Prelude
| Copyright | (c) The University of Glasgow 2001 |
|---|---|
| License | BSD-style (see the file libraries/base/LICENSE) |
| Maintainer | [email protected] |
| Stability | stable |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
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.
Standard types, classes and related functions
Basic data types
Instances
| Bounded Bool | Since: base-2.1 |
| Enum Bool | Since: base-2.1 |
| Eq Bool | |
| Data Bool | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Ord Bool | |
| Read Bool | Since: base-2.1 |
| Show Bool | Since: base-2.1 |
| Ix Bool | Since: base-2.1 |
| Generic Bool | Since: base-4.6.0.0 |
| FiniteBits Bool | Since: base-4.7.0.0 |
Defined in Data.Bits MethodsfiniteBitSize :: Bool -> Int Source countLeadingZeros :: Bool -> Int Source countTrailingZeros :: Bool -> Int Source | |
| Bits Bool |
Interpret Since: base-4.7.0.0 |
Defined in Data.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 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 | |
| Storable Bool | Since: base-2.1 |
Defined in Foreign.Storable | |
| type Rep Bool | |
(&&) :: Bool -> Bool -> Bool infixr 3 Source
Boolean "and", lazy in the second argument
(||) :: Bool -> Bool -> Bool infixr 2 Source
Boolean "or", lazy in the second argument
Boolean "not"
otherwise is defined as the value True. It helps to make guards more readable. eg.
f x | x < 0 = ...
| otherwise = ...
The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). 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
| Monad Maybe | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| MonadFix Maybe | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| Applicative Maybe | Since: base-2.1 |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methodsfold :: Monoid m => Maybe m -> m Source foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source foldr :: (a -> b -> b) -> b -> Maybe a -> b Source foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source foldl :: (b -> a -> b) -> b -> Maybe a -> b Source foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source foldr1 :: (a -> a -> a) -> Maybe a -> a Source foldl1 :: (a -> a -> a) -> Maybe a -> a Source toList :: Maybe a -> [a] Source null :: Maybe a -> Bool Source length :: Maybe a -> Int Source elem :: Eq a => a -> Maybe a -> Bool Source maximum :: Ord a => Maybe a -> a Source minimum :: Ord a => Maybe a -> a Source | |
| Traversable Maybe | Since: base-2.1 |
| MonadPlus Maybe | Since: base-2.1 |
| Alternative Maybe | Since: base-2.1 |
| MonadZip Maybe | Since: base-4.8.0.0 |
| Show1 Maybe | Since: base-4.9.0.0 |
| Read1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes MethodsliftReadsPrec :: (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 | |
| Ord1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Eq1 Maybe | Since: base-4.9.0.0 |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Data a => Data (Maybe a) | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Show a => Show (Maybe a) | Since: base-2.1 |
| Generic (Maybe a) | Since: base-4.6.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) |
Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Generic1 Maybe | Since: base-4.6.0.0 |
| type Rep (Maybe a) | |
Defined in GHC.Generics | |
| type Rep1 Maybe | |
maybe :: b -> (a -> b) -> Maybe a -> b Source
The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.
Examples
Basic usage:
>>> maybe False odd (Just 3) True
>>> maybe False odd Nothing False
Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:
>>> import 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 b is either Left a or Right b.
The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").
Examples
The type Either String Int is the type of values which can be either a String 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 >>> s Left "foo" >>> let n = Right 3 :: Either String Int >>> n Right 3 >>> :type s s :: Either String Int >>> :type n n :: Either String Int
The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:
>>> let s = Left "foo" :: Either String Int >>> let n = Right 3 :: Either String Int >>> fmap (*2) s Left "foo" >>> fmap (*2) n Right 6
The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.
>>> import Data.Char ( digitToInt, isDigit )
>>> :{
let parseEither :: Char -> Either String Int
parseEither c
| isDigit c = Right (digitToInt c)
| otherwise = Left "parse error"
>>> :}
The following should work, since both '1' and '2' can be parsed as Ints.
>>> :{
let parseMultiple :: Either String Int
parseMultiple = do
x <- parseEither '1'
y <- parseEither '2'
return (x + y)
>>> :}
>>> parseMultiple Right 3
But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:
>>> :{
let parseMultiple :: Either String Int
parseMultiple = do
x <- parseEither 'm'
y <- parseEither '2'
return (x + y)
>>> :}
>>> parseMultiple Left "parse error"
Instances
| Show2 Either | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read2 Either | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes MethodsliftReadsPrec2 :: (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 | |
| Ord2 Either | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Eq2 Either | Since: base-4.9.0.0 |
| Bifunctor Either | Since: base-4.8.0.0 |
| Bifoldable Either | Since: base-4.10.0.0 |
| Bitraversable Either | Since: base-4.10.0.0 |
Defined in Data.Bitraversable Methodsbitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Either a b -> f (Either c d) Source | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Functor (Either a) | Since: base-3.0 |
| MonadFix (Either e) | Since: base-4.3.0.0 |
Defined in Control.Monad.Fix | |
| Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => Either a m -> m Source foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source toList :: Either a a0 -> [a0] Source null :: Either a a0 -> Bool Source length :: Either a a0 -> Int Source elem :: Eq a0 => a0 -> Either a a0 -> Bool Source maximum :: Ord a0 => Either a a0 -> a0 Source minimum :: Ord a0 => Either a a0 -> a0 Source | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Show a => Show1 (Either a) | Since: base-4.9.0.0 |
| Read a => Read1 (Either a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes MethodsliftReadsPrec :: (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 | |
| Ord a => Ord1 (Either a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Eq a => Eq1 (Either a) | Since: base-4.9.0.0 |
| Generic1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| (Data a, Data b) => Data (Either a b) | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
Defined in Data.Either Methodscompare :: 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 | |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 |
| Generic (Either a b) | Since: base-4.6.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| type Rep1 (Either a :: Type -> Type) | |
Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" '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) | |
Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" '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 a, apply the first function to a; if it is Right b, apply the second function to b.
Examples
We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):
>>> let s = Left "foo" :: Either String Int >>> let n = Right 3 :: Either String Int >>> either length (*2) s 3 >>> either length (*2) n 6
Instances
| Bounded Ordering | Since: base-2.1 |
| Enum Ordering | Since: base-2.1 |
Defined in GHC.Enum Methodssucc :: 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 | |
| Eq Ordering | |
| Data Ordering | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Read Ordering | Since: base-2.1 |
| Show Ordering | Since: base-2.1 |
| Ix Ordering | Since: base-2.1 |
Defined in GHC.Ix Methodsrange :: (Ordering, Ordering) -> [Ordering] Source index :: (Ordering, Ordering) -> Ordering -> Int Source unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int Source inRange :: (Ordering, Ordering) -> Ordering -> Bool Source rangeSize :: (Ordering, Ordering) -> Int Source unsafeRangeSize :: (Ordering, Ordering) -> Int Source | |
| Generic Ordering | Since: base-4.6.0.0 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Monoid Ordering | Since: base-2.1 |
| type Rep Ordering | |
The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type Char.
To convert a Char to or from the corresponding Int value defined by Unicode, use toEnum and fromEnum from the Enum class respectively (or equivalently ord and chr).
Instances
| Bounded Char | Since: base-2.1 |
| Enum Char | Since: base-2.1 |
| Eq Char | |
| Data Char | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Ord Char | |
| Read Char | Since: base-2.1 |
| Show Char | Since: base-2.1 |
| Ix Char | Since: base-2.1 |
| Storable Char | Since: base-2.1 |
Defined in Foreign.Storable | |
| IsChar Char | Since: base-2.1 |
| PrintfArg Char | Since: base-2.1 |
Defined in Text.Printf | |
| Generic1 (URec Char :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UChar m -> m Source foldMap :: Monoid m => (a -> m) -> UChar a -> m Source foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source foldr :: (a -> b -> b) -> b -> UChar a -> b Source foldr' :: (a -> b -> b) -> b -> UChar a -> b Source foldl :: (b -> a -> b) -> b -> UChar a -> b Source foldl' :: (b -> a -> b) -> b -> UChar a -> b Source foldr1 :: (a -> a -> a) -> UChar a -> a Source foldl1 :: (a -> a -> a) -> UChar a -> a Source toList :: UChar a -> [a] Source null :: UChar a -> Bool Source length :: UChar a -> Int Source elem :: Eq a => a -> UChar a -> Bool Source maximum :: Ord a => UChar a -> a Source minimum :: Ord a => UChar a -> a Source | |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: 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 | |
| Show (URec Char p) | Since: base-4.9.0.0 |
| Generic (URec Char p) | Since: base-4.9.0.0 |
| data URec Char (p :: k) |
Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Char :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Char p) | |
Defined in GHC.Generics | |
A String is a list of characters. String constants in Haskell are values of type String.
See Data.List for operations on lists.
Tuples
Extract the first component of a pair.
Extract the second component of a pair.
curry :: ((a, b) -> c) -> a -> b -> c Source
curry converts an uncurried function to a curried function.
Examples
>>> curry fst 1 2 1
uncurry :: (a -> b -> c) -> (a, b) -> c Source
uncurry converts a curried function to a function on pairs.
Examples
>>> uncurry (+) (1,2) 3
>>> uncurry ($) (show, 1) "1"
>>> map (uncurry max) [(1,2), (3,4), (6,8)] [2,4,8]
Basic type classes
The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.
The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:
- Reflexivity
-
x == x=True - Symmetry
-
x == y=y == x - Transitivity
- if
x == y && y == z=True, thenx == z=True - Substitutivity
- if
x == y=Trueandfis a "public" function whose return type is an instance ofEq, thenf x == f y=True - Negation
-
x /= y=not (x == y)
Minimal complete definition: either == or /=.
Instances
| Eq Bool | |
| Eq Char | |
| Eq Double |
Note that due to the presence of >>> 0/0 == (0/0 :: Double) False Also note that >>> 0 == (-0 :: Double) True >>> recip 0 == recip (-0 :: Double) False |
| Eq Float |
Note that due to the presence of >>> 0/0 == (0/0 :: Float) False Also note that >>> 0 == (-0 :: Float) True >>> recip 0 == recip (-0 :: Float) False |
| Eq Int | |
| Eq Int8 | Since: base-2.1 |
| Eq Int16 | Since: base-2.1 |
| Eq Int32 | Since: base-2.1 |
| Eq Int64 | Since: base-2.1 |
| Eq Integer | |
| Eq Natural | Since: base-4.8.0.0 |
| Eq Ordering | |
| Eq Word | |
| Eq Word8 | Since: base-2.1 |
| Eq Word16 | Since: base-2.1 |
| Eq Word32 | Since: base-2.1 |
| Eq Word64 | Since: base-2.1 |
| Eq SomeTypeRep | |
Defined in Data.Typeable.Internal Methods(==) :: SomeTypeRep -> SomeTypeRep -> Bool Source (/=) :: SomeTypeRep -> SomeTypeRep -> Bool Source | |
| Eq () | |
| Eq TyCon | |
| Eq Module | |
| Eq TrName | |
| Eq BigNat | |
| Eq SrcLoc | Since: base-4.9.0.0 |
| Eq GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methods(==) :: GeneralCategory -> GeneralCategory -> Bool Source (/=) :: GeneralCategory -> GeneralCategory -> Bool Source | |
| Eq Number | Since: base-4.6.0.0 |
| Eq Lexeme | Since: base-2.1 |
| Eq Fingerprint | Since: base-4.4.0.0 |
Defined in GHC.Fingerprint.Type Methods(==) :: Fingerprint -> Fingerprint -> Bool Source (/=) :: Fingerprint -> Fingerprint -> Bool Source | |
| Eq IOMode | Since: base-4.2.0.0 |
| Eq IntPtr | |
| Eq WordPtr | |
| Eq CUIntMax | |
| Eq CIntMax | |
| Eq CUIntPtr | |
| Eq CIntPtr | |
| Eq CSUSeconds | |
Defined in Foreign.C.Types Methods(==) :: CSUSeconds -> CSUSeconds -> Bool Source (/=) :: CSUSeconds -> CSUSeconds -> Bool Source | |
| Eq CUSeconds | |
| Eq CTime | |
| Eq CClock | |
| Eq CSigAtomic | |
Defined in Foreign.C.Types Methods(==) :: CSigAtomic -> CSigAtomic -> Bool Source (/=) :: CSigAtomic -> CSigAtomic -> Bool Source | |
| Eq CWchar | |
| Eq CSize | |
| Eq CPtrdiff | |
| Eq CDouble | |
| Eq CFloat | |
| Eq CBool | |
| Eq CULLong | |
| Eq CLLong | |
| Eq CULong | |
| Eq CLong | |
| Eq CUInt | |
| Eq CInt | |
| Eq CUShort | |
| Eq CShort | |
| Eq CUChar | |
| Eq CSChar | |
| Eq CChar | |
| Eq SomeNat | Since: base-4.7.0.0 |
| Eq SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits Methods(==) :: SomeSymbol -> SomeSymbol -> Bool Source (/=) :: SomeSymbol -> SomeSymbol -> Bool Source | |
| Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods(==) :: DecidedStrictness -> DecidedStrictness -> Bool Source (/=) :: DecidedStrictness -> DecidedStrictness -> Bool Source | |
| Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods(==) :: SourceStrictness -> SourceStrictness -> Bool Source (/=) :: SourceStrictness -> SourceStrictness -> Bool Source | |
| Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods(==) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source | |
| Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods(==) :: Associativity -> Associativity -> Bool Source (/=) :: Associativity -> Associativity -> Bool Source | |
| Eq Fixity | Since: base-4.6.0.0 |
| Eq Any | Since: base-2.1 |
| Eq All | Since: base-2.1 |
| Eq ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods(==) :: ArithException -> ArithException -> Bool Source (/=) :: ArithException -> ArithException -> Bool Source | |
| Eq ErrorCall | Since: base-4.7.0.0 |
| Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception Methods(==) :: IOException -> IOException -> Bool Source (/=) :: IOException -> IOException -> Bool Source | |
| Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO Methods(==) :: MaskingState -> MaskingState -> Bool Source (/=) :: MaskingState -> MaskingState -> Bool Source | |
| Eq BufferState | Since: base-4.2.0.0 |
Defined in GHC.IO.Buffer Methods(==) :: BufferState -> BufferState -> Bool Source (/=) :: BufferState -> BufferState -> Bool Source | |
| Eq CodingProgress | Since: base-4.4.0.0 |
Defined in GHC.IO.Encoding.Types Methods(==) :: CodingProgress -> CodingProgress -> Bool Source (/=) :: CodingProgress -> CodingProgress -> Bool Source | |
| Eq SeekMode | Since: base-4.2.0.0 |
| Eq IODeviceType | Since: base-4.2.0.0 |
Defined in GHC.IO.Device Methods(==) :: IODeviceType -> IODeviceType -> Bool Source (/=) :: IODeviceType -> IODeviceType -> Bool Source | |
| Eq NewlineMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods(==) :: NewlineMode -> NewlineMode -> Bool Source (/=) :: NewlineMode -> NewlineMode -> Bool Source | |
| Eq Newline | Since: base-4.2.0.0 |
| Eq BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methods(==) :: BufferMode -> BufferMode -> Bool Source (/=) :: BufferMode -> BufferMode -> Bool Source | |
| Eq Handle | Since: base-4.1.0.0 |
| Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception Methods(==) :: IOErrorType -> IOErrorType -> Bool Source (/=) :: IOErrorType -> IOErrorType -> Bool Source | |
| Eq ExitCode | |
| Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods(==) :: ArrayException -> ArrayException -> Bool Source (/=) :: ArrayException -> ArrayException -> Bool Source | |
| Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods(==) :: AsyncException -> AsyncException -> Bool Source (/=) :: AsyncException -> AsyncException -> Bool Source | |
| Eq Errno | Since: base-2.1 |
| Eq Fd | |
| Eq CNfds | |
| Eq CSocklen | |
| Eq CTimer | |
| Eq CKey | |
| Eq CId | |
| Eq CFsFilCnt | |
| Eq CFsBlkCnt | |
| Eq CClockId | |
| Eq CBlkCnt | |
| Eq CBlkSize | |
| Eq CRLim | |
| Eq CTcflag | |
| Eq CSpeed | |
| Eq CCc | |
| Eq CUid | |
| Eq CNlink | |
| Eq CGid | |
| Eq CSsize | |
| Eq CPid | |
| Eq COff | |
| Eq CMode | |
| Eq CIno | |
| Eq CDev | |
| Eq Lifetime | Since: base-4.8.1.0 |
| Eq Event | Since: base-4.4.0.0 |
| Eq ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods(==) :: ThreadStatus -> ThreadStatus -> Bool Source (/=) :: ThreadStatus -> ThreadStatus -> Bool Source | |
| Eq BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods(==) :: BlockReason -> BlockReason -> Bool Source (/=) :: BlockReason -> BlockReason -> Bool Source | |
| Eq ThreadId | Since: base-4.2.0.0 |
| Eq TimeoutKey | Since: base-4.7.0.0 |
Defined in GHC.Event.TimerManager Methods(==) :: TimeoutKey -> TimeoutKey -> Bool Source (/=) :: TimeoutKey -> TimeoutKey -> Bool Source | |
| Eq FdKey | Since: base-4.4.0.0 |
| Eq HandlePosn | Since: base-4.1.0.0 |
Defined in GHC.IO.Handle Methods(==) :: HandlePosn -> HandlePosn -> Bool Source (/=) :: HandlePosn -> HandlePosn -> Bool Source | |
| Eq Version | Since: base-2.1 |
| Eq ByteOrder | Since: base-4.11.0.0 |
| Eq Unique | |
| Eq Timeout | |
| Eq Fixity | Since: base-4.0.0.0 |
| Eq ConstrRep | Since: base-4.0.0.0 |
| Eq DataRep | Since: base-4.0.0.0 |
| Eq Constr |
Equality of constructors Since: base-4.0.0.0 |
| Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts Methods(==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool Source | |
| Eq Void | Since: base-4.8.0.0 |
| Eq a => Eq [a] | |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Eq a => Eq (Ratio a) | Since: base-2.1 |
| Eq (StablePtr a) | Since: base-2.1 |
| Eq (Ptr a) | Since: base-2.1 |
| Eq (FunPtr a) | |
| Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Eq (MVar a) | Since: base-4.1.0.0 |
| Eq a => Eq (Down a) | Since: base-4.6.0.0 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Eq a => Eq (Last a) | Since: base-2.1 |
| Eq a => Eq (First a) | Since: base-2.1 |
| Eq (IORef a) |
Pointer equality. Since: base-4.0.0.0 |
| Eq (ForeignPtr a) | Since: base-2.1 |
Defined in GHC.ForeignPtr Methods(==) :: ForeignPtr a -> ForeignPtr a -> Bool Source (/=) :: ForeignPtr a -> ForeignPtr a -> Bool Source | |
| Eq (TVar a) | Since: base-4.8.0.0 |
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
| Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
| Eq (StableName a) | Since: base-2.1 |
Defined in GHC.StableName Methods(==) :: StableName a -> StableName a -> Bool Source (/=) :: StableName a -> StableName a -> Bool Source | |
| Eq (Chan a) | Since: base-4.4.0.0 |
| Eq a => Eq (Option a) | Since: base-4.9.0.0 |
| Eq m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source | |
| Eq a => Eq (Last a) | Since: base-4.9.0.0 |
| Eq a => Eq (First a) | Since: base-4.9.0.0 |
| Eq a => Eq (Max a) | Since: base-4.9.0.0 |
| Eq a => Eq (Min a) | Since: base-4.9.0.0 |
| Eq a => Eq (Complex a) | Since: base-2.1 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| Eq (V1 p) | Since: base-4.9.0.0 |
| Eq (U1 p) | Since: base-4.9.0.0 |
| Eq (TypeRep a) | Since: base-2.1 |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq (STRef s a) |
Pointer equality. Since: base-2.1 |
| (Ix i, Eq e) => Eq (Array i e) | Since: base-2.1 |
| Eq (Proxy s) | Since: base-4.7.0.0 |
| Eq (IOArray i e) | Since: base-4.1.0.0 |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| Eq (Fixed a) | Since: base-2.1 |
| Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Eq (URec Float p) | |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| Eq (STArray s i e) | Since: base-2.1 |
| Eq (a :~: b) | Since: base-4.7.0.0 |
| Eq (Coercion a b) | Since: base-4.7.0.0 |
| Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
| Eq (f a) => Eq (Ap f a) | Since: base-4.12.0.0 |
| Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
| Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| Eq (a :~~: b) | Since: base-4.10.0.0 |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a) | Since: base-4.9.0.0 |
| (Eq1 f, Eq1 g, Eq a) => Eq (Product f g a) | Since: base-4.9.0.0 |
| Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
| Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a) | Since: base-4.9.0.0 |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Eq a => Ord a where Source
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.
The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:
- Transitivity
- if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
-
x <= x=True - Antisymmetry
- if
x <= y && y <= x=True, thenx == y=True
Note that the following operator interactions are expected to hold:
-
x >= y=y <= x -
x < y=x <= y && x /= y -
x > y=y < x -
x < y=compare x y == LT -
x > y=compare x y == GT -
x == y=compare x y == EQ -
min x y == if x <= y then x else y=True -
max x y == if x >= y then x else y=True
Note that (7.) and (8.) do not require min and max to return either of their arguments. The result is merely required to equal one of the arguments in terms of (==).
Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering Source
(<) :: a -> a -> Bool infix 4 Source
(<=) :: a -> a -> Bool infix 4 Source
(>) :: a -> a -> Bool infix 4 Source
Instances
| Ord Bool | |
| Ord Char | |
| Ord Double |
Note that due to the presence of >>> 0/0 <= (0/0 :: Double) False Also note that, due to the same, >>> (0/0 :: Double) > 1 False >>> compare (0/0 :: Double) 1 GT |
Defined in GHC.Classes | |
| Ord Float |
Note that due to the presence of >>> 0/0 <= (0/0 :: Float) False Also note that, due to the same, >>> (0/0 :: Float) > 1 False >>> compare (0/0 :: Float) 1 GT |
Defined in GHC.Classes | |
| Ord Int | |
| Ord Int8 | Since: base-2.1 |
| Ord Int16 | Since: base-2.1 |
| Ord Int32 | Since: base-2.1 |
| Ord Int64 | Since: base-2.1 |
| Ord Integer | |
| Ord Natural | Since: base-4.8.0.0 |
| Ord Ordering | |
Defined in GHC.Classes | |
| Ord Word | |
| Ord Word8 | Since: base-2.1 |
| Ord Word16 | Since: base-2.1 |
Defined in GHC.Word | |
| Ord Word32 | Since: base-2.1 |
Defined in GHC.Word | |
| Ord Word64 | Since: base-2.1 |
Defined in GHC.Word | |
| Ord SomeTypeRep | |
Defined in Data.Typeable.Internal Methodscompare :: SomeTypeRep -> SomeTypeRep -> Ordering Source (<) :: SomeTypeRep -> SomeTypeRep -> Bool Source (<=) :: SomeTypeRep -> SomeTypeRep -> Bool Source (>) :: SomeTypeRep -> SomeTypeRep -> Bool Source (>=) :: SomeTypeRep -> SomeTypeRep -> Bool Source max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep Source | |
| Ord () | |
| Ord TyCon | |
Defined in GHC.Classes | |
| Ord BigNat | |
Defined in GHC.Integer.Type | |
| Ord GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode Methodscompare :: GeneralCategory -> GeneralCategory -> Ordering Source (<) :: GeneralCategory -> GeneralCategory -> Bool Source (<=) :: GeneralCategory -> GeneralCategory -> Bool Source (>) :: GeneralCategory -> GeneralCategory -> Bool Source (>=) :: GeneralCategory -> GeneralCategory -> Bool Source max :: GeneralCategory -> GeneralCategory -> GeneralCategory Source min :: GeneralCategory -> GeneralCategory -> GeneralCategory Source | |
| Ord Fingerprint | Since: base-4.4.0.0 |
Defined in GHC.Fingerprint.Type Methodscompare :: Fingerprint -> Fingerprint -> Ordering Source (<) :: Fingerprint -> Fingerprint -> Bool Source (<=) :: Fingerprint -> Fingerprint -> Bool Source (>) :: Fingerprint -> Fingerprint -> Bool Source (>=) :: Fingerprint -> Fingerprint -> Bool Source max :: Fingerprint -> Fingerprint -> Fingerprint Source min :: Fingerprint -> Fingerprint -> Fingerprint Source | |
| Ord IOMode | Since: base-4.2.0.0 |
Defined in GHC.IO.IOMode | |
| Ord IntPtr | |
Defined in Foreign.Ptr | |
| Ord WordPtr | |
| Ord CUIntMax | |
Defined in Foreign.C.Types | |
| Ord CIntMax | |
| Ord CUIntPtr | |
Defined in Foreign.C.Types | |
| Ord CIntPtr | |
| Ord CSUSeconds | |
Defined in Foreign.C.Types Methodscompare :: CSUSeconds -> CSUSeconds -> Ordering Source (<) :: CSUSeconds -> CSUSeconds -> Bool Source (<=) :: CSUSeconds -> CSUSeconds -> Bool Source (>) :: CSUSeconds -> CSUSeconds -> Bool Source (>=) :: CSUSeconds -> CSUSeconds -> Bool Source max :: CSUSeconds -> CSUSeconds -> CSUSeconds Source min :: CSUSeconds -> CSUSeconds -> CSUSeconds Source | |
| Ord CUSeconds | |
Defined in Foreign.C.Types | |
| Ord CTime | |
Defined in Foreign.C.Types | |
| Ord CClock | |
Defined in Foreign.C.Types | |
| Ord CSigAtomic | |
Defined in Foreign.C.Types Methodscompare :: CSigAtomic -> CSigAtomic -> Ordering Source (<) :: CSigAtomic -> CSigAtomic -> Bool Source (<=) :: CSigAtomic -> CSigAtomic -> Bool Source (>) :: CSigAtomic -> CSigAtomic -> Bool Source (>=) :: CSigAtomic -> CSigAtomic -> Bool Source max :: CSigAtomic -> CSigAtomic -> CSigAtomic Source min :: CSigAtomic -> CSigAtomic -> CSigAtomic Source | |
| Ord CWchar | |
Defined in Foreign.C.Types | |
| Ord CSize | |
Defined in Foreign.C.Types | |
| Ord CPtrdiff | |
Defined in Foreign.C.Types | |
| Ord CDouble | |
| Ord CFloat | |
Defined in Foreign.C.Types | |
| Ord CBool | |
Defined in Foreign.C.Types | |
| Ord CULLong | |
| Ord CLLong | |
Defined in Foreign.C.Types | |
| Ord CULong | |
Defined in Foreign.C.Types | |
| Ord CLong | |
Defined in Foreign.C.Types | |
| Ord CUInt | |
Defined in Foreign.C.Types | |
| Ord CInt | |
| Ord CUShort | |
| Ord CShort | |
Defined in Foreign.C.Types | |
| Ord CUChar | |
Defined in Foreign.C.Types | |
| Ord CSChar | |
Defined in Foreign.C.Types | |
| Ord CChar | |
Defined in Foreign.C.Types | |
| Ord SomeNat | Since: base-4.7.0.0 |
| Ord SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits Methodscompare :: SomeSymbol -> SomeSymbol -> Ordering Source (<) :: SomeSymbol -> SomeSymbol -> Bool Source (<=) :: SomeSymbol -> SomeSymbol -> Bool Source (>) :: SomeSymbol -> SomeSymbol -> Bool Source (>=) :: SomeSymbol -> SomeSymbol -> Bool Source max :: SomeSymbol -> SomeSymbol -> SomeSymbol Source min :: SomeSymbol -> SomeSymbol -> SomeSymbol Source | |
| Ord DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: DecidedStrictness -> DecidedStrictness -> Ordering Source (<) :: DecidedStrictness -> DecidedStrictness -> Bool Source (<=) :: DecidedStrictness -> DecidedStrictness -> Bool Source (>) :: DecidedStrictness -> DecidedStrictness -> Bool Source (>=) :: DecidedStrictness -> DecidedStrictness -> Bool Source max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness Source | |
| Ord SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: SourceStrictness -> SourceStrictness -> Ordering Source (<) :: SourceStrictness -> SourceStrictness -> Bool Source (<=) :: SourceStrictness -> SourceStrictness -> Bool Source (>) :: SourceStrictness -> SourceStrictness -> Bool Source (>=) :: SourceStrictness -> SourceStrictness -> Bool Source max :: SourceStrictness -> SourceStrictness -> SourceStrictness Source min :: SourceStrictness -> SourceStrictness -> SourceStrictness Source | |
| Ord SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: SourceUnpackedness -> SourceUnpackedness -> Ordering Source (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool Source max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness Source | |
| Ord Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methodscompare :: Associativity -> Associativity -> Ordering Source (<) :: Associativity -> Associativity -> Bool Source (<=) :: Associativity -> Associativity -> Bool Source (>) :: Associativity -> Associativity -> Bool Source (>=) :: Associativity -> Associativity -> Bool Source max :: Associativity -> Associativity -> Associativity Source min :: Associativity -> Associativity -> Associativity Source | |
| Ord Fixity | Since: base-4.6.0.0 |
Defined in GHC.Generics | |
| Ord Any | Since: base-2.1 |
| Ord All | Since: base-2.1 |
| Ord ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methodscompare :: ArithException -> ArithException -> Ordering Source (<) :: ArithException -> ArithException -> Bool Source (<=) :: ArithException -> ArithException -> Bool Source (>) :: ArithException -> ArithException -> Bool Source (>=) :: ArithException -> ArithException -> Bool Source max :: ArithException -> ArithException -> ArithException Source min :: ArithException -> ArithException -> ArithException Source | |
| Ord ErrorCall | Since: base-4.7.0.0 |
Defined in GHC.Exception | |
| Ord SeekMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Device | |
| Ord NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methodscompare :: NewlineMode -> NewlineMode -> Ordering Source (<) :: NewlineMode -> NewlineMode -> Bool Source (<=) :: NewlineMode -> NewlineMode -> Bool Source (>) :: NewlineMode -> NewlineMode -> Bool Source (>=) :: NewlineMode -> NewlineMode -> Bool Source max :: NewlineMode -> NewlineMode -> NewlineMode Source min :: NewlineMode -> NewlineMode -> NewlineMode Source | |
| Ord Newline | Since: base-4.3.0.0 |
| Ord BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types Methodscompare :: BufferMode -> BufferMode -> Ordering Source (<) :: BufferMode -> BufferMode -> Bool Source (<=) :: BufferMode -> BufferMode -> Bool Source (>) :: BufferMode -> BufferMode -> Bool Source (>=) :: BufferMode -> BufferMode -> Bool Source max :: BufferMode -> BufferMode -> BufferMode Source min :: BufferMode -> BufferMode -> BufferMode Source | |
| Ord ExitCode | |
Defined in GHC.IO.Exception | |
| Ord ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methodscompare :: ArrayException -> ArrayException -> Ordering Source (<) :: ArrayException -> ArrayException -> Bool Source (<=) :: ArrayException -> ArrayException -> Bool Source (>) :: ArrayException -> ArrayException -> Bool Source (>=) :: ArrayException -> ArrayException -> Bool Source max :: ArrayException -> ArrayException -> ArrayException Source min :: ArrayException -> ArrayException -> ArrayException Source | |
| Ord AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methodscompare :: AsyncException -> AsyncException -> Ordering Source (<) :: AsyncException -> AsyncException -> Bool Source (<=) :: AsyncException -> AsyncException -> Bool Source (>) :: AsyncException -> AsyncException -> Bool Source (>=) :: AsyncException -> AsyncException -> Bool Source max :: AsyncException -> AsyncException -> AsyncException Source min :: AsyncException -> AsyncException -> AsyncException Source | |
| Ord Fd | |
| Ord CNfds | |
Defined in System.Posix.Types | |
| Ord CSocklen | |
Defined in System.Posix.Types | |
| Ord CTimer | |
Defined in System.Posix.Types | |
| Ord CKey | |
| Ord CId | |
| Ord CFsFilCnt | |
Defined in System.Posix.Types | |
| Ord CFsBlkCnt | |
Defined in System.Posix.Types | |
| Ord CClockId | |
Defined in System.Posix.Types | |
| Ord CBlkCnt | |
| Ord CBlkSize | |
Defined in System.Posix.Types | |
| Ord CRLim | |
Defined in System.Posix.Types | |
| Ord CTcflag | |
| Ord CSpeed | |
Defined in System.Posix.Types | |
| Ord CCc | |
| Ord CUid | |
| Ord CNlink | |
Defined in System.Posix.Types | |
| Ord CGid | |
| Ord CSsize | |
Defined in System.Posix.Types | |
| Ord CPid | |
| Ord COff | |
| Ord CMode | |
Defined in System.Posix.Types | |
| Ord CIno | |
| Ord CDev | |
| Ord ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methodscompare :: ThreadStatus -> ThreadStatus -> Ordering Source (<) :: ThreadStatus -> ThreadStatus -> Bool Source (<=) :: ThreadStatus -> ThreadStatus -> Bool Source (>) :: ThreadStatus -> ThreadStatus -> Bool Source (>=) :: ThreadStatus -> ThreadStatus -> Bool Source max :: ThreadStatus -> ThreadStatus -> ThreadStatus Source min :: ThreadStatus -> ThreadStatus -> ThreadStatus Source | |
| Ord BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methodscompare :: BlockReason -> BlockReason -> Ordering Source (<) :: BlockReason -> BlockReason -> Bool Source (<=) :: BlockReason -> BlockReason -> Bool Source (>) :: BlockReason -> BlockReason -> Bool Source (>=) :: BlockReason -> BlockReason -> Bool Source max :: BlockReason -> BlockReason -> BlockReason Source min :: BlockReason -> BlockReason -> BlockReason Source | |
| Ord ThreadId | Since: base-4.2.0.0 |
Defined in GHC.Conc.Sync | |
| Ord Version | Since: base-2.1 |
| Ord ByteOrder | Since: base-4.11.0.0 |
Defined in GHC.ByteOrder | |
| Ord Unique | |
Defined in Data.Unique | |
| Ord Void | Since: base-4.8.0.0 |
| Ord a => Ord [a] | |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Integral a => Ord (Ratio a) | Since: base-2.0.1 |
| Ord (Ptr a) | Since: base-2.1 |
| Ord (FunPtr a) | |
| Ord p => Ord (Par1 p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
Defined in GHC.Base Methodscompare :: NonEmpty a -> NonEmpty a -> Ordering Source (<) :: NonEmpty a -> NonEmpty a -> Bool Source (<=) :: NonEmpty a -> NonEmpty a -> Bool Source (>) :: NonEmpty a -> NonEmpty a -> Bool Source (>=) :: NonEmpty a -> NonEmpty a -> Bool Source | |
| Ord a => Ord (Down a) | Since: base-4.6.0.0 |
Defined in Data.Ord | |
| Ord a => Ord (Product a) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Ord a => Ord (Sum a) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Ord a => Ord (Dual a) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Ord a => Ord (Last a) | Since: base-2.1 |
Defined in Data.Monoid | |
| Ord a => Ord (First a) | Since: base-2.1 |
| Ord (ForeignPtr a) | Since: base-2.1 |
Defined in GHC.ForeignPtr Methodscompare :: ForeignPtr a -> ForeignPtr a -> Ordering Source (<) :: ForeignPtr a -> ForeignPtr a -> Bool Source (<=) :: ForeignPtr a -> ForeignPtr a -> Bool Source (>) :: ForeignPtr a -> ForeignPtr a -> Bool Source (>=) :: ForeignPtr a -> ForeignPtr a -> Bool Source max :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a Source min :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a Source | |
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methodscompare :: Identity a -> Identity a -> Ordering Source (<) :: Identity a -> Identity a -> Bool Source (<=) :: Identity a -> Identity a -> Bool Source (>) :: Identity a -> Identity a -> Bool Source (>=) :: Identity a -> Identity a -> Bool Source | |
| Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
Defined in Control.Applicative | |
| Ord a => Ord (Option a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ord m => Ord (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodscompare :: WrappedMonoid m -> WrappedMonoid m -> Ordering Source (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source | |
| Ord a => Ord (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ord a => Ord (First a) | Since: base-4.9.0.0 |
| Ord a => Ord (Max a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Ord a => Ord (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
Defined in Data.Either Methodscompare :: Either a b -> Either a b -> Ordering Source (<) :: Either a b -> Either a b -> Bool Source (<=) :: Either a b -> Either a b -> Bool Source (>) :: Either a b -> Either a b -> Bool Source (>=) :: Either a b -> Either a b -> Bool Source | |
| Ord (V1 p) | Since: base-4.9.0.0 |
| Ord (U1 p) | Since: base-4.7.0.0 |
| Ord (TypeRep a) | Since: base-4.4.0.0 |
Defined in Data.Typeable.Internal | |
| (Ord a, Ord b) => Ord (a, b) | |
Defined in GHC.Classes | |
| (Ix i, Ord e) => Ord (Array i e) | Since: base-2.1 |
Defined in GHC.Arr | |
| Ord (Proxy s) | Since: base-4.7.0.0 |
| Ord a => Ord (Arg a b) | Since: base-4.9.0.0 |
| Ord (Fixed a) | Since: base-2.1 |
| Ord (f p) => Ord (Rec1 f p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: URec Word p -> URec Word p -> Ordering Source (<) :: URec Word p -> URec Word p -> Bool Source (<=) :: URec Word p -> URec Word p -> Bool Source (>) :: URec Word p -> URec Word p -> Bool Source (>=) :: URec Word p -> URec Word p -> Bool Source | |
| Ord (URec Int p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: URec Int p -> URec Int p -> Ordering Source (<) :: URec Int p -> URec Int p -> Bool Source (<=) :: URec Int p -> URec Int p -> Bool Source (>) :: URec Int p -> URec Int p -> Bool Source (>=) :: URec Int p -> URec Int p -> Bool Source | |
| Ord (URec Float p) | |
Defined in GHC.Generics Methodscompare :: URec Float p -> URec Float p -> Ordering Source (<) :: URec Float p -> URec Float p -> Bool Source (<=) :: URec Float p -> URec Float p -> Bool Source (>) :: URec Float p -> URec Float p -> Bool Source (>=) :: URec Float p -> URec Float p -> Bool Source | |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: URec Double p -> URec Double p -> Ordering Source (<) :: URec Double p -> URec Double p -> Bool Source (<=) :: URec Double p -> URec Double p -> Bool Source (>) :: URec Double p -> URec Double p -> Bool Source (>=) :: URec Double p -> URec Double p -> Bool Source max :: URec Double p -> URec Double p -> URec Double p Source min :: URec Double p -> URec Double p -> URec Double p Source | |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: URec Char p -> URec Char p -> Ordering Source (<) :: URec Char p -> URec Char p -> Bool Source (<=) :: URec Char p -> URec Char p -> Bool Source (>) :: URec Char p -> URec Char p -> Bool Source (>=) :: URec Char p -> URec Char p -> Bool Source | |
| Ord (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering Source (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool Source max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p Source | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
Defined in GHC.Classes | |
| Ord (a :~: b) | Since: base-4.7.0.0 |
Defined in Data.Type.Equality | |
| Ord (Coercion a b) | Since: base-4.7.0.0 |
Defined in Data.Type.Coercion Methodscompare :: Coercion a b -> Coercion a b -> Ordering Source (<) :: Coercion a b -> Coercion a b -> Bool Source (<=) :: Coercion a b -> Coercion a b -> Bool Source (>) :: Coercion a b -> Coercion a b -> Bool Source (>=) :: Coercion a b -> Coercion a b -> Bool Source | |
| Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Ord (f a) => Ord (Ap f a) | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
| Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Ord c => Ord (K1 i c p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics Methodscompare :: (f :+: g) p -> (f :+: g) p -> Ordering Source (<) :: (f :+: g) p -> (f :+: g) p -> Bool Source (<=) :: (f :+: g) p -> (f :+: g) p -> Bool Source (>) :: (f :+: g) p -> (f :+: g) p -> Bool Source (>=) :: (f :+: g) p -> (f :+: g) p -> Bool Source | |
| (Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics Methodscompare :: (f :*: g) p -> (f :*: g) p -> Ordering Source (<) :: (f :*: g) p -> (f :*: g) p -> Bool Source (<=) :: (f :*: g) p -> (f :*: g) p -> Bool Source (>) :: (f :*: g) p -> (f :*: g) p -> Bool Source (>=) :: (f :*: g) p -> (f :*: g) p -> Bool Source | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d) -> (a, b, c, d) -> Ordering Source (<) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source (<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source (>) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source (>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source | |
| Ord (a :~~: b) | Since: base-4.10.0.0 |
Defined in Data.Type.Equality Methodscompare :: (a :~~: b) -> (a :~~: b) -> Ordering Source (<) :: (a :~~: b) -> (a :~~: b) -> Bool Source (<=) :: (a :~~: b) -> (a :~~: b) -> Bool Source (>) :: (a :~~: b) -> (a :~~: b) -> Bool Source (>=) :: (a :~~: b) -> (a :~~: b) -> Bool Source | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Product f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methodscompare :: Product f g a -> Product f g a -> Ordering Source (<) :: Product f g a -> Product f g a -> Bool Source (<=) :: Product f g a -> Product f g a -> Bool Source (>) :: Product f g a -> Product f g a -> Bool Source (>=) :: Product f g a -> Product f g a -> Bool Source max :: Product f g a -> Product f g a -> Product f g a Source min :: Product f g a -> Product f g a -> Product f g a Source | |
| Ord (f p) => Ord (M1 i c f p) | Since: base-4.7.0.0 |
Defined in GHC.Generics Methodscompare :: M1 i c f p -> M1 i c f p -> Ordering Source (<) :: M1 i c f p -> M1 i c f p -> Bool Source (<=) :: M1 i c f p -> M1 i c f p -> Bool Source (>) :: M1 i c f p -> M1 i c f p -> Bool Source (>=) :: M1 i c f p -> M1 i c f p -> Bool Source | |
| Ord (f (g p)) => Ord ((f :.: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics Methodscompare :: (f :.: g) p -> (f :.: g) p -> Ordering Source (<) :: (f :.: g) p -> (f :.: g) p -> Bool Source (<=) :: (f :.: g) p -> (f :.: g) p -> Bool Source (>) :: (f :.: g) p -> (f :.: g) p -> Bool Source (>=) :: (f :.: g) p -> (f :.: g) p -> Bool Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering Source (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methodscompare :: Compose f g a -> Compose f g a -> Ordering Source (<) :: Compose f g a -> Compose f g a -> Bool Source (<=) :: Compose f g a -> Compose f g a -> Bool Source (>) :: Compose f g a -> Compose f g a -> Bool Source (>=) :: Compose f g a -> Compose f g a -> Bool Source max :: Compose f g a -> Compose f g a -> Compose f g a Source min :: Compose f g a -> Compose f g a -> Compose f g a Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering Source (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering Source (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering Source (<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source (<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source (>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source (>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool Source max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source | |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum, the following should hold:
- The calls
succ maxBoundandpred minBoundshould result in a runtime error. -
fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum 7 :: Boolis an error. -
enumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBound
Methods
the successor of a value. For numeric types, succ adds 1.
the 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). For example:
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 For example:
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 = []. For example:
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 = [] For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.
Instances
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Int8 | Since: base-2.1 |
| Bounded Int16 | Since: base-2.1 |
| Bounded Int32 | Since: base-2.1 |
| Bounded Int64 | Since: base-2.1 |
| Bounded Ordering | Since: base-2.1 |
| Bounded Word | Since: base-2.1 |
| Bounded Word8 | Since: base-2.1 |
| Bounded Word16 | Since: base-2.1 |
| Bounded Word32 | Since: base-2.1 |
| Bounded Word64 | Since: base-2.1 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded () | Since: base-2.1 |
| Bounded GeneralCategory | Since: base-2.1 |
Defined in GHC.Unicode | |
| Bounded IntPtr | |
| Bounded WordPtr | |
| Bounded CUIntMax | |
| Bounded CIntMax | |
| Bounded CUIntPtr | |
| Bounded CIntPtr | |
| Bounded CSigAtomic | |
Defined in Foreign.C.Types | |
| Bounded CWchar | |
| Bounded CSize | |
| Bounded CPtrdiff | |
| Bounded CBool | |
| Bounded CULLong | |
| Bounded CLLong | |
| Bounded CULong | |
| Bounded CLong | |
| Bounded CUInt | |
| Bounded CInt | |
| Bounded CUShort | |
| Bounded CShort | |
| Bounded CUChar | |
| Bounded CSChar | |
| Bounded CChar | |
| Bounded DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Bounded Any | Since: base-2.1 |
| Bounded All | Since: base-2.1 |
| Bounded Fd | |
| Bounded CNfds | |
| Bounded CSocklen | |
| Bounded CKey | |
| Bounded CId | |
| Bounded CFsFilCnt | |
| Bounded CFsBlkCnt | |
| Bounded CClockId | |
| Bounded CBlkCnt | |
| Bounded CBlkSize | |
| Bounded CRLim | |
| Bounded CTcflag | |
| Bounded CUid | |
| Bounded CNlink | |
| Bounded CGid | |
| Bounded CSsize | |
| Bounded CPid | |
| Bounded COff | |
| Bounded CMode | |
| Bounded CIno | |
| Bounded CDev | |
| Bounded ByteOrder | Since: base-4.11.0.0 |
| Bounded a => Bounded (Down a) | Since: base-4.14.0.0 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Bounded m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| Bounded (Proxy t) | Since: base-4.7.0.0 |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
| a ~ b => Bounded (a :~: b) | Since: base-4.7.0.0 |
| Coercible a b => Bounded (Coercion a b) | Since: base-4.7.0.0 |
| (Applicative f, Bounded a) => Bounded (Ap f a) | Since: base-4.12.0.0 |
| Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
| (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
| a ~~ b => Bounded (a :~~: b) | Since: base-4.10.0.0 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
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
| Bounded Int | Since: base-2.1 |
| Enum Int | Since: base-2.1 |
Defined in GHC.Enum | |
| Eq Int | |
| Integral Int | Since: base-2.0.1 |
| Data Int | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Num Int | Since: base-2.1 |
| Ord Int | |
| Read Int | Since: base-2.1 |
| Real Int | Since: base-2.0.1 |
Defined in GHC.Real MethodstoRational :: Int -> Rational Source | |
| Show Int | Since: base-2.1 |
| Ix Int | Since: base-2.1 |
| FiniteBits Int | Since: base-4.6.0.0 |
Defined in Data.Bits MethodsfiniteBitSize :: Int -> Int Source countLeadingZeros :: Int -> Int Source countTrailingZeros :: Int -> Int Source | |
| Bits Int | Since: base-2.1 |
Defined in Data.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 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 | |
| Storable Int | Since: base-2.1 |
| PrintfArg Int | Since: base-2.1 |
Defined in Text.Printf | |
| Generic1 (URec Int :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 length :: UInt a -> Int Source elem :: Eq a => a -> UInt a -> Bool Source maximum :: Ord a => UInt a -> a Source minimum :: Ord a => UInt a -> a Source | |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Ord (URec Int p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: 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 | |
| Show (URec Int p) | Since: base-4.9.0.0 |
| Generic (URec Int p) | Since: base-4.9.0.0 |
| data URec Int (p :: k) |
Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Int :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Int p) | |
Defined in GHC.Generics | |
Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.
For more information about this type's representation, see the comments in its implementation.
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
| Enum Float | Since: base-2.1 |
| Eq Float |
Note that due to the presence of >>> 0/0 == (0/0 :: Float) False Also note that >>> 0 == (-0 :: Float) True >>> recip 0 == recip (-0 :: Float) False |
| Floating Float | Since: base-2.1 |
| Fractional Float |
Note that due to the presence of >>> 0/0 * (recip 0/0 :: Float) NaN Since: base-2.1 |
| Data Float | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Float -> c Float Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Float Source toConstr :: Float -> Constr Source dataTypeOf :: Float -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Float) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Float) Source gmapT :: (forall b. Data b => b -> b) -> Float -> Float Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Float -> r Source gmapQ :: (forall d. Data d => d -> u) -> Float -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Float -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Float -> m Float Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Float -> m Float Source | |
| Num Float |
Note that due to the presence of >>> 0/0 + (negate 0/0 :: Float) NaN Also note that due to the presence of -0, >>> 0 + (-0 :: Float) 0.0 Since: base-2.1 |
| Ord Float |
Note that due to the presence of >>> 0/0 <= (0/0 :: Float) False Also note that, due to the same, >>> (0/0 :: Float) > 1 False >>> compare (0/0 :: Float) 1 GT |
Defined in GHC.Classes | |
| Read Float | Since: base-2.1 |
| Real Float | Since: base-2.1 |
Defined in GHC.Float MethodstoRational :: Float -> Rational Source | |
| RealFloat Float | Since: base-2.1 |
Defined in GHC.Float MethodsfloatRadix :: 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 isInfinite :: Float -> Bool Source isDenormalized :: Float -> Bool Source isNegativeZero :: Float -> Bool Source | |
| RealFrac Float | Since: base-2.1 |
| Show Float | Since: base-2.1 |
| Storable Float | Since: base-2.1 |
Defined in Foreign.Storable | |
| PrintfArg Float | Since: base-2.1 |
Defined in Text.Printf | |
| Generic1 (URec Float :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UFloat m -> m Source foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source foldr :: (a -> b -> b) -> b -> UFloat a -> b Source foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source foldl :: (b -> a -> b) -> b -> UFloat a -> b Source foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source foldr1 :: (a -> a -> a) -> UFloat a -> a Source foldl1 :: (a -> a -> a) -> UFloat a -> a Source toList :: UFloat a -> [a] Source null :: UFloat a -> Bool Source length :: UFloat a -> Int Source elem :: Eq a => a -> UFloat a -> Bool Source maximum :: Ord a => UFloat a -> a Source minimum :: Ord a => UFloat a -> a Source | |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
Defined in GHC.Generics Methodscompare :: URec Float p -> URec Float p -> Ordering Source (<) :: URec Float p -> URec Float p -> Bool Source (<=) :: URec Float p -> URec Float p -> Bool Source (>) :: URec Float p -> URec Float p -> Bool Source (>=) :: URec Float p -> URec Float p -> Bool Source | |
| Show (URec Float p) | |
| Generic (URec Float p) | |
| data URec Float (p :: k) |
Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Float :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Float p) | |
Defined in GHC.Generics | |
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Enum Double | Since: base-2.1 |
Defined in GHC.Float Methodssucc :: Double -> Double Source pred :: Double -> Double Source toEnum :: Int -> Double Source fromEnum :: Double -> Int Source enumFrom :: Double -> [Double] Source enumFromThen :: Double -> Double -> [Double] Source enumFromTo :: Double -> Double -> [Double] Source enumFromThenTo :: Double -> Double -> Double -> [Double] Source | |
| Eq Double |
Note that due to the presence of >>> 0/0 == (0/0 :: Double) False Also note that >>> 0 == (-0 :: Double) True >>> recip 0 == recip (-0 :: Double) False |
| Floating Double | Since: base-2.1 |
Defined in GHC.Float Methodsexp :: 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 | |
| Fractional Double |
Note that due to the presence of >>> 0/0 * (recip 0/0 :: Double) NaN Since: base-2.1 |
| Data Double | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Num Double |
Note that due to the presence of >>> 0/0 + (negate 0/0 :: Double) NaN Also note that due to the presence of -0, >>> 0 + (-0 :: Double) 0.0 Since: base-2.1 |
| Ord Double |
Note that due to the presence of >>> 0/0 <= (0/0 :: Double) False Also note that, due to the same, >>> (0/0 :: Double) > 1 False >>> compare (0/0 :: Double) 1 GT |
Defined in GHC.Classes | |
| Read Double | Since: base-2.1 |
| Real Double | Since: base-2.1 |
Defined in GHC.Float MethodstoRational :: Double -> Rational Source | |
| RealFloat Double | Since: base-2.1 |
Defined in GHC.Float MethodsfloatRadix :: 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 | |
| RealFrac Double | Since: base-2.1 |
| Show Double | Since: base-2.1 |
| Storable Double | Since: base-2.1 |
Defined in Foreign.Storable MethodssizeOf :: 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 | |
| PrintfArg Double | Since: base-2.1 |
Defined in Text.Printf | |
| Generic1 (URec Double :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UDouble m -> m Source foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source foldr :: (a -> b -> b) -> b -> UDouble a -> b Source foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source foldl :: (b -> a -> b) -> b -> UDouble a -> b Source foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source foldr1 :: (a -> a -> a) -> UDouble a -> a Source foldl1 :: (a -> a -> a) -> UDouble a -> a Source toList :: UDouble a -> [a] Source null :: UDouble a -> Bool Source length :: UDouble a -> Int Source elem :: Eq a => a -> UDouble a -> Bool Source maximum :: Ord a => UDouble a -> a Source minimum :: Ord a => UDouble a -> a Source | |
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: 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 | |
| Show (URec Double p) | Since: base-4.9.0.0 |
| Generic (URec Double p) | Since: base-4.9.0.0 |
| data URec Double (p :: k) |
Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Double :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Double p) | |
Defined in GHC.Generics | |
type Rational = Ratio Integer Source
Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.
A Word is an unsigned integral type, with the same size as Int.
Instances
| Bounded Word | Since: base-2.1 |
| Enum Word | Since: base-2.1 |
| Eq Word | |
| Integral Word | Since: base-2.1 |
| Data Word | Since: base-4.0.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 | |
| Num Word | Since: base-2.1 |
| Ord Word | |
| Read Word | Since: base-4.5.0.0 |
| Real Word | Since: base-2.1 |
Defined in GHC.Real MethodstoRational :: Word -> Rational Source | |
| Show Word | Since: base-2.1 |
| Ix Word | Since: base-4.6.0.0 |
| FiniteBits Word | Since: base-4.6.0.0 |
Defined in Data.Bits MethodsfiniteBitSize :: Word -> Int Source countLeadingZeros :: Word -> Int Source countTrailingZeros :: Word -> Int Source | |
| Bits Word | Since: base-2.1 |
Defined in Data.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 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 | |
| Storable Word | Since: base-2.1 |
Defined in Foreign.Storable | |
| PrintfArg Word | Since: base-2.1 |
Defined in Text.Printf | |
| Generic1 (URec Word :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UWord m -> m Source foldMap :: Monoid m => (a -> m) -> UWord a -> m Source foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source foldr :: (a -> b -> b) -> b -> UWord a -> b Source foldr' :: (a -> b -> b) -> b -> UWord a -> b Source foldl :: (b -> a -> b) -> b -> UWord a -> b Source foldl' :: (b -> a -> b) -> b -> UWord a -> b Source foldr1 :: (a -> a -> a) -> UWord a -> a Source foldl1 :: (a -> a -> a) -> UWord a -> a Source toList :: UWord a -> [a] Source null :: UWord a -> Bool Source length :: UWord a -> Int Source elem :: Eq a => a -> UWord a -> Bool Source maximum :: Ord a => UWord a -> a Source minimum :: Ord a => UWord a -> a Source | |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methodscompare :: 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 | |
| Show (URec Word p) | Since: base-4.9.0.0 |
| Generic (URec Word p) | Since: base-4.9.0.0 |
| data URec Word (p :: k) |
Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Word :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Word p) | |
Defined in GHC.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 + x fromInteger 0is the additive identity-
x + fromInteger 0=x negategives the additive inverse-
x + negate x=fromInteger 0 - Associativity of
(*) -
(x * y) * z=x * (y * z) fromInteger 1is the multiplicative identity-
x * 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)
Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.
Methods
(+) :: a -> a -> a infixl 6 Source
(-) :: a -> a -> a infixl 6 Source
(*) :: a -> a -> a infixl 7 Source
Unary negation.
Absolute value.
Sign of a number. The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).
fromInteger :: Integer -> a Source
Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.
Instances
class (Num a, Ord a) => Real a where Source
Methods
toRational :: a -> Rational Source
the rational equivalent of its real argument with full precision
Instances
class (Real a, Enum a) => Integral a where Source
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the div/mod and quot/rem pairs, given suitable Euclidean functions f and g:
-
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g y -
x=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.
Methods
quot :: a -> a -> a infixl 7 Source
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a) Source
divMod :: a -> a -> (a, a) Source
toInteger :: a -> Integer Source
conversion to Integer
Instances
class Num a => Fractional a where Source
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:
recipgives the multiplicative inverse-
x * recip x=recip x * x=fromInteger 1
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 Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.
Instances
| Fractional Double |
Note that due to the presence of >>> 0/0 * (recip 0/0 :: Double) NaN Since: base-2.1 |
| Fractional Float |
Note that due to the presence of >>> 0/0 * (recip 0/0 :: Float) NaN Since: base-2.1 |
| Fractional CDouble | |
| Fractional CFloat | |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| RealFloat a => Fractional (Complex a) | Since: base-2.1 |
| Fractional a => Fractional (Op a b) | |
| HasResolution a => Fractional (Fixed a) | Since: base-2.1 |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
class Fractional a => Floating a where Source
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (+), (*) and exp are customarily expected to define an exponential field and have the following properties:
-
exp (a + b)=exp a * exp b -
exp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class (Real a, Fractional a) => RealFrac a where Source
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) Source
The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:
-
nis an integral number with the same sign asx; and -
fis 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 x returns the integer nearest x between zero and x
round :: Integral b => a -> b Source
round x returns the nearest integer to x; the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source
ceiling x returns the least integer not less than x
floor :: Integral b => a -> b Source
floor x returns the greatest integer not greater than x
Instances
| RealFrac Double | Since: base-2.1 |
| RealFrac Float | Since: base-2.1 |
| RealFrac CDouble | |
| RealFrac CFloat | |
| Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
| RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
| HasResolution a => RealFrac (Fixed a) | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
class (RealFrac a, Floating a) => RealFloat a where Source
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer Source
a constant function, returning the radix of the representation (often 2)
floatDigits :: a -> Int Source
a constant function, returning the number of digits of floatRadix in the significand
floatRange :: a -> (Int, Int) Source
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) Source
The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.
encodeFloat :: Integer -> Int -> a Source
encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.
significand :: 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 computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.
Instances
Numeric functions
subtract :: Num a => a -> a -> a Source
Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.
even :: Integral a => a -> Bool Source
odd :: Integral a => a -> Bool Source
gcd :: Integral a => a -> a -> a Source
gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.
lcm :: Integral a => a -> a -> a Source
lcm x y is the smallest positive integer that both x 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
realToFrac :: (Real a, Fractional b) => a -> b Source
general coercion to fractional types
Semigroups and Monoids
class Semigroup a where Source
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 Source
An associative operation.
>>> [1,2,3] <> [4,5,6] [1,2,3,4,5,6]
Instances
| Semigroup Ordering | Since: base-4.9.0.0 |
| Semigroup () | Since: base-4.9.0.0 |
| Semigroup Any | Since: base-4.9.0.0 |
| Semigroup All | Since: base-4.9.0.0 |
| Semigroup Lifetime | Since: base-4.10.0.0 |
| Semigroup Event | Since: base-4.10.0.0 |
| Semigroup Void | Since: base-4.9.0.0 |
| Semigroup [a] | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Semigroup (Endo a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Option a) | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) | 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 (Last a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
| Semigroup (Equivalence a) | |
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 (Comparison 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 (Predicate a) | |
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| Semigroup (U1 p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (ST s a) | Since: base-4.11.0.0 |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) | |
| Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
class Semigroup a => Monoid a where Source
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x <> mempty = x- Left identity
mempty <> x = x- Associativity
-
x <> (y <> z) = (x <> y) <> z(Semigrouplaw) - Concatenation
mconcat = foldr (<>) mempty
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.
Minimal complete definition
Methods
Identity of mappend
>>> "Hello world" <> mempty "Hello world"
An associative operation
NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.
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 Ordering | Since: base-2.1 |
| Monoid () | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid All | Since: base-2.1 |
| Monoid Lifetime |
Since: base-4.8.0.0 |
| Monoid Event | Since: base-4.4.0.0 |
| Monoid [a] | Since: base-2.1 |
| Semigroup a => Monoid (Maybe a) |
Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Last a) | Since: base-2.1 |
| Monoid (First a) | Since: base-2.1 |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
| Monoid m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsmempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source | |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| Monoid (Equivalence a) | |
Defined in Data.Functor.Contravariant Methodsmempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source | |
| Monoid (Comparison a) | |
Defined in Data.Functor.Contravariant Methodsmempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source | |
| Monoid (Predicate a) | |
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid a => Monoid (ST s a) | Since: base-4.11.0.0 |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Monoid a => Monoid (Op a b) | |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| (Applicative f, Monoid a) => Monoid (Ap f a) | Since: base-4.12.0.0 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Monads and functors
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.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source
Using ApplicativeDo: 'fmap f as' can be understood as the do expression
do a <- as pure (f a)
with an inferred Functor constraint.
(<$) :: a -> f b -> f a infixl 4 Source
Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.
Using ApplicativeDo: 'a <$ bs' can be understood as the do expression
do bs pure a
with an inferred Functor constraint.
Instances
| Functor [] | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| Functor Par1 | Since: base-4.9.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Functor NoIO | Since: base-4.8.0.0 |
| Functor ReadP | Since: base-2.1 |
| Functor ReadPrec | Since: base-2.1 |
| Functor Down | Since: base-4.11.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Functor Last | Since: base-4.8.0.0 |
| Functor First | Since: base-4.8.0.0 |
| Functor STM | Since: base-4.3.0.0 |
| Functor Handler | Since: base-4.6.0.0 |
| Functor Identity | Since: base-4.8.0.0 |
| Functor ZipList | Since: base-2.1 |
| Functor ArgDescr | Since: base-4.6.0.0 |
| Functor OptDescr | Since: base-4.6.0.0 |
| Functor ArgOrder | Since: base-4.6.0.0 |
| Functor Option | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| Functor First | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| Functor Complex | Since: base-4.9.0.0 |
| Functor (Either a) | Since: base-3.0 |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Functor ((,) a) | Since: base-2.1 |
| Functor (ST s) | Since: base-2.1 |
| Functor (Array i) | Since: base-2.1 |
| Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Arrow a => Functor (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source | |
| Monad m => Functor (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source | |
| Functor (ST s) | Since: base-2.1 |
| Functor (Arg a) | Since: base-4.9.0.0 |
| Functor f => Functor (Rec1 f) | Since: base-4.9.0.0 |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Double :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0 |
| Functor ((,,) a b) | Since: base-4.14.0.0 |
| Functor f => Functor (Alt f) | Since: base-4.8.0.0 |
| Functor f => Functor (Ap f) | Since: base-4.12.0.0 |
| Functor (Const m :: Type -> Type) | Since: base-2.1 |
| Functor m => Functor (Kleisli m a) | Since: base-4.14.0.0 |
| Arrow a => Functor (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source | |
| Functor ((->) r :: Type -> Type) | Since: base-2.1 |
| Functor (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| Functor ((,,,) a b c) | Since: base-4.14.0.0 |
| (Functor f, Functor g) => Functor (Sum f g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Product f g) | Since: base-4.9.0.0 |
| Functor f => Functor (M1 i c f) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :.: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (Compose f g) | Since: base-4.9.0.0 |
(<$>) :: 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, <$> is function application lifted over a Functor.
Examples
Convert from a Maybe Int to a Maybe
String using show:
>>> show <$> Nothing Nothing >>> show <$> Just 3 Just "3"
Convert from an Either Int Int to an Either Int String using show:
>>> show <$> Left 17 Left 17 >>> show <$> Right 17 Right "17"
Double each element of a list:
>>> (*2) <$> [1,2,3] [2,4,6]
Apply even to the second element of a pair:
>>> even <$> (2,2) (2,True)
class Functor f => Applicative f where Source
A functor with application, providing operations to
- embed pure expressions (
pure), and - sequence computations and combine their results (
<*>andliftA2).
A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:
(<*>) = liftA2 id
liftA2 f x y = f <$> x <*> y
Further, any definition must satisfy the following:
- Identity
pure id <*> v = v
- Composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
- Homomorphism
pure f <*> pure x = pure (f x)
- Interchange
u <*> pure y = pure ($ y) <*> u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: 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.
Using ApplicativeDo: 'fs <*> as' can be understood as the do expression
do f <- fs a <- as pure (f a)
(*>) :: f a -> f b -> f b infixl 4 Source
Sequence actions, discarding the value of the first argument.
'as *> bs' can be understood as the do expression
do as bs
This is a tad complicated for our ApplicativeDo extension which will give it a Monad constraint. For an Applicative constraint we write it of the form
do _ <- as b <- bs pure b
(<*) :: f a -> f b -> f a infixl 4 Source
Sequence actions, discarding the value of the second argument.
Using ApplicativeDo: 'as <* bs' can be understood as the do expression
do a <- as bs pure a
Instances
| Applicative [] | Since: base-2.1 |
| Applicative Maybe | Since: base-2.1 |
| Applicative IO | Since: base-2.1 |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Applicative NoIO | Since: base-4.8.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative ReadPrec | Since: base-4.6.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Applicative Sum | Since: base-4.8.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Applicative Last | Since: base-4.8.0.0 |
| Applicative First | Since: base-4.8.0.0 |
| Applicative STM | Since: base-4.8.0.0 |
| Applicative Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Applicative ZipList |
f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)
where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}
Since: base-2.1 |
| Applicative Option | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Applicative Complex | Since: base-4.9.0.0 |
| Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Applicative ((,) a) |
For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)
Since: base-2.1 |
| Applicative (ST s) | Since: base-4.4.0.0 |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methodspure :: 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 | |
| Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methodspure :: 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 | |
| Applicative (ST s) | Since: base-2.1 |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow Methodspure :: 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 | |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methodspure :: 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 ((->) r :: Type -> Type) | Since: base-2.1 |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base Methodspure :: 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 f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methodspure :: 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 (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methodspure :: 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 | |
class Applicative m => Monad m where Source
The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
return a >>= k = k a- Right identity
m >>= return = m- Associativity
m >>= (\x -> k x >>= h) = (m >>= k) >>= h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: forall a b. 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 >>= bs' can be understood as the do expression
do a <- as bs a
(>>) :: forall a b. 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 >> bs' can be understood as the do expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad NoIO | Since: base-4.4.0.0 |
| Monad ReadP | Since: base-2.1 |
| Monad ReadPrec | Since: base-2.1 |
| Monad Down | Since: base-4.11.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Monad Last | Since: base-4.8.0.0 |
| Monad First | Since: base-4.8.0.0 |
| Monad STM | Since: base-4.3.0.0 |
| Monad Identity | Since: base-4.8.0.0 |
| Monad Option | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Monad Complex | Since: base-4.9.0.0 |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad (ST s) | Since: base-2.1 |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in 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 m => Monad (WrappedMonad m) | 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 | |
| Monad (ST s) | Since: base-2.1 |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
| Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
| Monad ((->) r :: Type -> Type) | Since: base-2.1 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
class Monad m => MonadFail m 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
Since: base-4.9.0.0
Instances
| MonadFail [] | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadFail IO | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| MonadFail ReadP | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadP | |
| MonadFail ReadPrec | Since: base-4.9.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
| MonadFail (ST s) | Since: base-4.11.0.0 |
| MonadFail (ST s) | Since: base-4.10 |
Defined in Control.Monad.ST.Lazy.Imp | |
| MonadFail f => MonadFail (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Monoid | |
mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source
Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.
As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.
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.
As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source
Same as >>=, but with the arguments interchanged.
Folds and traversals
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
length = getSum . foldMap (Sum . const 1)
sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b Source
Right-associative fold of a structure.
In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.
For a general Foldable structure this should be semantically identical to,
foldr f z = foldr f z . toList
foldl :: (b -> a -> b) -> b -> t a -> b Source
Left-associative fold of a structure.
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. This means that foldl' will diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that 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 \(\mathcal{O}(n)\) elements long, which then must be evaluated from the outside-in.
For a general Foldable structure this should be semantically identical to,
foldl f z = foldl f z . toList
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.
foldr1 f = foldr1 f . toList
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.
foldl1 f = foldl1 f . toList
elem :: Eq a => a -> t a -> Bool infix 4 Source
Does the element occur in the structure?
Since: base-4.8.0.0
maximum :: forall a. Ord a => t a -> a Source
The largest element of a non-empty structure.
Since: base-4.8.0.0
minimum :: forall a. Ord a => t a -> a Source
The least element of a non-empty structure.
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.
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.
Since: base-4.8.0.0
Instances
| Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methodsfold :: 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 Maybe | Since: base-2.1 |
Defined in Data.Foldable Methodsfold :: 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 Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => Product m -> m Source foldMap :: Monoid m => (a -> m) -> Product a -> m Source foldMap' :: Monoid m => (a -> m) -> Product a -> m Source foldr :: (a -> b -> b) -> b -> Product a -> b Source foldr' :: (a -> b -> b) -> b -> Product a -> b Source foldl :: (b -> a -> b) -> b -> Product a -> b Source foldl' :: (b -> a -> b) -> b -> Product a -> b Source foldr1 :: (a -> a -> a) -> Product a -> a Source foldl1 :: (a -> a -> a) -> Product a -> a Source toList :: Product a -> [a] Source null :: Product a -> Bool Source length :: Product a -> Int Source elem :: Eq a => a -> Product a -> Bool Source maximum :: Ord a => Product a -> a Source minimum :: Ord a => Product a -> a Source | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 elem :: Eq a => a -> Sum a -> Bool Source maximum :: Ord a => Sum a -> a Source minimum :: Ord a => Sum a -> a Source | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methodsfold :: 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 ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methodsfold :: 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 Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => Option m -> m Source foldMap :: Monoid m => (a -> m) -> Option a -> m Source foldMap' :: Monoid m => (a -> m) -> Option a -> m Source foldr :: (a -> b -> b) -> b -> Option a -> b Source foldr' :: (a -> b -> b) -> b -> Option a -> b Source foldl :: (b -> a -> b) -> b -> Option a -> b Source foldl' :: (b -> a -> b) -> b -> Option a -> b Source foldr1 :: (a -> a -> a) -> Option a -> a Source foldl1 :: (a -> a -> a) -> Option a -> a Source toList :: Option a -> [a] Source null :: Option a -> Bool Source length :: Option a -> Int Source elem :: Eq a => a -> Option a -> Bool Source maximum :: Ord a => Option a -> a Source minimum :: Ord a => Option a -> a Source | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: 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 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 First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: 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 Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: 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 elem :: Eq a => a -> Max a -> Bool Source maximum :: Ord a => Max a -> a Source minimum :: Ord a => Max a -> a Source | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: 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 elem :: Eq a => a -> Min a -> Bool Source maximum :: Ord a => Min a -> a Source minimum :: Ord a => Min a -> a Source | |
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methodsfold :: 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 (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 elem :: Eq a => a -> V1 a -> Bool Source maximum :: Ord a => V1 a -> a Source minimum :: Ord a => V1 a -> a Source | |
| Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 elem :: Eq a => a -> U1 a -> Bool Source maximum :: Ord a => U1 a -> a Source minimum :: Ord a => U1 a -> a Source | |
| Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UAddr m -> m Source foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source foldr :: (a -> b -> b) -> b -> UAddr a -> b Source foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source foldl :: (b -> a -> b) -> b -> UAddr a -> b Source foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source foldr1 :: (a -> a -> a) -> UAddr a -> a Source foldl1 :: (a -> a -> a) -> UAddr a -> a Source toList :: UAddr a -> [a] Source null :: UAddr a -> Bool Source length :: UAddr a -> Int Source elem :: Eq a => a -> UAddr a -> Bool Source maximum :: Ord a => UAddr a -> a Source minimum :: Ord a => UAddr a -> a Source | |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UChar m -> m Source foldMap :: Monoid m => (a -> m) -> UChar a -> m Source foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source foldr :: (a -> b -> b) -> b -> UChar a -> b Source foldr' :: (a -> b -> b) -> b -> UChar a -> b Source foldl :: (b -> a -> b) -> b -> UChar a -> b Source foldl' :: (b -> a -> b) -> b -> UChar a -> b Source foldr1 :: (a -> a -> a) -> UChar a -> a Source foldl1 :: (a -> a -> a) -> UChar a -> a Source toList :: UChar a -> [a] Source null :: UChar a -> Bool Source length :: UChar a -> Int Source elem :: Eq a => a -> UChar a -> Bool Source maximum :: Ord a => UChar a -> a Source minimum :: Ord a => UChar a -> a Source | |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UDouble m -> m Source foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source foldr :: (a -> b -> b) -> b -> UDouble a -> b Source foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source foldl :: (b -> a -> b) -> b -> UDouble a -> b Source foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source foldr1 :: (a -> a -> a) -> UDouble a -> a Source foldl1 :: (a -> a -> a) -> UDouble a -> a Source toList :: UDouble a -> [a] Source null :: UDouble a -> Bool Source length :: UDouble a -> Int Source elem :: Eq a => a -> UDouble a -> Bool Source maximum :: Ord a => UDouble a -> a Source minimum :: Ord a => UDouble a -> a Source | |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => UFloat m -> m Source foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source foldr :: (a -> b -> b) -> b -> UFloat a -> b Source foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source foldl :: (b -> a -> b) -> b -> UFloat a -> b Source foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source foldr1 :: (a -> a -> a) -> UFloat a -> a Source foldl1 :: (a -> a -> a) -> UFloat a -> a Source toList :: UFloat a -> [a] Source null :: UFloat a -> Bool Source length :: UFloat a -> Int Source elem :: Eq a => a -> UFloat a -> Bool Source maximum :: Ord a => UFloat a -> a Source minimum :: Ord a => UFloat a -> a Source | |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 length :: UInt a -> Int Source elem :: Eq a => a -> UInt a -> Bool Source maximum :: Ord a => UInt a -> a Source minimum :: Ord a => UInt a -> a Source | |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: 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 f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methodsfold :: 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 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 (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methodsfold :: 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 (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => (f :+: g) m -> m Source foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source toList :: (f :+: g) a -> [a] Source null :: (f :+: g) a -> Bool Source length :: (f :+: g) a -> Int Source elem :: Eq a => a -> (f :+: g) a -> Bool Source maximum :: Ord a => (f :+: g) a -> a Source minimum :: Ord a => (f :+: g) a -> a Source | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methodsfold :: 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 (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methodsfold :: 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 (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 | |
| (Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methodsfold :: 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 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methodsfold :: 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 | |
class (Functor t, Foldable t) => Traversable t where Source
Functors representing data structures that can be traversed from left to right.
A definition of traverse must satisfy the following laws:
- Naturality
-
t . traverse f = traverse (t . f)for every applicative transformationt - Identity
traverse Identity = Identity- Composition
traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f
A definition of sequenceA must satisfy the following laws:
- Naturality
-
t . sequenceA = sequenceA . fmap tfor every applicative transformationt - Identity
sequenceA . fmap Identity = Identity- Composition
sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the Applicative operations, i.e.
t (pure x) = pure x t (f <*> x) = t f <*> t x
and the identity functor Identity and composition functors Compose are from Data.Functor.Identity and Data.Functor.Compose.
A result of the naturality law is a purity law for traverse
traverse pure = pure
(The naturality law is implied by parametricity and thus so is the purity law [1, p15].)
Instances are similar to Functor, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for <*> imply a form of associativity.
The superclass instances should satisfy the following:
- In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). - In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
References: [1] The Essence of the Iterator Pattern, Jeremy Gibbons and Bruno C. d. S. Oliveira
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_.
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_.
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_.
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_.
Instances
| Traversable [] | Since: base-2.1 |
Defined in Data.Traversable | |
| Traversable Maybe | Since: base-2.1 |
| Traversable Par1 | Since: base-4.9.0.0 |
| Traversable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable Down | Since: base-4.12.0.0 |
| Traversable Product | Since: base-4.8.0.0 |
Defined in Data.Traversable | |
| Traversable Sum | Since: base-4.8.0.0 |
| Traversable Dual | Since: base-4.8.0.0 |
| Traversable Last | Since: base-4.8.0.0 |
| Traversable First | Since: base-4.8.0.0 |
| Traversable Identity | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable ZipList | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable Option | Since: base-4.9.0.0 |
| Traversable Last | Since: base-4.9.0.0 |
| Traversable First | Since: base-4.9.0.0 |
| Traversable Max | Since: base-4.9.0.0 |
| Traversable Min | Since: base-4.9.0.0 |
| Traversable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
| Traversable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Ix i => Traversable (Array i) | Since: base-2.1 |
Defined in Data.Traversable | |
| Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Traversable (Arg a) | Since: base-4.9.0.0 |
| Traversable f => Traversable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| Traversable f => Traversable (Alt f) | Since: base-4.12.0.0 |
| Traversable f => Traversable (Ap f) | Since: base-4.12.0.0 |
| Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Traversable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable Methodstraverse :: 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) | Since: base-4.9.0.0 |
Defined in Data.Traversable Methodstraverse :: 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 (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum | |
| (Traversable f, Traversable g) => Traversable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methodstraverse :: 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 (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| (Traversable f, Traversable g) => Traversable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable Methodstraverse :: 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 (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methodstraverse :: 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 | |
Miscellaneous functions
Identity function.
id x = x
const x is a unary function which evaluates to x for all inputs.
>>> const 42 "hello" 42
>>> map (const 42) [0..3] [42,42,42,42]
(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source
Function composition.
flip :: (a -> b -> c) -> b -> a -> c Source
flip f takes its (first) two arguments in the reverse order of f.
>>> flip (++) "hello" "world" "worldhello"
($) :: forall r a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source
Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.
Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed.
until :: (a -> Bool) -> (a -> a) -> a -> a Source
until p f yields the result of applying f until p holds.
asTypeOf :: a -> a -> a Source
asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.
error :: forall (r :: RuntimeRep). forall (a :: TYPE r). HasCallStack => [Char] -> a Source
error stops execution and displays an error message.
errorWithoutStackTrace :: forall (r :: RuntimeRep). forall (a :: TYPE r). [Char] -> a Source
A variant of error that does not produce a stack trace.
Since: base-4.9.0.0
undefined :: forall (r :: RuntimeRep). forall (a :: TYPE r). HasCallStack => a Source
A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.
seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 Source
The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.
($!) :: forall r a (b :: TYPE r). (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, ...]
>>> map (+1) [1, 2, 3]
(++) :: [a] -> [a] -> [a] infixr 5 Source
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
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]
>>> filter odd [1, 2, 3] [1,3]
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
(!!) :: [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.
null :: Foldable t => t a -> Bool Source
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Since: base-4.8.0.0
length :: Foldable t => t a -> Int Source
Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Since: base-4.8.0.0
reverse xs returns the elements of xs in reverse order. xs must be finite.
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.
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.
any :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether any element of the structure satisfies the predicate.
all :: Foldable t => (a -> Bool) -> t a -> Bool Source
Determines whether all elements of the structure satisfy the predicate.
concat :: Foldable t => t [a] -> [a] Source
The concatenation of all the elements of a container of lists.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source
Map a function over all the elements of a container and concatenate the resulting lists.
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.
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, ...]
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that
head (scanr f z xs) == foldr f z xs.
scanr1 :: (a -> a -> a) -> [a] -> [a] Source
\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting value argument.
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), ...]
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.
repeat x is an infinite list, with x the value of every element.
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.
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.
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:
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general genericTake, in which n may be of any integral type.
drop :: Int -> [a] -> [a] Source
drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general genericDrop, in which n may be of any integral type.
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:
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] == []
dropWhile :: (a -> Bool) -> [a] -> [a] Source
dropWhile p xs returns the suffix remaining after takeWhile p xs:
dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3] dropWhile (< 9) [1,2,3] == [] dropWhile (< 0) [1,2,3] == [1,2,3]
span :: (a -> Bool) -> [a] -> ([a], [a]) Source
span, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that satisfy p and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
span p xs is equivalent to (takeWhile p xs, dropWhile p xs)
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 (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
break p is equivalent to span (not . p).
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 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])
It is equivalent to (take n xs, drop n xs) when n is not _|_ (splitAt _|_ xs = _|_). splitAt is an instance of the more general genericSplitAt, in which n may be of any integral type.
Searching lists
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source
notElem is the negation of elem.
lookup :: Eq a => a -> [(a, b)] -> Maybe b Source
\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association list.
>>> lookup 2 [(1, "first"), (2, "second"), (3, "third")] Just "second"
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 [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]
If one input list is short, excess elements of the longer list are discarded:
zip [1] ['a', 'b'] = [(1, 'a')] zip [1, 2] ['a'] = [(1, 'a')]
zip is right-lazy:
zip [] _|_ = [] zip _|_ [] = _|_
zip is capable of list fusion, but it is restricted to its first list argument and its resulting list.
zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source
zip3 takes three lists and returns a list of triples, analogous to zip. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums:
>>> zipWith (+) [1, 2, 3] [4, 5, 6] [5,7,9]
zipWith is right-lazy:
zipWith f [] _|_ = []
zipWith is capable of list fusion, but it is restricted to its first list argument and its resulting list.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source
The zipWith3 function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to zipWith. It is capable of list fusion, but it is restricted to its first list argument and its resulting list.
unzip :: [(a, b)] -> ([a], [b]) Source
unzip transforms a list of pairs into a list of first components and a list of second components.
unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source
The unzip3 function takes a list of triples and returns three lists, analogous to unzip.
Functions on strings
lines :: String -> [String] Source
lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
>>> lines "" []
>>> lines "\n" [""]
>>> lines "one" ["one"]
>>> lines "one\n" ["one"]
>>> lines "one\n\n" ["one",""]
>>> lines "one\ntwo" ["one","two"]
>>> lines "one\ntwo\n" ["one","two"]
Thus lines s contains at least as many elements as newlines in s.
words :: String -> [String] Source
words breaks a string up into a list of words, which were delimited by white space.
>>> words "Lorem ipsum\ndolor" ["Lorem","ipsum","dolor"]
unlines :: [String] -> String Source
unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.
>>> unlines ["Hello", "World", "!"] "Hello\nWorld\n!\n"
unwords :: [String] -> String Source
unwords is an inverse operation to words. It joins words with separating spaces.
>>> unwords ["Lorem", "ipsum", "dolor"] "Lorem ipsum dolor"
Converting to and from String
Converting to String
type ShowS = String -> String Source
The shows functions return a function that prepends the output String to an existing String. This allows constant-time concatenation of results using function composition.
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 = 5
Note that right-associativity of :^: is ignored. For example,
-
show (Leaf 1 :^: Leaf 2 :^: Leaf 3)produces the string"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.
A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.
showList :: [a] -> ShowS Source
The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.
Instances
shows :: Show a => a -> ShowS Source
equivalent to showsPrec with a precedence of 0.
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.
showParen :: Bool -> ShowS -> ShowS Source
utility function that surrounds the inner show function with parentheses when the Bool parameter is True.
Converting from String
type ReadS a = String -> [(a, String)] Source
A parser for a type a, represented as a function that takes a String and returns a list of possible parses as (a,String) pairs.
Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf ReadP).
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 = 5
Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefault
Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.
readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.
As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:
instance Read T where readPrec = ... 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.
The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.
Instances
| Read Bool | Since: base-2.1 |
| Read Char | Since: base-2.1 |
| Read Double | Since: base-2.1 |
| Read Float | Since: base-2.1 |
| Read Int | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Read Int16 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Read Integer | Since: base-2.1 |
| Read Natural | Since: base-4.8.0.0 |
| Read Ordering | Since: base-2.1 |
| Read Word | Since: base-4.5.0.0 |
| Read Word8 | Since: base-2.1 |
| Read Word16 | Since: base-2.1 |
| Read Word32 | Since: base-2.1 |
| Read Word64 | Since: base-2.1 |
| Read () | Since: base-2.1 |
| Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read MethodsreadsPrec :: Int -> ReadS GeneralCategory Source readList :: ReadS [GeneralCategory] Source | |
| Read Lexeme | Since: base-2.1 |
| Read IOMode | Since: base-4.2.0.0 |
| Read IntPtr | |
| Read WordPtr | |
| Read CUIntMax | |
| Read CIntMax | |
| Read CUIntPtr | |
| Read CIntPtr | |
| Read CSUSeconds | |
Defined in Foreign.C.Types MethodsreadsPrec :: Int -> ReadS CSUSeconds Source readList :: ReadS [CSUSeconds] Source | |
| Read CUSeconds | |
| Read CTime | |
| Read CClock | |
| Read CSigAtomic | |
Defined in Foreign.C.Types MethodsreadsPrec :: Int -> ReadS CSigAtomic Source readList :: ReadS [CSigAtomic] Source | |
| Read CWchar | |
| Read CSize | |
| Read CPtrdiff | |
| Read CDouble | |
| Read CFloat | |
| Read CBool | |
| Read CULLong | |
| Read CLLong | |
| Read CULong | |
| Read CLong | |
| Read CUInt | |
| Read CInt | |
| Read CUShort | |
| Read CShort | |
| Read CUChar | |
| Read CSChar | |
| Read CChar | |
| Read SomeNat | Since: base-4.7.0.0 |
| Read SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits MethodsreadsPrec :: Int -> ReadS SomeSymbol Source readList :: ReadS [SomeSymbol] Source | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics MethodsreadsPrec :: Int -> ReadS DecidedStrictness Source readList :: ReadS [DecidedStrictness] Source | |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics MethodsreadsPrec :: Int -> ReadS SourceStrictness Source readList :: ReadS [SourceStrictness] Source | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics MethodsreadsPrec :: Int -> ReadS SourceUnpackedness Source readList :: ReadS [SourceUnpackedness] Source | |
| Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics MethodsreadsPrec :: Int -> ReadS Associativity Source readList :: ReadS [Associativity] Source | |
| Read Fixity | Since: base-4.6.0.0 |
| Read Any | Since: base-2.1 |
| Read All | Since: base-2.1 |
| Read SeekMode | Since: base-4.2.0.0 |
| Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types MethodsreadsPrec :: Int -> ReadS NewlineMode Source readList :: ReadS [NewlineMode] Source | |
| Read Newline | Since: base-4.3.0.0 |
| Read BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types MethodsreadsPrec :: Int -> ReadS BufferMode Source readList :: ReadS [BufferMode] Source | |
| Read ExitCode | |
| Read Fd | |
| Read CNfds | |
| Read CSocklen | |
| Read CKey | |
| Read CId | |
| Read CFsFilCnt | |
| Read CFsBlkCnt | |
| Read CClockId | |
| Read CBlkCnt | |
| Read CBlkSize | |
| Read CRLim | |
| Read CTcflag | |
| Read CSpeed | |
| Read CCc | |
| Read CUid | |
| Read CNlink | |
| Read CGid | |
| Read CSsize | |
| Read CPid | |
| Read COff | |
| Read CMode | |
| Read CIno | |
| Read CDev | |
| Read Version | Since: base-2.1 |
| Read ByteOrder | Since: base-4.11.0.0 |
| Read GCDetails | Since: base-4.10.0.0 |
| Read RTSStats | Since: base-4.10.0.0 |
| Read Void |
Reading a Since: base-4.8.0.0 |
| Read a => Read [a] | Since: base-2.1 |
| Read a => Read (Maybe a) | Since: base-2.1 |
| (Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
| Read p => Read (Par1 p) | Since: base-4.7.0.0 |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Read a => Read (Down a) |
This instance would be equivalent to the derived instances of the Since: base-4.7.0.0 |
| Read a => Read (Product a) | Since: base-2.1 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Read a => Read (Dual a) | Since: base-2.1 |
| Read a => Read (Last a) | Since: base-2.1 |
| Read a => Read (First a) | Since: base-2.1 |
| Read a => Read (Identity a) |
This instance would be equivalent to the derived instances of the Since: base-4.8.0.0 |
| Read a => Read (ZipList a) | Since: base-4.7.0.0 |
| Read a => Read (Option a) | Since: base-4.9.0.0 |
| Read m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (WrappedMonoid m) Source readList :: ReadS [WrappedMonoid m] Source readPrec :: ReadPrec (WrappedMonoid m) Source readListPrec :: ReadPrec [WrappedMonoid m] Source | |
| Read a => Read (Last a) | Since: base-4.9.0.0 |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Read a => Read (Max a) | Since: base-4.9.0.0 |
| Read a => Read (Min a) | Since: base-4.9.0.0 |
| Read a => Read (Complex a) | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| Read (U1 p) | Since: base-4.9.0.0 |
| (Read a, Read b) => Read (a, b) | Since: base-2.1 |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| Read (Proxy t) | Since: base-4.7.0.0 |
| (Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
| HasResolution a => Read (Fixed a) | Since: base-4.3.0.0 |
| Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
| a ~ b => Read (a :~: b) | Since: base-4.7.0.0 |
| Coercible a b => Read (Coercion a b) | Since: base-4.7.0.0 |
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
| Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
| Read a => Read (Const a b) |
This instance would be equivalent to the derived instances of the Since: base-4.8.0.0 |
| Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
| a ~~ b => Read (a :~~: b) | Since: base-4.10.0.0 |
| (Read1 f, Read1 g, Read a) => Read (Sum f g a) | Since: base-4.9.0.0 |
| (Read1 f, Read1 g, Read a) => Read (Product f g a) | Since: base-4.9.0.0 |
| Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
| (Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | 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) | 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) | 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) | 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) | 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) | 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) | 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 m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
Defined in GHC.Read | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
Defined in GHC.Read MethodsreadsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Read MethodsreadsPrec :: 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 | |
reads :: Read a => ReadS a Source
equivalent to readsPrec with a precedence of 0.
readParen :: Bool -> ReadS a -> ReadS a Source
readParen True p parses what p parses, but surrounded with parentheses.
readParen False p parses what p parses, but optionally surrounded with parentheses.
read :: Read a => String -> a Source
The read function reads input from a string, which must be completely consumed by the input process. read fails with an error if the parse is unsuccessful, and it is therefore discouraged from being used in real applications. Use readMaybe or readEither for safe alternatives.
>>> read "123" :: Int 123
>>> read "hello" :: Int *** Exception: Prelude.read: no parse
The lex function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, lex returns a single successful `lexeme' consisting of the empty string. (Thus lex "" = [("","")].) If there is no legal lexeme at the beginning of the input string, 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 a is a computation which, when performed, does some I/O before returning a value of type a.
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
| Monad IO | Since: base-2.1 |
| Functor IO | Since: base-2.1 |
| MonadFix IO | Since: base-2.1 |
Defined in Control.Monad.Fix | |
| MonadFail IO | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| Applicative IO | Since: base-2.1 |
| GHCiSandboxIO IO | Since: base-4.4.0.0 |
Defined in GHC.GHCi MethodsghciStepIO :: IO a -> IO a Source | |
| MonadPlus IO | Since: base-4.9.0.0 |
| Alternative IO | Since: base-4.9.0.0 |
| MonadIO IO | Since: base-4.9.0.0 |
Defined in Control.Monad.IO.Class | |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| a ~ () => HPrintfType (IO a) | Since: base-4.7.0.0 |
Defined in Text.Printf | |
| a ~ () => PrintfType (IO a) | Since: base-4.7.0.0 |
Defined in Text.Printf | |
Simple I/O operations
Output functions
putChar :: Char -> IO () Source
Write a character to the standard output device (same as hPutChar stdout).
putStr :: String -> IO () Source
Write a string to the standard output device (same as hPutStr stdout).
putStrLn :: String -> IO () Source
The same as putStr, but adds a newline character.
print :: Show a => a -> IO () Source
The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
Input functions
Read a character from the standard input device (same as hGetChar stdin).
Read a line from the standard input device (same as hGetLine stdin).
getContents :: IO String Source
The getContents operation returns all user input as a single string, which is read lazily as it is needed (same as hGetContents stdin).
interact :: (String -> String) -> IO () Source
The interact function takes a function of type String->String as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.
Files
File and directory names are values of type String, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.
readFile :: FilePath -> IO String Source
The readFile function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with getContents.
writeFile :: FilePath -> String -> IO () Source
The computation writeFile file str function writes the string str, to the file file.
appendFile :: FilePath -> String -> IO () Source
The computation appendFile file str function appends the string str, to the file file.
Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
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.
readLn :: Read a => IO a Source
The readLn function combines getLine and readIO.
Exception handling in the I/O monad
type IOError = IOException Source
The Haskell 2010 type for exceptions in the IO monad. Any I/O operation may raise an IOError instead of returning a result. For a more general type of exception, including also those that arise in pure code, see Exception.
In Haskell 2010, this is an opaque type.
ioError :: IOError -> IO a Source
Raise an IOError in the IO monad.
userError :: String -> IOError Source
Construct an IOError value with a string describing the error. The fail method of the IO instance of the Monad class raises a userError, thus:
instance Monad IO where ... fail s = ioError (userError s)
© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/Prelude.html