| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
GhcPrelude
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
- 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
- type String = [Char]
- 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 #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
seq :: forall (r :: RuntimeRep) a (b :: TYPE r). a -> b -> b infixr 0 #
The value of seq a b is bottom if a is bottom, and
otherwise equal to b. In other words, it evaluates the first
argument a to weak head normal form (WHNF). seq is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression seq a b does
not guarantee that a will be evaluated before b.
The only guarantee given by seq is that the both a
and b will be evaluated before seq returns a value.
In particular, this means that b may be evaluated before
a. If you need to guarantee a specific order of evaluation,
you must use the function pseq from the "parallel" package.
filter :: (a -> Bool) -> [a] -> [a] #
\(\mathcal{O}(n)\). filter, applied to a predicate and a list, returns
the list of those elements that satisfy the predicate; i.e.,
filter p xs = [ x | x <- xs, p x]
>>>filter odd [1, 2, 3][1,3]
zip :: [a] -> [b] -> [(a, b)] #
\(\mathcal{O}(\min(m,n))\). zip takes two lists and returns a list of
corresponding pairs.
zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]
If one input list is short, excess elements of the longer list are discarded:
zip [1] ['a', 'b'] = [(1, 'a')] zip [1, 2] ['a'] = [(1, 'a')]
zip is right-lazy:
zip [] _|_ = [] zip _|_ [] = _|_
zip is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
print :: Show a => a -> IO () #
The print function outputs a value of any printable type to the
standard output device.
Printable types are those that are instances of class Show; print
converts values to strings for output using the show operation and
adds a newline.
For example, a program to print the first 20 integers and their powers of 2 could be written as:
main = print ([(n, 2^n) | n <- [0..19]])
map :: (a -> b) -> [a] -> [b] #
\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to
each element of xs, i.e.,
map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn] map f [x1, x2, ...] == [f x1, f x2, ...]
>>>map (+1) [1, 2, 3]
($) :: forall (r :: RuntimeRep) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 #
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 #
general coercion from integral types
realToFrac :: (Real a, Fractional b) => a -> b #
general coercion to fractional types
The Bounded class is used to name the upper and lower limits of a
type. Ord is not a superclass of Bounded since types that are not
totally ordered may also have upper and lower bounds.
The Bounded class may be derived for any enumeration type;
minBound is the first constructor listed in the data declaration
and maxBound is the last.
Bounded may also be derived for single-constructor datatypes whose
constituent types are in Bounded.
Instances
Class Enum defines operations on sequentially ordered types.
The enumFrom... methods are used in Haskell's translation of
arithmetic sequences.
Instances of Enum may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by fromEnum from 0 through n-1.
See Chapter 10 of the Haskell Report for more details.
For any type that is an instance of class Bounded as well as Enum,
the following should hold:
- The calls
succmaxBoundpredminBound fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::BoolenumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBoundMethods
the successor of a value. For numeric types, succ adds 1.
the predecessor of a value. For numeric types, pred subtracts 1.
Convert from an Int.
Convert to an Int.
It is implementation-dependent what fromEnum returns when
applied to a value that is too large to fit in an Int.
Used in Haskell's translation of [n..] with [n..] = enumFrom n,
a possible implementation being enumFrom n = n : enumFrom (succ n).
For example:
enumFrom 4 :: [Integer] = [4,5,6,7,...]
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] #
Used in Haskell's translation of [n,n'..]
with [n,n'..] = enumFromThen n n', a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n'),
worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] #
Used in Haskell's translation of [n..m] with
[n..m] = enumFromTo n m, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = [].
For example:
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] #
Used in Haskell's translation of [n,n'..m] with
[n,n'..m] = enumFromThenTo n n' m, a possible implementation
being enumFromThenTo n n' m = worker (f x) (c x) n m,
x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
enumFromThenTo 6 8 2 :: [Int] = []
Instances
The Eq class defines equality (==) and inequality (/=).
All the basic datatypes exported by the Prelude are instances of Eq,
and Eq may be derived for any datatype whose constituents are also
instances of Eq.
The Haskell Report defines no laws for Eq. However, == is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing non-normalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:
Instances
class Fractional a => Floating a where #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for Floating. However, (, +)(
and *)exp are customarily expected to define an exponential field and have
the following properties:
exp (a + b)=exp a * exp bexp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh
Instances
class Num a => Fractional a where #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for Fractional. However, ( and
+)( are customarily expected to define a division ring and have the
following properties:*)
recipgives the multiplicative inversex * recip x=recip x * x=fromInteger 1
Note that it isn't customarily expected that a type instance of
Fractional implement a field. However, all instances in base do.
Minimal complete definition
fromRational, (recip | (/))
Methods
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a #
Conversion from a Rational (that is Ratio IntegerfromRational
to a value of type Rational, so such literals have type
(.Fractional a) => a
Instances
| Fractional CFloat | |
| Fractional CDouble | |
| Fractional NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (/) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime # recip :: NominalDiffTime -> NominalDiffTime # fromRational :: Rational -> NominalDiffTime # | |
| Fractional DiffTime | |
| Fractional EdgeWeight Source # | |
Defined in CFG Methods (/) :: EdgeWeight -> EdgeWeight -> EdgeWeight # recip :: EdgeWeight -> EdgeWeight # fromRational :: Rational -> EdgeWeight # | |
| 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 #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for Integral. However, Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the div/mod and quot/rem pairs, given
suitable Euclidean functions f and g:
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g yx=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for Integer's instance, is
abs.
Methods
quot :: a -> a -> a infixl 7 #
integer division truncated toward zero
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
integer division truncated toward negative infinity
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
conversion to Integer
Instances
class Applicative m => Monad (m :: Type -> Type) where #
The Monad class defines the basic operations over a monad,
a concept from a branch of mathematics known as category theory.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an abstract datatype of actions.
Haskell's do expressions provide a convenient syntax for writing
monadic expressions.
Instances of Monad should satisfy the following:
- Left identity
returna>>=k = k a- Right identity
m>>=return= m- Associativity
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the Monad and Applicative operations should relate as follows:
The above laws imply:
and that pure and (<*>) satisfy the applicative functor laws.
The instances of Monad for lists, Maybe and IO
defined in the Prelude satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'as ' can be understood as the >>= bsdo expression
do a <- as bs a
(>>) :: m a -> m b -> m b infixl 1 #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'as ' can be understood as the >> bsdo expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] | 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 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 # (>>) :: Capability a -> Capability b -> Capability b # return :: a -> Capability a # | |
| Monad P | Since: base-2.1 |
| Monad UniqSM Source # | |
| Monad CoreM Source # | |
| Monad P Source # | |
| Monad PD Source # | |
| Monad UnifyResultM Source # | |
Defined in Unify Methods (>>=) :: UnifyResultM a -> (a -> UnifyResultM b) -> UnifyResultM b # (>>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b # return :: a -> UnifyResultM a # | |
| Monad LiftM Source # | |
| Monad LlvmM Source # | |
| Monad FCode Source # | |
| Monad CmmParse Source # | |
| Monad PV Source # | |
| Monad Hsc Source # | |
| Monad CompPipeline Source # | |
Defined in PipelineMonad Methods (>>=) :: CompPipeline a -> (a -> CompPipeline b) -> CompPipeline b # (>>) :: CompPipeline a -> CompPipeline b -> CompPipeline b # return :: a -> CompPipeline a # | |
| Monad Ghc Source # | |
| Monad SimplM Source # | |
| Monad TcPluginM Source # | |
| Monad CpsRn Source # | |
| Monad MetaTyVarUpdateResult Source # | |
Defined in TcUnify Methods (>>=) :: MetaTyVarUpdateResult a -> (a -> MetaTyVarUpdateResult b) -> MetaTyVarUpdateResult b # (>>) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult b # return :: a -> MetaTyVarUpdateResult a # | |
| Monad TcS Source # | |
| Monad NatM Source # | |
| 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 # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # return :: a -> WrappedMonad m a # | |
| ArrowApply a => Monad (ArrowMonad a) | Since: base-2.1 |
Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # return :: a0 -> ArrowMonad a a0 # | |
| Monad (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| Monad m => Monad (MaybeT m) | |
| Monad (State s) Source # | |
| Monad (MaybeErr err) Source # | |
| Monad (SetM s) | |
| Monad (CmdLineP s) Source # | |
| Monad m => Monad (EwM m) Source # | |
| Monad (IOEnv m) Source # | |
| Monad (RegM freeRegs) Source # | |
| Monad m => Monad (GhcT m) Source # | |
| 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 # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # return :: a -> WhenMissing f x a # | |
| (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 (ExceptT e m) | |
| Monad m => Monad (Stream m a) Source # | |
| Monad ((->) r :: Type -> Type) | Since: base-2.1 |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Monad ((,,,) a b c) | Since: base-4.14.0.0 |
| (Monad f, Monad g) => Monad (Product f g) | Since: base-4.9.0.0 |
| (Monad f, Applicative f) => Monad (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMatched f x y a -> (a -> WhenMatched f x y b) -> WhenMatched f x y b # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # return :: a -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Monad (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # return :: a -> WhenMissing f k x a # | |
| 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 # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # return :: a -> WhenMatched f k x y a # | |
| (Monoid w, Monad m) => Monad (RWST r w s m) | |
| Monad m => Monad (RWST r w s m) | |
class Functor (f :: Type -> Type) where #
A type f is a Functor if it provides a function fmap which, given any types a and b
lets you apply any function from (a -> b) to turn an f a into an f b, preserving the
structure of f. Furthermore f needs to adhere to the following:
Note, that the second law follows from the free theorem of the type fmap and
the first law, so you need only check that the former condition holds.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b #
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
Unary negation.
Absolute value.
Sign of a number.
The functions abs and signum should satisfy the law:
abs x * signum x == x
For real numbers, the signum is either -1 (negative), 0 (zero)
or 1 (positive).
fromInteger :: Integer -> a #
Conversion from an Integer.
An integer literal represents the application of the function
fromInteger to the appropriate value of type Integer,
so such literals have type (.Num a) => a
Instances
The Ord class is used for totally ordered datatypes.
Instances of Ord can be derived for any user-defined datatype whose
constituent types are in Ord. The declared order of the constructors in
the data declaration determines the ordering in derived Ord instances. The
Ordering datatype allows a single comparison to determine the precise
ordering of two objects.
The Haskell Report defines no laws for Ord. However, <= is customarily
expected to implement a non-strict partial order and have the following
properties:
- Transitivity
- if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
x <= x=True- Antisymmetry
- if
x <= y && y <= x=True, thenx == y=True
Note that the following operator interactions are expected to hold:
x >= y=y <= xx < y=x <= y && x /= yx > y=y < xx < y=compare x y == LTx > y=compare x y == GTx == y=compare x y == EQmin x y == if x <= y then x else y=Truemax x y == if x >= y then x else y=True
Note that (7.) and (8.) do not require min and max to return either of
their arguments. The result is merely required to equal one of the
arguments in terms of (==).
Minimal complete definition: either compare or <=.
Using compare can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering #
(<) :: a -> a -> Bool infix 4 #
(<=) :: a -> a -> Bool infix 4 #
(>) :: a -> a -> Bool infix 4 #
Instances
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 Version | Since: base-2.1 |
| 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 Methods readsPrec :: Int -> ReadS BufferMode # readList :: ReadS [BufferMode] # readPrec :: ReadPrec BufferMode # readListPrec :: ReadPrec [BufferMode] # | |
| Read Newline | Since: base-4.3.0.0 |
| Read NewlineMode | Since: base-4.3.0.0 |
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode # readList :: ReadS [NewlineMode] # readPrec :: ReadPrec NewlineMode # readListPrec :: ReadPrec [NewlineMode] # | |
| 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 Methods readsPrec :: Int -> ReadS Associativity # readList :: ReadS [Associativity] # | |
| Read SourceUnpackedness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceUnpackedness # readList :: ReadS [SourceUnpackedness] # | |
| Read SourceStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness # readList :: ReadS [SourceStrictness] # | |
| Read DecidedStrictness | Since: base-4.9.0.0 |
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness # readList :: ReadS [DecidedStrictness] # | |
| Read SomeSymbol | Since: base-4.7.0.0 |
Defined in GHC.TypeLits Methods readsPrec :: Int -> ReadS SomeSymbol # readList :: ReadS [SomeSymbol] # readPrec :: ReadPrec SomeSymbol # readListPrec :: ReadPrec [SomeSymbol] # | |
| 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 Methods readsPrec :: Int -> ReadS CSigAtomic # readList :: ReadS [CSigAtomic] # readPrec :: ReadPrec CSigAtomic # readListPrec :: ReadPrec [CSigAtomic] # | |
| Read CClock | |
| Read CTime | |
| Read CUSeconds | |
| Read CSUSeconds | |
Defined in Foreign.C.Types Methods readsPrec :: Int -> ReadS CSUSeconds # readList :: ReadS [CSUSeconds] # readPrec :: ReadPrec CSUSeconds # readListPrec :: ReadPrec [CSUSeconds] # | |
| Read CIntPtr | |
| Read CUIntPtr | |
| Read CIntMax | |
| Read CUIntMax | |
| Read WordPtr | |
| Read IntPtr | |
| Read IOMode | Since: base-4.2.0.0 |
| Read Lexeme | Since: base-2.1 |
| Read GeneralCategory | Since: base-2.1 |
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory # readList :: ReadS [GeneralCategory] # | |
| Read ShortByteString | |
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString # readList :: ReadS [ShortByteString] # | |
| Read ByteString | |
Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
| Read ByteString | |
Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString # readList :: ReadS [ByteString] # readPrec :: ReadPrec ByteString # readListPrec :: ReadPrec [ByteString] # | |
| Read IntSet | |
| Read FileType | |
| Read Permissions | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS Permissions # readList :: ReadS [Permissions] # readPrec :: ReadPrec Permissions # readListPrec :: ReadPrec [Permissions] # | |
| Read XdgDirectory | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectory # readList :: ReadS [XdgDirectory] # | |
| Read XdgDirectoryList | |
Defined in System.Directory.Internal.Common Methods readsPrec :: Int -> ReadS XdgDirectoryList # readList :: ReadS [XdgDirectoryList] # | |
| Read PlatformMini | |
Defined in GHC.Platform Methods readsPrec :: Int -> ReadS PlatformMini # readList :: ReadS [PlatformMini] # | |
| Read Platform | |
| Read PlatformWordSize | |
Defined in GHC.Platform Methods readsPrec :: Int -> ReadS PlatformWordSize # readList :: ReadS [PlatformWordSize] # | |
| Read Arch | |
| Read OS | |
| Read ArmISA | |
| Read ArmISAExt | |
| Read ArmABI | |
| Read PPC_64ABI | |
| Read IntegerLibrary | |
Defined in GHC.Platform Methods readsPrec :: Int -> ReadS IntegerLibrary # readList :: ReadS [IntegerLibrary] # | |
| Read Mix | |
| Read BoxLabel | |
| Read CondBox | |
| Read HpcPos | |
| Read Hash | |
| Read DayOfWeek | |
| Read GroupEntry | |
Defined in System.Posix.User Methods readsPrec :: Int -> ReadS GroupEntry # readList :: ReadS [GroupEntry] # readPrec :: ReadPrec GroupEntry # readListPrec :: ReadPrec [GroupEntry] # | |
| Read UserEntry | |
| Read RTLDFlags | |
| Read PlatformConstants Source # | |
Defined in PlatformConstants Methods readsPrec :: Int -> ReadS PlatformConstants # readList :: ReadS [PlatformConstants] # | |
| Read IsBoot Source # | |
| 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 (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) # readList :: ReadS [WrappedMonoid m] # readPrec :: ReadPrec (WrappedMonoid m) # readListPrec :: ReadPrec [WrappedMonoid m] # | |
| 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) | |
| 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 w, Read1 m, Read a) => Read (WriterT w m a) | |
| (Read e, Read1 m, Read a) => Read (ExceptT 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 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1 |
| (Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1 |
Defined in GHC.Read | |
class (Num a, Ord a) => Real a where #
Methods
toRational :: a -> Rational #
the rational equivalent of its real argument with full precision
Instances
class (RealFrac a, Floating a) => RealFloat a where #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE
Methods
floatRadix :: a -> Integer #
a constant function, returning the radix of the representation
(often 2)
floatDigits :: a -> Int #
a constant function, returning the number of digits of
floatRadix in the significand
floatRange :: a -> (Int, Int) #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> (Integer, Int) #
The function decodeFloat applied to a real floating-point
number returns the significand expressed as an Integer and an
appropriately scaled exponent (an Int). If decodeFloat x(m,n), then x is equal in value to m*b^^n, where b
is the floating-point radix, and furthermore, either m and n
are both zero or else b^(d-1) <= , where abs m < b^dd is
the value of floatDigits xdecodeFloat 0 = (0,0)decodeFloat (-0.0) = (0,0)decodeFloat xisNaN xisInfinite xTrue.
encodeFloat :: Integer -> Int -> a #
encodeFloat performs the inverse of decodeFloat in the
sense that for finite x with the exception of -0.0,
uncurry encodeFloat (decodeFloat x) = xencodeFloat m nm*b^^n (or ±Infinity if overflow
occurs); usually the closer, but if m contains too many bits,
the result may be rounded in the wrong direction.
exponent corresponds to the second component of decodeFloat.
exponent 0 = 0x,
exponent x = snd (decodeFloat x) + floatDigits xx is a finite floating-point number, it is equal in value to
significand x * b ^^ exponent xb is the
floating-point radix.
The behaviour is unspecified on infinite or NaN values.
significand :: a -> a #
The first component of decodeFloat, scaled to lie in the open
interval (-1,1), either 0.0 or of absolute value >= 1/b,
where b is the floating-point radix.
The behaviour is unspecified on infinite or NaN values.
scaleFloat :: Int -> a -> a #
multiplies a floating-point number by an integer power of the radix
True if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool #
True if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool #
True if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool #
True if the argument is an IEEE negative zero
True if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating x and y, atan2 y x(x,y). atan2 y x-pi,
pi]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported. atan2 y 1y in a type
that is RealFloat, should return the same value as atan yatan2 is provided, but implementors
can provide a more accurate implementation.
Instances
class (Real a, Fractional a) => RealFrac a where #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) #
The function properFraction takes a real fractional number x
and returns a pair (n,f) such that x = n+f, and:
nis an integral number with the same sign asx; andfis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the ceiling, floor, truncate
and round functions are in terms of properFraction.
truncate :: Integral b => a -> b #
truncate xx between zero and x
round :: Integral b => a -> b #
round xx;
the even integer if x is equidistant between two integers
ceiling :: Integral b => a -> b #
ceiling xx
floor :: Integral b => a -> b #
floor xx
Instances
| RealFrac CFloat | |
| RealFrac CDouble | |
| RealFrac NominalDiffTime | |
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods properFraction :: Integral b => NominalDiffTime -> (b, NominalDiffTime) # truncate :: Integral b => NominalDiffTime -> b # round :: Integral b => NominalDiffTime -> b # ceiling :: Integral b => NominalDiffTime -> b # floor :: Integral b => NominalDiffTime -> b # | |
| RealFrac DiffTime | |
| Integral a => RealFrac (Ratio a) | Since: base-2.0.1 |
| RealFrac a => RealFrac (Identity a) | Since: base-4.9.0.0 |
| 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 |
Conversion of values to readable Strings.
Derived instances of Show have the following properties, which
are compatible with derived instances of Read:
- The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. - If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. - the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. - If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of Show is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5Note that right-associativity of :^: is ignored. For example,
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int | the operator precedence of the enclosing
context (a number from |
| -> a | the value to be converted to a |
| -> ShowS |
Convert a value to a readable String.
showsPrec should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of Read and Show satisfy the following:
That is, readsPrec parses the string produced by
showsPrec, and delivers the value that showsPrec started with.
Instances
class Monad m => MonadFail (m :: Type -> Type) where #
When a value is bound in do-notation, the pattern on the left
hand side of <- might not match. In this case, this class
provides a function to recover.
A Monad without a MonadFail instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (~pat).
Instances of MonadFail should satisfy the following law: fail s should
be a left zero for >>=,
fail s >>= f = fail s
If your Monad is also MonadPlus, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Instances
class Functor f => Applicative (f :: Type -> Type) where #
A functor with application, providing operations to
A minimal complete definition must include implementations of pure
and of either <*> or liftA2. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
pureid<*>v = v- Composition
pure(.)<*>u<*>v<*>w = u<*>(v<*>w)- Homomorphism
puref<*>purex =pure(f x)- Interchange
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the Functor instance for f will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If f is also a Monad, it should satisfy
(which implies that pure and <*> satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 #
Sequential application.
A few functors support an implementation of <*> that is more
efficient than the default one.
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 #
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 #
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 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 |
| Applicative Identity | Since: base-4.8.0.0 |
| 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 |
| Applicative Down | Since: base-4.11.0.0 |
| Applicative ReadPrec | Since: base-4.6.0.0 |
| Applicative ReadP | Since: base-4.6.0.0 |
| Applicative NonEmpty | Since: base-4.9.0.0 |
| 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 # (<*>) :: Capability (a -> b) -> Capability a -> Capability b # liftA2 :: (a -> b -> c) -> Capability a -> Capability b -> Capability c # (*>) :: Capability a -> Capability b -> Capability b # (<*) :: Capability a -> Capability b -> Capability a # | |
| Applicative P | Since: base-4.5.0.0 |
| Applicative Pair Source # | |
| Applicative UniqSM Source # | |
| Applicative CoreM Source # | |
| Applicative P Source # | |
| Applicative PD Source # | |
| Applicative UnifyResultM Source # | |
Defined in Unify Methods pure :: a -> UnifyResultM a # (<*>) :: UnifyResultM (a -> b) -> UnifyResultM a -> UnifyResultM b # liftA2 :: (a -> b -> c) -> UnifyResultM a -> UnifyResultM b -> UnifyResultM c # (*>) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM b # (<*) :: UnifyResultM a -> UnifyResultM b -> UnifyResultM a # | |
| Applicative LiftM Source # | |
| Applicative LlvmM Source # | |
| Applicative FCode Source # | |
| Applicative CmmParse Source # | |
| Applicative PV Source # | |
| Applicative Hsc Source # | |
| Applicative CompPipeline Source # | |
Defined in PipelineMonad Methods pure :: a -> CompPipeline a # (<*>) :: CompPipeline (a -> b) -> CompPipeline a -> CompPipeline b # liftA2 :: (a -> b -> c) -> CompPipeline a -> CompPipeline b -> CompPipeline c # (*>) :: CompPipeline a -> CompPipeline b -> CompPipeline b # (<*) :: CompPipeline a -> CompPipeline b -> CompPipeline a # | |
| Applicative Ghc Source # | |
| Applicative SimplM Source # | |
| Applicative TcPluginM Source # | |
| Applicative CpsRn Source # | |
| Applicative MetaTyVarUpdateResult Source # | |
Defined in TcUnify Methods pure :: a -> MetaTyVarUpdateResult a # (<*>) :: MetaTyVarUpdateResult (a -> b) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b # liftA2 :: (a -> b -> c) -> MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult c # (*>) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult b # (<*) :: MetaTyVarUpdateResult a -> MetaTyVarUpdateResult b -> MetaTyVarUpdateResult a # | |
| Applicative TcS Source # | |
| Applicative NatM Source # | |
| Applicative (Either e) | Since: base-3.0 |
| 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 # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a # | |
| Arrow a => Applicative (ArrowMonad a) | Since: base-4.6.0.0 |
Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 # | |
| Applicative (Proxy :: Type -> Type) | Since: base-4.7.0.0 |
| (Functor m, Monad m) => Applicative (MaybeT m) | |
| Applicative (State s) Source # | |
| Applicative (MaybeErr err) Source # | |
| Applicative (SetM s) | |
| Applicative (CmdLineP s) Source # | |
Defined in CmdLineParser | |
| Monad m => Applicative (EwM m) Source # | |
| Applicative (IOEnv m) Source # | |
| Applicative (RegM freeRegs) Source # | |
Defined in RegAlloc.Linear.State Methods pure :: a -> RegM freeRegs a # (<*>) :: RegM freeRegs (a -> b) -> RegM freeRegs a -> RegM freeRegs b # liftA2 :: (a -> b -> c) -> RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs c # (*>) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs b # (<*) :: RegM freeRegs a -> RegM freeRegs b -> RegM freeRegs a # | |
| Applicative m => Applicative (GhcT m) 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 |
| Arrow a => Applicative (WrappedArrow a b) | Since: base-2.1 |
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # | |
| Applicative m => Applicative (Kleisli m a) | Since: base-4.14.0.0 |
Defined in Control.Arrow | |
| Monoid m => Applicative (Const m :: Type -> Type) | Since: base-2.0.1 |
| 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 # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a # | |
| (Monoid w, Applicative m) => Applicative (WriterT w m) | |
Defined in Control.Monad.Trans.Writer.Lazy | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Strict | |
| (Functor m, Monad m) => Applicative (StateT s m) | |
Defined in Control.Monad.Trans.State.Lazy | |
| Applicative m => Applicative (ReaderT r m) | |
Defined in Control.Monad.Trans.Reader | |
| (Functor m, Monad m) => Applicative (ExceptT e m) | |
Defined in Control.Monad.Trans.Except | |
| Monad m => Applicative (Stream m a) Source # | |
Defined in Stream | |
| Applicative ((->) r :: Type -> Type) | Since: base-2.1 |
| Monoid c => Applicative (K1 i c :: Type -> Type) | Since: base-4.12.0.0 |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
| (Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) | Since: base-4.14.0.0 |
Defined in GHC.Base | |
| (Applicative f, Applicative g) => Applicative (Product f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Product | |
| (Monad f, Applicative f) => Applicative (WhenMatched f x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a # | |
| (Applicative f, Monad f) => Applicative (WhenMissing f k x) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a # | |
| Applicative (ContT r m) | |
Defined in Control.Monad.Trans.Cont | |
| Applicative f => Applicative (M1 i c f) | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (f :.: g) | Since: base-4.9.0.0 |
| (Applicative f, Applicative g) => Applicative (Compose f g) | Since: base-4.9.0.0 |
Defined in Data.Functor.Compose | |
| (Monad f, Applicative f) => Applicative (WhenMatched f k x y) | Equivalent to Since: containers-0.5.9 |
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a # | |
| (Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.Strict | |
| (Functor m, Monad m) => Applicative (RWST r w s m) | |
Defined in Control.Monad.Trans.RWS.CPS | |
class Foldable (t :: Type -> Type) where #
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define foldr:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
length = getSum . foldMap (Sum . const 1)
sum, product, maximum, and minimum should all be essentially
equivalent to foldMap forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a Functor instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b #
Right-associative fold of a structure.
In the case of lists, foldr, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that, since the head of the resulting expression is produced by
an application of the operator to the first element of the list,
foldr can produce a terminating expression from an infinite list.
For a general Foldable structure this should be semantically identical
to,
foldr f z =foldrf z .toList
foldl :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure.
In the case of lists, foldl, when applied to a binary
operator, a starting value (typically the left-identity of the operator),
and a list, reduces the list using the binary operator, from left to
right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. This means that foldl' will
diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to
use foldl' instead of foldl. The reason for this is that latter does
not force the "inner" results (e.g. z `f` x1 in the above example)
before applying them to the operator (e.g. to (`f` x2)). This results
in a thunk chain \(\mathcal{O}(n)\) elements long, which then must be
evaluated from the outside-in.
For a general Foldable structure this should be semantically identical
to,
foldl f z =foldlf z .toList
foldl' :: (b -> a -> b) -> b -> t a -> b #
Left-associative fold of a structure but with strict application of the operator.
This ensures that each step of the fold is forced to weak head normal
form before being applied, avoiding the collection of thunks that would
otherwise occur. This is often what you want to strictly reduce a finite
list to a single, monolithic result (e.g. length).
For a general Foldable structure this should be semantically identical
to,
foldl' f z =foldl'f z .toList
Since: base-4.6.0.0
foldr1 :: (a -> a -> a) -> t a -> a #
A variant of foldr that has no base case,
and thus may only be applied to non-empty structures.
foldr1f =foldr1f .toList
foldl1 :: (a -> a -> a) -> t a -> a #
A variant of foldl that has no base case,
and thus may only be applied to non-empty structures.
foldl1f =foldl1f .toList
Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.
Since: base-4.8.0.0
Returns the size/length of a finite structure as an Int. The
default implementation is optimized for structures that are similar to
cons-lists, because there is no general way to do better.
Since: base-4.8.0.0
elem :: Eq a => a -> t a -> Bool infix 4 #
Does the element occur in the structure?
Since: base-4.8.0.0
maximum :: Ord a => t a -> a #
The largest element of a non-empty structure.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a #
The least element of a non-empty structure.
Since: base-4.8.0.0
The sum function computes the sum of the numbers of a structure.
Since: base-4.8.0.0
product :: Num a => t a -> a #
The product function computes the product of the numbers of a
structure.
Since: base-4.8.0.0
Instances
| Foldable [] | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m # foldMap :: Monoid m => (a -> m) -> [a] -> m # foldMap' :: Monoid m => (a -> m) -> [a] -> m # foldr :: (a -> b -> b) -> b -> [a] -> b # foldr' :: (a -> b -> b) -> b -> [a] -> b # foldl :: (b -> a -> b) -> b -> [a] -> b # foldl' :: (b -> a -> b) -> b -> [a] -> b # foldr1 :: (a -> a -> a) -> [a] -> a # foldl1 :: (a -> a -> a) -> [a] -> a # elem :: Eq a => a -> [a] -> Bool # maximum :: Ord a => [a] -> a # | |
| Foldable Maybe | Since: base-2.1 |
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m # foldMap :: Monoid m => (a -> m) -> Maybe a -> m # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m # foldr :: (a -> b -> b) -> b -> Maybe a -> b # foldr' :: (a -> b -> b) -> b -> Maybe a -> b # foldl :: (b -> a -> b) -> b -> Maybe a -> b # foldl' :: (b -> a -> b) -> b -> Maybe a -> b # foldr1 :: (a -> a -> a) -> Maybe a -> a # foldl1 :: (a -> a -> a) -> Maybe a -> a # elem :: Eq a => a -> Maybe a -> Bool # maximum :: Ord a => Maybe a -> a # minimum :: Ord a => Maybe a -> a # | |
| Foldable Par1 | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m # foldMap :: Monoid m => (a -> m) -> Par1 a -> m # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m # foldr :: (a -> b -> b) -> b -> Par1 a -> b # foldr' :: (a -> b -> b) -> b -> Par1 a -> b # foldl :: (b -> a -> b) -> b -> Par1 a -> b # foldl' :: (b -> a -> b) -> b -> Par1 a -> b # foldr1 :: (a -> a -> a) -> Par1 a -> a # foldl1 :: (a -> a -> a) -> Par1 a -> a # elem :: Eq a => a -> Par1 a -> Bool # maximum :: Ord a => Par1 a -> a # | |
| Foldable Complex | Since: base-4.9.0.0 |
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m # foldMap :: Monoid m => (a -> m) -> Option a -> m # foldMap' :: Monoid m => (a -> m) -> Option a -> m # foldr :: (a -> b -> b) -> b -> Option a -> b # foldr' :: (a -> b -> b) -> b -> Option a -> b # foldl :: (b -> a -> b) -> b -> Option a -> b # foldl' :: (b -> a -> b) -> b -> Option a -> b # foldr1 :: (a -> a -> a) -> Option a -> a # foldl1 :: (a -> a -> a) -> Option a -> a # elem :: Eq a => a -> Option a -> Bool # maximum :: Ord a => Option a -> a # minimum :: Ord a => Option a -> a # | |
| Foldable ZipList | Since: base-4.9.0.0 |
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m # foldMap :: Monoid m => (a -> m) -> ZipList a -> m # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m # foldr :: (a -> b -> b) -> b -> ZipList a -> b # foldr' :: (a -> b -> b) -> b -> ZipList a -> b # foldl :: (b -> a -> b) -> b -> ZipList a -> b # foldl' :: (b -> a -> b) -> b -> ZipList a -> b # foldr1 :: (a -> a -> a) -> ZipList a -> a # foldl1 :: (a -> a -> a) -> ZipList a -> a # elem :: Eq a => a -> ZipList a -> Bool # maximum :: Ord a => ZipList a -> a # minimum :: Ord a => ZipList a -> a # | |
| Foldable Identity | Since: base-4.8.0.0 |
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m # foldMap :: Monoid m => (a -> m) -> Identity a -> m # foldMap' :: Monoid m => (a -> m) -> Identity a -> m # foldr :: (a -> b -> b) -> b -> Identity a -> b # foldr' :: (a -> b -> b) -> b -> Identity a -> b # foldl :: (b -> a -> b) -> b -> Identity a -> b # foldl' :: (b -> a -> b) -> b -> Identity a -> b # foldr1 :: (a -> a -> a) -> Identity a -> a # foldl1 :: (a -> a -> a) -> Identity a -> a # elem :: Eq a => a -> Identity a -> Bool # maximum :: Ord a => Identity a -> a # minimum :: Ord a => Identity a -> a # | |
| Foldable First | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable Last | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Foldable Down | Since: base-4.12.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m # foldMap :: Monoid m => (a -> m) -> Down a -> m # foldMap' :: Monoid m => (a -> m) -> Down a -> m # foldr :: (a -> b -> b) -> b -> Down a -> b # foldr' :: (a -> b -> b) -> b -> Down a -> b # foldl :: (b -> a -> b) -> b -> Down a -> b # foldl' :: (b -> a -> b) -> b -> Down a -> b # foldr1 :: (a -> a -> a) -> Down a -> a # foldl1 :: (a -> a -> a) -> Down a -> a # elem :: Eq a => a -> Down a -> Bool # maximum :: Ord a => Down a -> a # | |
| Foldable NonEmpty | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b # foldr1 :: (a -> a -> a) -> NonEmpty a -> a # foldl1 :: (a -> a -> a) -> NonEmpty a -> a # elem :: Eq a => a -> NonEmpty a -> Bool # maximum :: Ord a => NonEmpty a -> a # minimum :: Ord a => NonEmpty a -> a # | |
| Foldable IntMap | Folds in order of increasing key. |
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m # foldMap :: Monoid m => (a -> m) -> IntMap a -> m # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m # foldr :: (a -> b -> b) -> b -> IntMap a -> b # foldr' :: (a -> b -> b) -> b -> IntMap a -> b # foldl :: (b -> a -> b) -> b -> IntMap a -> b # foldl' :: (b -> a -> b) -> b -> IntMap a -> b # foldr1 :: (a -> a -> a) -> IntMap a -> a # foldl1 :: (a -> a -> a) -> IntMap a -> a # elem :: Eq a => a -> IntMap a -> Bool # maximum :: Ord a => IntMap a -> a # minimum :: Ord a => IntMap a -> a # | |
| Foldable SCC | Since: containers-0.5.9 |
Defined in Data.Graph Methods fold :: Monoid m => SCC m -> m # foldMap :: Monoid m => (a -> m) -> SCC a -> m # foldMap' :: Monoid m => (a -> m) -> SCC a -> m # foldr :: (a -> b -> b) -> b -> SCC a -> b # foldr' :: (a -> b -> b) -> b -> SCC a -> b # foldl :: (b -> a -> b) -> b -> SCC a -> b # foldl' :: (b -> a -> b) -> b -> SCC a -> b # foldr1 :: (a -> a -> a) -> SCC a -> a # foldl1 :: (a -> a -> a) -> SCC a -> a # elem :: Eq a => a -> SCC a -> Bool # maximum :: Ord a => SCC a -> a # | |
| Foldable Tree | |
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m # foldMap :: Monoid m => (a -> m) -> Tree a -> m # foldMap' :: Monoid m => (a -> m) -> Tree a -> m # foldr :: (a -> b -> b) -> b -> Tree a -> b # foldr' :: (a -> b -> b) -> b -> Tree a -> b # foldl :: (b -> a -> b) -> b -> Tree a -> b # foldl' :: (b -> a -> b) -> b -> Tree a -> b # foldr1 :: (a -> a -> a) -> Tree a -> a # foldl1 :: (a -> a -> a) -> Tree a -> a # elem :: Eq a => a -> Tree a -> Bool # maximum :: Ord a => Tree a -> a # | |
| Foldable Seq | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m # foldMap :: Monoid m => (a -> m) -> Seq a -> m # foldMap' :: Monoid m => (a -> m) -> Seq a -> m # foldr :: (a -> b -> b) -> b -> Seq a -> b # foldr' :: (a -> b -> b) -> b -> Seq a -> b # foldl :: (b -> a -> b) -> b -> Seq a -> b # foldl' :: (b -> a -> b) -> b -> Seq a -> b # foldr1 :: (a -> a -> a) -> Seq a -> a # foldl1 :: (a -> a -> a) -> Seq a -> a # elem :: Eq a => a -> Seq a -> Bool # maximum :: Ord a => Seq a -> a # | |
| Foldable FingerTree | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m # foldr :: (a -> b -> b) -> b -> FingerTree a -> b # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b # foldl :: (b -> a -> b) -> b -> FingerTree a -> b # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b # foldr1 :: (a -> a -> a) -> FingerTree a -> a # foldl1 :: (a -> a -> a) -> FingerTree a -> a # toList :: FingerTree a -> [a] # null :: FingerTree a -> Bool # length :: FingerTree a -> Int # elem :: Eq a => a -> FingerTree a -> Bool # maximum :: Ord a => FingerTree a -> a # minimum :: Ord a => FingerTree a -> a # sum :: Num a => FingerTree a -> a # product :: Num a => FingerTree a -> a # | |
| Foldable Digit | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m # foldMap :: Monoid m => (a -> m) -> Digit a -> m # foldMap' :: Monoid m => (a -> m) -> Digit a -> m # foldr :: (a -> b -> b) -> b -> Digit a -> b # foldr' :: (a -> b -> b) -> b -> Digit a -> b # foldl :: (b -> a -> b) -> b -> Digit a -> b # foldl' :: (b -> a -> b) -> b -> Digit a -> b # foldr1 :: (a -> a -> a) -> Digit a -> a # foldl1 :: (a -> a -> a) -> Digit a -> a # elem :: Eq a => a -> Digit a -> Bool # maximum :: Ord a => Digit a -> a # minimum :: Ord a => Digit a -> a # | |
| Foldable Node | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m # foldMap :: Monoid m => (a -> m) -> Node a -> m # foldMap' :: Monoid m => (a -> m) -> Node a -> m # foldr :: (a -> b -> b) -> b -> Node a -> b # foldr' :: (a -> b -> b) -> b -> Node a -> b # foldl :: (b -> a -> b) -> b -> Node a -> b # foldl' :: (b -> a -> b) -> b -> Node a -> b # foldr1 :: (a -> a -> a) -> Node a -> a # foldl1 :: (a -> a -> a) -> Node a -> a # elem :: Eq a => a -> Node a -> Bool # maximum :: Ord a => Node a -> a # | |
| Foldable Elem | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m # foldMap :: Monoid m => (a -> m) -> Elem a -> m # foldMap' :: Monoid m => (a -> m) -> Elem a -> m # foldr :: (a -> b -> b) -> b -> Elem a -> b # foldr' :: (a -> b -> b) -> b -> Elem a -> b # foldl :: (b -> a -> b) -> b -> Elem a -> b # foldl' :: (b -> a -> b) -> b -> Elem a -> b # foldr1 :: (a -> a -> a) -> Elem a -> a # foldl1 :: (a -> a -> a) -> Elem a -> a # elem :: Eq a => a -> Elem a -> Bool # maximum :: Ord a => Elem a -> a # | |
| Foldable ViewL | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m # foldMap :: Monoid m => (a -> m) -> ViewL a -> m # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m # foldr :: (a -> b -> b) -> b -> ViewL a -> b # foldr' :: (a -> b -> b) -> b -> ViewL a -> b # foldl :: (b -> a -> b) -> b -> ViewL a -> b # foldl' :: (b -> a -> b) -> b -> ViewL a -> b # foldr1 :: (a -> a -> a) -> ViewL a -> a # foldl1 :: (a -> a -> a) -> ViewL a -> a # elem :: Eq a => a -> ViewL a -> Bool # maximum :: Ord a => ViewL a -> a # minimum :: Ord a => ViewL a -> a # | |
| Foldable ViewR | |
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m # foldMap :: Monoid m => (a -> m) -> ViewR a -> m # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m # foldr :: (a -> b -> b) -> b -> ViewR a -> b # foldr' :: (a -> b -> b) -> b -> ViewR a -> b # foldl :: (b -> a -> b) -> b -> ViewR a -> b # foldl' :: (b -> a -> b) -> b -> ViewR a -> b # foldr1 :: (a -> a -> a) -> ViewR a -> a # foldl1 :: (a -> a -> a) -> ViewR a -> a # elem :: Eq a => a -> ViewR a -> Bool # maximum :: Ord a => ViewR a -> a # minimum :: Ord a => ViewR a -> a # | |
| Foldable Set | Folds in order of increasing key. |
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m # foldMap :: Monoid m => (a -> m) -> Set a -> m # foldMap' :: Monoid m => (a -> m) -> Set a -> m # foldr :: (a -> b -> b) -> b -> Set a -> b # foldr' :: (a -> b -> b) -> b -> Set a -> b # foldl :: (b -> a -> b) -> b -> Set a -> b # foldl' :: (b -> a -> b) -> b -> Set a -> b # foldr1 :: (a -> a -> a) -> Set a -> a # foldl1 :: (a -> a -> a) -> Set a -> a # elem :: Eq a => a -> Set a -> Bool # maximum :: Ord a => Set a -> a # | |
| Foldable GenClosure | |
Defined in GHC.Exts.Heap.Closures Methods fold :: Monoid m => GenClosure m -> m # foldMap :: Monoid m => (a -> m) -> GenClosure a -> m # foldMap' :: Monoid m => (a -> m) -> GenClosure a -> m # foldr :: (a -> b -> b) -> b -> GenClosure a -> b # foldr' :: (a -> b -> b) -> b -> GenClosure a -> b # foldl :: (b -> a -> b) -> b -> GenClosure a -> b # foldl' :: (b -> a -> b) -> b -> GenClosure a -> b # foldr1 :: (a -> a -> a) -> GenClosure a -> a # foldl1 :: (a -> a -> a) -> GenClosure a -> a # toList :: GenClosure a -> [a] # null :: GenClosure a -> Bool # length :: GenClosure a -> Int # elem :: Eq a => a -> GenClosure a -> Bool # maximum :: Ord a => GenClosure a -> a # minimum :: Ord a => GenClosure a -> a # sum :: Num a => GenClosure a -> a # product :: Num a => GenClosure a -> a # | |
| Foldable SizedSeq | |
Defined in SizedSeq Methods fold :: Monoid m => SizedSeq m -> m # foldMap :: Monoid m => (a -> m) -> SizedSeq a -> m # foldMap' :: Monoid m => (a -> m) -> SizedSeq a -> m # foldr :: (a -> b -> b) -> b -> SizedSeq a -> b # foldr' :: (a -> b -> b) -> b -> SizedSeq a -> b # foldl :: (b -> a -> b) -> b -> SizedSeq a -> b # foldl' :: (b -> a -> b) -> b -> SizedSeq a -> b # foldr1 :: (a -> a -> a) -> SizedSeq a -> a # foldl1 :: (a -> a -> a) -> SizedSeq a -> a # elem :: Eq a => a -> SizedSeq a -> Bool # maximum :: Ord a => SizedSeq a -> a # minimum :: Ord a => SizedSeq a -> a # | |
| Foldable UniqueMap Source # | |
Defined in Hoopl.Collections Methods fold :: Monoid m => UniqueMap m -> m # foldMap :: Monoid m => (a -> m) -> UniqueMap a -> m # foldMap' :: Monoid m => (a -> m) -> UniqueMap a -> m # foldr :: (a -> b -> b) -> b -> UniqueMap a -> b # foldr' :: (a -> b -> b) -> b -> UniqueMap a -> b # foldl :: (b -> a -> b) -> b -> UniqueMap a -> b # foldl' :: (b -> a -> b) -> b -> UniqueMap a -> b # foldr1 :: (a -> a -> a) -> UniqueMap a -> a # foldl1 :: (a -> a -> a) -> UniqueMap a -> a # toList :: UniqueMap a -> [a] # length :: UniqueMap a -> Int # elem :: Eq a => a -> UniqueMap a -> Bool # maximum :: Ord a => UniqueMap a -> a # minimum :: Ord a => UniqueMap a -> a # | |
| Foldable Pair Source # | |
Defined in Pair Methods fold :: Monoid m => Pair m -> m # foldMap :: Monoid m => (a -> m) -> Pair a -> m # foldMap' :: Monoid m => (a -> m) -> Pair a -> m # foldr :: (a -> b -> b) -> b -> Pair a -> b # foldr' :: (a -> b -> b) -> b -> Pair a -> b # foldl :: (b -> a -> b) -> b -> Pair a -> b # foldl' :: (b -> a -> b) -> b -> Pair a -> b # foldr1 :: (a -> a -> a) -> Pair a -> a # foldl1 :: (a -> a -> a) -> Pair a -> a # elem :: Eq a => a -> Pair a -> Bool # maximum :: Ord a => Pair a -> a # | |
| Foldable OrdList Source # | |
Defined in OrdList Methods fold :: Monoid m => OrdList m -> m # foldMap :: Monoid m => (a -> m) -> OrdList a -> m # foldMap' :: Monoid m => (a -> m) -> OrdList a -> m # foldr :: (a -> b -> b) -> b -> OrdList a -> b # foldr' :: (a -> b -> b) -> b -> OrdList a -> b # foldl :: (b -> a -> b) -> b -> OrdList a -> b # foldl' :: (b -> a -> b) -> b -> OrdList a -> b # foldr1 :: (a -> a -> a) -> OrdList a -> a # foldl1 :: (a -> a -> a) -> OrdList a -> a # elem :: Eq a => a -> OrdList a -> Bool # maximum :: Ord a => OrdList a -> a # minimum :: Ord a => OrdList a -> a # | |
| Foldable NonDetUniqFM Source # | Inherently nondeterministic. If you use this please provide a justification why it doesn't introduce nondeterminism. See Note [Deterministic UniqFM] in UniqDFM to learn about determinism. |
Defined in UniqFM Methods fold :: Monoid m => NonDetUniqFM m -> m # foldMap :: Monoid m => (a -> m) -> NonDetUniqFM a -> m # foldMap' :: Monoid m => (a -> m) -> NonDetUniqFM a -> m # foldr :: (a -> b -> b) -> b -> NonDetUniqFM a -> b # foldr' :: (a -> b -> b) -> b -> NonDetUniqFM a -> b # foldl :: (b -> a -> b) -> b -> NonDetUniqFM a -> b # foldl' :: (b -> a -> b) -> b -> NonDetUniqFM a -> b # foldr1 :: (a -> a -> a) -> NonDetUniqFM a -> a # foldl1 :: (a -> a -> a) -> NonDetUniqFM a -> a # toList :: NonDetUniqFM a -> [a] # null :: NonDetUniqFM a -> Bool # length :: NonDetUniqFM a -> Int # elem :: Eq a => a -> NonDetUniqFM a -> Bool # maximum :: Ord a => NonDetUniqFM a -> a # minimum :: Ord a => NonDetUniqFM a -> a # sum :: Num a => NonDetUniqFM a -> a # product :: Num a => NonDetUniqFM a -> a # | |
| Foldable UniqDFM Source # | Deterministic, in O(n log n). |
Defined in UniqDFM Methods fold :: Monoid m => UniqDFM m -> m # foldMap :: Monoid m => (a -> m) -> UniqDFM a -> m # foldMap' :: Monoid m => (a -> m) -> UniqDFM a -> m # foldr :: (a -> b -> b) -> b -> UniqDFM a -> b # foldr' :: (a -> b -> b) -> b -> UniqDFM a -> b # foldl :: (b -> a -> b) -> b -> UniqDFM a -> b # foldl' :: (b -> a -> b) -> b -> UniqDFM a -> b # foldr1 :: (a -> a -> a) -> UniqDFM a -> a # foldl1 :: (a -> a -> a) -> UniqDFM a -> a # elem :: Eq a => a -> UniqDFM a -> Bool # maximum :: Ord a => UniqDFM a -> a # minimum :: Ord a => UniqDFM a -> a # | |
| Foldable BooleanFormula Source # | |
Defined in BooleanFormula Methods fold :: Monoid m => BooleanFormula m -> m # foldMap :: Monoid m => (a -> m) -> BooleanFormula a -> m # foldMap' :: Monoid m => (a -> m) -> BooleanFormula a -> m # foldr :: (a -> b -> b) -> b -> BooleanFormula a -> b # foldr' :: (a -> b -> b) -> b -> BooleanFormula a -> b # foldl :: (b -> a -> b) -> b -> BooleanFormula a -> b # foldl' :: (b -> a -> b) -> b -> BooleanFormula a -> b # foldr1 :: (a -> a -> a) -> BooleanFormula a -> a # foldl1 :: (a -> a -> a) -> BooleanFormula a -> a # toList :: BooleanFormula a -> [a] # null :: BooleanFormula a -> Bool # length :: BooleanFormula a -> Int # elem :: Eq a => a -> BooleanFormula a -> Bool # maximum :: Ord a => BooleanFormula a -> a # minimum :: Ord a => BooleanFormula a -> a # sum :: Num a => BooleanFormula a -> a # product :: Num a => BooleanFormula a -> a # | |
| Foldable Bag Source # | |
Defined in Bag Methods fold :: Monoid m => Bag m -> m # foldMap :: Monoid m => (a -> m) -> Bag a -> m # foldMap' :: Monoid m => (a -> m) -> Bag a -> m # foldr :: (a -> b -> b) -> b -> Bag a -> b # foldr' :: (a -> b -> b) -> b -> Bag a -> b # foldl :: (b -> a -> b) -> b -> Bag a -> b # foldl' :: (b -> a -> b) -> b -> Bag a -> b # foldr1 :: (a -> a -> a) -> Bag a -> a # foldl1 :: (a -> a -> a) -> Bag a -> a # elem :: Eq a => a -> Bag a -> Bool # maximum :: Ord a => Bag a -> a # | |
| Foldable FieldLbl Source # | |
Defined in FieldLabel Methods fold :: Monoid m => FieldLbl m -> m # foldMap :: Monoid m => (a -> m) -> FieldLbl a -> m # foldMap' :: Monoid m => (a -> m) -> FieldLbl a -> m # foldr :: (a -> b -> b) -> b -> FieldLbl a -> b # foldr' :: (a -> b -> b) -> b -> FieldLbl a -> b # foldl :: (b -> a -> b) -> b -> FieldLbl a -> b # foldl' :: (b -> a -> b) -> b -> FieldLbl a -> b # foldr1 :: (a -> a -> a) -> FieldLbl a -> a # foldl1 :: (a -> a -> a) -> FieldLbl a -> a # elem :: Eq a => a -> FieldLbl a -> Bool # maximum :: Ord a => FieldLbl a -> a # minimum :: Ord a => FieldLbl a -> a # | |
| Foldable IdentifierDetails Source # | |
Defined in HieTypes Methods fold :: Monoid m => IdentifierDetails m -> m # foldMap :: Monoid m => (a -> m) -> IdentifierDetails a -> m # foldMap' :: Monoid m => (a -> m) -> IdentifierDetails a -> m # foldr :: (a -> b -> b) -> b -> IdentifierDetails a -> b # foldr' :: (a -> b -> b) -> b -> IdentifierDetails a -> b # foldl :: (b -> a -> b) -> b -> IdentifierDetails a -> b # foldl' :: (b -> a -> b) -> b -> IdentifierDetails a -> b # foldr1 :: (a -> a -> a) -> IdentifierDetails a -> a # foldl1 :: (a -> a -> a) -> IdentifierDetails a -> a # toList :: IdentifierDetails a -> [a] # null :: IdentifierDetails a -> Bool # length :: IdentifierDetails a -> Int # elem :: Eq a => a -> IdentifierDetails a -> Bool # maximum :: Ord a => IdentifierDetails a -> a # minimum :: Ord a => IdentifierDetails a -> a # sum :: Num a => IdentifierDetails a -> a # product :: Num a => IdentifierDetails a -> a # | |
| Foldable NodeInfo Source # | |
Defined in HieTypes Methods fold :: Monoid m => NodeInfo m -> m # foldMap :: Monoid m => (a -> m) -> NodeInfo a -> m # foldMap' :: Monoid m => (a -> m) -> NodeInfo a -> m # foldr :: (a -> b -> b) -> b -> NodeInfo a -> b # foldr' :: (a -> b -> b) -> b -> NodeInfo a -> b # foldl :: (b -> a -> b) -> b -> NodeInfo a -> b # foldl' :: (b -> a -> b) -> b -> NodeInfo a -> b # foldr1 :: (a -> a -> a) -> NodeInfo a -> a # foldl1 :: (a -> a -> a) -> NodeInfo a -> a # elem :: Eq a => a -> NodeInfo a -> Bool # maximum :: Ord a => NodeInfo a -> a # minimum :: Ord a => NodeInfo a -> a # | |
| Foldable HieAST Source # | |
Defined in HieTypes Methods fold :: Monoid m => HieAST m -> m # foldMap :: Monoid m => (a -> m) -> HieAST a -> m # foldMap' :: Monoid m => (a -> m) -> HieAST a -> m # foldr :: (a -> b -> b) -> b -> HieAST a -> b # foldr' :: (a -> b -> b) -> b -> HieAST a -> b # foldl :: (b -> a -> b) -> b -> HieAST a -> b # foldl' :: (b -> a -> b) -> b -> HieAST a -> b # foldr1 :: (a -> a -> a) -> HieAST a -> a # foldl1 :: (a -> a -> a) -> HieAST a -> a # elem :: Eq a => a -> HieAST a -> Bool # maximum :: Ord a => HieAST a -> a # minimum :: Ord a => HieAST a -> a # | |
| Foldable HieASTs Source # | |
Defined in HieTypes Methods fold :: Monoid m => HieASTs m -> m # foldMap :: Monoid m => (a -> m) -> HieASTs a -> m # foldMap' :: Monoid m => (a -> m) -> HieASTs a -> m # foldr :: (a -> b -> b) -> b -> HieASTs a -> b # foldr' :: (a -> b -> b) -> b -> HieASTs a -> b # foldl :: (b -> a -> b) -> b -> HieASTs a -> b # foldl' :: (b -> a -> b) -> b -> HieASTs a -> b # foldr1 :: (a -> a -> a) -> HieASTs a -> a # foldl1 :: (a -> a -> a) -> HieASTs a -> a # elem :: Eq a => a -> HieASTs a -> Bool # maximum :: Ord a => HieASTs a -> a # minimum :: Ord a => HieASTs a -> a # | |
| Foldable HieArgs Source # | |
Defined in HieTypes Methods fold :: Monoid m => HieArgs m -> m # foldMap :: Monoid m => (a -> m) -> HieArgs a -> m # foldMap' :: Monoid m => (a -> m) -> HieArgs a -> m # foldr :: (a -> b -> b) -> b -> HieArgs a -> b # foldr' :: (a -> b -> b) -> b -> HieArgs a -> b # foldl :: (b -> a -> b) -> b -> HieArgs a -> b # foldl' :: (b -> a -> b) -> b -> HieArgs a -> b # foldr1 :: (a -> a -> a) -> HieArgs a -> a # foldl1 :: (a -> a -> a) -> HieArgs a -> a # elem :: Eq a => a -> HieArgs a -> Bool # maximum :: Ord a => HieArgs a -> a # minimum :: Ord a => HieArgs a -> a # | |
| Foldable HieType Source # | |
Defined in HieTypes Methods fold :: Monoid m => HieType m -> m # foldMap :: Monoid m => (a -> m) -> HieType a -> m # foldMap' :: Monoid m => (a -> m) -> HieType a -> m # foldr :: (a -> b -> b) -> b -> HieType a -> b # foldr' :: (a -> b -> b) -> b -> HieType a -> b # foldl :: (b -> a -> b) -> b -> HieType a -> b # foldl' :: (b -> a -> b) -> b -> HieType a -> b # foldr1 :: (a -> a -> a) -> HieType a -> a # foldl1 :: (a -> a -> a) -> HieType a -> a # elem :: Eq a => a -> HieType a -> Bool # maximum :: Ord a => HieType a -> a # minimum :: Ord a => HieType a -> a # | |
| Foldable LabelMap Source # | |
Defined in Hoopl.Label Methods fold :: Monoid m => LabelMap m -> m # foldMap :: Monoid m => (a -> m) -> LabelMap a -> m # foldMap' :: Monoid m => (a -> m) -> LabelMap a -> m # foldr :: (a -> b -> b) -> b -> LabelMap a -> b # foldr' :: (a -> b -> b) -> b -> LabelMap a -> b # foldl :: (b -> a -> b) -> b -> LabelMap a -> b # foldl' :: (b -> a -> b) -> b -> LabelMap a -> b # foldr1 :: (a -> a -> a) -> LabelMap a -> a # foldl1 :: (a -> a -> a) -> LabelMap a -> a # elem :: Eq a => a -> LabelMap a -> Bool # maximum :: Ord a => LabelMap a -> a # minimum :: Ord a => LabelMap a -> a # | |
| Foldable RecordPatSynField Source # | |
Defined in GHC.Hs.Binds Methods fold :: Monoid m => RecordPatSynField m -> m # foldMap :: Monoid m => (a -> m) -> RecordPatSynField a -> m # foldMap' :: Monoid m => (a -> m) -> RecordPatSynField a -> m # foldr :: (a -> b -> b) -> b -> RecordPatSynField a -> b # foldr' :: (a -> b -> b) -> b -> RecordPatSynField a -> b # foldl :: (b -> a -> b) -> b -> RecordPatSynField a -> b # foldl' :: (b -> a -> b) -> b -> RecordPatSynField a -> b # foldr1 :: (a -> a -> a) -> RecordPatSynField a -> a # foldl1 :: (a -> a -> a) -> RecordPatSynField a -> a # toList :: RecordPatSynField a -> [a] # null :: RecordPatSynField a -> Bool # length :: RecordPatSynField a -> Int # elem :: Eq a => a -> RecordPatSynField a -> Bool # maximum :: Ord a => RecordPatSynField a -> a # minimum :: Ord a => RecordPatSynField a -> a # sum :: Num a => RecordPatSynField a -> a # product :: Num a => RecordPatSynField a -> a # | |
| Foldable AnnProvenance Source # | |
Defined in GHC.Hs.Decls Methods fold :: Monoid m => AnnProvenance m -> m # foldMap :: Monoid m => (a -> m) -> AnnProvenance a -> m # foldMap' :: Monoid m => (a -> m) -> AnnProvenance a -> m # foldr :: (a -> b -> b) -> b -> AnnProvenance a -> b # foldr' :: (a -> b -> b) -> b -> AnnProvenance a -> b # foldl :: (b -> a -> b) -> b -> AnnProvenance a -> b # foldl' :: (b -> a -> b) -> b -> AnnProvenance a -> b # foldr1 :: (a -> a -> a) -> AnnProvenance a -> a # foldl1 :: (a -> a -> a) -> AnnProvenance a -> a # toList :: AnnProvenance a -> [a] # null :: AnnProvenance a -> Bool # length :: AnnProvenance a -> Int | |