| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
GHC.Prelude
Description
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]
- ($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (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 -> Type) where
- foldMap :: Monoid m => (a -> m) -> t a -> m
- foldr :: (a -> b -> b) -> b -> t a -> b
- foldl :: (b -> a -> b) -> b -> t a -> b
- foldl' :: (b -> a -> b) -> b -> t a -> b
- foldr1 :: (a -> a -> a) -> t a -> a
- foldl1 :: (a -> a -> a) -> t a -> a
- 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
- 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
- class Semigroup a => Monoid a where
- data Bool
- type String = [Char]
- 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
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- appendFile :: FilePath -> String -> IO ()
- writeFile :: FilePath -> String -> IO ()
- readFile :: FilePath -> IO String
- interact :: (String -> String) -> IO ()
- getContents :: IO String
- getLine :: IO String
- getChar :: IO Char
- putStrLn :: String -> IO ()
- putStr :: String -> IO ()
- putChar :: Char -> IO ()
- ioError :: IOError -> IO a
- type FilePath = String
- userError :: String -> IOError
- type IOError = IOException
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- and :: Foldable t => t Bool -> Bool
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- unwords :: [String] -> String
- words :: String -> [String]
- unlines :: [String] -> String
- lines :: String -> [String]
- read :: Read a => String -> a
- reads :: Read a => ReadS a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- type ReadS a = String -> [(a, String)]
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- odd :: Integral a => a -> Bool
- even :: Integral a => a -> Bool
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- showChar :: Char -> ShowS
- shows :: Show a => a -> ShowS
- type ShowS = String -> String
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- (!!) :: [a] -> Int -> a
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- reverse :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- drop :: Int -> [a] -> [a]
- take :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- cycle :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- iterate :: (a -> 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]
- init :: [a] -> [a]
- last :: [a] -> a
- tail :: [a] -> [a]
- head :: [a] -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- subtract :: Num a => a -> a -> a
- asTypeOf :: a -> a -> a
- until :: (a -> Bool) -> (a -> a) -> a -> a
- ($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b
- flip :: (a -> b -> c) -> b -> a -> c
- (.) :: (b -> c) -> (a -> b) -> a -> c
- const :: a -> b -> a
- id :: a -> a
- (=<<) :: Monad m => (a -> m b) -> m a -> m 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
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
Documentation
(++) :: [a] -> [a] -> [a] infixr 5 Source #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
seq :: forall {r :: RuntimeRep} a (b :: TYPE r). a -> b -> b #
filter :: (a -> Bool) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
>>>filter odd [1, 2, 3][1,3]
zip :: [a] -> [b] -> [(a, b)] Source #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
>>>zip [1, 2] ['a', 'b'][(1, 'a'), (2, 'b')]
If one input list is 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 [] _|_[]>>>zip _|_ []_|_
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
print :: Show a => a -> IO () Source #
The print function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show; print
converts values to strings for output using the show operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
map :: (a -> b) -> [a] -> [b] Source #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3][2,3,4]
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #
Application operator. This operator is redundant, since ordinary
application (f x) means the same as (f . However, $ x)$ has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as map ($ 0) xszipWith ($) fs xs
Note that ( is levity-polymorphic in its result type, so that
$)foo where $ Truefoo :: Bool -> Int# is well-typed.
fromIntegral :: (Integral a, Num b) => a -> b Source #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b Source #
general coercion to fractional types
class Bounded a where Source #
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
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] Source #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n', a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n'),
worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] Source #
Used in Haskell's translation of [n..m] with
[n..m] = enumFromTo n m, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = [].
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] Source #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
Instances
class Fractional a => Floating a where Source #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
Minimal complete definition
fromRational, (recip | (/))
Methods
(/) :: a -> a -> a infixl 7 Source #
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a Source #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CFloat | |
| Fractional CDouble | |
| Fractional NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (/) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime Source # | |
| Fractional DiffTime | |
| Fractional EdgeWeight # | |
Defined in GHC.CmmToAsm.CFG Methods (/) :: EdgeWeight -> EdgeWeight -> EdgeWeight Source # recip :: EdgeWeight -> EdgeWeight Source # fromRational :: Rational -> EdgeWeight Source # | |
| Integral a => Fractional (Ratio a) | Since: base-2.0.1 |
| 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 |
| HasResolution a => Fractional (Fixed a) | Since: base-2.1 |
| Fractional a => Fractional (Const a b) | Since: base-4.9.0.0 |
class (Real a, Enum a) => Integral a where Source #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
Methods
quot :: a -> a -> a infixl 7 Source #
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source #
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source #
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source #
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a) Source #
divMod :: a -> a -> (a, a) Source #
toInteger :: a -> Integer Source #
conversion to Integer
Instances
class Applicative m => Monad (m :: Type -> Type) where Source #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: m a -> m b -> m b infixl 1 Source #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] | Since: base-2.1 |
| Monad Maybe | Since: base-2.1 |
| Monad IO | Since: base-2.1 |
| Monad Par1 | Since: base-4.9.0.0 |
| Monad Q | |
| Monad Solo | Since: base-4.15 |
| Monad Complex | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Monad Option | Since: base-4.9.0.0 |
| Monad Identity | Since: base-4.8.0.0 |
| Monad STM | Since: base-4.3.0.0 |
| Monad First | Since: base-4.8.0.0 |
| Monad Last | Since: base-4.8.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Monad Down | Since: base-4.11.0.0 |
| Monad ReadPrec | Since: base-2.1 |
| Monad ReadP | Since: base-2.1 |
| Monad NonEmpty | Since: base-4.9.0.0 |
| Monad PutM | |
| Monad Get | |
| Monad Put | |
| Monad Tree | |
| Monad Seq | |
| Monad Capability | |
Defined in System.Console.Terminfo.Base Methods (>>=) :: Capability a -> (a -> Capability b) -> Capability b Source # (>>) :: Capability a -> Capability b -> Capability b Source # return :: a -> Capability a Source # | |
| Monad P | Since: base-2.1 |
| Monad UniqSM # | |
| Monad UnifyResultM # | |
Defined in GHC.Core.Unify Methods (>>=) :: UnifyResultM a -> (a -> UnifyResultM b) -> UnifyResultM b Source # (>>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b Source # return :: a -> UnifyResultM a Source # | |
| Monad P # | |
| Monad PV # | |
| Monad LiftM # | |
| Monad Hsc # | |
| Monad CompPipeline # | |
Defined in GHC.Driver.Pipeline.Monad Methods (>>=) :: CompPipeline a -> (a -> CompPipeline b) -> CompPipeline b Source # (>>) :: CompPipeline a -> CompPipeline b -> CompPipeline b Source # return :: a -> CompPipeline a Source # | |
| Monad Ghc # | |
| Monad CoreM # | |
| Monad SimplM # | |
| Monad TcPluginM # | |
| Monad PD # | |
| Monad MetaTyVarUpdateResult # | |
Defined in GHC.Tc.Utils.Unify Methods (>>=) :: MetaTyVarUpdateResult a -> (a -> MetaTyVarUpdateResult b) -> MetaTyVarUpdateResult b Source # (>>) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult b Source # return :: a -> MetaTyVarUpdateResult a Source # | |
| Monad TcS # | |
| Monad CpsRn # | |
| Monad LlvmM # | |
| Monad NatM # | |
| Monad FCode # | |
| Monad CmmParse # | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Monad (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Monad ((,) a) | Since: base-4.9.0.0 |
| Monad (ST s) | Since: base-2.1 |
| Monad m => Monad (WrappedMonad m) | Since: base-4.7.0.0 |
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # | |
| ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # | |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Monad m => Monad (MaybeT m) | |
| Monad m => Monad (ListT m) | |
| Monad (State s) # | |
| Monad (MaybeErr err) # | |
| Monad (SetM s) | |
| Monad (CmdLineP s) # | |
| Monad m => Monad (EwM m) # | |
| Monad (IOEnv m) # | |
| Monad m => Monad (GhcT m) # | |
| Monad (RegM freeRegs) # | |
| Monad f => Monad (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Monad ((,,) a b) | Since: base-4.14.0.0 |
| Monad m => Monad (Kleisli m a) | Since: base-4.14.0.0 |
| Monad f => Monad (Ap f) | Since: base-4.12.0.0 |
| Monad f => Monad (Alt f) | Since: base-4.8.0.0 |
| (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 Source # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # return :: a -> WhenMissing f x a Source # | |
| Monad m => Monad (ExceptT e m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| (Monoid w, Monad m) => Monad (WriterT w m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (StateT s m) | |
| Monad m => Monad (ReaderT r m) | |
| Monad m => Monad (IdentityT m) | |
| (Monad m, Error e) => Monad (ErrorT e m) | |
| Monad m => Monad (Stream m a) # | |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| Monad ((->) r) | Since: base-2.1 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| (Monad f, 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 Source # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # return :: a -> WhenMatched f x y a Source # | |
| (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 Source # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # return :: a -> WhenMissing f k x a Source # | |
| Monad (ContT r m) | |
| 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 Source # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # return :: a -> WhenMatched f k x y a Source # | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| Monad m => Monad (RWST r w s m) | |
class Functor (f :: Type -> Type) where Source #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
Using ApplicativeDo: 'fmap f asdo expression
do a <- as pure (f a)
with an inferred Functor constraint.
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
(+) :: a -> a -> a infixl 6 Source #
(-) :: a -> a -> a infixl 6 Source #
(*) :: a -> a -> a infixl 7 Source #
Unary negation.
Absolute value.
Sign of a number.
The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero)
or 1 (positive).
fromInteger :: Integer -> a Source #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
Instances
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 Bool | Since: base-2.1 |
| Read Char | Since: base-2.1 |
| Read Double | Since: base-2.1 |
| Read Float | Since: base-2.1 |
| Read Int | Since: base-2.1 |
| Read Int8 | Since: base-2.1 |
| Read Int16 | Since: base-2.1 |
| Read Int32 | Since: base-2.1 |
| Read Int64 | Since: base-2.1 |
| Read Integer | Since: base-2.1 |
| Read Natural | Since: base-4.8.0.0 |
| Read Ordering | Since: base-2.1 |
| Read Word | Since: base-4.5.0.0 |
| Read Word8 | Since: base-2.1 |
| Read Word16 | Since: base-2.1 |
| Read Word32 | Since: base-2.1 |
| Read Word64 | Since: base-2.1 |
| Read () | Since: base-2.1 |
| Read Void | Reading a Since: base-4.8.0.0 |
| Read ByteOrder | Since: base-4.11.0.0 |
| Read CDev | |
| Read CIno | |
| Read CMode | |
| Read COff | |
| Read CPid | |
| Read CSsize | |
| Read CGid | |
| Read CNlink | |
| Read CUid | |
| Read CCc | |
| Read CSpeed | |
| Read CTcflag | |
| Read CRLim | |
| Read CBlkSize | |
| Read CBlkCnt | |
| Read CClockId | |
| Read CFsBlkCnt | |
| Read CFsFilCnt | |
| Read CId | |
| Read CKey | |
| Read CSocklen | |
| Read CNfds | |
| Read Fd | |
| Read ExitCode | |
| Read BufferMode | Since: base-4.2.0.0 |
Defined in GHC.IO.Handle.Types | |
| Read Newline | Since: base-4.3.0.0 |
| Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types | |
| Read SeekMode | Since: base-4.2.0.0 |
| Read All | Since: base-2.1 |
| Read Any | Since: base-2.1 |
| Read Fixity | Since: base-4.6.0.0 |
| Read Associativity | Since: base-4.6.0.0 |
Defined in GHC.Generics | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Read CChar | |
| Read CSChar | |
| Read CUChar | |
| Read CShort | |
| Read CUShort | |
| Read CInt | |
| Read CUInt | |
| Read CLong | |
| Read CULong | |
| Read CLLong | |
| Read CULLong | |
| Read CBool | |
| Read CFloat | |
| Read CDouble | |
| Read CPtrdiff | |
| Read CSize | |
| Read CWchar | |
| Read CSigAtomic | |
Defined in Foreign.C.Types | |
| Read CClock | |
| Read CTime | |
| Read CUSeconds | |
| Read CSUSeconds | |
Defined in Foreign.C.Types | |
| Read CIntPtr | |
| Read CUIntPtr | |
| Read CIntMax | |
| Read CUIntMax | |
| Read WordPtr | |
| Read IntPtr | |
| Read SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits | |
| Read SomeNat | Since: base-4.7.0.0 |
| Read IOMode | Since: base-4.2.0.0 |
| Read Lexeme | Since: base-2.1 |
| Read GeneralCategory | Since: base-2.1 |
| Read Version | Since: base-2.1 |
| Read ShortByteString | |
Defined in Data.ByteString.Short.Internal | |
| Read ByteString | |
Defined in Data.ByteString.Lazy.Internal | |
| Read ByteString | |
Defined in Data.ByteString.Internal | |
| Read IntSet | |
| Read FileType | |
| Read Permissions | |
Defined in System.Directory.Internal.Common | |
| Read XdgDirectory | |
Defined in System.Directory.Internal.Common | |
| Read XdgDirectoryList | |
Defined in System.Directory.Internal.Common | |
| Read PlatformMini | |
Defined in GHC.Platform | |
| Read Platform | |
| Read PlatformWordSize | |
Defined in GHC.Platform | |
| Read Arch | |
| Read OS | |
| Read ArmISA | |
| Read ArmISAExt | |
| Read ArmABI | |
| Read PPC_64ABI | |
| Read Mix | |
| Read BoxLabel | |
| Read CondBox | |
| Read HpcPos | |
| Read Hash | |
| Read DayOfWeek | |
| Read GroupEntry | |
Defined in System.Posix.User | |
| Read UserEntry | |
| Read RTLDFlags | |
| Read Backend # | |
| Read PlatformConstants # | |
Defined in GHC.Settings | |
| Read a => Read [a] | Since: base-2.1 |
| Read a => Read (Maybe a) | Since: base-2.1 |
| (Integral a, Read a) => Read (Ratio a) | Since: base-2.1 |
| Read p => Read (Par1 p) | Since: base-4.7.0.0 |
| Read a => Read (a) | Since: base-4.15 |
| Read a => Read (Complex a) | Since: base-2.1 |
| Read a => Read (Min a) | Since: base-4.9.0.0 |
| Read a => Read (Max a) | Since: base-4.9.0.0 |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Read a => Read (Last a) | Since: base-4.9.0.0 |
| Read m => Read (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods readsPrec :: Int -> ReadS (WrappedMonoid m) Source # readList :: ReadS [WrappedMonoid m] Source # readPrec :: ReadPrec (WrappedMonoid m) Source # readListPrec :: ReadPrec [WrappedMonoid m] Source # | |
| Read a => Read (Option a) | Since: base-4.9.0.0 |
| Read a => Read (ZipList a) | Since: base-4.7.0.0 |
| Read a => Read (Identity a) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read a => Read (First a) | Since: base-2.1 |
| Read a => Read (Last a) | Since: base-2.1 |
| Read a => Read (Dual a) | Since: base-2.1 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Read a => Read (Product a) | Since: base-2.1 |
| 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 (NonEmpty a) | Since: base-4.11.0.0 |
| Read e => Read (IntMap e) | |
| Read vertex => Read (SCC vertex) | Since: containers-0.5.9 |
| Read a => Read (Tree a) | |
| 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 b) => Read (Either a b) | Since: base-3.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| Read (U1 p) | Since: base-4.9.0.0 |
| (Read a, Read b) => Read (a, b) | Since: base-2.1 |
| (Ix ix, Read ix, Read e, IArray UArray e) => Read (UArray ix e) | |
| (Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1 |
| HasResolution a => Read (Fixed a) | Since: base-4.3.0.0 |
| (Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
| Read (Proxy t) | Since: base-4.7.0.0 |
| (Ord k, Read k, Read e) => Read (Map k e) | |
| (Read1 m, Read a) => Read (MaybeT m a) | |
| (Read1 m, Read a) => Read (ListT m a) | |
| Read (f p) => Read (Rec1 f p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c) => Read (a, b, c) | Since: base-2.1 |
| Read a => Read (Const a b) | This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f a) => Read (Ap f a) | Since: base-4.12.0.0 |
| Read (f a) => Read (Alt f a) | Since: base-4.8.0.0 |
| Coercible a b => Read (Coercion a b) | Since: base-4.7.0.0 |
| a ~ b => Read (a :~: b) | Since: base-4.7.0.0 |
| (Read e, Read1 m, Read a) => Read (ExceptT e m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read1 f, Read a) => Read (IdentityT f a) | |
| (Read e, Read1 m, Read a) => Read (ErrorT e m a) | |
| Read c => Read (K1 i c p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d) => Read (a, b, c, d) | Since: base-2.1 |
| (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 |
| a ~~ b => Read (a :~~: b) | Since: base-4.10.0.0 |
| Read (f p) => Read (M1 i c f p) | Since: base-4.7.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) | Since: base-4.7.0.0 |
| (Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) | Since: base-2.1 |
| (Read1 f, Read1 g, Read a) => Read (Compose f g a) | Since: base-4.9.0.0 |
| (Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1 |
Defined in GHC.Read | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
Defined in GHC.Read | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # | |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # | |
class (Num a, Ord a) => Real a where Source #
Methods
toRational :: a -> Rational Source #
the rational equivalent of its real argument with full precision
Instances
class (RealFrac a, Floating a) => RealFloat a where Source #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer Source #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int Source #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) Source #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) Source #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a Source #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a Source #
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a Source #
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool Source #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool Source #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) Source #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b Source #
truncate xx between zero and x
round :: Integral b => a -> b Source #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b Source #
ceiling xx
floor :: Integral b => a -> b Source #
floor xx
Instances
| RealFrac CFloat | |
| RealFrac CDouble | |
| RealFrac NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods properFraction :: Integral b => NominalDiffTime -> (b, NominalDiffTime) Source # truncate :: Integral b => NominalDiffTime -> b Source # round :: Integral b => NominalDiffTime -> b Source # ceiling :: Integral b => NominalDiffTime -> b Source # floor :: Integral b => NominalDiffTime -> b Source # | |
| RealFrac DiffTime | |
Defined in Data.Time.Clock.Internal.DiffTime | |
| Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
Defined in Data.Functor.Identity | |
| RealFrac a => RealFrac (Down a) | Since: base-4.14.0.0 |
| HasResolution a => RealFrac (Fixed a) | Since: base-2.1 |
| RealFrac a => RealFrac (Const a b) | Since: base-4.9.0.0 |
Defined in Data.Functor.Const | |
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 Source #
When a value is bound in do-notation, the pattern on the left
hand side of <- might not match. In this case, this class
provides a function to recover.
A Monad without a MonadFail instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat).
Instances of MonadFail should satisfy the following law: fail s should
be a left zero for >>=,
fail s >>= f = fail s
If your Monad is also MonadPlus, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Instances
class Functor f => Applicative (f :: Type -> Type) where Source #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
Using ApplicativeDo: 'fs ' can be understood as
the <*> asdo expression
do f <- fs a <- as pure (f a)
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
'as ' can be understood as the *> bsdo expression
do as bs
This is a tad complicated for our ApplicativeDo extension
which will give it a Monad constraint. For an Applicative
constraint we write it of the form
do _ <- as b <- bs pure b
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Using ApplicativeDo: 'as ' can be understood as
the <* bsdo expression
do a <- as bs pure a
Instances
| Applicative [] | Since: base-2.1 |
| Applicative Maybe | Since: base-2.1 |
| Applicative IO | Since: base-2.1 |
| Applicative Par1 | Since: base-4.9.0.0 |
| Applicative Q | |
| Applicative Solo | Since: base-4.15 |
| Applicative Complex | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Applicative Option | Since: base-4.9.0.0 |
| Applicative ZipList | f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)where (\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}Since: base-2.1 |
Defined in Control.Applicative | |
| Applicative Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity | |
| Applicative STM | Since: base-4.8.0.0 |
| Applicative First | Since: base-4.8.0.0 |
| Applicative Last | Since: base-4.8.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Applicative Sum | Since: base-4.8.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative ReadPrec | Since: base-4.6.0.0 |
Defined in Text.ParserCombinators.ReadPrec | |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
Defined in GHC.Base | |
| Applicative PutM | |
| Applicative Get | |
| Applicative Put | |
| Applicative Tree | |
| Applicative Seq | Since: containers-0.5.4 |
| Applicative Capability | |
Defined in System.Console.Terminfo.Base Methods pure :: a -> Capability a Source # (<*>) :: Capability (a -> b) -> Capability a -> Capability b Source # liftA2 :: (a -> b -> c) -> Capability a -> Capability b -> Capability c Source # (*>) :: Capability a -> Capability b -> Capability b Source # (<*) :: Capability a -> Capability b -> Capability a Source # | |
| Applicative P | Since: base-4.5.0.0 |
| Applicative UniqSM # | |
| Applicative Pair # | |
| Applicative UnifyResultM # | |
Defined in GHC.Core.Unify Methods pure :: a -> UnifyResultM a Source # (<*>) :: UnifyResultM (a -> b) -> UnifyResultM a -> UnifyResultM b Source # liftA2 :: (a -> b -> c) -> UnifyResultM a -> UnifyResultM b -> UnifyResultM c Source # (*>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b Source # (<*) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM a Source # | |
| Applicative P # | |
| Applicative PV # | |
| Applicative LiftM # | |
| Applicative Hsc # | |
| Applicative CompPipeline # | |
Defined in GHC.Driver.Pipeline.Monad Methods pure :: a -> CompPipeline a Source # (<*>) :: CompPipeline (a -> b) -> CompPipeline a -> CompPipeline b Source # liftA2 :: (a -> b -> c) -> CompPipeline a -> CompPipeline b -> CompPipeline c Source # (*>) :: CompPipeline a -> CompPipeline b -> CompPipeline b Source # (<*) :: CompPipeline a -> CompPipeline b -> CompPipeline a Source # | |
| Applicative Ghc # | |
| Applicative CoreM # | |
| Applicative SimplM # | |
| Applicative TcPluginM # | |
Defined in GHC.Tc.Types | |
| Applicative PD # | |
| Applicative MetaTyVarUpdateResult # | |
Defined in GHC.Tc.Utils.Unify Methods pure :: a -> MetaTyVarUpdateResult a Source # (<*>) :: MetaTyVarUpdateResult (a -> b) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b Source # liftA2 :: (a -> b -> c) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult c Source # (*>) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult b Source # (<*) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult a Source # | |
| Applicative TcS # | |
| Applicative CpsRn # | |
| Applicative MatchResult # | Product is an "or" on falliblity---the combined match result is infallible only if the left and right argument match results both were. This is useful for combining a bunch of alternatives together and then
getting the overall falliblity of the entire group. See |
Defined in GHC.HsToCore.Monad Methods pure :: a -> MatchResult a Source # (<*>) :: MatchResult (a -> b) -> MatchResult a -> MatchResult b Source # liftA2 :: (a -> b -> c) -> MatchResult a -> MatchResult b -> MatchResult c Source # (*>) :: MatchResult a -> MatchResult b -> MatchResult b Source # (<*) :: MatchResult a -> MatchResult b -> MatchResult a Source # | |
| Applicative LlvmM # | |
| Applicative NatM # | |
| Applicative FCode # | |
| Applicative CmmParse # | |
Defined in GHC.StgToCmm.ExtCode | |
| Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
| Applicative (U1 :: Type -> Type) | Since: base-4.9.0.0 |
| Monoid a => Applicative ((,) a) | For tuples, the ("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)Since: base-2.1 |
| Applicative (ST s) | Since: base-4.4.0.0 |
| Monad m => Applicative (WrappedMonad m) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # | |
| Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # | |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| (Functor m, Monad m) => Applicative (MaybeT m) | |
Defined in Control.Monad.Trans.Maybe | |
| Applicative m => Applicative (ListT m) | |
Defined in Control.Monad.Trans.List | |
| Applicative (State s) # | |
Defined in GHC.Utils.Monad.State | |
| Applicative (MaybeErr err) # | |
Defined in GHC.Data.Maybe Methods pure :: a -> MaybeErr err a Source # (<*>) :: MaybeErr err (a -> b) -> MaybeErr err a -> MaybeErr err b Source # liftA2 :: (a -> b -> c) -> MaybeErr err a -> MaybeErr err b -> MaybeErr err c Source # (*>) :: MaybeErr err a -> MaybeErr err b -> MaybeErr err b Source # (<*) :: MaybeErr err a -> MaybeErr err b -> MaybeErr err a Source # | |
| Applicative (SetM s) | |
| Applicative (CmdLineP s) # | |
Defined in GHC.Driver.CmdLine Methods pure :: a -> CmdLineP s a Source # (<*>) :: CmdLineP s (a -> b) -> CmdLineP s a -> CmdLineP s b Source # liftA2 :: (a -> b -> c) -> CmdLineP s a -> CmdLineP s b -> CmdLineP s c Source # (*>) :: CmdLineP s a -> CmdLineP s b -> CmdLineP s b Source # (<*) :: CmdLineP s a -> CmdLineP s b -> CmdLineP s a Source # | |
| Monad m => Applicative (EwM m) # | |
| Applicative (IOEnv m) # | |
| Applicative m => Applicative (GhcT m) # | |
| Applicative (RegM freeRegs) # | |
Defined in GHC.CmmToAsm.Reg.Linear.State Methods pure :: a -> RegM freeRegs a Source # (<*>) :: RegM freeRegs (a -> b) -> RegM freeRegs a -> RegM freeRegs b Source # liftA2 :: (a -> b -> c) -> RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs c Source # (*>) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs b Source # (<*) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs a Source # | |
| Applicative f => Applicative (Rec1 f) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b) => Applicative ((,,) a b) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # | |
| Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source # | |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
Defined in Data.Functor.Const | |
| Applicative f => Applicative (Ap f) | Since: base-4.12.0.0 |
| Applicative f => Applicative (Alt f) | Since: base-4.8.0.0 |
| (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 Source # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c Source # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a Source # | |
| (Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a Source # (<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c Source # (*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # | |
| Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a Source # (<*>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b Source # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c Source # (*>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b Source # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a Source # | |
| Applicative m => Applicative (IdentityT m) | |
Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a Source # (<*>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b Source # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c Source # (*>) :: IdentityT m a -> IdentityT m b -> IdentityT m b Source # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a Source # | |
| (Functor m, Monad m) => Applicative (ErrorT e m) | |
Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a Source # (<*>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b Source # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c Source # (*>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b Source # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a Source # | |
| Monad m => Applicative (Stream m a) # | |
Defined in GHC.Data.Stream Methods pure :: a0 -> Stream m a a0 Source # (<*>) :: Stream m a (a0 -> b) -> Stream m a a0 -> Stream m a b Source # liftA2 :: (a0 -> b -> c) -> Stream m a a0 -> Stream m a b -> Stream m a c Source # (*>) :: Stream m a a0 -> Stream m a b -> Stream m a b Source # (<*) :: Stream m a a0 -> Stream m a b -> Stream m a a0 Source # | |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Applicative ((->) r) | Since: base-2.1 |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source # | |
| (Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source # | |
| (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 Source # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c Source # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a Source # | |
| (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 Source # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c Source # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a Source # | |
| Applicative (ContT r m) | |
Defined in Control.Monad.Trans.Cont | |
| Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source # | |
| (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 Source # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c Source # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # | |
| (Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
| (Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
| (Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.CPS Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # | |
class Foldable (t :: Type -> Type) where Source #
The Foldable class represents data structures that can be reduced to a summary value one element at a time. Strict left-associative folds are a good fit for space-efficient reduction, while lazy right-associative folds are a good fit for corecursive iteration, or for folds that short-circuit after processing an initial subsequence of the structure's elements.
Instances can be derived automatically by enabling the DeriveFoldable
extension. For example, a derived instance for a binary tree might be:
{-# LANGUAGE DeriveFoldable #-}
data Tree a = Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving FoldableA more detailed description can be found in the overview section of Data.Foldable.
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source #
Map each element of the structure into a monoid, and combine the
results with (. This fold is right-associative and lazy in the
accumulator. For strict left-associative folds consider <>)foldMap`
instead.
Examples
Basic usage:
>>>foldMap Sum [1, 3, 5]Sum {getSum = 9}
>>>foldMap Product [1, 3, 5]Product {getProduct = 15}
>>>foldMap (replicate 3) [1, 2, 3][1,1,1,2,2,2,3,3,3]
When a Monoid's ( is lazy in its second argument, <>)foldMap can
return a result even from an unbounded structure. For example, lazy
accumulation enables Data.ByteString.Builder to efficiently serialise
large data structures and produce the output incrementally:
>>>import qualified Data.ByteString.Lazy as L>>>import qualified Data.ByteString.Builder as B>>>let bld :: Int -> B.Builder; bld i = B.intDec i <> B.word8 0x20>>>let lbs = B.toLazyByteString $ foldMap bld [0..]>>>L.take 64 lbs"0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24"
foldr :: (a -> b -> b) -> b -> t a -> b Source #
Right-associative fold of a structure, lazy in the accumulator.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that since the head of the resulting expression is produced by an
application of the operator to the first element of the list, given an
operator lazy in its right argument, foldr can produce a terminating
expression from an unbounded list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
Examples
Basic usage:
>>>foldr (||) False [False, True, False]True
>>>foldr (||) False []False
>>>foldr (\c acc -> acc ++ [c]) "foo" ['a', 'b', 'c', 'd']"foodcba"
Infinite structures
⚠️ Applying foldr to infinite structures usually doesn't terminate.
It may still terminate under one of the following conditions:
- the folding function is short-circuiting
- the folding function is lazy on its second argument
Short-circuiting
( short-circuits on ||)True values, so the following terminates
because there is a True value finitely far from the left side:
>>>foldr (||) False (True : repeat False)True
But the following doesn't terminate:
>>>foldr (||) False (repeat False ++ [True])* Hangs forever *
Laziness in the second argument
Applying foldr to infinite structures terminates when the operator is
lazy in its second argument (the initial accumulator is never used in
this case, and so could be left undefined, but [] is more clear):
>>>take 5 $ foldr (\i acc -> i : fmap (+3) acc) [] (repeat 1)[1,4,7,10,13]
foldl :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure, lazy in the accumulator. This is rarely what you want, but can work well for structures with efficient right-to-left sequencing and an operator that is lazy in its left argument.
In the case of lists, foldl, when applied to a binary operator, a
starting value (typically the left-identity of the operator), and a
list, reduces the list using the binary operator, from left to right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. Like all left-associative folds,
foldl will diverge if given an infinite list.
If you want an efficient strict left-fold, you probably want to use
foldl` instead of foldl. The reason for this is that the latter
does not force the inner results (e.g. z `f` x1 in the above
example) before applying them to the operator (e.g. to (`f` x2)).
This results in a thunk chain \(\mathcal{O}(n)\) elements long, which
then must be evaluated from the outside-in.
For a general Foldable structure this should be semantically identical
to:
foldl f z =foldlf z .toList
Examples
The first example is a strict fold, which in practice is best performed
with foldl`.
>>>foldl (+) 42 [1,2,3,4]52
Though the result below is lazy, the input is reversed before prepending it to the initial accumulator, so corecursion begins only after traversing the entire input string.
>>>foldl (\acc c -> c : acc) "abcd" "efgh""hgfeabcd"
A left fold of a structure that is infinite on the right cannot terminate, even when for any finite input the fold just returns the initial accumulator:
>>>foldl (\a _ -> a) 0 $ repeat 1* Hangs forever *
foldl' :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to Weak Head Normal
Form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a
finite structure to a single strict result (e.g. sum).
For a general Foldable structure this should be semantically identical
to,
foldl' f z =foldl'f z .toList
Since: base-4.6.0.0
foldr1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
Examples
Basic usage:
>>>foldr1 (+) [1..4]10
>>>foldr1 (+) []Exception: Prelude.foldr1: empty list
>>>foldr1 (+) Nothing*** Exception: foldr1: empty structure
>>>foldr1 (-) [1..4]-2
>>>foldr1 (&&) [True, False, True, True]False
>>>foldr1 (||) [False, False, True, True]True
>>>foldr1 (+) [1..]* Hangs forever *
foldl1 :: (a -> a -> a) -> t a -> a Source #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
This function is non-total and will raise a runtime exception if the structure happens to be empty.
foldl1f =foldl1f .toList
Examples
Basic usage:
>>>foldl1 (+) [1..4]10
>>>foldl1 (+) []*** Exception: Prelude.foldl1: empty list
>>>foldl1 (+) Nothing*** Exception: foldl1: empty structure
>>>foldl1 (-) [1..4]-8
>>>foldl1 (&&) [True, False, True, True]False
>>>foldl1 (||) [False, False, True, True]True
>>>foldl1 (+) [1..]* Hangs forever *
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 left-most 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 left-most.
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 Source #
Does the element occur in the structure?
Note: elem is often used in infix form.
Examples
Basic usage:
>>>3 `elem` []False
>>>3 `elem` [1,2]False
>>>3 `elem` [1,2,3,4,5]True
For infinite structures, the default implementation of elem
terminates if the sought-after value exists at a finite distance
from the left side of the structure:
>>>3 `elem` [1..]True
>>>3 `elem` ([4..] ++ [3])* Hangs forever *
Since: base-4.8.0.0
maximum :: Ord a => t a -> a Source #
The largest element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty. A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the maximum in faster than linear time.
Examples
Basic usage:
>>>maximum [1..10]10
>>>maximum []*** Exception: Prelude.maximum: empty list
>>>maximum Nothing*** Exception: maximum: empty structure
Since: base-4.8.0.0
minimum :: Ord a => t a -> a Source #
The least element of a non-empty structure.
This function is non-total and will raise a runtime exception if the structure happens to be empty A structure that supports random access and maintains its elements in order should provide a specialised implementation to return the minimum in faster than linear time.
Examples
Basic usage:
>>>minimum [1..10]1
>>>minimum []*** Exception: Prelude.minimum: empty list
>>>minimum Nothing*** Exception: minimum: empty structure
Since: base-4.8.0.0
sum :: Num a => t a -> a Source #
The sum function computes the sum of the numbers of a structure.
Examples
Basic usage:
>>>sum []0
>>>sum [42]42
>>>sum [1..10]55
>>>sum [4.1, 2.0, 1.7]7.8
>>>sum [1..]* Hangs forever *
Since: base-4.8.0.0
product :: Num a => t a -> a Source #
The product function computes the product of the numbers of a
structure.
Examples
Basic usage:
>>>product []1
>>>product [42]42
>>>product [1..10]3628800
>>>product [4.1, 2.0, 1.7]13.939999999999998
>>>product [1..]* Hangs forever *
Since: base-4.8.0.0
Instances
| Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # | |
| Foldable Solo | Since: base-4.15 |
Defined in Data.Foldable Methods fold :: Monoid m => Solo m -> m Source # foldMap :: Monoid m => (a -> m) -> Solo a -> m Source # foldMap' :: Monoid m => (a -> m) -> Solo a -> m Source # foldr :: (a -> b -> b) -> b -> Solo a -> b Source # foldr' :: (a -> b -> b) -> b -> Solo a -> b Source # foldl :: (b -> a -> b) -> b -> Solo a -> b Source # foldl' :: (b -> a -> b) -> b -> Solo a -> b Source # foldr1 :: (a -> a -> a) -> Solo a -> a Source # foldl1 :: (a -> a -> a) -> Solo a -> a Source # toList :: Solo a -> [a] Source # null :: Solo a -> Bool Source # length :: Solo a -> Int Source # elem :: Eq a => a -> Solo a -> Bool Source # maximum :: Ord a => Solo a -> a Source # minimum :: Ord a => Solo a -> a Source # | |
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m Source # foldMap :: Monoid m => (a -> m) -> Complex a -> m Source # foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source # foldr :: (a -> b -> b) -> b -> Complex a -> b Source # foldr' :: (a -> b -> b) -> b -> Complex a -> b Source # foldl :: (b -> a -> b) -> b -> Complex a -> b Source # foldl' :: (b -> a -> b) -> b -> Complex a -> b Source # foldr1 :: (a -> a -> a) -> Complex a -> a Source # foldl1 :: (a -> a -> a) -> Complex a -> a Source # toList :: Complex a -> [a] Source # null :: Complex a -> Bool Source # length :: Complex a -> Int Source # elem :: Eq a => a -> Complex a -> Bool Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
| Foldable Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m Source # foldMap :: Monoid m => (a -> m) -> Option a -> m Source # foldMap' :: Monoid m => (a -> m) -> Option a -> m Source # foldr :: (a -> b -> b) -> b -> Option a -> b Source # foldr' :: (a -> b -> b) -> b -> Option a -> b Source # foldl :: (b -> a -> b) -> b -> Option a -> b Source # foldl' :: (b -> a -> b) -> b -> Option a -> b Source # foldr1 :: (a -> a -> a) -> Option a -> a Source # foldl1 :: (a -> a -> a) -> Option a -> a Source # toList :: Option a -> [a] Source # null :: Option a -> Bool Source # length :: Option a -> Int Source # elem :: Eq a => a -> Option a -> Bool Source # maximum :: Ord a => Option a -> a Source # minimum :: Ord a => Option a -> a Source # | |
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # | |
| Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m Source # foldMap :: Monoid m => (a -> m) -> IntMap a -> m Source # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m Source # foldr :: (a -> b -> b) -> b -> IntMap a -> b Source # foldr' :: (a -> b -> b) -> b -> IntMap a -> b Source # foldl :: (b -> a -> b) -> b -> IntMap a -> b Source # foldl' :: (b -> a -> b) -> b -> IntMap a -> b Source # foldr1 :: (a -> a -> a) -> IntMap a -> a Source # foldl1 :: (a -> a -> a) -> IntMap a -> a Source # toList :: IntMap a -> [a] Source # null :: IntMap a -> Bool Source # length :: IntMap a -> Int Source # elem :: Eq a => a -> IntMap a -> Bool Source # maximum :: Ord a => IntMap a -> a Source # minimum :: Ord a => IntMap a -> a Source # | |
| Foldable SCC | Since: containers-0.5.9 |
Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m Source # foldMap :: Monoid m => (a -> m) -> SCC a -> m Source # foldMap' :: Monoid m => (a -> m) -> SCC a -> m Source # foldr :: (a -> b -> b) -> b -> SCC a -> b Source # foldr' :: (a -> b -> b) -> b -> SCC a -> b Source # foldl :: (b -> a -> b) -> b -> SCC a -> b Source # foldl' :: (b -> a -> b) -> b -> SCC a -> b Source # foldr1 :: (a -> a -> a) -> SCC a -> a Source # foldl1 :: (a -> a -> a) -> SCC a -> a Source # toList :: SCC a -> [a] Source # null :: SCC a -> Bool Source # length :: SCC a -> Int Source # elem :: Eq a => a -> SCC a -> Bool Source # maximum :: Ord a => SCC a -> a Source # minimum :: Ord a => SCC a -> a Source # | |
| Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m Source # foldMap :: Monoid m => (a -> m) -> Tree a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source # foldr :: (a -> b -> b) -> b -> Tree a -> b Source # foldr' :: (a -> b -> b) -> b -> Tree a -> b Source # foldl :: (b -> a -> b) -> b -> Tree a -> b Source # foldl' :: (b -> a -> b) -> b -> Tree a -> b Source # foldr1 :: (a -> a -> a) -> Tree a -> a Source # foldl1 :: (a -> a -> a) -> Tree a -> a Source # toList :: Tree a -> [a] Source # null :: Tree a -> Bool Source # length :: Tree a -> Int Source # elem :: Eq a => a -> Tree a -> Bool Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # | |
| Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m Source # foldMap :: Monoid m => (a -> m) -> Seq a -> m Source # foldMap' :: Monoid m => (a -> m) -> Seq a -> m Source # foldr :: (a -> b -> b) -> b -> Seq a -> b Source # foldr' :: (a -> b -> b) -> b -> Seq a -> b Source # foldl :: (b -> a -> b) -> b -> Seq a -> b Source # foldl' :: (b -> a -> b) -> b -> Seq a -> b Source # foldr1 :: (a -> a -> a) -> Seq a -> a Source # foldl1 :: (a -> a -> a) -> Seq a -> a Source # toList :: Seq a -> [a] Source # null :: Seq a -> Bool Source # length :: Seq a -> Int Source # elem :: Eq a => a -> Seq a -> Bool Source # maximum :: Ord a => Seq a -> a Source # minimum :: Ord a => Seq a -> a Source # | |
| Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m Source # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m Source # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m Source # foldr :: (a -> b -> b) -> b -> FingerTree a -> b Source # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b Source # foldl :: (b -> a -> b) -> b -> FingerTree a -> b Source # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b Source # foldr1 :: (a -> a -> a) -> FingerTree a -> a Source # foldl1 :: (a -> a -> a) -> FingerTree a -> a Source # toList :: FingerTree a -> [a] Source # null :: FingerTree a -> Bool Source # length :: FingerTree a -> Int Source # elem :: Eq a => a -> FingerTree a -> Bool Source # maximum :: Ord a => FingerTree a -> a Source # minimum :: Ord a => FingerTree a -> a Source # sum :: Num a => FingerTree a -> a Source # product :: Num a => FingerTree a -> a Source # | |
| Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m Source # foldMap :: Monoid m => (a -> m) -> Digit a -> m Source # foldMap' :: Monoid m => (a -> m) -> Digit a -> m Source # foldr :: (a -> b -> b) -> b -> Digit a -> b Source # foldr' :: (a -> b -> b) -> b -> Digit a -> b Source # foldl :: (b -> a -> b) -> b -> Digit a -> b Source # foldl' :: (b -> a -> b) -> b -> Digit a -> b Source # foldr1 :: (a -> a -> a) -> Digit a -> a Source # foldl1 :: (a -> a -> a) -> Digit a -> a Source # toList :: Digit a -> [a] Source # null :: Digit a -> Bool Source # length :: Digit a -> Int Source # elem :: Eq a => a -> Digit a -> Bool Source # maximum :: Ord a => Digit a -> a Source # minimum :: Ord a => Digit a -> a Source # | |
| Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m Source # foldMap :: Monoid m => (a -> m) -> Node a -> m Source # foldMap' :: Monoid m => (a -> m) -> Node a -> m Source # foldr :: (a -> b -> b) -> b -> Node a -> b Source # foldr' :: (a -> b -> b) -> b -> Node a -> b Source # foldl :: (b -> a -> b) -> b -> Node a -> b Source # foldl' :: (b -> a -> b) -> b -> Node a -> b Source # foldr1 :: (a -> a -> a) -> Node a -> a Source # foldl1 :: (a -> a -> a) -> Node a -> a Source # toList :: Node a -> [a] Source # null :: Node a -> Bool Source # length :: Node a -> Int Source # elem :: Eq a => a -> Node a -> Bool Source # maximum :: Ord a => Node a -> a Source # minimum :: Ord a => Node a -> a Source # | |
| Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m Source # foldMap :: Monoid m => (a -> m) -> Elem a -> m Source # foldMap' :: Monoid m => (a -> m) -> Elem a -> m Source # foldr :: (a -> b -> b) -> b -> Elem a -> b Source # foldr' :: (a -> b -> b) -> b -> Elem a -> b Source # foldl :: (b -> a -> b) -> b -> Elem a -> b Source # foldl' :: (b -> a -> b) -> b -> Elem a -> b Source # foldr1 :: (a -> a -> a) -> Elem a -> a Source # foldl1 :: (a -> a -> a) -> Elem a -> a Source # toList :: Elem a -> [a] Source # null :: Elem a -> Bool Source # length :: Elem a -> Int Source # elem :: Eq a => a -> Elem a -> Bool Source # maximum :: Ord a => Elem a -> a Source # minimum :: Ord a => Elem a -> a Source # | |
| Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewL a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m Source # foldr :: (a -> b -> b) -> b -> ViewL a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewL a -> b Source # foldl :: (b -> a -> b) -> b -> ViewL a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewL a -> b Source # foldr1 :: (a -> a -> a) -> ViewL a -> a Source # foldl1 :: (a -> a -> a) -> ViewL a -> a Source # toList :: ViewL a -> [a] Source # null :: ViewL a -> Bool Source # length :: ViewL a -> Int Source # elem :: Eq a => a -> ViewL a -> Bool Source # maximum :: Ord a => ViewL a -> a Source # minimum :: Ord a => ViewL a -> a Source # | |
| Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewR a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m Source # foldr :: (a -> b -> b) -> b -> ViewR a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewR a -> b Source # foldl :: (b -> a -> b) -> b -> ViewR a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewR a -> b Source # foldr1 :: (a -> a -> a) -> ViewR a -> a Source # foldl1 :: (a -> a -> a) -> ViewR a -> a Source # toList :: ViewR a -> [a] Source # null :: ViewR a -> Bool Source # length :: ViewR a -> Int Source # elem :: Eq a => a -> ViewR a -> Bool Source # maximum :: Ord a => ViewR a -> a Source # minimum :: Ord a => ViewR a -> a Source # | |
| Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m Source # foldMap :: Monoid m => (a -> m) -> Set a -> m Source # foldMap' :: Monoid m => (a -> m) -> Set a -> m Source # foldr :: (a -> b -> b) -> b -> Set a -> b Source # foldr' :: (a -> b -> b) -> b -> Set a -> b Source # foldl :: (b -> a -> b) -> b -> Set a -> b Source # foldl' :: (b -> a -> b) -> b -> Set a -> b Source # foldr1 :: (a -> a -> a) -> Set a -> a Source # foldl1 :: (a -> a -> a) -> Set a -> a Source # toList :: Set a -> [a] Source # null :: Set a -> Bool Source # length :: Set a -> Int Source # elem :: Eq a => a -> Set a -> Bool Source # maximum :: Ord a => Set a -> a Source # minimum :: Ord a => Set a -> a Source # | |
| Foldable GenClosure | |
Defined in GHC.Exts.Heap.Closures Methods fold :: Monoid m => GenClosure m -> m Source # foldMap :: Monoid m => (a -> m) -> GenClosure a -> m Source # foldMap' :: Monoid m => (a -> m) -> GenClosure a -> m Source # foldr :: (a -> b -> b) -> b -> GenClosure a -> b Source # foldr' :: (a -> b -> b) -> b -> GenClosure a -> b Source # foldl :: (b -> a -> b) -> b -> GenClosure a -> b Source # foldl' :: (b -> a -> b) -> b -> GenClosure a -> b Source # foldr1 :: (a -> a -> a) -> GenClosure a -> a Source # foldl1 :: (a -> a -> a) -> GenClosure a -> a Source # toList :: GenClosure a -> [a] Source # null :: GenClosure a -> Bool Source # length :: GenClosure a -> Int Source # elem :: Eq a => a -> GenClosure a -> Bool Source # maximum :: Ord a => GenClosure a -> a Source # minimum :: Ord a => GenClosure a -> a Source # sum :: Num a => GenClosure a -> a Source # product :: Num a => GenClosure a -> a Source # | |
| Foldable SizedSeq | |
Defined in SizedSeq Methods fold :: Monoid m => SizedSeq m -> m Source # foldMap :: Monoid m => (a -> m) -> SizedSeq a -> m Source # foldMap' :: Monoid m => (a -> m) -> SizedSeq a -> m Source # foldr :: (a -> b -> b) -> b -> SizedSeq a -> b Source # foldr' :: (a -> b -> b) -> b -> SizedSeq a -> b Source # foldl :: (b -> a -> b) -> b -> SizedSeq a -> b Source # foldl' :: (b -> a -> b) -> b -> SizedSeq a -> b Source # foldr1 :: (a -> a -> a) -> SizedSeq a -> a Source # foldl1 :: (a -> a -> a) -> SizedSeq a -> a Source # toList :: SizedSeq a -> [a] Source # null :: SizedSeq a -> Bool Source # length :: SizedSeq a -> Int Source # elem :: Eq a => a -> SizedSeq a -> Bool Source # maximum :: Ord a => SizedSeq a -> a Source # minimum :: Ord a => SizedSeq a -> a Source # | |
| Foldable UniqueMap # | |
Defined in GHC.Cmm.Dataflow.Collections Methods fold :: Monoid m => UniqueMap m -> m Source # foldMap :: Monoid m => (a -> m) -> UniqueMap a -> m Source # foldMap' :: Monoid m => (a -> m) -> UniqueMap a -> m Source # foldr :: (a -> b -> b) -> b -> UniqueMap a -> b Source # foldr' :: (a -> b -> b) -> b -> UniqueMap a -> b Source # foldl :: (b -> a -> b) -> b -> UniqueMap a -> b Source # foldl' :: (b -> a -> b) -> b -> UniqueMap a -> b Source # foldr1 :: (a -> a -> a) -> UniqueMap a -> a Source # foldl1 :: (a -> a -> a) -> UniqueMap a -> a Source # toList :: UniqueMap a -> [a] Source # null :: UniqueMap a -> Bool Source # length :: UniqueMap a -> Int Source # elem :: Eq a => a -> UniqueMap a -> Bool Source # maximum :: Ord a => UniqueMap a -> a Source # minimum :: Ord a => UniqueMap a -> a Source # | |
| Foldable GenWithIsBoot # | |
Defined in GHC.Unit.Types Methods fold :: Monoid m => GenWithIsBoot m -> m Source # foldMap :: Monoid m => (a -> m) -> GenWithIsBoot a -> m Source # foldMap' :: Monoid m => (a -> m) -> GenWithIsBoot a -> m Source # foldr :: (a -> b -> b) -> b -> GenWithIsBoot a -> b Source # foldr' :: (a -> b -> b) -> b -> GenWithIsBoot a -> b Source # foldl :: (b -> a -> b) -> b -> GenWithIsBoot a -> b Source # foldl' :: (b -> a -> b) -> b -> GenWithIsBoot a -> b Source # foldr1 :: (a -> a -> a) -> GenWithIsBoot a -> a Source # foldl1 :: (a -> a -> a) -> GenWithIsBoot a -> a Source # toList :: GenWithIsBoot a -> [a] Source # null :: GenWithIsBoot a -> Bool Source # length :: GenWithIsBoot a -> Int Source # elem :: Eq a => a -> GenWithIsBoot a -> Bool Source # maximum :: Ord a => GenWithIsBoot a -> a Source # minimum :: Ord a => GenWithIsBoot a -> a Source # sum :: Num a => GenWithIsBoot a -> a Source # product :: Num a => GenWithIsBoot a -> a Source # | |
| Foldable Pair # | |
Defined in GHC.Data.Pair Methods fold :: Monoid m => Pair m -> m Source # foldMap :: Monoid m => (a -> m) -> Pair a -> m Source # foldMap' :: Monoid m => (a -> m) -> Pair a -> m Source # foldr :: (a -> b -> b) -> b -> Pair a -> b Source # foldr' :: (a -> b -> b) -> b -> Pair a -> b Source # foldl :: (b -> a -> b) -> b -> Pair a -> b Source # foldl' :: (b -> a -> b) -> b -> Pair a -> b Source # foldr1 :: (a -> a -> a) -> Pair a -> a Source # foldl1 :: (a -> a -> a) -> Pair a -> a Source # toList :: Pair a -> [a] Source # null :: Pair a -> Bool Source # length :: Pair a -> Int Source # elem :: Eq a => a -> Pair a -> Bool Source # maximum :: Ord a => Pair a -> a Source # minimum :: Ord a => Pair a -> a Source # | |
| Foldable OrdList # | |
Defined in GHC.Data.OrdList Methods fold :: Monoid m => OrdList m -> m Source # foldMap :: Monoid m => (a -> m) -> OrdList a -> m Source # foldMap' :: Monoid m => (a -> m) -> OrdList a -> m Source # foldr :: (a -> b -> b) -> b -> OrdList a -> b Source # foldr' :: (a -> b -> b) -> b -> OrdList a -> b Source # foldl :: (b -> a -> b) -> b -> OrdList a -> b Source # foldl' :: (b -> a -> b) -> b -> OrdList a -> b Source # foldr1 :: (a -> a -> a) -> OrdList a -> a Source # foldl1 :: (a -> a -> a) -> OrdList a -> a Source # toList :: OrdList a -> [a] Source # null :: OrdList a -> Bool Source # length :: OrdList a -> Int Source # elem :: Eq a => a -> OrdList a -> Bool Source # maximum :: Ord a => OrdList a -> a Source # minimum :: Ord a => OrdList a -> a Source # | |
| Foldable BooleanFormula # | |
Defined in GHC.Data.BooleanFormula Methods fold :: Monoid m => BooleanFormula m -> m Source # foldMap :: Monoid m => (a -> m) -> BooleanFormula a -> m Source # foldMap' :: Monoid m => (a -> m) -> BooleanFormula a -> m Source # foldr :: (a -> b -> b) -> b -> BooleanFormula a -> b Source # foldr' :: (a -> b -> b) -> b -> BooleanFormula a -> b Source # foldl :: (b -> a -> b) -> b -> BooleanFormula a -> b Source # foldl' :: (b -> a -> b) -> b -> BooleanFormula a -> b Source # foldr1 :: (a -> a -> a) -> BooleanFormula a -> a Source # foldl1 :: (a -> a -> a) -> BooleanFormula a -> a Source # toList :: BooleanFormula a -> [a] Source # null :: BooleanFormula a -> Bool Source # length :: BooleanFormula a -> Int Source # elem :: Eq a => a -> BooleanFormula a -> Bool Source # maximum :: Ord a => BooleanFormula a -> a Source # minimum :: Ord a => BooleanFormula a -> a Source # sum :: Num a => BooleanFormula a -> a Source # product :: Num a => BooleanFormula a -> a Source # | |
| Foldable Bag # | |
Defined in GHC.Data.Bag Methods fold :: Monoid m => Bag m -> m Source # foldMap :: Monoid m => (a -> m) -> Bag a -> m Source # foldMap' :: Monoid m => (a -> m) -> Bag a -> m Source # foldr :: (a -> b -> b) -> b -> Bag a -> b Source # foldr' :: (a -> b -> b) -> b -> Bag a -> b Source # foldl :: (b -> a -> b) -> b -> Bag a -> b Source # foldl' :: (b -> a -> b) -> b -> Bag a -> b Source # foldr1 :: (a -> a -> a) -> Bag a -> a Source # foldl1 :: (a -> a -> a) -> Bag a -> a Source # toList :: Bag a -> [a] Source # null :: Bag a -> Bool Source # length :: Bag a -> Int Source # elem :: Eq a => a -> Bag a -> Bool Source # maximum :: Ord a => Bag a -> a Source # minimum :: Ord a => Bag a -> a Source # | |
| Foldable FieldLbl # | |
Defined in GHC.Types.FieldLabel Methods fold :: Monoid m => FieldLbl m -> m Source # foldMap :: Monoid m => (a -> m) -> FieldLbl a -> m Source # foldMap' :: Monoid m => (a -> m) -> FieldLbl a -> m Source # foldr :: (a -> b -> b) -> b -> FieldLbl a -> b Source # foldr' :: (a -> b -> b) -> b -> FieldLbl a -> b Source # foldl :: (b -> a -> b) -> b -> FieldLbl a -> b Source # foldl' :: (b -> a -> b) -> b -> FieldLbl a -> b Source # foldr1 :: (a -> a -> a) -> FieldLbl a -> a Source # foldl1 :: (a -> a -> a) -> FieldLbl a -> a Source # toList :: FieldLbl a -> [a] Source # null :: FieldLbl a -> Bool Source # length :: FieldLbl a -> Int Source # elem :: Eq a => a -> FieldLbl a -> Bool Source # maximum :: Ord a => FieldLbl a -> a Source # minimum :: Ord a => FieldLbl a -> a Source # | |
| Foldable LabelMap # | |
Defined in GHC.Cmm.Dataflow.Label Methods fold :: Monoid m => LabelMap m -> m Source # foldMap :: Monoid m => (a -> m) -> LabelMap a -> m Source # foldMap' :: Monoid m => (a -> m) -> LabelMap a -> m Source # foldr :: (a -> b -> b) -> b -> LabelMap a -> b Source # foldr' :: (a -> b -> b) -> b -> LabelMap a -> b Source # foldl :: (b -> a -> b) -> b -> LabelMap a -> b Source # foldl' :: (b -> a -> b) -> b -> LabelMap a -> b Source # foldr1 :: (a -> a -> a) -> LabelMap a -> a Source # foldl1 :: (a -> a -> a) -> LabelMap a -> a Source # toList :: LabelMap a -> [a] Source # null :: LabelMap a -> Bool Source # length :: LabelMap a -> Int Source # elem :: Eq a => a -> LabelMap a -> Bool Source # maximum :: Ord a => LabelMap a -> a Source # minimum :: Ord a => LabelMap a -> a Source # | |
| Foldable RecordPatSynField # | |
Defined in GHC.Hs.Binds Methods fold :: Monoid m => RecordPatSynField m -> m Source # foldMap :: Monoid m => (a -> m) -> RecordPatSynField a -> m Source # foldMap' :: Monoid m => (a -> m) -> RecordPatSynField a -> m Source # foldr :: (a -> b -> b) -> b -> RecordPatSynField a -> b Source # foldr' :: (a -> b -> b) -> b -> RecordPatSynField a -> b Source # foldl :: (b -> a -> b) -> b -> RecordPatSynField a -> b Source # foldl' :: (b -> a -> b) -> b -> RecordPatSynField a -> b Source # foldr1 :: (a -> a -> a) -> RecordPatSynField a -> a Source # foldl1 :: (a -> a -> a) -> RecordPatSynField a -> a Source # toList :: RecordPatSynField a -> [a] Source # null :: RecordPatSynField a -> Bool Source # length :: RecordPatSynField a -> Int Source # elem :: Eq a => a -> RecordPatSynField a -> Bool Source # maximum :: Ord a => RecordPatSynField a -> a Source # minimum :: Ord a => RecordPatSynField a -> a Source # sum :: Num a => RecordPatSynField a -> a Source # product :: Num a => RecordPatSynField a -> a Source # | |
| Foldable AnnProvenance # | |
Defined in GHC.Hs.Decls Methods fold :: Monoid m => AnnProvenance m -> m Source # foldMap :: Monoid m => (a -> m) -> AnnProvenance a -> m Source # foldMap' :: Monoid m => (a -> m) -> AnnProvenance a -> m Source # foldr :: (a -> b -> b) -> b -> AnnProvenance a -> b Source # foldr' :: (a -> b -> b) -> b -> AnnProvenance a -> b Source # foldl :: (b -> a -> b) -> b -> AnnProvenance a -> b Source # foldl' :: (b -> a -> b) -> b -> AnnProvenance a -> b Source # foldr1 :: (a -> a -> a) -> AnnProvenance a -> a Source # foldl1 :: (a -> a -> a) -> AnnProvenance a -> a Source # toList :: AnnProvenance a -> [a] Source # null :: AnnProvenance a -> Bool Source # length :: AnnProvenance a -> Int Source # elem :: Eq a => a -> AnnProvenance a -> Bool Source # maximum :: Ord a => AnnProvenance a -> a Source # minimum :: Ord a => AnnProvenance a -> a Source # sum :: Num a => AnnProvenance a -> a Source # product :: Num a => AnnProvenance a -> a Source # | |
| Foldable IdentifierDetails # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => IdentifierDetails m -> m Source # foldMap :: Monoid m => (a -> m) -> IdentifierDetails a -> m Source # foldMap' :: Monoid m => (a -> m) -> IdentifierDetails a -> m Source # foldr :: (a -> b -> b) -> b -> IdentifierDetails a -> b Source # foldr' :: (a -> b -> b) -> b -> IdentifierDetails a -> b Source # foldl :: (b -> a -> b) -> b -> IdentifierDetails a -> b Source # foldl' :: (b -> a -> b) -> b -> IdentifierDetails a -> b Source # foldr1 :: (a -> a -> a) -> IdentifierDetails a -> a Source # foldl1 :: (a -> a -> a) -> IdentifierDetails a -> a Source # toList :: IdentifierDetails a -> [a] Source # null :: IdentifierDetails a -> Bool Source # length :: IdentifierDetails a -> Int Source # elem :: Eq a => a -> IdentifierDetails a -> Bool Source # maximum :: Ord a => IdentifierDetails a -> a Source # minimum :: Ord a => IdentifierDetails a -> a Source # sum :: Num a => IdentifierDetails a -> a Source # product :: Num a => IdentifierDetails a -> a Source # | |
| Foldable NodeInfo # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => NodeInfo m -> m Source # foldMap :: Monoid m => (a -> m) -> NodeInfo a -> m Source # foldMap' :: Monoid m => (a -> m) -> NodeInfo a -> m Source # foldr :: (a -> b -> b) -> b -> NodeInfo a -> b Source # foldr' :: (a -> b -> b) -> b -> NodeInfo a -> b Source # foldl :: (b -> a -> b) -> b -> NodeInfo a -> b Source # foldl' :: (b -> a -> b) -> b -> NodeInfo a -> b Source # foldr1 :: (a -> a -> a) -> NodeInfo a -> a Source # foldl1 :: (a -> a -> a) -> NodeInfo a -> a Source # toList :: NodeInfo a -> [a] Source # null :: NodeInfo a -> Bool Source # length :: NodeInfo a -> Int Source # elem :: Eq a => a -> NodeInfo a -> Bool Source # maximum :: Ord a => NodeInfo a -> a Source # minimum :: Ord a => NodeInfo a -> a Source # | |
| Foldable SourcedNodeInfo # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => SourcedNodeInfo m -> m Source # foldMap :: Monoid m => (a -> m) -> SourcedNodeInfo a -> m Source # foldMap' :: Monoid m => (a -> m) -> SourcedNodeInfo a -> m Source # foldr :: (a -> b -> b) -> b -> SourcedNodeInfo a -> b Source # foldr' :: (a -> b -> b) -> b -> SourcedNodeInfo a -> b Source # foldl :: (b -> a -> b) -> b -> SourcedNodeInfo a -> b Source # foldl' :: (b -> a -> b) -> b -> SourcedNodeInfo a -> b Source # foldr1 :: (a -> a -> a) -> SourcedNodeInfo a -> a Source # foldl1 :: (a -> a -> a) -> SourcedNodeInfo a -> a Source # toList :: SourcedNodeInfo a -> [a] Source # null :: SourcedNodeInfo a -> Bool Source # length :: SourcedNodeInfo a -> Int Source # elem :: Eq a => a -> SourcedNodeInfo a -> Bool Source # maximum :: Ord a => SourcedNodeInfo a -> a Source # minimum :: Ord a => SourcedNodeInfo a -> a Source # sum :: Num a => SourcedNodeInfo a -> a Source # product :: Num a => SourcedNodeInfo a -> a Source # | |
| Foldable HieAST # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => HieAST m -> m Source # foldMap :: Monoid m => (a -> m) -> HieAST a -> m Source # foldMap' :: Monoid m => (a -> m) -> HieAST a -> m Source # foldr :: (a -> b -> b) -> b -> HieAST a -> b Source # foldr' :: (a -> b -> b) -> b -> HieAST a -> b Source # foldl :: (b -> a -> b) -> b -> HieAST a -> b Source # foldl' :: (b -> a -> b) -> b -> HieAST a -> b Source # foldr1 :: (a -> a -> a) -> HieAST a -> a Source # foldl1 :: (a -> a -> a) -> HieAST a -> a Source # toList :: HieAST a -> [a] Source # null :: HieAST a -> Bool Source # length :: HieAST a -> Int Source # elem :: Eq a => a -> HieAST a -> Bool Source # maximum :: Ord a => HieAST a -> a Source # minimum :: Ord a => HieAST a -> a Source # | |
| Foldable HieASTs # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => HieASTs m -> m Source # foldMap :: Monoid m => (a -> m) -> HieASTs a -> m Source # foldMap' :: Monoid m => (a -> m) -> HieASTs a -> m Source # foldr :: (a -> b -> b) -> b -> HieASTs a -> b Source # foldr' :: (a -> b -> b) -> b -> HieASTs a -> b Source # foldl :: (b -> a -> b) -> b -> HieASTs a -> b Source # foldl' :: (b -> a -> b) -> b -> HieASTs a -> b Source # foldr1 :: (a -> a -> a) -> HieASTs a -> a Source # foldl1 :: (a -> a -> a) -> HieASTs a -> a Source # toList :: HieASTs a -> [a] Source # null :: HieASTs a -> Bool Source # length :: HieASTs a -> Int Source # elem :: Eq a => a -> HieASTs a -> Bool Source # maximum :: Ord a => HieASTs a -> a Source # minimum :: Ord a => HieASTs a -> a Source # | |
| Foldable HieArgs # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => HieArgs m -> m Source # foldMap :: Monoid m => (a -> m) -> HieArgs a -> m Source # foldMap' :: Monoid m => (a -> m) -> HieArgs a -> m Source # foldr :: (a -> b -> b) -> b -> HieArgs a -> b Source # foldr' :: (a -> b -> b) -> b -> HieArgs a -> b Source # foldl :: (b -> a -> b) -> b -> HieArgs a -> b Source # foldl' :: (b -> a -> b) -> b -> HieArgs a -> b Source # foldr1 :: (a -> a -> a) -> HieArgs a -> a Source # foldl1 :: (a -> a -> a) -> HieArgs a -> a Source # toList :: HieArgs a -> [a] Source # null :: HieArgs a -> Bool Source # length :: HieArgs a -> Int Source # elem :: Eq a => a -> HieArgs a -> Bool Source # maximum :: Ord a => HieArgs a -> a Source # minimum :: Ord a => HieArgs a -> a Source # | |
| Foldable HieType # | |
Defined in GHC.Iface.Ext.Types Methods fold :: Monoid m => HieType m -> m Source # foldMap :: Monoid m => (a -> m) -> HieType a -> m Source # foldMap' :: Monoid m => (a -> m) -> HieType a -> m Source # foldr :: (a -> b -> b) -> b -> HieType a -> b Source # foldr' :: (a -> b -> b) -> b -> HieType a -> b Source # foldl :: (b -> a -> b) -> b -> HieType a -> b Source # foldl' :: (b -> a -> b) -> b -> HieType a -> b Source # foldr1 :: (a -> a -> a) -> HieType a -> a Source # foldl1 :: (a -> a -> a) -> HieType a -> a Source # toList :: HieType a -> [a] Source # null :: HieType a -> Bool Source # length :: HieType a -> Int Source # elem :: Eq a => a -> HieType a -> Bool Source # maximum :: Ord a => HieType a -> a Source # minimum :: Ord a => HieType a -> a Source # | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |
| Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # | |
| Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # | |
| Foldable (UAddr :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # | |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |
| Foldable (UDouble :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # | |
| Foldable (UFloat :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # | |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |
| Foldable ((,) a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # | |
| Foldable (Array i) | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # | |
| Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # | |
| Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # | |
| Foldable (Map k) | Folds in order of increasing key. |
Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m Source # foldMap :: Monoid m => (a -> m) -> Map k a -> m Source # foldMap' :: Monoid m => (a -> m) -> Map k a -> m Source # foldr :: (a -> b -> b) -> b -> Map k a -> b Source # foldr' :: (a -> b -> b) -> b -> Map k a -> b Source # foldl :: (b -> a -> b) -> b -> Map k a -> b Source # foldl' :: (b -> a -> b) -> b -> Map k a -> b Source # foldr1 :: (a -> a -> a) -> Map k a -> a Source # foldl1 :: (a -> a -> a) -> Map k a -> a Source # toList :: Map k a -> [a] Source # null :: Map k a -> Bool Source # length :: Map k a -> Int Source # elem :: Eq a => a -> Map k a -> Bool Source # maximum :: Ord a => Map k a -> a Source # minimum :: Ord a => Map k a -> a Source # | |
| Foldable f => Foldable (MaybeT f) | |
Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m Source # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldr1 :: (a -> a -> a) -> MaybeT f a -> a Source # foldl1 :: (a -> a -> a) -> MaybeT f a -> a Source # toList :: MaybeT f a -> [a] Source # null :: MaybeT f a -> Bool Source # length :: MaybeT f a -> Int Source # elem :: Eq a => a -> MaybeT f a -> Bool Source # maximum :: Ord a => MaybeT f a -> a Source # minimum :: Ord a => MaybeT f a -> a Source # | |
| Foldable (DbOpenMode mode) | |
Defined in GHC.Unit.Database Methods fold :: Monoid m => DbOpenMode mode m -> m Source # foldMap :: Monoid m => (a -> m) -> DbOpenMode mode a -> m Source # foldMap' :: Monoid m => (a -> m) -> DbOpenMode mode a -> m Source # foldr :: (a -> b -> b) -> b -> DbOpenMode mode a -> b Source # foldr' :: (a -> b -> b) -> b -> DbOpenMode mode a -> b Source # foldl :: (b -> a -> b) -> b -> DbOpenMode mode a -> b Source # foldl' :: (b -> a -> b) -> b -> DbOpenMode mode a -> b Source # foldr1 :: (a -> a -> a) -> DbOpenMode mode a -> a Source # foldl1 :: (a -> a -> a) -> DbOpenMode mode a -> a Source # toList :: DbOpenMode mode a -> [a] Source # null :: DbOpenMode mode a -> Bool Source # length :: DbOpenMode mode a -> Int Source # elem :: Eq a => a -> DbOpenMode mode a -> Bool Source # maximum :: Ord a => DbOpenMode mode a -> a Source # minimum :: Ord a => DbOpenMode mode a -> a Source # sum :: Num a => DbOpenMode mode a -> a Source # product :: Num a => DbOpenMode mode a -> a Source # | |
| Foldable f => Foldable (ListT f) | |
Defined in Control.Monad.Trans.List Methods fold :: Monoid m => ListT f m -> m Source # foldMap :: Monoid m => (a -> m) -> ListT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ListT f a -> m Source # foldr :: (a -> b -> b) -> b -> ListT f a -> b Source # foldr' :: (a -> b -> b) -> b -> ListT f a -> b Source # foldl :: (b -> a -> b) -> b -> ListT f a -> b Source # foldl' :: (b -> a -> b) -> b -> ListT f a -> b Source # foldr1 :: (a -> a -> a) -> ListT f a -> a Source # foldl1 :: (a -> a -> a) -> ListT f a -> a Source # toList :: ListT f a -> [a] Source # null :: ListT f a -> Bool Source # length :: ListT f a -> Int Source # elem :: Eq a => a -> ListT f a -> Bool Source # maximum :: Ord a => ListT f a -> a Source # minimum :: Ord a => ListT f a -> a Source # | |
| Foldable (GenLocated l) # | |
Defined in GHC.Types.SrcLoc Methods fold :: Monoid m => GenLocated l m -> m Source # foldMap :: Monoid m => (a -> m) -> GenLocated l a -> m Source # foldMap' :: Monoid m => (a -> m) -> GenLocated l a -> m Source # foldr :: (a -> b -> b) -> b -> GenLocated l a -> b Source # foldr' :: (a -> b -> b) -> b -> GenLocated l a -> b Source # foldl :: (b -> a -> b) -> b -> GenLocated l a -> b Source # foldl' :: (b -> a -> b) -> b -> GenLocated l a -> b Source # foldr1 :: (a -> a -> a) -> GenLocated l a -> a Source # foldl1 :: (a -> a -> a) -> GenLocated l a -> a Source # toList :: GenLocated l a -> [a] Source # null :: GenLocated l a -> Bool Source # length :: GenLocated l a -> Int Source # elem :: Eq a => a -> GenLocated l a -> Bool Source # maximum :: Ord a => GenLocated l a -> a Source # minimum :: Ord a => GenLocated l a -> a Source # sum :: Num a => GenLocated l a -> a Source # product :: Num a => GenLocated l a -> a Source # | |
| Foldable (NonDetUniqFM key) # | Inherently nondeterministic. If you use this please provide a justification why it doesn't introduce nondeterminism. See Note [Deterministic UniqFM] in GHC.Types.Unique.DFM to learn about determinism. |
Defined in GHC.Types.Unique.FM Methods fold :: Monoid m => NonDetUniqFM key m -> m Source # foldMap :: Monoid m => (a -> m) -> NonDetUniqFM key a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonDetUniqFM key a -> m Source # foldr :: (a -> b -> b) -> b -> NonDetUniqFM key a -> b Source # foldr' :: (a -> b -> b) -> b -> NonDetUniqFM key a -> b Source # foldl :: (b -> a -> b) -> b -> NonDetUniqFM key a -> b Source # foldl' :: (b -> a -> b) -> b -> NonDetUniqFM key a -> b Source # foldr1 :: (a -> a -> a) -> NonDetUniqFM key a -> a Source # foldl1 :: (a -> a -> a) -> NonDetUniqFM key a -> a Source # toList :: NonDetUniqFM key a -> [a] Source # null :: NonDetUniqFM key a -> Bool Source # length :: NonDetUniqFM key a -> Int Source # elem :: Eq a => a -> NonDetUniqFM key a -> Bool Source # maximum :: Ord a => NonDetUniqFM key a -> a Source # minimum :: Ord a => NonDetUniqFM key a -> a Source # sum :: Num a => NonDetUniqFM key a -> a Source # product :: Num a => NonDetUniqFM key a -> a Source # | |
| Foldable (UniqDFM key) # | Deterministic, in O(n log n). |
Defined in GHC.Types.Unique.DFM Methods fold :: Monoid m => UniqDFM key m -> m Source # foldMap :: Monoid m => (a -> m) -> UniqDFM key a -> m Source # foldMap' :: Monoid m => (a -> m) -> UniqDFM key a -> m Source # foldr :: (a -> b -> b) -> b -> UniqDFM key a -> b Source # foldr' :: (a -> b -> b) -> b -> UniqDFM key a -> b Source # foldl :: (b -> a -> b) -> b -> UniqDFM key a -> b Source # foldl' :: (b -> a -> b) -> b -> UniqDFM key a -> b Source # foldr1 :: (a -> a -> a) -> UniqDFM key a -> a Source # foldl1 :: (a -> a -> a) -> UniqDFM key a -> a Source # toList :: UniqDFM key a -> [a] Source # null :: UniqDFM key a -> Bool Source # length :: UniqDFM key a -> Int Source # elem :: Eq a => a -> UniqDFM key a -> Bool Source # maximum :: Ord a => UniqDFM key a -> a Source # minimum :: Ord a => UniqDFM key a -> a Source # | |
| Foldable (HsRecField' id) # | |
Defined in GHC.Hs.Pat Methods fold :: Monoid m => HsRecField' id m -> m Source # foldMap :: Monoid m => (a -> m) -> HsRecField' id a -> m Source # foldMap' :: Monoid m => (a -> m) -> HsRecField' id a -> m Source # foldr :: (a -> b -> b) -> b -> HsRecField' id a -> b Source # foldr' :: (a -> b -> b) -> b -> HsRecField' id a -> b Source # foldl :: (b -> a -> b) -> b -> HsRecField' id a -> b Source # foldl' :: (b -> a -> b) -> b -> HsRecField' id a -> b Source # foldr1 :: (a -> a -> a) -> HsRecField' id a -> a Source # foldl1 :: (a -> a -> a) -> HsRecField' id a -> a Source # toList :: HsRecField' id a -> [a] Source # null :: HsRecField' id a -> Bool Source # length :: HsRecField' id a -> Int Source # elem :: Eq a => a -> HsRecField' id a -> Bool Source # maximum :: Ord a => HsRecField' id a -> a Source # minimum :: Ord a => HsRecField' id a -> a Source # sum :: Num a => HsRecField' id a -> a Source # product :: Num a => HsRecField' id a -> a Source # | |
| Foldable (HsRecFields p) # | |
Defined in GHC.Hs.Pat Methods fold :: Monoid m => HsRecFields p m -> m Source # foldMap :: Monoid m => (a -> m) -> HsRecFields p a -> m Source # foldMap' :: Monoid m => (a -> m) -> HsRecFields p a -> m Source # foldr :: (a -> b -> b) -> b -> HsRecFields p a -> b Source # foldr' :: (a -> b -> b) -> b -> HsRecFields p a -> b Source # foldl :: (b -> a -> b) -> b -> HsRecFields p a -> b Source # foldl' :: (b -> a -> b) -> b -> HsRecFields p a -> b Source # foldr1 :: (a -> a -> a) -> HsRecFields p a -> a Source # foldl1 :: (a -> a -> a) -> HsRecFields p a -> a Source # toList :: HsRecFields p a -> [a] Source # null :: HsRecFields p a -> Bool Source # length :: HsRecFields p a -> Int Source # elem :: Eq a => a -> HsRecFields p a -> Bool Source # maximum :: Ord a => HsRecFields p a -> a Source # minimum :: Ord a => HsRecFields p a -> a Source # sum :: Num a => HsRecFields p a -> a Source # product :: Num a => HsRecFields p a -> a Source # | |
| Foldable f => Foldable (Rec1 f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # | |
| Foldable (Const m :: Type -> Type) | Since: base-4.7.0.0 |
Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldr :: (a -> b -> b) -> b -> Const m a -> b Source # foldr' :: (a -> b -> b) -> b -> Const m a -> b Source # foldl :: (b -> a -> b) -> b -> Const m a -> b Source # foldl' :: (b -> a -> b) -> b -> Const m a -> b Source # foldr1 :: (a -> a -> a) -> Const m a -> a Source # foldl1 :: (a -> a -> a) -> Const m a -> a Source # toList :: Const m a -> [a] Source # null :: Const m a -> Bool Source # length :: Const m a -> Int Source # elem :: Eq a => a -> Const m a -> Bool Source # maximum :: Ord a => Const m a -> a Source # minimum :: Ord a => Const m a -> a Source # | |
| Foldable f => Foldable (Ap f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # | |
| Foldable f => Foldable (Alt f) | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # | |
| Foldable f => Foldable (ExceptT e f) | |
Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a Source # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a Source # toList :: ExceptT e f a -> [a] Source # null :: ExceptT e f a -> Bool Source # length :: ExceptT e f a -> Int Source # elem :: Eq a => a -> ExceptT e f a -> Bool Source # maximum :: Ord a => ExceptT e f a -> a Source # minimum :: Ord a => ExceptT e f a -> a Source # | |
| Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
| Foldable f => Foldable (WriterT w f) | |
Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # | |
| Foldable f => Foldable (IdentityT f) | |
Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m Source # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldr1 :: (a -> a -> a) -> IdentityT f a -> a Source # foldl1 :: (a -> a -> a) -> IdentityT f a -> a Source # toList :: IdentityT f a -> [a] Source # null :: IdentityT f a -> Bool Source # length :: IdentityT f a -> Int Source # elem :: Eq a => a -> IdentityT f a -> Bool Source # maximum :: Ord a => IdentityT f a -> a Source # minimum :: Ord a => IdentityT f a -> a Source # | |
| Foldable f => Foldable (ErrorT e f) | |
Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a Source # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a Source # toList :: ErrorT e f a -> [a] Source # null :: ErrorT e f a -> Bool Source # length :: ErrorT e f a -> Int Source # elem :: Eq a => a -> ErrorT e f a -> Bool Source # maximum :: Ord a => ErrorT e f a -> a Source # minimum :: Ord a => ErrorT e f a -> a Source # | |
| Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source # toList :: (f :*: g) a -> [a] Source # null :: (f :*: g) a -> Bool Source # length :: (f :*: g) a -> Int Source # elem :: Eq a => a -> (f :*: g) a -> Bool Source # maximum :: Ord a => (f :*: g) a -> a Source # minimum :: Ord a => (f :*: g) a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source # foldr :: (a -> b -> b) -> b -> Product f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source # foldl :: (b -> a -> b) -> b -> Product f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source # foldr1 :: (a -> a -> a) -> Product f g a -> a Source # foldl1 :: (a -> a -> a) -> Product f g a -> a Source # toList :: Product f g a -> [a] Source # null :: Product f g a -> Bool Source # length :: Product f g a -> Int Source # elem :: Eq a => a -> Product f g a -> Bool Source # maximum :: Ord a => Product f g a -> a Source # minimum :: Ord a => Product f g a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Sum f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldr1 :: (a -> a -> a) -> Sum f g a -> a Source # foldl1 :: (a -> a -> a) -> Sum f g a -> a Source # toList :: Sum f g a -> [a] Source # null :: Sum f g a -> Bool Source # length :: Sum f g a -> Int Source # elem :: Eq a => a -> Sum f g a -> Bool Source # maximum :: Ord a => Sum f g a -> a Source # minimum :: Ord a => Sum f g a -> a Source # | |
| Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # | |
| (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 Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # | |
| (Foldable f, Foldable g) => Foldable (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldr1 :: (a -> a -> a) -> Compose f g a -> a Source # foldl1 :: (a -> a -> a) -> Compose f g a -> a Source # toList :: Compose f g a -> [a] Source # null :: Compose f g a -> Bool Source # length :: Compose f g a -> Int Source # elem :: Eq a => a -> Compose f g a -> Bool Source # maximum :: Ord a => Compose f g a -> a Source # minimum :: Ord a => Compose f g a -> a Source # | |
class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where Source #
Functors representing data structures that can be traversed from left to right, performing an action on each element.
A more detailed description can be found in the overview section of Data.Traversable.
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see traverse_.
Examples
Basic usage:
In the first two examples we show each evaluated action mapping to the output structure.
>>>traverse Just [1,2,3,4]Just [1,2,3,4]
>>>traverse id [Right 1, Right 2, Right 3, Right 4]Right [1,2,3,4]
In the next examples, we show that Nothing and Left values short
circuit the created structure.
>>>traverse (const Nothing) [1,2,3,4]Nothing
>>>traverse (\x -> if odd x then Just x else Nothing) [1,2,3,4]Nothing
>>>traverse id [Right 1, Right 2, Right 3, Right 4, Left 0]Left 0
sequenceA :: Applicative f => t (f a) -> f (t a) Source #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see sequenceA_.
Examples
Basic usage:
For the first two examples we show sequenceA fully evaluating a a structure and collecting the results.
>>>sequenceA [Just 1, Just 2, Just 3]Just [1,2,3]
>>>sequenceA [Right 1, Right 2, Right 3]Right [1,2,3]
The next two example show Nothing and Just will short circuit
the resulting structure if present in the input. For more context,
check the Traversable instances for Either and Maybe.
>>>sequenceA [Just 1, Just 2, Just 3, Nothing]Nothing
>>>sequenceA [Right 1, Right 2, Right 3, Left 4]Left 4
mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see mapM_.
Examples
sequence :: Monad m => t (m a) -> m (t a) Source #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see sequence_.
Examples
Basic usage:
The first two examples are instances where the input and
and output of sequence are isomorphic.
>>>sequence $ Right [1,2,3,4][Right 1,Right 2,Right 3,Right 4]
>>>sequence $ [Right 1,Right 2,Right 3,Right 4]Right [1,2,3,4]
The following examples demonstrate short circuit behavior
for sequence.
>>>sequence $ Left [1,2,3,4]Left [1,2,3,4]
>>>sequence $ [Left 0, Right 1,Right 2,Right 3,Right 4]Left 0
Instances
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Minimal complete definition
Instances
class Semigroup a => Monoid a where Source #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
x<>mempty= x- Left identity
mempty<>x = x- Associativity
x(<>(y<>z) = (x<>y)<>zSemigrouplaw)- Concatenation
mconcat=foldr(<>)mempty
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"
mappend :: a -> a -> a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation mappend = (<>)mappend is a synonym for
(<>), it is expected that the two functions are defined the same
way. In a future GHC release mappend will be removed from Monoid.
Fold a list using the monoid.
For most types, the default definition for mconcat will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
Instances
| Bounded Bool | Since: base-2.1 |
| Enum Bool | Since: base-2.1 |
| Eq Bool | |
| Data Bool | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Bool -> c Bool Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Bool Source # toConstr :: Bool -> Constr Source # dataTypeOf :: Bool -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Bool) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Bool) Source # gmapT :: (forall b. Data b => b -> b) -> Bool -> Bool Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Bool -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Bool -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Bool -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Bool -> m Bool Source # | |
| Ord Bool | |
| Read Bool | Since: base-2.1 |
| Show Bool | Since: base-2.1 |
| Ix Bool | Since: base-2.1 |
| Generic Bool | Since: base-4.6.0.0 |
| Storable Bool | Since: base-2.1 |
Defined in Foreign.Storable Methods sizeOf :: Bool -> Int Source # alignment :: Bool -> Int Source # peekElemOff :: Ptr Bool -> Int -> IO Bool Source # pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Bool Source # pokeByteOff :: Ptr b -> Int -> Bool -> IO () Source # | |
| Bits Bool | Interpret Since: base-4.7.0.0 |
Defined in Data.Bits Methods (.&.) :: Bool -> Bool -> Bool Source # (.|.) :: Bool -> Bool -> Bool Source # xor :: Bool -> Bool -> Bool Source # complement :: Bool -> Bool Source # shift :: Bool -> Int -> Bool Source # rotate :: Bool -> Int -> Bool Source # setBit :: Bool -> Int -> Bool Source # clearBit :: Bool -> Int -> Bool Source # complementBit :: Bool -> Int -> Bool Source # testBit :: Bool -> Int -> Bool Source # bitSizeMaybe :: Bool -> Maybe Int Source # bitSize :: Bool -> Int Source # isSigned :: Bool -> Bool Source # shiftL :: Bool -> Int -> Bool Source # unsafeShiftL :: Bool -> Int -> Bool Source # shiftR :: Bool -> Int -> Bool Source # unsafeShiftR :: Bool -> Int -> Bool Source # rotateL :: Bool -> Int -> Bool Source # | |
| FiniteBits Bool | Since: base-4.7.0.0 |
| Binary Bool | |
| NFData Bool | |
Defined in Control.DeepSeq | |
| HpcHash Bool | |
| SingKind Bool | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep Bool | |
| Outputable Bool # | |
| Binary Bool # | |
| Lift Bool | |
| IArray UArray Bool | |
Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Bool -> (i, i) Source # numElements :: Ix i => UArray i Bool -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Bool)] -> UArray i Bool unsafeAt :: Ix i => UArray i Bool -> Int -> Bool unsafeReplace :: Ix i => UArray i Bool -> [(Int, Bool)] -> UArray i Bool unsafeAccum :: Ix i => (Bool -> e' -> Bool) -> UArray i Bool -> [(Int, e')] -> UArray i Bool unsafeAccumArray :: Ix i => (Bool -> e' -> Bool) -> Bool -> (i, i) -> [(Int, e')] -> UArray i Bool | |
| SingI 'False | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| SingI 'True | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| MArray (STUArray s) Bool (ST s) | |
Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Bool -> ST s (i, i) Source # getNumElements :: Ix i => STUArray s i Bool -> ST s Int newArray :: Ix i => (i, i) -> Bool -> ST s (STUArray s i Bool) Source # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) Source # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Bool) unsafeRead :: Ix i => STUArray s i Bool -> Int -> ST s Bool unsafeWrite :: Ix i => STUArray s i Bool -> Int -> Bool -> ST s () | |
| type Rep Bool | |
| type DemoteRep Bool | |
Defined in GHC.Generics | |
| data Sing (a :: Bool) | |
Instances
| Bounded Char | Since: base-2.1 |
| Enum Char | Since: base-2.1 |
| Eq Char | |
| Data Char | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Char -> c Char Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Char Source # toConstr :: Char -> Constr Source # dataTypeOf :: Char -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Char) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Char) Source # gmapT :: (forall b. Data b => b -> b) -> Char -> Char Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Char -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Char -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Char -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Char -> m Char Source # | |
| Ord Char | |
| Read Char | Since: base-2.1 |
| Show Char | Since: base-2.1 |
| Ix Char | Since: base-2.1 |
| PrintfArg Char | Since: base-2.1 |
Defined in Text.Printf | |
| IsChar Char | Since: base-2.1 |
| Storable Char | Since: base-2.1 |
Defined in Foreign.Storable Methods sizeOf :: Char -> Int Source # alignment :: Char -> Int Source # peekElemOff :: Ptr Char -> Int -> IO Char Source # pokeElemOff :: Ptr Char -> Int -> Char -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Char Source # pokeByteOff :: Ptr b -> Int -> Char -> IO () Source # | |
| Binary Char | |
| NFData Char | |
Defined in Control.DeepSeq | |
| HpcHash Char | |
| ErrorList Char | |
| Outputable Char # | |
| Binary Char # | |
| Lift Char | |
| IArray UArray Char | |
Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Char -> (i, i) Source # numElements :: Ix i => UArray i Char -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Char)] -> UArray i Char unsafeAt :: Ix i => UArray i Char -> Int -> Char unsafeReplace :: Ix i => UArray i Char -> [(Int, Char)] -> UArray i Char unsafeAccum :: Ix i => (Char -> e' -> Char) -> UArray i Char -> [(Int, e')] -> UArray i Char unsafeAccumArray :: Ix i => (Char -> e' -> Char) -> Char -> (i, i) -> [(Int, e')] -> UArray i Char | |
| Generic1 (URec Char :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # | |
| Traversable (UChar :: Type -> Type) | Since: base-4.9.0.0 |
| OutputCap [Char] | |
Defined in System.Console.Terminfo.Base | |
| TermStr [Char] | |
Defined in System.Console.Terminfo.Base | |
| MArray (STUArray s) Char (ST s) | |
Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Char -> ST s (i, i) Source # getNumElements :: Ix i => STUArray s i Char -> ST s Int newArray :: Ix i => (i, i) -> Char -> ST s (STUArray s i Char) Source # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Char) Source # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Char) unsafeRead :: Ix i => STUArray s i Char -> Int -> ST s Char unsafeWrite :: Ix i => STUArray s i Char -> Int -> Char -> ST s () | |
| Functor (URec Char :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Char p) | Since: base-4.9.0.0 |
| Ord (URec Char p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Show (URec Char p) | Since: base-4.9.0.0 |
| Generic (URec Char p) | Since: base-4.9.0.0 |
| data URec Char (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Char :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Char p) | |
Defined in GHC.Generics | |
Instances
Instances
Instances
| Bounded Int | Since: base-2.1 |
| Enum Int | Since: base-2.1 |
Defined in GHC.Enum | |
| Eq Int | |
| Integral Int | Since: base-2.0.1 |
| Data Int | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Int -> c Int Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Int Source # toConstr :: Int -> Constr Source # dataTypeOf :: Int -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Int) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Int) Source # gmapT :: (forall b. Data b => b -> b) -> Int -> Int Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Int -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Int -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Int -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Int -> m Int Source # | |
| Num Int | Since: base-2.1 |
| Ord Int | |
| Read Int | Since: base-2.1 |
| Real Int | Since: base-2.0.1 |
| Show Int | Since: base-2.1 |
| Ix Int | Since: base-2.1 |
| PrintfArg Int | Since: base-2.1 |
Defined in Text.Printf | |
| Storable Int | Since: base-2.1 |
Defined in Foreign.Storable | |
| Bits Int | Since: base-2.1 |
Defined in Data.Bits Methods (.&.) :: Int -> Int -> Int Source # (.|.) :: Int -> Int -> Int Source # xor :: Int -> Int -> Int Source # complement :: Int -> Int Source # shift :: Int -> Int -> Int Source # rotate :: Int -> Int -> Int Source # setBit :: Int -> Int -> Int Source # clearBit :: Int -> Int -> Int Source # complementBit :: Int -> Int -> Int Source # testBit :: Int -> Int -> Bool Source # bitSizeMaybe :: Int -> Maybe Int Source # bitSize :: Int -> Int Source # isSigned :: Int -> Bool Source # shiftL :: Int -> Int -> Int Source # unsafeShiftL :: Int -> Int -> Int Source # shiftR :: Int -> Int -> Int Source # unsafeShiftR :: Int -> Int -> Int Source # rotateL :: Int -> Int -> Int Source # | |
| FiniteBits Int | Since: base-4.6.0.0 |
| Binary Int | |
| NFData Int | |
Defined in Control.DeepSeq | |
| HpcHash Int | |
| Outputable Int # | |
| Uniquable Int # | |
| Binary Int # | |
| Lift Int | |
| IArray UArray Int | |
Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Int -> (i, i) Source # numElements :: Ix i => UArray i Int -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Int)] -> UArray i Int unsafeAt :: Ix i => UArray i Int -> Int -> Int unsafeReplace :: Ix i => UArray i Int -> [(Int, Int)] -> UArray i Int unsafeAccum :: Ix i => (Int -> e' -> Int) -> UArray i Int -> [(Int, e')] -> UArray i Int unsafeAccumArray :: Ix i => (Int -> e' -> Int) -> Int -> (i, i) -> [(Int, e')] -> UArray i Int | |
| Generic1 (URec Int :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # | |
| Traversable (UInt :: Type -> Type) | Since: base-4.9.0.0 |
| Binary (IdentifierDetails TypeIndex) # | |
Defined in GHC.Iface.Ext.Types | |
| Binary (NodeInfo TypeIndex) # | |
| Binary (SourcedNodeInfo TypeIndex) # | |
Defined in GHC.Iface.Ext.Types | |
| Binary (HieAST TypeIndex) # | |
| Binary (HieASTs TypeIndex) # | |
| Binary (HieArgs TypeIndex) # | |
| Binary (HieType TypeIndex) # | |
| MArray (STUArray s) Int (ST s) | |
Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Int -> ST s (i, i) Source # getNumElements :: Ix i => STUArray s i Int -> ST s Int newArray :: Ix i => (i, i) -> Int -> ST s (STUArray s i Int) Source # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int) Source # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Int) unsafeRead :: Ix i => STUArray s i Int -> Int -> ST s Int unsafeWrite :: Ix i => STUArray s i Int -> Int -> Int -> ST s () | |
| Functor (URec Int :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Int p) | Since: base-4.9.0.0 |
| Ord (URec Int p) | Since: base-4.9.0.0 |
| Show (URec Int p) | Since: base-4.9.0.0 |
| Generic (URec Int p) | Since: base-4.9.0.0 |
| data URec Int (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Int :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Int p) | |
Defined in GHC.Generics | |
Instances
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
| Monad Maybe | Since: base-2.1 |
| Functor Maybe | Since: base-2.1 |
| MonadFix Maybe | Since: base-2.1 |
| MonadFail Maybe | Since: base-4.9.0.0 |
| Applicative Maybe | Since: base-2.1 |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # | |
| Traversable Maybe | Since: base-2.1 |
| 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 Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Maybe a) Source # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Maybe a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Maybe a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Maybe a] Source # | |
| Show1 Maybe | Since: base-4.9.0.0 |
| Alternative Maybe | Since: base-2.1 |
| MonadPlus Maybe | Since: base-2.1 |
| NFData1 Maybe | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
| MonadThrow Maybe | |
| Lift a => Lift (Maybe a :: Type) | |
| Eq a => Eq (Maybe a) | Since: base-2.1 |
| Data a => Data (Maybe a) | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Maybe a -> c (Maybe a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Maybe a) Source # toConstr :: Maybe a -> Constr Source # dataTypeOf :: Maybe a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Maybe a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Maybe a)) Source # gmapT :: (forall b. Data b => b -> b) -> Maybe a -> Maybe a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Maybe a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Maybe a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Maybe a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Maybe a -> m (Maybe a) Source # | |
| Ord a => Ord (Maybe a) | Since: base-2.1 |
| Read a => Read (Maybe a) | Since: base-2.1 |
| Show a => Show (Maybe a) | Since: base-2.1 |
| Generic (Maybe a) | Since: base-4.6.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Maybe a) | Lift a semigroup into Since 4.11.0: constraint on inner Since: base-2.1 |
| Binary a => Binary (Maybe a) | |
| NFData a => NFData (Maybe a) | |
Defined in Control.DeepSeq | |
| SingKind a => SingKind (Maybe a) | Since: base-4.9.0.0 |
Defined in GHC.Generics Associated Types type DemoteRep (Maybe a) | |
| Outputable a => Outputable (Maybe a) # | |
| Binary a => Binary (Maybe a) # | |
| Generic1 Maybe | Since: base-4.6.0.0 |
| 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 Rep (Maybe a) | |
Defined in GHC.Generics | |
| type DemoteRep (Maybe a) | |
Defined in GHC.Generics | |
| data Sing (b :: Maybe a) | |
| type Rep1 Maybe | |
Instances
| Bounded Ordering | Since: base-2.1 |
| Enum Ordering | Since: base-2.1 |
Defined in GHC.Enum Methods succ :: Ordering -> Ordering Source # pred :: Ordering -> Ordering Source # toEnum :: Int -> Ordering Source # fromEnum :: Ordering -> Int Source # enumFrom :: Ordering -> [Ordering] Source # enumFromThen :: Ordering -> Ordering -> [Ordering] Source # enumFromTo :: Ordering -> Ordering -> [Ordering] Source # enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source # | |
| Eq Ordering | |
| Data Ordering | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ordering -> c Ordering Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Ordering Source # toConstr :: Ordering -> Constr Source # dataTypeOf :: Ordering -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Ordering) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Ordering) Source # gmapT :: (forall b. Data b => b -> b) -> Ordering -> Ordering Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ordering -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Ordering -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Ordering -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ordering -> m Ordering Source # | |
| Ord Ordering | |
Defined in GHC.Classes | |
| Read Ordering | Since: base-2.1 |
| Show Ordering | Since: base-2.1 |
| Ix Ordering | Since: base-2.1 |
Defined in GHC.Ix | |
| Generic Ordering | Since: base-4.6.0.0 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Monoid Ordering | Since: base-2.1 |
| Binary Ordering | |
| NFData Ordering | |
Defined in Control.DeepSeq | |
| Outputable Ordering # | |
| type Rep Ordering | |
Instances
Instances
| Bounded Word | Since: base-2.1 |
| Enum Word | Since: base-2.1 |
| Eq Word | |
| Integral Word | Since: base-2.1 |
Defined in GHC.Real | |
| Data Word | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Word -> c Word Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Word Source # toConstr :: Word -> Constr Source # dataTypeOf :: Word -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Word) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Word) Source # gmapT :: (forall b. Data b => b -> b) -> Word -> Word Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Word -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Word -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Word -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Word -> m Word Source # | |
| Num Word | Since: base-2.1 |
| Ord Word | |
| Read Word | Since: base-4.5.0.0 |
| Real Word | Since: base-2.1 |
| Show Word | Since: base-2.1 |
| Ix Word | Since: base-4.6.0.0 |
| PrintfArg Word | Since: base-2.1 |
Defined in Text.Printf | |
| Storable Word | Since: base-2.1 |
Defined in Foreign.Storable Methods sizeOf :: Word -> Int Source # alignment :: Word -> Int Source # peekElemOff :: Ptr Word -> Int -> IO Word Source # pokeElemOff :: Ptr Word -> Int -> Word -> IO () Source # peekByteOff :: Ptr b -> Int -> IO Word Source # pokeByteOff :: Ptr b -> Int -> Word -> IO () Source # | |
| Bits Word | Since: base-2.1 |
Defined in Data.Bits Methods (.&.) :: Word -> Word -> Word Source # (.|.) :: Word -> Word -> Word Source # xor :: Word -> Word -> Word Source # complement :: Word -> Word Source # shift :: Word -> Int -> Word Source # rotate :: Word -> Int -> Word Source # setBit :: Word -> Int -> Word Source # clearBit :: Word -> Int -> Word Source # complementBit :: Word -> Int -> Word Source # testBit :: Word -> Int -> Bool Source # bitSizeMaybe :: Word -> Maybe Int Source # bitSize :: Word -> Int Source # isSigned :: Word -> Bool Source # shiftL :: Word -> Int -> Word Source # unsafeShiftL :: Word -> Int -> Word Source # shiftR :: Word -> Int -> Word Source # unsafeShiftR :: Word -> Int -> Word Source # rotateL :: Word -> Int -> Word Source # | |
| FiniteBits Word | Since: base-4.6.0.0 |
| Binary Word | |
| NFData Word | |
Defined in Control.DeepSeq | |
| Outputable Word # | |
| Lift Word | |
| IArray UArray Word | |
Defined in Data.Array.Base Methods bounds :: Ix i => UArray i Word -> (i, i) Source # numElements :: Ix i => UArray i Word -> Int unsafeArray :: Ix i => (i, i) -> [(Int, Word)] -> UArray i Word unsafeAt :: Ix i => UArray i Word -> Int -> Word unsafeReplace :: Ix i => UArray i Word -> [(Int, Word)] -> UArray i Word unsafeAccum :: Ix i => (Word -> e' -> Word) -> UArray i Word -> [(Int, e')] -> UArray i Word unsafeAccumArray :: Ix i => (Word -> e' -> Word) -> Word -> (i, i) -> [(Int, e')] -> UArray i Word | |
| Generic1 (URec Word :: k -> Type) | Since: base-4.9.0.0 |
| Foldable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # | |
| Traversable (UWord :: Type -> Type) | Since: base-4.9.0.0 |
| MArray (STUArray s) Word (ST s) | |
Defined in Data.Array.Base Methods getBounds :: Ix i => STUArray s i Word -> ST s (i, i) Source # getNumElements :: Ix i => STUArray s i Word -> ST s Int newArray :: Ix i => (i, i) -> Word -> ST s (STUArray s i Word) Source # newArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word) Source # unsafeNewArray_ :: Ix i => (i, i) -> ST s (STUArray s i Word) unsafeRead :: Ix i => STUArray s i Word -> Int -> ST s Word unsafeWrite :: Ix i => STUArray s i Word -> Int -> Word -> ST s () | |
| Functor (URec Word :: Type -> Type) | Since: base-4.9.0.0 |
| Eq (URec Word p) | Since: base-4.9.0.0 |
| Ord (URec Word p) | Since: base-4.9.0.0 |
Defined in GHC.Generics | |
| Show (URec Word p) | Since: base-4.9.0.0 |
| Generic (URec Word p) | Since: base-4.9.0.0 |
| data URec Word (p :: k) | Used for marking occurrences of Since: base-4.9.0.0 |
| type Rep1 (URec Word :: k -> Type) | |
Defined in GHC.Generics | |
| type Rep (URec Word p) | |
Defined in GHC.Generics | |
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
| Bifunctor Either | Since: base-4.8.0.0 |
| 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) Source # liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Either a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Either a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Either a b] Source # | |
| Show2 Either | Since: base-4.9.0.0 |
Defined in Data.Functor.Classes | |
| NFData2 Either | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
| (Lift a, Lift b) => Lift (Either a b :: Type) | |
| Monad (Either e) | Since: base-4.4.0.0 |
| Functor (Either a) | Since: base-3.0 |
| MonadFix (Either e) | Since: base-4.3.0.0 |
| Applicative (Either e) | Since: base-3.0 |
Defined in Data.Either | |
| Foldable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # | |
| Traversable (Either a) | Since: base-4.7.0.0 |
Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source # | |
| 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) Source # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Either a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Either a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Either a a0] Source # | |
| Show a => Show1 (Either a) | Since: base-4.9.0.0 |
| NFData a => NFData1 (Either a) | Since: deepseq-1.4.3.0 |
Defined in Control.DeepSeq | |
| e ~ SomeException => MonadThrow (Either e) | |
| e ~ SomeException => MonadCatch (Either e) | Since: exceptions-0.8.3 |
| e ~ SomeException => MonadMask (Either e) | Since: exceptions-0.8.3 |
Defined in Control.Monad.Catch Methods mask :: ((forall a. Either e a -> Either e a) -> Either e b) -> Either e b Source # uninterruptibleMask :: ((forall a. Either e a -> Either e a) -> Either e b) -> Either e b Source # generalBracket :: Either e a -> (a -> ExitCase b -> Either e c) -> (a -> Either e b) -> Either e (b, c) Source # | |
| Generic1 (Either a :: Type -> Type) | Since: base-4.6.0.0 |
| (Eq a, Eq b) => Eq (Either a b) | Since: base-2.1 |
| (Data a, Data b) => Data (Either a b) | Since: base-4.0.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Either a b -> c (Either a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Either a b) Source # toConstr :: Either a b -> Constr Source # dataTypeOf :: Either a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Either a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Either a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Either a b -> Either a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Either a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Either a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Either a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Either a b -> m (Either a b) Source # | |
| (Ord a, Ord b) => Ord (Either a b) | Since: base-2.1 |
| (Read a, Read b) => Read (Either a b) | Since: base-3.0 |
| (Show a, Show b) => Show (Either a b) | Since: base-3.0 |
| Generic (Either a b) | Since: base-4.6.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| (Binary a, Binary b) => Binary (Either a b) | |
| (NFData a, NFData b) => NFData (Either a b) | |
Defined in Control.DeepSeq | |
| (Outputable a, Outputable b) => Outputable (Either a b) # | |
| (Binary a, Binary b) => Binary (Either a b) # | |
| type Rep1 (Either a :: Type -> Type) | |
Defined in GHC.Generics type Rep1 (Either a :: Type -> Type) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) | |
| type Rep (Either a b) | |
Defined in GHC.Generics type Rep (Either a b) = D1 ('MetaData "Either" "Data.Either" "base" 'False) (C1 ('MetaCons "Left" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)) :+: C1 ('MetaCons "Right" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b))) | |
appendFile :: FilePath -> String -> IO () Source #
The computation appendFile file str function appends the string str,
to the file file.
Note that writeFile and appendFile write a literal string
to a file. To write a value of any printable type, as with print,
use the show function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
writeFile :: FilePath -> String -> IO () Source #
The computation writeFile file str function writes the string str,
to the file file.
readFile :: FilePath -> IO String Source #
The readFile function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with getContents.
interact :: (String -> String) -> IO () Source #
The interact function takes a function of type String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
getContents :: IO String Source #
The getContents operation returns all user input as a single string,
which is read lazily as it is needed
(same as hGetContents stdin).
type FilePath = String Source #
File and directory names are values of type String, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
type IOError = IOException Source #
notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #
notElem is the negation of elem.
Examples
Basic usage:
>>>3 `notElem` []True
>>>3 `notElem` [1,2]True
>>>3 `notElem` [1,2,3,4,5]False
For infinite structures, notElem terminates if the value exists at a
finite distance from the left side of the structure:
>>>3 `notElem` [1..]False
>>>3 `notElem` ([4..] ++ [3])* Hangs forever *
all :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether all elements of the structure satisfy the predicate.
Examples
Basic usage:
>>>all (> 3) []True
>>>all (> 3) [1,2]False
>>>all (> 3) [1,2,3,4,5]False
>>>all (> 3) [1..]False
>>>all (> 3) [4..]* Hangs forever *
any :: Foldable t => (a -> Bool) -> t a -> Bool Source #
Determines whether any element of the structure satisfies the predicate.
Examples
Basic usage:
>>>any (> 3) []False
>>>any (> 3) [1,2]False
>>>any (> 3) [1,2,3,4,5]True
>>>any (> 3) [1..]True
>>>any (> 3) [0, -1..]* Hangs forever *
or :: Foldable t => t Bool -> Bool Source #
or returns the disjunction of a container of Bools. For the
result to be False, the container must be finite; True, however,
results from a True value finitely far from the left end.
Examples
Basic usage:
>>>or []False
>>>or [True]True
>>>or [False]False
>>>or [True, True, False]True
>>>or (True : repeat False) -- Infinite list [True,False,False,False,...True
>>>or (repeat False)* Hangs forever *
and :: Foldable t => t Bool -> Bool Source #
and returns the conjunction of a container of Bools. For the
result to be True, the container must be finite; False, however,
results from a False value finitely far from the left end.
Examples
Basic usage:
>>>and []True
>>>and [True]True
>>>and [False]False
>>>and [True, True, False]False
>>>and (False : repeat True) -- Infinite list [False,True,True,True,...False
>>>and (repeat True)* Hangs forever *
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #
Map a function over all the elements of a container and concatenate the resulting lists.
Examples
Basic usage:
>>>concatMap (take 3) [[1..], [10..], [100..], [1000..]][1,2,3,10,11,12,100,101,102,1000,1001,1002]
>>>concatMap (take 3) (Just [1..])[1,2,3]
concat :: Foldable t => t [a] -> [a] Source #
The concatenation of all the elements of a container of lists.
Examples
Basic usage:
>>>concat (Just [1, 2, 3])[1,2,3]
>>>concat (Left 42)[]
>>>concat [[1, 2, 3], [4, 5], [6], []][1,2,3,4,5,6]
sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see sequence.
sequence_ is just like sequenceA_, but specialised to monadic
actions.
words :: String -> [String] Source #
words breaks a string up into a list of words, which were delimited
by white space.
>>>words "Lorem ipsum\ndolor"["Lorem","ipsum","dolor"]
lines :: String -> [String] Source #
lines breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
>>>lines ""[]
>>>lines "\n"[""]
>>>lines "one"["one"]
>>>lines "one\n"["one"]
>>>lines "one\n\n"["one",""]
>>>lines "one\ntwo"["one","two"]
>>>lines "one\ntwo\n"["one","two"]
Thus lines ss.
read :: Read a => String -> a Source #
The read function reads input from a string, which must be
completely consumed by the input process. read fails with an error if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use readMaybe or readEither for safe alternatives.
>>>read "123" :: Int123
>>>read "hello" :: Int*** Exception: Prelude.read: no parse
either :: (a -> c) -> (b -> c) -> Either a b -> c Source #
Case analysis for the Either type.
If the value is Left aa;
if it is Right bb.
Examples
We create two values of type Either String IntLeft constructor and another using the Right constructor. Then
we apply "either" the length function (if we have a String)
or the "times-two" function (if we have an Int):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
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 Source #
lcm x yx and y divide.
gcd :: Integral a => a -> a -> a Source #
gcd x yx and y of which
every common factor of x and y is also a factor; for example
gcd 4 2 = 2gcd (-4) 6 = 2gcd 0 44. gcd 0 00.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types, abs minBound < 0minBound0 or minBound
(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to an integral power
(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to a non-negative integral power
showString :: String -> ShowS Source #
utility function converting a String to a show function that
simply prepends the string unchanged.
showChar :: Char -> ShowS Source #
utility function converting a Char to a show function that
simply prepends the character unchanged.
unzip :: [(a, b)] -> ([a], [b]) Source #
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")
zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #
The zipWith3 function takes a function which combines three
elements, as well as three lists and returns a list of 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] Source #
\(\mathcal{O}(\min(m,n))\). zipWith generalises zip by zipping with the
function given as the first argument, instead of a tupling function.
zipWith (,) xs ys == zip xs ys zipWith f [x1,x2,x3..] [y1,y2,y3..] == [f x1 y1, f x2 y2, f x3 y3..]
For example, zipWith (+)
>>>zipWith (+) [1, 2, 3] [4, 5, 6][5,7,9]
zipWith is right-lazy:
>>>zipWith f [] _|_[]
zipWith is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
(!!) :: [a] -> Int -> a infixl 9 Source #
List index (subscript) operator, starting from 0.
It is an instance of the more general genericIndex,
which takes an index of any integral type.
>>>['a', 'b', 'c'] !! 0'a'>>>['a', 'b', 'c'] !! 2'c'>>>['a', 'b', 'c'] !! 3Exception: Prelude.!!: index too large>>>['a', 'b', 'c'] !! (-1)Exception: Prelude.!!: negative index
lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #
\(\mathcal{O}(n)\). lookup key assocs looks up a key in an association
list.
>>>lookup 2 []Nothing>>>lookup 2 [(1, "first")]Nothing>>>lookup 2 [(1, "first"), (2, "second"), (3, "third")]Just "second"
reverse :: [a] -> [a] Source #
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 *
break :: (a -> Bool) -> [a] -> ([a], [a]) Source #
break, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
do not satisfy p and second element is the remainder of the list:
>>>break (> 3) [1,2,3,4,1,2,3,4]([1,2,3],[4,1,2,3,4])>>>break (< 9) [1,2,3]([],[1,2,3])>>>break (> 9) [1,2,3]([1,2,3],[])
span :: (a -> Bool) -> [a] -> ([a], [a]) Source #
span, applied to a predicate p and a list xs, returns a tuple where
first element is longest prefix (possibly empty) of xs of elements that
satisfy p and second element is the remainder of the list:
>>>span (< 3) [1,2,3,4,1,2,3,4]([1,2],[3,4,1,2,3,4])>>>span (< 9) [1,2,3]([1,2,3],[])>>>span (< 0) [1,2,3]([],[1,2,3])
splitAt :: Int -> [a] -> ([a], [a]) Source #
splitAt n xs returns a tuple where first element is xs prefix of
length n and second element is the remainder of the list:
>>>splitAt 6 "Hello World!"("Hello ","World!")>>>splitAt 3 [1,2,3,4,5]([1,2,3],[4,5])>>>splitAt 1 [1,2,3]([1],[2,3])>>>splitAt 3 [1,2,3]([1,2,3],[])>>>splitAt 4 [1,2,3]([1,2,3],[])>>>splitAt 0 [1,2,3]([],[1,2,3])>>>splitAt (-1) [1,2,3]([],[1,2,3])
It is equivalent to ( 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.
drop :: Int -> [a] -> [a] Source #
drop n xs returns the suffix of xs
after the first n elements, or [] if n > .length xs
>>>drop 6 "Hello World!""World!">>>drop 3 [1,2,3,4,5][4,5]>>>drop 3 [1,2][]>>>drop 3 [][]>>>drop (-1) [1,2][1,2]>>>drop 0 [1,2][1,2]
It is an instance of the more general genericDrop,
in which n may be of any integral type.
take :: Int -> [a] -> [a] Source #
take n, applied to a list xs, returns the prefix of xs
of length n, or xs itself if n > .length xs
>>>take 5 "Hello World!""Hello">>>take 3 [1,2,3,4,5][1,2,3]>>>take 3 [1,2][1,2]>>>take 3 [][]>>>take (-1) [1,2][]>>>take 0 [1,2][]
It is an instance of the more general genericTake,
in which n may be of any integral type.
takeWhile :: (a -> Bool) -> [a] -> [a] Source #
takeWhile, applied to a predicate p and a list xs, returns the
longest prefix (possibly empty) of xs of elements that satisfy p.
>>>takeWhile (< 3) [1,2,3,4,1,2,3,4][1,2]>>>takeWhile (< 9) [1,2,3][1,2,3]>>>takeWhile (< 0) [1,2,3][]
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>>>cycle [42][42,42,42,42,42,42,42,42,42,42...>>>cycle [2, 5, 7][2,5,7,2,5,7,2,5,7,2,5,7...
replicate :: Int -> a -> [a] Source #
replicate n x is a list of length n with x the value of
every element.
It is an instance of the more general genericReplicate,
in which n may be of any integral type.
>>>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.
>>>repeat 17[17,17,17,17,17,17,17,17,17...
iterate :: (a -> a) -> a -> [a] Source #
iterate f x returns an infinite list of repeated applications
of f to x:
iterate f x == [x, f x, f (f x), ...]
Note that iterate is lazy, potentially leading to thunk build-up if
the consumer doesn't force each iterate. See iterate' for a strict
variant of this function.
>>>iterate not True[True,False,True,False...>>>iterate (+3) 42[42,45,48,51,54,57,60,63...
scanr1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). 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]>>>scanr1 (+) [1..]* Hangs forever *
scanr :: (a -> b -> b) -> b -> [a] -> [b] Source #
\(\mathcal{O}(n)\). scanr is the right-to-left dual of scanl. Note that the order of parameters on the accumulating function are reversed compared to scanl.
Also note that
head (scanr f z xs) == foldr f z xs.
>>>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"]>>>scanr (+) 0 [1..]* Hangs forever *
scanl1 :: (a -> a -> a) -> [a] -> [a] Source #
\(\mathcal{O}(n)\). scanl1 is a variant of scanl that has no starting
value argument:
scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]
>>>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] Source #
\(\mathcal{O}(n)\). scanl is similar to foldl, but returns a list of
successive reduced values from the left:
scanl f z [x1, x2, ...] == [z, z `f` x1, (z `f` x1) `f` x2, ...]
Note that
last (scanl f z xs) == foldl f z xs
>>>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 *
\(\mathcal{O}(n)\). 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
\(\mathcal{O}(n)\). 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
\(\mathcal{O}(1)\). Extract the elements after the head of a list, which must be non-empty.
>>>tail [1, 2, 3][2,3]>>>tail [1][]>>>tail []Exception: Prelude.tail: empty list
\(\mathcal{O}(1)\). Extract the first element of a list, which must be non-empty.
>>>head [1, 2, 3]1>>>head [1..]1>>>head []Exception: Prelude.head: empty list
maybe :: b -> (a -> b) -> Maybe a -> b Source #
The maybe function takes a default value, a function, and a Maybe
value. If the Maybe value is Nothing, the function returns the
default value. Otherwise, it applies the function to the value inside
the Just and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using readMaybe. If we succeed,
return twice the integer; that is, apply (*2) to it. If instead
we fail to parse an integer, return 0 by default:
>>>import 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""
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
An infix synonym for fmap.
The name of this operator is an allusion to $.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas $ is function application, <$> is function
application lifted over a Functor.
Examples
Convert from a Maybe IntMaybe
Stringshow:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an Either Int IntEither IntString using show:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply even to the second element of a pair:
>>>even <$> (2,2)(2,True)
uncurry :: (a -> b -> c) -> (a, b) -> c Source #
uncurry converts a curried function to a function on pairs.
Examples
>>>uncurry (+) (1,2)3
>>>uncurry ($) (show, 1)"1"
>>>map (uncurry max) [(1,2), (3,4), (6,8)][2,4,8]
until :: (a -> Bool) -> (a -> a) -> a -> a Source #
until p ff until p holds.
($!) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
flip :: (a -> b -> c) -> b -> a -> c Source #
flip ff.
>>>flip (++) "hello" "world""worldhello"
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]
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as >>=, but with the arguments interchanged.
undefined :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => a Source #
errorWithoutStackTrace :: forall (r :: RuntimeRep) (a :: TYPE r). [Char] -> a Source #
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 Source #
error stops execution and displays an error message.