but implemented using only Applicative's methods: liftA f a = pure f <*> a

As such this function may be used to implement a Functor instance from an Applicative one.

Examples

Expand

Using the Applicative instance for Lists:

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

Or the Applicative instance for Maybe

>>> liftA (+1) (Just 3)
Just 4

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.

Example

Expand
>>> liftA2 (,) (Just 3) (Just 5)
Just (3,5)
>>> liftA2 (+) [1, 2, 3] [4, 5, 6]
[5,6,7,6,7,8,7,8,9]

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

Lift a ternary function to actions.

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

Repeat an action indefinitely.

Examples

Expand

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

Note that "forever" isn't necessarily non-terminating. If the action is in a MonadPlus and short-circuits after some number of iterations. then forever actually returns mzero, effectively short-circuiting its caller.

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

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

Expand

Basic usage:

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

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. This is forM_ generalised to Applicative actions.

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

Examples

Expand

Basic usage:

>>> 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.

sequenceA_ is just like sequence_, but generalised to Applicative actions.

Examples

Expand

Basic usage:

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

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

This generalizes the list-based filter function.

runIdentity (filterM (Identity . p) xs) == filter p xs

Examples

Expand
>>> filterM (\x -> do
      putStrLn ("Keep: " ++ show x ++ "?")
      answer <- getLine
      pure (answer == "y"))
    [1, 2, 3]
Keep: 1?
y
Keep: 2?
n
Keep: 3?
y
[1,3]
>>> filterM (\x -> do
      putStr (show x)
      x' <- readLn
      pure (x == x'))
    [1, 2, 3]
12
22
33
[2,3]

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

Like replicateM, but discards the result.

Examples

Expand
>>> replicateM_ 3 (putStr "a")
aaa

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. This function should not be different from its default implementation as pure. The justification for the existence of this function is merely historic.

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

Expand
>>> join [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
[1,2,3,4,5,6,7,8,9]
>>> join (Just (Just 3))
Just 3

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

An alternative name for this function is 'bind', but some people may refer to it as 'flatMap', which results from it being equivialent to

\x f -> join (fmap f x) :: Monad m => m a -> (a -> m b) -> m b

which can be seen as mapping a value with Monad m => m a -> m (m b) and then 'flattening' m (m b) to m b using join.

(>>) :: 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

or in terms of (>>=) as

as >>= const bs

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

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

as >>= f == f =<< as

(>=>) :: 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

or in terms of (>>=) as

bs a >>= cs

(<=<) :: 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. This is equivalent to fmap but specialised to Monads.

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.

Examples

Expand
>>> liftM2 (+) [0,1] [0,2]
[0,2,1,3]
>>> liftM2 (+) (Just 1) Nothing
Nothing
>>> liftM2 (+) (+ 3) (* 2) 5
18

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.

mapM_ is just like traverse_, but specialised to monadic actions.

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.

forM_ is just like for_, but specialised to monadic actions.

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.

sequence_ is just like sequenceA_, but specialised to monadic actions.

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, lazy in the accumulator.

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, given an operator lazy in its right argument, foldr can produce a terminating expression from an unbounded list.

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

foldr f z = foldr f z . toList

Examples

Expand

Basic usage:

>>> foldr (||) False [False, True, False]
True
>>> foldr (||) False []
False
>>> foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']
"foodcba"
Infinite structures

⚠️ Applying foldr to infinite structures usually doesn't terminate.

It may still terminate under one of the following conditions:

  • the folding function is short-circuiting
  • the folding function is lazy on its second argument
Short-circuiting

(||) short-circuits on True values, so the following terminates because there is a True value finitely far from the left side:

>>> foldr (||) False (True : repeat False)
True

But the following doesn't terminate:

>>> foldr (||) False (repeat False ++ [True])
* Hangs forever *
Laziness in the second argument

Applying foldr to infinite structures terminates when the operator is lazy in its second argument (the initial accumulator is never used in this case, and so could be left undefined, but [] is more clear):

>>> take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)
[1,4,7,10,13]

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 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

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

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

Expand

Basic usage:

>>> 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}

Folds of unbounded structures do not terminate when the monoid's (<>) operator is strict:

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

Lazy corecursive folds of unbounded structures are fine:

>>> 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

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

Map each element of the structure into a monoid, and combine the results with (<>). This fold is right-associative and lazy in the accumulator. For strict left-associative folds consider foldMap' instead.

Examples

Expand

Basic usage:

>>> foldMap Sum [1, 3, 5]
Sum {getSum = 9}
>>> foldMap Product [1, 3, 5]
Product {getProduct = 15}
>>> foldMap (replicate 3) [1, 2, 3]
[1,1,1,2,2,2,3,3,3]

When a Monoid's (<>) is lazy in its second argument, foldMap can return a result even from an unbounded structure. For example, lazy accumulation enables Data.ByteString.Builder to efficiently serialise large data structures and produce the output incrementally:

>>> import qualified Data.ByteString.Lazy as L
>>> import qualified Data.ByteString.Builder as B
>>> let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20
>>> let lbs = B.toLazyByteString $ foldMap bld [0..]
>>> L.take 64 lbs
"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"

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?

Note: elem is often used in infix form.

Examples

Expand

Basic usage:

>>> 3 `elem` []
False
>>> 3 `elem` [1,2]
False
>>> 3 `elem` [1,2,3,4,5]
True

For infinite structures, the default implementation of elem terminates if the sought-after value exists at a finite distance from the left side of the structure:

>>> 3 `elem` [1..]
True
>>> 3 `elem` ([4..] ++ [3])
* Hangs forever *

@since base-4.8.0.0

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

notElem is the negation of elem.

Examples

Expand

Basic usage:

>>> 3 `notElem` []
True
>>> 3 `notElem` [1,2]
True
>>> 3 `notElem` [1,2,3,4,5]
False

For infinite structures, notElem terminates if the value exists at a finite distance from the left side of the structure:

>>> 3 `notElem` [1..]
False
>>> 3 `notElem` ([4..] ++ [3])
* Hangs forever *

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

Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.

Examples

Expand

Basic usage:

>>> null []
True
>>> null [1]
False

null is expected to terminate even for infinite structures. The default implementation terminates provided the structure is bounded on the left (there is a leftmost element).

>>> null [1..]
False

@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 just counts elements starting with the leftmost. Instances for structures that can compute the element count faster than via element-by-element counting, should provide a specialised implementation.

Examples

Expand

Basic usage:

>>> length []
0
>>> length ['a', 'b', 'c']
3
>>> length [1..]
* Hangs forever *

@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.

Examples

Expand

Basic usage:

>>> sum []
0
>>> sum [42]
42
>>> sum [1..10]
55
>>> sum [4.1, 2.0, 1.7]
7.8
>>> sum [1..]
* Hangs forever *

@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.

Examples

Expand

Basic usage:

>>> product []
1
>>> product [42]
42
>>> product [1..10]
3628800
>>> product [4.1, 2.0, 1.7]
13.939999999999998
>>> product [1..]
* Hangs forever *

@since base-4.8.0.0

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

Determines whether all elements of the structure satisfy the predicate.

Examples

Expand

Basic usage:

>>> all (> 3) []
True
>>> all (> 3) [1,2]
False
>>> all (> 3) [1,2,3,4,5]
False
>>> all (> 3) [1..]
False
>>> all (> 3) [4..]
* Hangs forever *

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

Determines whether any element of the structure satisfies the predicate.

Examples

Expand

Basic usage:

>>> any (> 3) []
False
>>> any (> 3) [1,2]
False
>>> any (> 3) [1,2,3,4,5]
True
>>> any (> 3) [1..]
True
>>> any (> 3) [0, -1..]
* Hangs forever *

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.

Examples

Expand

Basic usage:

>>> and []
True
>>> and [True]
True
>>> and [False]
False
>>> and [True, True, False]
False
>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False
>>> and (repeat True)
* Hangs forever *

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.

Examples

Expand

Basic usage:

>>> or []
False
>>> or [True]
True
>>> or [False]
False
>>> or [True, True, False]
True
>>> or (True : repeat False) -- Infinite list [True,False,False,False,...
True
>>> or (repeat False)
* Hangs forever *

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

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

Expand

Basic usage:

>>> toList Nothing
[]
>>> toList (Just 42)
[42]
>>> toList (Left "foo")
[]
>>> toList (Node (Leaf 5) 17 (Node Empty 12 (Leaf 8)))
[5,17,12,8]

For lists, toList is the identity:

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

@since base-4.8.0.0

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

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

Examples

Expand

Basic usage:

>>> concat (Just [1, 2, 3])
[1,2,3]
>>> concat (Left 42)
[]
>>> concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

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

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

Examples

Expand

Basic usage:

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>> concatMap (take 3) (Just [1..])
[1,2,3]

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_.

Examples

Expand

Basic usage:

In the first two examples we show each evaluated action mapping to the output structure.

>>> traverse Just [1,2,3,4]
Just [1,2,3,4]
>>> traverse id [Right 1, Right 2, Right 3, Right 4]
Right [1,2,3,4]

In the next examples, we show that Nothing and Left values short circuit the created structure.

>>> traverse (const Nothing) [1,2,3,4]
Nothing
>>> traverse (\x -> if odd x then Just x else Nothing)  [1,2,3,4]
Nothing
>>> traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]
Left 0

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_.

Examples

Expand

Basic usage:

For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.

>>> sequenceA [Just 1, Just 2, Just 3]
Just [1,2,3]
>>> sequenceA [Right 1, Right 2, Right 3]
Right [1,2,3]

The next two example show Nothing and Just will short circuit the resulting structure if present in the input. For more context, check the Traversable instances for Either and Maybe.

>>> sequenceA [Just 1, Just 2, Just 3, Nothing]
Nothing
>>> sequenceA [Right 1, Right 2, Right 3, Left 4]
Left 4

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_.

Examples

Expand

mapM is literally a traverse with a type signature restricted to Monad. Its implementation may be more efficient due to additional power of Monad.

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_.

Examples

Expand

Basic usage:

The first two examples are instances where the input and and output of sequence are isomorphic.

>>> sequence $ Right [1,2,3,4]
[Right 1,Right 2,Right 3,Right 4]
>>> sequence $ [Right 1,Right 2,Right 3,Right 4]
Right [1,2,3,4]

The following examples demonstrate short circuit behavior for sequence.

>>> sequence $ Left [1,2,3,4]
Left [1,2,3,4]
>>> sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]
Left 0

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.

Examples

Expand
>>> some (putStr "la")
lalalalalalalalala... * goes on forever *
>>> some Nothing
nothing
>>> take 5 <$> some (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case some parser will attempt to parse parser one or more times until it fails.

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

Zero or more.

Examples

Expand
>>> many (putStr "la")
lalalalalalalalala... * goes on forever *
>>> many Nothing
Just []
>>> take 5 <$> many (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case many parser will attempt to parse parser zero or more times until it fails.

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

One or none.

It is useful for modelling any computation that is allowed to fail.

Examples

Expand

Using the Alternative instance of Control.Monad.Except, the following functions:

>>> import Control.Monad.Except
>>> canFail = throwError "it failed" :: Except String Int
>>> final = return 42                :: Except String Int

Can be combined by allowing the first function to fail:

>>> runExcept $ canFail *> final
Left "it failed"
>>> runExcept $ optional canFail *> final
Right 42

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

The sum of a collection of actions using (<|>), generalizing concat.

asum is just like msum, but generalised to Alternative.

Examples

Expand

Basic usage:

>>> 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

Expand

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

As an example of signalling 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,

Examples

Expand
when debug (putStrLn "Debugging")

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

>>> putStr "pi:" >> when False (print 3.14159)
pi:

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

The reverse of when.

Examples

Expand
>>> do x <- getLine
       unless (x == "hi") (putStrLn "hi!")
comingupwithexamplesisdifficult
hi!
>>> unless (pi > exp 1) Nothing
Just ()

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

Expand
>>> 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

Expand
>>> 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.

secondbimap id

Examples

Expand
>>> 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.

bifoldbifoldMap id id

Examples

Expand

Basic usage:

>>> bifold (Right [1, 2, 3])
[1,2,3]
>>> bifold (Left [5, 6])
[5,6]
>>> bifold ([1, 2, 3], [4, 5])
[1,2,3,4,5]
>>> bifold (Product 6, Product 7)
Product {getProduct = 42}
>>> bifold (Sum 6, Sum 7)
Sum {getSum = 13}

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

Examples

Expand

Basic usage:

>>> bifoldMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
>>> bifoldMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
>>> bifoldMap (take 3) (fmap digitToInt) (Right "89")
[8,9]

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

Examples

Expand

Basic usage:

> bifoldr (+) (*) 3 (5, 7)
26 -- 5 + (7 * 3)

> bifoldr (+) (*) 3 (7, 5)
22 -- 7 + (5 * 3)

> bifoldr (+) (*) 3 (Right 5)
15 -- 5 * 3

> bifoldr (+) (*) 3 (Left 5)
8 -- 5 + 3

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.

Examples

Expand

Basic usage:

> bifoldl (+) (*) 3 (5, 7)
56 -- (5 + 3) * 7

> bifoldl (+) (*) 3 (7, 5)
50 -- (7 + 3) * 5

> bifoldl (+) (*) 3 (Right 5)
15 -- 5 * 3

> bifoldl (+) (*) 3 (Left 5)
8 -- 5 + 3

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.

Examples

Expand

Basic usage:

>>> bifoldr1 (+) (5, 7)
12
>>> bifoldr1 (+) (Right 7)
7
>>> bifoldr1 (+) (Left 5)
5
> bifoldr1 (+) (BiList [1, 2] [3, 4])
10 -- 1 + (2 + (3 + 4))
>>> bifoldr1 (+) (BiList [1, 2] [])
3

On empty structures, this function throws an exception:

>>> bifoldr1 (+) (BiList [] [])
*** Exception: bifoldr1: empty structure
...

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.

Examples

Expand

Basic usage:

>>> bifoldl1 (+) (5, 7)
12
>>> bifoldl1 (+) (Right 7)
7
>>> bifoldl1 (+) (Left 5)
5
> bifoldl1 (+) (BiList [1, 2] [3, 4])
10 -- ((1 + 2) + 3) + 4
>>> bifoldl1 (+) (BiList [1, 2] [])
3

On empty structures, this function throws an exception:

>>> bifoldl1 (+) (BiList [] [])
*** Exception: bifoldl1: empty structure
...

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.

Examples

Expand

Basic usage:

>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 ("Hello", True)
"Hello"
"True"
42
>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Right True)
"True"
42
>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Left "Hello")
"Hello"
42

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.

Examples

Expand

Basic usage:

>>> bitraverse_ print (print . show) ("Hello", True)
"Hello"
"True"
>>> bitraverse_ print (print . show) (Right True)
"True"
>>> bitraverse_ print (print . show) (Left "Hello")
"Hello"

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.

Examples

Expand

Basic usage:

>>> bifor_ ("Hello", True) print (print . show)
"Hello"
"True"
>>> bifor_ (Right True) print (print . show)
"True"
>>> bifor_ (Left "Hello") print (print . show)
"Hello"

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.

Examples

Expand

Basic usage:

>>> bisequence_ (print "Hello", print "World")
"Hello"
"World"
>>> bisequence_ (Left (print "Hello"))
"Hello"
>>> bisequence_ (Right (print "World"))
"World"

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.

Examples

Expand

Basic usage:

>>> biasum (Nothing, Nothing)
Nothing
>>> biasum (Nothing, Just 42)
Just 42
>>> biasum (Just 18, Nothing)
Just 18
>>> biasum (Just 18, Just 42)
Just 18

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.

Examples

Expand

Basic usage:

>>> biList (18, 42)
[18,42]
>>> biList (Left 18)
[18]

Since: base-4.10.0.0

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

Test whether the structure is empty.

Examples

Expand

Basic usage:

>>> binull (18, 42)
False
>>> binull (Right 42)
False
>>> binull (BiList [] [])
True

Since: base-4.10.0.0

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

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

Examples

Expand

Basic usage:

>>> bilength (True, 42)
2
>>> bilength (Right 42)
1
>>> bilength (BiList [1,2,3] [4,5])
5
>>> bilength (BiList [] [])
0

On infinite structures, this function hangs:

> bilength (BiList [1..] [])
* Hangs forever *

Since: base-4.10.0.0

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

Does the element occur in the structure?

Examples

Expand

Basic usage:

>>> bielem 42 (17, 42)
True
>>> bielem 42 (17, 43)
False
>>> bielem 42 (Left 42)
True
>>> bielem 42 (Right 13)
False
>>> bielem 42 (BiList [1..5] [1..100])
True
>>> bielem 42 (BiList [1..5] [1..41])
False

Since: base-4.10.0.0

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

The largest element of a non-empty structure.

Examples

Expand

Basic usage:

>>> bimaximum (42, 17)
42
>>> bimaximum (Right 42)
42
>>> bimaximum (BiList [13, 29, 4] [18, 1, 7])
29
>>> bimaximum (BiList [13, 29, 4] [])
29

On empty structures, this function throws an exception:

>>> bimaximum (BiList [] [])
*** Exception: bimaximum: 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.

Examples

Expand

Basic usage:

>>> biminimum (42, 17)
17
>>> biminimum (Right 42)
42
>>> biminimum (BiList [13, 29, 4] [18, 1, 7])
1
>>> biminimum (BiList [13, 29, 4] [])
4

On empty structures, this function throws an exception:

>>> biminimum (BiList [] [])
*** Exception: biminimum: 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.

Examples

Expand

Basic usage:

>>> bisum (42, 17)
59
>>> bisum (Right 42)
42
>>> bisum (BiList [13, 29, 4] [18, 1, 7])
72
>>> bisum (BiList [13, 29, 4] [])
46
>>> bisum (BiList [] [])
0

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.

Examples

Expand

Basic usage:

>>> biproduct (42, 17)
714
>>> biproduct (Right 42)
42
>>> biproduct (BiList [13, 29, 4] [18, 1, 7])
190008
>>> biproduct (BiList [13, 29, 4] [])
1508
>>> biproduct (BiList [] [])
1

Since: base-4.10.0.0

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

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

Examples

Expand

Basic usage:

>>> biconcat ([1, 2, 3], [4, 5])
[1,2,3,4,5]
>>> biconcat (Left [1, 2, 3])
[1,2,3]
>>> biconcat (BiList [[1, 2, 3, 4, 5], [6, 7, 8]] [[9]])
[1,2,3,4,5,6,7,8,9]

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.

Examples

Expand

Basic usage:

>>> biconcatMap (take 3) (fmap digitToInt) ([1..], "89")
[1,2,3,8,9]
>>> biconcatMap (take 3) (fmap digitToInt) (Left [1..])
[1,2,3]
>>> biconcatMap (take 3) (fmap digitToInt) (Right "89")
[8,9]

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.

Examples

Expand

Basic usage:

>>> biand (True, False)
False
>>> biand (True, True)
True
>>> biand (Left True)
True

Empty structures yield True:

>>> biand (BiList [] [])
True

A False value finitely far from the left end yields False (short circuit):

>>> biand (BiList [True, True, False, True] (repeat True))
False

A False value infinitely far from the left end hangs:

> biand (BiList (repeat True) [False])
* Hangs forever *

An infinitely True value hangs:

> biand (BiList (repeat True) [])
* Hangs forever *

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.

Examples

Expand

Basic usage:

>>> bior (True, False)
True
>>> bior (False, False)
False
>>> bior (Left True)
True

Empty structures yield False:

>>> bior (BiList [] [])
False

A True value finitely far from the left end yields True (short circuit):

>>> bior (BiList [False, False, True, False] (repeat False))
True

A True value infinitely far from the left end hangs:

> bior (BiList (repeat False) [True])
* Hangs forever *

An infinitely False value hangs:

> bior (BiList (repeat False) [])
* Hangs forever *

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. Empty structures yield False.

Examples

Expand

Basic usage:

>>> biany even isDigit (27, 't')
False
>>> biany even isDigit (27, '8')
True
>>> biany even isDigit (26, 't')
True
>>> biany even isDigit (Left 27)
False
>>> biany even isDigit (Left 26)
True
>>> biany even isDigit (BiList [27, 53] ['t', '8'])
True

Empty structures yield False:

>>> biany even isDigit (BiList [] [])
False

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. Empty structures yield True.

Examples

Expand

Basic usage:

>>> biall even isDigit (27, 't')
False
>>> biall even isDigit (26, '8')
True
>>> biall even isDigit (Left 27)
False
>>> biall even isDigit (Left 26)
True
>>> biall even isDigit (BiList [26, 52] ['3', '8'])
True

Empty structures yield True:

>>> biall even isDigit (BiList [] [])
True

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.

Examples

Expand

Basic usage:

>>> bimaximumBy compare (42, 17)
42
>>> bimaximumBy compare (Left 17)
17
>>> bimaximumBy compare (BiList [42, 17, 23] [-5, 18])
42

On empty structures, this function throws an exception:

>>> bimaximumBy compare (BiList [] [])
*** Exception: bifoldr1: empty structure
...

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.

Examples

Expand

Basic usage:

>>> biminimumBy compare (42, 17)
17
>>> biminimumBy compare (Left 17)
17
>>> biminimumBy compare (BiList [42, 17, 23] [-5, 18])
-5

On empty structures, this function throws an exception:

>>> biminimumBy compare (BiList [] [])
*** Exception: bifoldr1: empty structure
...

Since: base-4.10.0.0

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

binotElem is the negation of bielem.

Examples

Expand

Basic usage:

>>> binotElem 42 (17, 42)
False
>>> binotElem 42 (17, 43)
True
>>> binotElem 42 (Left 42)
False
>>> binotElem 42 (Right 13)
True
>>> binotElem 42 (BiList [1..5] [1..100])
False
>>> binotElem 42 (BiList [1..5] [1..41])
True

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.

Examples

Expand

Basic usage:

>>> bifind even (27, 53)
Nothing
>>> bifind even (27, 52)
Just 52
>>> bifind even (26, 52)
Just 26

Empty structures always yield Nothing:

>>> bifind even (BiList [] [])
Nothing

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_.

Examples

Expand

Basic usage:

>>> bitraverse listToMaybe (find odd) (Left [])
Nothing
>>> bitraverse listToMaybe (find odd) (Left [1, 2, 3])
Just (Left 1)
>>> bitraverse listToMaybe (find odd) (Right [4, 5])
Just (Right 5)
>>> bitraverse listToMaybe (find odd) ([1, 2, 3], [4, 5])
Just (1,5)
>>> bitraverse listToMaybe (find odd) ([], [4, 5])
Nothing

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_.

bisequencebitraverse id id

Examples

Expand

Basic usage:

>>> bisequence (Just 4, Nothing)
Nothing
>>> bisequence (Just 4, Just 5)
Just (4,5)
>>> bisequence ([1, 2, 3], [4, 5])
[(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]

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_.

Examples

Expand

Basic usage:

>>> bifor (Left []) listToMaybe (find even)
Nothing
>>> bifor (Left [1, 2, 3]) listToMaybe (find even)
Just (Left 1)
>>> bifor (Right [4, 5]) listToMaybe (find even)
Just (Right 4)
>>> bifor ([1, 2, 3], [4, 5]) listToMaybe (find even)
Just (1,4)
>>> bifor ([], [4, 5]) listToMaybe (find even)
Nothing

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.

Examples

Expand

Basic usage:

>>> bimapAccumL (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(8,("True","oof"))

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 bifoldr; 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.

Examples

Expand

Basic usage:

>>> bimapAccumR (\acc bool -> (acc + 1, show bool)) (\acc string -> (acc * 2, reverse string)) 3 (True, "foo")
(7,("True","oof"))

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 using (<|>), generalizing concat.

msum is just like asum, but specialised to MonadPlus.

Examples

Expand

Basic usage, using the MonadPlus instance for Maybe:

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

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

Direct MonadPlus equivalent of filter.

Examples

Expand

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

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples

Expand
>>> length $ filter id [True, True, False, True]
3
>>> Just (Just 3) >>= id
Just 3
>>> foldr id 0 [(^3), (*5), (+2)]
1000

const :: a -> b -> a #

const x y always evaluates to x, ignoring its second argument.

const x = \_ -> x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples

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

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

Right to left function composition.

(f . g) x = f (g x)
f . id = f = id . f

Examples

Expand
>>> map ((*2) . length) [[], [0, 1, 2], [0]]
[0,6,2]
>>> foldr (.) id [(+1), (*3), (^3)] 2
25
>>> let (...) = (.).(.) in ((*2)...(+)) 5 10
30

($) :: (a -> b) -> a -> b infixr 0 #

($) is the function application operator.

Applying ($) to a function f and an argument x gives the same result as applying f to x directly. The definition is akin to this:

($) :: (a -> b) -> a -> b
($) f x = f x

This is id specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is the same as (a -> b) -> a -> b.

On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.

The order of operations is very different between ($) and normal function application. Normal function application has precedence 10 - higher than any operator - and associates to the left. So these two definitions are equivalent:

expr = min 5 1 + 5
expr = ((min 5) 1) + 5

($) has precedence 0 (the lowest) and associates to the right, so these are equivalent:

expr = min 5 $ 1 + 5
expr = (min 5) (1 + 5)

Examples

Expand

A common use cases of ($) is to avoid parentheses in complex expressions.

For example, instead of using nested parentheses in the following Haskell function:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum (mapMaybe readMaybe (words s))

we can deploy the function application operator:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum $ mapMaybe readMaybe $ words s

($) is also used as a section (a partially applied operator), in order to indicate that we wish to apply some yet-unspecified function to a given value. For example, to apply the argument 5 to a list of functions:

applyFive :: [Int]
applyFive = map ($ 5) [(+1), (2^)]
>>> [6, 32]

Technical Remark (Representation Polymorphism)

Expand

($) is fully representation-polymorphic. This allows it to also be used with arguments of unlifted and even unboxed kinds, such as unboxed integers:

fastMod :: Int -> Int -> Int
fastMod (I# x) (I# m) = I# $ remInt# x m

(&) :: 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 $.

This is a version of flip id, where id is specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is (a -> b) -> a -> b. flipping this yields a -> (a -> b) -> b which is the type signature of &

Examples

Expand
>>> 5 & (+1) & show
"6"
>>> sqrt $ [1 / n^2 | n <- [1..1000]] & sum & (*6)
3.1406380562059946

@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 f x y = f y x
flip . flip = id

Examples

Expand
>>> flip (++) "hello" "world"
"worldhello"
>>> let (.>) = flip (.) in (+1) .> show $ 5
"6"

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.

When f is strict, this means that because, by the definition of strictness, f ⊥ = ⊥ and such the least defined fixed point of any strict function is .

Examples

Expand

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,

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.

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

Using fix, we can implement versions of repeat as fix . (:) and cycle as fix . (++)

>>> take 10 $ fix (0:)
[0,0,0,0,0,0,0,0,0,0]
>>> map (fix (\rec n -> if n < 2 then n else rec (n - 1) + rec (n - 2))) [1..10]
[1,1,2,3,5,8,13,21,34,55]

Implementation Details

Expand

The current implementation of fix uses structural sharing

fix f = let x = f x in x

A more straightforward but non-sharing version would look like

fix f = f (fix f)

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.

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

Examples

Expand
>>> sortBy (compare `on` length) [[0, 1, 2], [0, 1], [], [0]]
[[],[0],[0,1],[0,1,2]]
>>> ((+) `on` length) [1, 2, 3] [-1]
4
>>> ((,) `on` (*2)) 2 3
(4,6)

Algebraic properties

Expand
  • (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})
  • ((*) `on` f) `on` g = (*) `on` (f . g)
  • flip on f . flip on g = flip on (g . f)

Miscellaneous functions

($!) :: (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 :: 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 :: HasCallStack => [Char] -> a #

error stops execution and displays an error message.

undefined :: 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 #

(++) appends 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.

Performance considerations

Expand

This function takes linear time in the number of elements of the first list. Thus it is better to associate repeated applications of (++) to the right (which is the default behaviour): xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs. For the same reason concat = foldr (++) [] has linear performance, while foldl (++) [] is prone to quadratic slowdown

Examples

Expand
>>> [1, 2, 3] ++ [4, 5, 6]
[1,2,3,4,5,6]
>>> [] ++ [1, 2, 3]
[1,2,3]
>>> [3, 2, 1] ++ []
[3,2,1]

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 p is equivalent to span (not . p) and consequently to (takeWhile (not . p) xs, dropWhile (not . p) xs), even if p is _|_.

Laziness

Expand
>>> break undefined []
([],[])
>>> fst (break (const True) undefined)
*** Exception: Prelude.undefined
>>> fst (break (const True) (undefined : undefined))
[]
>>> take 1 (fst (break (const False) (1 : undefined)))
[1]

break produces the first component of the tuple lazily:

>>> take 10 (fst (break (const False) [1..]))
[1,2,3,4,5,6,7,8,9,10]

Examples

Expand
>>> 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],[])

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

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

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

Examples

Expand
>>> 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]

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

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

Examples

Expand
>>> 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]

Examples

Expand
>>> filter odd [1, 2, 3]
[1,3]
>>> filter (\l -> length l > 3) ["Hello", ", ", "World", "!"]
["Hello","World"]
>>> filter (/= 3) [1, 2, 3, 4, 3, 2, 1]
[1,2,4,2,1]

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

\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list. For the result to be Nothing, the list must be finite.

Examples

Expand
>>> lookup 2 []
Nothing
>>> lookup 2 [(1, "first")]
Nothing
>>> 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, ...]

this means that map id == id

Examples

Expand
>>> map (+1) [1, 2, 3]
[2,3,4]
>>> map id [1, 2, 3]
[1,2,3]
>>> map (\n -> 3 * n + 1) [1, 2, 3]
[4,7,10]

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.

Examples

Expand
>>> replicate 0 True
[]
>>> replicate (-1) True
[]
>>> replicate 4 True
[True,True,True,True]

reverse :: [a] -> [a] #

\(\mathcal{O}(n)\). reverse xs returns the elements of xs in reverse order. xs must be finite.

Laziness

Expand

reverse is lazy in its elements.

>>> head (reverse [undefined, 1])
1
>>> reverse (1 : 2 : undefined)
*** Exception: Prelude.undefined

Examples

Expand
>>> reverse []
[]
>>> reverse [42]
[42]
>>> reverse [2,5,7]
[7,5,2]
>>> reverse [1..]
* Hangs forever *

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

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

span p xs is equivalent to (takeWhile p xs, dropWhile p xs), even if p is _|_.

Laziness

Expand
>>> span undefined []
([],[])
>>> fst (span (const False) undefined)
*** Exception: Prelude.undefined
>>> fst (span (const False) (undefined : undefined))
[]
>>> take 1 (fst (span (const True) (1 : undefined)))
[1]

span produces the first component of the tuple lazily:

>>> take 10 (fst (span (const True) [1..]))
[1,2,3,4,5,6,7,8,9,10]

Examples

Expand
>>> 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])

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.

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

Laziness

Expand
>>> take 0 undefined
[]
>>> take 2 (1 : 2 : undefined)
[1,2]

Examples

Expand
>>> 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]
[]

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.

Laziness

Expand
>>> takeWhile (const False) undefined
*** Exception: Prelude.undefined
>>> takeWhile (const False) (undefined : undefined)
[]
>>> take 1 (takeWhile (const True) (1 : undefined))
[1]

Examples

Expand
>>> 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 is right-lazy:

>>> zip [] undefined
[]
>>> zip undefined []
*** Exception: Prelude.undefined
...

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

Examples

Expand
>>> zip [1, 2, 3] ['a', 'b', 'c']
[(1,'a'),(2,'b'),(3,'c')]

If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:

>>> zip [1] ['a', 'b']
[(1,'a')]
>>> zip [1, 2] ['a']
[(1,'a')]
>>> zip [] [1..]
[]
>>> zip [1..] []
[]

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.

zipWith (,) xs ys == zip xs ys
zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]

zipWith is right-lazy:

>>> let f = undefined
>>> zipWith f [] undefined
[]

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

Examples

Expand

zipWith (+) can be applied to two lists to produce the list of corresponding sums:

>>> zipWith (+) [1, 2, 3] [4, 5, 6]
[5,7,9]
>>> zipWith (++) ["hello ", "foo"] ["world!", "bar"]
["hello world!","foobar"]

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

Strip out duplicates

String

Re-exported from Data.String:

lines :: String -> [String] #

Splits the argument into a list of lines stripped of their terminating \n characters. The \n terminator is optional in a final non-empty line of the argument string.

When the argument string is empty, or ends in a \n character, it can be recovered by passing the result of lines to the unlines function. Otherwise, unlines appends the missing terminating \n. This makes unlines . lines idempotent:

(unlines . lines) . (unlines . lines) = (unlines . lines)

Examples

Expand
>>> lines ""           -- empty input contains no lines
[]
>>> lines "\n"         -- single empty line
[""]
>>> lines "one"        -- single unterminated line
["one"]
>>> lines "one\n"      -- single non-empty line
["one"]
>>> lines "one\n\n"    -- second line is empty
["one",""]
>>> lines "one\ntwo"   -- second line is unterminated
["one","two"]
>>> lines "one\ntwo\n" -- two non-empty lines
["one","two"]

unlines :: [String] -> String #

Appends a \n character to each input string, then concatenates the results. Equivalent to foldMap (s -> s ++ "\n").

Examples

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

Note that unlines . lines /= id when the input is not \n-terminated:

>>> unlines . lines $ "foo\nbar"
"foo\nbar\n"

unwords :: [String] -> String #

unwords joins words with separating spaces (U+0020 SPACE).

unwords is neither left nor right inverse of words:

>>> words (unwords [" "])
[]
>>> unwords (words "foo\nbar")
"foo bar"

Examples

Expand
>>> unwords ["Lorem", "ipsum", "dolor"]
"Lorem ipsum dolor"
>>> unwords ["foo", "bar", "", "baz"]
"foo bar  baz"

words :: String -> [String] #

words breaks a string up into a list of words, which were delimited by white space (as defined by isSpace). This function trims any white spaces at the beginning and at the end.

Examples

Expand
>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]
>>> words " foo bar "
["foo","bar"]

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 infixr 0 #

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

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.

Text

tshow :: Show a => a -> 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.

Surrogate code points in replacement character returned by OnDecodeError will be automatically remapped to the replacement char U+FFFD.

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.