Copyright | (c) The University of Glasgow 2001 |
---|---|
License | BSD-style (see the file libraries/base/LICENSE) |
Maintainer | libraries@haskell.org |
Stability | stable |
Portability | portable |
Safe Haskell | Trustworthy |
Language | Haskell2010 |
Prelude
Description
The Prelude: a standard module. The Prelude is imported by default into all Haskell modules unless either there is an explicit import statement for it, or the NoImplicitPrelude extension is enabled.
Synopsis
- data Bool
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- otherwise :: Bool
- data Maybe a
- maybe :: b -> (a -> b) -> Maybe a -> b
- data Either a b
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- data Ordering
- data Char
- type String = [Char]
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- curry :: ((a, b) -> c) -> a -> b -> c
- uncurry :: (a -> b -> c) -> (a, b) -> c
- class Eq a where
- class Eq a => Ord a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Bounded a where
- data Int
- data Integer
- data Float
- data Double
- type Rational = Ratio Integer
- data Word
- class Num a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (Real a, Enum a) => Integral a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class Fractional a => Floating a where
- class (Real a, Fractional a) => RealFrac a where
- class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
- subtract :: Num a => a -> a -> a
- even :: Integral a => a -> Bool
- odd :: Integral a => a -> Bool
- gcd :: Integral a => a -> a -> a
- lcm :: Integral a => a -> a -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- class Functor (f :: Type -> Type) where
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- class Functor f => Applicative (f :: Type -> Type) where
- class Applicative m => Monad (m :: Type -> Type) where
- class Monad m => MonadFail (m :: Type -> Type) where
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- class Foldable (t :: Type -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldl' :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- elem :: Eq a => a -> t a -> Bool
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- id :: a -> a
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- flip :: (a -> b -> c) -> b -> a -> c
- ($) :: (a -> b) -> a -> b
- until :: (a -> Bool) -> (a -> a) -> a -> a
- asTypeOf :: a -> a -> a
- error :: HasCallStack => [Char] -> a
- errorWithoutStackTrace :: [Char] -> a
- undefined :: HasCallStack => a
- seq :: a -> b -> b
- ($!) :: (a -> b) -> a -> b
- map :: (a -> b) -> [a] -> [b]
- (++) :: [a] -> [a] -> [a]
- filter :: (a -> Bool) -> [a] -> [a]
- head :: HasCallStack => [a] -> a
- last :: HasCallStack => [a] -> a
- tail :: HasCallStack => [a] -> [a]
- init :: HasCallStack => [a] -> [a]
- (!!) :: HasCallStack => [a] -> Int -> a
- null :: Foldable t => t a -> Bool
- length :: Foldable t => t a -> Int
- reverse :: [a] -> [a]
- and :: Foldable t => t Bool -> Bool
- or :: Foldable t => t Bool -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- concat :: Foldable t => t [a] -> [a]
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- iterate :: (a -> a) -> a -> [a]
- repeat :: a -> [a]
- replicate :: Int -> a -> [a]
- cycle :: HasCallStack => [a] -> [a]
- take :: Int -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- span :: (a -> Bool) -> [a] -> ([a], [a])
- break :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- zip :: [a] -> [b] -> [(a, b)]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- unzip :: [(a, b)] -> ([a], [b])
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- lines :: String -> [String]
- words :: String -> [String]
- unlines :: [String] -> String
- unwords :: [String] -> String
- type ShowS = String -> String
- class Show a where
- shows :: Show a => a -> ShowS
- showChar :: Char -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- type ReadS a = String -> [(a, String)]
- class Read a where
- reads :: Read a => ReadS a
- readParen :: Bool -> ReadS a -> ReadS a
- read :: Read a => String -> a
- lex :: ReadS String
- data IO a
- putChar :: Char -> IO ()
- putStr :: String -> IO ()
- putStrLn :: String -> IO ()
- print :: Show a => a -> IO ()
- getChar :: IO Char
- getLine :: IO String
- getContents :: IO String
- interact :: (String -> String) -> IO ()
- type FilePath = String
- readFile :: FilePath -> IO String
- writeFile :: FilePath -> String -> IO ()
- appendFile :: FilePath -> String -> IO ()
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- type IOError = IOException
- ioError :: IOError -> IO a
- userError :: String -> IOError
- class a ~# b => (a :: k) ~ (b :: k)
Standard types, classes and related functions
Basic data types
Instances
Bits Bool | Interpret @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Bool -> Bool -> Bool Source # (.|.) :: Bool -> Bool -> Bool Source # xor :: Bool -> Bool -> Bool Source # complement :: Bool -> Bool Source # shift :: Bool -> Int -> Bool Source # rotate :: Bool -> Int -> Bool Source # setBit :: Bool -> Int -> Bool Source # clearBit :: Bool -> Int -> Bool Source # complementBit :: Bool -> Int -> Bool Source # testBit :: Bool -> Int -> Bool Source # bitSizeMaybe :: Bool -> Maybe Int Source # bitSize :: Bool -> Int Source # isSigned :: Bool -> Bool Source # shiftL :: Bool -> Int -> Bool Source # unsafeShiftL :: Bool -> Int -> Bool Source # shiftR :: Bool -> Int -> Bool Source # unsafeShiftR :: Bool -> Int -> Bool Source # rotateL :: Bool -> Int -> Bool Source # | |||||
FiniteBits Bool | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Bool -> Int Source # countLeadingZeros :: Bool -> Int Source # countTrailingZeros :: Bool -> Int Source # | |||||
Data Bool | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool Source # toConstr :: Bool -> Constr Source # dataTypeOf :: Bool -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) Source # gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # | |||||
Bounded Bool | @since base-2.01 | ||||
Enum Bool | @since base-2.01 | ||||
Storable Bool | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Bool -> Int Source # alignment :: Bool -> Int Source # peekElemOff :: Ptr Bool -> Int -> IO Bool Source # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Bool Source # pokeByteOff :: Ptr b -> Int -> Bool -> IO () Source # | |||||
Generic Bool | |||||
Defined in GHC.Internal.Generics | |||||
SingKind Bool | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Ix Bool | @since base-2.01 | ||||
Defined in GHC.Internal.Ix | |||||
Read Bool | @since base-2.01 | ||||
Show Bool | @since base-2.01 | ||||
Eq Bool | |||||
Ord Bool | |||||
SingI 'False | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
SingI 'True | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type DemoteRep Bool | |||||
Defined in GHC.Internal.Generics | |||||
type Rep Bool | @since base-4.6.0.0 | ||||
data Sing (a :: Bool) | |||||
The Maybe
type encapsulates an optional value. A value of type
either contains a value of type Maybe
aa
(represented as
),
or it is empty (represented as Just
aNothing
). Using Maybe
is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error
.
The Maybe
type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing
. A richer
error monad can be built using the Either
type.
Instances
MonadZip Maybe Source # | Since: base-4.8.0.0 | ||||
Eq1 Maybe Source # | Since: base-4.9.0.0 | ||||
Ord1 Maybe Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
Read1 Maybe Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] Source # | |||||
Show1 Maybe Source # | Since: base-4.9.0.0 | ||||
Alternative Maybe | Picks the leftmost @since base-2.01 | ||||
Applicative Maybe | @since base-2.01 | ||||
Functor Maybe | @since base-2.01 | ||||
Monad Maybe | @since base-2.01 | ||||
MonadPlus Maybe | Picks the leftmost @since base-2.01 | ||||
MonadFail Maybe | @since base-4.9.0.0 | ||||
MonadFix Maybe | @since base-2.01 | ||||
Foldable Maybe | @since base-2.01 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |||||
Traversable Maybe | @since base-2.01 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Generic1 Maybe | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner @since base-2.01 | ||||
Semigroup a => Semigroup (Maybe a) | @since base-4.9.0.0 | ||||
Data a => Data (Maybe a) | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) Source # toConstr :: Maybe a -> Constr Source # dataTypeOf :: Maybe a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) Source # gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # | |||||
Generic (Maybe a) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
SingKind a => SingKind (Maybe a) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Read a => Read (Maybe a) | @since base-2.01 | ||||
Show a => Show (Maybe a) | @since base-2.01 | ||||
Eq a => Eq (Maybe a) | @since base-2.01 | ||||
Ord a => Ord (Maybe a) | @since base-2.01 | ||||
Defined in GHC.Internal.Maybe | |||||
SingI ('Nothing :: Maybe a) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
SingI a2 => SingI ('Just a2 :: Maybe a1) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep1 Maybe | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type DemoteRep (Maybe a) | |||||
Defined in GHC.Internal.Generics | |||||
type Rep (Maybe a) | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
data Sing (b :: Maybe a) | |||||
maybe :: b -> (a -> b) -> Maybe a -> b Source #
The maybe
function takes a default value, a function, and a Maybe
value. If the Maybe
value is Nothing
, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just
and returns the result.
Examples
Basic usage:
>>>
maybe False odd (Just 3)
True
>>>
maybe False odd Nothing
False
Read an integer from a string using readMaybe
. If we succeed,
return twice the integer; that is, apply (*2)
to it. If instead
we fail to parse an integer, return 0
by default:
>>>
import 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
""
The Either
type represents values with two possibilities: a value of
type
is either Either
a b
or Left
a
.Right
b
The Either
type is sometimes used to represent a value which is
either correct or an error; by convention, the Left
constructor is
used to hold an error value and the Right
constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type
is the type of values which can be either
a Either
String
Int
String
or an Int
. The Left
constructor can be used only on
String
s, and the Right
constructor can be used only on Int
s:
>>>
let s = Left "foo" :: Either String Int
>>>
s
Left "foo">>>
let n = Right 3 :: Either String Int
>>>
n
Right 3>>>
:type s
s :: Either String Int>>>
:type n
n :: Either String Int
The fmap
from our Functor
instance will ignore Left
values, but
will apply the supplied function to values contained in a Right
:
>>>
let s = Left "foo" :: Either String Int
>>>
let n = Right 3 :: Either String Int
>>>
fmap (*2) s
Left "foo">>>
fmap (*2) n
Right 6
The Monad
instance for Either
allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int
from a Char
, or fail.
>>>
import Data.Char ( digitToInt, isDigit )
>>>
:{
let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>
:}
The following should work, since both '1'
and '2'
can be
parsed as Int
s.
>>>
:{
let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>
:}
>>>
parseMultiple
Right 3
But the following should fail overall, since the first operation where
we attempt to parse 'm'
as an Int
will fail:
>>>
:{
let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>
:}
>>>
parseMultiple
Left "parse error"
Instances
Bifoldable Either Source # | Since: base-4.10.0.0 | ||||
Defined in Data.Bifoldable | |||||
Bifoldable1 Either Source # | |||||
Bifunctor Either Source # | Since: base-4.8.0.0 | ||||
Bitraversable Either Source # | Since: base-4.10.0.0 | ||||
Defined in Data.Bitraversable Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source # | |||||
Eq2 Either Source # | Since: base-4.9.0.0 | ||||
Ord2 Either Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
Read2 Either Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) Source # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] Source # | |||||
Show2 Either Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
Generic1 (Either a :: Type -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Eq a => Eq1 (Either a) Source # | Since: base-4.9.0.0 | ||||
Ord a => Ord1 (Either a) Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes | |||||
Read a => Read1 (Either a) Source # | Since: base-4.9.0.0 | ||||
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) Source # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] Source # | |||||
Show a => Show1 (Either a) Source # | Since: base-4.9.0.0 | ||||
Applicative (Either e) | @since base-3.0 | ||||
Defined in GHC.Internal.Data.Either | |||||
Functor (Either a) | @since base-3.0 | ||||
Monad (Either e) | @since base-4.4.0.0 | ||||
MonadFix (Either e) | @since base-4.3.0.0 | ||||
Foldable (Either a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |||||
Traversable (Either a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source # | |||||
Semigroup (Either a b) | @since base-4.9.0.0 | ||||
(Data a, Data b) => Data (Either a b) | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Either a b -> c (Either a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) Source # toConstr :: Either a b -> Constr Source # dataTypeOf :: Either a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # | |||||
Generic (Either a b) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
(Read a, Read b) => Read (Either a b) | @since base-3.0 | ||||
(Show a, Show b) => Show (Either a b) | @since base-3.0 | ||||
(Eq a, Eq b) => Eq (Either a b) | @since base-2.01 | ||||
(Ord a, Ord b) => Ord (Either a b) | @since base-2.01 | ||||
Defined in GHC.Internal.Data.Either Methods compare :: Either a b -> Either a b -> Ordering Source # (<) :: Either a b -> Either a b -> Bool Source # (<=) :: Either a b -> Either a b -> Bool Source # (>) :: Either a b -> Either a b -> Bool Source # (>=) :: Either a b -> Either a b -> Bool Source # | |||||
type Rep1 (Either a :: Type -> Type) | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |||||
type Rep (Either a b) | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics type Rep (Either a b) = D1 ('MetaData "Either" "GHC.Internal.Data.Either" "ghc-internal" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))) |
either :: (a -> c) -> (b -> c) -> Either a b -> c Source #
Case analysis for the Either
type.
If the value is
, apply the first function to Left
aa
;
if it is
, apply the second function to Right
bb
.
Examples
We create two values of type
, one using the
Either
String
Int
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
Instances
Monoid Ordering | @since base-2.01 |
Semigroup Ordering | @since base-4.9.0.0 |
Data Ordering | @since base-4.0.0.0 |
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering Source # toConstr :: Ordering -> Constr Source # dataTypeOf :: Ordering -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) Source # gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # | |
Bounded Ordering | @since base-2.01 |
Enum Ordering | @since base-2.01 |
Defined in GHC.Internal.Enum Methods succ :: Ordering -> Ordering Source # pred :: Ordering -> Ordering Source # toEnum :: Int -> Ordering Source # fromEnum :: Ordering -> Int Source # enumFrom :: Ordering -> [Ordering] Source # enumFromThen :: Ordering -> Ordering -> [Ordering] Source # enumFromTo :: Ordering -> Ordering -> [Ordering] Source # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source # | |
Generic Ordering | |
Defined in GHC.Internal.Generics | |
Ix Ordering | @since base-2.01 |
Defined in GHC.Internal.Ix | |
Read Ordering | @since base-2.01 |
Show Ordering | @since base-2.01 |
Eq Ordering | |
Ord Ordering | |
Defined in GHC.Classes | |
type Rep Ordering | @since base-4.6.0.0 |
The character type Char
represents Unicode codespace
and its elements are code points as in definitions
D9 and D10 of the Unicode Standard.
Character literals in Haskell are single-quoted: 'Q'
, 'Я'
or 'Ω'
.
To represent a single quote itself use '\''
, and to represent a backslash
use '\\'
. The full grammar can be found in the section 2.6 of the
Haskell 2010 Language Report.
To specify a character by its code point one can use decimal, hexadecimal
or octal notation: '\65'
, '\x41'
and '\o101'
are all alternative forms
of 'A'
. The largest code point is '\x10ffff'
.
There is a special escape syntax for ASCII control characters:
Escape | Alternatives | Meaning |
---|---|---|
'\NUL' | '\0' | null character |
'\SOH' | '\1' | start of heading |
'\STX' | '\2' | start of text |
'\ETX' | '\3' | end of text |
'\EOT' | '\4' | end of transmission |
'\ENQ' | '\5' | enquiry |
'\ACK' | '\6' | acknowledge |
'\BEL' | '\7' , '\a' | bell (alert) |
'\BS' | '\8' , '\b' | backspace |
'\HT' | '\9' , '\t' | horizontal tab |
'\LF' | '\10' , '\n' | line feed (new line) |
'\VT' | '\11' , '\v' | vertical tab |
'\FF' | '\12' , '\f' | form feed |
'\CR' | '\13' , '\r' | carriage return |
'\SO' | '\14' | shift out |
'\SI' | '\15' | shift in |
'\DLE' | '\16' | data link escape |
'\DC1' | '\17' | device control 1 |
'\DC2' | '\18' | device control 2 |
'\DC3' | '\19' | device control 3 |
'\DC4' | '\20' | device control 4 |
'\NAK' | '\21' | negative acknowledge |
'\SYN' | '\22' | synchronous idle |
'\ETB' | '\23' | end of transmission block |
'\CAN' | '\24' | cancel |
'\EM' | '\25' | end of medium |
'\SUB' | '\26' | substitute |
'\ESC' | '\27' | escape |
'\FS' | '\28' | file separator |
'\GS' | '\29' | group separator |
'\RS' | '\30' | record separator |
'\US' | '\31' | unit separator |
'\SP' | '\32' , ' ' | space |
'\DEL' | '\127' | delete |
Instances
IsChar Char Source # | Since: base-2.1 | ||||
PrintfArg Char Source # | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
Data Char | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char Source # toConstr :: Char -> Constr Source # dataTypeOf :: Char -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) Source # gmapT :: (forall b. Data b => b -> b) -> Char -> Char Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # | |||||
Bounded Char | @since base-2.01 | ||||
Enum Char | @since base-2.01 | ||||
Storable Char | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Char -> Int Source # alignment :: Char -> Int Source # peekElemOff :: Ptr Char -> Int -> IO Char Source # pokeElemOff :: Ptr Char -> Int -> Char -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Char Source # pokeByteOff :: Ptr b -> Int -> Char -> IO () Source # | |||||
Ix Char | @since base-2.01 | ||||
Defined in GHC.Internal.Ix | |||||
Read Char | @since base-2.01 | ||||
Show Char | @since base-2.01 | ||||
Eq Char | |||||
Ord Char | |||||
TestCoercion SChar | @since base-4.18.0.0 | ||||
Defined in GHC.Internal.TypeLits | |||||
TestEquality SChar | @since base-4.18.0.0 | ||||
Defined in GHC.Internal.TypeLits | |||||
Generic1 (URec Char :: k -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Foldable (UChar :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |||||
Traversable (UChar :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Functor (URec Char :: Type -> Type) | @since base-4.9.0.0 | ||||
Generic (URec Char p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Show (URec Char p) | @since base-4.9.0.0 | ||||
Eq (URec Char p) | @since base-4.9.0.0 | ||||
Ord (URec Char p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Char p -> URec Char p -> Ordering Source # (<) :: URec Char p -> URec Char p -> Bool Source # (<=) :: URec Char p -> URec Char p -> Bool Source # (>) :: URec Char p -> URec Char p -> Bool Source # (>=) :: URec Char p -> URec Char p -> Bool Source # | |||||
data URec Char (p :: k) | Used for marking occurrences of @since base-4.9.0.0 | ||||
type Compare (a :: Char) (b :: Char) | |||||
Defined in GHC.Internal.Data.Type.Ord | |||||
type Rep1 (URec Char :: k -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep (URec Char p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics |
String
is an alias for a list of characters.
String constants in Haskell are values of type String
.
That means if you write a string literal like "hello world"
,
it will have the type [Char]
, which is the same as String
.
Note: You can ask the compiler to automatically infer different types
with the -XOverloadedStrings
language extension, for example
"hello world" :: Text
. See IsString
for more information.
Because String
is just a list of characters, you can use normal list functions
to do basic string manipulation. See Data.List for operations on lists.
Performance considerations
[Char]
is a relatively memory-inefficient type.
It is a linked list of boxed word-size characters, internally it looks something like:
╭─────┬───┬──╮ ╭─────┬───┬──╮ ╭─────┬───┬──╮ ╭────╮ │ (:) │ │ ─┼─>│ (:) │ │ ─┼─>│ (:) │ │ ─┼─>│ [] │ ╰─────┴─┼─┴──╯ ╰─────┴─┼─┴──╯ ╰─────┴─┼─┴──╯ ╰────╯ v v v 'a' 'b' 'c'
The String
"abc" will use 5*3+1 = 16
(in general 5n+1
)
words of space in memory.
Furthermore, operations like (++)
(string concatenation) are O(n)
(in the left argument).
For historical reasons, the base
library uses String
in a lot of places
for the conceptual simplicity, but library code dealing with user-data
should use the text
package for Unicode text, or the the
bytestring package
for binary data.
Tuples
curry :: ((a, b) -> c) -> a -> b -> c Source #
Convert an uncurried function to a curried function.
Examples
>>>
curry fst 1 2
1
uncurry :: (a -> b -> c) -> (a, b) -> c Source #
uncurry
converts a curried function to a function on pairs.
Examples
>>>
uncurry (+) (1,2)
3
>>>
uncurry ($) (show, 1)
"1"
>>>
map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]
Basic type classes
The Eq
class defines equality (==
) and inequality (/=
).
All the basic datatypes exported by the Prelude are instances of Eq
,
and Eq
may be derived for any datatype whose constituents are also
instances of Eq
.
The Haskell Report defines no laws for Eq
. However, instances are
encouraged to follow these properties:
Instances
Eq ByteArray Source # | Since: base-4.17.0.0 |
Eq Timeout Source # | |
Eq BigNat | |
Eq Void | @since base-4.8.0.0 |
Eq ByteOrder | @since base-4.11.0.0 |
Eq ClosureType | |
Defined in GHC.Internal.ClosureTypes Methods (==) :: ClosureType -> ClosureType -> Bool Source # (/=) :: ClosureType -> ClosureType -> Bool Source # | |
Eq BlockReason | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync Methods (==) :: BlockReason -> BlockReason -> Bool Source # (/=) :: BlockReason -> BlockReason -> Bool Source # | |
Eq ThreadId | @since base-4.2.0.0 |
Eq ThreadStatus | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync Methods (==) :: ThreadStatus -> ThreadStatus -> Bool Source # (/=) :: ThreadStatus -> ThreadStatus -> Bool Source # | |
Eq Constr | Equality of constructors @since base-4.0.0.0 |
Eq ConstrRep | @since base-4.0.0.0 |
Eq DataRep | @since base-4.0.0.0 |
Eq Fixity | @since base-4.0.0.0 |
Eq All | @since base-2.01 |
Eq Any | @since base-2.01 |
Eq SomeTypeRep | |
Defined in GHC.Internal.Data.Typeable.Internal Methods (==) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # | |
Eq Unique | |
Eq Version | @since base-2.01 |
Eq ControlMessage | @since base-4.4.0.0 |
Eq Event | @since base-4.4.0.0 |
Eq EventLifetime | @since base-4.8.0.0 |
Eq Lifetime | @since base-4.8.1.0 |
Eq FdKey | @since base-4.4.0.0 |
Eq State | @since base-4.4.0.0 |
Eq TimeoutKey | |
Defined in GHC.Internal.Event.TimeOut Methods (==) :: TimeoutKey -> TimeoutKey -> Bool Source # (/=) :: TimeoutKey -> TimeoutKey -> Bool Source # | |
Eq State | @since base-4.7.0.0 |
Eq Unique | @since base-4.4.0.0 |
Eq ErrorCall | @since base-4.7.0.0 |
Eq ArithException | @since base-3.0 |
Defined in GHC.Internal.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool Source # (/=) :: ArithException -> ArithException -> Bool Source # | |
Eq SpecConstrAnnotation | @since base-4.3.0.0 |
Defined in GHC.Internal.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source # | |
Eq Fingerprint | @since base-4.4.0.0 |
Defined in GHC.Internal.Fingerprint.Type Methods (==) :: Fingerprint -> Fingerprint -> Bool Source # (/=) :: Fingerprint -> Fingerprint -> Bool Source # | |
Eq Errno | @since base-2.01 |
Eq CBool | |
Eq CChar | |
Eq CClock | |
Eq CDouble | |
Eq CFloat | |
Eq CInt | |
Eq CIntMax | |
Eq CIntPtr | |
Eq CLLong | |
Eq CLong | |
Eq CPtrdiff | |
Eq CSChar | |
Eq CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods (==) :: CSUSeconds -> CSUSeconds -> Bool Source # (/=) :: CSUSeconds -> CSUSeconds -> Bool Source # | |
Eq CShort | |
Eq CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods (==) :: CSigAtomic -> CSigAtomic -> Bool Source # (/=) :: CSigAtomic -> CSigAtomic -> Bool Source # | |
Eq CSize | |
Eq CTime | |
Eq CUChar | |
Eq CUInt | |
Eq CUIntMax | |
Eq CUIntPtr | |
Eq CULLong | |
Eq CULong | |
Eq CUSeconds | |
Eq CUShort | |
Eq CWchar | |
Eq IntPtr | |
Eq WordPtr | |
Eq Associativity | @since base-4.6.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: Associativity -> Associativity -> Bool Source # (/=) :: Associativity -> Associativity -> Bool Source # | |
Eq DecidedStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # | |
Eq Fixity | @since base-4.6.0.0 |
Eq SourceStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool Source # (/=) :: SourceStrictness -> SourceStrictness -> Bool Source # | |
Eq SourceUnpackedness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # | |
Eq MaskingState | @since base-4.3.0.0 |
Defined in GHC.Internal.IO Methods (==) :: MaskingState -> MaskingState -> Bool Source # (/=) :: MaskingState -> MaskingState -> Bool Source # | |
Eq BufferState | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Buffer Methods (==) :: BufferState -> BufferState -> Bool Source # (/=) :: BufferState -> BufferState -> Bool Source # | |
Eq IODeviceType | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Device Methods (==) :: IODeviceType -> IODeviceType -> Bool Source # (/=) :: IODeviceType -> IODeviceType -> Bool Source # | |
Eq SeekMode | @since base-4.2.0.0 |
Eq CodingProgress | @since base-4.4.0.0 |
Defined in GHC.Internal.IO.Encoding.Types Methods (==) :: CodingProgress -> CodingProgress -> Bool Source # (/=) :: CodingProgress -> CodingProgress -> Bool Source # | |
Eq ArrayException | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool Source # (/=) :: ArrayException -> ArrayException -> Bool Source # | |
Eq AsyncException | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool Source # (/=) :: AsyncException -> AsyncException -> Bool Source # | |
Eq ExitCode | |
Eq IOErrorType | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool Source # (/=) :: IOErrorType -> IOErrorType -> Bool Source # | |
Eq IOException | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception Methods (==) :: IOException -> IOException -> Bool Source # (/=) :: IOException -> IOException -> Bool Source # | |
Eq HandlePosn | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Handle Methods (==) :: HandlePosn -> HandlePosn -> Bool Source # (/=) :: HandlePosn -> HandlePosn -> Bool Source # | |
Eq BufferMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types Methods (==) :: BufferMode -> BufferMode -> Bool Source # (/=) :: BufferMode -> BufferMode -> Bool Source # | |
Eq Handle | @since base-4.1.0.0 |
Eq Newline | @since base-4.2.0.0 |
Eq NewlineMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types Methods (==) :: NewlineMode -> NewlineMode -> Bool Source # (/=) :: NewlineMode -> NewlineMode -> Bool Source # | |
Eq IOMode | @since base-4.2.0.0 |
Eq InfoProv | |
Eq Int16 | @since base-2.01 |
Eq Int32 | @since base-2.01 |
Eq Int64 | @since base-2.01 |
Eq Int8 | @since base-2.01 |
Eq IoSubSystem | |
Defined in GHC.Internal.RTS.Flags Methods (==) :: IoSubSystem -> IoSubSystem -> Bool Source # (/=) :: IoSubSystem -> IoSubSystem -> Bool Source # | |
Eq StackEntry | |
Defined in GHC.Internal.Stack.CloneStack Methods (==) :: StackEntry -> StackEntry -> Bool Source # (/=) :: StackEntry -> StackEntry -> Bool Source # | |
Eq SrcLoc | @since base-4.9.0.0 |
Eq CBlkCnt | |
Eq CBlkSize | |
Eq CCc | |
Eq CClockId | |
Eq CDev | |
Eq CFsBlkCnt | |
Eq CFsFilCnt | |
Eq CGid | |
Eq CId | |
Eq CIno | |
Eq CKey | |
Eq CMode | |
Eq CNfds | |
Eq CNlink | |
Eq COff | |
Eq CPid | |
Eq CRLim | |
Eq CSocklen | |
Eq CSpeed | |
Eq CSsize | |
Eq CTcflag | |
Eq CTimer | |
Eq CUid | |
Eq Fd | |
Eq Lexeme | @since base-2.01 |
Eq Number | @since base-4.6.0.0 |
Eq SomeChar | |
Eq SomeSymbol | @since base-4.7.0.0 |
Defined in GHC.Internal.TypeLits Methods (==) :: SomeSymbol -> SomeSymbol -> Bool Source # (/=) :: SomeSymbol -> SomeSymbol -> Bool Source # | |
Eq SomeNat | @since base-4.7.0.0 |
Eq GeneralCategory | @since base-2.01 |
Defined in GHC.Internal.Unicode Methods (==) :: GeneralCategory -> GeneralCategory -> Bool Source # (/=) :: GeneralCategory -> GeneralCategory -> Bool Source # | |
Eq Word16 | @since base-2.01 |
Eq Word32 | @since base-2.01 |
Eq Word64 | @since base-2.01 |
Eq Word8 | @since base-2.01 |
Eq Module | |
Eq Ordering | |
Eq TrName | |
Eq TyCon | |
Eq Integer | |
Eq Natural | |
Eq () | |
Eq Bool | |
Eq Char | |
Eq Double | Note that due to the presence of
Also note that
|
Eq Float | Note that due to the presence of
Also note that
|
Eq Int | |
Eq Word | |
Eq (Chan a) Source # | Since: base-4.4.0.0 |
Eq (MutableByteArray s) Source # | Since: base-4.17.0.0 |
Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool Source # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool Source # | |
Eq a => Eq (Complex a) Source # | Since: base-2.1 |
Eq a => Eq (First a) Source # | Since: base-4.9.0.0 |
Eq a => Eq (Last a) Source # | Since: base-4.9.0.0 |
Eq a => Eq (Max a) Source # | Since: base-4.9.0.0 |
Eq a => Eq (Min a) Source # | Since: base-4.9.0.0 |
Eq m => Eq (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # | |
Eq a => Eq (NonEmpty a) | @since base-4.9.0.0 |
Eq (TVar a) | @since base-4.8.0.0 |
Eq a => Eq (And a) | @since base-4.16 |
Eq a => Eq (Iff a) | @since base-4.16 |
Eq a => Eq (Ior a) | @since base-4.16 |
Eq a => Eq (Xor a) | @since base-4.16 |
Eq a => Eq (Identity a) | @since base-4.8.0.0 |
Eq a => Eq (First a) | @since base-2.01 |
Eq a => Eq (Last a) | @since base-2.01 |
Eq a => Eq (Down a) | @since base-4.6.0.0 |
Eq a => Eq (Dual a) | @since base-2.01 |
Eq a => Eq (Product a) | @since base-2.01 |
Eq a => Eq (Sum a) | @since base-2.01 |
Eq (ConstPtr a) | |
Eq (ForeignPtr a) | @since base-2.01 |
Defined in GHC.Internal.ForeignPtr Methods (==) :: ForeignPtr a -> ForeignPtr a -> Bool Source # (/=) :: ForeignPtr a -> ForeignPtr a -> Bool Source # | |
Eq a => Eq (ZipList a) | @since base-4.7.0.0 |
Eq p => Eq (Par1 p) | @since base-4.7.0.0 |
Eq (IOPort a) | @since base-4.1.0.0 |
Eq (IORef a) | Pointer equality. @since base-4.0.0.0 |
Eq (MVar a) | Compares the underlying pointers. @since base-4.1.0.0 |
Eq (FunPtr a) | |
Eq (Ptr a) | @since base-2.01 |
Eq a => Eq (Ratio a) | @since base-2.01 |
Eq (StablePtr a) | @since base-2.01 |
Eq (StableName a) | @since base-2.01 |
Defined in GHC.Internal.StableName Methods (==) :: StableName a -> StableName a -> Bool Source # (/=) :: StableName a -> StableName a -> Bool Source # | |
Eq (SChar c) | @since base-4.19.0.0 |
Eq (SSymbol s) | @since base-4.19.0.0 |
Eq (SNat n) | @since base-4.19.0.0 |
Eq a => Eq (Maybe a) | @since base-2.01 |
Eq a => Eq (Solo a) | |
Eq a => Eq [a] | |
Eq (Fixed a) Source # | Since: base-2.1 |
Eq a => Eq (Arg a b) Source # | Since: base-4.9.0.0 |
(Ix i, Eq e) => Eq (Array i e) | @since base-2.01 |
(Eq a, Eq b) => Eq (Either a b) | @since base-2.01 |
Eq (Proxy s) | @since base-4.7.0.0 |
Eq (TypeRep a) | @since base-2.01 |
Eq (U1 p) | @since base-4.9.0.0 |
Eq (V1 p) | @since base-4.9.0.0 |
Eq (IOArray i e) | @since base-4.1.0.0 |
Eq (STRef s a) | Pointer equality. @since base-2.01 |
(Eq a, Eq b) => Eq (a, b) | |
Eq (STArray s i e) | @since base-2.01 |
Eq a => Eq (Const a b) | @since base-4.9.0.0 |
Eq (f a) => Eq (Ap f a) | @since base-4.12.0.0 |
Eq (f a) => Eq (Alt f a) | @since base-4.8.0.0 |
Eq (Coercion a b) | @since base-4.7.0.0 |
Eq (a :~: b) | @since base-4.7.0.0 |
Eq (OrderingI a b) | |
(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a) | @since base-4.18.0.0 |
Defined in GHC.Internal.Generics Methods (==) :: Generically1 f a -> Generically1 f a -> Bool Source # (/=) :: Generically1 f a -> Generically1 f a -> Bool Source # | |
Eq (f p) => Eq (Rec1 f p) | @since base-4.7.0.0 |
Eq (URec (Ptr ()) p) | @since base-4.9.0.0 |
Eq (URec Char p) | @since base-4.9.0.0 |
Eq (URec Double p) | @since base-4.9.0.0 |
Eq (URec Float p) | |
Eq (URec Int p) | @since base-4.9.0.0 |
Eq (URec Word p) | @since base-4.9.0.0 |
(Eq a, Eq b, Eq c) => Eq (a, b, c) | |
(Eq (f a), Eq (g a)) => Eq (Product f g a) Source # | Since: base-4.18.0.0 |
(Eq (f a), Eq (g a)) => Eq (Sum f g a) Source # | Since: base-4.18.0.0 |
Eq (a :~~: b) | @since base-4.10.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | @since base-4.7.0.0 |
(Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | @since base-4.7.0.0 |
Eq c => Eq (K1 i c p) | @since base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
Eq (f (g a)) => Eq (Compose f g a) Source # | Since: base-4.18.0.0 |
Eq (f (g p)) => Eq ((f :.: g) p) | @since base-4.7.0.0 |
Eq (f p) => Eq (M1 i c f p) | @since base-4.7.0.0 |
(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Eq a => Ord a where Source #
The Ord
class is used for totally ordered datatypes.
Instances of Ord
can be derived for any user-defined datatype whose
constituent types are in Ord
. The declared order of the constructors in
the data declaration determines the ordering in derived Ord
instances. The
Ordering
datatype allows a single comparison to determine the precise
ordering of two objects.
Ord
, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x
=True
- Transitivity
- if
x <= y && y <= z
=True
, thenx <= z
=True
- Reflexivity
x <= x
=True
- Antisymmetry
- if
x <= y && y <= x
=True
, thenx == y
=True
The following operator interactions are expected to hold:
x >= y
=y <= x
x < y
=x <= y && x /= y
x > y
=y < x
x < y
=compare x y == LT
x > y
=compare x y == GT
x == y
=compare x y == EQ
min x y == if x <= y then x else y
=True
max x y == if x >= y then x else y
=True
Note that (7.) and (8.) do not require min
and max
to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==)
.
Minimal complete definition: either compare
or <=
.
Using compare
can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering Source #
(<) :: a -> a -> Bool infix 4 Source #
(<=) :: a -> a -> Bool infix 4 Source #
(>) :: a -> a -> Bool infix 4 Source #
Instances
Ord ByteArray Source # | Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions. Since: base-4.17.0.0 |
Defined in Data.Array.Byte | |
Ord BigNat | |
Ord Void | @since base-4.8.0.0 |
Ord ByteOrder | @since base-4.11.0.0 |
Defined in GHC.Internal.ByteOrder | |
Ord ClosureType | |
Defined in GHC.Internal.ClosureTypes Methods compare :: ClosureType -> ClosureType -> Ordering Source # (<) :: ClosureType -> ClosureType -> Bool Source # (<=) :: ClosureType -> ClosureType -> Bool Source # (>) :: ClosureType -> ClosureType -> Bool Source # (>=) :: ClosureType -> ClosureType -> Bool Source # max :: ClosureType -> ClosureType -> ClosureType Source # min :: ClosureType -> ClosureType -> ClosureType Source # | |
Ord BlockReason | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync Methods compare :: BlockReason -> BlockReason -> Ordering Source # (<) :: BlockReason -> BlockReason -> Bool Source # (<=) :: BlockReason -> BlockReason -> Bool Source # (>) :: BlockReason -> BlockReason -> Bool Source # (>=) :: BlockReason -> BlockReason -> Bool Source # max :: BlockReason -> BlockReason -> BlockReason Source # min :: BlockReason -> BlockReason -> BlockReason Source # | |
Ord ThreadId | @since base-4.2.0.0 |
Defined in GHC.Internal.Conc.Sync | |
Ord ThreadStatus | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync Methods compare :: ThreadStatus -> ThreadStatus -> Ordering Source # (<) :: ThreadStatus -> ThreadStatus -> Bool Source # (<=) :: ThreadStatus -> ThreadStatus -> Bool Source # (>) :: ThreadStatus -> ThreadStatus -> Bool Source # (>=) :: ThreadStatus -> ThreadStatus -> Bool Source # max :: ThreadStatus -> ThreadStatus -> ThreadStatus Source # min :: ThreadStatus -> ThreadStatus -> ThreadStatus Source # | |
Ord All | @since base-2.01 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord Any | @since base-2.01 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord SomeTypeRep | |
Defined in GHC.Internal.Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering Source # (<) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>) :: SomeTypeRep -> SomeTypeRep -> Bool Source # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool Source # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source # | |
Ord Unique | |
Ord Version | @since base-2.01 |
Defined in GHC.Internal.Data.Version | |
Ord TimeoutKey | |
Defined in GHC.Internal.Event.TimeOut Methods compare :: TimeoutKey -> TimeoutKey -> Ordering Source # (<) :: TimeoutKey -> TimeoutKey -> Bool Source # (<=) :: TimeoutKey -> TimeoutKey -> Bool Source # (>) :: TimeoutKey -> TimeoutKey -> Bool Source # (>=) :: TimeoutKey -> TimeoutKey -> Bool Source # max :: TimeoutKey -> TimeoutKey -> TimeoutKey Source # min :: TimeoutKey -> TimeoutKey -> TimeoutKey Source # | |
Ord Unique | @since base-4.4.0.0 |
Ord ErrorCall | @since base-4.7.0.0 |
Defined in GHC.Internal.Exception | |
Ord ArithException | @since base-3.0 |
Defined in GHC.Internal.Exception.Type Methods compare :: ArithException -> ArithException -> Ordering Source # (<) :: ArithException -> ArithException -> Bool Source # (<=) :: ArithException -> ArithException -> Bool Source # (>) :: ArithException -> ArithException -> Bool Source # (>=) :: ArithException -> ArithException -> Bool Source # max :: ArithException -> ArithException -> ArithException Source # min :: ArithException -> ArithException -> ArithException Source # | |
Ord Fingerprint | @since base-4.4.0.0 |
Defined in GHC.Internal.Fingerprint.Type Methods compare :: Fingerprint -> Fingerprint -> Ordering Source # (<) :: Fingerprint -> Fingerprint -> Bool Source # (<=) :: Fingerprint -> Fingerprint -> Bool Source # (>) :: Fingerprint -> Fingerprint -> Bool Source # (>=) :: Fingerprint -> Fingerprint -> Bool Source # max :: Fingerprint -> Fingerprint -> Fingerprint Source # min :: Fingerprint -> Fingerprint -> Fingerprint Source # | |
Ord CBool | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CChar | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CClock | |
Ord CDouble | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CFloat | |
Ord CInt | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CIntMax | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CIntPtr | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CLLong | |
Ord CLong | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CPtrdiff | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CSChar | |
Ord CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types Methods compare :: CSUSeconds -> CSUSeconds -> Ordering Source # (<) :: CSUSeconds -> CSUSeconds -> Bool Source # (<=) :: CSUSeconds -> CSUSeconds -> Bool Source # (>) :: CSUSeconds -> CSUSeconds -> Bool Source # (>=) :: CSUSeconds -> CSUSeconds -> Bool Source # max :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # min :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # | |
Ord CShort | |
Ord CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types Methods compare :: CSigAtomic -> CSigAtomic -> Ordering Source # (<) :: CSigAtomic -> CSigAtomic -> Bool Source # (<=) :: CSigAtomic -> CSigAtomic -> Bool Source # (>) :: CSigAtomic -> CSigAtomic -> Bool Source # (>=) :: CSigAtomic -> CSigAtomic -> Bool Source # max :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # min :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # | |
Ord CSize | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CTime | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CUChar | |
Ord CUInt | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CUIntMax | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CUIntPtr | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CULLong | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CULong | |
Ord CUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CUShort | |
Defined in GHC.Internal.Foreign.C.Types | |
Ord CWchar | |
Ord IntPtr | |
Ord WordPtr | |
Defined in GHC.Internal.Foreign.Ptr | |
Ord Associativity | @since base-4.6.0.0 |
Defined in GHC.Internal.Generics Methods compare :: Associativity -> Associativity -> Ordering Source # (<) :: Associativity -> Associativity -> Bool Source # (<=) :: Associativity -> Associativity -> Bool Source # (>) :: Associativity -> Associativity -> Bool Source # (>=) :: Associativity -> Associativity -> Bool Source # max :: Associativity -> Associativity -> Associativity Source # min :: Associativity -> Associativity -> Associativity Source # | |
Ord DecidedStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering Source # (<) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>) :: DecidedStrictness -> DecidedStrictness -> Bool Source # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool Source # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source # | |
Ord Fixity | @since base-4.6.0.0 |
Ord SourceStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering Source # (<) :: SourceStrictness -> SourceStrictness -> Bool Source # (<=) :: SourceStrictness -> SourceStrictness -> Bool Source # (>) :: SourceStrictness -> SourceStrictness -> Bool Source # (>=) :: SourceStrictness -> SourceStrictness -> Bool Source # max :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # min :: SourceStrictness -> SourceStrictness -> SourceStrictness Source # | |
Ord SourceUnpackedness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering Source # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source # | |
Ord SeekMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Device | |
Ord ArrayException | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering Source # (<) :: ArrayException -> ArrayException -> Bool Source # (<=) :: ArrayException -> ArrayException -> Bool Source # (>) :: ArrayException -> ArrayException -> Bool Source # (>=) :: ArrayException -> ArrayException -> Bool Source # max :: ArrayException -> ArrayException -> ArrayException Source # min :: ArrayException -> ArrayException -> ArrayException Source # | |
Ord AsyncException | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering Source # (<) :: AsyncException -> AsyncException -> Bool Source # (<=) :: AsyncException -> AsyncException -> Bool Source # (>) :: AsyncException -> AsyncException -> Bool Source # (>=) :: AsyncException -> AsyncException -> Bool Source # max :: AsyncException -> AsyncException -> AsyncException Source # min :: AsyncException -> AsyncException -> AsyncException Source # | |
Ord ExitCode | |
Defined in GHC.Internal.IO.Exception | |
Ord BufferMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types Methods compare :: BufferMode -> BufferMode -> Ordering Source # (<) :: BufferMode -> BufferMode -> Bool Source # (<=) :: BufferMode -> BufferMode -> Bool Source # (>) :: BufferMode -> BufferMode -> Bool Source # (>=) :: BufferMode -> BufferMode -> Bool Source # max :: BufferMode -> BufferMode -> BufferMode Source # min :: BufferMode -> BufferMode -> BufferMode Source # | |
Ord Newline | @since base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Ord NewlineMode | @since base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types Methods compare :: NewlineMode -> NewlineMode -> Ordering Source # (<) :: NewlineMode -> NewlineMode -> Bool Source # (<=) :: NewlineMode -> NewlineMode -> Bool Source # (>) :: NewlineMode -> NewlineMode -> Bool Source # (>=) :: NewlineMode -> NewlineMode -> Bool Source # max :: NewlineMode -> NewlineMode -> NewlineMode Source # min :: NewlineMode -> NewlineMode -> NewlineMode Source # | |
Ord IOMode | @since base-4.2.0.0 |
Ord Int16 | @since base-2.01 |
Defined in GHC.Internal.Int | |
Ord Int32 | @since base-2.01 |
Defined in GHC.Internal.Int | |
Ord Int64 | @since base-2.01 |
Defined in GHC.Internal.Int | |
Ord Int8 | @since base-2.01 |
Ord CBlkCnt | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CBlkSize | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CCc | |
Ord CClockId | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CDev | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CFsBlkCnt | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CFsFilCnt | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CGid | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CId | |
Ord CIno | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CKey | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CMode | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CNfds | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CNlink | |
Defined in GHC.Internal.System.Posix.Types | |
Ord COff | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CPid | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CRLim | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CSocklen | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CSpeed | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CSsize | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CTcflag | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CTimer | |
Defined in GHC.Internal.System.Posix.Types | |
Ord CUid | |
Defined in GHC.Internal.System.Posix.Types | |
Ord Fd | |
Ord SomeChar | |
Defined in GHC.Internal.TypeLits | |
Ord SomeSymbol | @since base-4.7.0.0 |
Defined in GHC.Internal.TypeLits Methods compare :: SomeSymbol -> SomeSymbol -> Ordering Source # (<) :: SomeSymbol -> SomeSymbol -> Bool Source # (<=) :: SomeSymbol -> SomeSymbol -> Bool Source # (>) :: SomeSymbol -> SomeSymbol -> Bool Source # (>=) :: SomeSymbol -> SomeSymbol -> Bool Source # max :: SomeSymbol -> SomeSymbol -> SomeSymbol Source # min :: SomeSymbol -> SomeSymbol -> SomeSymbol Source # | |
Ord SomeNat | @since base-4.7.0.0 |
Defined in GHC.Internal.TypeNats | |
Ord GeneralCategory | @since base-2.01 |
Defined in GHC.Internal.Unicode Methods compare :: GeneralCategory -> GeneralCategory -> Ordering Source # (<) :: GeneralCategory -> GeneralCategory -> Bool Source # (<=) :: GeneralCategory -> GeneralCategory -> Bool Source # (>) :: GeneralCategory -> GeneralCategory -> Bool Source # (>=) :: GeneralCategory -> GeneralCategory -> Bool Source # max :: GeneralCategory -> GeneralCategory -> GeneralCategory Source # min :: GeneralCategory -> GeneralCategory -> GeneralCategory Source # | |
Ord Word16 | @since base-2.01 |
Ord Word32 | @since base-2.01 |
Ord Word64 | @since base-2.01 |
Ord Word8 | @since base-2.01 |
Defined in GHC.Internal.Word | |
Ord Ordering | |
Defined in GHC.Classes | |
Ord TyCon | |
Defined in GHC.Classes | |
Ord Integer | |
Ord Natural | |
Ord () | |
Ord Bool | |
Ord Char | |
Ord Double | IEEE 754 IEEE 754-2008, section 5.11 requires that if at least one of arguments of
IEEE 754-2008, section 5.10 defines Thus, users must be extremely cautious when using Moving further, the behaviour of IEEE 754-2008 compliant |
Ord Float | See |
Defined in GHC.Classes | |
Ord Int | |
Ord Word | |
Ord a => Ord (First a) Source # | Since: base-4.9.0.0 |
Ord a => Ord (Last a) Source # | Since: base-4.9.0.0 |
Ord a => Ord (Max a) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Ord a => Ord (Min a) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Ord m => Ord (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # | |
Ord a => Ord (NonEmpty a) | @since base-4.9.0.0 |
Defined in GHC.Internal.Base Methods compare :: NonEmpty a -> NonEmpty a -> Ordering Source # (<) :: NonEmpty a -> NonEmpty a -> Bool Source # (<=) :: NonEmpty a -> NonEmpty a -> Bool Source # (>) :: NonEmpty a -> NonEmpty a -> Bool Source # (>=) :: NonEmpty a -> NonEmpty a -> Bool Source # | |
Ord a => Ord (Identity a) | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods compare :: Identity a -> Identity a -> Ordering Source # (<) :: Identity a -> Identity a -> Bool Source # (<=) :: Identity a -> Identity a -> Bool Source # (>) :: Identity a -> Identity a -> Bool Source # (>=) :: Identity a -> Identity a -> Bool Source # | |
Ord a => Ord (First a) | @since base-2.01 |
Defined in GHC.Internal.Data.Monoid | |
Ord a => Ord (Last a) | @since base-2.01 |
Ord a => Ord (Down a) | @since base-4.6.0.0 |
Ord a => Ord (Dual a) | @since base-2.01 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord a => Ord (Product a) | @since base-2.01 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord a => Ord (Sum a) | @since base-2.01 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord (ConstPtr a) | |
Defined in GHC.Internal.Foreign.C.ConstPtr Methods compare :: ConstPtr a -> ConstPtr a -> Ordering Source # (<) :: ConstPtr a -> ConstPtr a -> Bool Source # (<=) :: ConstPtr a -> ConstPtr a -> Bool Source # (>) :: ConstPtr a -> ConstPtr a -> Bool Source # (>=) :: ConstPtr a -> ConstPtr a -> Bool Source # | |
Ord (ForeignPtr a) | @since base-2.01 |
Defined in GHC.Internal.ForeignPtr Methods compare :: ForeignPtr a -> ForeignPtr a -> Ordering Source # (<) :: ForeignPtr a -> ForeignPtr a -> Bool Source # (<=) :: ForeignPtr a -> ForeignPtr a -> Bool Source # (>) :: ForeignPtr a -> ForeignPtr a -> Bool Source # (>=) :: ForeignPtr a -> ForeignPtr a -> Bool Source # max :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a Source # min :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a Source # | |
Ord a => Ord (ZipList a) | @since base-4.7.0.0 |
Defined in GHC.Internal.Functor.ZipList | |
Ord p => Ord (Par1 p) | @since base-4.7.0.0 |
Ord (FunPtr a) | |
Defined in GHC.Internal.Ptr | |
Ord (Ptr a) | @since base-2.01 |
Defined in GHC.Internal.Ptr | |
Integral a => Ord (Ratio a) | @since base-2.0.1 |
Defined in GHC.Internal.Real | |
Ord (SChar c) | @since base-4.19.0.0 |
Defined in GHC.Internal.TypeLits | |
Ord (SSymbol s) | @since base-4.19.0.0 |
Defined in GHC.Internal.TypeLits | |
Ord (SNat n) | @since base-4.19.0.0 |
Ord a => Ord (Maybe a) | @since base-2.01 |
Defined in GHC.Internal.Maybe | |
Ord a => Ord (Solo a) | |
Ord a => Ord [a] | |
Ord (Fixed a) Source # | Since: base-2.1 |
Ord a => Ord (Arg a b) Source # | Since: base-4.9.0.0 |
(Ix i, Ord e) => Ord (Array i e) | @since base-2.01 |
Defined in GHC.Internal.Arr | |
(Ord a, Ord b) => Ord (Either a b) | @since base-2.01 |
Defined in GHC.Internal.Data.Either Methods compare :: Either a b -> Either a b -> Ordering Source # (<) :: Either a b -> Either a b -> Bool Source # (<=) :: Either a b -> Either a b -> Bool Source # (>) :: Either a b -> Either a b -> Bool Source # (>=) :: Either a b -> Either a b -> Bool Source # | |
Ord (Proxy s) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Proxy | |
Ord (TypeRep a) | @since base-4.4.0.0 |
Defined in GHC.Internal.Data.Typeable.Internal | |
Ord (U1 p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
Ord (V1 p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
(Ord a, Ord b) => Ord (a, b) | |
Ord a => Ord (Const a b) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const | |
Ord (f a) => Ord (Ap f a) | @since base-4.12.0.0 |
Ord (f a) => Ord (Alt f a) | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Ord (Coercion a b) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Type.Coercion Methods compare :: Coercion a b -> Coercion a b -> Ordering Source # (<) :: Coercion a b -> Coercion a b -> Bool Source # (<=) :: Coercion a b -> Coercion a b -> Bool Source # (>) :: Coercion a b -> Coercion a b -> Bool Source # (>=) :: Coercion a b -> Coercion a b -> Bool Source # max :: Coercion a b -> Coercion a b -> Coercion a b Source # min :: Coercion a b -> Coercion a b -> Coercion a b Source # | |
Ord (a :~: b) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Type.Equality | |
(Generic1 f, Ord (Rep1 f a)) => Ord (Generically1 f a) | @since base-4.18.0.0 |
Defined in GHC.Internal.Generics Methods compare :: Generically1 f a -> Generically1 f a -> Ordering Source # (<) :: Generically1 f a -> Generically1 f a -> Bool Source # (<=) :: Generically1 f a -> Generically1 f a -> Bool Source # (>) :: Generically1 f a -> Generically1 f a -> Bool Source # (>=) :: Generically1 f a -> Generically1 f a -> Bool Source # max :: Generically1 f a -> Generically1 f a -> Generically1 f a Source # min :: Generically1 f a -> Generically1 f a -> Generically1 f a Source # | |
Ord (f p) => Ord (Rec1 f p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
Ord (URec (Ptr ()) p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering Source # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source # | |
Ord (URec Char p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Char p -> URec Char p -> Ordering Source # (<) :: URec Char p -> URec Char p -> Bool Source # (<=) :: URec Char p -> URec Char p -> Bool Source # (>) :: URec Char p -> URec Char p -> Bool Source # (>=) :: URec Char p -> URec Char p -> Bool Source # | |
Ord (URec Double p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Double p -> URec Double p -> Ordering Source # (<) :: URec Double p -> URec Double p -> Bool Source # (<=) :: URec Double p -> URec Double p -> Bool Source # (>) :: URec Double p -> URec Double p -> Bool Source # (>=) :: URec Double p -> URec Double p -> Bool Source # max :: URec Double p -> URec Double p -> URec Double p Source # min :: URec Double p -> URec Double p -> URec Double p Source # | |
Ord (URec Float p) | |
Defined in GHC.Internal.Generics Methods compare :: URec Float p -> URec Float p -> Ordering Source # (<) :: URec Float p -> URec Float p -> Bool Source # (<=) :: URec Float p -> URec Float p -> Bool Source # (>) :: URec Float p -> URec Float p -> Bool Source # (>=) :: URec Float p -> URec Float p -> Bool Source # max :: URec Float p -> URec Float p -> URec Float p Source # min :: URec Float p -> URec Float p -> URec Float p Source # | |
Ord (URec Int p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Int p -> URec Int p -> Ordering Source # (<) :: URec Int p -> URec Int p -> Bool Source # (<=) :: URec Int p -> URec Int p -> Bool Source # (>) :: URec Int p -> URec Int p -> Bool Source # (>=) :: URec Int p -> URec Int p -> Bool Source # | |
Ord (URec Word p) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics Methods compare :: URec Word p -> URec Word p -> Ordering Source # (<) :: URec Word p -> URec Word p -> Bool Source # (<=) :: URec Word p -> URec Word p -> Bool Source # (>) :: URec Word p -> URec Word p -> Bool Source # (>=) :: URec Word p -> URec Word p -> Bool Source # | |
(Ord a, Ord b, Ord c) => Ord (a, b, c) | |
Defined in GHC.Classes | |
(Ord (f a), Ord (g a)) => Ord (Product f g a) Source # | Since: base-4.18.0.0 |
Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering Source # (<) :: Product f g a -> Product f g a -> Bool Source # (<=) :: Product f g a -> Product f g a -> Bool Source # (>) :: Product f g a -> Product f g a -> Bool Source # (>=) :: Product f g a -> Product f g a -> Bool Source # max :: Product f g a -> Product f g a -> Product f g a Source # min :: Product f g a -> Product f g a -> Product f g a Source # | |
(Ord (f a), Ord (g a)) => Ord (Sum f g a) Source # | Since: base-4.18.0.0 |
Defined in Data.Functor.Sum | |
Ord (a :~~: b) | @since base-4.10.0.0 |
Defined in GHC.Internal.Data.Type.Equality Methods compare :: (a :~~: b) -> (a :~~: b) -> Ordering Source # (<) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (<=) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (>) :: (a :~~: b) -> (a :~~: b) -> Bool Source # (>=) :: (a :~~: b) -> (a :~~: b) -> Bool Source # | |
(Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :*: g) p -> (f :*: g) p -> Ordering Source # (<) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (<=) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (>) :: (f :*: g) p -> (f :*: g) p -> Bool Source # (>=) :: (f :*: g) p -> (f :*: g) p -> Bool Source # | |
(Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :+: g) p -> (f :+: g) p -> Ordering Source # (<) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (<=) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (>) :: (f :+: g) p -> (f :+: g) p -> Bool Source # (>=) :: (f :+: g) p -> (f :+: g) p -> Bool Source # | |
Ord c => Ord (K1 i c p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics | |
(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering Source # (<) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (>) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # (>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source # max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # | |
Ord (f (g a)) => Ord (Compose f g a) Source # | Since: base-4.18.0.0 |
Defined in Data.Functor.Compose Methods compare :: Compose f g a -> Compose f g a -> Ordering Source # (<) :: Compose f g a -> Compose f g a -> Bool Source # (<=) :: Compose f g a -> Compose f g a -> Bool Source # (>) :: Compose f g a -> Compose f g a -> Bool Source # (>=) :: Compose f g a -> Compose f g a -> Bool Source # max :: Compose f g a -> Compose f g a -> Compose f g a Source # min :: Compose f g a -> Compose f g a -> Compose f g a Source # | |
Ord (f (g p)) => Ord ((f :.: g) p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: (f :.: g) p -> (f :.: g) p -> Ordering Source # (<) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (<=) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (>) :: (f :.: g) p -> (f :.: g) p -> Bool Source # (>=) :: (f :.: g) p -> (f :.: g) p -> Bool Source # | |
Ord (f p) => Ord (M1 i c f p) | @since base-4.7.0.0 |
Defined in GHC.Internal.Generics Methods compare :: M1 i c f p -> M1 i c f p -> Ordering Source # (<) :: M1 i c f p -> M1 i c f p -> Bool Source # (<=) :: M1 i c f p -> M1 i c f p -> Bool Source # (>) :: M1 i c f p -> M1 i c f p -> Bool Source # (>=) :: M1 i c f p -> M1 i c f p -> Bool Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering Source # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering Source # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering Source # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source # max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source # min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source # min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source # min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source # min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # | |
(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering Source # (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source # max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # |
Class Enum
defines operations on sequentially ordered types.
The enumFrom
... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum
may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum
from 0
through n-1
.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded
as well as Enum
,
the following should hold:
- The calls
andsucc
maxBound
should result in a runtime error.pred
minBound
fromEnum
andtoEnum
should give a runtime error if the result value is not representable in the result type. For example,
is an error.toEnum
7 ::Bool
enumFrom
andenumFromThen
should be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound enumFromThen x y = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = maxBound | otherwise = minBound
Methods
Successor of a value. For numeric types, succ
adds 1.
Predecessor of a value. For numeric types, pred
subtracts 1.
Convert from an 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
.
Used in Haskell's translation of [n..]
with [n..] = enumFrom n
,
a possible implementation being enumFrom n = n : enumFrom (succ n)
.
Examples
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] Source #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n'
, a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n')
,
worker s v = v : worker s (s v)
, x = fromEnum n' - fromEnum n
and
f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y
Examples
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] Source #
Used in Haskell's translation of [n..m]
with
[n..m] = enumFromTo n m
, a possible implementation being
enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []
Examples
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] Source #
Used in Haskell's translation of [n,n'..m]
with
[n,n'..m] = enumFromThenTo n n' m
, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m
,
x = fromEnum n' - fromEnum n
, c x = bool (>=) ((x 0)
f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y
and
worker s c v m | c v m = v : worker s c (s v) m | otherwise = []
Examples
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
class Bounded a where Source #
The Bounded
class is used to name the upper and lower limits of a
type. Ord
is not a superclass of Bounded
since types that are not
totally ordered may also have upper and lower bounds.
The Bounded
class may be derived for any enumeration type;
minBound
is the first constructor listed in the data
declaration
and maxBound
is the last.
Bounded
may also be derived for single-constructor datatypes whose
constituent types are in Bounded
.
Instances
Bounded ByteOrder | @since base-4.11.0.0 |
Bounded All | @since base-2.01 |
Bounded Any | @since base-2.01 |
Bounded CBool | |
Bounded CChar | |
Bounded CInt | |
Bounded CIntMax | |
Bounded CIntPtr | |
Bounded CLLong | |
Bounded CLong | |
Bounded CPtrdiff | |
Bounded CSChar | |
Bounded CShort | |
Bounded CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
Bounded CSize | |
Bounded CUChar | |
Bounded CUInt | |
Bounded CUIntMax | |
Bounded CUIntPtr | |
Bounded CULLong | |
Bounded CULong | |
Bounded CUShort | |
Bounded CWchar | |
Bounded IntPtr | |
Bounded WordPtr | |
Bounded Associativity | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Bounded DecidedStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Bounded SourceStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Bounded SourceUnpackedness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Bounded Int16 | @since base-2.01 |
Bounded Int32 | @since base-2.01 |
Bounded Int64 | @since base-2.01 |
Bounded Int8 | @since base-2.01 |
Bounded CBlkCnt | |
Bounded CBlkSize | |
Bounded CClockId | |
Bounded CDev | |
Bounded CFsBlkCnt | |
Bounded CFsFilCnt | |
Bounded CGid | |
Bounded CId | |
Bounded CIno | |
Bounded CKey | |
Bounded CMode | |
Bounded CNfds | |
Bounded CNlink | |
Bounded COff | |
Bounded CPid | |
Bounded CRLim | |
Bounded CSocklen | |
Bounded CSsize | |
Bounded CTcflag | |
Bounded CUid | |
Bounded Fd | |
Bounded GeneralCategory | @since base-2.01 |
Defined in GHC.Internal.Unicode | |
Bounded Word16 | @since base-2.01 |
Bounded Word32 | @since base-2.01 |
Bounded Word64 | @since base-2.01 |
Bounded Word8 | @since base-2.01 |
Bounded Ordering | @since base-2.01 |
Bounded () | @since base-2.01 |
Bounded Bool | @since base-2.01 |
Bounded Char | @since base-2.01 |
Bounded Int | @since base-2.01 |
Bounded Levity | @since base-4.16.0.0 |
Bounded VecCount | @since base-4.10.0.0 |
Bounded VecElem | @since base-4.10.0.0 |
Bounded Word | @since base-2.01 |
Bounded a => Bounded (First a) Source # | Since: base-4.9.0.0 |
Bounded a => Bounded (Last a) Source # | Since: base-4.9.0.0 |
Bounded a => Bounded (Max a) Source # | Since: base-4.9.0.0 |
Bounded a => Bounded (Min a) Source # | Since: base-4.9.0.0 |
Bounded m => Bounded (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Bounded a => Bounded (And a) | @since base-4.16 |
Bounded a => Bounded (Iff a) | @since base-4.16 |
Bounded a => Bounded (Ior a) | @since base-4.16 |
Bounded a => Bounded (Xor a) | @since base-4.16 |
Bounded a => Bounded (Identity a) | @since base-4.9.0.0 |
Bounded a => Bounded (Down a) | Swaps @since base-4.14.0.0 |
Bounded a => Bounded (Dual a) | @since base-2.01 |
Bounded a => Bounded (Product a) | @since base-2.01 |
Bounded a => Bounded (Sum a) | @since base-2.01 |
Bounded a => Bounded (Solo a) | |
Bounded (Proxy t) | @since base-4.7.0.0 |
(Bounded a, Bounded b) => Bounded (a, b) | @since base-2.01 |
Bounded a => Bounded (Const a b) | @since base-4.9.0.0 |
(Applicative f, Bounded a) => Bounded (Ap f a) | @since base-4.12.0.0 |
Coercible a b => Bounded (Coercion a b) | @since base-4.7.0.0 |
a ~ b => Bounded (a :~: b) | @since base-4.7.0.0 |
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | @since base-2.01 |
a ~~ b => Bounded (a :~~: b) | @since base-4.10.0.0 |
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | @since base-2.01 |
Bounded (f (g a)) => Bounded (Compose f g a) Source # | Since: base-4.19.0.0 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | @since base-2.01 |
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | @since base-2.01 |
Numbers
GHC.Internal.Numeric types
A fixed-precision integer type with at least the range [-2^29 .. 2^29-1]
.
The exact range for a given implementation can be determined by using
minBound
and maxBound
from the Bounded
class.
Instances
PrintfArg Int Source # | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
Bits Int | @since base-2.01 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Int -> Int -> Int Source # (.|.) :: Int -> Int -> Int Source # xor :: Int -> Int -> Int Source # complement :: Int -> Int Source # shift :: Int -> Int -> Int Source # rotate :: Int -> Int -> Int Source # setBit :: Int -> Int -> Int Source # clearBit :: Int -> Int -> Int Source # complementBit :: Int -> Int -> Int Source # testBit :: Int -> Int -> Bool Source # bitSizeMaybe :: Int -> Maybe Int Source # bitSize :: Int -> Int Source # isSigned :: Int -> Bool Source # shiftL :: Int -> Int -> Int Source # unsafeShiftL :: Int -> Int -> Int Source # shiftR :: Int -> Int -> Int Source # unsafeShiftR :: Int -> Int -> Int Source # rotateL :: Int -> Int -> Int Source # | |||||
FiniteBits Int | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Int -> Int Source # countLeadingZeros :: Int -> Int Source # countTrailingZeros :: Int -> Int Source # | |||||
Data Int | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int Source # toConstr :: Int -> Constr Source # dataTypeOf :: Int -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) Source # gmapT :: (forall b. Data b => b -> b) -> Int -> Int Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # | |||||
Bounded Int | @since base-2.01 | ||||
Enum Int | @since base-2.01 | ||||
Defined in GHC.Internal.Enum | |||||
Storable Int | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable | |||||
Ix Int | @since base-2.01 | ||||
Num Int | @since base-2.01 | ||||
Read Int | @since base-2.01 | ||||
Integral Int | @since base-2.0.1 | ||||
Real Int | @since base-2.0.1 | ||||
Defined in GHC.Internal.Real Methods toRational :: Int -> Rational Source # | |||||
Show Int | @since base-2.01 | ||||
Eq Int | |||||
Ord Int | |||||
Generic1 (URec Int :: k -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Foldable (UInt :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |||||
Traversable (UInt :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Functor (URec Int :: Type -> Type) | @since base-4.9.0.0 | ||||
Generic (URec Int p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Show (URec Int p) | @since base-4.9.0.0 | ||||
Eq (URec Int p) | @since base-4.9.0.0 | ||||
Ord (URec Int p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Int p -> URec Int p -> Ordering Source # (<) :: URec Int p -> URec Int p -> Bool Source # (<=) :: URec Int p -> URec Int p -> Bool Source # (>) :: URec Int p -> URec Int p -> Bool Source # (>=) :: URec Int p -> URec Int p -> Bool Source # | |||||
data URec Int (p :: k) | Used for marking occurrences of @since base-4.9.0.0 | ||||
type Rep1 (URec Int :: k -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep (URec Int p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics |
Instances
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
PrintfArg Float Source # | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
Data Float | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source # toConstr :: Float -> Constr Source # dataTypeOf :: Float -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source # gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source # | |||||
Floating Float | @since base-2.01 | ||||
Defined in GHC.Internal.Float Methods exp :: Float -> Float Source # log :: Float -> Float Source # sqrt :: Float -> Float Source # (**) :: Float -> Float -> Float Source # logBase :: Float -> Float -> Float Source # sin :: Float -> Float Source # cos :: Float -> Float Source # tan :: Float -> Float Source # asin :: Float -> Float Source # acos :: Float -> Float Source # atan :: Float -> Float Source # sinh :: Float -> Float Source # cosh :: Float -> Float Source # tanh :: Float -> Float Source # asinh :: Float -> Float Source # acosh :: Float -> Float Source # atanh :: Float -> Float Source # log1p :: Float -> Float Source # expm1 :: Float -> Float Source # | |||||
RealFloat Float | @since base-2.01 | ||||
Defined in GHC.Internal.Float Methods floatRadix :: Float -> Integer Source # floatDigits :: Float -> Int Source # floatRange :: Float -> (Int, Int) Source # decodeFloat :: Float -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Float Source # exponent :: Float -> Int Source # significand :: Float -> Float Source # scaleFloat :: Int -> Float -> Float Source # isNaN :: Float -> Bool Source # isInfinite :: Float -> Bool Source # isDenormalized :: Float -> Bool Source # isNegativeZero :: Float -> Bool Source # | |||||
Storable Float | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Float -> Int Source # alignment :: Float -> Int Source # peekElemOff :: Ptr Float -> Int -> IO Float Source # pokeElemOff :: Ptr Float -> Int -> Float -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Float Source # pokeByteOff :: Ptr b -> Int -> Float -> IO () Source # | |||||
Read Float | @since base-2.01 | ||||
Eq Float | Note that due to the presence of
Also note that
| ||||
Ord Float | See | ||||
Defined in GHC.Classes | |||||
Generic1 (URec Float :: k -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Foldable (UFloat :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |||||
Traversable (UFloat :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Functor (URec Float :: Type -> Type) | @since base-4.9.0.0 | ||||
Generic (URec Float p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Show (URec Float p) | |||||
Eq (URec Float p) | |||||
Ord (URec Float p) | |||||
Defined in GHC.Internal.Generics Methods compare :: URec Float p -> URec Float p -> Ordering Source # (<) :: URec Float p -> URec Float p -> Bool Source # (<=) :: URec Float p -> URec Float p -> Bool Source # (>) :: URec Float p -> URec Float p -> Bool Source # (>=) :: URec Float p -> URec Float p -> Bool Source # max :: URec Float p -> URec Float p -> URec Float p Source # min :: URec Float p -> URec Float p -> URec Float p Source # | |||||
data URec Float (p :: k) | Used for marking occurrences of @since base-4.9.0.0 | ||||
type Rep1 (URec Float :: k -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep (URec Float p) | |||||
Defined in GHC.Internal.Generics |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
PrintfArg Double Source # | Since: base-2.1 | ||||
Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source # parseFormat :: Double -> ModifierParser Source # | |||||
Data Double | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Double -> c Double Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Double Source # toConstr :: Double -> Constr Source # dataTypeOf :: Double -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Double) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Double) Source # gmapT :: (forall b. Data b => b -> b) -> Double -> Double Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Double -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Double -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Double -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Double -> m Double Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Double -> m Double Source # | |||||
Floating Double | @since base-2.01 | ||||
Defined in GHC.Internal.Float Methods exp :: Double -> Double Source # log :: Double -> Double Source # sqrt :: Double -> Double Source # (**) :: Double -> Double -> Double Source # logBase :: Double -> Double -> Double Source # sin :: Double -> Double Source # cos :: Double -> Double Source # tan :: Double -> Double Source # asin :: Double -> Double Source # acos :: Double -> Double Source # atan :: Double -> Double Source # sinh :: Double -> Double Source # cosh :: Double -> Double Source # tanh :: Double -> Double Source # asinh :: Double -> Double Source # acosh :: Double -> Double Source # atanh :: Double -> Double Source # log1p :: Double -> Double Source # expm1 :: Double -> Double Source # | |||||
RealFloat Double | @since base-2.01 | ||||
Defined in GHC.Internal.Float Methods floatRadix :: Double -> Integer Source # floatDigits :: Double -> Int Source # floatRange :: Double -> (Int, Int) Source # decodeFloat :: Double -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Double Source # exponent :: Double -> Int Source # significand :: Double -> Double Source # scaleFloat :: Int -> Double -> Double Source # isNaN :: Double -> Bool Source # isInfinite :: Double -> Bool Source # isDenormalized :: Double -> Bool Source # isNegativeZero :: Double -> Bool Source # | |||||
Storable Double | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Double -> Int Source # alignment :: Double -> Int Source # peekElemOff :: Ptr Double -> Int -> IO Double Source # pokeElemOff :: Ptr Double -> Int -> Double -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Double Source # pokeByteOff :: Ptr b -> Int -> Double -> IO () Source # | |||||
Read Double | @since base-2.01 | ||||
Eq Double | Note that due to the presence of
Also note that
| ||||
Ord Double | IEEE 754 IEEE 754-2008, section 5.11 requires that if at least one of arguments of
IEEE 754-2008, section 5.10 defines Thus, users must be extremely cautious when using Moving further, the behaviour of IEEE 754-2008 compliant | ||||
Generic1 (URec Double :: k -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Foldable (UDouble :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |||||
Traversable (UDouble :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Functor (URec Double :: Type -> Type) | @since base-4.9.0.0 | ||||
Generic (URec Double p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Show (URec Double p) | @since base-4.9.0.0 | ||||
Eq (URec Double p) | @since base-4.9.0.0 | ||||
Ord (URec Double p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Double p -> URec Double p -> Ordering Source # (<) :: URec Double p -> URec Double p -> Bool Source # (<=) :: URec Double p -> URec Double p -> Bool Source # (>) :: URec Double p -> URec Double p -> Bool Source # (>=) :: URec Double p -> URec Double p -> Bool Source # max :: URec Double p -> URec Double p -> URec Double p Source # min :: URec Double p -> URec Double p -> URec Double p Source # | |||||
data URec Double (p :: k) | Used for marking occurrences of @since base-4.9.0.0 | ||||
type Rep1 (URec Double :: k -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep (URec Double p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics |
Instances
PrintfArg Word Source # | Since: base-2.1 | ||||
Defined in Text.Printf | |||||
Bits Word | @since base-2.01 | ||||
Defined in GHC.Internal.Bits Methods (.&.) :: Word -> Word -> Word Source # (.|.) :: Word -> Word -> Word Source # xor :: Word -> Word -> Word Source # complement :: Word -> Word Source # shift :: Word -> Int -> Word Source # rotate :: Word -> Int -> Word Source # setBit :: Word -> Int -> Word Source # clearBit :: Word -> Int -> Word Source # complementBit :: Word -> Int -> Word Source # testBit :: Word -> Int -> Bool Source # bitSizeMaybe :: Word -> Maybe Int Source # bitSize :: Word -> Int Source # isSigned :: Word -> Bool Source # shiftL :: Word -> Int -> Word Source # unsafeShiftL :: Word -> Int -> Word Source # shiftR :: Word -> Int -> Word Source # unsafeShiftR :: Word -> Int -> Word Source # rotateL :: Word -> Int -> Word Source # | |||||
FiniteBits Word | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Bits Methods finiteBitSize :: Word -> Int Source # countLeadingZeros :: Word -> Int Source # countTrailingZeros :: Word -> Int Source # | |||||
Data Word | @since base-4.0.0.0 | ||||
Defined in GHC.Internal.Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word Source # toConstr :: Word -> Constr Source # dataTypeOf :: Word -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) Source # gmapT :: (forall b. Data b => b -> b) -> Word -> Word Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # | |||||
Bounded Word | @since base-2.01 | ||||
Enum Word | @since base-2.01 | ||||
Storable Word | @since base-2.01 | ||||
Defined in GHC.Internal.Foreign.Storable Methods sizeOf :: Word -> Int Source # alignment :: Word -> Int Source # peekElemOff :: Ptr Word -> Int -> IO Word Source # pokeElemOff :: Ptr Word -> Int -> Word -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Word Source # pokeByteOff :: Ptr b -> Int -> Word -> IO () Source # | |||||
Ix Word | @since base-4.6.0.0 | ||||
Defined in GHC.Internal.Ix | |||||
Num Word | @since base-2.01 | ||||
Read Word | @since base-4.5.0.0 | ||||
Integral Word | @since base-2.01 | ||||
Defined in GHC.Internal.Real | |||||
Real Word | @since base-2.01 | ||||
Defined in GHC.Internal.Real Methods toRational :: Word -> Rational Source # | |||||
Show Word | @since base-2.01 | ||||
Eq Word | |||||
Ord Word | |||||
Generic1 (URec Word :: k -> Type) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Foldable (UWord :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |||||
Traversable (UWord :: Type -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
Functor (URec Word :: Type -> Type) | @since base-4.9.0.0 | ||||
Generic (URec Word p) | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
Show (URec Word p) | @since base-4.9.0.0 | ||||
Eq (URec Word p) | @since base-4.9.0.0 | ||||
Ord (URec Word p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Methods compare :: URec Word p -> URec Word p -> Ordering Source # (<) :: URec Word p -> URec Word p -> Bool Source # (<=) :: URec Word p -> URec Word p -> Bool Source # (>) :: URec Word p -> URec Word p -> Bool Source # (>=) :: URec Word p -> URec Word p -> Bool Source # | |||||
data URec Word (p :: k) | Used for marking occurrences of @since base-4.9.0.0 | ||||
type Rep1 (URec Word :: k -> Type) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
type Rep (URec Word p) | @since base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics |
GHC.Internal.Numeric type classes
Basic numeric class.
The Haskell Report defines no laws for Num
. However, (
and +
)(
are
customarily expected to define a ring and have the following properties:*
)
- Associativity of
(
+
) (x + y) + z
=x + (y + z)
- Commutativity of
(
+
) x + y
=y + x
is the additive identityfromInteger
0x + fromInteger 0
=x
negate
gives the additive inversex + negate x
=fromInteger 0
- Associativity of
(
*
) (x * y) * z
=x * (y * z)
is the multiplicative identityfromInteger
1x * fromInteger 1
=x
andfromInteger 1 * x
=x
- Distributivity of
(
with respect to*
)(
+
) a * (b + c)
=(a * b) + (a * c)
and(b + c) * a
=(b * a) + (c * a)
- Coherence with
toInteger
- if the type also implements
Integral
, thenfromInteger
is a left inverse fortoInteger
, i.e.fromInteger (toInteger i) == i
Note that it isn't customarily expected that a type instance of both Num
and Ord
implement an ordered ring. Indeed, in base
only Integer
and
Rational
do.
Methods
(+) :: a -> a -> a infixl 6 Source #
(-) :: a -> a -> a infixl 6 Source #
(*) :: a -> a -> a infixl 7 Source #
Unary negation.
Absolute value.
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 :: Integer -> a Source #
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
Instances
class (Num a, Ord a) => Real a where Source #
Real numbers.
The Haskell report defines no laws for Real
, however Real
instances
are customarily expected to adhere to the following law:
- Coherence with
fromRational
- if the type also implements
Fractional
, thenfromRational
is a left inverse fortoRational
, i.e.fromRational (toRational i) = i
The law does not hold for Float
, Double
, CFloat
,
CDouble
, etc., because these types contain non-finite values,
which cannot be roundtripped through Rational
.
Methods
toRational :: a -> Rational Source #
Rational equivalent of its real argument with full precision.
Instances
class (Real a, Enum a) => Integral a where Source #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral
. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div
/mod
and quot
/rem
pairs, given
suitable Euclidean functions f
and g
:
x
=y * quot x y + rem x y
withrem x y
=fromInteger 0
org (rem x y)
<g y
x
=y * div x y + mod x y
withmod x y
=fromInteger 0
orf (mod x y)
<f y
An example of a suitable Euclidean function, for Integer
's instance, is
abs
.
In addition, toInteger
should be total, and fromInteger
should be a left
inverse for it, i.e. fromInteger (toInteger i) = i
.
Methods
quot :: a -> a -> a infixl 7 Source #
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 :: a -> a -> a infixl 7 Source #
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 :: a -> a -> a infixl 7 Source #
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 :: a -> a -> a infixl 7 Source #
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 :: a -> a -> (a, a) Source #
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
divMod :: a -> a -> (a, a) Source #
WARNING: This function is partial (because it throws when 0 is passed as
the divisor) for all the integer types in base
.
toInteger :: a -> Integer Source #
Conversion to Integer
.
Instances
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional
. However, (
and
+
)(
are customarily expected to define a division ring and have the
following properties:*
)
recip
gives the multiplicative inversex * recip x
=recip x * x
=fromInteger 1
- Totality of
toRational
toRational
is total- Coherence with
toRational
- if the type also implements
Real
, thenfromRational
is a left inverse fortoRational
, i.e.fromRational (toRational i) = i
Note that it isn't customarily expected that a type instance of
Fractional
implement a field. However, all instances in base
do.
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7 Source #
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a Source #
Conversion from a Rational
(that is
).
A floating literal stands for an application of Ratio
Integer
fromRational
to a value of type Rational
, so such literals have type
(
.Fractional
a) => a
Instances
Fractional CDouble | |
Fractional CFloat | |
RealFloat a => Fractional (Complex a) Source # | Since: base-2.1 |
Fractional a => Fractional (Identity a) | @since base-4.9.0.0 |
Fractional a => Fractional (Down a) | @since base-4.14.0.0 |
Integral a => Fractional (Ratio a) | @since base-2.0.1 |
HasResolution a => Fractional (Fixed a) Source # | Since: base-2.1 |
Fractional a => Fractional (Op a b) Source # | |
Fractional a => Fractional (Const a b) | @since base-4.9.0.0 |
Fractional (f (g a)) => Fractional (Compose f g a) Source # | Since: base-4.20.0.0 |
class Fractional a => Floating a where Source #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating
. However, (
, +
)(
and *
)exp
are customarily expected to define an exponential field and have
the following properties:
exp (a + b)
=exp a * exp b
exp (fromInteger 0)
=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class (Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) Source #
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 asx
; andf
is a fraction with the same type and sign asx
, and with absolute value less than1
.
The default definitions of the ceiling
, floor
, truncate
and round
functions are in terms of properFraction
.
truncate :: Integral b => a -> b Source #
returns the integer nearest truncate
xx
between zero and x
round :: Integral b => a -> b Source #
returns the nearest integer to round
xx
;
the even integer if x
is equidistant between two integers
ceiling :: Integral b => a -> b Source #
returns the least integer not less than ceiling
xx
floor :: Integral b => a -> b Source #
returns the greatest integer not greater than floor
xx
Instances
RealFrac CDouble | |
RealFrac CFloat | |
RealFrac a => RealFrac (Identity a) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
RealFrac a => RealFrac (Down a) | @since base-4.14.0.0 |
Integral a => RealFrac (Ratio a) | @since base-2.0.1 |
HasResolution a => RealFrac (Fixed a) Source # | Since: base-2.1 |
RealFrac a => RealFrac (Const a b) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const | |
RealFrac (f (g a)) => RealFrac (Compose f g a) Source # | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose |
class (RealFrac a, Floating a) => RealFloat a where Source #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer Source #
a constant function, returning the radix of the representation
(often 2
)
floatDigits :: a -> Int Source #
a constant function, returning the number of digits of
floatRadix
in the significand
floatRange :: a -> (Int, Int) Source #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) Source #
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
yields decodeFloat
x(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) <=
, where abs
m < b^dd
is
the value of
.
In particular, floatDigits
x
. If the type
contains a negative zero, also decodeFloat
0 = (0,0)
.
The result of decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or isNaN
x
is isInfinite
xTrue
.
encodeFloat :: Integer -> Int -> a Source #
encodeFloat
performs the inverse of decodeFloat
in the
sense that for finite x
with the exception of -0.0
,
.
uncurry
encodeFloat
(decodeFloat
x) = x
is one of the two closest representable
floating-point numbers to encodeFloat
m nm*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
corresponds to the second component of decodeFloat
.
and for finite nonzero exponent
0 = 0x
,
.
If exponent
x = snd (decodeFloat
x) + floatDigits
xx
is a finite floating-point number, it is equal in value to
, where significand
x * b ^^ exponent
xb
is the
floating-point radix.
The behaviour is unspecified on infinite or NaN
values.
significand :: a -> a Source #
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 :: Int -> a -> a Source #
multiplies a floating-point number by an integer power of the radix
True
if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool Source #
True
if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source #
True
if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool Source #
True
if the argument is an IEEE negative zero
True
if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x
and y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point atan2
y x(x,y)
.
returns a value in the range [atan2
y x-pi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with atan2
y 1y
in a type
that is RealFloat
, should return the same value as
.
A default definition of atan
yatan2
is provided, but implementors
can provide a more accurate implementation.
Instances
GHC.Internal.Numeric functions
gcd :: Integral a => a -> a -> a Source #
is the non-negative factor of both gcd
x yx
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 44
.
= gcd
0 00
.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types,
,
the result may be negative if one of the arguments is abs
minBound
< 0
(and
necessarily is if the other is minBound
0
or
) for such types.minBound
lcm :: Integral a => a -> a -> a Source #
is the smallest positive integer that both lcm
x yx
and y
divide.
(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to a non-negative integral power
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to an integral power
fromIntegral :: (Integral a, Num b) => a -> b Source #
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.
realToFrac :: (Real a, Fractional b) => a -> b Source #
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
Semigroups and Monoids
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
You can alternatively define sconcat
instead of (<>
), in which case the
laws are:
@since base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 Source #
An associative operation.
Examples
>>>
[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!
Instances
Semigroup ByteArray Source # | Since: base-4.17.0.0 |
Semigroup Void | @since base-4.9.0.0 |
Semigroup All | @since base-4.9.0.0 |
Semigroup Any | @since base-4.9.0.0 |
Semigroup Event | @since base-4.10.0.0 |
Semigroup EventLifetime | @since base-4.11.0.0 |
Semigroup Lifetime | @since base-4.10.0.0 |
Semigroup ExceptionContext | |
Defined in GHC.Internal.Exception.Context Methods (<>) :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # sconcat :: NonEmpty ExceptionContext -> ExceptionContext Source # stimes :: Integral b => b -> ExceptionContext -> ExceptionContext Source # | |
Semigroup Ordering | @since base-4.9.0.0 |
Semigroup () | @since base-4.9.0.0 |
Semigroup (Comparison a) Source # |
(<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a' |
Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a Source # sconcat :: NonEmpty (Comparison a) -> Comparison a Source # stimes :: Integral b => b -> Comparison a -> Comparison a Source # | |
Semigroup (Equivalence a) Source # |
(<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv' a b |
Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a Source # sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source # stimes :: Integral b => b -> Equivalence a -> Equivalence a Source # | |
Semigroup (Predicate a) Source # |
(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a |
Semigroup (First a) Source # | Since: base-4.9.0.0 |
Semigroup (Last a) Source # | Since: base-4.9.0.0 |
Ord a => Semigroup (Max a) Source # | Since: base-4.9.0.0 |
Ord a => Semigroup (Min a) Source # | Since: base-4.9.0.0 |
Monoid m => Semigroup (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # | |
Semigroup (NonEmpty a) | @since base-4.9.0.0 |
Semigroup a => Semigroup (STM a) | @since base-4.17.0.0 |
Bits a => Semigroup (And a) | @since base-4.16 |
FiniteBits a => Semigroup (Iff a) | This constraint is arguably
too strong. However, as some types (such as @since base-4.16 |
Bits a => Semigroup (Ior a) | @since base-4.16 |
Bits a => Semigroup (Xor a) | @since base-4.16 |
Semigroup a => Semigroup (Identity a) | @since base-4.9.0.0 |
Ord a => Semigroup (Max a) | @since base-4.11.0.0 |
Ord a => Semigroup (Min a) | @since base-4.11.0.0 |
Semigroup (First a) | @since base-4.9.0.0 |
Semigroup (Last a) | @since base-4.9.0.0 |
Semigroup a => Semigroup (Down a) | @since base-4.11.0.0 |
Semigroup a => Semigroup (Dual a) | @since base-4.9.0.0 |
Semigroup (Endo a) | @since base-4.9.0.0 |
Num a => Semigroup (Product a) | @since base-4.9.0.0 |
Num a => Semigroup (Sum a) | @since base-4.9.0.0 |
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods (<>) :: Generically a -> Generically a -> Generically a Source # sconcat :: NonEmpty (Generically a) -> Generically a Source # stimes :: Integral b => b -> Generically a -> Generically a Source # | |
Semigroup p => Semigroup (Par1 p) | @since base-4.12.0.0 |
Semigroup a => Semigroup (IO a) | @since base-4.10.0.0 |
Semigroup a => Semigroup (Maybe a) | @since base-4.9.0.0 |
Semigroup a => Semigroup (Solo a) | @since base-4.15 |
Semigroup [a] | @since base-4.9.0.0 |
Semigroup a => Semigroup (Op a b) Source # |
(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a |
Semigroup (Either a b) | @since base-4.9.0.0 |
Semigroup (Proxy s) | @since base-4.9.0.0 |
Semigroup (U1 p) | @since base-4.12.0.0 |
Semigroup (V1 p) | @since base-4.12.0.0 |
Semigroup a => Semigroup (ST s a) | @since base-4.11.0.0 |
(Semigroup a, Semigroup b) => Semigroup (a, b) | @since base-4.9.0.0 |
Semigroup b => Semigroup (a -> b) | @since base-4.9.0.0 |
Semigroup a => Semigroup (Const a b) | @since base-4.9.0.0 |
(Applicative f, Semigroup a) => Semigroup (Ap f a) | @since base-4.12.0.0 |
Alternative f => Semigroup (Alt f a) | @since base-4.9.0.0 |
Semigroup (f p) => Semigroup (Rec1 f p) | @since base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | @since base-4.9.0.0 |
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source # | Since: base-4.16.0.0 |
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | @since base-4.12.0.0 |
Semigroup c => Semigroup (K1 i c p) | @since base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | @since base-4.9.0.0 |
Semigroup (f (g a)) => Semigroup (Compose f g a) Source # | Since: base-4.16.0.0 |
Semigroup (f (g p)) => Semigroup ((f :.: g) p) | @since base-4.12.0.0 |
Semigroup (f p) => Semigroup (M1 i c f p) | @since base-4.12.0.0 |
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | @since base-4.9.0.0 |
class Semigroup a => Monoid a where Source #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x
<>
mempty
= x- Left identity
mempty
<>
x = x- Associativity
x
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law)- Concatenation
mconcat
=foldr
(<>
)mempty
You can alternatively define mconcat
instead of mempty
, in which case the
laws are:
- Unit
mconcat
(pure
x) = x- Multiplication
mconcat
(join
xss) =mconcat
(fmap
mconcat
xss)- Subclass
mconcat
(toList
xs) =sconcat
xs
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base-4.11.0.0.
Methods
Identity of mappend
Examples
>>>
"Hello world" <> mempty
"Hello world"
>>>
mempty <> [1, 2, 3]
[1,2,3]
mappend :: a -> a -> a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation
since base-4.11.0.0.
Should it be implemented manually, since mappend
= (<>
)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
.
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!"
Instances
Monoid ByteArray Source # | Since: base-4.17.0.0 |
Monoid All | @since base-2.01 |
Monoid Any | @since base-2.01 |
Monoid Event | @since base-4.4.0.0 |
Monoid EventLifetime | @since base-4.8.0.0 |
Monoid Lifetime |
@since base-4.8.0.0 |
Monoid ExceptionContext | |
Defined in GHC.Internal.Exception.Context Methods mempty :: ExceptionContext Source # mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # mconcat :: [ExceptionContext] -> ExceptionContext Source # | |
Monoid Ordering | @since base-2.01 |
Monoid () | @since base-2.01 |
Monoid (Comparison a) Source # |
mempty :: Comparison a mempty = Comparison _ _ -> EQ |
Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source # mappend :: Comparison a -> Comparison a -> Comparison a Source # mconcat :: [Comparison a] -> Comparison a Source # | |
Monoid (Equivalence a) Source # |
mempty :: Equivalence a mempty = Equivalence _ _ -> True |
Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source # mappend :: Equivalence a -> Equivalence a -> Equivalence a Source # mconcat :: [Equivalence a] -> Equivalence a Source # | |
Monoid (Predicate a) Source # |
mempty :: Predicate a mempty = _ -> True |
(Ord a, Bounded a) => Monoid (Max a) Source # | Since: base-4.9.0.0 |
(Ord a, Bounded a) => Monoid (Min a) Source # | Since: base-4.9.0.0 |
Monoid m => Monoid (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source # | |
Monoid a => Monoid (STM a) | @since base-4.17.0.0 |
FiniteBits a => Monoid (And a) | This constraint is arguably too strong. However,
as some types (such as @since base-4.16 |
FiniteBits a => Monoid (Iff a) | This constraint is arguably
too strong. However, as some types (such as @since base-4.16 |
Bits a => Monoid (Ior a) | @since base-4.16 |
Bits a => Monoid (Xor a) | @since base-4.16 |
Monoid a => Monoid (Identity a) | @since base-4.9.0.0 |
Ord a => Monoid (Max a) | @since base-4.8.0.0 |
Ord a => Monoid (Min a) | @since base-4.8.0.0 |
Monoid (First a) | @since base-2.01 |
Monoid (Last a) | @since base-2.01 |
Monoid a => Monoid (Down a) | @since base-4.11.0.0 |
Monoid a => Monoid (Dual a) | @since base-2.01 |
Monoid (Endo a) | @since base-2.01 |
Num a => Monoid (Product a) | @since base-2.01 |
Num a => Monoid (Sum a) | @since base-2.01 |
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source # | |
Monoid p => Monoid (Par1 p) | @since base-4.12.0.0 |
Monoid a => Monoid (IO a) | @since base-4.9.0.0 |
Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner @since base-2.01 |
Monoid a => Monoid (Solo a) | @since base-4.15 |
Monoid [a] | @since base-2.01 |
Monoid a => Monoid (Op a b) Source # |
mempty :: Op a b mempty = Op _ -> mempty |
Monoid (Proxy s) | @since base-4.7.0.0 |
Monoid (U1 p) | @since base-4.12.0.0 |
Monoid a => Monoid (ST s a) | @since base-4.11.0.0 |
(Monoid a, Monoid b) => Monoid (a, b) | @since base-2.01 |
Monoid b => Monoid (a -> b) | @since base-2.01 |
Monoid a => Monoid (Const a b) | @since base-4.9.0.0 |
(Applicative f, Monoid a) => Monoid (Ap f a) | @since base-4.12.0.0 |
Alternative f => Monoid (Alt f a) | @since base-4.8.0.0 |
Monoid (f p) => Monoid (Rec1 f p) | @since base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | @since base-2.01 |
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source # | Since: base-4.16.0.0 |
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | @since base-4.12.0.0 |
Monoid c => Monoid (K1 i c p) | @since base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | @since base-2.01 |
Monoid (f (g a)) => Monoid (Compose f g a) Source # | Since: base-4.16.0.0 |
Monoid (f (g p)) => Monoid ((f :.: g) p) | @since base-4.12.0.0 |
Monoid (f p) => Monoid (M1 i c f p) | @since base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | @since base-2.01 |
Monads and functors
class Functor (f :: Type -> Type) where Source #
A type f
is a Functor if it provides a function fmap
which, given any types a
and b
lets you apply any function from (a -> b)
to turn an f a
into an f b
, preserving the
structure of f
. Furthermore f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap
and
the first law, so you need only check that the former condition holds.
See these articles by School of Haskell or
David Luposchainsky
for an explanation.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
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
instance that allows
both the last and the penultimate parameters to be mapped over.Bifunctor
Examples
Convert from a
to a Maybe
IntMaybe String
using show
:
>>>
fmap show Nothing
Nothing>>>
fmap show (Just 3)
Just "3"
Convert from an
to an
Either
Int IntEither 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)
Instances
Functor Complex Source # | Since: base-4.9.0.0 |
Functor First Source # | Since: base-4.9.0.0 |
Functor Last Source # | Since: base-4.9.0.0 |
Functor Max Source # | Since: base-4.9.0.0 |
Functor Min Source # | Since: base-4.9.0.0 |
Functor ArgDescr Source # | Since: base-4.7.0.0 |
Functor ArgOrder Source # | Since: base-4.7.0.0 |
Functor OptDescr Source # | Since: base-4.7.0.0 |
Functor NonEmpty | @since base-4.9.0.0 |
Functor STM | @since base-4.3.0.0 |
Functor Handler | @since base-4.6.0.0 |
Functor Identity | @since base-4.8.0.0 |
Functor First | @since base-4.8.0.0 |
Functor Last | @since base-4.8.0.0 |
Functor Down | @since base-4.11.0.0 |
Functor Dual | @since base-4.8.0.0 |
Functor Product | @since base-4.8.0.0 |
Functor Sum | @since base-4.8.0.0 |
Functor ZipList | @since base-2.01 |
Functor NoIO | @since base-4.8.0.0 |
Functor Par1 | @since base-4.9.0.0 |
Functor P | @since base-4.8.0.0 |
Functor ReadP | @since base-2.01 |
Functor ReadPrec | @since base-2.01 |
Functor IO | @since base-2.01 |
Functor Maybe | @since base-2.01 |
Functor Solo | @since base-4.15 |
Functor [] | @since base-2.01 |
Monad m => Functor (WrappedMonad m) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
Functor (Arg a) Source # | Since: base-4.9.0.0 |
Functor (Array i) | @since base-2.01 |
Arrow a => Functor (ArrowMonad a) | @since base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
Functor (ST s) | @since base-2.01 |
Functor (Either a) | @since base-3.0 |
Functor (StateL s) | @since base-4.0 |
Functor (StateR s) | @since base-4.0 |
Functor (Proxy :: Type -> Type) | @since base-4.7.0.0 |
Functor (U1 :: Type -> Type) | @since base-4.9.0.0 |
Functor (V1 :: Type -> Type) | @since base-4.9.0.0 |
Functor (ST s) | @since base-2.01 |
Functor ((,) a) | @since base-2.01 |
Arrow a => Functor (WrappedArrow a b) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
Functor m => Functor (Kleisli m a) | @since base-4.14.0.0 |
Functor (Const m :: Type -> Type) | @since base-2.01 |
Monad m => Functor (StateT s m) | @since base-4.18.0.0 |
Functor f => Functor (Ap f) | @since base-4.12.0.0 |
Functor f => Functor (Alt f) | @since base-4.8.0.0 |
(Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
Functor f => Functor (Rec1 f) | @since base-4.9.0.0 |
Functor (URec (Ptr ()) :: Type -> Type) | @since base-4.9.0.0 |
Functor (URec Char :: Type -> Type) | @since base-4.9.0.0 |
Functor (URec Double :: Type -> Type) | @since base-4.9.0.0 |
Functor (URec Float :: Type -> Type) | @since base-4.9.0.0 |
Functor (URec Int :: Type -> Type) | @since base-4.9.0.0 |
Functor (URec Word :: Type -> Type) | @since base-4.9.0.0 |
Functor ((,,) a b) | @since base-4.14.0.0 |
(Functor f, Functor g) => Functor (Product f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (Sum f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :*: g) | @since base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :+: g) | @since base-4.9.0.0 |
Functor (K1 i c :: Type -> Type) | @since base-4.9.0.0 |
Functor ((,,,) a b c) | @since base-4.14.0.0 |
Functor ((->) r) | @since base-2.01 |
(Functor f, Functor g) => Functor (Compose f g) Source # | Since: base-4.9.0.0 |
(Functor f, Functor g) => Functor (f :.: g) | @since base-4.9.0.0 |
Functor f => Functor (M1 i c f) | @since base-4.9.0.0 |
Functor ((,,,,) a b c d) | @since base-4.18.0.0 |
Functor ((,,,,,) a b c d e) | @since base-4.18.0.0 |
Functor ((,,,,,,) a b c d e f) | @since base-4.18.0.0 |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
An infix synonym for fmap
.
The name of this operator is an allusion to $
.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $
is function application, <$>
is function
application lifted over a Functor
.
Examples
Convert from a
to a Maybe
Int
using Maybe
String
show
:
>>>
show <$> Nothing
Nothing
>>>
show <$> Just 3
Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using show
:
>>>
show <$> 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 <$> (2,2)
(2,True)
class Functor f => Applicative (f :: Type -> Type) where Source #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*>
or liftA2
. If it defines both, then they must behave
the same as their default definitions:
(<*>
) =liftA2
id
liftA2
f x y = f<$>
x<*>
y
Further, any definition must satisfy the following:
- Identity
pure
id
<*>
v = v- Composition
pure
(.)<*>
u<*>
v<*>
w = u<*>
(v<*>
w)- Homomorphism
pure
f<*>
pure
x =pure
(f x)- Interchange
u
<*>
pure
y =pure
($
y)<*>
u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor
instance for f
will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2
p (liftA2
q u v) =liftA2
f u .liftA2
g v
If f
is also a Monad
, it should satisfy
(which implies that pure
and <*>
satisfy the applicative functor laws).
Methods
Lift a value into the Structure.
Examples
>>>
pure 1 :: Maybe Int
Just 1
>>>
pure 'z' :: [Char]
"z"
>>>
pure (pure ":D") :: Maybe [String]
Just [":D"]
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
A few functors support an implementation of <*>
that is more
efficient than the default one.
Example
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
liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source #
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
>>>
liftA2 (,) (Just 3) (Just 5)
Just (3,5)
>>>
liftA2 (+) [1, 2, 3] [4, 5, 6]
[5,6,7,6,7,8,7,8,9]
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
Examples
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","")]
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Instances
Applicative Complex Source # | Since: base-4.9.0.0 |
Applicative First Source # | Since: base-4.9.0.0 |
Applicative Last Source # | Since: base-4.9.0.0 |
Applicative Max Source # | Since: base-4.9.0.0 |
Applicative Min Source # | Since: base-4.9.0.0 |
Applicative NonEmpty | @since base-4.9.0.0 |
Defined in GHC.Internal.Base | |
Applicative STM | @since base-4.8.0.0 |
Applicative Identity | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
Applicative First | @since base-4.8.0.0 |
Applicative Last | @since base-4.8.0.0 |
Applicative Down | @since base-4.11.0.0 |
Applicative Dual | @since base-4.8.0.0 |
Applicative Product | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
Applicative Sum | @since base-4.8.0.0 |
Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN = ZipList (zipWithN f xs1 ... xsN) where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..] = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..]) = ZipList {getZipList = ["a5","b6b6","c7c7c7"]} @since base-2.01 |
Defined in GHC.Internal.Functor.ZipList | |
Applicative NoIO | @since base-4.8.0.0 |
Applicative Par1 | @since base-4.9.0.0 |
Applicative P | @since base-4.5.0.0 |
Applicative ReadP | @since base-4.6.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
Applicative ReadPrec | @since base-4.6.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadPrec | |
Applicative IO | @since base-2.01 |
Applicative Maybe | @since base-2.01 |
Applicative Solo | @since base-4.15 |
Applicative [] | @since base-2.01 |
Monad m => Applicative (WrappedMonad m) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # | |
Arrow a => Applicative (ArrowMonad a) | @since base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
Applicative (ST s) | @since base-2.01 |
Applicative (Either e) | @since base-3.0 |
Defined in GHC.Internal.Data.Either | |
Applicative (StateL s) | @since base-4.0 |
Defined in GHC.Internal.Data.Functor.Utils | |
Applicative (StateR s) | @since base-4.0 |
Defined in GHC.Internal.Data.Functor.Utils | |
Applicative (Proxy :: Type -> Type) | @since base-4.7.0.0 |
Applicative (U1 :: Type -> Type) | @since base-4.9.0.0 |
Applicative (ST s) | @since base-4.4.0.0 |
Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002) ("hello world!",2017) @since base-2.01 |
Arrow a => Applicative (WrappedArrow a b) Source # | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
Applicative m => Applicative (Kleisli m a) | @since base-4.14.0.0 |
Defined in GHC.Internal.Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source # | |
Monoid m => Applicative (Const m :: Type -> Type) | @since base-2.0.1 |
Defined in GHC.Internal.Data.Functor.Const | |
Monad m => Applicative (StateT s m) | @since base-4.18.0.0 |
Defined in GHC.Internal.Data.Functor.Utils Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
Applicative f => Applicative (Ap f) | @since base-4.12.0.0 |
Applicative f => Applicative (Alt f) | @since base-4.8.0.0 |
(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods pure :: a -> Generically1 f a Source # (<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source # liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source # (*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source # (<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source # | |
Applicative f => Applicative (Rec1 f) | @since base-4.9.0.0 |
(Monoid a, Monoid b) => Applicative ((,,) a b) | @since base-4.14.0.0 |
Defined in GHC.Internal.Base | |
(Applicative f, Applicative g) => Applicative (Product f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source # | |
(Applicative f, Applicative g) => Applicative (f :*: g) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Monoid c => Applicative (K1 i c :: Type -> Type) | @since base-4.12.0.0 |
(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | @since base-4.14.0.0 |
Defined in GHC.Internal.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source # | |
Applicative ((->) r) | @since base-2.01 |
(Applicative f, Applicative g) => Applicative (Compose f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source # | |
(Applicative f, Applicative g) => Applicative (f :.: g) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Applicative f => Applicative (M1 i c f) | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics |
class Applicative m => Monad (m :: Type -> Type) where Source #
The Monad
class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do
expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad
should satisfy the following:
- Left identity
return
a>>=
k = k a- Right identity
m
>>=
return
= m- Associativity
m
>>=
(\x -> k x>>=
h) = (m>>=
k)>>=
h
Furthermore, the Monad
and Applicative
operations should relate as follows:
The above laws imply:
and that pure
and (<*>
) satisfy the applicative functor laws.
The instances of Monad
for List
, Maybe
and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as
' can be understood as the >>=
bsdo
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
.
(>>) :: m a -> m b -> m b infixl 1 Source #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as
' can be understood as the >>
bsdo
expression
do as bs
or in terms of
as(>>=)
as >>= const bs
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.
Instances
Monad Complex Source # | Since: base-4.9.0.0 |
Monad First Source # | Since: base-4.9.0.0 |
Monad Last Source # | Since: base-4.9.0.0 |
Monad Max Source # | Since: base-4.9.0.0 |
Monad Min Source # | Since: base-4.9.0.0 |
Monad NonEmpty | @since base-4.9.0.0 |
Monad STM | @since base-4.3.0.0 |
Monad Identity | @since base-4.8.0.0 |
Monad First | @since base-4.8.0.0 |
Monad Last | @since base-4.8.0.0 |
Monad Down | @since base-4.11.0.0 |
Monad Dual | @since base-4.8.0.0 |
Monad Product | @since base-4.8.0.0 |
Monad Sum | @since base-4.8.0.0 |
Monad NoIO | @since base-4.4.0.0 |
Monad Par1 | @since base-4.9.0.0 |
Monad P | @since base-2.01 |
Monad ReadP | @since base-2.01 |
Monad ReadPrec | @since base-2.01 |
Monad IO | @since base-2.01 |
Monad Maybe | @since base-2.01 |
Monad Solo | @since base-4.15 |
Monad [] | @since base-2.01 |
Monad m => Monad (WrappedMonad m) Source # | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # | |
ArrowApply a => Monad (ArrowMonad a) | @since base-2.01 |
Defined in GHC.Internal.Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # | |
Monad (ST s) | @since base-2.01 |
Monad (Either e) | @since base-4.4.0.0 |
Monad (Proxy :: Type -> Type) | @since base-4.7.0.0 |
Monad (U1 :: Type -> Type) | @since base-4.9.0.0 |
Monad (ST s) | @since base-2.01 |
Monoid a => Monad ((,) a) | @since base-4.9.0.0 |
Monad m => Monad (Kleisli m a) | @since base-4.14.0.0 |
Monad m => Monad (StateT s m) | @since base-4.18.0.0 |
Monad f => Monad (Ap f) | @since base-4.12.0.0 |
Monad f => Monad (Alt f) | @since base-4.8.0.0 |
Monad f => Monad (Rec1 f) | @since base-4.9.0.0 |
(Monoid a, Monoid b) => Monad ((,,) a b) | @since base-4.14.0.0 |
(Monad f, Monad g) => Monad (Product f g) Source # | Since: base-4.9.0.0 |
(Monad f, Monad g) => Monad (f :*: g) | @since base-4.9.0.0 |
(Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | @since base-4.14.0.0 |
Monad ((->) r) | @since base-2.01 |
Monad f => Monad (M1 i c f) | @since base-4.9.0.0 |
class Monad m => MonadFail (m :: Type -> Type) where Source #
When a value is bound in do
-notation, the pattern on the left
hand side of <-
might not match. In this case, this class
provides a function to recover.
A Monad
without a MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat
).
Instances of MonadFail
should satisfy the following law: fail s
should
be a left zero for >>=
,
fail s >>= f = fail s
If your Monad
is also MonadPlus
, a popular definition is
fail _ = mzero
fail s
should be an action that runs in the monad itself, not an
exception (except in instances of MonadIO
). In particular,
fail
should not be implemented in terms of error
.
@since base-4.9.0.0
Instances
MonadFail P | @since base-4.9.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
MonadFail ReadP | @since base-4.9.0.0 |
MonadFail ReadPrec | @since base-4.9.0.0 |
MonadFail IO | @since base-4.9.0.0 |
MonadFail Maybe | @since base-4.9.0.0 |
MonadFail [] | @since base-4.9.0.0 |
Defined in GHC.Internal.Control.Monad.Fail | |
MonadFail f => MonadFail (Ap f) | @since base-4.12.0.0 |
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence
.
sequence_
is just like sequenceA_
, but specialised to monadic
actions.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=
, but with the arguments interchanged.
as >>= f == f =<< as
Folds and traversals
class Foldable (t :: Type -> Type) where Source #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-} data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a) deriving Foldable
A more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source #
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
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"
foldr :: (a -> b -> b) -> b -> t a -> b Source #
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
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 :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.
In the case of lists, foldl
, when applied to a binary operator, a
starting value (typically the left-identity of the operator), and a
list, reduces the list using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. Like all left-associative folds,
foldl
will diverge if given an infinite list.
If you want an efficient strict left-fold, you probably want to use
foldl'
instead of foldl
. The reason for this is that the latter
does not force the inner results (e.g. z `f` x1
in the above
example) before applying them to the operator (e.g. to (`f` x2)
).
This results in a thunk chain O(n) elements long, which then must be
evaluated from the outside-in.
For a general Foldable
structure this should be semantically identical
to:
foldl f z =foldl
f z .toList
Examples
The first example is a strict fold, which in practice is best performed
with foldl'
.
>>>
foldl (+) 42 [1,2,3,4]
52
Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.
>>>
foldl (\acc c -> c : acc) "abcd" "efgh"
"hgfeabcd"
A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:
>>>
foldl (\a _ -> a) 0 $ repeat 1
* Hangs forever *
WARNING: When it comes to lists, you always want to use either foldl'
or foldr
instead.
foldl' :: (b -> a -> b) -> b -> t a -> b Source #
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
foldr1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldr
that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>
foldr1 (+) [1..4]
10
>>>
foldr1 (+) []
Exception: Prelude.foldr1: empty list
>>>
foldr1 (+) Nothing
*** Exception: foldr1: empty structure
>>>
foldr1 (-) [1..4]
-2
>>>
foldr1 (&&) [True, False, True, True]
False
>>>
foldr1 (||) [False, False, True, True]
True
>>>
foldr1 (+) [1..]
* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldl
that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1
f =foldl1
f .toList
Examples
Basic usage:
>>>
foldl1 (+) [1..4]
10
>>>
foldl1 (+) []
*** Exception: Prelude.foldl1: empty list
>>>
foldl1 (+) Nothing
*** Exception: foldl1: empty structure
>>>
foldl1 (-) [1..4]
-8
>>>
foldl1 (&&) [True, False, True, True]
False
>>>
foldl1 (||) [False, False, True, True]
True
>>>
foldl1 (+) [1..]
* Hangs forever *
elem :: Eq a => a -> t a -> Bool infix 4 Source #
Does the element occur in the structure?
Note: elem
is often used in infix form.
Examples
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
maximum :: Ord a => t a -> a Source #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>
maximum [1..10]
10
>>>
maximum []
*** Exception: Prelude.maximum: empty list
>>>
maximum Nothing
*** Exception: maximum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
@since base-4.8.0.0
minimum :: Ord a => t a -> a Source #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>
minimum [1..10]
1
>>>
minimum []
*** Exception: Prelude.minimum: empty list
>>>
minimum Nothing
*** Exception: minimum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
@since base-4.8.0.0
sum :: Num a => t a -> a Source #
The sum
function computes the sum of the numbers of a structure.
Examples
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 :: Num a => t a -> a Source #
The product
function computes the product of the numbers of a
structure.
Examples
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
Instances
Foldable Complex Source # | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m Source # foldMap :: Monoid m => (a -> m) -> Complex a -> m Source # foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source # foldr :: (a -> b -> b) -> b -> Complex a -> b Source # foldr' :: (a -> b -> b) -> b -> Complex a -> b Source # foldl :: (b -> a -> b) -> b -> Complex a -> b Source # foldl' :: (b -> a -> b) -> b -> Complex a -> b Source # foldr1 :: (a -> a -> a) -> Complex a -> a Source # foldl1 :: (a -> a -> a) -> Complex a -> a Source # toList :: Complex a -> [a] Source # null :: Complex a -> Bool Source # length :: Complex a -> Int Source # elem :: Eq a => a -> Complex a -> Bool Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # | |
Foldable First Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
Foldable Last Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
Foldable Max Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # | |
Foldable Min Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # | |
Foldable NonEmpty | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # | |
Foldable Identity | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # | |
Foldable First | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
Foldable Last | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
Foldable Down | @since base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # | |
Foldable Dual | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # | |
Foldable Product | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |
Foldable Sum | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |
Foldable ZipList | @since base-4.9.0.0 |
Defined in GHC.Internal.Functor.ZipList Methods fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # | |
Foldable Par1 | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # | |
Foldable Maybe | @since base-2.01 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |
Foldable Solo | @since base-4.15 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Solo m -> m Source # foldMap :: Monoid m => (a -> m) -> Solo a -> m Source # foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source # foldr :: (a -> b -> b) -> b -> Solo a -> b Source # foldr' :: (a -> b -> b) -> b -> Solo a -> b Source # foldl :: (b -> a -> b) -> b -> Solo a -> b Source # foldl' :: (b -> a -> b) -> b -> Solo a -> b Source # foldr1 :: (a -> a -> a) -> Solo a -> a Source # foldl1 :: (a -> a -> a) -> Solo a -> a Source # toList :: Solo a -> [a] Source # null :: Solo a -> Bool Source # length :: Solo a -> Int Source # elem :: Eq a => a -> Solo a -> Bool Source # maximum :: Ord a => Solo a -> a Source # minimum :: Ord a => Solo a -> a Source # | |
Foldable [] | @since base-2.01 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # | |
Foldable (Arg a) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # | |
Foldable (Array i) | @since base-4.8.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # | |
Foldable (Either a) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |
Foldable (Proxy :: Type -> Type) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # | |
Foldable (U1 :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # | |
Foldable (UAddr :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # | |
Foldable (UChar :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |
Foldable (UDouble :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |
Foldable (UFloat :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |
Foldable (UInt :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |
Foldable (UWord :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |
Foldable (V1 :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # | |
Foldable ((,) a) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # | |
Foldable (Const m :: Type -> Type) | @since base-4.7.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldr :: (a -> b -> b) -> b -> Const m a -> b Source # foldr' :: (a -> b -> b) -> b -> Const m a -> b Source # foldl :: (b -> a -> b) -> b -> Const m a -> b Source # foldl' :: (b -> a -> b) -> b -> Const m a -> b Source # foldr1 :: (a -> a -> a) -> Const m a -> a Source # foldl1 :: (a -> a -> a) -> Const m a -> a Source # toList :: Const m a -> [a] Source # null :: Const m a -> Bool Source # length :: Const m a -> Int Source # elem :: Eq a => a -> Const m a -> Bool Source # maximum :: Ord a => Const m a -> a Source # minimum :: Ord a => Const m a -> a Source # | |
Foldable f => Foldable (Ap f) | @since base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # | |
Foldable f => Foldable (Alt f) | @since base-4.12.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # | |
Foldable f => Foldable (Rec1 f) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # | |
(Foldable f, Foldable g) => Foldable (Product f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source # foldr :: (a -> b -> b) -> b -> Product f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source # foldl :: (b -> a -> b) -> b -> Product f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source # foldr1 :: (a -> a -> a) -> Product f g a -> a Source # foldl1 :: (a -> a -> a) -> Product f g a -> a Source # toList :: Product f g a -> [a] Source # null :: Product f g a -> Bool Source # length :: Product f g a -> Int Source # elem :: Eq a => a -> Product f g a -> Bool Source # maximum :: Ord a => Product f g a -> a Source # minimum :: Ord a => Product f g a -> a Source # | |
(Foldable f, Foldable g) => Foldable (Sum f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldr1 :: (a -> a -> a) -> Sum f g a -> a Source # foldl1 :: (a -> a -> a) -> Sum f g a -> a Source # toList :: Sum f g a -> [a] Source # null :: Sum f g a -> Bool Source # length :: Sum f g a -> Int Source # elem :: Eq a => a -> Sum f g a -> Bool Source # maximum :: Ord a => Sum f g a -> a Source # minimum :: Ord a => Sum f g a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :*: g) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source # toList :: (f :*: g) a -> [a] Source # null :: (f :*: g) a -> Bool Source # length :: (f :*: g) a -> Int Source # elem :: Eq a => a -> (f :*: g) a -> Bool Source # maximum :: Ord a => (f :*: g) a -> a Source # minimum :: Ord a => (f :*: g) a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :+: g) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # | |
Foldable (K1 i c :: Type -> Type) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # | |
(Foldable f, Foldable g) => Foldable (Compose f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldr1 :: (a -> a -> a) -> Compose f g a -> a Source # foldl1 :: (a -> a -> a) -> Compose f g a -> a Source # toList :: Compose f g a -> [a] Source # null :: Compose f g a -> Bool Source # length :: Compose f g a -> Int Source # elem :: Eq a => a -> Compose f g a -> Bool Source # maximum :: Ord a => Compose f g a -> a Source # minimum :: Ord a => Compose f g a -> a Source # | |
(Foldable f, Foldable g) => Foldable (f :.: g) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # | |
Foldable f => Foldable (M1 i c f) | @since base-4.9.0.0 |
Defined in GHC.Internal.Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where Source #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative
(or,
therefore, Monad
) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #
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
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
sequenceA :: Applicative f => t (f a) -> f (t a) Source #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_
.
Examples
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 :: Monad m => (a -> m b) -> t a -> m (t b) Source #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_
.
Examples
sequence :: Monad m => t (m a) -> m (t a) Source #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_
.
Examples
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
Instances
Miscellaneous functions
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
>>>
length $ filter id [True, True, False, True]
3
>>>
Just (Just 3) >>= id
Just 3
>>>
foldr id 0 [(^3), (*5), (+2)]
1000
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
>>>
const 42 "hello"
42
>>>
map (const 42) [0..3]
[42,42,42,42]
(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source #
Right to left function composition.
(f . g) x = f (g x)
f . id = f = id . f
Examples
>>>
map ((*2) . length) [[], [0, 1, 2], [0]]
[0,6,2]
>>>
foldr (.) id [(+1), (*3), (^3)] 2
25
>>>
let (...) = (.).(.) in ((*2)...(+)) 5 10
30
flip :: (a -> b -> c) -> b -> a -> c Source #
takes its (first) two arguments in the reverse order of flip
ff
.
flip f x y = f y x
flip . flip = id
Examples
>>>
flip (++) "hello" "world"
"worldhello"
>>>
let (.>) = flip (.) in (+1) .> show $ 5
"6"
($) :: (a -> b) -> a -> b infixr 0 Source #
is the function application operator.($)
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 ($) f x = f x
This is
specialized from id
a -> a
to (a -> b) -> (a -> b)
which by the associativity of (->)
is the same as (a -> b) -> a -> b
.
On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.
The order of operations is very different between ($)
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
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)
($)
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
until :: (a -> Bool) -> (a -> a) -> a -> a Source #
yields the result of applying until
p ff
until p
holds.
errorWithoutStackTrace :: [Char] -> a Source #
A variant of error
that does not produce a stack trace.
@since base-4.9.0.0
undefined :: HasCallStack => a Source #
seq :: a -> b -> b infixr 0 Source #
The value of
is bottom if seq
a ba
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
does
not guarantee that seq
a ba
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.
($!) :: (a -> b) -> a -> b infixr 0 Source #
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.
List operations
map :: (a -> b) -> [a] -> [b] Source #
\(\mathcal{O}(n)\). 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
>>>
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]
(++) :: [a] -> [a] -> [a] infixr 5 Source #
(++)
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
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
>>>
[1, 2, 3] ++ [4, 5, 6]
[1,2,3,4,5,6]
>>>
[] ++ [1, 2, 3]
[1,2,3]
>>>
[3, 2, 1] ++ []
[3,2,1]
filter :: (a -> Bool) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). 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
>>>
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]
head :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}
at the top of the file. To disable it throughout a package put the same
options into ghc-options
section of Cabal file. To disable it in GHCi
put :set -Wno-x-partial -Wno-unrecognised-warning-flags
into ~/.ghci
config file.
See also the migration guide.
Examples
>>>
head [1, 2, 3]
1
>>>
head [1..]
1
>>>
head []
*** Exception: Prelude.head: empty list
last :: HasCallStack => [a] -> a Source #
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
WARNING: This function is partial. Consider using unsnoc
instead.
Examples
>>>
last [1, 2, 3]
3
>>>
last [1..]
* Hangs forever *
>>>
last []
*** Exception: Prelude.last: empty list
tail :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
To disable the warning about partiality put {-# OPTIONS_GHC -Wno-x-partial -Wno-unrecognised-warning-flags #-}
at the top of the file. To disable it throughout a package put the same
options into ghc-options
section of Cabal file. To disable it in GHCi
put :set -Wno-x-partial -Wno-unrecognised-warning-flags
into ~/.ghci
config file.
See also the migration guide.
Examples
>>>
tail [1, 2, 3]
[2,3]
>>>
tail [1]
[]
>>>
tail []
*** Exception: Prelude.tail: empty list
init :: HasCallStack => [a] -> [a] Source #
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
WARNING: This function is partial. Consider using unsnoc
instead.
Examples
>>>
init [1, 2, 3]
[1,2]
>>>
init [1]
[]
>>>
init []
*** Exception: Prelude.init: empty list
(!!) :: HasCallStack => [a] -> Int -> a infixl 9 Source #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex
,
which takes an index of any integral type.
WARNING: This function is partial, and should only be used if you are
sure that the indexing will not fail. Otherwise, use !?
.
WARNING: This function takes linear time in the index.
Examples
>>>
['a', 'b', 'c'] !! 0
'a'
>>>
['a', 'b', 'c'] !! 2
'c'
>>>
['a', 'b', 'c'] !! 3
*** Exception: Prelude.!!: index too large
>>>
['a', 'b', 'c'] !! (-1)
*** Exception: Prelude.!!: negative index
null :: Foldable t => t a -> Bool Source #
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
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 Source #
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
Basic usage:
>>>
length []
0
>>>
length ['a', 'b', 'c']
3>>>
length [1..]
* Hangs forever *
@since base-4.8.0.0
reverse :: [a] -> [a] Source #
\(\mathcal{O}(n)\). reverse
xs
returns the elements of xs
in reverse order.
xs
must be finite.
Laziness
reverse
is lazy in its elements.
>>>
head (reverse [undefined, 1])
1
>>>
reverse (1 : 2 : undefined)
*** Exception: Prelude.undefined
Examples
>>>
reverse []
[]
>>>
reverse [42]
[42]
>>>
reverse [2,5,7]
[7,5,2]
>>>
reverse [1..]
* Hangs forever *
Special folds
and :: Foldable t => t Bool -> Bool Source #
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
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 Source #
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
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 *
any :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether any element of the structure satisfies the predicate.
Examples
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 *
all :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether all elements of the structure satisfy the predicate.
Examples
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 *
concat :: Foldable t => t [a] -> [a] Source #
The concatenation of all the elements of a container of lists.
Examples
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] Source #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
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]
Building lists
Scans
scanl :: (b -> a -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanl
is similar to foldl
, but returns a list of
successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs
Examples
>>>
scanl (+) 0 [1..4]
[0,1,3,6,10]
>>>
scanl (+) 42 []
[42]
>>>
scanl (-) 100 [1..4]
[100,99,97,94,90]
>>>
scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["foo","afoo","bafoo","cbafoo","dcbafoo"]
>>>
take 10 (scanl (+) 0 [1..])
[0,1,3,6,10,15,21,28,36,45]
>>>
take 1 (scanl undefined 'a' undefined)
"a"
scanl1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanl1
is a variant of scanl
that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
Examples
>>>
scanl1 (+) [1..4]
[1,3,6,10]
>>>
scanl1 (+) []
[]
>>>
scanl1 (-) [1..4]
[1,-1,-4,-8]
>>>
scanl1 (&&) [True, False, True, True]
[True,False,False,False]
>>>
scanl1 (||) [False, False, True, True]
[False,False,True,True]
>>>
take 10 (scanl1 (+) [1..])
[1,3,6,10,15,21,28,36,45,55]
>>>
take 1 (scanl1 undefined ('a' : undefined))
"a"
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanr
is the right-to-left dual of scanl
. Note that the order of parameters on the accumulating function are reversed compared to scanl
.
Also note that
head (scanr f z xs) == foldr f z xs.
Examples
>>>
scanr (+) 0 [1..4]
[10,9,7,4,0]
>>>
scanr (+) 42 []
[42]
>>>
scanr (-) 100 [1..4]
[98,-97,99,-96,100]
>>>
scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']
["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]
>>>
force $ scanr (+) 0 [1..]
*** Exception: stack overflow
scanr1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanr1
is a variant of scanr
that has no starting
value argument.
Examples
>>>
scanr1 (+) [1..4]
[10,9,7,4]
>>>
scanr1 (+) []
[]
>>>
scanr1 (-) [1..4]
[-2,3,-1,4]
>>>
scanr1 (&&) [True, False, True, True]
[False,False,True,True]
>>>
scanr1 (||) [True, True, False, False]
[True,True,False,False]
>>>
force $ scanr1 (+) [1..]
*** Exception: stack overflow
Infinite lists
iterate :: (a -> a) -> a -> [a] Source #
iterate
f x
returns an infinite list of repeated applications
of f
to x
:
iterate f x == [x, f x, f (f x), ...]
Laziness
Note that iterate
is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate'
for a strict
variant of this function.
>>>
take 1 $ iterate undefined 42
[42]
Examples
>>>
take 10 $ iterate not True
[True,False,True,False,True,False,True,False,True,False]
>>>
take 10 $ iterate (+3) 42
[42,45,48,51,54,57,60,63,66,69]
iterate id ==
:repeat
>>>
take 10 $ iterate id 1
[1,1,1,1,1,1,1,1,1,1]
repeat
x
is an infinite list, with x
the value of every element.
Examples
>>>
take 10 $ repeat 17
[17,17,17,17,17,17,17,17,17, 17]
>>>
repeat undefined
[*** Exception: Prelude.undefined
replicate :: Int -> a -> [a] Source #
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
>>>
replicate 0 True
[]
>>>
replicate (-1) True
[]
>>>
replicate 4 True
[True,True,True,True]
cycle :: HasCallStack => [a] -> [a] Source #
cycle
ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
Examples
>>>
cycle []
*** Exception: Prelude.cycle: empty list
>>>
take 10 (cycle [42])
[42,42,42,42,42,42,42,42,42,42]
>>>
take 10 (cycle [2, 5, 7])
[2,5,7,2,5,7,2,5,7,2]
>>>
take 1 (cycle (42 : undefined))
[42]
Sublists
take :: Int -> [a] -> [a] Source #
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
>>>
take 0 undefined
[]>>>
take 2 (1 : 2 : undefined)
[1,2]
Examples
>>>
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]
[]
drop :: Int -> [a] -> [a] Source #
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
>>>
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]
takeWhile :: (a -> Bool) -> [a] -> [a] Source #
takeWhile
, applied to a predicate p
and a list xs
, returns the
longest prefix (possibly empty) of xs
of elements that satisfy p
.
Laziness
>>>
takeWhile (const False) undefined
*** Exception: Prelude.undefined
>>>
takeWhile (const False) (undefined : undefined)
[]
>>>
take 1 (takeWhile (const True) (1 : undefined))
[1]
Examples
>>>
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]
[]
span :: (a -> Bool) -> [a] -> ([a], [a]) Source #
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 (
, even if takeWhile
p xs, dropWhile
p xs)p
is _|_
.
Laziness
>>>
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
>>>
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])
break :: (a -> Bool) -> [a] -> ([a], [a]) Source #
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
and consequently to span
(not
. p)(
,
even if takeWhile
(not
. p) xs, dropWhile
(not
. p) xs)p
is _|_
.
Laziness
>>>
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
>>>
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],[])
splitAt :: Int -> [a] -> ([a], [a]) Source #
splitAt
n xs
returns a tuple where first element is xs
prefix of
length n
and second element is the remainder of the list:
splitAt
is an instance of the more general genericSplitAt
,
in which n
may be of any integral type.
Laziness
It is equivalent to (
unless take
n xs, drop
n xs)n
is _|_
:
splitAt _|_ xs = _|_
, not (_|_, _|_)
).
The first component of the tuple is produced lazily:
>>>
fst (splitAt 0 undefined)
[]
>>>
take 1 (fst (splitAt 10 (1 : undefined)))
[1]
Examples
>>>
splitAt 6 "Hello World!"
("Hello ","World!")
>>>
splitAt 3 [1,2,3,4,5]
([1,2,3],[4,5])
>>>
splitAt 1 [1,2,3]
([1],[2,3])
>>>
splitAt 3 [1,2,3]
([1,2,3],[])
>>>
splitAt 4 [1,2,3]
([1,2,3],[])
>>>
splitAt 0 [1,2,3]
([],[1,2,3])
>>>
splitAt (-1) [1,2,3]
([],[1,2,3])
Searching lists
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #
notElem
is the negation of elem
.
Examples
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 *
Zipping and unzipping lists
zip :: [a] -> [b] -> [(a, b)] Source #
\(\mathcal{O}(\min(m,n))\). 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
>>>
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] Source #
\(\mathcal{O}(\min(m,n))\). 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
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #
\(\mathcal{O}(\min(l,m,n))\). The zipWith3
function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith
.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
Examples
>>>
zipWith3 (\x y z -> [x, y, z]) "123" "abc" "xyz"
["1ax","2by","3cz"]
>>>
zipWith3 (\x y z -> (x * y) + z) [1, 2, 3] [4, 5, 6] [7, 8, 9]
[11,18,27]
unzip :: [(a, b)] -> ([a], [b]) Source #
unzip
transforms a list of pairs into a list of first components
and a list of second components.
Examples
>>>
unzip []
([],[])
>>>
unzip [(1, 'a'), (2, 'b')]
([1,2],"ab")
Functions on strings
lines :: String -> [String] Source #
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
>>>
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"]
Converting to and from String
Converting to String
Conversion of values to readable String
s.
Derived instances of Show
have the following properties, which
are compatible with derived instances of Read
:
- The result of
show
is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrec
will produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
x
is less thand
(associativity is ignored). Thus, ifd
is0
then the result is never surrounded in parentheses; ifd
is11
it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
show
will produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show
is equivalent to
instance (Show a) => Show (Tree a) where showsPrec d (Leaf m) = showParen (d > app_prec) $ showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec) $ showsPrec (up_prec+1) u . showString " :^: " . showsPrec (up_prec+1) v where up_prec = 5
Note that right-associativity of :^:
is ignored. For example,
produces the stringshow
(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)"
.
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> a | the value to be converted to a |
-> ShowS |
Convert a value to a readable String
.
showsPrec
should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read
and Show
satisfy the following:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that showsPrec
started with.
Instances
Show ByteArray Source # | Since: base-4.17.0.0 |
Show Timeout Source # | Since: base-4.0 |
Show Void | @since base-4.8.0.0 |
Show ByteOrder | @since base-4.11.0.0 |
Show ClosureType | |
Defined in GHC.Internal.ClosureTypes | |
Show BlockReason | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync | |
Show ThreadId | @since base-4.2.0.0 |
Show ThreadStatus | @since base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync | |
Show NestedAtomically | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show NoMatchingContinuationPrompt | @since base-4.18 |
Defined in GHC.Internal.Control.Exception.Base | |
Show NoMethodError | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show NonTermination | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show PatternMatchFail | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show RecConError | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show RecSelError | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show RecUpdError | @since base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
Show TypeError | @since base-4.9.0.0 |
Show Constr | @since base-4.0.0.0 |
Show ConstrRep | @since base-4.0.0.0 |
Show DataRep | @since base-4.0.0.0 |
Show DataType | @since base-4.0.0.0 |
Show Fixity | @since base-4.0.0.0 |
Show Dynamic | @since base-2.01 |
Show All | @since base-2.01 |
Show Any | @since base-2.01 |
Show SomeTypeRep | @since base-4.10.0.0 |
Defined in GHC.Internal.Data.Typeable.Internal | |
Show Version | @since base-2.01 |
Show ControlMessage | @since base-4.4.0.0 |
Show Event | @since base-4.4.0.0 |
Show EventLifetime | @since base-4.8.0.0 |
Show Lifetime | @since base-4.8.1.0 |
Show Timeout | @since base-4.4.0.0 |
Show FdKey | @since base-4.4.0.0 |
Show State | @since base-4.4.0.0 |
Show State | @since base-4.7.0.0 |
Show Unique | @since base-4.3.1.0 |
Show ErrorCall | @since base-4.0.0.0 |
Show ArithException | @since base-4.0.0.0 |
Defined in GHC.Internal.Exception.Type | |
Show SomeException | Since: ghc-internal-3.0 |
Defined in GHC.Internal.Exception.Type | |
Show Fingerprint | @since base-4.7.0.0 |
Defined in GHC.Internal.Fingerprint.Type | |
Show CBool | |
Show CChar | |
Show CClock | |
Show CDouble | |
Show CFloat | |
Show CInt | |
Show CIntMax | |
Show CIntPtr | |
Show CLLong | |
Show CLong | |
Show CPtrdiff | |
Show CSChar | |
Show CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
Show CShort | |
Show CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
Show CSize | |
Show CTime | |
Show CUChar | |
Show CUInt | |
Show CUIntMax | |
Show CUIntPtr | |
Show CULLong | |
Show CULong | |
Show CUSeconds | |
Show CUShort | |
Show CWchar | |
Show IntPtr | |
Show WordPtr | |
Show Associativity | @since base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
Show DecidedStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Show Fixity | @since base-4.6.0.0 |
Show SourceStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Show SourceUnpackedness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Show MaskingState | @since base-4.3.0.0 |
Defined in GHC.Internal.IO | |
Show SeekMode | @since base-4.2.0.0 |
Show CodingFailureMode | @since base-4.4.0.0 |
Defined in GHC.Internal.IO.Encoding.Failure | |
Show CodingProgress | @since base-4.4.0.0 |
Defined in GHC.Internal.IO.Encoding.Types | |
Show TextEncoding | @since base-4.3.0.0 |
Defined in GHC.Internal.IO.Encoding.Types | |
Show AllocationLimitExceeded | @since base-4.7.1.0 |
Defined in GHC.Internal.IO.Exception | |
Show ArrayException | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show AssertionFailed | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show AsyncException | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show BlockedIndefinitelyOnMVar | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show BlockedIndefinitelyOnSTM | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show CompactionFailed | @since base-4.10.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show Deadlock | @since base-4.1.0.0 |
Show ExitCode | |
Show FixIOException | @since base-4.11.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show IOErrorType | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show IOException | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show SomeAsyncException | @since base-4.7.0.0 |
Defined in GHC.Internal.IO.Exception | |
Show FD | @since base-4.1.0.0 |
Show HandlePosn | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Handle | |
Show FileLockingNotSupported | @since base-4.10.0.0 |
Defined in GHC.Internal.IO.Handle.Lock.Common | |
Show BufferMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Show Handle | @since base-4.1.0.0 |
Show HandleType | @since base-4.1.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Show Newline | @since base-4.3.0.0 |
Show NewlineMode | @since base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Show IOMode | @since base-4.2.0.0 |
Show IOPortException | |
Show InfoProv | |
Show Int16 | @since base-2.01 |
Show Int32 | @since base-2.01 |
Show Int64 | @since base-2.01 |
Show Int8 | @since base-2.01 |
Show CCFlags | @since base-4.8.0.0 |
Show ConcFlags | @since base-4.8.0.0 |
Show DebugFlags | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show DoCostCentres | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show DoHeapProfile | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show DoTrace | @since base-4.8.0.0 |
Show GCFlags | @since base-4.8.0.0 |
Show GiveGCStats | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show HpcFlags | @since base-4.20.0.0 |
Show IoSubSystem | |
Defined in GHC.Internal.RTS.Flags | |
Show MiscFlags | @since base-4.8.0.0 |
Show ParFlags | @since base-4.8.0.0 |
Show ProfFlags | @since base-4.8.0.0 |
Show RTSFlags | @since base-4.8.0.0 |
Show TickyFlags | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show TraceFlags | @since base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
Show FractionalExponentBase | |
Defined in GHC.Internal.Real | |
Show StackEntry | |
Defined in GHC.Internal.Stack.CloneStack | |
Show CallStack | @since base-4.9.0.0 |
Show SrcLoc | @since base-4.9.0.0 |
Show StaticPtrInfo | @since base-4.8.0.0 |
Defined in GHC.Internal.StaticPtr | |
Show GCDetails | @since base-4.10.0.0 |
Show RTSStats | @since base-4.10.0.0 |
Show CBlkCnt | |
Show CBlkSize | |
Show CCc | |
Show CClockId | |
Show CDev | |
Show CFsBlkCnt | |
Show CFsFilCnt | |
Show CGid | |
Show CId | |
Show CIno | |
Show CKey | |
Show CMode | |
Show CNfds | |
Show CNlink | |
Show COff | |
Show CPid | |
Show CRLim | |
Show CSocklen | |
Show CSpeed | |
Show CSsize | |
Show CTcflag | |
Show CTimer | |
Show CUid | |
Show Fd | |
Show Lexeme | @since base-2.01 |
Show Number | @since base-4.6.0.0 |
Show SomeChar | |
Show SomeSymbol | @since base-4.7.0.0 |
Defined in GHC.Internal.TypeLits | |
Show SomeNat | @since base-4.7.0.0 |
Show GeneralCategory | @since base-2.01 |
Defined in GHC.Internal.Unicode | |
Show Word16 | @since base-2.01 |
Show Word32 | @since base-2.01 |
Show Word64 | @since base-2.01 |
Show Word8 | @since base-2.01 |
Show KindRep | |
Show Module | @since base-4.9.0.0 |
Show Ordering | @since base-2.01 |
Show TrName | @since base-4.9.0.0 |
Show TyCon | @since base-2.01 |
Show TypeLitSort | @since base-4.11.0.0 |
Defined in GHC.Internal.Show | |
Show Integer | @since base-2.01 |
Show Natural | @since base-4.8.0.0 |
Show () | @since base-2.01 |
Show Bool | @since base-2.01 |
Show Char | @since base-2.01 |
Show Int | @since base-2.01 |
Show Levity | @since base-4.15.0.0 |
Show RuntimeRep | @since base-4.11.0.0 |
Defined in GHC.Internal.Show | |
Show VecCount | @since base-4.11.0.0 |
Show VecElem | @since base-4.11.0.0 |
Show Word | @since base-2.01 |
Show a => Show (Complex a) Source # | Since: base-2.1 |
Show a => Show (First a) Source # | Since: base-4.9.0.0 |
Show a => Show (Last a) Source # | Since: base-4.9.0.0 |
Show a => Show (Max a) Source # | Since: base-4.9.0.0 |
Show a => Show (Min a) Source # | Since: base-4.9.0.0 |
Show m => Show (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Show a => Show (NonEmpty a) | @since base-4.11.0.0 |
Show a => Show (And a) | @since base-4.16 |
Show a => Show (Iff a) | @since base-4.16 |
Show a => Show (Ior a) | @since base-4.16 |
Show a => Show (Xor a) | @since base-4.16 |
Show a => Show (Identity a) | This instance would be equivalent to the derived instances of the
@since base-4.8.0.0 |
Show a => Show (First a) | @since base-2.01 |
Show a => Show (Last a) | @since base-2.01 |
Show a => Show (Down a) | This instance would be equivalent to the derived instances of the
@since base-4.7.0.0 |
Show a => Show (Dual a) | @since base-2.01 |
Show a => Show (Product a) | @since base-2.01 |
Show a => Show (Sum a) | @since base-2.01 |
Show a => Show (ExceptionWithContext a) | |
Defined in GHC.Internal.Exception.Type | |
Show e => Show (NoBacktrace e) | |
Defined in GHC.Internal.Exception.Type | |
Show (ConstPtr a) | |
Show (ForeignPtr a) | @since base-2.01 |
Defined in GHC.Internal.ForeignPtr | |
Show a => Show (ZipList a) | @since base-4.7.0.0 |
Show p => Show (Par1 p) | @since base-4.7.0.0 |
Show (FunPtr a) | @since base-2.01 |
Show (Ptr a) | @since base-2.01 |
Show a => Show (Ratio a) | @since base-2.0.1 |
Show (SChar c) | @since base-4.18.0.0 |
Show (SSymbol s) | @since base-4.18.0.0 |
Show (SNat n) | @since base-4.18.0.0 |
Show a => Show (Maybe a) | @since base-2.01 |
Show a => Show (Solo a) | @since base-4.15 |
Show a => Show [a] | @since base-2.01 |
HasResolution a => Show (Fixed a) Source # | Since: base-2.1 |
(Show a, Show b) => Show (Arg a b) Source # | Since: base-4.9.0.0 |
(Ix a, Show a, Show b) => Show (Array a b) | @since base-2.01 |
(Show a, Show b) => Show (Either a b) | @since base-3.0 |
Show (Proxy s) | @since base-4.7.0.0 |
Show (TypeRep a) | |
Show (U1 p) | @since base-4.9.0.0 |
Show (V1 p) | @since base-4.9.0.0 |
Show (ST s a) | @since base-2.01 |
(Show a, Show b) => Show (a, b) | @since base-2.01 |
Show (a -> b) Source # | Since: base-2.1 |
Show a => Show (Const a b) | This instance would be equivalent to the derived instances of the
@since base-4.8.0.0 |
Show (f a) => Show (Ap f a) | @since base-4.12.0.0 |
Show (f a) => Show (Alt f a) | @since base-4.8.0.0 |
Show (Coercion a b) | @since base-4.7.0.0 |
Show (a :~: b) | @since base-4.7.0.0 |
Show (OrderingI a b) | |
Show (f p) => Show (Rec1 f p) | @since base-4.7.0.0 |
Show (URec Char p) | @since base-4.9.0.0 |
Show (URec Double p) | @since base-4.9.0.0 |
Show (URec Float p) | |
Show (URec Int p) | @since base-4.9.0.0 |
Show (URec Word p) | @since base-4.9.0.0 |
(Show a, Show b, Show c) => Show (a, b, c) | @since base-2.01 |
(Show (f a), Show (g a)) => Show (Product f g a) Source # | Since: base-4.18.0.0 |
(Show (f a), Show (g a)) => Show (Sum f g a) Source # | Since: base-4.18.0.0 |
Show (a :~~: b) | @since base-4.10.0.0 |
(Show (f p), Show (g p)) => Show ((f :*: g) p) | @since base-4.7.0.0 |
(Show (f p), Show (g p)) => Show ((f :+: g) p) | @since base-4.7.0.0 |
Show c => Show (K1 i c p) | @since base-4.7.0.0 |
(Show a, Show b, Show c, Show d) => Show (a, b, c, d) | @since base-2.01 |
Show (f (g a)) => Show (Compose f g a) Source # | Since: base-4.18.0.0 |
Show (f (g p)) => Show ((f :.: g) p) | @since base-4.7.0.0 |
Show (f p) => Show (M1 i c f p) | @since base-4.7.0.0 |
(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | @since base-2.01 |
(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | @since base-2.01 |
showChar :: Char -> ShowS Source #
utility function converting a Char
to a show function that
simply prepends the character unchanged.
showString :: String -> ShowS Source #
utility function converting a String
to a show function that
simply prepends the string unchanged.
Converting from String
Parsing of String
s, producing values.
Derived instances of Read
make the following assumptions, which
derived instances of Show
obey:
- If the constructor is defined to be an infix operator, then the
derived
Read
instance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Read
will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Read
instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read
in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5
Note that right-associativity of :^:
is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where readPrec = parens $ (prec app_prec $ do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec $ do u <- step readPrec Symbol ":^:" <- lexP v <- step readPrec return (u :^: v)) where app_prec = 10 up_prec = 5 readListPrec = readListPrecDefault
Why do both readsPrec
and readPrec
exist, and why does GHC opt to
implement readPrec
in derived Read
instances instead of readsPrec
?
The reason is that readsPrec
is based on the ReadS
type, and although
ReadS
is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec
, on the other hand, is based on a much more efficient ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the RankNTypes
language extension. Therefore, readPrec
(and its
cousin, readListPrec
) are marked as GHC-only. Nevertheless, it is
recommended to use readPrec
instead of readsPrec
whenever possible
for the efficiency improvements it brings.
As mentioned above, derived Read
instances in GHC will implement
readPrec
instead of readsPrec
. The default implementations of
readsPrec
(and its cousin, readList
) will simply use readPrec
under
the hood. If you are writing a Read
instance by hand, it is recommended
to write it like so:
instanceRead
T wherereadPrec
= ...readListPrec
=readListPrecDefault
Methods
Arguments
:: Int | the operator precedence of the enclosing
context (a number from |
-> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read
and Show
satisfy the following:
That is, readsPrec
parses the string produced by
showsPrec
, and delivers the value that
showsPrec
started with.
Instances
Read Void | Reading a @since base-4.8.0.0 |
Read ByteOrder | @since base-4.11.0.0 |
Read All | @since base-2.01 |
Read Any | @since base-2.01 |
Read Version | @since base-2.01 |
Read CBool | |
Read CChar | |
Read CClock | |
Read CDouble | |
Read CFloat | |
Read CInt | |
Read CIntMax | |
Read CIntPtr | |
Read CLLong | |
Read CLong | |
Read CPtrdiff | |
Read CSChar | |
Read CSUSeconds | |
Defined in GHC.Internal.Foreign.C.Types | |
Read CShort | |
Read CSigAtomic | |
Defined in GHC.Internal.Foreign.C.Types | |
Read CSize | |
Read CTime | |
Read CUChar | |
Read CUInt | |
Read CUIntMax | |
Read CUIntPtr | |
Read CULLong | |
Read CULong | |
Read CUSeconds | |
Read CUShort | |
Read CWchar | |
Read IntPtr | |
Read WordPtr | |
Read Associativity | @since base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
Read DecidedStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Read Fixity | @since base-4.6.0.0 |
Read SourceStrictness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Read SourceUnpackedness | @since base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
Read SeekMode | @since base-4.2.0.0 |
Read ExitCode | |
Read BufferMode | @since base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Read Newline | @since base-4.3.0.0 |
Read NewlineMode | @since base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
Read IOMode | @since base-4.2.0.0 |
Read Int16 | @since base-2.01 |
Read Int32 | @since base-2.01 |
Read Int64 | @since base-2.01 |
Read Int8 | @since base-2.01 |
Read GCDetails | @since base-4.10.0.0 |
Read RTSStats | @since base-4.10.0.0 |
Read CBlkCnt | |
Read CBlkSize | |
Read CCc | |
Read CClockId | |
Read CDev | |
Read CFsBlkCnt | |
Read CFsFilCnt | |
Read CGid | |
Read CId | |
Read CIno | |
Read CKey | |
Read CMode | |
Read CNfds | |
Read CNlink | |
Read COff | |
Read CPid | |
Read CRLim | |
Read CSocklen | |
Read CSpeed | |
Read CSsize | |
Read CTcflag | |
Read CUid | |
Read Fd | |
Read Lexeme | @since base-2.01 |
Read SomeChar | |
Read SomeSymbol | @since base-4.7.0.0 |
Defined in GHC.Internal.TypeLits | |
Read SomeNat | @since base-4.7.0.0 |
Read GeneralCategory | @since base-2.01 |
Defined in GHC.Internal.Read | |
Read Word16 | @since base-2.01 |
Read Word32 | @since base-2.01 |
Read Word64 | @since base-2.01 |
Read Word8 | @since base-2.01 |
Read Ordering | @since base-2.01 |
Read Integer | @since base-2.01 |
Read Natural | @since base-4.8.0.0 |
Read () | @since base-2.01 |
Read Bool | @since base-2.01 |
Read Char | @since base-2.01 |
Read Double | @since base-2.01 |
Read Float | @since base-2.01 |
Read Int | @since base-2.01 |
Read Word | @since base-4.5.0.0 |
Read a => Read (Complex a) Source # | Since: base-2.1 |
Read a => Read (First a) Source # | Since: base-4.9.0.0 |
Read a => Read (Last a) Source # | Since: base-4.9.0.0 |
Read a => Read (Max a) Source # | Since: base-4.9.0.0 |
Read a => Read (Min a) Source # | Since: base-4.9.0.0 |
Read m => Read (WrappedMonoid m) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source # readList :: ReadS [WrappedMonoid m] Source # readPrec :: ReadPrec (WrappedMonoid m) Source # readListPrec :: ReadPrec [WrappedMonoid m] Source # | |
Read a => Read (NonEmpty a) | @since base-4.11.0.0 |
Read a => Read (And a) | @since base-4.16 |
Read a => Read (Iff a) | @since base-4.16 |
Read a => Read (Ior a) | @since base-4.16 |
Read a => Read (Xor a) | @since base-4.16 |
Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
@since base-4.8.0.0 |
Read a => Read (First a) | @since base-2.01 |
Read a => Read (Last a) | @since base-2.01 |
Read a => Read (Down a) | This instance would be equivalent to the derived instances of the
@since base-4.7.0.0 |
Read a => Read (Dual a) | @since base-2.01 |
Read a => Read (Product a) | @since base-2.01 |
Read a => Read (Sum a) | @since base-2.01 |
Read a => Read (ZipList a) | @since base-4.7.0.0 |
Read p => Read (Par1 p) | @since base-4.7.0.0 |
(Integral a, Read a) => Read (Ratio a) | @since base-2.01 |
Read a => Read (Maybe a) | @since base-2.01 |
Read a => Read (Solo a) | @since base-4.15 |
Read a => Read [a] | @since base-2.01 |
HasResolution a => Read (Fixed a) Source # | Since: base-4.3.0.0 |
(Read a, Read b) => Read (Arg a b) Source # | Since: base-4.9.0.0 |
(Ix a, Read a, Read b) => Read (Array a b) | @since base-2.01 |
(Read a, Read b) => Read (Either a b) | @since base-3.0 |
Read (Proxy t) | @since base-4.7.0.0 |
Read (U1 p) | @since base-4.9.0.0 |
Read (V1 p) | @since base-4.9.0.0 |
(Read a, Read b) => Read (a, b) | @since base-2.01 |
Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
@since base-4.8.0.0 |
Read (f a) => Read (Ap f a) | @since base-4.12.0.0 |
Read (f a) => Read (Alt f a) | @since base-4.8.0.0 |
Coercible a b => Read (Coercion a b) | @since base-4.7.0.0 |
a ~ b => Read (a :~: b) | @since base-4.7.0.0 |
Read (f p) => Read (Rec1 f p) | @since base-4.7.0.0 |
(Read a, Read b, Read c) => Read (a, b, c) | @since base-2.01 |
(Read (f a), Read (g a)) => Read (Product f g a) Source # | Since: base-4.18.0.0 |
(Read (f a), Read (g a)) => Read (Sum f g a) Source # | Since: base-4.18.0.0 |
a ~~ b => Read (a :~~: b) | @since base-4.10.0.0 |
(Read (f p), Read (g p)) => Read ((f :*: g) p) | @since base-4.7.0.0 |
(Read (f p), Read (g p)) => Read ((f :+: g) p) | @since base-4.7.0.0 |
Read c => Read (K1 i c p) | @since base-4.7.0.0 |
(Read a, Read b, Read c, Read d) => Read (a, b, c, d) | @since base-2.01 |
Read (f (g a)) => Read (Compose f g a) Source # | Since: base-4.18.0.0 |
Read (f (g p)) => Read ((f :.: g) p) | @since base-4.7.0.0 |
Read (f p) => Read (M1 i c f p) | @since base-4.7.0.0 |
(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | @since base-2.01 |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | @since base-2.01 |
Defined in GHC.Internal.Read | |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | @since base-2.01 |
Defined in GHC.Internal.Read | |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | @since base-2.01 |
Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # | |
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | @since base-2.01 |
Defined in GHC.Internal.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # |
read :: Read a => String -> a Source #
The read
function reads input from a string, which must be
completely consumed by the input process. read
fails with an error
if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe
or readEither
for safe alternatives.
>>>
read "123" :: Int
123
>>>
read "hello" :: Int
*** Exception: Prelude.read: no parse
The lex
function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, lex
returns a
single successful `lexeme' consisting of the empty string. (Thus
.) If there is no legal lexeme at the
beginning of the input string, lex
"" = [("","")]lex
fails (i.e. returns []
).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
Basic Input and output
A value of type
is a computation which, when performed,
does some I/O before returning a value of type IO
aa
.
There is really only one way to "perform" an I/O action: bind it to
Main.main
in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the IO
monad and called
at some point, directly or indirectly, from Main.main
.
IO
is a monad, so IO
actions can be combined using either the do-notation
or the >>
and >>=
operations from the Monad
class.
Instances
MonadIO IO Source # | Since: base-4.9.0.0 |
Alternative IO | Takes the first non-throwing @since base-4.9.0.0 |
Applicative IO | @since base-2.01 |
Functor IO | @since base-2.01 |
Monad IO | @since base-2.01 |
MonadPlus IO | Takes the first non-throwing @since base-4.9.0.0 |
MonadFail IO | @since base-4.9.0.0 |
MonadFix IO | @since base-2.01 |
GHCiSandboxIO IO | @since base-4.4.0.0 |
Defined in GHC.Internal.GHCi Methods ghciStepIO :: IO a -> IO a Source # | |
a ~ () => HPrintfType (IO a) Source # | Since: base-4.7.0.0 |
Defined in Text.Printf | |
a ~ () => PrintfType (IO a) Source # | Since: base-4.7.0.0 |
Defined in Text.Printf | |
Monoid a => Monoid (IO a) | @since base-4.9.0.0 |
Semigroup a => Semigroup (IO a) | @since base-4.10.0.0 |
Simple I/O operations
Output functions
print :: Show a => a -> IO () Source #
The print
function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show
; print
converts values to strings for output using the show
operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
Input functions
getContents :: IO String Source #
The getContents
operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents
stdin
).
interact :: (String -> String) -> IO () Source #
The interact
function takes a function of type String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
Files
type FilePath = String Source #
File and directory names are values of type String
, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
readFile :: FilePath -> IO String Source #
The readFile
function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with getContents
.
writeFile :: FilePath -> String -> IO () Source #
The computation writeFile
file str
function writes the string str
,
to the file file
.
appendFile :: FilePath -> String -> IO () Source #
The computation appendFile
file str
function appends the string str
,
to the file file
.
Note that writeFile
and appendFile
write a literal string
to a file. To write a value of any printable type, as with print
,
use the show
function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
Exception handling in the I/O monad
type IOError = IOException Source #