| 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 :: HasCallStack => 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 Source # | 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 Source # | 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 Source # | 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 Source # | Since: base-2.1 | ||||
| Enum Bool Source # | Since: base-2.1 | ||||
| Storable Bool Source # | Since: base-2.1 | ||||
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 Source # | |||||
Defined in GHC.Internal.Generics | |||||
| SingKind Bool | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Ix Bool Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Ix | |||||
| Read Bool Source # | Since: base-2.1 | ||||
| Show Bool Source # | Since: base-2.1 | ||||
| Eq Bool Source # | |||||
| Ord Bool Source # | |||||
| 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 | |||||
| Lift Bool Source # | |||||
| type DemoteRep Bool Source # | |||||
Defined in GHC.Internal.Generics | |||||
| type Rep Bool Source # | Since: base-4.6.0.0 | ||||
| data Sing (a :: Bool) Source # | |||||
The Maybe type encapsulates an optional value. A value of type
Maybe aa (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
| 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 Source # | Picks the leftmost Since: base-2.1 | ||||
| Applicative Maybe Source # | Since: base-2.1 | ||||
| Functor Maybe Source # | Since: base-2.1 | ||||
| Monad Maybe Source # | Since: base-2.1 | ||||
| MonadPlus Maybe Source # | Picks the leftmost Since: base-2.1 | ||||
| MonadFail Maybe Source # | Since: base-4.9.0.0 | ||||
| MonadFix Maybe Source # | Since: base-2.1 | ||||
| MonadZip Maybe Source # | Since: ghc-internal-4.8.0.0 | ||||
| Foldable Maybe Source # | Since: base-2.1 | ||||
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 Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Maybe Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Lift a => Lift (Maybe a :: Type) Source # | |||||
| Semigroup a => Monoid (Maybe a) Source # | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 | ||||
| Semigroup a => Semigroup (Maybe a) Source # | Since: base-4.9.0.0 | ||||
| Data a => Data (Maybe a) Source # | 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) Source # | |||||
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) Source # | Since: base-2.1 | ||||
| Show a => Show (Maybe a) Source # | Since: base-2.1 | ||||
| Eq a => Eq (Maybe a) Source # | Since: base-2.1 | ||||
| Ord a => Ord (Maybe a) Source # | Since: base-2.1 | ||||
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 Source # | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type DemoteRep (Maybe a) Source # | |||||
Defined in GHC.Internal.Generics | |||||
| type Rep (Maybe a) Source # | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| data Sing (b :: Maybe a) Source # | |||||
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 NothingFalse
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 Either a bLeft aRight 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 Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: 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) sLeft "foo">>>fmap (*2) nRight 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 Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 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)>>>:}
>>>parseMultipleLeft "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) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| (Lift a, Lift b) => Lift (Either a b :: Type) Source # | |||||
| 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) Source # | Since: base-3.0 | ||||
Defined in GHC.Internal.Data.Either | |||||
| Functor (Either a) Source # | Since: base-3.0 | ||||
| Monad (Either e) Source # | Since: base-4.4.0.0 | ||||
| MonadFix (Either e) Source # | Since: base-4.3.0.0 | ||||
| Foldable (Either a) Source # | 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) Source # | 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) Source # | Since: base-4.9.0.0 | ||||
| (Data a, Data b) => Data (Either a b) Source # | 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) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| (Read a, Read b) => Read (Either a b) Source # | Since: base-3.0 | ||||
| (Show a, Show b) => Show (Either a b) Source # | Since: base-3.0 | ||||
| (Eq a, Eq b) => Eq (Either a b) Source # | Since: base-2.1 | ||||
| (Ord a, Ord b) => Ord (Either a b) Source # | Since: base-2.1 | ||||
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) Source # | 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) Source # | 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 Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft 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) s3>>>either length (*2) n6
Instances
| Monoid Ordering Source # | Since: base-2.1 |
| Semigroup Ordering Source # | Since: base-4.9.0.0 |
| Data Ordering Source # | 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 Source # | Since: base-2.1 |
| Enum Ordering Source # | Since: base-2.1 |
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 Source # | |
Defined in GHC.Internal.Generics | |
| Ix Ordering Source # | Since: base-2.1 |
Defined in GHC.Internal.Ix | |
| Read Ordering Source # | Since: base-2.1 |
| Show Ordering Source # | Since: base-2.1 |
| Eq Ordering Source # | |
| Ord Ordering Source # | |
Defined in GHC.Classes | |
| type Rep Ordering Source # | 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 Source # | 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 Source # | Since: base-2.1 | ||||
| Enum Char Source # | Since: base-2.1 | ||||
| Storable Char Source # | Since: base-2.1 | ||||
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 Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Ix | |||||
| Read Char Source # | Since: base-2.1 | ||||
| Show Char Source # | Since: base-2.1 | ||||
| Eq Char Source # | |||||
| Ord Char Source # | |||||
| TestCoercion SChar Source # | Since: base-4.18.0.0 | ||||
Defined in GHC.Internal.TypeLits | |||||
| TestEquality SChar Source # | Since: base-4.18.0.0 | ||||
Defined in GHC.Internal.TypeLits | |||||
| Lift Char Source # | |||||
| Generic1 (URec Char :: k -> Type) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Eq1 (UChar :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Ord1 (UChar :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Show1 (UChar :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Foldable (UChar :: Type -> Type) Source # | 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) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Char :: Type -> Type) Source # | Since: base-4.9.0.0 | ||||
| Generic (URec Char p) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Char p) Source # | Since: base-4.9.0.0 | ||||
| Eq (URec Char p) Source # | Since: base-4.9.0.0 | ||||
| Ord (URec Char p) Source # | 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) Source # | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| type Compare (a :: Char) (b :: Char) Source # | |||||
Defined in GHC.Internal.Data.Type.Ord | |||||
| type Rep1 (URec Char :: k -> Type) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Char p) Source # | 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 21
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
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 <= xx < y=x <= y && x /= yx > y=y < xx < y=compare x y == LTx > y=compare x y == GTx == y=compare x y == EQmin x y == if x <= y then x else y=Truemax 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 (==). Users who expect a stronger guarantee are advised
to write their own min and/or max functions.
The nuance of the above distinction is not always fully internalized by
developers, and in the past (tracing back to the Haskell 1.4 Report) the
specification for Ord asserted the stronger property that (min x y, max x
y) = (x, y) or (y, x), or in other words, that min and max will
return one of their arguments, using argument order as the tie-breaker if
the arguments are equal by comparison. A few list and
Foldable functions have behavior that is best understood
with this assumption in mind: all variations of minimumBy and maximumBy
(which can't use min and max in their implementations) are written such
that minimumBy and comparemaximumBy are respectively
equivalent to compareminimum and maximum (which do use min and max) only if
min and max adhere to this tie-breaking convention. Otherwise, if there
are multiple least or largest elements in a container, minimum and
maximum may not return the same one that minimumBy and
comparemaximumBy do (though they should return something that is
equal). (This is relevant for types with non-extensional equality, like
compareArg, but also in cases where the precise reference held
matters for memory-management reasons.) Unless there is a reason to deviate,
it is less confusing for implementors of Ord to respect this same
convention (as the default definitions of min and max do).
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
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
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould 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 = minBoundMethods
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
Numbers
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 Source # | Since: base-2.1 | ||||
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 Source # | 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 Source # | 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 Source # | Since: base-2.1 | ||||
| Enum Int Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Enum | |||||
| Storable Int Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Foreign.Storable | |||||
| Ix Int Source # | Since: base-2.1 | ||||
| Num Int Source # | Since: base-2.1 | ||||
| Read Int Source # | Since: base-2.1 | ||||
| Integral Int Source # | Since: base-2.0.1 | ||||
| Real Int Source # | Since: base-2.0.1 | ||||
Defined in GHC.Internal.Real Methods toRational :: Int -> Rational Source # | |||||
| Show Int Source # | Since: base-2.1 | ||||
| Eq Int Source # | |||||
| Ord Int Source # | |||||
| Lift Int Source # | |||||
| Generic1 (URec Int :: k -> Type) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Eq1 (UInt :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Ord1 (UInt :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Show1 (UInt :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Foldable (UInt :: Type -> Type) Source # | 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) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Int :: Type -> Type) Source # | Since: base-4.9.0.0 | ||||
| Generic (URec Int p) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Int p) Source # | Since: base-4.9.0.0 | ||||
| Eq (URec Int p) Source # | Since: base-4.9.0.0 | ||||
| Ord (URec Int p) Source # | 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) Source # | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| type Rep1 (URec Int :: k -> Type) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Int p) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int, the Integer type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (i.e., fits into an Int), the IS constructor is
used. Otherwise IP and IN constructors are used to store a BigNat
representing the positive or the negative value magnitude, respectively.
Invariant: IP and IN are used iff the value does not fit in IS.
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
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 Source # | 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 Source # | Since: base-2.1 | ||||
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 Source # | Since: base-2.1 | ||||
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 Source # | Since: base-2.1 | ||||
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 Source # | Since: base-2.1 | ||||
| Eq Double Source # | Note that due to the presence of
Also note that
| ||||
| Ord Double Source # | 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 | ||||
| Lift Double Source # | |||||
| Generic1 (URec Double :: k -> Type) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Eq1 (UDouble :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Ord1 (UDouble :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Show1 (UDouble :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Foldable (UDouble :: Type -> Type) Source # | 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) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Double :: Type -> Type) Source # | Since: base-4.9.0.0 | ||||
| Generic (URec Double p) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Double p) Source # | Since: base-4.9.0.0 | ||||
| Eq (URec Double p) Source # | Since: base-4.9.0.0 | ||||
| Ord (URec Double p) Source # | 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) Source # | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| type Rep1 (URec Double :: k -> Type) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Double p) Source # | 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 Source # | Since: base-2.1 | ||||
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 Source # | 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 Source # | 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 Source # | Since: base-2.1 | ||||
| Enum Word Source # | Since: base-2.1 | ||||
| Storable Word Source # | Since: base-2.1 | ||||
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 Source # | Since: base-4.6.0.0 | ||||
Defined in GHC.Internal.Ix | |||||
| Num Word Source # | Since: base-2.1 | ||||
| Read Word Source # | Since: base-4.5.0.0 | ||||
| Integral Word Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Real | |||||
| Real Word Source # | Since: base-2.1 | ||||
Defined in GHC.Internal.Real Methods toRational :: Word -> Rational Source # | |||||
| Show Word Source # | Since: base-2.1 | ||||
| Eq Word Source # | |||||
| Ord Word Source # | |||||
| Lift Word Source # | |||||
| Generic1 (URec Word :: k -> Type) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Eq1 (UWord :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Ord1 (UWord :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
Defined in Data.Functor.Classes | |||||
| Show1 (UWord :: Type -> Type) Source # | Since: base-4.21.0.0 | ||||
| Foldable (UWord :: Type -> Type) Source # | 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) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Data.Traversable | |||||
| Functor (URec Word :: Type -> Type) Source # | Since: base-4.9.0.0 | ||||
| Generic (URec Word p) Source # | |||||
Defined in GHC.Internal.Generics Associated Types
| |||||
| Show (URec Word p) Source # | Since: base-4.9.0.0 | ||||
| Eq (URec Word p) Source # | Since: base-4.9.0.0 | ||||
| Ord (URec Word p) Source # | 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) Source # | Used for marking occurrences of Since: base-4.9.0.0 | ||||
| type Rep1 (URec Word :: k -> Type) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
| type Rep (URec Word p) Source # | Since: base-4.9.0.0 | ||||
Defined in GHC.Internal.Generics | |||||
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 + xfromInteger0x + fromInteger 0=xnegategives the additive inversex + negate x=fromInteger 0- Associativity of
(*) (x * y) * z=x * (y * z)fromInteger1x * fromInteger 1=xandfromInteger 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, thenfromIntegeris 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
| Num Unique Source # | Since: base-4.4.0.0 |
Defined in GHC.Internal.Event.Unique | |
| Num CBool Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CClock Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CDouble Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CFloat Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CInt Source # | |
| Num CIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CLLong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CLong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CPtrdiff Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (-) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # (*) :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # negate :: CPtrdiff -> CPtrdiff Source # abs :: CPtrdiff -> CPtrdiff Source # signum :: CPtrdiff -> CPtrdiff Source # fromInteger :: Integer -> CPtrdiff Source # | |
| Num CSChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CSUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (-) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # (*) :: CSUSeconds -> CSUSeconds -> CSUSeconds Source # negate :: CSUSeconds -> CSUSeconds Source # abs :: CSUSeconds -> CSUSeconds Source # signum :: CSUSeconds -> CSUSeconds Source # fromInteger :: Integer -> CSUSeconds Source # | |
| Num CShort Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CSigAtomic Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (-) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # (*) :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # negate :: CSigAtomic -> CSigAtomic Source # abs :: CSigAtomic -> CSigAtomic Source # signum :: CSigAtomic -> CSigAtomic Source # fromInteger :: Integer -> CSigAtomic Source # | |
| Num CSize Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CTime Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUInt Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntMax -> CUIntMax -> CUIntMax Source # (-) :: CUIntMax -> CUIntMax -> CUIntMax Source # (*) :: CUIntMax -> CUIntMax -> CUIntMax Source # negate :: CUIntMax -> CUIntMax Source # abs :: CUIntMax -> CUIntMax Source # signum :: CUIntMax -> CUIntMax Source # fromInteger :: Integer -> CUIntMax Source # | |
| Num CUIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (-) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # (*) :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # negate :: CUIntPtr -> CUIntPtr Source # abs :: CUIntPtr -> CUIntPtr Source # signum :: CUIntPtr -> CUIntPtr Source # fromInteger :: Integer -> CUIntPtr Source # | |
| Num CULLong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CULong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods (+) :: CUSeconds -> CUSeconds -> CUSeconds Source # (-) :: CUSeconds -> CUSeconds -> CUSeconds Source # (*) :: CUSeconds -> CUSeconds -> CUSeconds Source # negate :: CUSeconds -> CUSeconds Source # abs :: CUSeconds -> CUSeconds Source # signum :: CUSeconds -> CUSeconds Source # fromInteger :: Integer -> CUSeconds Source # | |
| Num CUShort Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num CWchar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Num IntPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr | |
| Num WordPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr | |
| Num Int16 Source # | Since: base-2.1 |
| Num Int32 Source # | Since: base-2.1 |
| Num Int64 Source # | Since: base-2.1 |
| Num Int8 Source # | Since: base-2.1 |
| Num CBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CBlkSize Source # | |
Defined in GHC.Internal.System.Posix.Types Methods (+) :: CBlkSize -> CBlkSize -> CBlkSize Source # (-) :: CBlkSize -> CBlkSize -> CBlkSize Source # (*) :: CBlkSize -> CBlkSize -> CBlkSize Source # negate :: CBlkSize -> CBlkSize Source # abs :: CBlkSize -> CBlkSize Source # signum :: CBlkSize -> CBlkSize Source # fromInteger :: Integer -> CBlkSize Source # | |
| Num CCc Source # | |
| Num CClockId Source # | |
Defined in GHC.Internal.System.Posix.Types Methods (+) :: CClockId -> CClockId -> CClockId Source # (-) :: CClockId -> CClockId -> CClockId Source # (*) :: CClockId -> CClockId -> CClockId Source # negate :: CClockId -> CClockId Source # abs :: CClockId -> CClockId Source # signum :: CClockId -> CClockId Source # fromInteger :: Integer -> CClockId Source # | |
| Num CDev Source # | |
| Num CFsBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (-) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # (*) :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # negate :: CFsBlkCnt -> CFsBlkCnt Source # abs :: CFsBlkCnt -> CFsBlkCnt Source # signum :: CFsBlkCnt -> CFsBlkCnt Source # fromInteger :: Integer -> CFsBlkCnt Source # | |
| Num CFsFilCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods (+) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (-) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # (*) :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # negate :: CFsFilCnt -> CFsFilCnt Source # abs :: CFsFilCnt -> CFsFilCnt Source # signum :: CFsFilCnt -> CFsFilCnt Source # fromInteger :: Integer -> CFsFilCnt Source # | |
| Num CGid Source # | |
| Num CId Source # | |
| Num CIno Source # | |
| Num CKey Source # | |
| Num CMode Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CNfds Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CNlink Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num COff Source # | |
| Num CPid Source # | |
| Num CRLim Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CSocklen Source # | |
Defined in GHC.Internal.System.Posix.Types Methods (+) :: CSocklen -> CSocklen -> CSocklen Source # (-) :: CSocklen -> CSocklen -> CSocklen Source # (*) :: CSocklen -> CSocklen -> CSocklen Source # negate :: CSocklen -> CSocklen Source # abs :: CSocklen -> CSocklen Source # signum :: CSocklen -> CSocklen Source # fromInteger :: Integer -> CSocklen Source # | |
| Num CSpeed Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CSsize Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CTcflag Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Num CUid Source # | |
| Num Fd Source # | |
| Num Word16 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word32 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word64 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Num Word8 Source # | Since: base-2.1 |
| Num Integer Source # | Since: base-2.1 |
Defined in GHC.Internal.Num | |
| Num Natural Source # | Note that Since: base-4.8.0.0 |
Defined in GHC.Internal.Num | |
| Num Int Source # | Since: base-2.1 |
| Num Word Source # | Since: base-2.1 |
| RealFloat a => Num (Complex a) Source # | Since: base-2.1 |
Defined in Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source # (*) :: Complex a -> Complex a -> Complex a Source # negate :: Complex a -> Complex a Source # abs :: Complex a -> Complex a Source # signum :: Complex a -> Complex a Source # fromInteger :: Integer -> Complex a Source # | |
| Num a => Num (Max a) Source # | Since: base-4.9.0.0 |
| Num a => Num (Min a) Source # | Since: base-4.9.0.0 |
| Num a => Num (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods (+) :: Identity a -> Identity a -> Identity a Source # (-) :: Identity a -> Identity a -> Identity a Source # (*) :: Identity a -> Identity a -> Identity a Source # negate :: Identity a -> Identity a Source # abs :: Identity a -> Identity a Source # signum :: Identity a -> Identity a Source # fromInteger :: Integer -> Identity a Source # | |
| Num a => Num (Down a) Source # | Since: base-4.11.0.0 |
Defined in GHC.Internal.Data.Ord | |
| Num a => Num (Product a) Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source # (-) :: Product a -> Product a -> Product a Source # (*) :: Product a -> Product a -> Product a Source # negate :: Product a -> Product a Source # abs :: Product a -> Product a Source # signum :: Product a -> Product a Source # fromInteger :: Integer -> Product a Source # | |
| Num a => Num (Sum a) Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Integral a => Num (Ratio a) Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Real | |
| HasResolution a => Num (Fixed a) Source # | Multiplication is not associative or distributive:
Since: base-2.1 |
Defined in Data.Fixed | |
| Num a => Num (Op a b) Source # | |
Defined in Data.Functor.Contravariant | |
| Num a => Num (Const a b) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods (+) :: Const a b -> Const a b -> Const a b Source # (-) :: Const a b -> Const a b -> Const a b Source # (*) :: Const a b -> Const a b -> Const a b Source # negate :: Const a b -> Const a b Source # abs :: Const a b -> Const a b Source # signum :: Const a b -> Const a b Source # fromInteger :: Integer -> Const a b Source # | |
| (Applicative f, Num a) => Num (Ap f a) Source # | Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Monoid | |
| Num (f a) => Num (Alt f a) Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Num (f (g a)) => Num (Compose f g a) Source # | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods (+) :: Compose f g a -> Compose f g a -> Compose f g a Source # (-) :: Compose f g a -> Compose f g a -> Compose f g a Source # (*) :: Compose f g a -> Compose f g a -> Compose f g a Source # negate :: Compose f g a -> Compose f g a Source # abs :: Compose f g a -> Compose f g a Source # signum :: Compose f g a -> Compose f g a Source # fromInteger :: Integer -> Compose f g a Source # | |
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, thenfromRationalis 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
| Real CBool Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CBool -> Rational Source # | |
| Real CChar Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CChar -> Rational Source # | |
| Real CClock Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CClock -> Rational Source # | |
| Real CDouble Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CDouble -> Rational Source # | |
| Real CFloat Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CFloat -> Rational Source # | |
| Real CInt Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CInt -> Rational Source # | |
| Real CIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CIntMax -> Rational Source # | |
| Real CIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CIntPtr -> Rational Source # | |
| Real CLLong Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CLLong -> Rational Source # | |
| Real CLong Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CLong -> Rational Source # | |
| Real CPtrdiff Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CPtrdiff -> Rational Source # | |
| Real CSChar Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSChar -> Rational Source # | |
| Real CSUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSUSeconds -> Rational Source # | |
| Real CShort Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CShort -> Rational Source # | |
| Real CSigAtomic Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSigAtomic -> Rational Source # | |
| Real CSize Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CSize -> Rational Source # | |
| Real CTime Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CTime -> Rational Source # | |
| Real CUChar Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUChar -> Rational Source # | |
| Real CUInt Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUInt -> Rational Source # | |
| Real CUIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUIntMax -> Rational Source # | |
| Real CUIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUIntPtr -> Rational Source # | |
| Real CULLong Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CULLong -> Rational Source # | |
| Real CULong Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CULong -> Rational Source # | |
| Real CUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUSeconds -> Rational Source # | |
| Real CUShort Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CUShort -> Rational Source # | |
| Real CWchar Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods toRational :: CWchar -> Rational Source # | |
| Real IntPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr Methods toRational :: IntPtr -> Rational Source # | |
| Real WordPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr Methods toRational :: WordPtr -> Rational Source # | |
| Real Int16 Source # | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int16 -> Rational Source # | |
| Real Int32 Source # | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int32 -> Rational Source # | |
| Real Int64 Source # | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int64 -> Rational Source # | |
| Real Int8 Source # | Since: base-2.1 |
Defined in GHC.Internal.Int Methods toRational :: Int8 -> Rational Source # | |
| Real CBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CBlkCnt -> Rational Source # | |
| Real CBlkSize Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CBlkSize -> Rational Source # | |
| Real CCc Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CCc -> Rational Source # | |
| Real CClockId Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CClockId -> Rational Source # | |
| Real CDev Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CDev -> Rational Source # | |
| Real CFsBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CFsBlkCnt -> Rational Source # | |
| Real CFsFilCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CFsFilCnt -> Rational Source # | |
| Real CGid Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CGid -> Rational Source # | |
| Real CId Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CId -> Rational Source # | |
| Real CIno Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CIno -> Rational Source # | |
| Real CKey Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CKey -> Rational Source # | |
| Real CMode Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CMode -> Rational Source # | |
| Real CNfds Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CNfds -> Rational Source # | |
| Real CNlink Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CNlink -> Rational Source # | |
| Real COff Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: COff -> Rational Source # | |
| Real CPid Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CPid -> Rational Source # | |
| Real CRLim Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CRLim -> Rational Source # | |
| Real CSocklen Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CSocklen -> Rational Source # | |
| Real CSpeed Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CSpeed -> Rational Source # | |
| Real CSsize Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CSsize -> Rational Source # | |
| Real CTcflag Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CTcflag -> Rational Source # | |
| Real CUid Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: CUid -> Rational Source # | |
| Real Fd Source # | |
Defined in GHC.Internal.System.Posix.Types Methods toRational :: Fd -> Rational Source # | |
| Real Word16 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word16 -> Rational Source # | |
| Real Word32 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word32 -> Rational Source # | |
| Real Word64 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word64 -> Rational Source # | |
| Real Word8 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word Methods toRational :: Word8 -> Rational Source # | |
| Real Integer Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Integer -> Rational Source # | |
| Real Natural Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Real Methods toRational :: Natural -> Rational Source # | |
| Real Int Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Int -> Rational Source # | |
| Real Word Source # | Since: base-2.1 |
Defined in GHC.Internal.Real Methods toRational :: Word -> Rational Source # | |
| Real a => Real (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods toRational :: Identity a -> Rational Source # | |
| Real a => Real (Down a) Source # | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods toRational :: Down a -> Rational Source # | |
| Integral a => Real (Ratio a) Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods toRational :: Ratio a -> Rational Source # | |
| HasResolution a => Real (Fixed a) Source # | Since: base-2.1 |
Defined in Data.Fixed Methods toRational :: Fixed a -> Rational Source # | |
| Real a => Real (Const a b) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods toRational :: Const a b -> Rational Source # | |
| Real (f (g a)) => Real (Compose f g a) Source # | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods toRational :: Compose f g a -> Rational Source # | |
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 ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (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
| Integral CBool Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CInt Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CIntMax -> CIntMax -> CIntMax Source # rem :: CIntMax -> CIntMax -> CIntMax Source # div :: CIntMax -> CIntMax -> CIntMax Source # mod :: CIntMax -> CIntMax -> CIntMax Source # quotRem :: CIntMax -> CIntMax -> (CIntMax, CIntMax) Source # | |
| Integral CIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CIntPtr -> CIntPtr -> CIntPtr Source # rem :: CIntPtr -> CIntPtr -> CIntPtr Source # div :: CIntPtr -> CIntPtr -> CIntPtr Source # mod :: CIntPtr -> CIntPtr -> CIntPtr Source # quotRem :: CIntPtr -> CIntPtr -> (CIntPtr, CIntPtr) Source # | |
| Integral CLLong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CLong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CPtrdiff Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # rem :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # div :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # mod :: CPtrdiff -> CPtrdiff -> CPtrdiff Source # quotRem :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) Source # divMod :: CPtrdiff -> CPtrdiff -> (CPtrdiff, CPtrdiff) Source # | |
| Integral CSChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CShort Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CSigAtomic Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # rem :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # div :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # mod :: CSigAtomic -> CSigAtomic -> CSigAtomic Source # quotRem :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) Source # divMod :: CSigAtomic -> CSigAtomic -> (CSigAtomic, CSigAtomic) Source # toInteger :: CSigAtomic -> Integer Source # | |
| Integral CSize Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUChar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUInt Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUIntMax Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUIntMax -> CUIntMax -> CUIntMax Source # rem :: CUIntMax -> CUIntMax -> CUIntMax Source # div :: CUIntMax -> CUIntMax -> CUIntMax Source # mod :: CUIntMax -> CUIntMax -> CUIntMax Source # quotRem :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) Source # divMod :: CUIntMax -> CUIntMax -> (CUIntMax, CUIntMax) Source # | |
| Integral CUIntPtr Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # rem :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # div :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # mod :: CUIntPtr -> CUIntPtr -> CUIntPtr Source # quotRem :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) Source # divMod :: CUIntPtr -> CUIntPtr -> (CUIntPtr, CUIntPtr) Source # | |
| Integral CULLong Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CULLong -> CULLong -> CULLong Source # rem :: CULLong -> CULLong -> CULLong Source # div :: CULLong -> CULLong -> CULLong Source # mod :: CULLong -> CULLong -> CULLong Source # quotRem :: CULLong -> CULLong -> (CULLong, CULLong) Source # | |
| Integral CULong Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral CUShort Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods quot :: CUShort -> CUShort -> CUShort Source # rem :: CUShort -> CUShort -> CUShort Source # div :: CUShort -> CUShort -> CUShort Source # mod :: CUShort -> CUShort -> CUShort Source # quotRem :: CUShort -> CUShort -> (CUShort, CUShort) Source # | |
| Integral CWchar Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Integral IntPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr | |
| Integral WordPtr Source # | |
Defined in GHC.Internal.Foreign.Ptr Methods quot :: WordPtr -> WordPtr -> WordPtr Source # rem :: WordPtr -> WordPtr -> WordPtr Source # div :: WordPtr -> WordPtr -> WordPtr Source # mod :: WordPtr -> WordPtr -> WordPtr Source # quotRem :: WordPtr -> WordPtr -> (WordPtr, WordPtr) Source # | |
| Integral Int16 Source # | Since: base-2.1 |
| Integral Int32 Source # | Since: base-2.1 |
| Integral Int64 Source # | Since: base-2.1 |
| Integral Int8 Source # | Since: base-2.1 |
Defined in GHC.Internal.Int | |
| Integral CBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # rem :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # div :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # mod :: CBlkCnt -> CBlkCnt -> CBlkCnt Source # quotRem :: CBlkCnt -> CBlkCnt -> (CBlkCnt, CBlkCnt) Source # | |
| Integral CBlkSize Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CBlkSize -> CBlkSize -> CBlkSize Source # rem :: CBlkSize -> CBlkSize -> CBlkSize Source # div :: CBlkSize -> CBlkSize -> CBlkSize Source # mod :: CBlkSize -> CBlkSize -> CBlkSize Source # quotRem :: CBlkSize -> CBlkSize -> (CBlkSize, CBlkSize) Source # divMod :: CBlkSize -> CBlkSize -> (CBlkSize, CBlkSize) Source # | |
| Integral CClockId Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CClockId -> CClockId -> CClockId Source # rem :: CClockId -> CClockId -> CClockId Source # div :: CClockId -> CClockId -> CClockId Source # mod :: CClockId -> CClockId -> CClockId Source # quotRem :: CClockId -> CClockId -> (CClockId, CClockId) Source # divMod :: CClockId -> CClockId -> (CClockId, CClockId) Source # | |
| Integral CDev Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CFsBlkCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # rem :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # div :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # mod :: CFsBlkCnt -> CFsBlkCnt -> CFsBlkCnt Source # quotRem :: CFsBlkCnt -> CFsBlkCnt -> (CFsBlkCnt, CFsBlkCnt) Source # divMod :: CFsBlkCnt -> CFsBlkCnt -> (CFsBlkCnt, CFsBlkCnt) Source # | |
| Integral CFsFilCnt Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # rem :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # div :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # mod :: CFsFilCnt -> CFsFilCnt -> CFsFilCnt Source # quotRem :: CFsFilCnt -> CFsFilCnt -> (CFsFilCnt, CFsFilCnt) Source # divMod :: CFsFilCnt -> CFsFilCnt -> (CFsFilCnt, CFsFilCnt) Source # | |
| Integral CGid Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CId Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CIno Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CKey Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CMode Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CNfds Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CNlink Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral COff Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CPid Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CRLim Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CSocklen Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CSocklen -> CSocklen -> CSocklen Source # rem :: CSocklen -> CSocklen -> CSocklen Source # div :: CSocklen -> CSocklen -> CSocklen Source # mod :: CSocklen -> CSocklen -> CSocklen Source # quotRem :: CSocklen -> CSocklen -> (CSocklen, CSocklen) Source # divMod :: CSocklen -> CSocklen -> (CSocklen, CSocklen) Source # | |
| Integral CSsize Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral CTcflag Source # | |
Defined in GHC.Internal.System.Posix.Types Methods quot :: CTcflag -> CTcflag -> CTcflag Source # rem :: CTcflag -> CTcflag -> CTcflag Source # div :: CTcflag -> CTcflag -> CTcflag Source # mod :: CTcflag -> CTcflag -> CTcflag Source # quotRem :: CTcflag -> CTcflag -> (CTcflag, CTcflag) Source # | |
| Integral CUid Source # | |
Defined in GHC.Internal.System.Posix.Types | |
| Integral Fd Source # | |
| Integral Word16 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word32 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word64 Source # | Since: base-2.1 |
Defined in GHC.Internal.Word | |
| Integral Word8 Source # | Since: base-2.1 |
| Integral Integer Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # | |
| Integral Natural Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # | |
| Integral Int Source # | Since: base-2.0.1 |
| Integral Word Source # | Since: base-2.1 |
Defined in GHC.Internal.Real | |
| Integral a => Integral (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a Source # rem :: Identity a -> Identity a -> Identity a Source # div :: Identity a -> Identity a -> Identity a Source # mod :: Identity a -> Identity a -> Identity a Source # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) Source # divMod :: Identity a -> Identity a -> (Identity a, Identity a) Source # | |
| Integral a => Integral (Const a b) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b Source # rem :: Const a b -> Const a b -> Const a b Source # div :: Const a b -> Const a b -> Const a b Source # mod :: Const a b -> Const a b -> Const a b Source # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) Source # divMod :: Const a b -> Const a b -> (Const a b, Const a b) Source # | |
| Integral (f (g a)) => Integral (Compose f g a) Source # | Since: base-4.19.0.0 |
Defined in Data.Functor.Compose Methods quot :: Compose f g a -> Compose f g a -> Compose f g a Source # rem :: Compose f g a -> Compose f g a -> Compose f g a Source # div :: Compose f g a -> Compose f g a -> Compose f g a Source # mod :: Compose f g a -> Compose f g a -> Compose f g a Source # quotRem :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source # divMod :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source # | |
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:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1- Totality of
toRational toRationalis total- Coherence with
toRational - if the type also implements
Real, thenfromRationalis 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 Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CDouble Source # | |
| Fractional CFloat Source # | |
| RealFloat a => Fractional (Complex a) Source # | Since: base-2.1 |
| Fractional a => Fractional (Identity a) Source # | Since: base-4.9.0.0 |
| Fractional a => Fractional (Down a) Source # | Since: base-4.14.0.0 |
| Integral a => Fractional (Ratio a) Source # | 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) Source # | 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 bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
| Floating CDouble Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods exp :: CDouble -> CDouble Source # log :: CDouble -> CDouble Source # sqrt :: CDouble -> CDouble Source # (**) :: CDouble -> CDouble -> CDouble Source # logBase :: CDouble -> CDouble -> CDouble Source # sin :: CDouble -> CDouble Source # cos :: CDouble -> CDouble Source # tan :: CDouble -> CDouble Source # asin :: CDouble -> CDouble Source # acos :: CDouble -> CDouble Source # atan :: CDouble -> CDouble Source # sinh :: CDouble -> CDouble Source # cosh :: CDouble -> CDouble Source # tanh :: CDouble -> CDouble Source # asinh :: CDouble -> CDouble Source # acosh :: CDouble -> CDouble Source # atanh :: CDouble -> CDouble Source # log1p :: CDouble -> CDouble Source # expm1 :: CDouble -> CDouble Source # | |
| Floating CFloat Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods exp :: CFloat -> CFloat Source # log :: CFloat -> CFloat Source # sqrt :: CFloat -> CFloat Source # (**) :: CFloat -> CFloat -> CFloat Source # logBase :: CFloat -> CFloat -> CFloat Source # sin :: CFloat -> CFloat Source # cos :: CFloat -> CFloat Source # tan :: CFloat -> CFloat Source # asin :: CFloat -> CFloat Source # acos :: CFloat -> CFloat Source # atan :: CFloat -> CFloat Source # sinh :: CFloat -> CFloat Source # cosh :: CFloat -> CFloat Source # tanh :: CFloat -> CFloat Source # asinh :: CFloat -> CFloat Source # acosh :: CFloat -> CFloat Source # atanh :: CFloat -> CFloat Source # log1p :: CFloat -> CFloat Source # expm1 :: CFloat -> CFloat Source # | |
| Floating Double Source # | Since: base-2.1 |
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 # | |
| Floating Float Source # | Since: base-2.1 |
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 a => Floating (Complex a) Source # | Since: base-2.1 |
Defined in Data.Complex Methods exp :: Complex a -> Complex a Source # log :: Complex a -> Complex a Source # sqrt :: Complex a -> Complex a Source # (**) :: Complex a -> Complex a -> Complex a Source # logBase :: Complex a -> Complex a -> Complex a Source # sin :: Complex a -> Complex a Source # cos :: Complex a -> Complex a Source # tan :: Complex a -> Complex a Source # asin :: Complex a -> Complex a Source # acos :: Complex a -> Complex a Source # atan :: Complex a -> Complex a Source # sinh :: Complex a -> Complex a Source # cosh :: Complex a -> Complex a Source # tanh :: Complex a -> Complex a Source # asinh :: Complex a -> Complex a Source # acosh :: Complex a -> Complex a Source # atanh :: Complex a -> Complex a Source # log1p :: Complex a -> Complex a Source # expm1 :: Complex a -> Complex a Source # | |
| Floating a => Floating (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods exp :: Identity a -> Identity a Source # log :: Identity a -> Identity a Source # sqrt :: Identity a -> Identity a Source # (**) :: Identity a -> Identity a -> Identity a Source # logBase :: Identity a -> Identity a -> Identity a Source # sin :: Identity a -> Identity a Source # cos :: Identity a -> Identity a Source # tan :: Identity a -> Identity a Source # asin :: Identity a -> Identity a Source # acos :: Identity a -> Identity a Source # atan :: Identity a -> Identity a Source # sinh :: Identity a -> Identity a Source # cosh :: Identity a -> Identity a Source # tanh :: Identity a -> Identity a Source # asinh :: Identity a -> Identity a Source # acosh :: Identity a -> Identity a Source # atanh :: Identity a -> Identity a Source # log1p :: Identity a -> Identity a Source # expm1 :: Identity a -> Identity a Source # | |
| Floating a => Floating (Down a) Source # | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods exp :: Down a -> Down a Source # log :: Down a -> Down a Source # sqrt :: Down a -> Down a Source # (**) :: Down a -> Down a -> Down a Source # logBase :: Down a -> Down a -> Down a Source # sin :: Down a -> Down a Source # cos :: Down a -> Down a Source # tan :: Down a -> Down a Source # asin :: Down a -> Down a Source # acos :: Down a -> Down a Source # atan :: Down a -> Down a Source # sinh :: Down a -> Down a Source # cosh :: Down a -> Down a Source # tanh :: Down a -> Down a Source # asinh :: Down a -> Down a Source # acosh :: Down a -> Down a Source # atanh :: Down a -> Down a Source # log1p :: Down a -> Down a Source # expm1 :: Down a -> Down a Source # | |
| Floating a => Floating (Op a b) Source # | |
Defined in Data.Functor.Contravariant Methods exp :: Op a b -> Op a b Source # log :: Op a b -> Op a b Source # sqrt :: Op a b -> Op a b Source # (**) :: Op a b -> Op a b -> Op a b Source # logBase :: Op a b -> Op a b -> Op a b Source # sin :: Op a b -> Op a b Source # cos :: Op a b -> Op a b Source # tan :: Op a b -> Op a b Source # asin :: Op a b -> Op a b Source # acos :: Op a b -> Op a b Source # atan :: Op a b -> Op a b Source # sinh :: Op a b -> Op a b Source # cosh :: Op a b -> Op a b Source # tanh :: Op a b -> Op a b Source # asinh :: Op a b -> Op a b Source # acosh :: Op a b -> Op a b Source # atanh :: Op a b -> Op a b Source # log1p :: Op a b -> Op a b Source # expm1 :: Op a b -> Op a b Source # | |
| Floating a => Floating (Const a b) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods exp :: Const a b -> Const a b Source # log :: Const a b -> Const a b Source # sqrt :: Const a b -> Const a b Source # (**) :: Const a b -> Const a b -> Const a b Source # logBase :: Const a b -> Const a b -> Const a b Source # sin :: Const a b -> Const a b Source # cos :: Const a b -> Const a b Source # tan :: Const a b -> Const a b Source # asin :: Const a b -> Const a b Source # acos :: Const a b -> Const a b Source # atan :: Const a b -> Const a b Source # sinh :: Const a b -> Const a b Source # cosh :: Const a b -> Const a b Source # tanh :: Const a b -> Const a b Source # asinh :: Const a b -> Const a b Source # acosh :: Const a b -> Const a b Source # atanh :: Const a b -> Const a b Source # log1p :: Const a b -> Const a b Source # expm1 :: Const a b -> Const a b Source # | |
| Floating (f (g a)) => Floating (Compose f g a) Source # | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose Methods exp :: Compose f g a -> Compose f g a Source # log :: Compose f g a -> Compose f g a Source # sqrt :: Compose f g a -> Compose f g a Source # (**) :: Compose f g a -> Compose f g a -> Compose f g a Source # logBase :: Compose f g a -> Compose f g a -> Compose f g a Source # sin :: Compose f g a -> Compose f g a Source # cos :: Compose f g a -> Compose f g a Source # tan :: Compose f g a -> Compose f g a Source # asin :: Compose f g a -> Compose f g a Source # acos :: Compose f g a -> Compose f g a Source # atan :: Compose f g a -> Compose f g a Source # sinh :: Compose f g a -> Compose f g a Source # cosh :: Compose f g a -> Compose f g a Source # tanh :: Compose f g a -> Compose f g a Source # asinh :: Compose f g a -> Compose f g a Source # acosh :: Compose f g a -> Compose f g a Source # atanh :: Compose f g a -> Compose f g a Source # log1p :: Compose f g a -> Compose f g a Source # expm1 :: Compose f g a -> Compose f g a Source # | |
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:
nis an integral number with the same sign asx; andfis 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 #
truncate xx between zero and x
round :: Integral b => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source #
ceiling xx
floor :: Integral b => a -> b Source #
floor xx
Instances
| RealFrac CDouble Source # | |
| RealFrac CFloat Source # | |
| RealFrac a => RealFrac (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
| RealFrac a => RealFrac (Down a) Source # | Since: base-4.14.0.0 |
| Integral a => RealFrac (Ratio a) Source # | Since: base-2.0.1 |
| HasResolution a => RealFrac (Fixed a) Source # | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) Source # | 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
that exponent xx.
The relation to IEEE emin and emax is
floatRange x = (emin + 1, emax + 1)
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 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 floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite 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) = xencodeFloat 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.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
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, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Instances
| RealFloat CDouble Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CDouble -> Integer Source # floatDigits :: CDouble -> Int Source # floatRange :: CDouble -> (Int, Int) Source # decodeFloat :: CDouble -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> CDouble Source # exponent :: CDouble -> Int Source # significand :: CDouble -> CDouble Source # scaleFloat :: Int -> CDouble -> CDouble Source # isNaN :: CDouble -> Bool Source # isInfinite :: CDouble -> Bool Source # isDenormalized :: CDouble -> Bool Source # isNegativeZero :: CDouble -> Bool Source # | |
| RealFloat CFloat Source # | |
Defined in GHC.Internal.Foreign.C.Types Methods floatRadix :: CFloat -> Integer Source # floatDigits :: CFloat -> Int Source # floatRange :: CFloat -> (Int, Int) Source # decodeFloat :: CFloat -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> CFloat Source # exponent :: CFloat -> Int Source # significand :: CFloat -> CFloat Source # scaleFloat :: Int -> CFloat -> CFloat Source # isNaN :: CFloat -> Bool Source # isInfinite :: CFloat -> Bool Source # isDenormalized :: CFloat -> Bool Source # isNegativeZero :: CFloat -> Bool Source # | |
| RealFloat Double Source # | Since: base-2.1 |
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 # | |
| RealFloat Float Source # | Since: base-2.1 |
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 # | |
| RealFloat a => RealFloat (Identity a) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Identity Methods floatRadix :: Identity a -> Integer Source # floatDigits :: Identity a -> Int Source # floatRange :: Identity a -> (Int, Int) Source # decodeFloat :: Identity a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Identity a Source # exponent :: Identity a -> Int Source # significand :: Identity a -> Identity a Source # scaleFloat :: Int -> Identity a -> Identity a Source # isNaN :: Identity a -> Bool Source # isInfinite :: Identity a -> Bool Source # isDenormalized :: Identity a -> Bool Source # isNegativeZero :: Identity a -> Bool Source # | |
| RealFloat a => RealFloat (Down a) Source # | Since: base-4.14.0.0 |
Defined in GHC.Internal.Data.Ord Methods floatRadix :: Down a -> Integer Source # floatDigits :: Down a -> Int Source # floatRange :: Down a -> (Int, Int) Source # decodeFloat :: Down a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Down a Source # exponent :: Down a -> Int Source # significand :: Down a -> Down a Source # scaleFloat :: Int -> Down a -> Down a Source # isNaN :: Down a -> Bool Source # isInfinite :: Down a -> Bool Source # isDenormalized :: Down a -> Bool Source # isNegativeZero :: Down a -> Bool Source # | |
| RealFloat a => RealFloat (Const a b) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Functor.Const Methods floatRadix :: Const a b -> Integer Source # floatDigits :: Const a b -> Int Source # floatRange :: Const a b -> (Int, Int) Source # decodeFloat :: Const a b -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Const a b Source # exponent :: Const a b -> Int Source # significand :: Const a b -> Const a b Source # scaleFloat :: Int -> Const a b -> Const a b Source # isNaN :: Const a b -> Bool Source # isInfinite :: Const a b -> Bool Source # isDenormalized :: Const a b -> Bool Source # isNegativeZero :: Const a b -> Bool Source # | |
| RealFloat (f (g a)) => RealFloat (Compose f g a) Source # | Since: base-4.20.0.0 |
Defined in Data.Functor.Compose Methods floatRadix :: Compose f g a -> Integer Source # floatDigits :: Compose f g a -> Int Source # floatRange :: Compose f g a -> (Int, Int) Source # decodeFloat :: Compose f g a -> (Integer, Int) Source # encodeFloat :: Integer -> Int -> Compose f g a Source # exponent :: Compose f g a -> Int Source # significand :: Compose f g a -> Compose f g a Source # scaleFloat :: Int -> Compose f g a -> Compose f g a Source # isNaN :: Compose f g a -> Bool Source # isInfinite :: Compose f g a -> Bool Source # isDenormalized :: Compose f g a -> Bool Source # isNegativeZero :: Compose f g a -> Bool Source # isIEEE :: Compose f g a -> Bool Source # atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source # | |
Numeric functions
gcd :: Integral a => a -> a -> a Source #
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 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, abs minBound < 0minBound0 or minBound
lcm :: Integral a => a -> a -> a Source #
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 Source # | Since: base-4.9.0.0 |
| Semigroup All Source # | Since: base-4.9.0.0 |
| Semigroup Any Source # | Since: base-4.9.0.0 |
| Semigroup Event Source # | Since: base-4.10.0.0 |
| Semigroup EventLifetime Source # | Since: base-4.11.0.0 |
| Semigroup Lifetime Source # | Since: base-4.10.0.0 |
| Semigroup ExceptionContext Source # | |
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 Source # | Since: base-4.9.0.0 |
| Semigroup () Source # | 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) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (STM a) Source # | Since: base-4.17.0.0 |
| Bits a => Semigroup (And a) Source # | Since: base-4.16 |
| FiniteBits a => Semigroup (Iff a) Source # | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Semigroup (Ior a) Source # | Since: base-4.16 |
| Bits a => Semigroup (Xor a) Source # | Since: base-4.16 |
| Semigroup a => Semigroup (Identity a) Source # | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) Source # | Since: base-4.11.0.0 |
| Ord a => Semigroup (Min a) Source # | Since: base-4.11.0.0 |
| Semigroup (First a) Source # | Since: base-4.9.0.0 |
| Semigroup (Last a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) Source # | Since: base-4.11.0.0 |
| Semigroup a => Semigroup (Dual a) Source # | Since: base-4.9.0.0 |
| Semigroup (Endo a) Source # | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) Source # | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) Source # | Since: base-4.9.0.0 |
| (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source # | 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) Source # | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Q a) Source # | Since: ghc-internal-2.17.0.0 |
| Semigroup a => Semigroup (IO a) Source # | Since: base-4.10.0.0 |
| Semigroup a => Semigroup (Maybe a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Solo a) Source # | Since: base-4.15 |
| Semigroup [a] Source # | 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) Source # | Since: base-4.9.0.0 |
| Semigroup (Proxy s) Source # | Since: base-4.9.0.0 |
| Semigroup (U1 p) Source # | Since: base-4.12.0.0 |
| Semigroup (V1 p) Source # | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (ST s a) Source # | Since: base-4.11.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) Source # | Since: base-4.9.0.0 |
| Semigroup b => Semigroup (a -> b) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) Source # | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) Source # | Since: base-4.12.0.0 |
| Alternative f => Semigroup (Alt f a) Source # | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (Rec1 f p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source # | 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) Source # | Since: base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source # | 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) Source # | Since: base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) Source # | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source # | 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)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
You can alternatively define mconcat instead of mempty, in which case the
laws are:
- Unit
mconcat(purex) = x- Multiplication
mconcat(joinxss) =mconcat(fmapmconcatxss)- Subclass
mconcat(toListxs) =sconcatxs
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 newtypes 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 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 Source # | Since: base-2.1 |
| Monoid Any Source # | Since: base-2.1 |
| Monoid Event Source # | Since: base-4.4.0.0 |
| Monoid EventLifetime Source # | Since: base-4.8.0.0 |
| Monoid Lifetime Source # |
Since: base-4.8.0.0 |
| Monoid ExceptionContext Source # | |
Defined in GHC.Internal.Exception.Context Methods mempty :: ExceptionContext Source # mappend :: ExceptionContext -> ExceptionContext -> ExceptionContext Source # mconcat :: [ExceptionContext] -> ExceptionContext Source # | |
| Monoid Ordering Source # | Since: base-2.1 |
| Monoid () Source # | Since: base-2.1 |
| 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) Source # | Since: base-4.17.0.0 |
| FiniteBits a => Monoid (And a) Source # | This constraint is arguably too strong. However,
as some types (such as Since: base-4.16 |
| FiniteBits a => Monoid (Iff a) Source # | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Monoid (Ior a) Source # | Since: base-4.16 |
| Bits a => Monoid (Xor a) Source # | Since: base-4.16 |
| Monoid a => Monoid (Identity a) Source # | Since: base-4.9.0.0 |
| Ord a => Monoid (Max a) Source # | Since: base-4.8.0.0 |
| Ord a => Monoid (Min a) Source # | Since: base-4.8.0.0 |
| Monoid (First a) Source # | Since: base-2.1 |
| Monoid (Last a) Source # | Since: base-2.1 |
| Monoid a => Monoid (Down a) Source # | Since: base-4.11.0.0 |
| Monoid a => Monoid (Dual a) Source # | Since: base-2.1 |
| Monoid (Endo a) Source # | Since: base-2.1 |
| Num a => Monoid (Product a) Source # | Since: base-2.1 |
| Num a => Monoid (Sum a) Source # | Since: base-2.1 |
| (Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source # | 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) Source # | Since: base-4.12.0.0 |
| Monoid a => Monoid (Q a) Source # | Since: ghc-internal-2.17.0.0 |
| Monoid a => Monoid (IO a) Source # | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) Source # | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (Solo a) Source # | Since: base-4.15 |
| Monoid [a] Source # | Since: base-2.1 |
| Monoid a => Monoid (Op a b) Source # |
mempty :: Op a b mempty = Op _ -> mempty |
| Monoid (Proxy s) Source # | Since: base-4.7.0.0 |
| Monoid (U1 p) Source # | Since: base-4.12.0.0 |
| Monoid a => Monoid (ST s a) Source # | Since: base-4.11.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) Source # | Since: base-2.1 |
| Monoid b => Monoid (a -> b) Source # | Since: base-2.1 |
| Monoid a => Monoid (Const a b) Source # | Since: base-4.9.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) Source # | Since: base-4.12.0.0 |
| Alternative f => Monoid (Alt f a) Source # | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source # | Since: base-2.1 |
| (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) Source # | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source # | Since: base-2.1 |
| Monoid (f (g a)) => Monoid (Compose f g a) Source # | Since: base-4.16.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) Source # | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source # | Since: base-2.1 |
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 Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from 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 Source # | Since: base-4.9.0.0 |
| Functor STM Source # | Since: base-4.3.0.0 |
| Functor Handler Source # | Since: base-4.6.0.0 |
| Functor Identity Source # | Since: base-4.8.0.0 |
| Functor First Source # | Since: base-4.8.0.0 |
| Functor Last Source # | Since: base-4.8.0.0 |
| Functor Down Source # | Since: base-4.11.0.0 |
| Functor Dual Source # | Since: base-4.8.0.0 |
| Functor Product Source # | Since: base-4.8.0.0 |
| Functor Sum Source # | Since: base-4.8.0.0 |
| Functor ZipList Source # | Since: base-2.1 |
| Functor NoIO Source # | Since: base-4.8.0.0 |
| Functor Par1 Source # | Since: base-4.9.0.0 |
| Functor Q Source # | |
| Functor TyVarBndr Source # | |
| Functor P Source # | Since: base-4.8.0.0 |
| Functor ReadP Source # | Since: base-2.1 |
| Functor ReadPrec Source # | Since: base-2.1 |
| Functor IO Source # | Since: base-2.1 |
| Functor Maybe Source # | Since: base-2.1 |
| Functor Solo Source # | Since: base-4.15 |
| Functor [] Source # | Since: base-2.1 |
| 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 # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Functor (Arg a) Source # | Since: base-4.9.0.0 |
| Functor (Array i) Source # | Since: base-2.1 |
| Arrow a => Functor (ArrowMonad a) Source # | Since: base-4.6.0.0 |
Defined in GHC.Internal.Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Functor (ST s) Source # | Since: base-2.1 |
| Functor (Either a) Source # | Since: base-3.0 |
| Functor (StateL s) Source # | Since: base-4.0 |
| Functor (StateR s) Source # | Since: base-4.0 |
| Functor (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Functor (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (V1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (ST s) Source # | Since: base-2.1 |
| Functor ((,) a) Source # | Since: base-2.1 |
| 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 # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Functor m => Functor (Kleisli m a) Source # | Since: base-4.14.0.0 |
| Functor (Const m :: Type -> Type) Source # | Since: base-2.1 |
| Monad m => Functor (StateT s m) Source # | Since: base-4.18.0.0 |
| Functor f => Functor (Ap f) Source # | Since: base-4.12.0.0 |
| Functor f => Functor (Alt f) Source # | Since: base-4.8.0.0 |
| (Generic1 f, Functor (Rep1 f)) => Functor (Generically1 f) Source # | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods fmap :: (a -> b) -> Generically1 f a -> Generically1 f b Source # (<$) :: a -> Generically1 f b -> Generically1 f a Source # | |
| Functor f => Functor (Rec1 f) Source # | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor ((,,) a b) Source # | 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) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) Source # | Since: base-4.9.0.0 |
| Functor (K1 i c :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Functor ((,,,) a b c) Source # | Since: base-4.14.0.0 |
| Functor ((->) r) Source # | Since: base-2.1 |
| (Functor f, Functor g) => Functor (Compose f g) Source # | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) Source # | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) Source # | Since: base-4.9.0.0 |
| Functor ((,,,,) a b c d) Source # | Since: base-4.18.0.0 |
| Functor ((,,,,,) a b c d e) Source # | Since: base-4.18.0.0 |
| Functor ((,,,,,,) a b c d e f) Source # | 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, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing
>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17
>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
class Functor f => Applicative (f :: Type -> Type) where Source #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value into the Structure.
Examples
>>>pure 1 :: Maybe IntJust 1
>>>pure 'z' :: [Char]"z"
>>>pure (pure ":D") :: Maybe [String]Just [":D"]
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
Example
Used in combination with (<$>)(<*>)
>>>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 3Just 3
>>>Nothing *> Just 3Nothing
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 Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Base | |
| Applicative STM Source # | Since: base-4.8.0.0 |
| Applicative Identity Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Functor.Identity | |
| Applicative First Source # | Since: base-4.8.0.0 |
| Applicative Last Source # | Since: base-4.8.0.0 |
| Applicative Down Source # | Since: base-4.11.0.0 |
| Applicative Dual Source # | Since: base-4.8.0.0 |
| Applicative Product Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Semigroup.Internal | |
| Applicative Sum Source # | Since: base-4.8.0.0 |
| Applicative ZipList Source # | 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-2.1 |
Defined in GHC.Internal.Functor.ZipList | |
| Applicative NoIO Source # | Since: base-4.8.0.0 |
| Applicative Par1 Source # | Since: base-4.9.0.0 |
| Applicative Q Source # | |
| Applicative P Source # | Since: base-4.5.0.0 |
| Applicative ReadP Source # | Since: base-4.6.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
| Applicative ReadPrec Source # | Since: base-4.6.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadPrec | |
| Applicative IO Source # | Since: base-2.1 |
| Applicative Maybe Source # | Since: base-2.1 |
| Applicative Solo Source # | Since: base-4.15 |
| Applicative [] Source # | Since: base-2.1 |
| 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) Source # | 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) Source # | Since: base-2.1 |
| Applicative (Either e) Source # | Since: base-3.0 |
Defined in GHC.Internal.Data.Either | |
| Applicative (StateL s) Source # | Since: base-4.0 |
Defined in GHC.Internal.Data.Functor.Utils | |
| Applicative (StateR s) Source # | Since: base-4.0 |
Defined in GHC.Internal.Data.Functor.Utils | |
| Applicative (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Applicative (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Applicative (ST s) Source # | Since: base-4.4.0.0 |
| Monoid a => Applicative ((,) a) Source # | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| 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) Source # | 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) Source # | Since: base-2.0.1 |
Defined in GHC.Internal.Data.Functor.Const | |
| Monad m => Applicative (StateT s m) Source # | 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) Source # | Since: base-4.12.0.0 |
| Applicative f => Applicative (Alt f) Source # | Since: base-4.8.0.0 |
| (Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source # | 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) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Applicative ((,,) a b) Source # | 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) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Monoid c => Applicative (K1 i c :: Type -> Type) Source # | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source # | 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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Applicative f => Applicative (M1 i c f) Source # | 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
returna>>=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 equivalent to
\x f ->join(fmapf 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 >>= 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 Source # | Since: base-4.9.0.0 |
| Monad STM Source # | Since: base-4.3.0.0 |
| Monad Identity Source # | Since: base-4.8.0.0 |
| Monad First Source # | Since: base-4.8.0.0 |
| Monad Last Source # | Since: base-4.8.0.0 |
| Monad Down Source # | Since: base-4.11.0.0 |
| Monad Dual Source # | Since: base-4.8.0.0 |
| Monad Product Source # | Since: base-4.8.0.0 |
| Monad Sum Source # | Since: base-4.8.0.0 |
| Monad NoIO Source # | Since: base-4.4.0.0 |
| Monad Par1 Source # | Since: base-4.9.0.0 |
| Monad Q Source # | |
| Monad P Source # | Since: base-2.1 |
| Monad ReadP Source # | Since: base-2.1 |
| Monad ReadPrec Source # | Since: base-2.1 |
| Monad IO Source # | Since: base-2.1 |
| Monad Maybe Source # | Since: base-2.1 |
| Monad Solo Source # | Since: base-4.15 |
| Monad [] Source # | Since: base-2.1 |
| 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) Source # | Since: base-2.1 |
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) Source # | Since: base-2.1 |
| Monad (Either e) Source # | Since: base-4.4.0.0 |
| Monad (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
| Monad (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Monad (ST s) Source # | Since: base-2.1 |
| Monoid a => Monad ((,) a) Source # | Since: base-4.9.0.0 |
| Monad m => Monad (Kleisli m a) Source # | Since: base-4.14.0.0 |
| Monad m => Monad (StateT s m) Source # | Since: base-4.18.0.0 |
| Monad f => Monad (Ap f) Source # | Since: base-4.12.0.0 |
| Monad f => Monad (Alt f) Source # | Since: base-4.8.0.0 |
| Monad f => Monad (Rec1 f) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) Source # | 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) Source # | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) Source # | Since: base-4.14.0.0 |
| Monad ((->) r) Source # | Since: base-2.1 |
| Monad f => Monad (M1 i c f) Source # | 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 Q Source # | |
| MonadFail P Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Text.ParserCombinators.ReadP | |
| MonadFail ReadP Source # | Since: base-4.9.0.0 |
| MonadFail ReadPrec Source # | Since: base-4.9.0.0 |
| MonadFail IO Source # | Since: base-4.9.0.0 |
| MonadFail Maybe Source # | Since: base-4.9.0.0 |
| MonadFail [] Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Control.Monad.Fail | |
| MonadFail f => MonadFail (Ap f) Source # | 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 FoldableA 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 =foldrf 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 =foldlf 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.
foldl1f =foldl1f .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
equivalent to foldr1 maxmax. For the default implementation of max (max x y = if x <= y
then y else x), structure order is used as a tie-breaker: if there are
multiple largest elements, the rightmost of them is chosen (this is
equivalent to maximumBy compare
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
equivalent to foldr1 minmin. For the default implementation of min (min x y = if x <= y
then x else y), structure order is used as a tie-breaker: if there are
multiple least elements, the leftmost of them is chosen (this is
equivalent to minimumBy compare
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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 Source # | 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 TyVarBndr Source # | |
Defined in GHC.Internal.TH.Syntax Methods fold :: Monoid m => TyVarBndr m -> m Source # foldMap :: Monoid m => (a -> m) -> TyVarBndr a -> m Source # foldMap' :: Monoid m => (a -> m) -> TyVarBndr a -> m Source # foldr :: (a -> b -> b) -> b -> TyVarBndr a -> b Source # foldr' :: (a -> b -> b) -> b -> TyVarBndr a -> b Source # foldl :: (b -> a -> b) -> b -> TyVarBndr a -> b Source # foldl' :: (b -> a -> b) -> b -> TyVarBndr a -> b Source # foldr1 :: (a -> a -> a) -> TyVarBndr a -> a Source # foldl1 :: (a -> a -> a) -> TyVarBndr a -> a Source # toList :: TyVarBndr a -> [a] Source # null :: TyVarBndr a -> Bool Source # length :: TyVarBndr a -> Int Source # elem :: Eq a => a -> TyVarBndr a -> Bool Source # maximum :: Ord a => TyVarBndr a -> a Source # minimum :: Ord a => TyVarBndr a -> a Source # | |
| Foldable Maybe Source # | Since: base-2.1 |
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 Source # | 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 [] Source # | Since: base-2.1 |
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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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) Source # | 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
| Traversable Complex Source # | Since: base-4.9.0.0 |
Defined in Data.Complex | |
| Traversable First Source # | Since: base-4.9.0.0 |
| Traversable Last Source # | Since: base-4.9.0.0 |
| Traversable Max Source # | Since: base-4.9.0.0 |
| Traversable Min Source # | Since: base-4.9.0.0 |
| Traversable NonEmpty Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Identity Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable First Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Last Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Down Source # | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Dual Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Product Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Sum Source # | Since: base-4.8.0.0 |
| Traversable ZipList Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Functor.ZipList | |
| Traversable Par1 Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable TyVarBndr Source # | |
Defined in GHC.Internal.TH.Syntax Methods traverse :: Applicative f => (a -> f b) -> TyVarBndr a -> f (TyVarBndr b) Source # sequenceA :: Applicative f => TyVarBndr (f a) -> f (TyVarBndr a) Source # mapM :: Monad m => (a -> m b) -> TyVarBndr a -> m (TyVarBndr b) Source # sequence :: Monad m => TyVarBndr (m a) -> m (TyVarBndr a) Source # | |
| Traversable Maybe Source # | Since: base-2.1 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable Solo Source # | Since: base-4.15 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable [] Source # | Since: base-2.1 |
| Traversable (Arg a) Source # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ix i => Traversable (Array i) Source # | Since: base-2.1 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (Either a) Source # | 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 # | |
| Traversable (Proxy :: Type -> Type) Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (U1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Traversable (UAddr :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UChar :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UDouble :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UFloat :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UInt :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (UWord :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable (V1 :: Type -> Type) Source # | Since: base-4.9.0.0 |
| Traversable ((,) a) Source # | Since: base-4.7.0.0 |
| Traversable (Const m :: Type -> Type) Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Ap f) Source # | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Alt f) Source # | Since: base-4.12.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| Traversable f => Traversable (Rec1 f) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (Product f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 (Product f g b) Source # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 (Product f g a) Source # mapM :: Monad m => (a -> m b) -> Product f g a -> m (Product f g b) Source # sequence :: Monad m => Product f g (m a) -> m (Product f g a) Source # | |
| (Traversable f, Traversable g) => Traversable (Sum f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Traversable f, Traversable g) => Traversable (f :*: g) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source # sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) Source # sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) Source # | |
| (Traversable f, Traversable g) => Traversable (f :+: g) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) Source # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) Source # | |
| Traversable (K1 i c :: Type -> Type) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (Compose f g) Source # | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) Source # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) Source # mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) Source # sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) Source # | |
| (Traversable f, Traversable g) => Traversable (f :.: g) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source # | |
| Traversable f => Traversable (M1 i c f) Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Data.Traversable | |
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) >>= idJust 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)] 225
>>>let (...) = (.).(.) in ((*2)...(+)) 5 1030
flip :: (a -> b -> c) -> b -> a -> c Source #
flip ff.
flip f x y = f y x
flip . flip = id
Examples
>>>flip (++) "hello" "world""worldhello"
>>>let (.>) = flip (.) in (+1) .> show $ 5"6"
($) :: (a -> b) -> a -> b infixr 0 Source #
($)
Applying ($)f and an argument x gives the same result as applying f to x directly. The definition is akin to this:
($) :: (a -> b) -> a -> b ($) f x = f x
This is ida -> a to (a -> b) -> (a -> b) which by the associativity of (->)
is the same as (a -> b) -> a -> b.
On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.
The order of operations is very different between ($) 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 ($) is to avoid parentheses in complex expressions.
For example, instead of using nested parentheses in the following Haskell function:
-- | Sum numbers in a string: strSum "100 5 -7" == 98 strSum ::String->IntstrSum s =sum(mapMaybereadMaybe(wordss))
we can deploy the function application operator:
-- | Sum numbers in a string: strSum "100 5 -7" == 98 strSum ::String->IntstrSum s =sum$mapMaybereadMaybe$wordss
($) 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 #
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 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 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 #
Warning: This is a partial function, it throws an error on empty lists. Use pattern matching, uncons or listToMaybe instead. Consider refactoring to use Data.List.NonEmpty.
\(\mathcal{O}(1)\). 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 #
Warning: This is a partial function, it throws an error on empty lists. Replace it with drop 1, or use pattern matching or uncons instead. Consider refactoring to use Data.List.NonEmpty.
\(\mathcal{O}(1)\). 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 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 Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis 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
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill 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 = 5Note that right-associativity of :^: is ignored. For example,
show(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 Source # | Since: base-4.8.0.0 |
| Show ByteOrder Source # | Since: base-4.11.0.0 |
| Show ClosureType Source # | |
Defined in GHC.Internal.ClosureTypes | |
| Show BlockReason Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync | |
| Show ThreadId Source # | Since: base-4.2.0.0 |
| Show ThreadStatus Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.Conc.Sync | |
| Show NestedAtomically Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show NoMatchingContinuationPrompt Source # | Since: base-4.18 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show NoMethodError Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show NonTermination Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show PatternMatchFail Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show RecConError Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show RecSelError Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show RecUpdError Source # | Since: base-4.0 |
Defined in GHC.Internal.Control.Exception.Base | |
| Show TypeError Source # | Since: base-4.9.0.0 |
| Show Constr Source # | Since: base-4.0.0.0 |
| Show ConstrRep Source # | Since: base-4.0.0.0 |
| Show DataRep Source # | Since: base-4.0.0.0 |
| Show DataType Source # | Since: base-4.0.0.0 |
| Show Fixity Source # | Since: base-4.0.0.0 |
| Show Dynamic Source # | Since: base-2.1 |
| Show All Source # | Since: base-2.1 |
| Show Any Source # | Since: base-2.1 |
| Show SomeTypeRep Source # | Since: base-4.10.0.0 |
Defined in GHC.Internal.Data.Typeable.Internal | |
| Show Version Source # | Since: base-2.1 |
| Show ControlMessage Source # | Since: base-4.4.0.0 |
| Show Event Source # | Since: base-4.4.0.0 |
| Show EventLifetime Source # | Since: base-4.8.0.0 |
| Show Lifetime Source # | Since: base-4.8.1.0 |
| Show Timeout Source # | Since: base-4.4.0.0 |
| Show FdKey Source # | Since: base-4.4.0.0 |
| Show State Source # | Since: base-4.4.0.0 |
| Show State Source # | Since: base-4.7.0.0 |
| Show Unique Source # | Since: base-4.3.1.0 |
| Show ErrorCall Source # | Since: base-4.0.0.0 |
| Show ArithException Source # | Since: base-4.0.0.0 |
Defined in GHC.Internal.Exception.Type | |
| Show SomeException Source # | Since: ghc-internal-3.0 |
Defined in GHC.Internal.Exception.Type | |
| Show WhileHandling Source # | |
Defined in GHC.Internal.Exception.Type | |
| Show Fingerprint Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.Fingerprint.Type | |
| Show CBool Source # | |
| Show CChar Source # | |
| Show CClock Source # | |
| Show CDouble Source # | |
| Show CFloat Source # | |
| Show CInt Source # | |
| Show CIntMax Source # | |
| Show CIntPtr Source # | |
| Show CLLong Source # | |
| Show CLong Source # | |
| Show CPtrdiff Source # | |
| Show CSChar Source # | |
| Show CSUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Show CShort Source # | |
| Show CSigAtomic Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Show CSize Source # | |
| Show CTime Source # | |
| Show CUChar Source # | |
| Show CUInt Source # | |
| Show CUIntMax Source # | |
| Show CUIntPtr Source # | |
| Show CULLong Source # | |
| Show CULong Source # | |
| Show CUSeconds Source # | |
| Show CUShort Source # | |
| Show CWchar Source # | |
| Show IntPtr Source # | |
| Show WordPtr Source # | |
| Show ForeignSrcLang Source # | |
Defined in GHC.Internal.ForeignSrcLang | |
| Show Associativity Source # | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
| Show DecidedStrictness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show Fixity Source # | Since: base-4.6.0.0 |
| Show SourceStrictness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show SourceUnpackedness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Show MaskingState Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO | |
| Show SeekMode Source # | Since: base-4.2.0.0 |
| Show CodingFailureMode Source # | Since: base-4.4.0.0 |
Defined in GHC.Internal.IO.Encoding.Failure | |
| Show CodingProgress Source # | Since: base-4.4.0.0 |
Defined in GHC.Internal.IO.Encoding.Types | |
| Show TextEncoding Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO.Encoding.Types | |
| Show AllocationLimitExceeded Source # | Since: base-4.7.1.0 |
Defined in GHC.Internal.IO.Exception | |
| Show ArrayException Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show AssertionFailed Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show AsyncException Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show BlockedIndefinitelyOnMVar Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show BlockedIndefinitelyOnSTM Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show CompactionFailed Source # | Since: base-4.10.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show Deadlock Source # | Since: base-4.1.0.0 |
| Show ExitCode Source # | |
| Show FixIOException Source # | Since: base-4.11.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show IOErrorType Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show IOException Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show SomeAsyncException Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.IO.Exception | |
| Show FD Source # | Since: base-4.1.0.0 |
| Show HandlePosn Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Handle | |
| Show FileLockingNotSupported Source # | Since: base-4.10.0.0 |
Defined in GHC.Internal.IO.Handle.Lock.Common | |
| Show BufferMode Source # | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
| Show Handle Source # | Since: base-4.1.0.0 |
| Show HandleType Source # | Since: base-4.1.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
| Show Newline Source # | Since: base-4.3.0.0 |
| Show NewlineMode Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
| Show IOMode Source # | Since: base-4.2.0.0 |
| Show IoSubSystem Source # | |
Defined in GHC.Internal.IO.SubSystem | |
| Show IOPortException Source # | |
| Show InfoProv Source # | |
| Show Int16 Source # | Since: base-2.1 |
| Show Int32 Source # | Since: base-2.1 |
| Show Int64 Source # | Since: base-2.1 |
| Show Int8 Source # | Since: base-2.1 |
| Show Extension Source # | |
| Show CCFlags Source # | Since: base-4.8.0.0 |
| Show ConcFlags Source # | Since: base-4.8.0.0 |
| Show DebugFlags Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoCostCentres Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoHeapProfile Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show DoTrace Source # | Since: base-4.8.0.0 |
| Show GCFlags Source # | Since: base-4.8.0.0 |
| Show GiveGCStats Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show HpcFlags Source # | Since: base-4.20.0.0 |
| Show IoManagerFlag Source # | |
Defined in GHC.Internal.RTS.Flags | |
| Show MiscFlags Source # | Since: base-4.8.0.0 |
| Show ParFlags Source # | Since: base-4.8.0.0 |
| Show ProfFlags Source # | Since: base-4.8.0.0 |
| Show RTSFlags Source # | Since: base-4.8.0.0 |
| Show TickyFlags Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show TraceFlags Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.RTS.Flags | |
| Show FractionalExponentBase Source # | |
Defined in GHC.Internal.Real | |
| Show StackEntry Source # | |
Defined in GHC.Internal.Stack.CloneStack | |
| Show CallStack Source # | Since: base-4.9.0.0 |
| Show SrcLoc Source # | Since: base-4.9.0.0 |
| Show StaticPtrInfo Source # | Since: base-4.8.0.0 |
Defined in GHC.Internal.StaticPtr | |
| Show GCDetails Source # | Since: base-4.10.0.0 |
| Show RTSStats Source # | Since: base-4.10.0.0 |
| Show CBlkCnt Source # | |
| Show CBlkSize Source # | |
| Show CCc Source # | |
| Show CClockId Source # | |
| Show CDev Source # | |
| Show CFsBlkCnt Source # | |
| Show CFsFilCnt Source # | |
| Show CGid Source # | |
| Show CId Source # | |
| Show CIno Source # | |
| Show CKey Source # | |
| Show CMode Source # | |
| Show CNfds Source # | |
| Show CNlink Source # | |
| Show COff Source # | |
| Show CPid Source # | |
| Show CRLim Source # | |
| Show CSocklen Source # | |
| Show CSpeed Source # | |
| Show CSsize Source # | |
| Show CTcflag Source # | |
| Show CTimer Source # | |
| Show CUid Source # | |
| Show Fd Source # | |
| Show AnnLookup Source # | |
| Show AnnTarget Source # | |
| Show Bang Source # | |
| Show BndrVis Source # | |
| Show Body Source # | |
| Show Bytes Source # | |
| Show Callconv Source # | |
| Show Clause Source # | |
| Show Con Source # | |
| Show Dec Source # | |
| Show DecidedStrictness Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show DerivClause Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show DerivStrategy Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show DocLoc Source # | |
| Show Exp Source # | |
| Show FamilyResultSig Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Fixity Source # | |
| Show FixityDirection Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Foreign Source # | |
| Show FunDep Source # | |
| Show Guard Source # | |
| Show Info Source # | |
| Show InjectivityAnn Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Inline Source # | |
| Show Lit Source # | |
| Show Loc Source # | |
| Show Match Source # | |
| Show ModName Source # | |
| Show Module Source # | |
| Show ModuleInfo Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Name Source # | |
| Show NameFlavour Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show NameSpace Source # | |
| Show NamespaceSpecifier Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show OccName Source # | |
| Show Overlap Source # | |
| Show Pat Source # | |
| Show PatSynArgs Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show PatSynDir Source # | |
| Show Phases Source # | |
| Show PkgName Source # | |
| Show Pragma Source # | |
| Show Range Source # | |
| Show Role Source # | |
| Show RuleBndr Source # | |
| Show RuleMatch Source # | |
| Show Safety Source # | |
| Show SourceStrictness Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show SourceUnpackedness Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Specificity Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Stmt Source # | |
| Show TyLit Source # | |
| Show TySynEqn Source # | |
| Show Type Source # | |
| Show TypeFamilyHead Source # | |
Defined in GHC.Internal.TH.Syntax | |
| Show Lexeme Source # | Since: base-2.1 |
| Show Number Source # | Since: base-4.6.0.0 |
| Show SomeChar Source # | |
| Show SomeSymbol Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.TypeLits | |
| Show SomeNat Source # | Since: base-4.7.0.0 |
| Show GeneralCategory Source # | Since: base-2.1 |
Defined in GHC.Internal.Unicode | |
| Show Word16 Source # | Since: base-2.1 |
| Show Word32 Source # | Since: base-2.1 |
| Show Word64 Source # | Since: base-2.1 |
| Show Word8 Source # | Since: base-2.1 |
| Show KindRep Source # | |
| Show Module Source # | Since: base-4.9.0.0 |
| Show Ordering Source # | Since: base-2.1 |
| Show TrName Source # | Since: base-4.9.0.0 |
| Show TyCon Source # | Since: base-2.1 |
| Show TypeLitSort Source # | Since: base-4.11.0.0 |
Defined in GHC.Internal.Show | |
| Show Integer Source # | Since: base-2.1 |
| Show Natural Source # | Since: base-4.8.0.0 |
| Show () Source # | Since: base-2.1 |
| Show Bool Source # | Since: base-2.1 |
| Show Char Source # | Since: base-2.1 |
| Show Int Source # | Since: base-2.1 |
| Show Levity Source # | Since: base-4.15.0.0 |
| Show RuntimeRep Source # | Since: base-4.11.0.0 |
Defined in GHC.Internal.Show | |
| Show VecCount Source # | Since: base-4.11.0.0 |
| Show VecElem Source # | Since: base-4.11.0.0 |
| Show Word Source # | Since: base-2.1 |
| 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) Source # | Since: base-4.11.0.0 |
| Show a => Show (And a) Source # | Since: base-4.16 |
| Show a => Show (Iff a) Source # | Since: base-4.16 |
| Show a => Show (Ior a) Source # | Since: base-4.16 |
| Show a => Show (Xor a) Source # | Since: base-4.16 |
| Show a => Show (Identity a) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Show a => Show (First a) Source # | Since: base-2.1 |
| Show a => Show (Last a) Source # | Since: base-2.1 |
| Show a => Show (Down a) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Show a => Show (Dual a) Source # | Since: base-2.1 |
| Show a => Show (Product a) Source # | Since: base-2.1 |
| Show a => Show (Sum a) Source # | Since: base-2.1 |
| Show a => Show (ExceptionWithContext a) Source # | |
Defined in GHC.Internal.Exception.Type | |
| Show e => Show (NoBacktrace e) Source # | |
Defined in GHC.Internal.Exception.Type | |
| Show (ConstPtr a) Source # | |
| Show (ForeignPtr a) Source # | Since: base-2.1 |
Defined in GHC.Internal.ForeignPtr | |
| Show a => Show (ZipList a) Source # | Since: base-4.7.0.0 |
| Show p => Show (Par1 p) Source # | Since: base-4.7.0.0 |
| Show (FunPtr a) Source # | Since: base-2.1 |
| Show (Ptr a) Source # | Since: base-2.1 |
| Show a => Show (Ratio a) Source # | Since: base-2.0.1 |
| Show flag => Show (TyVarBndr flag) Source # | |
| Show (SChar c) Source # | Since: base-4.18.0.0 |
| Show (SSymbol s) Source # | Since: base-4.18.0.0 |
| Show (SNat n) Source # | Since: base-4.18.0.0 |
| Show a => Show (Maybe a) Source # | Since: base-2.1 |
| Show a => Show (Solo a) Source # | Since: base-4.15 |
| Show a => Show [a] Source # | Since: base-2.1 |
| 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) Source # | Since: base-2.1 |
| (Show a, Show b) => Show (Either a b) Source # | Since: base-3.0 |
| Show (Proxy s) Source # | Since: base-4.7.0.0 |
| Show (TypeRep a) Source # | |
| Show (U1 p) Source # | Since: base-4.9.0.0 |
| Show (UAddr p) Source # | Since: base-4.21.0.0 |
| Show (V1 p) Source # | Since: base-4.9.0.0 |
| Show (ST s a) Source # | Since: base-2.1 |
| (Show a, Show b) => Show (a, b) Source # | Since: base-2.1 |
| Show (a -> b) Source # | Since: base-2.1 |
| Show a => Show (Const a b) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Show (f a) => Show (Ap f a) Source # | Since: base-4.12.0.0 |
| Show (f a) => Show (Alt f a) Source # | Since: base-4.8.0.0 |
| Show (Coercion a b) Source # | Since: base-4.7.0.0 |
| Show (a :~: b) Source # | Since: base-4.7.0.0 |
| Show (OrderingI a b) Source # | |
| Show (f p) => Show (Rec1 f p) Source # | Since: base-4.7.0.0 |
| Show (URec Char p) Source # | Since: base-4.9.0.0 |
| Show (URec Double p) Source # | Since: base-4.9.0.0 |
| Show (URec Float p) Source # | |
| Show (URec Int p) Source # | Since: base-4.9.0.0 |
| Show (URec Word p) Source # | Since: base-4.9.0.0 |
| (Show a, Show b, Show c) => Show (a, b, c) Source # | Since: base-2.1 |
| (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) Source # | Since: base-4.10.0.0 |
| (Show (f p), Show (g p)) => Show ((f :*: g) p) Source # | Since: base-4.7.0.0 |
| (Show (f p), Show (g p)) => Show ((f :+: g) p) Source # | Since: base-4.7.0.0 |
| Show c => Show (K1 i c p) Source # | Since: base-4.7.0.0 |
| (Show a, Show b, Show c, Show d) => Show (a, b, c, d) Source # | Since: base-2.1 |
| Show (f (g a)) => Show (Compose f g a) Source # | Since: base-4.18.0.0 |
| Show (f (g p)) => Show ((f :.: g) p) Source # | Since: base-4.7.0.0 |
| Show (f p) => Show (M1 i c f p) Source # | Since: base-4.7.0.0 |
| (Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) Source # | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) Source # | Since: base-2.1 |
| (Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
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 Strings, 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
Readinstance 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
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance 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 = 5Note 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 = readListPrecDefaultWhy 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:
instanceReadT 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 Source # | Reading a Since: base-4.8.0.0 |
| Read ByteOrder Source # | Since: base-4.11.0.0 |
| Read All Source # | Since: base-2.1 |
| Read Any Source # | Since: base-2.1 |
| Read Version Source # | Since: base-2.1 |
| Read CBool Source # | |
| Read CChar Source # | |
| Read CClock Source # | |
| Read CDouble Source # | |
| Read CFloat Source # | |
| Read CInt Source # | |
| Read CIntMax Source # | |
| Read CIntPtr Source # | |
| Read CLLong Source # | |
| Read CLong Source # | |
| Read CPtrdiff Source # | |
| Read CSChar Source # | |
| Read CSUSeconds Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Read CShort Source # | |
| Read CSigAtomic Source # | |
Defined in GHC.Internal.Foreign.C.Types | |
| Read CSize Source # | |
| Read CTime Source # | |
| Read CUChar Source # | |
| Read CUInt Source # | |
| Read CUIntMax Source # | |
| Read CUIntPtr Source # | |
| Read CULLong Source # | |
| Read CULong Source # | |
| Read CUSeconds Source # | |
| Read CUShort Source # | |
| Read CWchar Source # | |
| Read IntPtr Source # | |
| Read WordPtr Source # | |
| Read Associativity Source # | Since: base-4.6.0.0 |
Defined in GHC.Internal.Generics | |
| Read DecidedStrictness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read Fixity Source # | Since: base-4.6.0.0 |
| Read SourceStrictness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read SourceUnpackedness Source # | Since: base-4.9.0.0 |
Defined in GHC.Internal.Generics | |
| Read SeekMode Source # | Since: base-4.2.0.0 |
| Read ExitCode Source # | |
| Read BufferMode Source # | Since: base-4.2.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
| Read Newline Source # | Since: base-4.3.0.0 |
| Read NewlineMode Source # | Since: base-4.3.0.0 |
Defined in GHC.Internal.IO.Handle.Types | |
| Read IOMode Source # | Since: base-4.2.0.0 |
| Read Int16 Source # | Since: base-2.1 |
| Read Int32 Source # | Since: base-2.1 |
| Read Int64 Source # | Since: base-2.1 |
| Read Int8 Source # | Since: base-2.1 |
| Read GCDetails Source # | Since: base-4.10.0.0 |
| Read RTSStats Source # | Since: base-4.10.0.0 |
| Read CBlkCnt Source # | |
| Read CBlkSize Source # | |
| Read CCc Source # | |
| Read CClockId Source # | |
| Read CDev Source # | |
| Read CFsBlkCnt Source # | |
| Read CFsFilCnt Source # | |
| Read CGid Source # | |
| Read CId Source # | |
| Read CIno Source # | |
| Read CKey Source # | |
| Read CMode Source # | |
| Read CNfds Source # | |
| Read CNlink Source # | |
| Read COff Source # | |
| Read CPid Source # | |
| Read CRLim Source # | |
| Read CSocklen Source # | |
| Read CSpeed Source # | |
| Read CSsize Source # | |
| Read CTcflag Source # | |
| Read CUid Source # | |
| Read Fd Source # | |
| Read Lexeme Source # | Since: base-2.1 |
| Read SomeChar Source # | |
| Read SomeSymbol Source # | Since: base-4.7.0.0 |
Defined in GHC.Internal.TypeLits | |
| Read SomeNat Source # | Since: base-4.7.0.0 |
| Read GeneralCategory Source # | Since: base-2.1 |
Defined in GHC.Internal.Read | |
| Read Word16 Source # | Since: base-2.1 |
| Read Word32 Source # | Since: base-2.1 |
| Read Word64 Source # | Since: base-2.1 |
| Read Word8 Source # | Since: base-2.1 |
| Read Ordering Source # | Since: base-2.1 |
| Read Integer Source # | Since: base-2.1 |
| Read Natural Source # | Since: base-4.8.0.0 |
| Read () Source # | Since: base-2.1 |
| Read Bool Source # | Since: base-2.1 |
| Read Char Source # | Since: base-2.1 |
| Read Double Source # | Since: base-2.1 |
| Read Float Source # | Since: base-2.1 |
| Read Int Source # | Since: base-2.1 |
| Read Word Source # | 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) Source # | Since: base-4.11.0.0 |
| Read a => Read (And a) Source # | Since: base-4.16 |
| Read a => Read (Iff a) Source # | Since: base-4.16 |
| Read a => Read (Ior a) Source # | Since: base-4.16 |
| Read a => Read (Xor a) Source # | Since: base-4.16 |
| Read a => Read (Identity a) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read a => Read (First a) Source # | Since: base-2.1 |
| Read a => Read (Last a) Source # | Since: base-2.1 |
| Read a => Read (Down a) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Read a => Read (Dual a) Source # | Since: base-2.1 |
| Read a => Read (Product a) Source # | Since: base-2.1 |
| Read a => Read (Sum a) Source # | Since: base-2.1 |
| Read a => Read (ZipList a) Source # | Since: base-4.7.0.0 |
| Read p => Read (Par1 p) Source # | Since: base-4.7.0.0 |
| (Integral a, Read a) => Read (Ratio a) Source # | Since: base-2.1 |
| Read a => Read (Maybe a) Source # | Since: base-2.1 |
| Read a => Read (Solo a) Source # | Since: base-4.15 |
| Read a => Read [a] Source # | Since: base-2.1 |
| 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) Source # | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) Source # | Since: base-3.0 |
| Read (Proxy t) Source # | Since: base-4.7.0.0 |
| Read (U1 p) Source # | Since: base-4.9.0.0 |
| Read (V1 p) Source # | Since: base-4.9.0.0 |
| (Read a, Read b) => Read (a, b) Source # | Since: base-2.1 |
| Read a => Read (Const a b) Source # | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f a) => Read (Ap f a) Source # | Since: base-4.12.0.0 |
| Read (f a) => Read (Alt f a) Source # | Since: base-4.8.0.0 |
| Coercible a b => Read (Coercion a b) Source # | Since: base-4.7.0.0 |
| a ~ b => Read (a :~: b) Source # | Since: base-4.7.0.0 |
| Read (f p) => Read (Rec1 f p) Source # | Since: base-4.7.0.0 |
| (Read a, Read b, Read c) => Read (a, b, c) Source # | Since: base-2.1 |
| (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) Source # | Since: base-4.10.0.0 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) Source # | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) Source # | Since: base-4.7.0.0 |
| Read c => Read (K1 i c p) Source # | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) Source # | Since: base-2.1 |
| Read (f (g a)) => Read (Compose f g a) Source # | Since: base-4.18.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) Source # | Since: base-4.7.0.0 |
| Read (f p) => Read (M1 i c f p) Source # | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) Source # | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) Source # | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
| (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) Source # | Since: base-2.1 |
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) Source # | Since: base-2.1 |
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) Source # | Since: base-2.1 |
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) Source # | Since: base-2.1 |
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" :: Int123
>>>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
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 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
| Alternative IO Source # | Takes the first non-throwing Since: base-4.9.0.0 |
| Applicative IO Source # | Since: base-2.1 |
| Functor IO Source # | Since: base-2.1 |
| Monad IO Source # | Since: base-2.1 |
| MonadPlus IO Source # | Takes the first non-throwing Since: base-4.9.0.0 |
| MonadFail IO Source # | Since: base-4.9.0.0 |
| MonadFix IO Source # | Since: base-2.1 |
| MonadIO IO Source # | Since: base-4.9.0.0 |
| GHCiSandboxIO IO Source # | Since: base-4.4.0.0 |
Defined in GHC.Internal.GHCi Methods ghciStepIO :: IO a -> IO a Source # | |
| Quasi IO Source # | |
Defined in GHC.Internal.TH.Syntax Methods qNewName :: String -> IO Name Source # qReport :: Bool -> String -> IO () Source # qRecover :: IO a -> IO a -> IO a Source # qLookupName :: Bool -> String -> IO (Maybe Name) Source # qReify :: Name -> IO Info Source # qReifyFixity :: Name -> IO (Maybe Fixity) Source # qReifyType :: Name -> IO Type Source # qReifyInstances :: Name -> [Type] -> IO [Dec] Source # qReifyRoles :: Name -> IO [Role] Source # qReifyAnnotations :: Data a => AnnLookup -> IO [a] Source # qReifyModule :: Module -> IO ModuleInfo Source # qReifyConStrictness :: Name -> IO [DecidedStrictness] Source # qRunIO :: IO a -> IO a Source # qGetPackageRoot :: IO FilePath Source # qAddDependentFile :: FilePath -> IO () Source # qAddTempFile :: String -> IO FilePath Source # qAddTopDecls :: [Dec] -> IO () Source # qAddForeignFilePath :: ForeignSrcLang -> String -> IO () Source # qAddModFinalizer :: Q () -> IO () Source # qAddCorePlugin :: String -> IO () Source # qGetQ :: Typeable a => IO (Maybe a) Source # qPutQ :: Typeable a => a -> IO () Source # qIsExtEnabled :: Extension -> IO Bool Source # qExtsEnabled :: IO [Extension] Source # | |
| Quote IO 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) Source # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) Source # | Since: base-4.10.0.0 |
Simple I/O operations
Output functions
putStr :: String -> IO () Source #
Write a string to the standard output device
putStr is implemented as hPutStr stdout
This operation may fail with the same errors, and has the same issues with concurrency, as hPutStr!
Examples
Note that the following do not put a newline.
>>>putStr "Hello, World!"Hello, World!
>>>putStr "\0052\0042\0050"4*2
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.
print is implemented as putStrLn . show
This operation may fail with the same errors, and has the same issues with concurrency, as hPutStr!
Examples
>>>print [1, 2, 3][1,2,3]
Be careful when using print for outputting strings,
as this will invoke show and cause strings to be printed
with quotation marks and non-ascii symbols escaped.
>>>print "λ :D""\995 :D"
A program to print the first 8 integers and their powers of 2 could be written as:
>>>print [(n, 2^n) | n <- [0..8]][(0,1),(1,2),(2,4),(3,8),(4,16),(5,32),(6,64),(7,128),(8,256)]
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.
getContents is implemented as hGetContents stdin
This operation may fail with the same errors as hGetContents.
Examples
>>>getContents >>= putStr> aaabbbccc :D aaabbbccc :D > I hope you have a great day I hope you have a great day > ^D
>>>getContents >>= print . length> abc > <3 > def ^D 11
interact :: (String -> String) -> IO () Source #
interact fstdin and applies f to it.
The resulting string is written to the stdout device.
Note that this operation is lazy, which allows to produce output even before all input has been consumed.
This operation may fail with the same errors as getContents and putStr.
Examples
>>>interact (\str -> str ++ str)> hi :) hi :) > ^D hi :)
>>>interact (const ":D"):D
>>>interact (show . words)> hello world! > I hope you have a great day > ^D ["hello","world!","I","hope","you","have","a","great","day"]
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.
This operation may fail with the same errors as hGetContents and openFile.
Examples
>>>readFile "~/hello_world""Greetings!"
>>>take 5 <$> readFile "/dev/zero""\NUL\NUL\NUL\NUL\NUL"
writeFile :: FilePath -> String -> IO () Source #
The computation writeFile file strstr,
to the file file.
This operation may fail with the same errors as hPutStr and withFile.
Examples
>>>writeFile "hello" "world" >> readFile "hello""world"
>>>writeFile "~/" "D:"*** Exception: ~/: withFile: inappropriate type (Is a directory)
appendFile :: FilePath -> String -> IO () Source #
The computation appendFile file strstr,
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.
This operation may fail with the same errors as hPutStr and withFile.
Examples
The following example could be more efficently written by acquiring a handle
instead with openFile and using the computations capable of writing to handles
such as hPutStr.
>>>let fn = "hello_world">>>in writeFile fn "hello" >> appendFile fn " world!" >> (readFile fn >>= putStrLn)"hello world!"
>>>let fn = "foo"; output = readFile' fn >>= putStrLn>>>in output >> appendFile fn (show [1,2,3]) >> outputthis is what's in the file this is what's in the file[1,2,3]
readIO :: Read a => String -> IO a Source #
The readIO function is similar to read except that it signals
parse failure to the IO monad instead of terminating the program.
This operation may fail with:
isUserErrorif there is no unambiguous parse.
Examples
>>>fmap (+ 1) (readIO "1")2
>>>readIO "not quite ()" :: IO ()*** Exception: user error (Prelude.readIO: no parse)
Exception handling in the I/O monad
type IOError = IOException Source #