| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Language.Lexer.Tlex.Prelude
Synopsis
- (++) :: [a] -> [a] -> [a]
- seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- print :: Show a => a -> IO ()
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- otherwise :: Bool
- map :: (a -> b) -> [a] -> [b]
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Bounded a where
- class Enum a where
- succ :: a -> a
- pred :: a -> a
- toEnum :: Int -> a
- fromEnum :: a -> Int
- enumFrom :: a -> [a]
- enumFromThen :: a -> a -> [a]
- enumFromTo :: a -> a -> [a]
- enumFromThenTo :: a -> a -> a -> [a]
- class Eq a where
- class Fractional a => Floating a where
- class Num a => Fractional a where
- (/) :: a -> a -> a
- recip :: a -> a
- fromRational :: Rational -> a
- class (Real a, Enum a) => Integral a where
- class Applicative m => Monad (m :: Type -> Type) where
- class Functor (f :: Type -> Type) where
- class Num a where
- class Eq a => Ord a where
- class Read a where
- class (Num a, Ord a) => Real a where
- toRational :: a -> Rational
- class (RealFrac a, Floating a) => RealFloat a where
- floatRadix :: a -> Integer
- floatDigits :: a -> Int
- floatRange :: a -> (Int, Int)
- decodeFloat :: a -> (Integer, Int)
- encodeFloat :: Integer -> Int -> a
- exponent :: a -> Int
- significand :: a -> a
- scaleFloat :: Int -> a -> a
- isNaN :: a -> Bool
- isInfinite :: a -> Bool
- isDenormalized :: a -> Bool
- isNegativeZero :: a -> Bool
- isIEEE :: a -> Bool
- atan2 :: a -> a -> a
- class (Real a, Fractional a) => RealFrac a where
- class Show a where
- class Monad m => MonadFail (m :: Type -> Type) where
- class Functor f => Applicative (f :: Type -> Type) where
- class Foldable (t :: TYPE LiftedRep -> Type) where
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
- traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
- sequenceA :: Applicative f => t (f a) -> f (t a)
- mapM :: Monad m => (a -> m b) -> t a -> m (t b)
- sequence :: Monad m => t (m a) -> m (t a)
- class Semigroup a where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- data Bool
- data Char
- data Double
- data Float
- data Int
- data Integer
- data Maybe a
- data Ordering
- type Rational = Ratio Integer
- data IO a
- data Word
- data Either a b
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- id :: a -> a
- read :: Read a => String -> a
- writeFile :: FilePath -> String -> IO ()
- readLn :: Read a => IO a
- readIO :: Read a => String -> IO a
- readFile :: FilePath -> IO String
- putStrLn :: String -> IO ()
- putStr :: String -> IO ()
- putChar :: Char -> IO ()
- interact :: (String -> String) -> IO ()
- getLine :: IO String
- getContents :: IO String
- getChar :: IO Char
- appendFile :: FilePath -> String -> IO ()
- ioError :: IOError -> IO a
- type FilePath = String
- type IOError = IOException
- userError :: String -> IOError
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- or :: Foldable t => t Bool -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- and :: Foldable t => t Bool -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- words :: String -> [String]
- unwords :: [String] -> String
- unlines :: [String] -> String
- lines :: String -> [String]
- reads :: Read a => ReadS a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- readParen :: Bool -> ReadS a -> ReadS a
- lex :: ReadS String
- type ReadS a = String -> [(a, String)]
- odd :: Integral a => a -> Bool
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- even :: Integral a => a -> Bool
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- type ShowS = String -> String
- shows :: Show a => a -> ShowS
- showString :: String -> ShowS
- showParen :: Bool -> ShowS -> ShowS
- showChar :: Char -> ShowS
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- takeWhile :: (a -> Bool) -> [a] -> [a]
- take :: Int -> [a] -> [a]
- splitAt :: Int -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- reverse :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- last :: [a] -> a
- iterate :: (a -> a) -> a -> [a]
- init :: [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- drop :: Int -> [a] -> [a]
- cycle :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- (!!) :: [a] -> Int -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- subtract :: Num a => a -> a -> a
- until :: (a -> Bool) -> (a -> a) -> a -> a
- flip :: (a -> b -> c) -> b -> a -> c
- asTypeOf :: a -> a -> a
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a
- errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a
- error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a
- (&&) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- module Control.Applicative
- module Control.Monad
- module Control.Monad.IO.Class
- evalState :: State s a -> s -> a
- evalStateT :: Monad m => StateT s m a -> s -> m a
- execState :: State s a -> s -> s
- execStateT :: Monad m => StateT s m a -> s -> m s
- mapState :: ((a, s) -> (b, s)) -> State s a -> State s b
- mapStateT :: (m (a, s) -> n (b, s)) -> StateT s m a -> StateT s n b
- runState :: State s a -> s -> (a, s)
- withState :: (s -> s) -> State s a -> State s a
- withStateT :: forall s (m :: Type -> Type) a. (s -> s) -> StateT s m a -> StateT s m a
- type State s = StateT s Identity
- newtype StateT s (m :: Type -> Type) a = StateT {
- runStateT :: s -> m (a, s)
- state :: forall (m :: Type -> Type) s a. Monad m => (s -> (a, s)) -> StateT s m a
- put :: forall (m :: Type -> Type) s. Monad m => s -> StateT s m ()
- modify' :: forall (m :: Type -> Type) s. Monad m => (s -> s) -> StateT s m ()
- liftPass :: Monad m => Pass w m (a, s) -> Pass w (StateT s m) a
- liftListen :: Monad m => Listen w m (a, s) -> Listen w (StateT s m) a
- liftCatch :: Catch e m (a, s) -> Catch e (StateT s m) a
- liftCallCC' :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b
- liftCallCC :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b
- gets :: forall (m :: Type -> Type) s a. Monad m => (s -> a) -> StateT s m a
- get :: forall (m :: Type -> Type) s. Monad m => StateT s m s
- module Data.Coerce
- class Foldable (t :: TYPE LiftedRep -> Type) where
- fold :: Monoid m => t m -> m
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldMap' :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl' :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- toList :: t a -> [a]
- null :: t a -> Bool
- length :: t a -> Int
- elem :: Eq a => a -> t a -> Bool
- maximum :: Ord a => t a -> a
- minimum :: Ord a => t a -> a
- sum :: Num a => t a -> a
- product :: Num a => t a -> a
- traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f ()
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f ()
- or :: Foldable t => t Bool -> Bool
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- msum :: (Foldable t, MonadPlus m) => t (m a) -> m a
- minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f ()
- forM_ :: (Foldable t, Monad m) => t a -> (a -> m b) -> m ()
- foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b
- foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b
- find :: Foldable t => (a -> Bool) -> t a -> Maybe a
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- asum :: (Foldable t, Alternative f) => t (f a) -> f a
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- and :: Foldable t => t Bool -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- const :: a -> b -> a
- (.) :: (b -> c) -> (a -> b) -> a -> c
- id :: a -> a
- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
- fix :: (a -> a) -> a
- (&) :: a -> (a -> b) -> b
- flip :: (a -> b -> c) -> b -> a -> c
- module Data.Functor
- module Data.Functor.Identity
- module Data.Functor.Compose
- class Ord a => Ix a
- type Type = TYPE LiftedRep
- data NonEmpty a = a :| [a]
- newtype Down a = Down {
- getDown :: a
- data Proxy (t :: k) = Proxy
- class Typeable (a :: k)
- data Word
- data Word8
Documentation
(++) :: [a] -> [a] -> [a] infixr 5 #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b infixr 0 #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). seq is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
filter :: (a -> Bool) -> [a] -> [a] #
\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
>>>filter odd [1, 2, 3][1,3]
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
>>>zip [1, 2] ['a', 'b'][(1,'a'),(2,'b')]
If one input list is shorter than the other, excess elements of the longer list are discarded, even if one of the lists is infinite:
>>>zip [1] ['a', 'b'][(1,'a')]>>>zip [1, 2] ['a'][(1,'a')]>>>zip [] [1..][]>>>zip [1..] [][]
zip is right-lazy:
>>>zip [] undefined[]>>>zip undefined []*** Exception: Prelude.undefined ...
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
print :: Show a => a -> IO () #
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]])
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3][2,3,4]
fromIntegral :: (Integral a, Num b) => a -> b #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
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 All | Since: base-2.1 |
| Bounded Any | Since: base-2.1 |
| Bounded IntPtr | |
| Bounded WordPtr | |
| Bounded Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| 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 Int16 | Since: base-2.1 |
| Bounded Int32 | Since: base-2.1 |
| Bounded Int64 | Since: base-2.1 |
| Bounded Int8 | Since: base-2.1 |
| Bounded Word16 | Since: base-2.1 |
| Bounded Word32 | Since: base-2.1 |
| Bounded Word64 | Since: base-2.1 |
| Bounded Word8 | Since: base-2.1 |
| Bounded Extension | |
| Bounded Ordering | Since: base-2.1 |
| Bounded QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter | |
| Bounded () | Since: base-2.1 |
| Bounded Bool | Since: base-2.1 |
| Bounded Char | Since: base-2.1 |
| Bounded Int | Since: base-2.1 |
| Bounded Levity | Since: base-4.16.0.0 |
| Bounded VecCount | Since: base-4.10.0.0 |
| Bounded VecElem | Since: base-4.10.0.0 |
| Bounded Word | Since: base-2.1 |
| Bounded a => Bounded (Identity a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
| Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Last 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 m => Bounded (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Bounded a => Bounded (a) | |
| Bounded (Proxy t) | Since: base-4.7.0.0 |
| (Bounded a, Bounded b) => Bounded (Pair a b) | |
| (Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1 |
| Bounded a => Bounded (Const a b) | Since: base-4.9.0.0 |
| Bounded b => Bounded (Tagged s b) | |
| (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1 |
| (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1 |
| (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 |
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
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] #
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] #
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] #
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 Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
The Haskell Report defines no laws for Eq. However, instances are
encouraged to follow these properties:
Instances
| Eq DotNetTime | |
Defined in Data.Aeson.Types.Internal | |
| Eq JSONPathElement | |
Defined in Data.Aeson.Types.Internal Methods (==) :: JSONPathElement -> JSONPathElement -> Bool # (/=) :: JSONPathElement -> JSONPathElement -> Bool # | |
| Eq SumEncoding | |
Defined in Data.Aeson.Types.Internal | |
| Eq Value | |
| Eq More | |
| Eq Pos | |
| Eq All | Since: base-2.1 |
| Eq Any | Since: base-2.1 |
| Eq SomeTypeRep | |
Defined in Data.Typeable.Internal | |
| Eq Unique | |
| Eq Version | Since: base-2.1 |
| Eq Void | Since: base-4.8.0.0 |
| Eq IntPtr | |
| Eq WordPtr | |
| Eq BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
| Eq ThreadId | Since: base-4.2.0.0 |
| Eq ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync | |
| Eq ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool # (/=) :: ArithException -> ArithException -> Bool # | |
| Eq SpecConstrAnnotation | Since: base-4.3.0.0 |
Defined in GHC.Exts Methods (==) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # (/=) :: SpecConstrAnnotation -> SpecConstrAnnotation -> Bool # | |
| Eq Fingerprint | Since: base-4.4.0.0 |
Defined in GHC.Fingerprint.Type | |
| Eq Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods (==) :: Associativity -> Associativity -> Bool # (/=) :: Associativity -> Associativity -> Bool # | |
| Eq DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
| Eq Fixity | Since: base-4.6.0.0 |
| Eq SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
| Eq SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
| Eq MaskingState | Since: base-4.3.0.0 |
Defined in GHC.IO | |
| Eq ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool # (/=) :: ArrayException -> ArrayException -> Bool # | |
| Eq AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool # (/=) :: AsyncException -> AsyncException -> Bool # | |
| Eq ExitCode | |
| Eq IOErrorType | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
| Eq IOException | Since: base-4.1.0.0 |
Defined in GHC.IO.Exception | |
| Eq Int16 | Since: base-2.1 |
| Eq Int32 | Since: base-2.1 |
| Eq Int64 | Since: base-2.1 |
| Eq Int8 | Since: base-2.1 |
| Eq SrcLoc | Since: base-4.9.0.0 |
| Eq Word16 | Since: base-2.1 |
| Eq Word32 | Since: base-2.1 |
| Eq Word64 | Since: base-2.1 |
| Eq Word8 | Since: base-2.1 |
| Eq ByteString | |
Defined in Data.ByteString.Internal | |
| Eq ByteString | |
Defined in Data.ByteString.Lazy.Internal | |
| Eq ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods (==) :: ShortByteString -> ShortByteString -> Bool # (/=) :: ShortByteString -> ShortByteString -> Bool # | |
| Eq IntSet | |
| Eq ByteArray | |
| Eq BigNat | |
| Eq ForeignSrcLang | |
Defined in GHC.ForeignSrcLang.Type Methods (==) :: ForeignSrcLang -> ForeignSrcLang -> Bool # (/=) :: ForeignSrcLang -> ForeignSrcLang -> Bool # | |
| Eq Extension | |
| Eq Module | |
| Eq Ordering | |
| Eq TrName | |
| Eq TyCon | |
| Eq Mode | |
| Eq Style | |
| Eq TextDetails | |
Defined in Text.PrettyPrint.Annotated.HughesPJ | |
| Eq Doc | |
| Eq StdGen | |
| Eq Scientific | Scientific numbers can be safely compared for equality. No magnitude |
Defined in Data.Scientific | |
| Eq AnnLookup | |
| Eq AnnTarget | |
| Eq Bang | |
| Eq Body | |
| Eq Bytes | |
| Eq Callconv | |
| Eq Clause | |
| Eq Con | |
| Eq Dec | |
| Eq DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DecidedStrictness -> DecidedStrictness -> Bool # (/=) :: DecidedStrictness -> DecidedStrictness -> Bool # | |
| Eq DerivClause | |
Defined in Language.Haskell.TH.Syntax | |
| Eq DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: DerivStrategy -> DerivStrategy -> Bool # (/=) :: DerivStrategy -> DerivStrategy -> Bool # | |
| Eq DocLoc | |
| Eq Exp | |
| Eq FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FamilyResultSig -> FamilyResultSig -> Bool # (/=) :: FamilyResultSig -> FamilyResultSig -> Bool # | |
| Eq Fixity | |
| Eq FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: FixityDirection -> FixityDirection -> Bool # (/=) :: FixityDirection -> FixityDirection -> Bool # | |
| Eq Foreign | |
| Eq FunDep | |
| Eq Guard | |
| Eq Info | |
| Eq InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: InjectivityAnn -> InjectivityAnn -> Bool # (/=) :: InjectivityAnn -> InjectivityAnn -> Bool # | |
| Eq Inline | |
| Eq Lit | |
| Eq Loc | |
| Eq Match | |
| Eq ModName | |
| Eq Module | |
| Eq ModuleInfo | |
Defined in Language.Haskell.TH.Syntax | |
| Eq Name | |
| Eq NameFlavour | |
Defined in Language.Haskell.TH.Syntax | |
| Eq NameSpace | |
| Eq OccName | |
| Eq Overlap | |
| Eq Pat | |
| Eq PatSynArgs | |
Defined in Language.Haskell.TH.Syntax | |
| Eq PatSynDir | |
| Eq Phases | |
| Eq PkgName | |
| Eq Pragma | |
| Eq Range | |
| Eq Role | |
| Eq RuleBndr | |
| Eq RuleMatch | |
| Eq Safety | |
| Eq SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceStrictness -> SourceStrictness -> Bool # (/=) :: SourceStrictness -> SourceStrictness -> Bool # | |
| Eq SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (/=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # | |
| Eq Specificity | |
Defined in Language.Haskell.TH.Syntax | |
| Eq Stmt | |
| Eq TyLit | |
| Eq TySynEqn | |
| Eq Type | |
| Eq TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods (==) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (/=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # | |
| Eq B | |
| Eq ShortText | |
| Eq Day | |
| Eq Month | |
| Eq Quarter | |
| Eq QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods (==) :: QuarterOfYear -> QuarterOfYear -> Bool # (/=) :: QuarterOfYear -> QuarterOfYear -> Bool # | |
| Eq DayOfWeek | |
| Eq AbsoluteTime | |
Defined in Data.Time.Clock.Internal.AbsoluteTime | |
| Eq DiffTime | |
| Eq NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (==) :: NominalDiffTime -> NominalDiffTime -> Bool # (/=) :: NominalDiffTime -> NominalDiffTime -> Bool # | |
| Eq UTCTime | |
| Eq UniversalTime | |
Defined in Data.Time.Clock.Internal.UniversalTime Methods (==) :: UniversalTime -> UniversalTime -> Bool # (/=) :: UniversalTime -> UniversalTime -> Bool # | |
| Eq TimeLocale | |
Defined in Data.Time.Format.Locale | |
| Eq LocalTime | |
| Eq TimeOfDay | |
| Eq TimeZone | |
| Eq NFAStateTrans Source # | |
Defined in Language.Lexer.Tlex.Machine.NFA Methods (==) :: NFAStateTrans -> NFAStateTrans -> Bool # (/=) :: NFAStateTrans -> NFAStateTrans -> Bool # | |
| Eq AcceptPriority Source # | |
Defined in Language.Lexer.Tlex.Machine.Pattern Methods (==) :: AcceptPriority -> AcceptPriority -> Bool # (/=) :: AcceptPriority -> AcceptPriority -> Bool # | |
| Eq StartState Source # | |
Defined in Language.Lexer.Tlex.Machine.Pattern | |
| Eq StateNum Source # | |
| Eq StateSet Source # | |
| Eq UUID | |
| Eq UnpackedUUID | |
| Eq Integer | |
| Eq Natural | |
| Eq () | |
| Eq Bool | |
| Eq Char | |
| Eq Double | Note that due to the presence of
Also note that
|
| Eq Float | Note that due to the presence of
Also note that
|
| Eq Int | |
| Eq Word | |
| Eq v => Eq (KeyMap v) | |
| Eq a => Eq (IResult a) | |
| Eq a => Eq (Result a) | |
| Eq a => Eq (ZipList a) | Since: base-4.7.0.0 |
| Eq a => Eq (Complex a) | Since: base-2.1 |
| Eq a => Eq (Identity a) | Since: base-4.8.0.0 |
| Eq a => Eq (Down a) | Since: base-4.6.0.0 |
| Eq a => Eq (First a) | Since: base-4.9.0.0 |
| Eq a => Eq (Last 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 m => Eq (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (==) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # | |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Eq (TVar a) | Since: base-4.8.0.0 |
| Eq (ForeignPtr a) | Since: base-2.1 |
Defined in GHC.ForeignPtr | |
| Eq p => Eq (Par1 p) | Since: base-4.7.0.0 |
| Eq (FunPtr a) | |
| Eq (Ptr a) | Since: base-2.1 |
| Eq a => Eq (Ratio a) | Since: base-2.1 |
| Eq (StableName a) | Since: base-2.1 |
Defined in GHC.StableName | |
| Eq vertex => Eq (SCC vertex) | Since: containers-0.5.9 |
| Eq a => Eq (IntMap a) | |
| Eq a => Eq (Seq a) | |
| Eq a => Eq (ViewL a) | |
| Eq a => Eq (ViewR a) | |
| Eq a => Eq (Set a) | |
| Eq a => Eq (Tree a) | |
| Eq (MutableByteArray s) | |
Defined in Data.Array.Byte Methods (==) :: MutableByteArray s -> MutableByteArray s -> Bool # (/=) :: MutableByteArray s -> MutableByteArray s -> Bool # | |
| Eq1 f => Eq (Fix f) | |
| (Functor f, Eq1 f) => Eq (Mu f) | |
| (Functor f, Eq1 f) => Eq (Nu f) | |
| Eq a => Eq (DNonEmpty a) | |
| Eq a => Eq (DList a) | |
| Eq (EnumSet k) | |
| Eq a => Eq (Hashed a) | Uses precomputed hash to detect inequality faster |
| Eq a => Eq (AnnotDetails a) | |
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods (==) :: AnnotDetails a -> AnnotDetails a -> Bool # (/=) :: AnnotDetails a -> AnnotDetails a -> Bool # | |
| Eq (Doc a) | |
| Eq a => Eq (Span a) | |
| Eq a => Eq (Array a) | |
| (Eq a, Prim a) => Eq (PrimArray a) | Since: primitive-0.6.4.0 |
| Eq a => Eq (SmallArray a) | |
Defined in Data.Primitive.SmallArray | |
| Eq g => Eq (StateGen g) | |
| Eq g => Eq (AtomicGen g) | |
| Eq g => Eq (IOGen g) | |
| Eq g => Eq (STGen g) | |
| Eq g => Eq (TGen g) | |
| Eq a => Eq (Maybe a) | |
| Eq flag => Eq (TyVarBndr flag) | |
| Eq a => Eq (Bag a) Source # | |
| Eq (SymEnumSet a) Source # | |
Defined in Language.Lexer.Tlex.Data.SymEnumSet | |
| Eq a => Eq (DFA a) Source # | |
| Eq m => Eq (DFABuilderContext m) Source # | |
Defined in Language.Lexer.Tlex.Machine.DFA Methods (==) :: DFABuilderContext m -> DFABuilderContext m -> Bool # (/=) :: DFABuilderContext m -> DFABuilderContext m -> Bool # | |
| Eq a => Eq (DFAState a) Source # | |
| Eq a => Eq (NFA a) Source # | |
| Eq a => Eq (NFAState a) Source # | |
| Eq a => Eq (Accept a) Source # | |
| Eq (Pattern e) Source # | |
| Eq a => Eq (StateArray a) Source # | |
Defined in Language.Lexer.Tlex.Machine.State | |
| Eq a => Eq (StateMap a) Source # | |
| Eq a => Eq (HashSet a) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
| Eq a => Eq (Vector a) | |
| (Prim a, Eq a) => Eq (Vector a) | |
| (Storable a, Eq a) => Eq (Vector a) | |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Eq a => Eq (a) | |
| Eq a => Eq [a] | |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| Eq (Fixed a) | Since: base-2.1 |
| Eq (Proxy s) | Since: base-4.7.0.0 |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| Eq (TypeRep a) | Since: base-2.1 |
| (Ix i, Eq e) => Eq (Array i e) | Since: base-2.1 |
| Eq (U1 p) | Since: base-4.9.0.0 |
| Eq (V1 p) | Since: base-4.9.0.0 |
| (Eq k, Eq a) => Eq (Map k a) | |
| Eq a => Eq (EnumMap k a) | |
| Eq (MutableArray s a) | |
Defined in Data.Primitive.Array Methods (==) :: MutableArray s a -> MutableArray s a -> Bool # (/=) :: MutableArray s a -> MutableArray s a -> Bool # | |
| Eq (MutablePrimArray s a) | |
Defined in Data.Primitive.PrimArray Methods (==) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool # (/=) :: MutablePrimArray s a -> MutablePrimArray s a -> Bool # | |
| Eq (SmallMutableArray s a) | |
Defined in Data.Primitive.SmallArray Methods (==) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # (/=) :: SmallMutableArray s a -> SmallMutableArray s a -> Bool # | |
| (Eq a, Eq b) => Eq (Either a b) | |
| (Eq a, Eq b) => Eq (These a b) | |
| (Eq a, Eq b) => Eq (Pair a b) | |
| (Eq a, Eq b) => Eq (These a b) | |
| (Eq k, Eq v) => Eq (HashMap k v) | Note that, in the presence of hash collisions, equal
In general, the lack of substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals. |
| (Eq k, Eq v) => Eq (Leaf k v) | |
| (Eq a, Eq b) => Eq (a, b) | |
| Eq a => Eq (Const a b) | Since: base-4.9.0.0 |
| Eq (f a) => Eq (Alt f a) | Since: base-4.8.0.0 |
| Eq (STArray s i e) | Since: base-2.1 |
| Eq (f p) => Eq (Rec1 f p) | Since: base-4.7.0.0 |
| Eq (URec (Ptr ()) p) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Eq (URec Double p) | Since: base-4.9.0.0 |
| Eq (URec Float p) | |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| Eq b => Eq (Tagged s b) | |
| (Eq (f a), Eq (g a), Eq a) => Eq (These1 f g a) | |
| (Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) | |
| (Eq a, Eq b, Eq c) => Eq (a, b, c) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Product f g a) | Since: base-4.9.0.0 |
| (Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a) | Since: base-4.9.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
| (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
| Eq c => Eq (K1 i c p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) | |
| (Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a) | Since: base-4.9.0.0 |
| Eq (f (g p)) => Eq ((f :.: g) p) | Since: base-4.7.0.0 |
| Eq (f p) => Eq (M1 i c f p) | Since: base-4.7.0.0 |
| (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
| (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1
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
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional Scientific | WARNING: These methods also compute
|
Defined in Data.Scientific Methods (/) :: Scientific -> Scientific -> Scientific # recip :: Scientific -> Scientific # fromRational :: Rational -> Scientific # | |
| Fractional DiffTime | |
| Fractional NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (/) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # recip :: NominalDiffTime -> NominalDiffTime # fromRational :: Rational -> NominalDiffTime # | |
| RealFloat a => Fractional (Complex a) | Since: base-2.1 |
| Fractional a => Fractional (Identity a) | Since: base-4.9.0.0 |
| Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| HasResolution a => Fractional (Fixed a) | Since: base-2.1 |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
| Fractional a => Fractional (Tagged s a) | |
class (Real a, Enum a) => Integral a where #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
| Integral IntPtr | |
Defined in Foreign.Ptr | |
| Integral WordPtr | |
Defined in Foreign.Ptr | |
| Integral Int16 | Since: base-2.1 |
| Integral Int32 | Since: base-2.1 |
| Integral Int64 | Since: base-2.1 |
| Integral Int8 | Since: base-2.1 |
| Integral Word16 | Since: base-2.1 |
| Integral Word32 | Since: base-2.1 |
| Integral Word64 | Since: base-2.1 |
| Integral Word8 | Since: base-2.1 |
| Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
| Integral Natural | Since: base-4.8.0.0 |
Defined in GHC.Real | |
| Integral Int | Since: base-2.0.1 |
| Integral Word | Since: base-2.1 |
| Integral a => Integral (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods quot :: Identity a -> Identity a -> Identity a # rem :: Identity a -> Identity a -> Identity a # div :: Identity a -> Identity a -> Identity a # mod :: Identity a -> Identity a -> Identity a # quotRem :: Identity a -> Identity a -> (Identity a, Identity a) # divMod :: Identity a -> Identity a -> (Identity a, Identity a) # | |
| Integral a => Integral (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods quot :: Const a b -> Const a b -> Const a b # rem :: Const a b -> Const a b -> Const a b # div :: Const a b -> Const a b -> Const a b # mod :: Const a b -> Const a b -> Const a b # quotRem :: Const a b -> Const a b -> (Const a b, Const a b) # divMod :: Const a b -> Const a b -> (Const a b, Const a b) # | |
| Integral a => Integral (Tagged s a) | |
Defined in Data.Tagged Methods quot :: Tagged s a -> Tagged s a -> Tagged s a # rem :: Tagged s a -> Tagged s a -> Tagged s a # div :: Tagged s a -> Tagged s a -> Tagged s a # mod :: Tagged s a -> Tagged s a -> Tagged s a # quotRem :: Tagged s a -> Tagged s a -> (Tagged s a, Tagged s a) # divMod :: Tagged s a -> Tagged s a -> (Tagged s a, Tagged s a) # | |
class Applicative m => Monad (m :: Type -> Type) where #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: m a -> m b -> m b infixl 1 #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad IResult | |
| Monad Parser | |
| Monad Result | |
| Monad Complex | Since: base-4.9.0.0 |
| Monad Identity | Since: base-4.8.0.0 |
| Monad Down | Since: base-4.11.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Monad STM | Since: base-4.3.0.0 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad P | Since: base-2.1 |
| Monad ReadP | Since: base-2.1 |
| Monad Put | |
| Monad Seq | |
| Monad Tree | |
| Monad DNonEmpty | |
| Monad DList | |
| Monad IO | Since: base-2.1 |
| Monad Array | |
| Monad SmallArray | |
Defined in Data.Primitive.SmallArray Methods (>>=) :: SmallArray a -> (a -> SmallArray b) -> SmallArray b # (>>) :: SmallArray a -> SmallArray b -> SmallArray b # return :: a -> SmallArray a # | |
| Monad Q | |
| Monad Vector | |
| Monad Id | |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad Maybe | Since: base-2.1 |
| Monad Solo | Since: base-4.15 |
| Monad [] | Since: base-2.1 |
| Monad (Parser i) | |
| 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 # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monad (SetM s) | |
| Semigroup a => Monad (These a) | |
| Semigroup a => Monad (These a) | |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Applicative f, Monad f) => Monad (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
| Monad (Tagged s) | |
| (Monad m, Error e) => Monad (ErrorT e m) | |
| Monad m => Monad (StateT s m) | |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| Monad ((->) r) | Since: base-2.1 |
| Monad f => Monad (M1 i c f) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Monad (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
class Functor (f :: Type -> Type) where #
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 #
fmap is used to apply a function of type (a -> b) to a value of type f a,
where f is a functor, to produce a value of type f b.
Note that for any type constructor with more than one parameter (e.g., Either),
only the last type parameter can be modified with fmap (e.g., b in `Either a b`).
Some type constructors with two parameters or more have a Bifunctor
Examples
Convert from a Maybe IntMaybe String
using show:
>>>fmap show NothingNothing>>>fmap show (Just 3)Just "3"
Convert from an Either Int IntEither Int String using show:
>>>fmap show (Left 17)Left 17>>>fmap show (Right 17)Right "17"
Double each element of a list:
>>>fmap (*2) [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>fmap even (2,2)(2,True)
It may seem surprising that the function is only applied to the last element of the tuple
compared to the list example above which applies it to every element in the list.
To understand, remember that tuples are type constructors with multiple type parameters:
a tuple of 3 elements (a,b,c) can also be written (,,) a b c and its Functor instance
is defined for Functor ((,,) a b) (i.e., only the third parameter is free to be mapped over
with fmap).
It explains why fmap can be used with tuples containing values of different types as in the
following example:
>>>fmap even ("hello", 1.0, 4)("hello",1.0,True)
Instances
Basic numeric class.
The Haskell Report defines no laws for Num. However, ( and +)( are
customarily expected to define a ring and have the following properties:*)
- Associativity of
(+) (x + y) + z=x + (y + z)- Commutativity of
(+) x + y=y + xfromInteger0x + fromInteger 0=xnegategives the additive inversex + negate x=fromInteger 0- Associativity of
(*) (x * y) * z=x * (y * z)fromInteger1x * fromInteger 1=xandfromInteger 1 * x=x- Distributivity of
(with respect to*)(+) a * (b + c)=(a * b) + (a * c)and(b + c) * a=(b * a) + (c * a)
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
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 #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
| Num Pos | |
| Num IntPtr | |
| Num WordPtr | |
| Num Int16 | Since: base-2.1 |
| Num Int32 | Since: base-2.1 |
| Num Int64 | Since: base-2.1 |
| Num Int8 | Since: base-2.1 |
| Num Word16 | Since: base-2.1 |
| Num Word32 | Since: base-2.1 |
| Num Word64 | Since: base-2.1 |
| Num Word8 | Since: base-2.1 |
| Num Scientific | WARNING: |
Defined in Data.Scientific Methods (+) :: Scientific -> Scientific -> Scientific # (-) :: Scientific -> Scientific -> Scientific # (*) :: Scientific -> Scientific -> Scientific # negate :: Scientific -> Scientific # abs :: Scientific -> Scientific # signum :: Scientific -> Scientific # fromInteger :: Integer -> Scientific # | |
| Num B | |
| Num DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
| Num NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (+) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # (-) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # (*) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # negate :: NominalDiffTime -> NominalDiffTime # abs :: NominalDiffTime -> NominalDiffTime # signum :: NominalDiffTime -> NominalDiffTime # fromInteger :: Integer -> NominalDiffTime # | |
| Num Integer | Since: base-2.1 |
| Num Natural | Note that Since: base-4.8.0.0 |
| Num Int | Since: base-2.1 |
| Num Word | Since: base-2.1 |
| RealFloat a => Num (Complex a) | Since: base-2.1 |
| Num a => Num (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| Num a => Num (Down a) | Since: base-4.11.0.0 |
| Num a => Num (Max a) | Since: base-4.9.0.0 |
| Num a => Num (Min a) | Since: base-4.9.0.0 |
| Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Num a => Num (Sum a) | Since: base-4.7.0.0 |
| Integral a => Num (Ratio a) | Since: base-2.0.1 |
| HasResolution a => Num (Fixed a) | Since: base-2.1 |
| Num a => Num (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
| Num (f a) => Num (Alt f a) | Since: base-4.8.0.0 |
| Num a => Num (Tagged s a) | |
Defined in Data.Tagged | |
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose
constituent types are in Ord. The declared order of the constructors in
the data declaration determines the ordering in derived Ord instances. The
Ordering datatype allows a single comparison to determine the precise
ordering of two objects.
Ord, as defined by the Haskell report, implements a total order and has the
following properties:
- Comparability
x <= y || y <= x=True- Transitivity
- if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
x <= x=True- Antisymmetry
- if
x <= y && y <= x=True, thenx == y=True
The following operator interactions are expected to hold:
x >= y=y <= xx < y=x <= y && x /= yx > y=y < xx < y=compare x y == LTx > y=compare x y == GTx == y=compare x y == EQmin x y == if x <= y then x else y=Truemax x y == if x >= y then x else y=True
Note that (7.) and (8.) do not require min and max to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==).
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
Instances
| Ord DotNetTime | |
Defined in Data.Aeson.Types.Internal Methods compare :: DotNetTime -> DotNetTime -> Ordering # (<) :: DotNetTime -> DotNetTime -> Bool # (<=) :: DotNetTime -> DotNetTime -> Bool # (>) :: DotNetTime -> DotNetTime -> Bool # (>=) :: DotNetTime -> DotNetTime -> Bool # max :: DotNetTime -> DotNetTime -> DotNetTime # min :: DotNetTime -> DotNetTime -> DotNetTime # | |
| Ord JSONPathElement | |
Defined in Data.Aeson.Types.Internal Methods compare :: JSONPathElement -> JSONPathElement -> Ordering # (<) :: JSONPathElement -> JSONPathElement -> Bool # (<=) :: JSONPathElement -> JSONPathElement -> Bool # (>) :: JSONPathElement -> JSONPathElement -> Bool # (>=) :: JSONPathElement -> JSONPathElement -> Bool # max :: JSONPathElement -> JSONPathElement -> JSONPathElement # min :: JSONPathElement -> JSONPathElement -> JSONPathElement # | |
| Ord Value | The ordering is total, consistent with Since: aeson-1.5.2.0 |
| Ord Pos | |
| Ord All | Since: base-2.1 |
| Ord Any | Since: base-2.1 |
| Ord SomeTypeRep | |
Defined in Data.Typeable.Internal Methods compare :: SomeTypeRep -> SomeTypeRep -> Ordering # (<) :: SomeTypeRep -> SomeTypeRep -> Bool # (<=) :: SomeTypeRep -> SomeTypeRep -> Bool # (>) :: SomeTypeRep -> SomeTypeRep -> Bool # (>=) :: SomeTypeRep -> SomeTypeRep -> Bool # max :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # min :: SomeTypeRep -> SomeTypeRep -> SomeTypeRep # | |
| Ord Unique | |
| Ord Version | Since: base-2.1 |
| Ord Void | Since: base-4.8.0.0 |
| Ord IntPtr | |
| Ord WordPtr | |
| Ord BlockReason | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods compare :: BlockReason -> BlockReason -> Ordering # (<) :: BlockReason -> BlockReason -> Bool # (<=) :: BlockReason -> BlockReason -> Bool # (>) :: BlockReason -> BlockReason -> Bool # (>=) :: BlockReason -> BlockReason -> Bool # max :: BlockReason -> BlockReason -> BlockReason # min :: BlockReason -> BlockReason -> BlockReason # | |
| Ord ThreadId | Since: base-4.2.0.0 |
Defined in GHC.Conc.Sync | |
| Ord ThreadStatus | Since: base-4.3.0.0 |
Defined in GHC.Conc.Sync Methods compare :: ThreadStatus -> ThreadStatus -> Ordering # (<) :: ThreadStatus -> ThreadStatus -> Bool # (<=) :: ThreadStatus -> ThreadStatus -> Bool # (>) :: ThreadStatus -> ThreadStatus -> Bool # (>=) :: ThreadStatus -> ThreadStatus -> Bool # max :: ThreadStatus -> ThreadStatus -> ThreadStatus # min :: ThreadStatus -> ThreadStatus -> ThreadStatus # | |
| Ord ArithException | Since: base-3.0 |
Defined in GHC.Exception.Type Methods compare :: ArithException -> ArithException -> Ordering # (<) :: ArithException -> ArithException -> Bool # (<=) :: ArithException -> ArithException -> Bool # (>) :: ArithException -> ArithException -> Bool # (>=) :: ArithException -> ArithException -> Bool # max :: ArithException -> ArithException -> ArithException # min :: ArithException -> ArithException -> ArithException # | |
| Ord Fingerprint | Since: base-4.4.0.0 |
Defined in GHC.Fingerprint.Type Methods compare :: Fingerprint -> Fingerprint -> Ordering # (<) :: Fingerprint -> Fingerprint -> Bool # (<=) :: Fingerprint -> Fingerprint -> Bool # (>) :: Fingerprint -> Fingerprint -> Bool # (>=) :: Fingerprint -> Fingerprint -> Bool # max :: Fingerprint -> Fingerprint -> Fingerprint # min :: Fingerprint -> Fingerprint -> Fingerprint # | |
| Ord Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods compare :: Associativity -> Associativity -> Ordering # (<) :: Associativity -> Associativity -> Bool # (<=) :: Associativity -> Associativity -> Bool # (>) :: Associativity -> Associativity -> Bool # (>=) :: Associativity -> Associativity -> Bool # max :: Associativity -> Associativity -> Associativity # min :: Associativity -> Associativity -> Associativity # | |
| Ord DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # | |
| Ord Fixity | Since: base-4.6.0.0 |
| Ord SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness # | |
| Ord SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # | |
| Ord ArrayException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods compare :: ArrayException -> ArrayException -> Ordering # (<) :: ArrayException -> ArrayException -> Bool # (<=) :: ArrayException -> ArrayException -> Bool # (>) :: ArrayException -> ArrayException -> Bool # (>=) :: ArrayException -> ArrayException -> Bool # max :: ArrayException -> ArrayException -> ArrayException # min :: ArrayException -> ArrayException -> ArrayException # | |
| Ord AsyncException | Since: base-4.2.0.0 |
Defined in GHC.IO.Exception Methods compare :: AsyncException -> AsyncException -> Ordering # (<) :: AsyncException -> AsyncException -> Bool # (<=) :: AsyncException -> AsyncException -> Bool # (>) :: AsyncException -> AsyncException -> Bool # (>=) :: AsyncException -> AsyncException -> Bool # max :: AsyncException -> AsyncException -> AsyncException # min :: AsyncException -> AsyncException -> AsyncException # | |
| Ord ExitCode | |
Defined in GHC.IO.Exception | |
| Ord Int16 | Since: base-2.1 |
| Ord Int32 | Since: base-2.1 |
| Ord Int64 | Since: base-2.1 |
| Ord Int8 | Since: base-2.1 |
| Ord Word16 | Since: base-2.1 |
| Ord Word32 | Since: base-2.1 |
| Ord Word64 | Since: base-2.1 |
| Ord Word8 | Since: base-2.1 |
| Ord ByteString | |
Defined in Data.ByteString.Internal Methods compare :: ByteString -> ByteString -> Ordering # (<) :: ByteString -> ByteString -> Bool # (<=) :: ByteString -> ByteString -> Bool # (>) :: ByteString -> ByteString -> Bool # (>=) :: ByteString -> ByteString -> Bool # max :: ByteString -> ByteString -> ByteString # min :: ByteString -> ByteString -> ByteString # | |
| Ord ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods compare :: ByteString -> ByteString -> Ordering # (<) :: ByteString -> ByteString -> Bool # (<=) :: ByteString -> ByteString -> Bool # (>) :: ByteString -> ByteString -> Bool # (>=) :: ByteString -> ByteString -> Bool # max :: ByteString -> ByteString -> ByteString # min :: ByteString -> ByteString -> ByteString # | |
| Ord ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods compare :: ShortByteString -> ShortByteString -> Ordering # (<) :: ShortByteString -> ShortByteString -> Bool # (<=) :: ShortByteString -> ShortByteString -> Bool # (>) :: ShortByteString -> ShortByteString -> Bool # (>=) :: ShortByteString -> ShortByteString -> Bool # max :: ShortByteString -> ShortByteString -> ShortByteString # min :: ShortByteString -> ShortByteString -> ShortByteString # | |
| Ord IntSet | |
| Ord ByteArray | Non-lexicographic ordering. This compares the lengths of the byte arrays first and uses a lexicographic ordering if the lengths are equal. Subject to change between major versions. |
| Ord BigNat | |
| Ord Extension | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Ord TyCon | |
| Ord Scientific | Scientific numbers can be safely compared for ordering. No magnitude |
Defined in Data.Scientific Methods compare :: Scientific -> Scientific -> Ordering # (<) :: Scientific -> Scientific -> Bool # (<=) :: Scientific -> Scientific -> Bool # (>) :: Scientific -> Scientific -> Bool # (>=) :: Scientific -> Scientific -> Bool # max :: Scientific -> Scientific -> Scientific # min :: Scientific -> Scientific -> Scientific # | |
| Ord AnnLookup | |
| Ord AnnTarget | |
| Ord Bang | |
| Ord Body | |
| Ord Bytes | |
| Ord Callconv | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Clause | |
| Ord Con | |
| Ord Dec | |
| Ord DecidedStrictness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DecidedStrictness -> DecidedStrictness -> Ordering # (<) :: DecidedStrictness -> DecidedStrictness -> Bool # (<=) :: DecidedStrictness -> DecidedStrictness -> Bool # (>) :: DecidedStrictness -> DecidedStrictness -> Bool # (>=) :: DecidedStrictness -> DecidedStrictness -> Bool # max :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # min :: DecidedStrictness -> DecidedStrictness -> DecidedStrictness # | |
| Ord DerivClause | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DerivClause -> DerivClause -> Ordering # (<) :: DerivClause -> DerivClause -> Bool # (<=) :: DerivClause -> DerivClause -> Bool # (>) :: DerivClause -> DerivClause -> Bool # (>=) :: DerivClause -> DerivClause -> Bool # max :: DerivClause -> DerivClause -> DerivClause # min :: DerivClause -> DerivClause -> DerivClause # | |
| Ord DerivStrategy | |
Defined in Language.Haskell.TH.Syntax Methods compare :: DerivStrategy -> DerivStrategy -> Ordering # (<) :: DerivStrategy -> DerivStrategy -> Bool # (<=) :: DerivStrategy -> DerivStrategy -> Bool # (>) :: DerivStrategy -> DerivStrategy -> Bool # (>=) :: DerivStrategy -> DerivStrategy -> Bool # max :: DerivStrategy -> DerivStrategy -> DerivStrategy # min :: DerivStrategy -> DerivStrategy -> DerivStrategy # | |
| Ord DocLoc | |
| Ord Exp | |
| Ord FamilyResultSig | |
Defined in Language.Haskell.TH.Syntax Methods compare :: FamilyResultSig -> FamilyResultSig -> Ordering # (<) :: FamilyResultSig -> FamilyResultSig -> Bool # (<=) :: FamilyResultSig -> FamilyResultSig -> Bool # (>) :: FamilyResultSig -> FamilyResultSig -> Bool # (>=) :: FamilyResultSig -> FamilyResultSig -> Bool # max :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig # min :: FamilyResultSig -> FamilyResultSig -> FamilyResultSig # | |
| Ord Fixity | |
| Ord FixityDirection | |
Defined in Language.Haskell.TH.Syntax Methods compare :: FixityDirection -> FixityDirection -> Ordering # (<) :: FixityDirection -> FixityDirection -> Bool # (<=) :: FixityDirection -> FixityDirection -> Bool # (>) :: FixityDirection -> FixityDirection -> Bool # (>=) :: FixityDirection -> FixityDirection -> Bool # max :: FixityDirection -> FixityDirection -> FixityDirection # min :: FixityDirection -> FixityDirection -> FixityDirection # | |
| Ord Foreign | |
Defined in Language.Haskell.TH.Syntax | |
| Ord FunDep | |
| Ord Guard | |
| Ord Info | |
| Ord InjectivityAnn | |
Defined in Language.Haskell.TH.Syntax Methods compare :: InjectivityAnn -> InjectivityAnn -> Ordering # (<) :: InjectivityAnn -> InjectivityAnn -> Bool # (<=) :: InjectivityAnn -> InjectivityAnn -> Bool # (>) :: InjectivityAnn -> InjectivityAnn -> Bool # (>=) :: InjectivityAnn -> InjectivityAnn -> Bool # max :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn # min :: InjectivityAnn -> InjectivityAnn -> InjectivityAnn # | |
| Ord Inline | |
| Ord Lit | |
| Ord Loc | |
| Ord Match | |
| Ord ModName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Module | |
| Ord ModuleInfo | |
Defined in Language.Haskell.TH.Syntax Methods compare :: ModuleInfo -> ModuleInfo -> Ordering # (<) :: ModuleInfo -> ModuleInfo -> Bool # (<=) :: ModuleInfo -> ModuleInfo -> Bool # (>) :: ModuleInfo -> ModuleInfo -> Bool # (>=) :: ModuleInfo -> ModuleInfo -> Bool # max :: ModuleInfo -> ModuleInfo -> ModuleInfo # min :: ModuleInfo -> ModuleInfo -> ModuleInfo # | |
| Ord Name | |
| Ord NameFlavour | |
Defined in Language.Haskell.TH.Syntax Methods compare :: NameFlavour -> NameFlavour -> Ordering # (<) :: NameFlavour -> NameFlavour -> Bool # (<=) :: NameFlavour -> NameFlavour -> Bool # (>) :: NameFlavour -> NameFlavour -> Bool # (>=) :: NameFlavour -> NameFlavour -> Bool # max :: NameFlavour -> NameFlavour -> NameFlavour # min :: NameFlavour -> NameFlavour -> NameFlavour # | |
| Ord NameSpace | |
| Ord OccName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Overlap | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Pat | |
| Ord PatSynArgs | |
Defined in Language.Haskell.TH.Syntax Methods compare :: PatSynArgs -> PatSynArgs -> Ordering # (<) :: PatSynArgs -> PatSynArgs -> Bool # (<=) :: PatSynArgs -> PatSynArgs -> Bool # (>) :: PatSynArgs -> PatSynArgs -> Bool # (>=) :: PatSynArgs -> PatSynArgs -> Bool # max :: PatSynArgs -> PatSynArgs -> PatSynArgs # min :: PatSynArgs -> PatSynArgs -> PatSynArgs # | |
| Ord PatSynDir | |
| Ord Phases | |
| Ord PkgName | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Pragma | |
| Ord Range | |
| Ord Role | |
| Ord RuleBndr | |
Defined in Language.Haskell.TH.Syntax | |
| Ord RuleMatch | |
| Ord Safety | |
| Ord SourceStrictness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: SourceStrictness -> SourceStrictness -> Ordering # (<) :: SourceStrictness -> SourceStrictness -> Bool # (<=) :: SourceStrictness -> SourceStrictness -> Bool # (>) :: SourceStrictness -> SourceStrictness -> Bool # (>=) :: SourceStrictness -> SourceStrictness -> Bool # max :: SourceStrictness -> SourceStrictness -> SourceStrictness # min :: SourceStrictness -> SourceStrictness -> SourceStrictness # | |
| Ord SourceUnpackedness | |
Defined in Language.Haskell.TH.Syntax Methods compare :: SourceUnpackedness -> SourceUnpackedness -> Ordering # (<) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (<=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>) :: SourceUnpackedness -> SourceUnpackedness -> Bool # (>=) :: SourceUnpackedness -> SourceUnpackedness -> Bool # max :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # min :: SourceUnpackedness -> SourceUnpackedness -> SourceUnpackedness # | |
| Ord Specificity | |
Defined in Language.Haskell.TH.Syntax Methods compare :: Specificity -> Specificity -> Ordering # (<) :: Specificity -> Specificity -> Bool # (<=) :: Specificity -> Specificity -> Bool # (>) :: Specificity -> Specificity -> Bool # (>=) :: Specificity -> Specificity -> Bool # max :: Specificity -> Specificity -> Specificity # min :: Specificity -> Specificity -> Specificity # | |
| Ord Stmt | |
| Ord TyLit | |
| Ord TySynEqn | |
Defined in Language.Haskell.TH.Syntax | |
| Ord Type | |
| Ord TypeFamilyHead | |
Defined in Language.Haskell.TH.Syntax Methods compare :: TypeFamilyHead -> TypeFamilyHead -> Ordering # (<) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (<=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>) :: TypeFamilyHead -> TypeFamilyHead -> Bool # (>=) :: TypeFamilyHead -> TypeFamilyHead -> Bool # max :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead # min :: TypeFamilyHead -> TypeFamilyHead -> TypeFamilyHead # | |
| Ord B | |
| Ord ShortText | |
| Ord Day | |
| Ord Month | |
| Ord Quarter | |
Defined in Data.Time.Calendar.Quarter | |
| Ord QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods compare :: QuarterOfYear -> QuarterOfYear -> Ordering # (<) :: QuarterOfYear -> QuarterOfYear -> Bool # (<=) :: QuarterOfYear -> QuarterOfYear -> Bool # (>) :: QuarterOfYear -> QuarterOfYear -> Bool # (>=) :: QuarterOfYear -> QuarterOfYear -> Bool # max :: QuarterOfYear -> QuarterOfYear -> QuarterOfYear # min :: QuarterOfYear -> QuarterOfYear -> QuarterOfYear # | |
| Ord DayOfWeek | |
| Ord AbsoluteTime | |
Defined in Data.Time.Clock.Internal.AbsoluteTime Methods compare :: AbsoluteTime -> AbsoluteTime -> Ordering # (<) :: AbsoluteTime -> AbsoluteTime -> Bool # (<=) :: AbsoluteTime -> AbsoluteTime -> Bool # (>) :: AbsoluteTime -> AbsoluteTime -> Bool # (>=) :: AbsoluteTime -> AbsoluteTime -> Bool # max :: AbsoluteTime -> AbsoluteTime -> AbsoluteTime # min :: AbsoluteTime -> AbsoluteTime -> AbsoluteTime # | |
| Ord DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
| Ord NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods compare :: NominalDiffTime -> NominalDiffTime -> Ordering # (<) :: NominalDiffTime -> NominalDiffTime -> Bool # (<=) :: NominalDiffTime -> NominalDiffTime -> Bool # (>) :: NominalDiffTime -> NominalDiffTime -> Bool # (>=) :: NominalDiffTime -> NominalDiffTime -> Bool # max :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # min :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # | |
| Ord UTCTime | |
Defined in Data.Time.Clock.Internal.UTCTime | |
| Ord UniversalTime | |
Defined in Data.Time.Clock.Internal.UniversalTime Methods compare :: UniversalTime -> UniversalTime -> Ordering # (<) :: UniversalTime -> UniversalTime -> Bool # (<=) :: UniversalTime -> UniversalTime -> Bool # (>) :: UniversalTime -> UniversalTime -> Bool # (>=) :: UniversalTime -> UniversalTime -> Bool # max :: UniversalTime -> UniversalTime -> UniversalTime # min :: UniversalTime -> UniversalTime -> UniversalTime # | |
| Ord TimeLocale | |
Defined in Data.Time.Format.Locale Methods compare :: TimeLocale -> TimeLocale -> Ordering # (<) :: TimeLocale -> TimeLocale -> Bool # (<=) :: TimeLocale -> TimeLocale -> Bool # (>) :: TimeLocale -> TimeLocale -> Bool # (>=) :: TimeLocale -> TimeLocale -> Bool # max :: TimeLocale -> TimeLocale -> TimeLocale # min :: TimeLocale -> TimeLocale -> TimeLocale # | |
| Ord LocalTime | |
Defined in Data.Time.LocalTime.Internal.LocalTime | |
| Ord TimeOfDay | |
Defined in Data.Time.LocalTime.Internal.TimeOfDay | |
| Ord TimeZone | |
Defined in Data.Time.LocalTime.Internal.TimeZone | |
| Ord AcceptPriority Source # | |
Defined in Language.Lexer.Tlex.Machine.Pattern Methods compare :: AcceptPriority -> AcceptPriority -> Ordering # (<) :: AcceptPriority -> AcceptPriority -> Bool # (<=) :: AcceptPriority -> AcceptPriority -> Bool # (>) :: AcceptPriority -> AcceptPriority -> Bool # (>=) :: AcceptPriority -> AcceptPriority -> Bool # max :: AcceptPriority -> AcceptPriority -> AcceptPriority # min :: AcceptPriority -> AcceptPriority -> AcceptPriority # | |
| Ord StateNum Source # | |
Defined in Language.Lexer.Tlex.Machine.State | |
| Ord UUID | |
| Ord UnpackedUUID | |
Defined in Data.UUID.Types.Internal | |
| Ord Integer | |
| Ord Natural | |
| Ord () | |
| Ord Bool | |
| Ord Char | |
| Ord Double | Note that due to the presence of
Also note that, due to the same,
|
| Ord Float | Note that due to the presence of
Also note that, due to the same,
|
| Ord Int | |
| Ord Word | |
| Ord v => Ord (KeyMap v) | |
Defined in Data.Aeson.KeyMap | |
| Ord a => Ord (ZipList a) | Since: base-4.7.0.0 |
| Ord a => Ord (Identity a) | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Ord a => Ord (Down a) | Since: base-4.6.0.0 |
| Ord a => Ord (First a) | Since: base-4.9.0.0 |
| Ord a => Ord (Last a) | Since: base-4.9.0.0 |
| Ord a => Ord (Max a) | Since: base-4.9.0.0 |
| Ord a => Ord (Min a) | Since: base-4.9.0.0 |
| Ord m => Ord (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering # (<) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>) :: WrappedMonoid m -> WrappedMonoid m -> Bool # (>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool # max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # | |
| Ord a => Ord (Dual a) | Since: base-2.1 |
| Ord a => Ord (Product a) | Since: base-2.1 |
| Ord a => Ord (Sum a) | Since: base-2.1 |
| Ord (ForeignPtr a) | Since: base-2.1 |
Defined in GHC.ForeignPtr Methods compare :: ForeignPtr a -> ForeignPtr a -> Ordering # (<) :: ForeignPtr a -> ForeignPtr a -> Bool # (<=) :: ForeignPtr a -> ForeignPtr a -> Bool # (>) :: ForeignPtr a -> ForeignPtr a -> Bool # (>=) :: ForeignPtr a -> ForeignPtr a -> Bool # max :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a # min :: ForeignPtr a -> ForeignPtr a -> ForeignPtr a # | |
| Ord p => Ord (Par1 p) | Since: base-4.7.0.0 |
| Ord (FunPtr a) | |
Defined in GHC.Ptr | |
| Ord (Ptr a) | Since: base-2.1 |
| Integral a => Ord (Ratio a) | Since: base-2.0.1 |
| Ord a => Ord (IntMap a) | |
Defined in Data.IntMap.Internal | |
| Ord a => Ord (Seq a) | |
| Ord a => Ord (ViewL a) | |
Defined in Data.Sequence.Internal | |
| Ord a => Ord (ViewR a) | |
Defined in Data.Sequence.Internal | |
| Ord a => Ord (Set a) | |
| Ord a => Ord (Tree a) | Since: containers-0.6.5 |
| Ord1 f => Ord (Fix f) | |
| (Functor f, Ord1 f) => Ord (Mu f) | |
| (Functor f, Ord1 f) => Ord (Nu f) | |
| Ord a => Ord (DNonEmpty a) | |
Defined in Data.DList.DNonEmpty.Internal | |
| Ord a => Ord (DList a) | |
| Ord (EnumSet k) | |
| Ord a => Ord (Hashed a) | |
Defined in Data.Hashable.Class | |
| Ord a => Ord (Array a) | Lexicographic ordering. Subject to change between major versions. |
Defined in Data.Primitive.Array | |
| (Ord a, Prim a) => Ord (PrimArray a) | Lexicographic ordering. Subject to change between major versions. Since: primitive-0.6.4.0 |
Defined in Data.Primitive.PrimArray | |
| Ord a => Ord (SmallArray a) | Lexicographic ordering. Subject to change between major versions. |
Defined in Data.Primitive.SmallArray Methods compare :: SmallArray a -> SmallArray a -> Ordering # (<) :: SmallArray a -> SmallArray a -> Bool # (<=) :: SmallArray a -> SmallArray a -> Bool # (>) :: SmallArray a -> SmallArray a -> Bool # (>=) :: SmallArray a -> SmallArray a -> Bool # max :: SmallArray a -> SmallArray a -> SmallArray a # min :: SmallArray a -> SmallArray a -> SmallArray a # | |
| Ord g => Ord (StateGen g) | |
Defined in System.Random.Internal | |
| Ord g => Ord (AtomicGen g) | |
Defined in System.Random.Stateful | |
| Ord g => Ord (IOGen g) | |
Defined in System.Random.Stateful | |
| Ord g => Ord (STGen g) | |
Defined in System.Random.Stateful | |
| Ord g => Ord (TGen g) | |
| Ord a => Ord (Maybe a) | |
| Ord flag => Ord (TyVarBndr flag) | |
Defined in Language.Haskell.TH.Syntax Methods compare :: TyVarBndr flag -> TyVarBndr flag -> Ordering # (<) :: TyVarBndr flag -> TyVarBndr flag -> Bool # (<=) :: TyVarBndr flag -> TyVarBndr flag -> Bool # (>) :: TyVarBndr flag -> TyVarBndr flag -> Bool # (>=) :: TyVarBndr flag -> TyVarBndr flag -> Bool # | |
| Ord a => Ord (HashSet a) | |
| Ord a => Ord (Vector a) | |
Defined in Data.Vector | |
| (Prim a, Ord a) => Ord (Vector a) | |
Defined in Data.Vector.Primitive | |
| (Storable a, Ord a) => Ord (Vector a) | |
Defined in Data.Vector.Storable | |
| Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Ord a => Ord (a) | |
| Ord a => Ord [a] | |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
| Ord (Fixed a) | Since: base-2.1 |
| Ord (Proxy s) | Since: base-4.7.0.0 |
| Ord a => Ord (Arg a b) | Since: base-4.9.0.0 |
| Ord (TypeRep a) | Since: base-4.4.0.0 |
| (Ix i, Ord e) => Ord (Array i e) | Since: base-2.1 |
| Ord (U1 p) | Since: base-4.7.0.0 |
| Ord (V1 p) | Since: base-4.9.0.0 |
| (Ord k, Ord v) => Ord (Map k v) | |
| Ord a => Ord (EnumMap k a) | |
Defined in Data.EnumMap.Base | |
| (Ord a, Ord b) => Ord (Either a b) | |
| (Ord a, Ord b) => Ord (These a b) | |
| (Ord a, Ord b) => Ord (Pair a b) | |
Defined in Data.Strict.Tuple | |
| (Ord a, Ord b) => Ord (These a b) | |
| (Ord k, Ord v) => Ord (HashMap k v) | The ordering is total and consistent with the |
Defined in Data.HashMap.Internal | |
| (Ord a, Ord b) => Ord (a, b) | |
| Ord a => Ord (Const a b) | Since: base-4.9.0.0 |
| Ord (f a) => Ord (Alt f a) | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Ord (f p) => Ord (Rec1 f p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord (URec (Ptr ()) p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering # (<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # (>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # | |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Ord (URec Double p) | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering # (<) :: URec Double p -> URec Double p -> Bool # (<=) :: URec Double p -> URec Double p -> Bool # (>) :: URec Double p -> URec Double p -> Bool # (>=) :: URec Double p -> URec Double p -> Bool # | |
| Ord (URec Float p) | |
Defined in GHC.Generics | |
| Ord (URec Int p) | Since: base-4.9.0.0 |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Ord b => Ord (Tagged s b) | |
| (Ord (f a), Ord (g a), Ord a) => Ord (These1 f g a) | |
Defined in Data.Functor.These | |
| (Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a) | |
Defined in Control.Monad.Trans.Error | |
| (Ord a, Ord b, Ord c) => Ord (a, b, c) | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Product f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods compare :: Product f g a -> Product f g a -> Ordering # (<) :: Product f g a -> Product f g a -> Bool # (<=) :: Product f g a -> Product f g a -> Bool # (>) :: Product f g a -> Product f g a -> Bool # (>=) :: Product f g a -> Product f g a -> Bool # | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Sum f g a) | Since: base-4.9.0.0 |
| (Ord (f p), Ord (g p)) => Ord ((f :*: g) 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 | |
| Ord c => Ord (K1 i c p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) | |
Defined in GHC.Classes | |
| (Ord1 f, Ord1 g, Ord a) => Ord (Compose f g a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods compare :: Compose f g a -> Compose f g a -> Ordering # (<) :: Compose f g a -> Compose f g a -> Bool # (<=) :: Compose f g a -> Compose f g a -> Bool # (>) :: Compose f g a -> Compose f g a -> Bool # (>=) :: Compose f g a -> Compose f g a -> Bool # | |
| Ord (f (g p)) => Ord ((f :.: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| Ord (f p) => Ord (M1 i c f p) | Since: base-4.7.0.0 |
| (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering # (<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering # (<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering # (<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering # (<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering # (<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) # | |
| (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | |
Defined in GHC.Classes Methods compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering # (<) :: (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 # (<=) :: (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 # (>) :: (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 # (>=) :: (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 # 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) # 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) # | |
Parsing of Strings, producing values.
Derived instances of Read make the following assumptions, which
derived instances of Show obey:
- If the constructor is defined to be an infix operator, then the
derived
Readinstance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
- If the constructor is defined using record syntax, the derived
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. - The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Read in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5Note that right-associativity of :^: is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefaultWhy do both readsPrec and readPrec exist, and why does GHC opt to
implement readPrec in derived Read instances instead of readsPrec?
The reason is that readsPrec is based on the ReadS type, and although
ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec, on the other hand, is based on a much more efficient ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the RankNTypes language extension. Therefore, readPrec (and its
cousin, readListPrec) are marked as GHC-only. Nevertheless, it is
recommended to use readPrec instead of readsPrec whenever possible
for the efficiency improvements it brings.
As mentioned above, derived Read instances in GHC will implement
readPrec instead of readsPrec. The default implementations of
readsPrec (and its cousin, readList) will simply use readPrec under
the hood. If you are writing a Read instance by hand, it is recommended
to write it like so:
instanceReadT wherereadPrec= ...readListPrec=readListPrecDefault
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> ReadS a |
attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that
showsPrec started with.
Instances
| Read DotNetTime | |
Defined in Data.Aeson.Types.Internal Methods readsPrec :: Int -> ReadS DotNetTime # readList :: ReadS [DotNetTime] # readPrec :: ReadPrec DotNetTime # readListPrec :: ReadPrec [DotNetTime] # | |
| Read Value | |
| Read All | Since: base-2.1 |
| Read Any | Since: base-2.1 |
| Read Version | Since: base-2.1 |
| Read Void | Reading a Since: base-4.8.0.0 |
| Read IntPtr | |
| Read WordPtr | |
| Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # | |
| Read Fixity | Since: base-4.6.0.0 |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # | |
| Read ExitCode | |
| Read Int16 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Read GCDetails | Since: base-4.10.0.0 |
| Read RTSStats | Since: base-4.10.0.0 |
| Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # | |
| Read Word16 | Since: base-2.1 |
| Read Word32 | Since: base-2.1 |
| Read Word64 | Since: base-2.1 |
| Read Word8 | Since: base-2.1 |
| Read Lexeme | Since: base-2.1 |
| Read ByteString | |
Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
| Read ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
| Read ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # | |
| Read IntSet | |
| Read Ordering | Since: base-2.1 |
| Read Scientific | Supports the skipping of parentheses and whitespaces. Example: > read " ( (( -1.0e+3 ) ))" :: Scientific -1000.0 (Note: This |
Defined in Data.Scientific Methods readsPrec :: Int -> ReadS Scientific # readList :: ReadS [Scientific] # readPrec :: ReadPrec Scientific # readListPrec :: ReadPrec [Scientific] # | |
| Read ShortText | |
| Read Month | Read as |
| Read Quarter | Read as |
| Read QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods readsPrec :: Int -> ReadS QuarterOfYear # readList :: ReadS [QuarterOfYear] # | |
| Read DayOfWeek | |
| Read DiffTime | |
| Read NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods readsPrec :: Int -> ReadS NominalDiffTime # readList :: ReadS [NominalDiffTime] # | |
| Read UUID | |
| Read UnpackedUUID | |
| Read Integer | Since: base-2.1 |
| Read Natural | Since: base-4.8.0.0 |
| Read () | Since: base-2.1 |
| 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 Word | Since: base-4.5.0.0 |
| Read v => Read (KeyMap v) | |
| Read a => Read (ZipList a) | Since: base-4.7.0.0 |
| Read a => Read (Complex 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 (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Read a => Read (Last 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 m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] # | |
| Read a => Read (Dual a) | Since: base-2.1 |
| Read a => Read (Product a) | Since: base-2.1 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Read p => Read (Par1 p) | Since: base-4.7.0.0 |
| (Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
| Read vertex => Read (SCC vertex) | Since: containers-0.5.9 |
| Read e => Read (IntMap e) | |
| Read a => Read (Seq a) | |
| Read a => Read (ViewL a) | |
| Read a => Read (ViewR a) | |
| (Read a, Ord a) => Read (Set a) | |
| Read a => Read (Tree a) | |
| Read1 f => Read (Fix f) | |
| (Functor f, Read1 f) => Read (Mu f) | |
| (Functor f, Read1 f) => Read (Nu f) | |
| Read a => Read (DNonEmpty a) | |
| Read a => Read (DList a) | |
| (Enum k, Read k) => Read (EnumSet k) | |
| Read a => Read (Array a) | |
| Read a => Read (SmallArray a) | |
Defined in Data.Primitive.SmallArray Methods readsPrec :: Int -> ReadS (SmallArray a) # readList :: ReadS [SmallArray a] # readPrec :: ReadPrec (SmallArray a) # readListPrec :: ReadPrec [SmallArray a] # | |
| Read a => Read (Maybe a) | |
| (Eq a, Hashable a, Read a) => Read (HashSet a) | |
| Read a => Read (Vector a) | |
| (Read a, Prim a) => Read (Vector a) | |
| (Read a, Storable a) => Read (Vector a) | |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Read a => Read (a) | Since: base-4.15 |
| Read a => Read [a] | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| HasResolution a => Read (Fixed a) | Since: base-4.3.0.0 |
| Read (Proxy t) | Since: base-4.7.0.0 |
| (Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| Read (U1 p) | Since: base-4.9.0.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| (Ord k, Read k, Read e) => Read (Map k e) | |
| (Enum k, Read k, Read a) => Read (EnumMap k a) | |
| (Read a, Read b) => Read (Either a b) | |
| (Read a, Read b) => Read (These a b) | |
| (Read a, Read b) => Read (Pair a b) | |
| (Read a, Read b) => Read (These a b) | |
| (Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) | |
| (Read a, Read b) => Read (a, b) | Since: base-2.1 |
| Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
| Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
| Read b => Read (Tagged s b) | |
| (Read (f a), Read (g a), Read a) => Read (These1 f g a) | |
| (Read e, Read1 m, Read a) => Read (ErrorT e m a) | |
| (Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
| (Read1 f, Read1 g, Read a) => Read (Product f g a) | Since: base-4.9.0.0 |
| (Read1 f, Read1 g, Read a) => Read (Sum f g a) | Since: base-4.9.0.0 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
| (Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
| Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
| (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 |
| (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 |
| (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 | |
class (Num a, Ord a) => Real a where #
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
| Real IntPtr | |
Defined in Foreign.Ptr Methods toRational :: IntPtr -> Rational # | |
| Real WordPtr | |
Defined in Foreign.Ptr Methods toRational :: WordPtr -> Rational # | |
| Real Int16 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int16 -> Rational # | |
| Real Int32 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int32 -> Rational # | |
| Real Int64 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int64 -> Rational # | |
| Real Int8 | Since: base-2.1 |
Defined in GHC.Int Methods toRational :: Int8 -> Rational # | |
| Real Word16 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word16 -> Rational # | |
| Real Word32 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word32 -> Rational # | |
| Real Word64 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word64 -> Rational # | |
| Real Word8 | Since: base-2.1 |
Defined in GHC.Word Methods toRational :: Word8 -> Rational # | |
| Real Scientific | WARNING: Avoid applying |
Defined in Data.Scientific Methods toRational :: Scientific -> Rational # | |
| Real DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime Methods toRational :: DiffTime -> Rational # | |
| Real NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods toRational :: NominalDiffTime -> Rational # | |
| Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
| Real Natural | Since: base-4.8.0.0 |
Defined in GHC.Real Methods toRational :: Natural -> Rational # | |
| Real Int | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Int -> Rational # | |
| Real Word | Since: base-2.1 |
Defined in GHC.Real Methods toRational :: Word -> Rational # | |
| Real a => Real (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods toRational :: Identity a -> Rational # | |
| Real a => Real (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods toRational :: Down a -> Rational # | |
| Integral a => Real (Ratio a) | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Ratio a -> Rational # | |
| HasResolution a => Real (Fixed a) | Since: base-2.1 |
Defined in Data.Fixed Methods toRational :: Fixed a -> Rational # | |
| Real a => Real (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods toRational :: Const a b -> Rational # | |
| Real a => Real (Tagged s a) | |
Defined in Data.Tagged Methods toRational :: Tagged s a -> Rational # | |
class (RealFrac a, Floating a) => RealFloat a where #
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 #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a #
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 #
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 #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b #
truncate xx between zero and x
round :: Integral b => a -> b #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b #
ceiling xx
floor :: Integral b => a -> b #
floor xx
Instances
| RealFrac Scientific | WARNING: the methods of the |
Defined in Data.Scientific Methods properFraction :: Integral b => Scientific -> (b, Scientific) # truncate :: Integral b => Scientific -> b # round :: Integral b => Scientific -> b # ceiling :: Integral b => Scientific -> b # floor :: Integral b => Scientific -> b # | |
| RealFrac DiffTime | |
| RealFrac NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods properFraction :: Integral b => NominalDiffTime -> (b, NominalDiffTime) # truncate :: Integral b => NominalDiffTime -> b # round :: Integral b => NominalDiffTime -> b # ceiling :: Integral b => NominalDiffTime -> b # floor :: Integral b => NominalDiffTime -> b # | |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
| RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
| Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
| HasResolution a => RealFrac (Fixed a) | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
| RealFrac a => RealFrac (Tagged s a) | |
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> a | the value to be converted to a |
| -> ShowS |
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
class Monad m => MonadFail (m :: Type -> Type) where #
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
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
Example
Used in combination with (, <$>)( can be used to build a record.<*>)
>>>data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}
>>>produceFoo :: Applicative f => f Foo
>>>produceBar :: Applicative f => f Bar>>>produceBaz :: Applicative f => f Baz
>>>mkState :: Applicative f => f MyState>>>mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz
(*>) :: f a -> f b -> f b infixl 4 #
Sequence actions, discarding the value of the first argument.
Examples
If used in conjunction with the Applicative instance for Maybe,
you can chain Maybe computations, with a possible "early return"
in case of Nothing.
>>>Just 2 *> Just 3Just 3
>>>Nothing *> Just 3Nothing
Of course a more interesting use case would be to have effectful computations instead of just returning pure values.
>>>import Data.Char>>>import Text.ParserCombinators.ReadP>>>let p = string "my name is " *> munch1 isAlpha <* eof>>>readP_to_S p "my name is Simon"[("Simon","")]
(<*) :: f a -> f b -> f a infixl 4 #
Sequence actions, discarding the value of the second argument.
Instances
| Applicative IResult | |
| Applicative Parser | |
| Applicative Result | |
| 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 Complex | Since: base-4.9.0.0 |
| Applicative Identity | Since: base-4.8.0.0 |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
| Applicative Sum | Since: base-4.8.0.0 |
| Applicative STM | Since: base-4.8.0.0 |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative P | Since: base-4.5.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative Put | |
| Applicative Seq | Since: containers-0.5.4 |
| Applicative Tree | |
| Applicative DNonEmpty | |
Defined in Data.DList.DNonEmpty.Internal | |
| Applicative DList | |
| Applicative IO | Since: base-2.1 |
| Applicative Array | |
| Applicative SmallArray | |
Defined in Data.Primitive.SmallArray Methods pure :: a -> SmallArray a # (<*>) :: SmallArray (a -> b) -> SmallArray a -> SmallArray b # liftA2 :: (a -> b -> c) -> SmallArray a -> SmallArray b -> SmallArray c # (*>) :: SmallArray a -> SmallArray b -> SmallArray b # (<*) :: SmallArray a -> SmallArray b -> SmallArray a # | |
| Applicative Q | |
| Applicative Vector | |
| Applicative Id | |
| Applicative NonEmpty | Since: base-4.9.0.0 |
| Applicative Maybe | Since: base-2.1 |
| Applicative Solo | Since: base-4.15 |
| Applicative [] | Since: base-2.1 |
| Applicative (Parser i) | |
| Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
| Applicative (Either e) | Since: base-3.0 |
| Applicative (StateL s) | Since: base-4.0 |
| Applicative (StateR s) | Since: base-4.0 |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Applicative (SetM s) | |
| Semigroup a => Applicative (These a) | |
| Semigroup a => Applicative (These a) | |
| Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Applicative f, Monad f) => Applicative (WhenMissing f x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
| Applicative (Tagged s) | |
| (Functor m, Monad m) => Applicative (ErrorT e m) | |
Defined in Control.Monad.Trans.Error | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
| (Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| Applicative ((->) r) | Since: base-2.1 |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
| Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
class Foldable (t :: TYPE LiftedRep -> Type) where #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving FoldableA more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure into a monoid, and combine the
results with (. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>)foldMap'
instead.
Examples
Basic usage:
>>>foldMap Sum [1, 3, 5]Sum {getSum = 9}
>>>foldMap Product [1, 3, 5]Product {getProduct = 15}
>>>foldMap (replicate 3) [1, 2, 3][1,1,1,2,2,2,3,3,3]
When a Monoid's ( is lazy in its second argument, <>)foldMap can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>import qualified Data.ByteString.Lazy as L>>>import qualified Data.ByteString.Builder as B>>>let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20>>>let lbs = B.toLazyByteString $ foldMap bld [0..]>>>L.take 64 lbs"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldr1 :: (a -> a -> a) -> t a -> a #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>foldr1 (+) [1..4]10
>>>foldr1 (+) []Exception: Prelude.foldr1: empty list
>>>foldr1 (+) Nothing*** Exception: foldr1: empty structure
>>>foldr1 (-) [1..4]-2
>>>foldr1 (&&) [True, False, True, True]False
>>>foldr1 (||) [False, False, True, True]True
>>>foldr1 (+) [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1f =foldl1f .toList
Examples
Basic usage:
>>>foldl1 (+) [1..4]10
>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list
>>>foldl1 (+) Nothing*** Exception: foldl1: empty structure
>>>foldl1 (-) [1..4]-8
>>>foldl1 (&&) [True, False, True, True]False
>>>foldl1 (||) [False, False, True, True]True
>>>foldl1 (+) [1..]* Hangs forever *
Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.
Examples
Basic usage:
>>>null []True
>>>null [1]False
null is expected to terminate even for infinite structures.
The default implementation terminates provided the structure
is bounded on the left (there is a leftmost element).
>>>null [1..]False
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int. The
default implementation just counts elements starting with the leftmost.
Instances for structures that can compute the element count faster
than via element-by-element counting, should provide a specialised
implementation.
Examples
Basic usage:
>>>length []0
>>>length ['a', 'b', 'c']3>>>length [1..]* Hangs forever *
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
Note: elem is often used in infix form.
Examples
Basic usage:
>>>3 `elem` []False
>>>3 `elem` [1,2]False
>>>3 `elem` [1,2,3,4,5]True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>3 `elem` [1..]True
>>>3 `elem` ([4..] ++ [3])* Hangs forever *
Since: base-4.8.0.0
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>maximum [1..10]10
>>>maximum []*** Exception: Prelude.maximum: empty list
>>>maximum Nothing*** Exception: maximum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>minimum [1..10]1
>>>minimum []*** Exception: Prelude.minimum: empty list
>>>minimum Nothing*** Exception: minimum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
The sum function computes the sum of the numbers of a structure.
Examples
Basic usage:
>>>sum []0
>>>sum [42]42
>>>sum [1..10]55
>>>sum [4.1, 2.0, 1.7]7.8
>>>sum [1..]* Hangs forever *
Since: base-4.8.0.0
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>product []1
>>>product [42]42
>>>product [1..10]3628800
>>>product [4.1, 2.0, 1.7]13.939999999999998
>>>product [1..]* Hangs forever *
Since: base-4.8.0.0
Instances
| Foldable KeyMap | |
Defined in Data.Aeson.KeyMap Methods fold :: Monoid m => KeyMap m -> m # foldMap :: Monoid m => (a -> m) -> KeyMap a -> m # foldMap' :: Monoid m => (a -> m) -> KeyMap a -> m # foldr :: (a -> b -> b) -> b -> KeyMap a -> b # foldr' :: (a -> b -> b) -> b -> KeyMap a -> b # foldl :: (b -> a -> b) -> b -> KeyMap a -> b # foldl' :: (b -> a -> b) -> b -> KeyMap a -> b # foldr1 :: (a -> a -> a) -> KeyMap a -> a # foldl1 :: (a -> a -> a) -> KeyMap a -> a # elem :: Eq a => a -> KeyMap a -> Bool # maximum :: Ord a => KeyMap a -> a # minimum :: Ord a => KeyMap a -> a # | |
| Foldable IResult | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => IResult m -> m # foldMap :: Monoid m => (a -> m) -> IResult a -> m # foldMap' :: Monoid m => (a -> m) -> IResult a -> m # foldr :: (a -> b -> b) -> b -> IResult a -> b # foldr' :: (a -> b -> b) -> b -> IResult a -> b # foldl :: (b -> a -> b) -> b -> IResult a -> b # foldl' :: (b -> a -> b) -> b -> IResult a -> b # foldr1 :: (a -> a -> a) -> IResult a -> a # foldl1 :: (a -> a -> a) -> IResult a -> a # elem :: Eq a => a -> IResult a -> Bool # maximum :: Ord a => IResult a -> a # minimum :: Ord a => IResult a -> a # | |
| Foldable Result | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => Result m -> m # foldMap :: Monoid m => (a -> m) -> Result a -> m # foldMap' :: Monoid m => (a -> m) -> Result a -> m # foldr :: (a -> b -> b) -> b -> Result a -> b # foldr' :: (a -> b -> b) -> b -> Result a -> b # foldl :: (b -> a -> b) -> b -> Result a -> b # foldl' :: (b -> a -> b) -> b -> Result a -> b # foldr1 :: (a -> a -> a) -> Result a -> a # foldl1 :: (a -> a -> a) -> Result a -> a # elem :: Eq a => a -> Result a -> Bool # maximum :: Ord a => Result a -> a # minimum :: Ord a => Result a -> a # | |
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
| Foldable SCC | Since: containers-0.5.9 |
Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m # foldMap :: Monoid m => (a -> m) -> SCC a -> m # foldMap' :: Monoid m => (a -> m) -> SCC a -> m # foldr :: (a -> b -> b) -> b -> SCC a -> b # foldr' :: (a -> b -> b) -> b -> SCC a -> b # foldl :: (b -> a -> b) -> b -> SCC a -> b # foldl' :: (b -> a -> b) -> b -> SCC a -> b # foldr1 :: (a -> a -> a) -> SCC a -> a # foldl1 :: (a -> a -> a) -> SCC a -> a # elem :: Eq a => a -> SCC a -> Bool # maximum :: Ord a => SCC a -> a # | |
| Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
| Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
| Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
| Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
| Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
| Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
| Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
| Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
| Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
| Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
| Foldable DNonEmpty | |
Defined in Data.DList.DNonEmpty.Internal Methods fold :: Monoid m => DNonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldr :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldl :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldr1 :: (a -> a -> a) -> DNonEmpty a -> a # foldl1 :: (a -> a -> a) -> DNonEmpty a -> a # toList :: DNonEmpty a -> [a] # length :: DNonEmpty a -> Int # elem :: Eq a => a -> DNonEmpty a -> Bool # maximum :: Ord a => DNonEmpty a -> a # minimum :: Ord a => DNonEmpty a -> a # | |
| Foldable DList | |
Defined in Data.DList.Internal Methods fold :: Monoid m => DList m -> m # foldMap :: Monoid m => (a -> m) -> DList a -> m # foldMap' :: Monoid m => (a -> m) -> DList a -> m # foldr :: (a -> b -> b) -> b -> DList a -> b # foldr' :: (a -> b -> b) -> b -> DList a -> b # foldl :: (b -> a -> b) -> b -> DList a -> b # foldl' :: (b -> a -> b) -> b -> DList a -> b # foldr1 :: (a -> a -> a) -> DList a -> a # foldl1 :: (a -> a -> a) -> DList a -> a # elem :: Eq a => a -> DList a -> Bool # maximum :: Ord a => DList a -> a # minimum :: Ord a => DList a -> a # | |
| Foldable Hashed | |
Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> m # foldMap :: Monoid m => (a -> m) -> Hashed a -> m # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m # foldr :: (a -> b -> b) -> b -> Hashed a -> b # foldr' :: (a -> b -> b) -> b -> Hashed a -> b # foldl :: (b -> a -> b) -> b -> Hashed a -> b # foldl' :: (b -> a -> b) -> b -> Hashed a -> b # foldr1 :: (a -> a -> a) -> Hashed a -> a # foldl1 :: (a -> a -> a) -> Hashed a -> a # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # | |
| Foldable Array | |
Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> m # foldMap' :: Monoid m => (a -> m) -> Array a -> m # foldr :: (a -> b -> b) -> b -> Array a -> b # foldr' :: (a -> b -> b) -> b -> Array a -> b # foldl :: (b -> a -> b) -> b -> Array a -> b # foldl' :: (b -> a -> b) -> b -> Array a -> b # foldr1 :: (a -> a -> a) -> Array a -> a # foldl1 :: (a -> a -> a) -> Array a -> a # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # | |
| Foldable SmallArray | |
Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m # foldMap' :: Monoid m => (a -> m) -> SmallArray a -> m # foldr :: (a -> b -> b) -> b -> SmallArray a -> b # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b # foldl :: (b -> a -> b) -> b -> SmallArray a -> b # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b # foldr1 :: (a -> a -> a) -> SmallArray a -> a # foldl1 :: (a -> a -> a) -> SmallArray a -> a # toList :: SmallArray a -> [a] # null :: SmallArray a -> Bool # length :: SmallArray a -> Int # elem :: Eq a => a -> SmallArray a -> Bool # maximum :: Ord a => SmallArray a -> a # minimum :: Ord a => SmallArray a -> a # sum :: Num a => SmallArray a -> a # product :: Num a => SmallArray a -> a # | |
| Foldable Maybe | |
Defined in Data.Strict.Maybe Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Bag Source # | |
Defined in Language.Lexer.Tlex.Data.Bag Methods fold :: Monoid m => Bag m -> m # foldMap :: Monoid m => (a -> m) -> Bag a -> m # foldMap' :: Monoid m => (a -> m) -> Bag a -> m # foldr :: (a -> b -> b) -> b -> Bag a -> b # foldr' :: (a -> b -> b) -> b -> Bag a -> b # foldl :: (b -> a -> b) -> b -> Bag a -> b # foldl' :: (b -> a -> b) -> b -> Bag a -> b # foldr1 :: (a -> a -> a) -> Bag a -> a # foldl1 :: (a -> a -> a) -> Bag a -> a # elem :: Eq a => a -> Bag a -> Bool # maximum :: Ord a => Bag a -> a # | |
| Foldable StateArray Source # | |
Defined in Language.Lexer.Tlex.Machine.State Methods fold :: Monoid m => StateArray m -> m # foldMap :: Monoid m => (a -> m) -> StateArray a -> m # foldMap' :: Monoid m => (a -> m) -> StateArray a -> m # foldr :: (a -> b -> b) -> b -> StateArray a -> b # foldr' :: (a -> b -> b) -> b -> StateArray a -> b # foldl :: (b -> a -> b) -> b -> StateArray a -> b # foldl' :: (b -> a -> b) -> b -> StateArray a -> b # foldr1 :: (a -> a -> a) -> StateArray a -> a # foldl1 :: (a -> a -> a) -> StateArray a -> a # toList :: StateArray a -> [a] # null :: StateArray a -> Bool # length :: StateArray a -> Int # elem :: Eq a => a -> StateArray a -> Bool # maximum :: Ord a => StateArray a -> a # minimum :: Ord a => StateArray a -> a # sum :: Num a => StateArray a -> a # product :: Num a => StateArray a -> a # | |
| Foldable HashSet | |
Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # | |
| Foldable Vector | |
Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldMap' :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable Methods fold :: Monoid m => Solo m -> m # foldMap :: Monoid m => (a -> m) -> Solo a -> m # foldMap' :: Monoid m => (a -> m) -> Solo a -> m # foldr :: (a -> b -> b) -> b -> Solo a -> b # foldr' :: (a -> b -> b) -> b -> Solo a -> b # foldl :: (b -> a -> b) -> b -> Solo a -> b # foldl' :: (b -> a -> b) -> b -> Solo a -> b # foldr1 :: (a -> a -> a) -> Solo a -> a # foldl1 :: (a -> a -> a) -> Solo a -> a # elem :: Eq a => a -> Solo a -> Bool # maximum :: Ord a => Solo a -> a # | |
| Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
| Foldable (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
| Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
| Foldable (U1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
| Foldable (UAddr :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # | |
| Foldable (UChar :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
| Foldable (UDouble :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
| Foldable (UFloat :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
| Foldable (UInt :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
| Foldable (UWord :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
| Foldable (V1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
| Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
| Foldable (EnumMap k) | |
Defined in Data.EnumMap.Base Methods fold :: Monoid m => EnumMap k m -> m # foldMap :: Monoid m => (a -> m) -> EnumMap k a -> m # foldMap' :: Monoid m => (a -> m) -> EnumMap k a -> m # foldr :: (a -> b -> b) -> b -> EnumMap k a -> b # foldr' :: (a -> b -> b) -> b -> EnumMap k a -> b # foldl :: (b -> a -> b) -> b -> EnumMap k a -> b # foldl' :: (b -> a -> b) -> b -> EnumMap k a -> b # foldr1 :: (a -> a -> a) -> EnumMap k a -> a # foldl1 :: (a -> a -> a) -> EnumMap k a -> a # toList :: EnumMap k a -> [a] # length :: EnumMap k a -> Int # elem :: Eq a => a -> EnumMap k a -> Bool # maximum :: Ord a => EnumMap k a -> a # minimum :: Ord a => EnumMap k a -> a # | |
| Foldable (Either e) | |
Defined in Data.Strict.Either Methods fold :: Monoid m => Either e m -> m # foldMap :: Monoid m => (a -> m) -> Either e a -> m # foldMap' :: Monoid m => (a -> m) -> Either e a -> m # foldr :: (a -> b -> b) -> b -> Either e a -> b # foldr' :: (a -> b -> b) -> b -> Either e a -> b # foldl :: (b -> a -> b) -> b -> Either e a -> b # foldl' :: (b -> a -> b) -> b -> Either e a -> b # foldr1 :: (a -> a -> a) -> Either e a -> a # foldl1 :: (a -> a -> a) -> Either e a -> a # elem :: Eq a => a -> Either e a -> Bool # maximum :: Ord a => Either e a -> a # minimum :: Ord a => Either e a -> a # | |
| Foldable (These a) | |
Defined in Data.Strict.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
| Foldable (Pair e) | |
Defined in Data.Strict.Tuple Methods fold :: Monoid m => Pair e m -> m # foldMap :: Monoid m => (a -> m) -> Pair e a -> m # foldMap' :: Monoid m => (a -> m) -> Pair e a -> m # foldr :: (a -> b -> b) -> b -> Pair e a -> b # foldr' :: (a -> b -> b) -> b -> Pair e a -> b # foldl :: (b -> a -> b) -> b -> Pair e a -> b # foldl' :: (b -> a -> b) -> b -> Pair e a -> b # foldr1 :: (a -> a -> a) -> Pair e a -> a # foldl1 :: (a -> a -> a) -> Pair e a -> a # elem :: Eq a => a -> Pair e a -> Bool # maximum :: Ord a => Pair e a -> a # minimum :: Ord a => Pair e a -> a # | |
| Foldable (These a) | |
Defined in Data.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
| Foldable (HashMap k) | |
Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # | |
| Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
| Foldable (Const m :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
| Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
| Foldable (Tagged s) | |
Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m # foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m # foldr :: (a -> b -> b) -> b -> Tagged s a -> b # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b # foldl :: (b -> a -> b) -> b -> Tagged s a -> b # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b # foldr1 :: (a -> a -> a) -> Tagged s a -> a # foldl1 :: (a -> a -> a) -> Tagged s a -> a # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # | |
| (Foldable f, Foldable g) => Foldable (These1 f g) | |
Defined in Data.Functor.These Methods fold :: Monoid m => These1 f g m -> m # foldMap :: Monoid m => (a -> m) -> These1 f g a -> m # foldMap' :: Monoid m => (a -> m) -> These1 f g a -> m # foldr :: (a -> b -> b) -> b -> These1 f g a -> b # foldr' :: (a -> b -> b) -> b -> These1 f g a -> b # foldl :: (b -> a -> b) -> b -> These1 f g a -> b # foldl' :: (b -> a -> b) -> b -> These1 f g a -> b # foldr1 :: (a -> a -> a) -> These1 f g a -> a # foldl1 :: (a -> a -> a) -> These1 f g a -> a # toList :: These1 f g a -> [a] # null :: These1 f g a -> Bool # length :: These1 f g a -> Int # elem :: Eq a => a -> These1 f g a -> Bool # maximum :: Ord a => These1 f g a -> a # minimum :: Ord a => These1 f g a -> a # | |
| Foldable f => Foldable (ErrorT e f) | |
Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # | |
| (Foldable f, Foldable g) => Foldable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # length :: (f :*: g) a -> Int # elem :: Eq a => a -> (f :*: g) a -> Bool # maximum :: Ord a => (f :*: g) a -> a # minimum :: Ord a => (f :*: g) a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # | |
| Foldable (K1 i c :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # | |
| (Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # | |
| Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # | |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where #
Functors representing data structures that can be transformed to
structures of the same shape by performing an Applicative (or,
therefore, Monad) action on each element from left to right.
A more detailed description of what same shape means, the various methods, how traversals are constructed, and example advanced use-cases can be found in the Overview section of Data.Traversable.
For the class laws see the Laws section of Data.Traversable.
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>traverse Just [1,2,3,4]Just [1,2,3,4]
>>>traverse id [Right 1, Right 2, Right 3, Right 4]Right [1,2,3,4]
In the next examples, we show that Nothing and Left values short
circuit the created structure.
>>>traverse (const Nothing) [1,2,3,4]Nothing
>>>traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]Nothing
>>>traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]Left 0
sequenceA :: Applicative f => t (f a) -> f (t a) #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>sequenceA [Just 1, Just 2, Just 3]Just [1,2,3]
>>>sequenceA [Right 1, Right 2, Right 3]Right [1,2,3]
The next two example show Nothing and Just will short circuit
the resulting structure if present in the input. For more context,
check the Traversable instances for Either and Maybe.
>>>sequenceA [Just 1, Just 2, Just 3, Nothing]Nothing
>>>sequenceA [Right 1, Right 2, Right 3, Left 4]Left 4
mapM :: Monad m => (a -> m b) -> t a -> m (t b) #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
Examples
sequence :: Monad m => t (m a) -> m (t a) #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence are isomorphic.
>>>sequence $ Right [1,2,3,4][Right 1,Right 2,Right 3,Right 4]
>>>sequence $ [Right 1,Right 2,Right 3,Right 4]Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence.
>>>sequence $ Left [1,2,3,4]Left [1,2,3,4]
>>>sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]Left 0
Instances
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Instances
| Semigroup More | |
| Semigroup All | Since: base-4.9.0.0 |
| Semigroup Any | Since: base-4.9.0.0 |
| Semigroup Void | Since: base-4.9.0.0 |
| Semigroup Builder | |
| Semigroup ByteString | |
Defined in Data.ByteString.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString # | |
| Semigroup ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods (<>) :: ByteString -> ByteString -> ByteString # sconcat :: NonEmpty ByteString -> ByteString # stimes :: Integral b => b -> ByteString -> ByteString # | |
| Semigroup ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods (<>) :: ShortByteString -> ShortByteString -> ShortByteString # sconcat :: NonEmpty ShortByteString -> ShortByteString # stimes :: Integral b => b -> ShortByteString -> ShortByteString # | |
| Semigroup IntSet | Since: containers-0.5.7 |
| Semigroup ByteArray | |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Semigroup Doc | |
| Semigroup ShortText | |
| Semigroup () | Since: base-4.9.0.0 |
| Semigroup (KeyMap v) | |
| Semigroup (IResult a) | |
| Semigroup (Parser a) | |
| Semigroup (Result a) | |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.11.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.11.0.0 |
| Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min 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 # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # | |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Semigroup (Endo a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Semigroup p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
| Semigroup (IntMap a) | Since: containers-0.5.7 |
| Semigroup (Seq a) | Since: containers-0.5.7 |
| Semigroup (MergeSet a) | |
| Ord a => Semigroup (Set a) | Since: containers-0.5.7 |
| Semigroup (DNonEmpty a) | |
| Semigroup (DList a) | |
| Semigroup (EnumSet k) | |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Semigroup (Doc a) | |
| Semigroup (Array a) | Since: primitive-0.6.3.0 |
| Semigroup (PrimArray a) | Since: primitive-0.6.4.0 |
| Semigroup (SmallArray a) | Since: primitive-0.6.3.0 |
Defined in Data.Primitive.SmallArray Methods (<>) :: SmallArray a -> SmallArray a -> SmallArray a # sconcat :: NonEmpty (SmallArray a) -> SmallArray a # stimes :: Integral b => b -> SmallArray a -> SmallArray a # | |
| Semigroup a => Semigroup (Maybe a) | |
| Semigroup a => Semigroup (Q a) | Since: template-haskell-2.17.0.0 |
| Semigroup (Bag a) Source # | |
| Enum a => Semigroup (SymEnumSet a) Source # | |
Defined in Language.Lexer.Tlex.Data.SymEnumSet Methods (<>) :: SymEnumSet a -> SymEnumSet a -> SymEnumSet a # sconcat :: NonEmpty (SymEnumSet a) -> SymEnumSet a # stimes :: Integral b => b -> SymEnumSet a -> SymEnumSet a # | |
| Enum e => Semigroup (Pattern e) Source # | |
| (Hashable a, Eq a) => Semigroup (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
| Semigroup (Vector a) | |
| Prim a => Semigroup (Vector a) | |
| Storable a => Semigroup (Vector a) | |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (a) | Since: base-4.15 |
| Semigroup [a] | Since: base-4.9.0.0 |
| Semigroup (Parser i a) | |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Semigroup (U1 p) | Since: base-4.12.0.0 |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| Ord k => Semigroup (Map k v) | |
| Semigroup (EnumMap k a) | |
| Semigroup (Either a b) | |
| (Semigroup a, Semigroup b) => Semigroup (These a b) | |
| (Semigroup a, Semigroup b) => Semigroup (Pair a b) | |
| (Semigroup a, Semigroup b) => Semigroup (These a b) | |
| (Eq k, Hashable k) => Semigroup (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Tagged s a) | |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
| (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) | Since: base-4.16.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f (g a)) => Semigroup (Compose f g a) | Since: base-4.16.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
class Semigroup a => Monoid a where #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
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 = (<>)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 More | |
| Monoid All | Since: base-2.1 |
| Monoid Any | Since: base-2.1 |
| Monoid Builder | |
| Monoid ByteString | |
Defined in Data.ByteString.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
| Monoid ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString # mappend :: ByteString -> ByteString -> ByteString # mconcat :: [ByteString] -> ByteString # | |
| Monoid ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods mappend :: ShortByteString -> ShortByteString -> ShortByteString # mconcat :: [ShortByteString] -> ShortByteString # | |
| Monoid IntSet | |
| Monoid ByteArray | |
| Monoid Ordering | Since: base-2.1 |
| Monoid Doc | |
| Monoid ShortText | |
| Monoid () | Since: base-2.1 |
| Monoid (KeyMap v) | |
| Monoid (IResult a) | |
| Monoid (Parser a) | |
| Monoid (Result a) | |
| Monoid a => Monoid (Identity a) | Since: base-4.9.0.0 |
| Ord a => Monoid (Max a) | Since: base-4.8.0.0 |
| Ord a => Monoid (Min a) | Since: base-4.8.0.0 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| (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 m => Monoid (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m # | |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Monoid (Endo a) | Since: base-2.1 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Monoid p => Monoid (Par1 p) | Since: base-4.12.0.0 |
| Monoid (IntMap a) | |
| Monoid (Seq a) | |
| Monoid (MergeSet a) | |
| Ord a => Monoid (Set a) | |
| Monoid (DList a) | |
| Monoid (EnumSet k) | |
| Monoid a => Monoid (IO a) | Since: base-4.9.0.0 |
| Monoid (Doc a) | |
| Monoid (Array a) | |
| Monoid (PrimArray a) | Since: primitive-0.6.4.0 |
| Monoid (SmallArray a) | |
Defined in Data.Primitive.SmallArray Methods mempty :: SmallArray a # mappend :: SmallArray a -> SmallArray a -> SmallArray a # mconcat :: [SmallArray a] -> SmallArray a # | |
| Semigroup a => Monoid (Maybe a) | |
| Monoid a => Monoid (Q a) | Since: template-haskell-2.17.0.0 |
| Monoid (Bag a) Source # | |
| Enum a => Monoid (SymEnumSet a) Source # | |
Defined in Language.Lexer.Tlex.Data.SymEnumSet Methods mempty :: SymEnumSet a # mappend :: SymEnumSet a -> SymEnumSet a -> SymEnumSet a # mconcat :: [SymEnumSet a] -> SymEnumSet a # | |
| Enum e => Monoid (Pattern e) Source # | |
| (Hashable a, Eq a) => Monoid (HashSet a) | \(O(n+m)\) To obtain good performance, the smaller set must be presented as the first argument. Examples
|
| Monoid (Vector a) | |
| Prim a => Monoid (Vector a) | |
| Storable a => Monoid (Vector a) | |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Monoid a => Monoid (a) | Since: base-4.15 |
| Monoid [a] | Since: base-2.1 |
| Monoid (Parser i a) | |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Monoid (U1 p) | Since: base-4.12.0.0 |
| Ord k => Monoid (Map k v) | |
| Monoid (EnumMap k a) | |
| (Monoid a, Monoid b) => Monoid (Pair a b) | |
| (Eq k, Hashable k) => Monoid (HashMap k v) | If a key occurs in both maps, the mapping from the first will be the mapping in the result. Examples
|
| Monoid b => Monoid (a -> b) | Since: base-2.1 |
| (Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1 |
| Monoid a => Monoid (Const a b) | Since: base-4.9.0.0 |
| Alternative f => Monoid (Alt f a) | Since: base-4.8.0.0 |
| Monoid (f p) => Monoid (Rec1 f p) | Since: base-4.12.0.0 |
| (Semigroup a, Monoid a) => Monoid (Tagged s a) | |
| (Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1 |
| (Monoid (f a), Monoid (g a)) => Monoid (Product f g a) | Since: base-4.16.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| Monoid c => Monoid (K1 i c p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1 |
| Monoid (f (g a)) => Monoid (Compose f g a) | Since: base-4.16.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) | Since: base-4.12.0.0 |
| Monoid (f p) => Monoid (M1 i c f p) | Since: base-4.12.0.0 |
| (Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1 |
Instances
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
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
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
| Storable Float | Since: base-2.1 |
| Floating Float | Since: base-2.1 |
| RealFloat Float | Since: base-2.1 |
Defined in GHC.Float Methods floatRadix :: Float -> Integer # floatDigits :: Float -> Int # floatRange :: Float -> (Int, Int) # decodeFloat :: Float -> (Integer, Int) # encodeFloat :: Integer -> Int -> Float # significand :: Float -> Float # scaleFloat :: Int -> Float -> Float # isInfinite :: Float -> Bool # isDenormalized :: Float -> Bool # isNegativeZero :: Float -> Bool # | |
| Read Float | Since: base-2.1 |
| Eq Float | Note that due to the presence of
Also note that
|
| Ord Float | Note that due to the presence of
Also note that, due to the same,
|
| Hashable Float | Note: prior to The Since: hashable-1.3.0.0 |
Defined in Data.Hashable.Class | |
| Prim Float | |
Defined in Data.Primitive.Types Methods alignment# :: Float -> Int# # indexByteArray# :: ByteArray# -> Int# -> Float # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Float #) # writeByteArray# :: MutableByteArray# s -> Int# -> Float -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Float -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Float # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Float #) # writeOffAddr# :: Addr# -> Int# -> Float -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Float -> State# s -> State# s # | |
| UniformRange Float | |
Defined in System.Random.Internal | |
| Unbox Float | |
Defined in Data.Vector.Unboxed.Base | |
| Lift Float | |
| Vector Vector Float | |
Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s Float -> ST s (Vector Float) # basicUnsafeThaw :: Vector Float -> ST s (Mutable Vector s Float) # basicLength :: Vector Float -> Int # basicUnsafeSlice :: Int -> Int -> Vector Float -> Vector Float # basicUnsafeIndexM :: Vector Float -> Int -> Box Float # basicUnsafeCopy :: Mutable Vector s Float -> Vector Float -> ST s () # | |
| MVector MVector Float | |
Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s Float -> Int # basicUnsafeSlice :: Int -> Int -> MVector s Float -> MVector s Float # basicOverlaps :: MVector s Float -> MVector s Float -> Bool # basicUnsafeNew :: Int -> ST s (MVector s Float) # basicInitialize :: MVector s Float -> ST s () # basicUnsafeReplicate :: Int -> Float -> ST s (MVector s Float) # basicUnsafeRead :: MVector s Float -> Int -> ST s Float # basicUnsafeWrite :: MVector s Float -> Int -> Float -> ST s () # basicClear :: MVector s Float -> ST s () # basicSet :: MVector s Float -> Float -> ST s () # basicUnsafeCopy :: MVector s Float -> MVector s Float -> ST s () # basicUnsafeMove :: MVector s Float -> MVector s Float -> ST s () # basicUnsafeGrow :: MVector s Float -> Int -> ST s (MVector s Float) # | |
| Generic1 (URec Float :: k -> Type) | |
| Foldable (UFloat :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
| Traversable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
| Functor (URec Float :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
| Generic (URec Float p) | |
| Show (URec Float p) | |
| Eq (URec Float p) | |
| Ord (URec Float p) | |
Defined in GHC.Generics | |
| newtype Vector Float | |
| data URec Float (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| newtype MVector s Float | |
| type Rep1 (URec Float :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep (URec Float p) | |
Defined in GHC.Generics | |
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
Arbitrary precision integers. In contrast with fixed-size integral types
such as Int, the Integer type represents the entire infinite range of
integers.
Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.
If the value is small (fit into an Int), IS constructor is used.
Otherwise Integer and IN constructors are used to store a BigNat
representing respectively the positive or the negative value magnitude.
Invariant: Integer and IN are used iff value doesn't fit in IS
Instances
| Enum Integer | Since: base-2.1 |
| Ix Integer | Since: base-2.1 |
Defined in GHC.Ix | |
| Num Integer | Since: base-2.1 |
| Read Integer | Since: base-2.1 |
| Integral Integer | Since: base-2.0.1 |
Defined in GHC.Real | |
| Real Integer | Since: base-2.0.1 |
Defined in GHC.Real Methods toRational :: Integer -> Rational # | |
| Show Integer | Since: base-2.1 |
| Eq Integer | |
| Ord Integer | |
| Hashable Integer | |
Defined in Data.Hashable.Class | |
| UniformRange Integer | |
Defined in System.Random.Internal | |
| Lift Integer | |
The Maybe type encapsulates an optional value. A value of type
Maybe aa (represented as Just aNothing). Using Maybe is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as error.
The Maybe type is also a monad. It is a simple kind of error
monad, where all errors are represented by Nothing. A richer
error monad can be built using the Either type.
Instances
| MonadFail Maybe | Since: base-4.9.0.0 |
Defined in Control.Monad.Fail | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Eq1 Maybe | Since: base-4.9.0.0 |
| Ord1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read1 Maybe | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Show1 Maybe | Since: base-4.9.0.0 |
| Traversable Maybe | Since: base-2.1 |
| Alternative Maybe | Since: base-2.1 |
| Applicative Maybe | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| MonadPlus Maybe | Since: base-2.1 |
| Hashable1 Maybe | |
Defined in Data.Hashable.Class | |
| Generic1 Maybe | |
| Lift a => Lift (Maybe a :: Type) | |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Generic (Maybe a) | |
| SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) | |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Show a => Show (Maybe a) | Since: base-2.1 |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Hashable a => Hashable (Maybe a) | |
Defined in Data.Hashable.Class | |
| SingI ('Nothing :: Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| SingI a2 => SingI ('Just a2 :: Maybe a1) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| type Rep1 Maybe | Since: base-4.6.0.0 |
| type DemoteRep (Maybe a) | |
Defined in GHC.Generics | |
| type Rep (Maybe a) | Since: base-4.6.0.0 |
Defined in GHC.Generics | |
| data Sing (b :: Maybe a) | |
Instances
| Monoid Ordering | Since: base-2.1 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Bounded Ordering | Since: base-2.1 |
| Enum Ordering | Since: base-2.1 |
| Generic Ordering | |
| Ix Ordering | Since: base-2.1 |
Defined in GHC.Ix Methods range :: (Ordering, Ordering) -> [Ordering] # index :: (Ordering, Ordering) -> Ordering -> Int # unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int # inRange :: (Ordering, Ordering) -> Ordering -> Bool # rangeSize :: (Ordering, Ordering) -> Int # unsafeRangeSize :: (Ordering, Ordering) -> Int # | |
| Read Ordering | Since: base-2.1 |
| Show Ordering | Since: base-2.1 |
| Eq Ordering | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Hashable Ordering | |
Defined in Data.Hashable.Class | |
| type Rep Ordering | Since: base-4.6.0.0 |
A value of type IO aa.
There is really only one way to "perform" an I/O action: bind it to
Main.main in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the IO monad and called
at some point, directly or indirectly, from Main.main.
IO is a monad, so IO actions can be combined using either the do-notation
or the >> and >>= operations from the Monad
class.
Instances
Instances
The Either type represents values with two possibilities: a value of
type Either a bLeft aRight b
The Either type is sometimes used to represent a value which is
either correct or an error; by convention, the Left constructor is
used to hold an error value and the Right constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type Either String IntString or an Int. The Left constructor can be used only on
Strings, and the Right constructor can be used only on Ints:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The fmap from our Functor instance will ignore Left values, but
will apply the supplied function to values contained in a Right:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The Monad instance for Either allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int from a Char, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both '1' and '2' can be
parsed as Ints.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse 'm' as an Int will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Eq2 Either | Since: base-4.9.0.0 |
| Ord2 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 Methods liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Either a b) # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] # | |
| Show2 Either | Since: base-4.9.0.0 |
| Hashable2 Either | |
Defined in Data.Hashable.Class | |
| Generic1 (Either a :: Type -> Type) | |
| (Lift a, Lift b) => Lift (Either a b :: Type) | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
| Eq a => Eq1 (Either a) | Since: base-4.9.0.0 |
| Ord a => Ord1 (Either a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read a => Read1 (Either a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Either a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] # | |
| Show a => Show1 (Either a) | Since: base-4.9.0.0 |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable | |
| Applicative (Either e) | Since: base-3.0 |
| Functor (Either a) | Since: base-3.0 |
| Monad (Either e) | Since: base-4.4.0.0 |
| Hashable a => Hashable1 (Either a) | |
Defined in Data.Hashable.Class | |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Generic (Either a b) | |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
| (Hashable a, Hashable b) => Hashable (Either a b) | |
Defined in Data.Hashable.Class | |
| type Rep1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
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) | Since: base-4.6.0.0 |
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))) | |
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
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]
read :: Read a => String -> a #
The read function reads input from a string, which must be
completely consumed by the input process. read fails with an error if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe or readEither for safe alternatives.
>>>read "123" :: Int123
>>>read "hello" :: Int*** Exception: Prelude.read: no parse
writeFile :: FilePath -> String -> IO () #
The computation writeFile file str function writes the string str,
to the file file.
readFile :: FilePath -> IO String #
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.
interact :: (String -> String) -> IO () #
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.
getContents :: IO String #
The getContents operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents stdin).
appendFile :: FilePath -> String -> IO () #
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]])
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.
type IOError = IOException #
The Haskell 2010 type for exceptions in the IO monad.
Any I/O operation may raise an IOException 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.
userError :: String -> IOError #
Construct an IOException 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)
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
sequence_ is just like sequenceA_, but specialised to monadic
actions.
or :: Foldable t => t Bool -> Bool #
or returns the disjunction of a container of Bools. For the
result to be False, the container must be finite; True, however,
results from a True value finitely far from the left end.
Examples
Basic usage:
>>>or []False
>>>or [True]True
>>>or [False]False
>>>or [True, True, False]True
>>>or (True : repeat False) -- Infinite list [True,False,False,False,...True
>>>or (repeat False)* Hangs forever *
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #
notElem is the negation of elem.
Examples
Basic usage:
>>>3 `notElem` []True
>>>3 `notElem` [1,2]True
>>>3 `notElem` [1,2,3,4,5]False
For infinite structures, notElem terminates if the value exists at a
finite distance from the left side of the structure:
>>>3 `notElem` [1..]False
>>>3 `notElem` ([4..] ++ [3])* Hangs forever *
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>concatMap (take 3) [[1..], [10..], [100..], [1000..]][1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>concatMap (take 3) (Just [1..])[1,2,3]
concat :: Foldable t => t [a] -> [a] #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>concat (Just [1, 2, 3])[1,2,3]
>>>concat (Left 42)[]
>>>concat [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>any (> 3) []False
>>>any (> 3) [1,2]False
>>>any (> 3) [1,2,3,4,5]True
>>>any (> 3) [1..]True
>>>any (> 3) [0, -1..]* Hangs forever *
and :: Foldable t => t Bool -> Bool #
and returns the conjunction of a container of Bools. For the
result to be True, the container must be finite; False, however,
results from a False value finitely far from the left end.
Examples
Basic usage:
>>>and []True
>>>and [True]True
>>>and [False]False
>>>and [True, True, False]False
>>>and (False : repeat True) -- Infinite list [False,True,True,True,...False
>>>and (repeat True)* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>all (> 3) []True
>>>all (> 3) [1,2]False
>>>all (> 3) [1,2,3,4,5]False
>>>all (> 3) [1..]False
>>>all (> 3) [4..]* Hangs forever *
words breaks a string up into a list of words, which were delimited
by white space.
>>>words "Lorem ipsum\ndolor"["Lorem","ipsum","dolor"]
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 ss.
either :: (a -> c) -> (b -> c) -> Either a b -> c #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
The lex function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space, lex returns a
single successful `lexeme' consisting of the empty string. (Thus
lex "" = [("","")]lex fails (i.e. returns []).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
lcm :: Integral a => a -> a -> a #
lcm x yx and y divide.
gcd :: Integral a => a -> a -> a #
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #
raise a number to an integral power
showString :: String -> ShowS #
utility function converting a String to a show function that
simply prepends the string unchanged.
utility function converting a Char to a show function that
simply prepends the character unchanged.
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] #
The zipWith3 function takes a function which combines three
elements, as well as three lists and returns a list of the function applied
to corresponding elements, analogous to zipWith.
It is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
zipWith3 (,,) xs ys zs == zip3 xs ys zs zipWith3 f [x1,x2,x3..] [y1,y2,y3..] [z1,z2,z3..] == [f x1 y1 z1, f x2 y2 z2, f x3 y3 z3..]
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] #
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example, zipWith (+)
>>>zipWith (+) [1, 2, 3] [4, 5, 6][5,7,9]
zipWith is right-lazy:
>>>let f = undefined>>>zipWith f [] undefined[]
zipWith is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
unzip :: [(a, b)] -> ([a], [b]) #
unzip transforms a list of pairs into a list of first components
and a list of second components.
>>>unzip []([],[])>>>unzip [(1, 'a'), (2, 'b')]([1,2],"ab")
takeWhile :: (a -> Bool) -> [a] -> [a] #
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p.
>>>takeWhile (< 3) [1,2,3,4,1,2,3,4][1,2]>>>takeWhile (< 9) [1,2,3][1,2,3]>>>takeWhile (< 0) [1,2,3][]
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.
splitAt :: Int -> [a] -> ([a], [a]) #
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 ( when take n xs, drop n xs)n is not _|_
(splitAt _|_ xs = _|_).
splitAt is an instance of the more general genericSplitAt,
in which n may be of any integral type.
span :: (a -> Bool) -> [a] -> ([a], [a]) #
span, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
>>>span (< 3) [1,2,3,4,1,2,3,4]([1,2],[3,4,1,2,3,4])>>>span (< 9) [1,2,3]([1,2,3],[])>>>span (< 0) [1,2,3]([],[1,2,3])
scanr1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanr1 is a variant of scanr that has no starting
value argument.
>>>scanr1 (+) [1..4][10,9,7,4]>>>scanr1 (+) [][]>>>scanr1 (-) [1..4][-2,3,-1,4]>>>scanr1 (&&) [True, False, True, True][False,False,True,True]>>>scanr1 (||) [True, True, False, False][True,True,False,False]>>>force $ scanr1 (+) [1..]*** Exception: stack overflow
scanr :: (a -> b -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>scanr (+) 0 [1..4][10,9,7,4,0]>>>scanr (+) 42 [][42]>>>scanr (-) 100 [1..4][98,-97,99,-96,100]>>>scanr (\nextChar reversedString -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["abcdfoo","bcdfoo","cdfoo","dfoo","foo"]>>>force $ scanr (+) 0 [1..]*** Exception: stack overflow
scanl1 :: (a -> a -> a) -> [a] -> [a] #
\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>scanl1 (+) [1..4][1,3,6,10]>>>scanl1 (+) [][]>>>scanl1 (-) [1..4][1,-1,-4,-8]>>>scanl1 (&&) [True, False, True, True][True,False,False,False]>>>scanl1 (||) [False, False, True, True][False,False,True,True]>>>scanl1 (+) [1..]* Hangs forever *
scanl :: (b -> a -> b) -> b -> [a] -> [b] #
\(\mathcal{O}(n)\). 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
>>>scanl (+) 0 [1..4][0,1,3,6,10]>>>scanl (+) 42 [][42]>>>scanl (-) 100 [1..4][100,99,97,94,90]>>>scanl (\reversedString nextChar -> nextChar : reversedString) "foo" ['a', 'b', 'c', 'd']["foo","afoo","bafoo","cbafoo","dcbafoo"]>>>scanl (+) 0 [1..]* Hangs forever *
reverse xs returns the elements of xs in reverse order.
xs must be finite.
>>>reverse [][]>>>reverse [42][42]>>>reverse [2,5,7][7,5,2]>>>reverse [1..]* Hangs forever *
replicate :: Int -> a -> [a] #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
>>>replicate 0 True[]>>>replicate (-1) True[]>>>replicate 4 True[True,True,True,True]
repeat x is an infinite list, with x the value of every element.
>>>take 20 $ repeat 17[17,17,17,17,17,17,17,17,17...
lookup :: Eq a => a -> [(a, b)] -> Maybe b #
\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association
list.
>>>lookup 2 []Nothing>>>lookup 2 [(1, "first")]Nothing>>>lookup 2 [(1, "first"), (2, "second"), (3, "third")]Just "second"
\(\mathcal{O}(n)\). Extract the last element of a list, which must be finite and non-empty.
>>>last [1, 2, 3]3>>>last [1..]* Hangs forever *>>>last []*** Exception: Prelude.last: empty list
iterate :: (a -> a) -> a -> [a] #
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.
>>>take 10 $ iterate not True[True,False,True,False...>>>take 10 $ iterate (+3) 42[42,45,48,51,54,57,60,63...
\(\mathcal{O}(n)\). Return all the elements of a list except the last one. The list must be non-empty.
>>>init [1, 2, 3][1,2]>>>init [1][]>>>init []*** Exception: Prelude.init: empty list
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.
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.
>>>cycle []*** Exception: Prelude.cycle: empty list>>>take 20 $ cycle [42][42,42,42,42,42,42,42,42,42,42...>>>take 20 $ cycle [2, 5, 7][2,5,7,2,5,7,2,5,7,2,5,7...
break :: (a -> Bool) -> [a] -> ([a], [a]) #
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
>>>break (> 3) [1,2,3,4,1,2,3,4]([1,2,3],[4,1,2,3,4])>>>break (< 9) [1,2,3]([],[1,2,3])>>>break (> 9) [1,2,3]([1,2,3],[])
(!!) :: [a] -> Int -> a infixl 9 #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex,
which takes an index of any integral type.
>>>['a', 'b', 'c'] !! 0'a'>>>['a', 'b', 'c'] !! 2'c'>>>['a', 'b', 'c'] !! 3*** Exception: Prelude.!!: index too large>>>['a', 'b', 'c'] !! (-1)*** Exception: Prelude.!!: negative index
maybe :: b -> (a -> b) -> Maybe a -> b #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import 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""
uncurry :: (a -> b -> c) -> (a, b) -> c #
uncurry converts a curried function to a function on pairs.
Examples
>>>uncurry (+) (1,2)3
>>>uncurry ($) (show, 1)"1"
>>>map (uncurry max) [(1,2), (3,4), (6,8)][2,4,8]
until :: (a -> Bool) -> (a -> a) -> a -> a #
until p ff until p holds.
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
>>>flip (++) "hello" "world""worldhello"
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #
Same as >>=, but with the arguments interchanged.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a #
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a #
A variant of error that does not produce a stack trace.
Since: base-4.9.0.0
error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a #
error stops execution and displays an error message.
module Control.Applicative
module Control.Monad
module Control.Monad.IO.Class
Arguments
| :: State s a | state-passing computation to execute |
| -> s | initial value |
| -> a | return value of the state computation |
evalStateT :: Monad m => StateT s m a -> s -> m a #
Evaluate a state computation with the given initial state and return the final value, discarding the final state.
evalStateTm s =liftMfst(runStateTm s)
Arguments
| :: State s a | state-passing computation to execute |
| -> s | initial value |
| -> s | final state |
execStateT :: Monad m => StateT s m a -> s -> m s #
Evaluate a state computation with the given initial state and return the final state, discarding the final value.
execStateTm s =liftMsnd(runStateTm s)
Arguments
| :: State s a | state-passing computation to execute |
| -> s | initial state |
| -> (a, s) | return value and final state |
Unwrap a state monad computation as a function.
(The inverse of state.)
withStateT :: forall s (m :: Type -> Type) a. (s -> s) -> StateT s m a -> StateT s m a #
withStateT f mm on a state modified by
applying f.
withStateTf m =modifyf >> m
type State s = StateT s Identity #
A state monad parameterized by the type s of the state to carry.
The return function leaves the state unchanged, while >>= uses
the final state of the first computation as the initial state of
the second.
newtype StateT s (m :: Type -> Type) a #
A state transformer monad parameterized by:
s- The state.m- The inner monad.
The return function leaves the state unchanged, while >>= uses
the final state of the first computation as the initial state of
the second.
Instances
| MonadTrans (StateT s) | |
Defined in Control.Monad.Trans.State.Strict | |
| MonadFail m => MonadFail (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| MonadFix m => MonadFix (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| MonadIO m => MonadIO (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| Contravariant m => Contravariant (StateT s m) | |
| (Functor m, MonadPlus m) => Alternative (StateT s m) | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| Functor m => Functor (StateT s m) | |
| Monad m => Monad (StateT s m) | |
| MonadPlus m => MonadPlus (StateT s m) | |
| PrimMonad m => PrimMonad (StateT s m) | |
| type PrimState (StateT s m) | |
Defined in Control.Monad.Primitive | |
Arguments
| :: forall (m :: Type -> Type) s a. Monad m | |
| => (s -> (a, s)) | pure state transformer |
| -> StateT s m a | equivalent state-passing computation |
Construct a state monad computation from a function.
(The inverse of runState.)
put :: forall (m :: Type -> Type) s. Monad m => s -> StateT s m () #
put ss.
liftPass :: Monad m => Pass w m (a, s) -> Pass w (StateT s m) a #
Lift a pass operation to the new monad.
liftListen :: Monad m => Listen w m (a, s) -> Listen w (StateT s m) a #
Lift a listen operation to the new monad.
liftCallCC' :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b #
In-situ lifting of a callCC operation to the new monad.
This version uses the current state on entering the continuation.
It does not satisfy the uniformity property (see Control.Monad.Signatures).
liftCallCC :: CallCC m (a, s) (b, s) -> CallCC (StateT s m) a b #
Uniform lifting of a callCC operation to the new monad.
This version rolls back to the original state on entering the
continuation.
get :: forall (m :: Type -> Type) s. Monad m => StateT s m s #
Fetch the current value of the state within the monad.
module Data.Coerce
class Foldable (t :: TYPE LiftedRep -> Type) where #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving FoldableA more detailed description can be found in the Overview section of Data.Foldable.
For the class laws see the Laws section of Data.Foldable.
Methods
fold :: Monoid m => t m -> m #
Given a structure with elements whose type is a Monoid, combine them
via the monoid's ( operator. This fold is right-associative and
lazy in the accumulator. When you need a strict left-associative fold,
use <>)foldMap' instead, with id as the map.
Examples
Basic usage:
>>>fold [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
>>>fold $ Node (Leaf (Sum 1)) (Sum 3) (Leaf (Sum 5))Sum {getSum = 9}
Folds of unbounded structures do not terminate when the monoid's
( operator is strict:<>)
>>>fold (repeat Nothing)* Hangs forever *
Lazy corecursive folds of unbounded structures are fine:
>>>take 12 $ fold $ map (\i -> [i..i+2]) [0..][0,1,2,1,2,3,2,3,4,3,4,5]>>>sum $ take 4000000 $ fold $ map (\i -> [i..i+2]) [0..]2666668666666
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure into a monoid, and combine the
results with (. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>)foldMap'
instead.
Examples
Basic usage:
>>>foldMap Sum [1, 3, 5]Sum {getSum = 9}
>>>foldMap Product [1, 3, 5]Product {getProduct = 15}
>>>foldMap (replicate 3) [1, 2, 3][1,1,1,2,2,2,3,3,3]
When a Monoid's ( is lazy in its second argument, <>)foldMap can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>import qualified Data.ByteString.Lazy as L>>>import qualified Data.ByteString.Builder as B>>>let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20>>>let lbs = B.toLazyByteString $ foldMap bld [0..]>>>L.take 64 lbs"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldMap' :: Monoid m => (a -> m) -> t a -> m #
A left-associative variant of foldMap that is strict in the
accumulator. Use this method for strict reduction when partial
results are merged via (.<>)
Examples
Define a Monoid over finite bit strings under xor. Use it to
strictly compute the xor of a list of Int values.
>>>:set -XGeneralizedNewtypeDeriving>>>import Data.Bits (Bits, FiniteBits, xor, zeroBits)>>>import Data.Foldable (foldMap')>>>import Numeric (showHex)>>>>>>newtype X a = X a deriving (Eq, Bounded, Enum, Bits, FiniteBits)>>>instance Bits a => Semigroup (X a) where X a <> X b = X (a `xor` b)>>>instance Bits a => Monoid (X a) where mempty = X zeroBits>>>>>>let bits :: [Int]; bits = [0xcafe, 0xfeed, 0xdeaf, 0xbeef, 0x5411]>>>(\ (X a) -> showString "0x" . showHex a $ "") $ foldMap' X bits"0x42"
Since: base-4.13.0.0
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure, lazy in the accumulator.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that since the head of the resulting expression is produced by an
application of the operator to the first element of the list, given an
operator lazy in its right argument, foldr can produce a terminating
expression from an unbounded list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
Examples
Basic usage:
>>>foldr (||) False [False, True, False]True
>>>foldr (||) False []False
>>>foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']"foodcba"
Infinite structures
⚠️ Applying foldr to infinite structures usually doesn't terminate.
It may still terminate under one of the following conditions:
- the folding function is short-circuiting
- the folding function is lazy on its second argument
Short-circuiting
( short-circuits on ||)True values, so the following terminates
because there is a True value finitely far from the left side:
>>>foldr (||) False (True : repeat False)True
But the following doesn't terminate:
>>>foldr (||) False (repeat False ++ [True])* Hangs forever *
Laziness in the second argument
Applying foldr to infinite structures terminates when the operator is
lazy in its second argument (the initial accumulator is never used in
this case, and so could be left undefined, but [] is more clear):
>>>take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)[1,4,7,10,13]
foldl' :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to Weak Head Normal
Form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a
finite structure to a single strict result (e.g. sum).
For a general Foldable structure this should be semantically identical
to,
foldl' f z =foldl'f z .toList
Since: base-4.6.0.0
foldr1 :: (a -> a -> a) -> t a -> a #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>foldr1 (+) [1..4]10
>>>foldr1 (+) []Exception: Prelude.foldr1: empty list
>>>foldr1 (+) Nothing*** Exception: foldr1: empty structure
>>>foldr1 (-) [1..4]-2
>>>foldr1 (&&) [True, False, True, True]False
>>>foldr1 (||) [False, False, True, True]True
>>>foldr1 (+) [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1f =foldl1f .toList
Examples
Basic usage:
>>>foldl1 (+) [1..4]10
>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list
>>>foldl1 (+) Nothing*** Exception: foldl1: empty structure
>>>foldl1 (-) [1..4]-8
>>>foldl1 (&&) [True, False, True, True]False
>>>foldl1 (||) [False, False, True, True]True
>>>foldl1 (+) [1..]* Hangs forever *
List of elements of a structure, from left to right. If the entire list is intended to be reduced via a fold, just fold the structure directly bypassing the list.
Examples
Basic usage:
>>>toList Nothing[]
>>>toList (Just 42)[42]
>>>toList (Left "foo")[]
>>>toList (Node (Leaf 5) 17 (Node Empty 12 (Leaf 8)))[5,17,12,8]
For lists, toList is the identity:
>>>toList [1, 2, 3][1,2,3]
Since: base-4.8.0.0
Test whether the structure is empty. The default implementation is Left-associative and lazy in both the initial element and the accumulator. Thus optimised for structures where the first element can be accessed in constant time. Structures where this is not the case should have a non-default implementation.
Examples
Basic usage:
>>>null []True
>>>null [1]False
null is expected to terminate even for infinite structures.
The default implementation terminates provided the structure
is bounded on the left (there is a leftmost element).
>>>null [1..]False
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int. The
default implementation just counts elements starting with the leftmost.
Instances for structures that can compute the element count faster
than via element-by-element counting, should provide a specialised
implementation.
Examples
Basic usage:
>>>length []0
>>>length ['a', 'b', 'c']3>>>length [1..]* Hangs forever *
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
Note: elem is often used in infix form.
Examples
Basic usage:
>>>3 `elem` []False
>>>3 `elem` [1,2]False
>>>3 `elem` [1,2,3,4,5]True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>3 `elem` [1..]True
>>>3 `elem` ([4..] ++ [3])* Hangs forever *
Since: base-4.8.0.0
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>maximum [1..10]10
>>>maximum []*** Exception: Prelude.maximum: empty list
>>>maximum Nothing*** Exception: maximum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>minimum [1..10]1
>>>minimum []*** Exception: Prelude.minimum: empty list
>>>minimum Nothing*** Exception: minimum: empty structure
WARNING: This function is partial for possibly-empty structures like lists.
Since: base-4.8.0.0
The sum function computes the sum of the numbers of a structure.
Examples
Basic usage:
>>>sum []0
>>>sum [42]42
>>>sum [1..10]55
>>>sum [4.1, 2.0, 1.7]7.8
>>>sum [1..]* Hangs forever *
Since: base-4.8.0.0
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>product []1
>>>product [42]42
>>>product [1..10]3628800
>>>product [4.1, 2.0, 1.7]13.939999999999998
>>>product [1..]* Hangs forever *
Since: base-4.8.0.0
Instances
| Foldable KeyMap | |
Defined in Data.Aeson.KeyMap Methods fold :: Monoid m => KeyMap m -> m # foldMap :: Monoid m => (a -> m) -> KeyMap a -> m # foldMap' :: Monoid m => (a -> m) -> KeyMap a -> m # foldr :: (a -> b -> b) -> b -> KeyMap a -> b # foldr' :: (a -> b -> b) -> b -> KeyMap a -> b # foldl :: (b -> a -> b) -> b -> KeyMap a -> b # foldl' :: (b -> a -> b) -> b -> KeyMap a -> b # foldr1 :: (a -> a -> a) -> KeyMap a -> a # foldl1 :: (a -> a -> a) -> KeyMap a -> a # elem :: Eq a => a -> KeyMap a -> Bool # maximum :: Ord a => KeyMap a -> a # minimum :: Ord a => KeyMap a -> a # | |
| Foldable IResult | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => IResult m -> m # foldMap :: Monoid m => (a -> m) -> IResult a -> m # foldMap' :: Monoid m => (a -> m) -> IResult a -> m # foldr :: (a -> b -> b) -> b -> IResult a -> b # foldr' :: (a -> b -> b) -> b -> IResult a -> b # foldl :: (b -> a -> b) -> b -> IResult a -> b # foldl' :: (b -> a -> b) -> b -> IResult a -> b # foldr1 :: (a -> a -> a) -> IResult a -> a # foldl1 :: (a -> a -> a) -> IResult a -> a # elem :: Eq a => a -> IResult a -> Bool # maximum :: Ord a => IResult a -> a # minimum :: Ord a => IResult a -> a # | |
| Foldable Result | |
Defined in Data.Aeson.Types.Internal Methods fold :: Monoid m => Result m -> m # foldMap :: Monoid m => (a -> m) -> Result a -> m # foldMap' :: Monoid m => (a -> m) -> Result a -> m # foldr :: (a -> b -> b) -> b -> Result a -> b # foldr' :: (a -> b -> b) -> b -> Result a -> b # foldl :: (b -> a -> b) -> b -> Result a -> b # foldl' :: (b -> a -> b) -> b -> Result a -> b # foldr1 :: (a -> a -> a) -> Result a -> a # foldl1 :: (a -> a -> a) -> Result a -> a # elem :: Eq a => a -> Result a -> Bool # maximum :: Ord a => Result a -> a # minimum :: Ord a => Result a -> a # | |
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
| Foldable SCC | Since: containers-0.5.9 |
Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m # foldMap :: Monoid m => (a -> m) -> SCC a -> m # foldMap' :: Monoid m => (a -> m) -> SCC a -> m # foldr :: (a -> b -> b) -> b -> SCC a -> b # foldr' :: (a -> b -> b) -> b -> SCC a -> b # foldl :: (b -> a -> b) -> b -> SCC a -> b # foldl' :: (b -> a -> b) -> b -> SCC a -> b # foldr1 :: (a -> a -> a) -> SCC a -> a # foldl1 :: (a -> a -> a) -> SCC a -> a # elem :: Eq a => a -> SCC a -> Bool # maximum :: Ord a => SCC a -> a # | |
| Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
| Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
| Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
| Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
| Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
| Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
| Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
| Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
| Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
| Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
| Foldable DNonEmpty | |
Defined in Data.DList.DNonEmpty.Internal Methods fold :: Monoid m => DNonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> DNonEmpty a -> m # foldr :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> DNonEmpty a -> b # foldl :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> DNonEmpty a -> b # foldr1 :: (a -> a -> a) -> DNonEmpty a -> a # foldl1 :: (a -> a -> a) -> DNonEmpty a -> a # toList :: DNonEmpty a -> [a] # length :: DNonEmpty a -> Int # elem :: Eq a => a -> DNonEmpty a -> Bool # maximum :: Ord a => DNonEmpty a -> a # minimum :: Ord a => DNonEmpty a -> a # | |
| Foldable DList | |
Defined in Data.DList.Internal Methods fold :: Monoid m => DList m -> m # foldMap :: Monoid m => (a -> m) -> DList a -> m # foldMap' :: Monoid m => (a -> m) -> DList a -> m # foldr :: (a -> b -> b) -> b -> DList a -> b # foldr' :: (a -> b -> b) -> b -> DList a -> b # foldl :: (b -> a -> b) -> b -> DList a -> b # foldl' :: (b -> a -> b) -> b -> DList a -> b # foldr1 :: (a -> a -> a) -> DList a -> a # foldl1 :: (a -> a -> a) -> DList a -> a # elem :: Eq a => a -> DList a -> Bool # maximum :: Ord a => DList a -> a # minimum :: Ord a => DList a -> a # | |
| Foldable Hashed | |
Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> m # foldMap :: Monoid m => (a -> m) -> Hashed a -> m # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m # foldr :: (a -> b -> b) -> b -> Hashed a -> b # foldr' :: (a -> b -> b) -> b -> Hashed a -> b # foldl :: (b -> a -> b) -> b -> Hashed a -> b # foldl' :: (b -> a -> b) -> b -> Hashed a -> b # foldr1 :: (a -> a -> a) -> Hashed a -> a # foldl1 :: (a -> a -> a) -> Hashed a -> a # elem :: Eq a => a -> Hashed a -> Bool # maximum :: Ord a => Hashed a -> a # minimum :: Ord a => Hashed a -> a # | |
| Foldable Array | |
Defined in Data.Primitive.Array Methods fold :: Monoid m => Array m -> m # foldMap :: Monoid m => (a -> m) -> Array a -> m # foldMap' :: Monoid m => (a -> m) -> Array a -> m # foldr :: (a -> b -> b) -> b -> Array a -> b # foldr' :: (a -> b -> b) -> b -> Array a -> b # foldl :: (b -> a -> b) -> b -> Array a -> b # foldl' :: (b -> a -> b) -> b -> Array a -> b # foldr1 :: (a -> a -> a) -> Array a -> a # foldl1 :: (a -> a -> a) -> Array a -> a # elem :: Eq a => a -> Array a -> Bool # maximum :: Ord a => Array a -> a # minimum :: Ord a => Array a -> a # | |
| Foldable SmallArray | |
Defined in Data.Primitive.SmallArray Methods fold :: Monoid m => SmallArray m -> m # foldMap :: Monoid m => (a -> m) -> SmallArray a -> m # foldMap' :: Monoid m => (a -> m) -> SmallArray a -> m # foldr :: (a -> b -> b) -> b -> SmallArray a -> b # foldr' :: (a -> b -> b) -> b -> SmallArray a -> b # foldl :: (b -> a -> b) -> b -> SmallArray a -> b # foldl' :: (b -> a -> b) -> b -> SmallArray a -> b # foldr1 :: (a -> a -> a) -> SmallArray a -> a # foldl1 :: (a -> a -> a) -> SmallArray a -> a # toList :: SmallArray a -> [a] # null :: SmallArray a -> Bool # length :: SmallArray a -> Int # elem :: Eq a => a -> SmallArray a -> Bool # maximum :: Ord a => SmallArray a -> a # minimum :: Ord a => SmallArray a -> a # sum :: Num a => SmallArray a -> a # product :: Num a => SmallArray a -> a # | |
| Foldable Maybe | |
Defined in Data.Strict.Maybe Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Bag Source # | |
Defined in Language.Lexer.Tlex.Data.Bag Methods fold :: Monoid m => Bag m -> m # foldMap :: Monoid m => (a -> m) -> Bag a -> m # foldMap' :: Monoid m => (a -> m) -> Bag a -> m # foldr :: (a -> b -> b) -> b -> Bag a -> b # foldr' :: (a -> b -> b) -> b -> Bag a -> b # foldl :: (b -> a -> b) -> b -> Bag a -> b # foldl' :: (b -> a -> b) -> b -> Bag a -> b # foldr1 :: (a -> a -> a) -> Bag a -> a # foldl1 :: (a -> a -> a) -> Bag a -> a # elem :: Eq a => a -> Bag a -> Bool # maximum :: Ord a => Bag a -> a # | |
| Foldable StateArray Source # | |
Defined in Language.Lexer.Tlex.Machine.State Methods fold :: Monoid m => StateArray m -> m # foldMap :: Monoid m => (a -> m) -> StateArray a -> m # foldMap' :: Monoid m => (a -> m) -> StateArray a -> m # foldr :: (a -> b -> b) -> b -> StateArray a -> b # foldr' :: (a -> b -> b) -> b -> StateArray a -> b # foldl :: (b -> a -> b) -> b -> StateArray a -> b # foldl' :: (b -> a -> b) -> b -> StateArray a -> b # foldr1 :: (a -> a -> a) -> StateArray a -> a # foldl1 :: (a -> a -> a) -> StateArray a -> a # toList :: StateArray a -> [a] # null :: StateArray a -> Bool # length :: StateArray a -> Int # elem :: Eq a => a -> StateArray a -> Bool # maximum :: Ord a => StateArray a -> a # minimum :: Ord a => StateArray a -> a # sum :: Num a => StateArray a -> a # product :: Num a => StateArray a -> a # | |
| Foldable HashSet | |
Defined in Data.HashSet.Internal Methods fold :: Monoid m => HashSet m -> m # foldMap :: Monoid m => (a -> m) -> HashSet a -> m # foldMap' :: Monoid m => (a -> m) -> HashSet a -> m # foldr :: (a -> b -> b) -> b -> HashSet a -> b # foldr' :: (a -> b -> b) -> b -> HashSet a -> b # foldl :: (b -> a -> b) -> b -> HashSet a -> b # foldl' :: (b -> a -> b) -> b -> HashSet a -> b # foldr1 :: (a -> a -> a) -> HashSet a -> a # foldl1 :: (a -> a -> a) -> HashSet a -> a # elem :: Eq a => a -> HashSet a -> Bool # maximum :: Ord a => HashSet a -> a # minimum :: Ord a => HashSet a -> a # | |
| Foldable Vector | |
Defined in Data.Vector Methods fold :: Monoid m => Vector m -> m # foldMap :: Monoid m => (a -> m) -> Vector a -> m # foldMap' :: Monoid m => (a -> m) -> Vector a -> m # foldr :: (a -> b -> b) -> b -> Vector a -> b # foldr' :: (a -> b -> b) -> b -> Vector a -> b # foldl :: (b -> a -> b) -> b -> Vector a -> b # foldl' :: (b -> a -> b) -> b -> Vector a -> b # foldr1 :: (a -> a -> a) -> Vector a -> a # foldl1 :: (a -> a -> a) -> Vector a -> a # elem :: Eq a => a -> Vector a -> Bool # maximum :: Ord a => Vector a -> a # minimum :: Ord a => Vector a -> a # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable Methods fold :: Monoid m => Solo m -> m # foldMap :: Monoid m => (a -> m) -> Solo a -> m # foldMap' :: Monoid m => (a -> m) -> Solo a -> m # foldr :: (a -> b -> b) -> b -> Solo a -> b # foldr' :: (a -> b -> b) -> b -> Solo a -> b # foldl :: (b -> a -> b) -> b -> Solo a -> b # foldl' :: (b -> a -> b) -> b -> Solo a -> b # foldr1 :: (a -> a -> a) -> Solo a -> a # foldl1 :: (a -> a -> a) -> Solo a -> a # elem :: Eq a => a -> Solo a -> Bool # maximum :: Ord a => Solo a -> a # | |
| Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 # toList :: Either a a0 -> [a0] # length :: Either a a0 -> Int # elem :: Eq a0 => a0 -> Either a a0 -> Bool # maximum :: Ord a0 => Either a a0 -> a0 # minimum :: Ord a0 => Either a a0 -> a0 # | |
| Foldable (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
| Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m # foldMap :: Monoid m => (a -> m) -> Array i a -> m # foldMap' :: Monoid m => (a -> m) -> Array i a -> m # foldr :: (a -> b -> b) -> b -> Array i a -> b # foldr' :: (a -> b -> b) -> b -> Array i a -> b # foldl :: (b -> a -> b) -> b -> Array i a -> b # foldl' :: (b -> a -> b) -> b -> Array i a -> b # foldr1 :: (a -> a -> a) -> Array i a -> a # foldl1 :: (a -> a -> a) -> Array i a -> a # elem :: Eq a => a -> Array i a -> Bool # maximum :: Ord a => Array i a -> a # minimum :: Ord a => Array i a -> a # | |
| Foldable (U1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m # foldMap :: Monoid m => (a -> m) -> U1 a -> m # foldMap' :: Monoid m => (a -> m) -> U1 a -> m # foldr :: (a -> b -> b) -> b -> U1 a -> b # foldr' :: (a -> b -> b) -> b -> U1 a -> b # foldl :: (b -> a -> b) -> b -> U1 a -> b # foldl' :: (b -> a -> b) -> b -> U1 a -> b # foldr1 :: (a -> a -> a) -> U1 a -> a # foldl1 :: (a -> a -> a) -> U1 a -> a # elem :: Eq a => a -> U1 a -> Bool # maximum :: Ord a => U1 a -> a # | |
| Foldable (UAddr :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m # foldMap :: Monoid m => (a -> m) -> UAddr a -> m # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m # foldr :: (a -> b -> b) -> b -> UAddr a -> b # foldr' :: (a -> b -> b) -> b -> UAddr a -> b # foldl :: (b -> a -> b) -> b -> UAddr a -> b # foldl' :: (b -> a -> b) -> b -> UAddr a -> b # foldr1 :: (a -> a -> a) -> UAddr a -> a # foldl1 :: (a -> a -> a) -> UAddr a -> a # elem :: Eq a => a -> UAddr a -> Bool # maximum :: Ord a => UAddr a -> a # minimum :: Ord a => UAddr a -> a # | |
| Foldable (UChar :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m # foldMap :: Monoid m => (a -> m) -> UChar a -> m # foldMap' :: Monoid m => (a -> m) -> UChar a -> m # foldr :: (a -> b -> b) -> b -> UChar a -> b # foldr' :: (a -> b -> b) -> b -> UChar a -> b # foldl :: (b -> a -> b) -> b -> UChar a -> b # foldl' :: (b -> a -> b) -> b -> UChar a -> b # foldr1 :: (a -> a -> a) -> UChar a -> a # foldl1 :: (a -> a -> a) -> UChar a -> a # elem :: Eq a => a -> UChar a -> Bool # maximum :: Ord a => UChar a -> a # minimum :: Ord a => UChar a -> a # | |
| Foldable (UDouble :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m # foldMap :: Monoid m => (a -> m) -> UDouble a -> m # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m # foldr :: (a -> b -> b) -> b -> UDouble a -> b # foldr' :: (a -> b -> b) -> b -> UDouble a -> b # foldl :: (b -> a -> b) -> b -> UDouble a -> b # foldl' :: (b -> a -> b) -> b -> UDouble a -> b # foldr1 :: (a -> a -> a) -> UDouble a -> a # foldl1 :: (a -> a -> a) -> UDouble a -> a # elem :: Eq a => a -> UDouble a -> Bool # maximum :: Ord a => UDouble a -> a # minimum :: Ord a => UDouble a -> a # | |
| Foldable (UFloat :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m # foldMap :: Monoid m => (a -> m) -> UFloat a -> m # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m # foldr :: (a -> b -> b) -> b -> UFloat a -> b # foldr' :: (a -> b -> b) -> b -> UFloat a -> b # foldl :: (b -> a -> b) -> b -> UFloat a -> b # foldl' :: (b -> a -> b) -> b -> UFloat a -> b # foldr1 :: (a -> a -> a) -> UFloat a -> a # foldl1 :: (a -> a -> a) -> UFloat a -> a # elem :: Eq a => a -> UFloat a -> Bool # maximum :: Ord a => UFloat a -> a # minimum :: Ord a => UFloat a -> a # | |
| Foldable (UInt :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m # foldMap :: Monoid m => (a -> m) -> UInt a -> m # foldMap' :: Monoid m => (a -> m) -> UInt a -> m # foldr :: (a -> b -> b) -> b -> UInt a -> b # foldr' :: (a -> b -> b) -> b -> UInt a -> b # foldl :: (b -> a -> b) -> b -> UInt a -> b # foldl' :: (b -> a -> b) -> b -> UInt a -> b # foldr1 :: (a -> a -> a) -> UInt a -> a # foldl1 :: (a -> a -> a) -> UInt a -> a # elem :: Eq a => a -> UInt a -> Bool # maximum :: Ord a => UInt a -> a # | |
| Foldable (UWord :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m # foldMap :: Monoid m => (a -> m) -> UWord a -> m # foldMap' :: Monoid m => (a -> m) -> UWord a -> m # foldr :: (a -> b -> b) -> b -> UWord a -> b # foldr' :: (a -> b -> b) -> b -> UWord a -> b # foldl :: (b -> a -> b) -> b -> UWord a -> b # foldl' :: (b -> a -> b) -> b -> UWord a -> b # foldr1 :: (a -> a -> a) -> UWord a -> a # foldl1 :: (a -> a -> a) -> UWord a -> a # elem :: Eq a => a -> UWord a -> Bool # maximum :: Ord a => UWord a -> a # minimum :: Ord a => UWord a -> a # | |
| Foldable (V1 :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldMap' :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
| Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m # foldMap :: Monoid m => (a -> m) -> Map k a -> m # foldMap' :: Monoid m => (a -> m) -> Map k a -> m # foldr :: (a -> b -> b) -> b -> Map k a -> b # foldr' :: (a -> b -> b) -> b -> Map k a -> b # foldl :: (b -> a -> b) -> b -> Map k a -> b # foldl' :: (b -> a -> b) -> b -> Map k a -> b # foldr1 :: (a -> a -> a) -> Map k a -> a # foldl1 :: (a -> a -> a) -> Map k a -> a # elem :: Eq a => a -> Map k a -> Bool # maximum :: Ord a => Map k a -> a # minimum :: Ord a => Map k a -> a # | |
| Foldable (EnumMap k) | |
Defined in Data.EnumMap.Base Methods fold :: Monoid m => EnumMap k m -> m # foldMap :: Monoid m => (a -> m) -> EnumMap k a -> m # foldMap' :: Monoid m => (a -> m) -> EnumMap k a -> m # foldr :: (a -> b -> b) -> b -> EnumMap k a -> b # foldr' :: (a -> b -> b) -> b -> EnumMap k a -> b # foldl :: (b -> a -> b) -> b -> EnumMap k a -> b # foldl' :: (b -> a -> b) -> b -> EnumMap k a -> b # foldr1 :: (a -> a -> a) -> EnumMap k a -> a # foldl1 :: (a -> a -> a) -> EnumMap k a -> a # toList :: EnumMap k a -> [a] # length :: EnumMap k a -> Int # elem :: Eq a => a -> EnumMap k a -> Bool # maximum :: Ord a => EnumMap k a -> a # minimum :: Ord a => EnumMap k a -> a # | |
| Foldable (Either e) | |
Defined in Data.Strict.Either Methods fold :: Monoid m => Either e m -> m # foldMap :: Monoid m => (a -> m) -> Either e a -> m # foldMap' :: Monoid m => (a -> m) -> Either e a -> m # foldr :: (a -> b -> b) -> b -> Either e a -> b # foldr' :: (a -> b -> b) -> b -> Either e a -> b # foldl :: (b -> a -> b) -> b -> Either e a -> b # foldl' :: (b -> a -> b) -> b -> Either e a -> b # foldr1 :: (a -> a -> a) -> Either e a -> a # foldl1 :: (a -> a -> a) -> Either e a -> a # elem :: Eq a => a -> Either e a -> Bool # maximum :: Ord a => Either e a -> a # minimum :: Ord a => Either e a -> a # | |
| Foldable (These a) | |
Defined in Data.Strict.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
| Foldable (Pair e) | |
Defined in Data.Strict.Tuple Methods fold :: Monoid m => Pair e m -> m # foldMap :: Monoid m => (a -> m) -> Pair e a -> m # foldMap' :: Monoid m => (a -> m) -> Pair e a -> m # foldr :: (a -> b -> b) -> b -> Pair e a -> b # foldr' :: (a -> b -> b) -> b -> Pair e a -> b # foldl :: (b -> a -> b) -> b -> Pair e a -> b # foldl' :: (b -> a -> b) -> b -> Pair e a -> b # foldr1 :: (a -> a -> a) -> Pair e a -> a # foldl1 :: (a -> a -> a) -> Pair e a -> a # elem :: Eq a => a -> Pair e a -> Bool # maximum :: Ord a => Pair e a -> a # minimum :: Ord a => Pair e a -> a # | |
| Foldable (These a) | |
Defined in Data.These Methods fold :: Monoid m => These a m -> m # foldMap :: Monoid m => (a0 -> m) -> These a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> These a a0 -> m # foldr :: (a0 -> b -> b) -> b -> These a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> These a a0 -> b # foldl :: (b -> a0 -> b) -> b -> These a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> These a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> These a a0 -> a0 # toList :: These a a0 -> [a0] # elem :: Eq a0 => a0 -> These a a0 -> Bool # maximum :: Ord a0 => These a a0 -> a0 # minimum :: Ord a0 => These a a0 -> a0 # | |
| Foldable (HashMap k) | |
Defined in Data.HashMap.Internal Methods fold :: Monoid m => HashMap k m -> m # foldMap :: Monoid m => (a -> m) -> HashMap k a -> m # foldMap' :: Monoid m => (a -> m) -> HashMap k a -> m # foldr :: (a -> b -> b) -> b -> HashMap k a -> b # foldr' :: (a -> b -> b) -> b -> HashMap k a -> b # foldl :: (b -> a -> b) -> b -> HashMap k a -> b # foldl' :: (b -> a -> b) -> b -> HashMap k a -> b # foldr1 :: (a -> a -> a) -> HashMap k a -> a # foldl1 :: (a -> a -> a) -> HashMap k a -> a # toList :: HashMap k a -> [a] # length :: HashMap k a -> Int # elem :: Eq a => a -> HashMap k a -> Bool # maximum :: Ord a => HashMap k a -> a # minimum :: Ord a => HashMap k a -> a # | |
| Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 # elem :: Eq a0 => a0 -> (a, a0) -> Bool # maximum :: Ord a0 => (a, a0) -> a0 # minimum :: Ord a0 => (a, a0) -> a0 # | |
| Foldable (Const m :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 # foldr :: (a -> b -> b) -> b -> Const m a -> b # foldr' :: (a -> b -> b) -> b -> Const m a -> b # foldl :: (b -> a -> b) -> b -> Const m a -> b # foldl' :: (b -> a -> b) -> b -> Const m a -> b # foldr1 :: (a -> a -> a) -> Const m a -> a # foldl1 :: (a -> a -> a) -> Const m a -> a # elem :: Eq a => a -> Const m a -> Bool # maximum :: Ord a => Const m a -> a # minimum :: Ord a => Const m a -> a # | |
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m # foldMap :: Monoid m => (a -> m) -> Ap f a -> m # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m # foldr :: (a -> b -> b) -> b -> Ap f a -> b # foldr' :: (a -> b -> b) -> b -> Ap f a -> b # foldl :: (b -> a -> b) -> b -> Ap f a -> b # foldl' :: (b -> a -> b) -> b -> Ap f a -> b # foldr1 :: (a -> a -> a) -> Ap f a -> a # foldl1 :: (a -> a -> a) -> Ap f a -> a # elem :: Eq a => a -> Ap f a -> Bool # maximum :: Ord a => Ap f a -> a # | |
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # | |
| Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b # foldr1 :: (a -> a -> a) -> Rec1 f a -> a # foldl1 :: (a -> a -> a) -> Rec1 f a -> a # elem :: Eq a => a -> Rec1 f a -> Bool # maximum :: Ord a => Rec1 f a -> a # minimum :: Ord a => Rec1 f a -> a # | |
| Foldable (Tagged s) | |
Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m # foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m # foldr :: (a -> b -> b) -> b -> Tagged s a -> b # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b # foldl :: (b -> a -> b) -> b -> Tagged s a -> b # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b # foldr1 :: (a -> a -> a) -> Tagged s a -> a # foldl1 :: (a -> a -> a) -> Tagged s a -> a # elem :: Eq a => a -> Tagged s a -> Bool # maximum :: Ord a => Tagged s a -> a # minimum :: Ord a => Tagged s a -> a # | |
| (Foldable f, Foldable g) => Foldable (These1 f g) | |
Defined in Data.Functor.These Methods fold :: Monoid m => These1 f g m -> m # foldMap :: Monoid m => (a -> m) -> These1 f g a -> m # foldMap' :: Monoid m => (a -> m) -> These1 f g a -> m # foldr :: (a -> b -> b) -> b -> These1 f g a -> b # foldr' :: (a -> b -> b) -> b -> These1 f g a -> b # foldl :: (b -> a -> b) -> b -> These1 f g a -> b # foldl' :: (b -> a -> b) -> b -> These1 f g a -> b # foldr1 :: (a -> a -> a) -> These1 f g a -> a # foldl1 :: (a -> a -> a) -> These1 f g a -> a # toList :: These1 f g a -> [a] # null :: These1 f g a -> Bool # length :: These1 f g a -> Int # elem :: Eq a => a -> These1 f g a -> Bool # maximum :: Ord a => These1 f g a -> a # minimum :: Ord a => These1 f g a -> a # | |
| Foldable f => Foldable (ErrorT e f) | |
Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a # toList :: ErrorT e f a -> [a] # null :: ErrorT e f a -> Bool # length :: ErrorT e f a -> Int # elem :: Eq a => a -> ErrorT e f a -> Bool # maximum :: Ord a => ErrorT e f a -> a # minimum :: Ord a => ErrorT e f a -> a # | |
| (Foldable f, Foldable g) => Foldable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m # foldMap :: Monoid m => (a -> m) -> Product f g a -> m # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m # foldr :: (a -> b -> b) -> b -> Product f g a -> b # foldr' :: (a -> b -> b) -> b -> Product f g a -> b # foldl :: (b -> a -> b) -> b -> Product f g a -> b # foldl' :: (b -> a -> b) -> b -> Product f g a -> b # foldr1 :: (a -> a -> a) -> Product f g a -> a # foldl1 :: (a -> a -> a) -> Product f g a -> a # toList :: Product f g a -> [a] # null :: Product f g a -> Bool # length :: Product f g a -> Int # elem :: Eq a => a -> Product f g a -> Bool # maximum :: Ord a => Product f g a -> a # minimum :: Ord a => Product f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m # foldr :: (a -> b -> b) -> b -> Sum f g a -> b # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b # foldl :: (b -> a -> b) -> b -> Sum f g a -> b # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b # foldr1 :: (a -> a -> a) -> Sum f g a -> a # foldl1 :: (a -> a -> a) -> Sum f g a -> a # elem :: Eq a => a -> Sum f g a -> Bool # maximum :: Ord a => Sum f g a -> a # minimum :: Ord a => Sum f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # length :: (f :*: g) a -> Int # elem :: Eq a => a -> (f :*: g) a -> Bool # maximum :: Ord a => (f :*: g) a -> a # minimum :: Ord a => (f :*: g) a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # | |
| Foldable (K1 i c :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m # foldr :: (a -> b -> b) -> b -> K1 i c a -> b # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b # foldl :: (b -> a -> b) -> b -> K1 i c a -> b # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b # foldr1 :: (a -> a -> a) -> K1 i c a -> a # foldl1 :: (a -> a -> a) -> K1 i c a -> a # elem :: Eq a => a -> K1 i c a -> Bool # maximum :: Ord a => K1 i c a -> a # minimum :: Ord a => K1 i c a -> a # | |
| (Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m # foldr :: (a -> b -> b) -> b -> Compose f g a -> b # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b # foldl :: (b -> a -> b) -> b -> Compose f g a -> b # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b # foldr1 :: (a -> a -> a) -> Compose f g a -> a # foldl1 :: (a -> a -> a) -> Compose f g a -> a # toList :: Compose f g a -> [a] # null :: Compose f g a -> Bool # length :: Compose f g a -> Int # elem :: Eq a => a -> Compose f g a -> Bool # maximum :: Ord a => Compose f g a -> a # minimum :: Ord a => Compose f g a -> a # | |
| (Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a # toList :: (f :.: g) a -> [a] # length :: (f :.: g) a -> Int # elem :: Eq a => a -> (f :.: g) a -> Bool # maximum :: Ord a => (f :.: g) a -> a # minimum :: Ord a => (f :.: g) a -> a # | |
| Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b # foldr1 :: (a -> a -> a) -> M1 i c f a -> a # foldl1 :: (a -> a -> a) -> M1 i c f a -> a # elem :: Eq a => a -> M1 i c f a -> Bool # maximum :: Ord a => M1 i c f a -> a # minimum :: Ord a => M1 i c f a -> a # | |
traverse_ :: (Foldable t, Applicative f) => (a -> f b) -> t a -> f () #
Map each element of a structure to an Applicative action, evaluate these
actions from left to right, and ignore the results. For a version that
doesn't ignore the results see traverse.
traverse_ is just like mapM_, but generalised to Applicative actions.
Examples
Basic usage:
>>>traverse_ print ["Hello", "world", "!"]"Hello" "world" "!"
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
sequence_ is just like sequenceA_, but specialised to monadic
actions.
sequenceA_ :: (Foldable t, Applicative f) => t (f a) -> f () #
Evaluate each action in the structure from left to right, and
ignore the results. For a version that doesn't ignore the results
see sequenceA.
sequenceA_ is just like sequence_, but generalised to Applicative
actions.
Examples
Basic usage:
>>>sequenceA_ [print "Hello", print "world", print "!"]"Hello" "world" "!"
or :: Foldable t => t Bool -> Bool #
or returns the disjunction of a container of Bools. For the
result to be False, the container must be finite; True, however,
results from a True value finitely far from the left end.
Examples
Basic usage:
>>>or []False
>>>or [True]True
>>>or [False]False
>>>or [True, True, False]True
>>>or (True : repeat False) -- Infinite list [True,False,False,False,...True
>>>or (repeat False)* Hangs forever *
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 #
notElem is the negation of elem.
Examples
Basic usage:
>>>3 `notElem` []True
>>>3 `notElem` [1,2]True
>>>3 `notElem` [1,2,3,4,5]False
For infinite structures, notElem terminates if the value exists at a
finite distance from the left side of the structure:
>>>3 `notElem` [1..]False
>>>3 `notElem` ([4..] ++ [3])* Hangs forever *
minimumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #
The least element of a non-empty structure with respect to the given comparison function.
Examples
Basic usage:
>>>minimumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]"!"
WARNING: This function is partial for possibly-empty structures like lists.
maximumBy :: Foldable t => (a -> a -> Ordering) -> t a -> a #
The largest element of a non-empty structure with respect to the given comparison function.
Examples
Basic usage:
>>>maximumBy (compare `on` length) ["Hello", "World", "!", "Longest", "bar"]"Longest"
WARNING: This function is partial for possibly-empty structures like lists.
for_ :: (Foldable t, Applicative f) => t a -> (a -> f b) -> f () #
for_ is traverse_ with its arguments flipped. For a version
that doesn't ignore the results see for. This
is forM_ generalised to Applicative actions.
for_ is just like forM_, but generalised to Applicative actions.
Examples
Basic usage:
>>>for_ [1..4] print1 2 3 4
foldrM :: (Foldable t, Monad m) => (a -> b -> m b) -> b -> t a -> m b #
Right-to-left monadic fold over the elements of a structure.
Given a structure t with elements (a, b, c, ..., x, y), the result of
a fold with an operator function f is equivalent to:
foldrM f z t = do
yy <- f y z
xx <- f x yy
...
bb <- f b cc
aa <- f a bb
return aa -- Just @return z@ when the structure is emptyFor a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c,
their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:
(f1 >=> f2) a = f1 a >>= f2
Another way of thinking about foldrM is that it amounts to an application
to z of a Kleisli composition:
foldrM f z t = f y >=> f x >=> ... >=> f b >=> f a $ z
The monadic effects of foldrM are sequenced from right to left, and e.g.
folds of infinite lists will diverge.
If at some step the bind operator ( short-circuits (as with, e.g.,
>>=)mzero in a MonadPlus), the evaluated effects will be from a tail of the
element sequence. If you want to evaluate the monadic effects in
left-to-right order, or perhaps be able to short-circuit after an initial
sequence of elements, you'll need to use foldlM instead.
If the monadic effects don't short-circuit, the outermost application of
f is to the leftmost element a, so that, ignoring effects, the result
looks like a right fold:
a `f` (b `f` (c `f` (... (x `f` (y `f` z))))).
Examples
Basic usage:
>>>let f i acc = do { print i ; return $ i : acc }>>>foldrM f [] [0..3]3 2 1 0 [0,1,2,3]
foldlM :: (Foldable t, Monad m) => (b -> a -> m b) -> b -> t a -> m b #
Left-to-right monadic fold over the elements of a structure.
Given a structure t with elements (a, b, ..., w, x, y), the result of
a fold with an operator function f is equivalent to:
foldlM f z t = do
aa <- f z a
bb <- f aa b
...
xx <- f ww x
yy <- f xx y
return yy -- Just @return z@ when the structure is emptyFor a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c,
their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:
(f1 >=> f2) a = f1 a >>= f2
Another way of thinking about foldlM is that it amounts to an application
to z of a Kleisli composition:
foldlM f z t =
flip f a >=> flip f b >=> ... >=> flip f x >=> flip f y $ zThe monadic effects of foldlM are sequenced from left to right.
If at some step the bind operator ( short-circuits (as with, e.g.,
>>=)mzero in a MonadPlus), the evaluated effects will be from an initial
segment of the element sequence. If you want to evaluate the monadic
effects in right-to-left order, or perhaps be able to short-circuit after
processing a tail of the sequence of elements, you'll need to use foldrM
instead.
If the monadic effects don't short-circuit, the outermost application of
f is to the rightmost element y, so that, ignoring effects, the result
looks like a left fold:
((((z `f` a) `f` b) ... `f` w) `f` x) `f` y
Examples
Basic usage:
>>>let f a e = do { print e ; return $ e : a }>>>foldlM f [] [0..3]0 1 2 3 [3,2,1,0]
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>concatMap (take 3) [[1..], [10..], [100..], [1000..]][1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>concatMap (take 3) (Just [1..])[1,2,3]
concat :: Foldable t => t [a] -> [a] #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>concat (Just [1, 2, 3])[1,2,3]
>>>concat (Left 42)[]
>>>concat [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
asum :: (Foldable t, Alternative f) => t (f a) -> f a #
The sum of a collection of actions, generalizing concat.
asum is just like msum, but generalised to Alternative.
Examples
Basic usage:
>>>asum [Just "Hello", Nothing, Just "World"]Just "Hello"
any :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>any (> 3) []False
>>>any (> 3) [1,2]False
>>>any (> 3) [1,2,3,4,5]True
>>>any (> 3) [1..]True
>>>any (> 3) [0, -1..]* Hangs forever *
and :: Foldable t => t Bool -> Bool #
and returns the conjunction of a container of Bools. For the
result to be True, the container must be finite; False, however,
results from a False value finitely far from the left end.
Examples
Basic usage:
>>>and []True
>>>and [True]True
>>>and [False]False
>>>and [True, True, False]False
>>>and (False : repeat True) -- Infinite list [False,True,True,True,...False
>>>and (repeat True)* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>all (> 3) []True
>>>all (> 3) [1,2]False
>>>all (> 3) [1,2,3,4,5]False
>>>all (> 3) [1..]False
>>>all (> 3) [4..]* Hangs forever *
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]
fix ff,
i.e. the least defined x such that f x = x.
For example, we can write the factorial function using direct recursion as
>>>let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5120
This uses the fact that Haskell’s let introduces recursive bindings. We can
rewrite this definition using fix,
>>>fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5120
Instead of making a recursive call, we introduce a dummy parameter rec;
when used within fix, this parameter then refers to fix’s argument, hence
the recursion is reintroduced.
flip :: (a -> b -> c) -> b -> a -> c #
flip ff.
>>>flip (++) "hello" "world""worldhello"
module Data.Functor
module Data.Functor.Identity
module Data.Functor.Compose
The Ix class is used to map a contiguous subrange of values in
a type onto integers. It is used primarily for array indexing
(see the array package).
The first argument (l,u) of each of these operations is a pair
specifying the lower and upper bounds of a contiguous subrange of values.
An implementation is entitled to assume the following laws about these operations:
Minimal complete definition
range, (index | unsafeIndex), inRange
Instances
| Ix Void | Since: base-4.8.0.0 |
| Ix IntPtr | |
| Ix WordPtr | |
Defined in Foreign.Ptr | |
| Ix Associativity | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods range :: (Associativity, Associativity) -> [Associativity] # index :: (Associativity, Associativity) -> Associativity -> Int # unsafeIndex :: (Associativity, Associativity) -> Associativity -> Int # inRange :: (Associativity, Associativity) -> Associativity -> Bool # rangeSize :: (Associativity, Associativity) -> Int # unsafeRangeSize :: (Associativity, Associativity) -> Int # | |
| Ix DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods range :: (DecidedStrictness, DecidedStrictness) -> [DecidedStrictness] # index :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Int # unsafeIndex :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Int # inRange :: (DecidedStrictness, DecidedStrictness) -> DecidedStrictness -> Bool # rangeSize :: (DecidedStrictness, DecidedStrictness) -> Int # unsafeRangeSize :: (DecidedStrictness, DecidedStrictness) -> Int # | |
| Ix SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods range :: (SourceStrictness, SourceStrictness) -> [SourceStrictness] # index :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Int # unsafeIndex :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Int # inRange :: (SourceStrictness, SourceStrictness) -> SourceStrictness -> Bool # rangeSize :: (SourceStrictness, SourceStrictness) -> Int # unsafeRangeSize :: (SourceStrictness, SourceStrictness) -> Int # | |
| Ix SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods range :: (SourceUnpackedness, SourceUnpackedness) -> [SourceUnpackedness] # index :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Int # unsafeIndex :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Int # inRange :: (SourceUnpackedness, SourceUnpackedness) -> SourceUnpackedness -> Bool # rangeSize :: (SourceUnpackedness, SourceUnpackedness) -> Int # unsafeRangeSize :: (SourceUnpackedness, SourceUnpackedness) -> Int # | |
| Ix Int16 | Since: base-2.1 |
| Ix Int32 | Since: base-2.1 |
| Ix Int64 | Since: base-2.1 |
| Ix Int8 | Since: base-2.1 |
| Ix Word16 | Since: base-2.1 |
| Ix Word32 | Since: base-2.1 |
| Ix Word64 | Since: base-2.1 |
| Ix Word8 | Since: base-2.1 |
| Ix Ordering | Since: base-2.1 |
Defined in GHC.Ix Methods range :: (Ordering, Ordering) -> [Ordering] # index :: (Ordering, Ordering) -> Ordering -> Int # unsafeIndex :: (Ordering, Ordering) -> Ordering -> Int # inRange :: (Ordering, Ordering) -> Ordering -> Bool # rangeSize :: (Ordering, Ordering) -> Int # unsafeRangeSize :: (Ordering, Ordering) -> Int # | |
| Ix Day | |
| Ix Month | |
| Ix Quarter | |
Defined in Data.Time.Calendar.Quarter | |
| Ix QuarterOfYear | |
Defined in Data.Time.Calendar.Quarter Methods range :: (QuarterOfYear, QuarterOfYear) -> [QuarterOfYear] # index :: (QuarterOfYear, QuarterOfYear) -> QuarterOfYear -> Int # unsafeIndex :: (QuarterOfYear, QuarterOfYear) -> QuarterOfYear -> Int # inRange :: (QuarterOfYear, QuarterOfYear) -> QuarterOfYear -> Bool # rangeSize :: (QuarterOfYear, QuarterOfYear) -> Int # unsafeRangeSize :: (QuarterOfYear, QuarterOfYear) -> Int # | |
| Ix DayOfWeek | |
Defined in Data.Time.Calendar.Week Methods range :: (DayOfWeek, DayOfWeek) -> [DayOfWeek] # index :: (DayOfWeek, DayOfWeek) -> DayOfWeek -> Int # unsafeIndex :: (DayOfWeek, DayOfWeek) -> DayOfWeek -> Int # inRange :: (DayOfWeek, DayOfWeek) -> DayOfWeek -> Bool # rangeSize :: (DayOfWeek, DayOfWeek) -> Int # unsafeRangeSize :: (DayOfWeek, DayOfWeek) -> Int # | |
| Ix StateNum Source # | |
Defined in Language.Lexer.Tlex.Machine.State Methods range :: (StateNum, StateNum) -> [StateNum] # index :: (StateNum, StateNum) -> StateNum -> Int # unsafeIndex :: (StateNum, StateNum) -> StateNum -> Int # inRange :: (StateNum, StateNum) -> StateNum -> Bool # rangeSize :: (StateNum, StateNum) -> Int # unsafeRangeSize :: (StateNum, StateNum) -> Int # | |
| Ix Integer | Since: base-2.1 |
Defined in GHC.Ix | |
| Ix Natural | Since: base-4.8.0.0 |
Defined in GHC.Ix | |
| Ix () | Since: base-2.1 |
| Ix Bool | Since: base-2.1 |
| Ix Char | Since: base-2.1 |
| Ix Int | Since: base-2.1 |
| Ix Word | Since: base-4.6.0.0 |
| Ix a => Ix (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity Methods range :: (Identity a, Identity a) -> [Identity a] # index :: (Identity a, Identity a) -> Identity a -> Int # unsafeIndex :: (Identity a, Identity a) -> Identity a -> Int # inRange :: (Identity a, Identity a) -> Identity a -> Bool # rangeSize :: (Identity a, Identity a) -> Int # unsafeRangeSize :: (Identity a, Identity a) -> Int # | |
| Ix a => Ix (Down a) | Since: base-4.14.0.0 |
| Ix a => Ix (a) | |
| Ix (Proxy s) | Since: base-4.7.0.0 |
Defined in Data.Proxy | |
| (Ix a, Ix b) => Ix (Pair a b) | |
Defined in Data.Strict.Tuple Methods range :: (Pair a b, Pair a b) -> [Pair a b] # index :: (Pair a b, Pair a b) -> Pair a b -> Int # unsafeIndex :: (Pair a b, Pair a b) -> Pair a b -> Int # inRange :: (Pair a b, Pair a b) -> Pair a b -> Bool # rangeSize :: (Pair a b, Pair a b) -> Int # unsafeRangeSize :: (Pair a b, Pair a b) -> Int # | |
| (Ix a, Ix b) => Ix (a, b) | Since: base-2.1 |
| Ix a => Ix (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const Methods range :: (Const a b, Const a b) -> [Const a b] # index :: (Const a b, Const a b) -> Const a b -> Int # unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int # inRange :: (Const a b, Const a b) -> Const a b -> Bool # rangeSize :: (Const a b, Const a b) -> Int # unsafeRangeSize :: (Const a b, Const a b) -> Int # | |
| Ix b => Ix (Tagged s b) | |
Defined in Data.Tagged Methods range :: (Tagged s b, Tagged s b) -> [Tagged s b] # index :: (Tagged s b, Tagged s b) -> Tagged s b -> Int # unsafeIndex :: (Tagged s b, Tagged s b) -> Tagged s b -> Int # inRange :: (Tagged s b, Tagged s b) -> Tagged s b -> Bool # rangeSize :: (Tagged s b, Tagged s b) -> Int # unsafeRangeSize :: (Tagged s b, Tagged s b) -> Int # | |
| (Ix a1, Ix a2, Ix a3) => Ix (a1, a2, a3) | Since: base-2.1 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3), (a1, a2, a3)) -> [(a1, a2, a3)] # index :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Int # unsafeIndex :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Int # inRange :: ((a1, a2, a3), (a1, a2, a3)) -> (a1, a2, a3) -> Bool # rangeSize :: ((a1, a2, a3), (a1, a2, a3)) -> Int # unsafeRangeSize :: ((a1, a2, a3), (a1, a2, a3)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4) => Ix (a1, a2, a3, a4) | Since: base-2.1 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> [(a1, a2, a3, a4)] # index :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Int # unsafeIndex :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Int # inRange :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> (a1, a2, a3, a4) -> Bool # rangeSize :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4), (a1, a2, a3, a4)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5) => Ix (a1, a2, a3, a4, a5) | Since: base-2.1 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> [(a1, a2, a3, a4, a5)] # index :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Int # inRange :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> (a1, a2, a3, a4, a5) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5), (a1, a2, a3, a4, a5)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6) => Ix (a1, a2, a3, a4, a5, a6) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> [(a1, a2, a3, a4, a5, a6)] # index :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> (a1, a2, a3, a4, a5, a6) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> (a1, a2, a3, a4, a5, a6) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> (a1, a2, a3, a4, a5, a6) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6), (a1, a2, a3, a4, a5, a6)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7) => Ix (a1, a2, a3, a4, a5, a6, a7) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> [(a1, a2, a3, a4, a5, a6, a7)] # index :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> (a1, a2, a3, a4, a5, a6, a7) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> (a1, a2, a3, a4, a5, a6, a7) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> (a1, a2, a3, a4, a5, a6, a7) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7), (a1, a2, a3, a4, a5, a6, a7)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8) => Ix (a1, a2, a3, a4, a5, a6, a7, a8) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> [(a1, a2, a3, a4, a5, a6, a7, a8)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> (a1, a2, a3, a4, a5, a6, a7, a8) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> (a1, a2, a3, a4, a5, a6, a7, a8) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> (a1, a2, a3, a4, a5, a6, a7, a8) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8), (a1, a2, a3, a4, a5, a6, a7, a8)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9), (a1, a2, a3, a4, a5, a6, a7, a8, a9)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA, Ix aB) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA, Ix aB, Ix aC) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA, Ix aB, Ix aC, Ix aD) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA, Ix aB, Ix aC, Ix aD, Ix aE) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE)) -> Int # | |
| (Ix a1, Ix a2, Ix a3, Ix a4, Ix a5, Ix a6, Ix a7, Ix a8, Ix a9, Ix aA, Ix aB, Ix aC, Ix aD, Ix aE, Ix aF) => Ix (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF) | Since: base-4.15.0.0 |
Defined in GHC.Ix Methods range :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> [(a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)] # index :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF) -> Int # unsafeIndex :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF) -> Int # inRange :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF) -> Bool # rangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> Int # unsafeRangeSize :: ((a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF), (a1, a2, a3, a4, a5, a6, a7, a8, a9, aA, aB, aC, aD, aE, aF)) -> Int # | |
Non-empty (and non-strict) list type.
Since: base-4.9.0.0
Constructors
| a :| [a] infixr 5 |
Instances
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
| Eq1 NonEmpty | Since: base-4.10.0.0 |
| Ord1 NonEmpty | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes | |
| Read1 NonEmpty | Since: base-4.10.0.0 |
Defined in Data.Functor.Classes | |
| Show1 NonEmpty | Since: base-4.10.0.0 |
| Traversable NonEmpty | Since: base-4.9.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
| Functor NonEmpty | Since: base-4.9.0.0 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Hashable1 NonEmpty | Since: hashable-1.3.1.0 |
Defined in Data.Hashable.Class | |
| Generic1 NonEmpty | |
| Lift a => Lift (NonEmpty a :: Type) | Since: template-haskell-2.15.0.0 |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| IsList (NonEmpty a) | Since: base-4.9.0.0 |
| Generic (NonEmpty a) | |
| Read a => Read (NonEmpty a) | Since: base-4.11.0.0 |
| Show a => Show (NonEmpty a) | Since: base-4.11.0.0 |
| Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0 |
| Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0 |
| Hashable a => Hashable (NonEmpty a) | |
Defined in Data.Hashable.Class | |
| type Rep1 NonEmpty | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep1 NonEmpty = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":|" ('InfixI 'LeftAssociative 9) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 []))) | |
| type Item (NonEmpty a) | |
| type Rep (NonEmpty a) | Since: base-4.6.0.0 |
Defined in GHC.Generics type Rep (NonEmpty a) = D1 ('MetaData "NonEmpty" "GHC.Base" "base" 'False) (C1 ('MetaCons ":|" ('InfixI 'LeftAssociative 9) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 [a]))) | |
The Down type allows you to reverse sort order conveniently. A value of type
Down aa (represented as Down a
If a has an Ordthen sortWith by .Down x
>>>compare True FalseGT
>>>compare (Down True) (Down False)LT
If a has a BoundedminBoundmaxBound
>>>minBound :: Int-9223372036854775808
>>>minBound :: Down IntDown 9223372036854775807
All other instances of Down aa.
Since: base-4.6.0.0
Instances
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
| Eq1 Down | Since: base-4.12.0.0 |
| Ord1 Down | Since: base-4.12.0.0 |
Defined in Data.Functor.Classes | |
| Read1 Down | Since: base-4.12.0.0 |
Defined in Data.Functor.Classes | |
| Show1 Down | Since: base-4.12.0.0 |
| Traversable Down | Since: base-4.12.0.0 |
| Applicative Down | Since: base-4.11.0.0 |
| Functor Down | Since: base-4.11.0.0 |
| Monad Down | Since: base-4.11.0.0 |
| Generic1 Down | |
| Unbox a => Vector Vector (Down a) | |
Defined in Data.Vector.Unboxed.Base Methods basicUnsafeFreeze :: Mutable Vector s (Down a) -> ST s (Vector (Down a)) # basicUnsafeThaw :: Vector (Down a) -> ST s (Mutable Vector s (Down a)) # basicLength :: Vector (Down a) -> Int # basicUnsafeSlice :: Int -> Int -> Vector (Down a) -> Vector (Down a) # basicUnsafeIndexM :: Vector (Down a) -> Int -> Box (Down a) # basicUnsafeCopy :: Mutable Vector s (Down a) -> Vector (Down a) -> ST s () # | |
| Unbox a => MVector MVector (Down a) | |
Defined in Data.Vector.Unboxed.Base Methods basicLength :: MVector s (Down a) -> Int # basicUnsafeSlice :: Int -> Int -> MVector s (Down a) -> MVector s (Down a) # basicOverlaps :: MVector s (Down a) -> MVector s (Down a) -> Bool # basicUnsafeNew :: Int -> ST s (MVector s (Down a)) # basicInitialize :: MVector s (Down a) -> ST s () # basicUnsafeReplicate :: Int -> Down a -> ST s (MVector s (Down a)) # basicUnsafeRead :: MVector s (Down a) -> Int -> ST s (Down a) # basicUnsafeWrite :: MVector s (Down a) -> Int -> Down a -> ST s () # basicClear :: MVector s (Down a) -> ST s () # basicSet :: MVector s (Down a) -> Down a -> ST s () # basicUnsafeCopy :: MVector s (Down a) -> MVector s (Down a) -> ST s () # basicUnsafeMove :: MVector s (Down a) -> MVector s (Down a) -> ST s () # basicUnsafeGrow :: MVector s (Down a) -> Int -> ST s (MVector s (Down a)) # | |
| Storable a => Storable (Down a) | Since: base-4.14.0.0 |
| Monoid a => Monoid (Down a) | Since: base-4.11.0.0 |
| Semigroup a => Semigroup (Down a) | Since: base-4.11.0.0 |
| Bits a => Bits (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods (.&.) :: Down a -> Down a -> Down a # (.|.) :: Down a -> Down a -> Down a # xor :: Down a -> Down a -> Down a # complement :: Down a -> Down a # shift :: Down a -> Int -> Down a # rotate :: Down a -> Int -> Down a # setBit :: Down a -> Int -> Down a # clearBit :: Down a -> Int -> Down a # complementBit :: Down a -> Int -> Down a # testBit :: Down a -> Int -> Bool # bitSizeMaybe :: Down a -> Maybe Int # shiftL :: Down a -> Int -> Down a # unsafeShiftL :: Down a -> Int -> Down a # shiftR :: Down a -> Int -> Down a # unsafeShiftR :: Down a -> Int -> Down a # rotateL :: Down a -> Int -> Down a # | |
| FiniteBits a => FiniteBits (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods finiteBitSize :: Down a -> Int # countLeadingZeros :: Down a -> Int # countTrailingZeros :: Down a -> Int # | |
| Bounded a => Bounded (Down a) | Swaps Since: base-4.14.0.0 |
| Floating a => Floating (Down a) | Since: base-4.14.0.0 |
| RealFloat a => RealFloat (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods floatRadix :: Down a -> Integer # floatDigits :: Down a -> Int # floatRange :: Down a -> (Int, Int) # decodeFloat :: Down a -> (Integer, Int) # encodeFloat :: Integer -> Int -> Down a # significand :: Down a -> Down a # scaleFloat :: Int -> Down a -> Down a # isInfinite :: Down a -> Bool # isDenormalized :: Down a -> Bool # isNegativeZero :: Down a -> Bool # | |
| Generic (Down a) | |
| Ix a => Ix (Down a) | Since: base-4.14.0.0 |
| Num a => Num (Down 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 |
| Fractional a => Fractional (Down a) | Since: base-4.14.0.0 |
| Real a => Real (Down a) | Since: base-4.14.0.0 |
Defined in Data.Ord Methods toRational :: Down a -> Rational # | |
| RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
| Show a => Show (Down a) | This instance would be equivalent to the derived instances of the
Since: base-4.7.0.0 |
| Eq a => Eq (Down a) | Since: base-4.6.0.0 |
| Ord a => Ord (Down a) | Since: base-4.6.0.0 |
| Prim a => Prim (Down a) | Since: primitive-0.6.5.0 |
Defined in Data.Primitive.Types Methods alignment# :: Down a -> Int# # indexByteArray# :: ByteArray# -> Int# -> Down a # readByteArray# :: MutableByteArray# s -> Int# -> State# s -> (# State# s, Down a #) # writeByteArray# :: MutableByteArray# s -> Int# -> Down a -> State# s -> State# s # setByteArray# :: MutableByteArray# s -> Int# -> Int# -> Down a -> State# s -> State# s # indexOffAddr# :: Addr# -> Int# -> Down a # readOffAddr# :: Addr# -> Int# -> State# s -> (# State# s, Down a #) # writeOffAddr# :: Addr# -> Int# -> Down a -> State# s -> State# s # setOffAddr# :: Addr# -> Int# -> Int# -> Down a -> State# s -> State# s # | |
| Unbox a => Unbox (Down a) | |
Defined in Data.Vector.Unboxed.Base | |
| type Rep1 Down | Since: base-4.12.0.0 |
Defined in GHC.Generics | |
| newtype MVector s (Down a) | |
Defined in Data.Vector.Unboxed.Base | |
| type Rep (Down a) | Since: base-4.12.0.0 |
Defined in GHC.Generics | |
| newtype Vector (Down a) | |
Defined in Data.Vector.Unboxed.Base | |
Proxy is a type that holds no data, but has a phantom parameter of
arbitrary type (or even kind). Its use is to provide type information, even
though there is no value available of that type (or it may be too costly to
create one).
Historically, Proxy :: Proxy aundefined :: a
>>>Proxy :: Proxy (Void, Int -> Int)Proxy
Proxy can even hold types of higher kinds,
>>>Proxy :: Proxy EitherProxy
>>>Proxy :: Proxy FunctorProxy
>>>Proxy :: Proxy complicatedStructureProxy
Constructors
| Proxy |
Instances
| Generic1 (Proxy :: k -> Type) | |
| Foldable (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m # foldMap :: Monoid m => (a -> m) -> Proxy a -> m # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m # foldr :: (a -> b -> b) -> b -> Proxy a -> b # foldr' :: (a -> b -> b) -> b -> Proxy a -> b # foldl :: (b -> a -> b) -> b -> Proxy a -> b # foldl' :: (b -> a -> b) -> b -> Proxy a -> b # foldr1 :: (a -> a -> a) -> Proxy a -> a # foldl1 :: (a -> a -> a) -> Proxy a -> a # elem :: Eq a => a -> Proxy a -> Bool # maximum :: Ord a => Proxy a -> a # minimum :: Ord a => Proxy a -> a # | |
| Eq1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
| Ord1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Read1 (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| Show1 (Proxy :: TYPE LiftedRep -> Type) | Since: base-4.9.0.0 |
| Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Alternative (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Functor (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| MonadPlus (Proxy :: Type -> Type) | Since: base-4.9.0.0 |
| Hashable1 (Proxy :: Type -> Type) | |
Defined in Data.Hashable.Class | |
| Monoid (Proxy s) | Since: base-4.7.0.0 |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Bounded (Proxy t) | Since: base-4.7.0.0 |
| Enum (Proxy s) | Since: base-4.7.0.0 |
| Generic (Proxy t) | |
| Ix (Proxy s) | Since: base-4.7.0.0 |
Defined in Data.Proxy | |
| Read (Proxy t) | Since: base-4.7.0.0 |
| Show (Proxy s) | Since: base-4.7.0.0 |
| Eq (Proxy s) | Since: base-4.7.0.0 |
| Ord (Proxy s) | Since: base-4.7.0.0 |
| Hashable (Proxy a) | |
Defined in Data.Hashable.Class | |
| type Rep1 (Proxy :: k -> Type) | Since: base-4.6.0.0 |
| type Rep (Proxy t) | Since: base-4.6.0.0 |
The class Typeable allows a concrete representation of a type to
be calculated.
Minimal complete definition
typeRep#
Instances
8-bit unsigned integer type