| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Hedgehog.Internal.Prelude
Description
Mostly for compatibility across different base Prelude changes.
Synopsis
- class Semigroup a where
- class Monad m => MonadFail (m :: Type -> Type )
- (++) :: [a] -> [a] -> [a]
- seq :: forall (r :: RuntimeRep ) a (b :: TYPE r). a -> b -> b
- zip :: [a] -> [b] -> [(a, b)]
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- otherwise :: Bool
- ($) :: 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
- 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
where
- (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
- data Bool
- data Char
- data Double
- data Float
- data Int
- data Integer
- data Maybe a
- data Ordering
- type Rational = Ratio Integer
- data IO a
- data Word
- data Either a b
- type String = [ Char ]
- mapM_ :: ( Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- unzip :: [(a, b)] -> ([a], [b])
- id :: a -> a
- uncurry :: (a -> b -> c) -> (a, b) -> c
- 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 ()
- 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])
- 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
- 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
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- undefined :: forall (r :: RuntimeRep ) (a :: TYPE r). HasCallStack => a
- errorWithoutStackTrace :: forall (r :: RuntimeRep ) (a :: TYPE r). [ Char ] -> a
- error :: forall (r :: RuntimeRep ) (a :: TYPE r). HasCallStack => [ Char ] -> a
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool
Documentation
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Minimal complete definition
Methods
(<>) :: a -> a -> a infixr 6 Source #
An associative operation.
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
sconcat :: NonEmpty a -> a Source #
Reduce a non-empty list with
<>
The default definition should be sufficient, but this can be overridden for efficiency.
>>>import Data.List.NonEmpty>>>sconcat $ "Hello" :| [" ", "Haskell", "!"]"Hello Haskell!"
stimes :: Integral b => b -> a -> a Source #
Repeat a value
n
times.
Given that this works on a
Semigroup
it is allowed to fail if
you request 0 or fewer repetitions, and the default definition
will do so.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in
\(\mathcal{O}(1)\)
by
picking
stimes =
or
stimesIdempotent
stimes =
respectively.
stimesIdempotentMonoid
>>>stimes 4 [1][1,1,1,1]
Instances
class Monad m => MonadFail (m :: Type -> Type ) Source #
When a value is bound in
do
-notation, the pattern on the left
hand side of
<-
might not match. In this case, this class
provides a function to recover.
A
Monad
without a
MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (
~pat
).
Instances of
MonadFail
should satisfy the following law:
fail s
should
be a left zero for
>>=
,
fail s >>= f = fail s
If your
Monad
is also
MonadPlus
, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Minimal complete definition
Instances
(++) :: [a] -> [a] -> [a] infixr 5 Source #
Append two lists, i.e.,
[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn] [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]
If the first list is not finite, the result is the first list.
seq :: forall (r :: RuntimeRep ) a (b :: TYPE r). a -> b -> b infixr 0 Source #
The value of
seq a b
is bottom if
a
is bottom, and
otherwise equal to
b
. In other words, it evaluates the first
argument
a
to weak head normal form (WHNF).
seq
is usually
introduced to improve performance by avoiding unneeded laziness.
A note on evaluation order: the expression
seq a b
does
not
guarantee that
a
will be evaluated before
b
.
The only guarantee given by
seq
is that the both
a
and
b
will be evaluated before
seq
returns a value.
In particular, this means that
b
may be evaluated before
a
. If you need to guarantee a specific order of evaluation,
you must use the function
pseq
from the "parallel" package.
zip :: [a] -> [b] -> [(a, b)] Source #
\(\mathcal{O}(\min(m,n))\)
.
zip
takes two lists and returns a list of
corresponding pairs.
zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]
If one input list is short, excess elements of the longer list are discarded:
zip [1] ['a', 'b'] = [(1, 'a')] zip [1, 2] ['a'] = [(1, 'a')]
zip
is right-lazy:
zip [] _|_ = [] zip _|_ [] = _|_
zip
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
($) :: forall (r :: RuntimeRep ) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #
Application operator. This operator is redundant, since ordinary
application
(f x)
means the same as
(f
. However,
$
x)
$
has
low, right-associative binding precedence, so it sometimes allows
parentheses to be omitted; for example:
f $ g $ h x = f (g (h x))
It is also useful in higher-order situations, such as
,
or
map
(
$
0) xs
.
zipWith
(
$
) fs xs
Note that
(
is levity-polymorphic in its result type, so that
$
)
foo
where
$
True
foo :: Bool -> Int#
is well-typed.
fromIntegral :: ( Integral a, Num b) => a -> b Source #
general coercion from integral types
realToFrac :: ( Real a, Fractional b) => a -> b Source #
general coercion to fractional types
class Bounded a where Source #
The
Bounded
class is used to name the upper and lower limits of a
type.
Ord
is not a superclass of
Bounded
since types that are not
totally ordered may also have upper and lower bounds.
The
Bounded
class may be derived for any enumeration type;
minBound
is the first constructor listed in the
data
declaration
and
maxBound
is the last.
Bounded
may also be derived for single-constructor datatypes whose
constituent types are in
Bounded
.
Instances
| Bounded Bool |
Since: base-2.1 |
| Bounded Char |
Since: base-2.1 |
| Bounded Int |
Since: base-2.1 |
| Bounded Int8 |
Since: base-2.1 |
| Bounded Int16 |
Since: base-2.1 |
| Bounded Int32 |
Since: base-2.1 |
| Bounded Int64 |
Since: base-2.1 |
| Bounded Ordering |
Since: base-2.1 |
| Bounded Word |
Since: base-2.1 |
| Bounded Word8 |
Since: base-2.1 |
| Bounded Word16 |
Since: base-2.1 |
| Bounded Word32 |
Since: base-2.1 |
| Bounded Word64 |
Since: base-2.1 |
| Bounded VecCount |
Since: base-4.10.0.0 |
| Bounded VecElem |
Since: base-4.10.0.0 |
| Bounded () |
Since: base-2.1 |
| Bounded Color | |
| Bounded ColorIntensity | |
|
Defined in System.Console.ANSI.Types |
|
| Bounded ConsoleLayer | |
|
Defined in System.Console.ANSI.Types |
|
| Bounded BlinkSpeed | |
|
Defined in System.Console.ANSI.Types |
|
| Bounded Underlining | |
|
Defined in System.Console.ANSI.Types |
|
| Bounded ConsoleIntensity | |
|
Defined in System.Console.ANSI.Types |
|
| Bounded DecidedStrictness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| Bounded SourceStrictness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| Bounded SourceUnpackedness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| Bounded Associativity |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| Bounded All |
Since: base-2.1 |
| Bounded Any |
Since: base-2.1 |
| Bounded GeneralCategory |
Since: base-2.1 |
|
Defined in GHC.Unicode |
|
| Bounded Extension | |
| Bounded a => Bounded ( Identity a) |
Since: base-4.9.0.0 |
| Bounded a => Bounded ( Min a) |
Since: base-4.9.0.0 |
| Bounded a => Bounded ( Max a) |
Since: base-4.9.0.0 |
| Bounded a => Bounded ( First a) |
Since: base-4.9.0.0 |
| Bounded a => Bounded ( Last a) |
Since: base-4.9.0.0 |
| Bounded m => Bounded ( WrappedMonoid m) |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup |
|
| Bounded a => Bounded ( Dual a) |
Since: base-2.1 |
| Bounded a => Bounded ( Sum a) |
Since: base-2.1 |
| Bounded a => Bounded ( Product a) |
Since: base-2.1 |
| Bounded a => Bounded ( Down a) |
Since: base-4.14.0.0 |
| ( Bounded a, Bounded b) => Bounded (a, b) |
Since: base-2.1 |
| Bounded ( Proxy t) |
Since: base-4.7.0.0 |
| ( Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) |
Since: base-2.1 |
| Bounded a => Bounded ( Const a b) |
Since: base-4.9.0.0 |
| ( Applicative f, Bounded a) => Bounded ( Ap f a) |
Since: base-4.12.0.0 |
| Bounded b => Bounded ( Tagged s b) | |
| ( Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
Since: base-2.1 |
| ( Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
Since: base-2.1 |
Class
Enum
defines operations on sequentially ordered types.
The
enumFrom
... methods are used in Haskell's translation of
arithmetic sequences.
Instances of
Enum
may be derived for any enumeration type (types
whose constructors have no fields). The nullary constructors are
assumed to be numbered left-to-right by
fromEnum
from
0
through
n-1
.
See Chapter 10 of the
Haskell Report
for more details.
For any type that is an instance of class
Bounded
as well as
Enum
,
the following should hold:
-
The calls
succmaxBoundpredminBound -
fromEnumandtoEnumshould give a runtime error if the result value is not representable in the result type. For example,toEnum7 ::Bool -
enumFromandenumFromThenshould be defined with an implicit bound, thus:
enumFrom x = enumFromTo x maxBound
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = maxBound
| otherwise = minBound
Methods
the successor of a value. For numeric types,
succ
adds 1.
the predecessor of a value. For numeric types,
pred
subtracts 1.
Convert from an
Int
.
Convert to an
Int
.
It is implementation-dependent what
fromEnum
returns when
applied to a value that is too large to fit in an
Int
.
Used in Haskell's translation of
[n..]
with
[n..] = enumFrom n
,
a possible implementation being
enumFrom n = n : enumFrom (succ n)
.
For example:
-
enumFrom 4 :: [Integer] = [4,5,6,7,...]
-
enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]
enumFromThen :: a -> a -> [a] Source #
Used in Haskell's translation of
[n,n'..]
with
[n,n'..] = enumFromThen n n'
, a possible implementation being
enumFromThen n n' = n : n' : worker (f x) (f x n')
,
worker s v = v : worker s (s v)
,
x = fromEnum n' - fromEnum n
and
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
For example:
-
enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
-
enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]
enumFromTo :: a -> a -> [a] Source #
Used in Haskell's translation of
[n..m]
with
[n..m] = enumFromTo n m
, a possible implementation being
enumFromTo n m
| n <= m = n : enumFromTo (succ n) m
| otherwise = []
.
For example:
-
enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
-
enumFromTo 42 1 :: [Integer] = []
enumFromThenTo :: a -> a -> a -> [a] Source #
Used in Haskell's translation of
[n,n'..m]
with
[n,n'..m] = enumFromThenTo n n' m
, a possible implementation
being
enumFromThenTo n n' m = worker (f x) (c x) n m
,
x = fromEnum n' - fromEnum n
,
c x = bool (>=) (
(x
0)
f n y
| n > 0 = f (n - 1) (succ y)
| n < 0 = f (n + 1) (pred y)
| otherwise = y
and
worker s c v m
| c v m = v : worker s c (s v) m
| otherwise = []
For example:
-
enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
-
enumFromThenTo 6 8 2 :: [Int] = []
Instances
The
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 Source #
Trigonometric and hyperbolic functions and related functions.
The Haskell Report defines no laws for
Floating
. However,
(
,
+
)
(
and
*
)
exp
are customarily expected to define an exponential field and have
the following properties:
-
exp (a + b)=exp a * exp b -
exp (fromInteger 0)=fromInteger 1
Minimal complete definition
pi , exp , log , sin , cos , asin , acos , atan , sinh , cosh , asinh , acosh , atanh
Instances
class Num a => Fractional a where Source #
Fractional numbers, supporting real division.
The Haskell Report defines no laws for
Fractional
. However,
(
and
+
)
(
are customarily expected to define a division ring and have the
following properties:
*
)
-
recipgives the multiplicative inverse -
x * recip x=recip x * x=fromInteger 1
Note that it
isn't
customarily expected that a type instance of
Fractional
implement a field. However, all instances in
base
do.
Minimal complete definition
fromRational , ( recip | (/) )
Methods
(/) :: a -> a -> a infixl 7 Source #
Fractional division.
Reciprocal fraction.
fromRational :: Rational -> a Source #
Conversion from a
Rational
(that is
).
A floating literal stands for an application of
Ratio
Integer
fromRational
to a value of type
Rational
, so such literals have type
(
.
Fractional
a) => a
Instances
| Fractional NominalDiffTime | |
|
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods (/) :: NominalDiffTime -> NominalDiffTime -> NominalDiffTime Source # |
|
| Fractional CoverPercentage Source # | |
|
Defined in Hedgehog.Internal.Property Methods (/) :: CoverPercentage -> CoverPercentage -> CoverPercentage Source # |
|
| Integral a => Fractional ( Ratio a) |
Since: base-2.0.1 |
| Fractional a => Fractional ( Identity a) |
Since: base-4.9.0.0 |
| RealFloat a => Fractional ( Complex a) |
Since: base-2.1 |
| 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 |
| Fractional a => Fractional ( Tagged s a) | |
class ( Real a, Enum a) => Integral a where Source #
Integral numbers, supporting integer division.
The Haskell Report defines no laws for
Integral
. However,
Integral
instances are customarily expected to define a Euclidean domain and have the
following properties for the
div
/
mod
and
quot
/
rem
pairs, given
suitable Euclidean functions
f
and
g
:
-
x=y * quot x y + rem x ywithrem x y=fromInteger 0org (rem x y)<g y -
x=y * div x y + mod x ywithmod x y=fromInteger 0orf (mod x y)<f y
An example of a suitable Euclidean function, for
Integer
's instance, is
abs
.
Methods
quot :: a -> a -> a infixl 7 Source #
integer division truncated toward zero
rem :: a -> a -> a infixl 7 Source #
integer remainder, satisfying
(x `quot` y)*y + (x `rem` y) == x
div :: a -> a -> a infixl 7 Source #
integer division truncated toward negative infinity
mod :: a -> a -> a infixl 7 Source #
integer modulus, satisfying
(x `div` y)*y + (x `mod` y) == x
quotRem :: a -> a -> (a, a) Source #
divMod :: a -> a -> (a, a) Source #
toInteger :: a -> Integer Source #
conversion to
Integer
Instances
class Applicative m => Monad (m :: Type -> Type ) where Source #
The
Monad
class defines the basic operations over a
monad
,
a concept from a branch of mathematics known as
category theory
.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an
abstract datatype
of actions.
Haskell's
do
expressions provide a convenient syntax for writing
monadic expressions.
Instances of
Monad
should satisfy the following:
- Left identity
-
returna>>=k = k a - Right identity
-
m>>=return= m - Associativity
-
m>>=(\x -> k x>>=h) = (m>>=k)>>=h
Furthermore, the
Monad
and
Applicative
operations should relate as follows:
The above laws imply:
and that
pure
and (
<*>
) satisfy the applicative functor laws.
The instances of
Monad
for lists,
Maybe
and
IO
defined in the
Prelude
satisfy these laws.
Minimal complete definition
Methods
(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source #
Sequentially compose two actions, passing any value produced by the first as an argument to the second.
'
as
' can be understood as the
>>=
bs
do
expression
do a <- as bs a
(>>) :: m a -> m b -> m b infixl 1 Source #
Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.
'
as
' can be understood as the
>>
bs
do
expression
do as bs
Inject a value into the monadic type.
Instances
| Monad [] |
Since: base-2.1 |
| Monad Maybe |
Since: base-2.1 |
| Monad IO |
Since: base-2.1 |
| Monad Par1 |
Since: base-4.9.0.0 |
| Monad Q | |
| Monad Identity |
Since: base-4.8.0.0 |
| 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 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 Put | |
| Monad Tree | |
| Monad Seq | |
| Monad P |
Since: base-2.1 |
| 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 ( ST s) |
Since: base-2.1 |
| Monad m => Monad ( WrappedMonad m) |
Since: base-4.7.0.0 |
|
Defined in Control.Applicative Methods (>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b Source # (>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # return :: a -> WrappedMonad m a Source # |
|
| ArrowApply a => Monad ( ArrowMonad a) |
Since: base-2.1 |
|
Defined in Control.Arrow Methods (>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b Source # (>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # return :: a0 -> ArrowMonad a a0 Source # |
|
| Monad ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| Monad m => Monad ( MaybeT m) | |
| Monad m => Monad ( ListT m) | |
| Monad m => Monad ( ResourceT m) | |
| Monad m => Monad ( NodeT m) Source # | |
| Monad m => Monad ( TreeT m) Source # | |
| Monad m => Monad ( GenT m) Source # | |
| Monad m => Monad ( TestT m) Source # | |
| Monad m => Monad ( PropertyT 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 ( ReaderT r m) | |
| Monad m => Monad ( Kleisli m a) |
Since: base-4.14.0.0 |
| Monad f => Monad ( Ap f) |
Since: base-4.12.0.0 |
| Monad f => Monad ( Alt f) |
Since: base-4.8.0.0 |
| ( Applicative f, Monad f) => Monad ( WhenMissing f x) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.IntMap.Internal Methods (>>=) :: WhenMissing f x a -> (a -> WhenMissing f x b) -> WhenMissing f x b Source # (>>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # return :: a -> WhenMissing f x a Source # |
|
| Monad m => Monad ( ExceptT e m) | |
| ( Monoid w, Monad m) => Monad ( WriterT w m) | |
| Monad m => Monad ( StateT s m) | |
| ( Monad m, Error e) => Monad ( ErrorT e m) | |
| Monad m => Monad ( IdentityT m) | |
| Monad m => Monad ( StateT s m) | |
| ( Monoid w, Monad m) => Monad ( WriterT w m) | |
| Monad ( Tagged s) | |
| ( Monoid w, Functor m, Monad m) => Monad ( AccumT w m) | |
| Monad m => Monad ( WriterT w m) | |
| Monad m => Monad ( SelectT r m) | |
| 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 Source # (>>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # return :: a -> WhenMatched f x y a Source # |
|
| ( Applicative f, Monad f) => Monad ( WhenMissing f k x) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods (>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b Source # (>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # return :: a -> WhenMissing f k x a Source # |
|
| Monad ( ContT r m) | |
| Monad f => Monad ( M1 i c f) |
Since: base-4.9.0.0 |
| ( Monad f, Applicative f) => Monad ( WhenMatched f k x y) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods (>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b Source # (>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # return :: a -> WhenMatched f k x y a Source # |
|
| ( Monoid w, Monad m) => Monad ( RWST r w s m) | |
| ( Monoid w, Monad m) => Monad ( RWST r w s m) | |
| Monad m => Monad ( RWST r w s m) | |
class Functor (f :: Type -> Type ) where Source #
A type
f
is a Functor if it provides a function
fmap
which, given any types
a
and
b
lets you apply any function from
(a -> b)
to turn an
f a
into an
f b
, preserving the
structure of
f
. Furthermore
f
needs to adhere to the following:
Note, that the second law follows from the free theorem of the type
fmap
and
the first law, so you need only check that the former condition holds.
Minimal complete definition
Methods
fmap :: (a -> b) -> f a -> f b Source #
Using
ApplicativeDo
: '
' can be understood as
the
fmap
f as
do
expression
do a <- as pure (f a)
with an inferred
Functor
constraint.
Instances
| Functor [] |
Since: base-2.1 |
| Functor Maybe |
Since: base-2.1 |
| Functor IO |
Since: base-2.1 |
| Functor Par1 |
Since: base-4.9.0.0 |
| Functor Q | |
| Functor Async | |
| Functor Concurrently | |
|
Defined in Control.Concurrent.Async Methods fmap :: (a -> b) -> Concurrently a -> Concurrently b Source # (<$) :: a -> Concurrently b -> Concurrently a Source # |
|
| Functor Identity |
Since: base-4.8.0.0 |
| Functor Complex |
Since: base-4.9.0.0 |
| Functor Min |
Since: base-4.9.0.0 |
| Functor Max |
Since: base-4.9.0.0 |
| Functor First |
Since: base-4.9.0.0 |
| Functor Last |
Since: base-4.9.0.0 |
| Functor Option |
Since: base-4.9.0.0 |
| Functor ZipList |
Since: base-2.1 |
| Functor Handler |
Since: base-4.6.0.0 |
| Functor STM |
Since: base-4.3.0.0 |
| Functor First |
Since: base-4.8.0.0 |
| Functor Last |
Since: base-4.8.0.0 |
| Functor Dual |
Since: base-4.8.0.0 |
| Functor Sum |
Since: base-4.8.0.0 |
| Functor Product |
Since: base-4.8.0.0 |
| Functor Down |
Since: base-4.11.0.0 |
| Functor ReadPrec |
Since: base-2.1 |
| Functor ReadP |
Since: base-2.1 |
| Functor NonEmpty |
Since: base-4.9.0.0 |
| Functor Put | |
| Functor IntMap | |
| Functor Tree | |
| Functor Seq | |
| Functor FingerTree | |
|
Defined in Data.Sequence.Internal Methods fmap :: (a -> b) -> FingerTree a -> FingerTree b Source # (<$) :: a -> FingerTree b -> FingerTree a Source # |
|
| Functor Digit | |
| Functor Node | |
| Functor Elem | |
| Functor ViewL | |
| Functor ViewR | |
| Functor Doc | |
| Functor AnnotDetails | |
|
Defined in Text.PrettyPrint.Annotated.HughesPJ Methods fmap :: (a -> b) -> AnnotDetails a -> AnnotDetails b Source # (<$) :: a -> AnnotDetails b -> AnnotDetails a Source # |
|
| Functor Span | |
| Functor Window | |
| Functor Doc | |
| Functor SimpleDoc | |
| Functor P |
Since: base-4.8.0.0 |
| Functor Range Source # | |
| Functor Coverage Source # | |
| Functor Label Source # | |
| Functor Concrete Source # | |
| Functor Pos Source # | |
| Functor Report Source # | |
| Functor ( Either a) |
Since: base-3.0 |
| Functor ( V1 :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( U1 :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( (,) a) |
Since: base-2.1 |
| Functor ( ST s) |
Since: base-2.1 |
| Functor ( Array i) |
Since: base-2.1 |
| Functor ( Arg a) |
Since: base-4.9.0.0 |
| Functor ( ST s) |
Since: base-2.1 |
| Monad m => Functor ( WrappedMonad m) |
Since: base-2.1 |
|
Defined in Control.Applicative Methods fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # (<$) :: a -> WrappedMonad m b -> WrappedMonad m a Source # |
|
| Arrow a => Functor ( ArrowMonad a) |
Since: base-4.6.0.0 |
|
Defined in Control.Arrow Methods fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # (<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # |
|
| Functor ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| Functor ( Map k) | |
| Functor m => Functor ( MaybeT m) | |
| Monad m => Functor ( Handler m) | |
| Functor m => Functor ( Concurrently m) | |
|
Defined in Control.Concurrent.Async.Lifted Methods fmap :: (a -> b) -> Concurrently m a -> Concurrently m b Source # (<$) :: a -> Concurrently m b -> Concurrently m a Source # |
|
| Functor m => Functor ( ListT m) | |
| Functor m => Functor ( ResourceT m) | |
| Functor m => Functor ( NodeT m) Source # | |
| Functor m => Functor ( TreeT m) Source # | |
| Functor ( Vec n) Source # | |
| Functor m => Functor ( GenT m) Source # | |
| Functor m => Functor ( TestT m) Source # | |
| Functor m => Functor ( PropertyT m) Source # | |
| Functor f => Functor ( Rec1 f) |
Since: base-4.9.0.0 |
| Functor ( URec Char :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec Double :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec Float :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec Int :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec Word :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec ( Ptr ()) :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( (,,) a b) |
Since: base-4.14.0.0 |
| Functor ( Const m :: Type -> Type ) |
Since: base-2.1 |
| Functor m => Functor ( ReaderT r m) | |
| Arrow a => Functor ( WrappedArrow a b) |
Since: base-2.1 |
|
Defined in Control.Applicative Methods fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # (<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # |
|
| Functor m => Functor ( Kleisli m a) |
Since: base-4.14.0.0 |
| Functor f => Functor ( Ap f) |
Since: base-4.12.0.0 |
| Functor f => Functor ( Alt f) |
Since: base-4.8.0.0 |
| ( Applicative f, Monad f) => Functor ( WhenMissing f x) |
Since: containers-0.5.9 |
|
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # (<$) :: a -> WhenMissing f x b -> WhenMissing f x a Source # |
|
| Functor m => Functor ( ExceptT e m) | |
| Functor m => Functor ( WriterT w m) | |
| Functor m => Functor ( StateT s m) | |
| Functor m => Functor ( ErrorT e m) | |
| Functor m => Functor ( IdentityT m) | |
| Functor m => Functor ( StateT s m) | |
| Functor m => Functor ( WriterT w m) | |
| Functor ( Tagged s) | |
| Functor m => Functor ( AccumT w m) | |
| Functor m => Functor ( WriterT w m) | |
| Functor m => Functor ( SelectT r m) | |
| Functor ((->) r :: Type -> Type ) |
Since: base-2.1 |
| Functor ( K1 i c :: Type -> Type ) |
Since: base-4.9.0.0 |
| ( Functor f, Functor g) => Functor (f :+: g) |
Since: base-4.9.0.0 |
| ( Functor f, Functor g) => Functor (f :*: g) |
Since: base-4.9.0.0 |
| Functor ( (,,,) a b c) |
Since: base-4.14.0.0 |
| ( Functor f, Functor g) => Functor ( Product f g) |
Since: base-4.9.0.0 |
| ( Functor f, Functor g) => Functor ( Sum f g) |
Since: base-4.9.0.0 |
| Functor f => Functor ( WhenMatched f x y) |
Since: containers-0.5.9 |
|
Defined in Data.IntMap.Internal Methods fmap :: (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # (<$) :: a -> WhenMatched f x y b -> WhenMatched f x y a Source # |
|
| ( Applicative f, Monad f) => Functor ( WhenMissing f k x) |
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # (<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a Source # |
|
| Functor ( ContT r m) | |
| Functor f => Functor ( M1 i c f) |
Since: base-4.9.0.0 |
| ( Functor f, Functor g) => Functor (f :.: g) |
Since: base-4.9.0.0 |
| ( Functor f, Functor g) => Functor ( Compose f g) |
Since: base-4.9.0.0 |
| Functor f => Functor ( WhenMatched f k x y) |
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # (<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # |
|
| Functor m => Functor ( RWST r w s m) | |
| Functor m => Functor ( RWST r w s m) | |
| Functor m => Functor ( RWST r w s m) | |
Basic numeric class.
The Haskell Report defines no laws for
Num
. However,
(
and
+
)
(
are
customarily expected to define a ring and have the following properties:
*
)
-
Associativity of
(+) -
(x + y) + z=x + (y + z) -
Commutativity of
(+) -
x + y=y + x -
fromInteger0 -
x + fromInteger 0=x -
negategives the additive inverse -
x + negate x=fromInteger 0 -
Associativity of
(*) -
(x * y) * z=x * (y * z) -
fromInteger1 -
x * fromInteger 1=xandfromInteger 1 * x=x -
Distributivity of
(with respect to*)(+) -
a * (b + c)=(a * b) + (a * c)and(b + c) * a=(b * a) + (c * a)
Note that it
isn't
customarily expected that a type instance of both
Num
and
Ord
implement an ordered ring. Indeed, in
base
only
Integer
and
Rational
do.
Methods
(+) :: a -> a -> a infixl 6 Source #
(-) :: a -> a -> a infixl 6 Source #
(*) :: a -> a -> a infixl 7 Source #
Unary negation.
Absolute value.
Sign of a number.
The functions
abs
and
signum
should satisfy the law:
abs x * signum x == x
For real numbers, the
signum
is either
-1
(negative),
0
(zero)
or
1
(positive).
fromInteger :: Integer -> a Source #
Conversion from an
Integer
.
An integer literal represents the application of the function
fromInteger
to the appropriate value of type
Integer
,
so such literals have type
(
.
Num
a) => a
Instances
class Eq a => Ord a where Source #
The
Ord
class is used for totally ordered datatypes.
Instances of
Ord
can be derived for any user-defined datatype whose
constituent types are in
Ord
. The declared order of the constructors in
the data declaration determines the ordering in derived
Ord
instances. The
Ordering
datatype allows a single comparison to determine the precise
ordering of two objects.
The Haskell Report defines no laws for
Ord
. However,
<=
is customarily
expected to implement a non-strict partial order and have the following
properties:
- Transitivity
-
if
x <= y && y <= z=True, thenx <= z=True - Reflexivity
-
x <= x=True - Antisymmetry
-
if
x <= y && y <= x=True, thenx == y=True
Note that the following operator interactions are expected to hold:
-
x >= y=y <= x -
x < y=x <= y && x /= y -
x > y=y < x -
x < y=compare x y == LT -
x > y=compare x y == GT -
x == y=compare x y == EQ -
min x y == if x <= y then x else y=True -
max x y == if x >= y then x else y=True
Note that (7.) and (8.) do
not
require
min
and
max
to return either of
their arguments. The result is merely required to
equal
one of the
arguments in terms of
(==)
.
Minimal complete definition: either
compare
or
<=
.
Using
compare
can be more efficient for complex types.
Methods
compare :: a -> a -> Ordering Source #
(<) :: a -> a -> Bool infix 4 Source #
(<=) :: a -> a -> Bool infix 4 Source #
(>) :: a -> a -> Bool infix 4 Source #
Instances
Parsing of
String
s, producing values.
Derived instances of
Read
make the following assumptions, which
derived instances of
Show
obey:
-
If the constructor is defined to be an infix operator, then the
derived
Readinstance will parse only infix applications of the constructor (not the prefix form). - Associativity is not used to reduce the occurrence of parentheses, although precedence may be.
-
If the constructor is defined using record syntax, the derived
Readwill parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. -
The derived
Readinstance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of
Read
in Haskell 2010 is equivalent to
instance (Read a) => Read (Tree a) where
readsPrec d r = readParen (d > app_prec)
(\r -> [(Leaf m,t) |
("Leaf",s) <- lex r,
(m,t) <- readsPrec (app_prec+1) s]) r
++ readParen (d > up_prec)
(\r -> [(u:^:v,w) |
(u,s) <- readsPrec (up_prec+1) r,
(":^:",t) <- lex s,
(v,w) <- readsPrec (up_prec+1) t]) r
where app_prec = 10
up_prec = 5
Note that right-associativity of
:^:
is unused.
The derived instance in GHC is equivalent to
instance (Read a) => Read (Tree a) where
readPrec = parens $ (prec app_prec $ do
Ident "Leaf" <- lexP
m <- step readPrec
return (Leaf m))
+++ (prec up_prec $ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))
where app_prec = 10
up_prec = 5
readListPrec = readListPrecDefault
Why do both
readsPrec
and
readPrec
exist, and why does GHC opt to
implement
readPrec
in derived
Read
instances instead of
readsPrec
?
The reason is that
readsPrec
is based on the
ReadS
type, and although
ReadS
is mentioned in the Haskell 2010 Report, it is not a very efficient
parser data structure.
readPrec
, on the other hand, is based on a much more efficient
ReadPrec
datatype (a.k.a "new-style parsers"), but its definition relies on the use
of the
RankNTypes
language extension. Therefore,
readPrec
(and its
cousin,
readListPrec
) are marked as GHC-only. Nevertheless, it is
recommended to use
readPrec
instead of
readsPrec
whenever possible
for the efficiency improvements it brings.
As mentioned above, derived
Read
instances in GHC will implement
readPrec
instead of
readsPrec
. The default implementations of
readsPrec
(and its cousin,
readList
) will simply use
readPrec
under
the hood. If you are writing a
Read
instance by hand, it is recommended
to write it like so:
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 Color | |
| Read ColorIntensity | |
|
Defined in System.Console.ANSI.Types Methods readsPrec :: Int -> ReadS ColorIntensity Source # readList :: ReadS [ ColorIntensity ] Source # readPrec :: ReadPrec ColorIntensity Source # readListPrec :: ReadPrec [ ColorIntensity ] Source # |
|
| Read ConsoleLayer | |
|
Defined in System.Console.ANSI.Types Methods readsPrec :: Int -> ReadS ConsoleLayer Source # readList :: ReadS [ ConsoleLayer ] Source # readPrec :: ReadPrec ConsoleLayer Source # readListPrec :: ReadPrec [ ConsoleLayer ] Source # |
|
| Read BlinkSpeed | |
|
Defined in System.Console.ANSI.Types Methods readsPrec :: Int -> ReadS BlinkSpeed Source # readList :: ReadS [ BlinkSpeed ] Source # readPrec :: ReadPrec BlinkSpeed Source # readListPrec :: ReadPrec [ BlinkSpeed ] Source # |
|
| Read Underlining | |
|
Defined in System.Console.ANSI.Types Methods readsPrec :: Int -> ReadS Underlining Source # readList :: ReadS [ Underlining ] Source # readPrec :: ReadPrec Underlining Source # readListPrec :: ReadPrec [ Underlining ] Source # |
|
| Read ConsoleIntensity | |
|
Defined in System.Console.ANSI.Types Methods readsPrec :: Int -> ReadS ConsoleIntensity Source # readList :: ReadS [ ConsoleIntensity ] Source # readPrec :: ReadPrec ConsoleIntensity Source # readListPrec :: ReadPrec [ ConsoleIntensity ] Source # |
|
| Read SGR | |
| Read DecidedStrictness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS DecidedStrictness Source # readList :: ReadS [ DecidedStrictness ] Source # readPrec :: ReadPrec DecidedStrictness Source # readListPrec :: ReadPrec [ DecidedStrictness ] Source # |
|
| Read SourceStrictness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS SourceStrictness Source # readList :: ReadS [ SourceStrictness ] Source # readPrec :: ReadPrec SourceStrictness Source # readListPrec :: ReadPrec [ SourceStrictness ] Source # |
|
| Read SourceUnpackedness |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| Read Associativity |
Since: base-4.6.0.0 |
|
Defined in GHC.Generics Methods readsPrec :: Int -> ReadS Associativity Source # readList :: ReadS [ Associativity ] Source # readPrec :: ReadPrec Associativity Source # readListPrec :: ReadPrec [ Associativity ] Source # |
|
| Read Fixity |
Since: base-4.6.0.0 |
| Read Void |
Reading a
Since: base-4.8.0.0 |
| Read Version |
Since: base-2.1 |
| Read ExitCode | |
| Read BufferMode |
Since: base-4.2.0.0 |
|
Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode Source # readList :: ReadS [ BufferMode ] Source # readPrec :: ReadPrec BufferMode Source # readListPrec :: ReadPrec [ BufferMode ] Source # |
|
| 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 Source # readList :: ReadS [ NewlineMode ] Source # readPrec :: ReadPrec NewlineMode Source # readListPrec :: ReadPrec [ NewlineMode ] Source # |
|
| Read All |
Since: base-2.1 |
| Read Any |
Since: base-2.1 |
| Read Lexeme |
Since: base-2.1 |
| Read GeneralCategory |
Since: base-2.1 |
|
Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory Source # readList :: ReadS [ GeneralCategory ] Source # readPrec :: ReadPrec GeneralCategory Source # readListPrec :: ReadPrec [ GeneralCategory ] Source # |
|
| Read ShortByteString | |
|
Defined in Data.ByteString.Short.Internal Methods readsPrec :: Int -> ReadS ShortByteString Source # readList :: ReadS [ ShortByteString ] Source # readPrec :: ReadPrec ShortByteString Source # readListPrec :: ReadPrec [ ShortByteString ] Source # |
|
| Read ByteString | |
|
Defined in Data.ByteString.Lazy.Internal Methods readsPrec :: Int -> ReadS ByteString Source # readList :: ReadS [ ByteString ] Source # readPrec :: ReadPrec ByteString Source # readListPrec :: ReadPrec [ ByteString ] Source # |
|
| Read ByteString | |
|
Defined in Data.ByteString.Internal Methods readsPrec :: Int -> ReadS ByteString Source # readList :: ReadS [ ByteString ] Source # readPrec :: ReadPrec ByteString Source # readListPrec :: ReadPrec [ ByteString ] Source # |
|
| Read IntSet | |
| Read Size Source # | |
| Read Seed 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 ( Identity a) |
This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| 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) Source # readList :: ReadS [ WrappedMonoid m] Source # readPrec :: ReadPrec ( WrappedMonoid m) Source # readListPrec :: ReadPrec [ WrappedMonoid m] Source # |
|
| Read a => Read ( Option a) |
Since: base-4.9.0.0 |
| Read a => Read ( ZipList a) |
Since: base-4.7.0.0 |
| Read a => Read ( 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 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 ( Window 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 a, Read a, Read b) => Read ( Array a b) |
Since: base-2.1 |
| HasResolution a => Read ( Fixed a) |
Since: base-4.3.0.0 |
| ( Read a, Read b) => Read ( Arg a b) |
Since: base-4.9.0.0 |
| Read ( Proxy t) |
Since: base-4.7.0.0 |
| ( Ord k, Read k, Read e) => Read ( Map k e) | |
| ( Read1 m, Read a) => Read ( MaybeT m a) | |
| ( Read1 m, Read a) => Read ( ListT m a) | |
| Read (f p) => Read ( Rec1 f p) |
Since: base-4.7.0.0 |
| ( Read a, Read b, Read c) => Read (a, b, c) |
Since: base-2.1 |
| Read a => Read ( Const a b) |
This instance would be equivalent to the derived instances of the
Since: base-4.8.0.0 |
| Read (f a) => Read ( Ap f a) |
Since: base-4.12.0.0 |
| Read (f a) => Read ( Alt f a) |
Since: base-4.8.0.0 |
| ( Read e, Read1 m, Read a) => Read ( ExceptT e m a) | |
| ( Read w, Read1 m, Read a) => Read ( WriterT w m a) | |
| ( Read e, Read1 m, Read a) => Read ( ErrorT e m a) | |
| ( Read1 f, Read a) => Read ( IdentityT f a) | |
| ( Read w, Read1 m, Read a) => Read ( WriterT w m a) | |
| Read b => Read ( Tagged s b) | |
| 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 |
| Read (f p) => Read ( M1 i c f p) |
Since: base-4.7.0.0 |
| Read (f (g p)) => Read ((f :.: g) p) |
Since: base-4.7.0.0 |
| ( Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) |
Since: base-2.1 |
| ( Read1 f, Read1 g, Read a) => Read ( Compose f g a) |
Since: base-4.9.0.0 |
| ( Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h) => Read (a, b, c, d, e, f, g, h) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i) => Read (a, b, c, d, e, f, g, h, i) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j) => Read (a, b, c, d, e, f, g, h, i, j) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k) => Read (a, b, c, d, e, f, g, h, i, j, k) |
Since: base-2.1 |
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (a, b, c, d, e, f, g, h, i, j, k, l) |
Since: base-2.1 |
|
Defined in GHC.Read |
|
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m) |
Since: base-2.1 |
|
Defined in GHC.Read |
|
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n) |
Since: base-2.1 |
|
Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # |
|
| ( Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) |
Since: base-2.1 |
|
Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # |
|
class ( Num a, Ord a) => Real a where Source #
Methods
toRational :: a -> Rational Source #
the rational equivalent of its real argument with full precision
Instances
class ( RealFrac a, Floating a) => RealFloat a where Source #
Efficient, machine-independent access to the components of a floating-point number.
Minimal complete definition
floatRadix , floatDigits , floatRange , decodeFloat , encodeFloat , isNaN , isInfinite , isDenormalized , isNegativeZero , isIEEE
Methods
floatRadix :: a -> Integer Source #
a constant function, returning the radix of the representation
(often
2
)
floatDigits :: a -> Int Source #
a constant function, returning the number of digits of
floatRadix
in the significand
floatRange :: a -> ( Int , Int ) Source #
a constant function, returning the lowest and highest values the exponent may assume
decodeFloat :: a -> ( Integer , Int ) Source #
The function
decodeFloat
applied to a real floating-point
number returns the significand expressed as an
Integer
and an
appropriately scaled exponent (an
Int
). If
yields
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^d
d
is
the value of
.
In particular,
floatDigits
x
. If the type
contains a negative zero, also
decodeFloat
0 = (0,0)
.
The result of
decodeFloat
(-0.0) = (0,0)
is unspecified if either of
decodeFloat
x
or
isNaN
x
is
isInfinite
x
True
.
encodeFloat :: Integer -> Int -> a Source #
encodeFloat
performs the inverse of
decodeFloat
in the
sense that for finite
x
with the exception of
-0.0
,
.
uncurry
encodeFloat
(
decodeFloat
x) = x
is one of the two closest representable
floating-point numbers to
encodeFloat
m n
m*b^^n
(or
±Infinity
if overflow
occurs); usually the closer, but if
m
contains too many bits,
the result may be rounded in the wrong direction.
exponent
corresponds to the second component of
decodeFloat
.
and for finite nonzero
exponent
0 = 0
x
,
.
If
exponent
x = snd (
decodeFloat
x) +
floatDigits
x
x
is a finite floating-point number, it is equal in value to
, where
significand
x * b ^^
exponent
x
b
is the
floating-point radix.
The behaviour is unspecified on infinite or
NaN
values.
significand :: a -> a Source #
The first component of
decodeFloat
, scaled to lie in the open
interval (
-1
,
1
), either
0.0
or of absolute value
>= 1/b
,
where
b
is the floating-point radix.
The behaviour is unspecified on infinite or
NaN
values.
scaleFloat :: Int -> a -> a Source #
multiplies a floating-point number by an integer power of the radix
True
if the argument is an IEEE "not-a-number" (NaN) value
isInfinite :: a -> Bool Source #
True
if the argument is an IEEE infinity or negative infinity
isDenormalized :: a -> Bool Source #
True
if the argument is too small to be represented in
normalized format
isNegativeZero :: a -> Bool Source #
True
if the argument is an IEEE negative zero
True
if the argument is an IEEE floating point number
a version of arctangent taking two real floating-point arguments.
For real floating
x
and
y
,
computes the angle
(from the positive x-axis) of the vector from the origin to the
point
atan2
y x
(x,y)
.
returns a value in the range [
atan2
y x
-pi
,
pi
]. It follows the Common Lisp semantics for the origin when
signed zeroes are supported.
, with
atan2
y 1
y
in a type
that is
RealFloat
, should return the same value as
.
A default definition of
atan
y
atan2
is provided, but implementors
can provide a more accurate implementation.
Instances
class ( Real a, Fractional a) => RealFrac a where Source #
Extracting components of fractions.
Minimal complete definition
Methods
properFraction :: Integral b => a -> (b, a) Source #
The function
properFraction
takes a real fractional number
x
and returns a pair
(n,f)
such that
x = n+f
, and:
-
nis an integral number with the same sign asx; and -
fis a fraction with the same type and sign asx, and with absolute value less than1.
The default definitions of the
ceiling
,
floor
,
truncate
and
round
functions are in terms of
properFraction
.
truncate :: Integral b => a -> b Source #
returns the integer nearest
truncate
x
x
between zero and
x
round :: Integral b => a -> b Source #
returns the nearest integer to
round
x
x
;
the even integer if
x
is equidistant between two integers
ceiling :: Integral b => a -> b Source #
returns the least integer not less than
ceiling
x
x
floor :: Integral b => a -> b Source #
returns the greatest integer not greater than
floor
x
x
Instances
| RealFrac NominalDiffTime | |
|
Defined in Data.Time.Clock.Internal.NominalDiffTime Methods properFraction :: Integral b => NominalDiffTime -> (b, NominalDiffTime ) Source # truncate :: Integral b => NominalDiffTime -> b Source # round :: Integral b => NominalDiffTime -> b Source # ceiling :: Integral b => NominalDiffTime -> b Source # floor :: Integral b => NominalDiffTime -> b Source # |
|
| Integral a => RealFrac ( Ratio a) |
Since: base-2.0.1 |
| RealFrac a => RealFrac ( Identity a) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Identity |
|
| RealFrac a => RealFrac ( Down a) |
Since: base-4.14.0.0 |
| HasResolution a => RealFrac ( Fixed a) |
Since: base-2.1 |
| RealFrac a => RealFrac ( Const a b) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Const |
|
| RealFrac a => RealFrac ( Tagged s a) | |
Conversion of values to readable
String
s.
Derived instances of
Show
have the following properties, which
are compatible with derived instances of
Read
:
-
The result of
showis a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. -
If the constructor is defined to be an infix operator, then
showsPrecwill produce infix applications of the constructor. -
the representation will be enclosed in parentheses if the
precedence of the top-level constructor in
xis less thand(associativity is ignored). Thus, ifdis0then the result is never surrounded in parentheses; ifdis11it is always surrounded in parentheses, unless it is an atomic expression. -
If the constructor is defined using record syntax, then
showwill produce the record-syntax form, with the fields given in the same order as the original declaration.
For example, given the declarations
infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a
the derived instance of
Show
is equivalent to
instance (Show a) => Show (Tree a) where
showsPrec d (Leaf m) = showParen (d > app_prec) $
showString "Leaf " . showsPrec (app_prec+1) m
where app_prec = 10
showsPrec d (u :^: v) = showParen (d > up_prec) $
showsPrec (up_prec+1) u .
showString " :^: " .
showsPrec (up_prec+1) v
where up_prec = 5
Note that right-associativity of
:^:
is ignored. For example,
-
show(Leaf 1 :^: Leaf 2 :^: Leaf 3)"Leaf 1 :^: (Leaf 2 :^: Leaf 3)".
Methods
Arguments
| :: Int |
the operator precedence of the enclosing
context (a number from
|
| -> a |
the value to be converted to a
|
| -> ShowS |
Convert a value to a readable
String
.
showsPrec
should satisfy the law
showsPrec d x r ++ s == showsPrec d x (r ++ s)
Derived instances of
Read
and
Show
satisfy the following:
That is,
readsPrec
parses the string produced by
showsPrec
, and delivers the value that
showsPrec
started with.
Instances
class Monad m => MonadFail (m :: Type -> Type ) where Source #
When a value is bound in
do
-notation, the pattern on the left
hand side of
<-
might not match. In this case, this class
provides a function to recover.
A
Monad
without a
MonadFail
instance may only be used in conjunction
with pattern that always match, such as newtypes, tuples, data types with
only a single data constructor, and irrefutable patterns (
~pat
).
Instances of
MonadFail
should satisfy the following law:
fail s
should
be a left zero for
>>=
,
fail s >>= f = fail s
If your
Monad
is also
MonadPlus
, a popular definition is
fail _ = mzero
Since: base-4.9.0.0
Instances
class Functor f => Applicative (f :: Type -> Type ) where Source #
A functor with application, providing operations to
-
embed pure expressions (
pure), and -
sequence computations and combine their results (
<*>andliftA2).
A minimal complete definition must include implementations of
pure
and of either
<*>
or
liftA2
. If it defines both, then they must behave
the same as their default definitions:
(<*>) =liftA2id
liftA2f x y = f<$>x<*>y
Further, any definition must satisfy the following:
- Identity
-
pureid<*>v = v - Composition
-
pure(.)<*>u<*>v<*>w = u<*>(v<*>w) - Homomorphism
-
puref<*>purex =pure(f x) - Interchange
-
u
<*>purey =pure($y)<*>u
The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:
As a consequence of these laws, the
Functor
instance for
f
will satisfy
It may be useful to note that supposing
forall x y. p (q x y) = f x . g y
it follows from the above that
liftA2p (liftA2q u v) =liftA2f u .liftA2g v
If
f
is also a
Monad
, it should satisfy
(which implies that
pure
and
<*>
satisfy the applicative functor laws).
Methods
Lift a value.
(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #
Sequential application.
A few functors support an implementation of
<*>
that is more
efficient than the default one.
Using
ApplicativeDo
: '
fs
' can be understood as
the
<*>
as
do
expression
do f <- fs a <- as pure (f a)
(*>) :: f a -> f b -> f b infixl 4 Source #
Sequence actions, discarding the value of the first argument.
'
as
' can be understood as the
*>
bs
do
expression
do as bs
This is a tad complicated for our
ApplicativeDo
extension
which will give it a
Monad
constraint. For an
Applicative
constraint we write it of the form
do _ <- as b <- bs pure b
(<*) :: f a -> f b -> f a infixl 4 Source #
Sequence actions, discarding the value of the second argument.
Using
ApplicativeDo
: '
as
' can be understood as
the
<*
bs
do
expression
do a <- as bs pure a
Instances
| Applicative [] |
Since: base-2.1 |
| Applicative Maybe |
Since: base-2.1 |
| Applicative IO |
Since: base-2.1 |
| Applicative Par1 |
Since: base-4.9.0.0 |
| Applicative Q | |
| Applicative Concurrently | |
|
Defined in Control.Concurrent.Async Methods pure :: a -> Concurrently a Source # (<*>) :: Concurrently (a -> b) -> Concurrently a -> Concurrently b Source # liftA2 :: (a -> b -> c) -> Concurrently a -> Concurrently b -> Concurrently c Source # (*>) :: Concurrently a -> Concurrently b -> Concurrently b Source # (<*) :: Concurrently a -> Concurrently b -> Concurrently a Source # |
|
| Applicative Identity |
Since: base-4.8.0.0 |
|
Defined in Data.Functor.Identity |
|
| Applicative Complex |
Since: base-4.9.0.0 |
|
Defined in Data.Complex |
|
| Applicative Min |
Since: base-4.9.0.0 |
| Applicative Max |
Since: base-4.9.0.0 |
| Applicative First |
Since: base-4.9.0.0 |
| Applicative Last |
Since: base-4.9.0.0 |
| Applicative Option |
Since: base-4.9.0.0 |
| Applicative ZipList |
f <$> ZipList xs1 <*> ... <*> ZipList xsN
= ZipList (zipWithN f xs1 ... xsN)
where
(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
= ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
= ZipList {getZipList = ["a5","b6b6","c7c7c7"]}
Since: base-2.1 |
|
Defined in Control.Applicative |
|
| Applicative STM |
Since: base-4.8.0.0 |
| Applicative First |
Since: base-4.8.0.0 |
| Applicative Last |
Since: base-4.8.0.0 |
| Applicative Dual |
Since: base-4.8.0.0 |
| Applicative Sum |
Since: base-4.8.0.0 |
| Applicative Product |
Since: base-4.8.0.0 |
|
Defined in Data.Semigroup.Internal |
|
| Applicative Down |
Since: base-4.11.0.0 |
| Applicative ReadPrec |
Since: base-4.6.0.0 |
|
Defined in Text.ParserCombinators.ReadPrec |
|
| Applicative ReadP |
Since: base-4.6.0.0 |
| Applicative NonEmpty |
Since: base-4.9.0.0 |
|
Defined in GHC.Base |
|
| Applicative Put | |
| Applicative Tree | |
| Applicative Seq |
Since: containers-0.5.4 |
| Applicative P |
Since: base-4.5.0.0 |
| Applicative ( Either e) |
Since: base-3.0 |
|
Defined in Data.Either |
|
| Applicative ( U1 :: Type -> Type ) |
Since: base-4.9.0.0 |
| Monoid a => Applicative ( (,) a) |
For tuples, the
("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)
Since: base-2.1 |
| Applicative ( ST s) |
Since: base-4.4.0.0 |
| Applicative ( ST s) |
Since: base-2.1 |
| Monad m => Applicative ( WrappedMonad m) |
Since: base-2.1 |
|
Defined in Control.Applicative Methods pure :: a -> WrappedMonad m a Source # (<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b Source # liftA2 :: (a -> b -> c) -> WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m c Source # (*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b Source # (<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a Source # |
|
| Arrow a => Applicative ( ArrowMonad a) |
Since: base-4.6.0.0 |
|
Defined in Control.Arrow Methods pure :: a0 -> ArrowMonad a a0 Source # (<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source # liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source # (*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source # (<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source # |
|
| Applicative ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| ( Functor m, Monad m) => Applicative ( MaybeT m) | |
|
Defined in Control.Monad.Trans.Maybe |
|
| MonadBaseControl IO m => Applicative ( Concurrently m) | |
|
Defined in Control.Concurrent.Async.Lifted Methods pure :: a -> Concurrently m a Source # (<*>) :: Concurrently m (a -> b) -> Concurrently m a -> Concurrently m b Source # liftA2 :: (a -> b -> c) -> Concurrently m a -> Concurrently m b -> Concurrently m c Source # (*>) :: Concurrently m a -> Concurrently m b -> Concurrently m b Source # (<*) :: Concurrently m a -> Concurrently m b -> Concurrently m a Source # |
|
| Applicative m => Applicative ( ListT m) | |
|
Defined in Control.Monad.Trans.List |
|
| Applicative m => Applicative ( ResourceT m) | |
|
Defined in Control.Monad.Trans.Resource.Internal Methods pure :: a -> ResourceT m a Source # (<*>) :: ResourceT m (a -> b) -> ResourceT m a -> ResourceT m b Source # liftA2 :: (a -> b -> c) -> ResourceT m a -> ResourceT m b -> ResourceT m c Source # (*>) :: ResourceT m a -> ResourceT m b -> ResourceT m b Source # (<*) :: ResourceT m a -> ResourceT m b -> ResourceT m a Source # |
|
| Applicative m => Applicative ( NodeT m) Source # | |
|
Defined in Hedgehog.Internal.Tree |
|
| Applicative m => Applicative ( TreeT m) Source # | |
|
Defined in Hedgehog.Internal.Tree |
|
| Monad m => Applicative ( GenT m) Source # | |
| Monad m => Applicative ( TestT m) Source # | |
|
Defined in Hedgehog.Internal.Property |
|
| Monad m => Applicative ( PropertyT m) Source # | |
|
Defined in Hedgehog.Internal.Property Methods pure :: a -> PropertyT m a Source # (<*>) :: PropertyT m (a -> b) -> PropertyT m a -> PropertyT m b Source # liftA2 :: (a -> b -> c) -> PropertyT m a -> PropertyT m b -> PropertyT m c Source # (*>) :: PropertyT m a -> PropertyT m b -> PropertyT m b Source # (<*) :: PropertyT m a -> PropertyT m b -> PropertyT m a Source # |
|
| Applicative f => Applicative ( Rec1 f) |
Since: base-4.9.0.0 |
| ( Monoid a, Monoid b) => Applicative ( (,,) a b) |
Since: base-4.14.0.0 |
|
Defined in GHC.Base |
|
| Monoid m => Applicative ( Const m :: Type -> Type ) |
Since: base-2.0.1 |
|
Defined in Data.Functor.Const |
|
| Applicative m => Applicative ( ReaderT r m) | |
|
Defined in Control.Monad.Trans.Reader Methods pure :: a -> ReaderT r m a Source # (<*>) :: ReaderT r m (a -> b) -> ReaderT r m a -> ReaderT r m b Source # liftA2 :: (a -> b -> c) -> ReaderT r m a -> ReaderT r m b -> ReaderT r m c Source # (*>) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m b Source # (<*) :: ReaderT r m a -> ReaderT r m b -> ReaderT r m a Source # |
|
| Arrow a => Applicative ( WrappedArrow a b) |
Since: base-2.1 |
|
Defined in Control.Applicative Methods pure :: a0 -> WrappedArrow a b a0 Source # (<*>) :: WrappedArrow a b (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 Source # liftA2 :: (a0 -> b0 -> c) -> WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b c Source # (*>) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b b0 Source # (<*) :: WrappedArrow a b a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 Source # |
|
| Applicative m => Applicative ( Kleisli m a) |
Since: base-4.14.0.0 |
|
Defined in Control.Arrow Methods pure :: a0 -> Kleisli m a a0 Source # (<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source # liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source # (*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source # (<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source # |
|
| Applicative f => Applicative ( Ap f) |
Since: base-4.12.0.0 |
| Applicative f => Applicative ( Alt f) |
Since: base-4.8.0.0 |
| ( Applicative f, Monad f) => Applicative ( WhenMissing f x) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMissing f x a Source # (<*>) :: WhenMissing f x (a -> b) -> WhenMissing f x a -> WhenMissing f x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x c Source # (*>) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x b Source # (<*) :: WhenMissing f x a -> WhenMissing f x b -> WhenMissing f x a Source # |
|
| ( Functor m, Monad m) => Applicative ( ExceptT e m) | |
|
Defined in Control.Monad.Trans.Except Methods pure :: a -> ExceptT e m a Source # (<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b Source # liftA2 :: (a -> b -> c) -> ExceptT e m a -> ExceptT e m b -> ExceptT e m c Source # (*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b Source # (<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a Source # |
|
| ( Monoid w, Applicative m) => Applicative ( WriterT w m) | |
|
Defined in Control.Monad.Trans.Writer.Lazy Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # |
|
| ( Functor m, Monad m) => Applicative ( StateT s m) | |
|
Defined in Control.Monad.Trans.State.Lazy Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # |
|
| ( Functor m, Monad m) => Applicative ( ErrorT e m) | |
|
Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a Source # (<*>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b Source # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c Source # (*>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b Source # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a Source # |
|
| Applicative m => Applicative ( IdentityT m) | |
|
Defined in Control.Monad.Trans.Identity Methods pure :: a -> IdentityT m a Source # (<*>) :: IdentityT m (a -> b) -> IdentityT m a -> IdentityT m b Source # liftA2 :: (a -> b -> c) -> IdentityT m a -> IdentityT m b -> IdentityT m c Source # (*>) :: IdentityT m a -> IdentityT m b -> IdentityT m b Source # (<*) :: IdentityT m a -> IdentityT m b -> IdentityT m a Source # |
|
| ( Functor m, Monad m) => Applicative ( StateT s m) | |
|
Defined in Control.Monad.Trans.State.Strict Methods pure :: a -> StateT s m a Source # (<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source # liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source # (*>) :: StateT s m a -> StateT s m b -> StateT s m b Source # (<*) :: StateT s m a -> StateT s m b -> StateT s m a Source # |
|
| ( Monoid w, Applicative m) => Applicative ( WriterT w m) | |
|
Defined in Control.Monad.Trans.Writer.Strict Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # |
|
| Applicative ( Tagged s) | |
|
Defined in Data.Tagged |
|
| ( Monoid w, Functor m, Monad m) => Applicative ( AccumT w m) | |
|
Defined in Control.Monad.Trans.Accum Methods pure :: a -> AccumT w m a Source # (<*>) :: AccumT w m (a -> b) -> AccumT w m a -> AccumT w m b Source # liftA2 :: (a -> b -> c) -> AccumT w m a -> AccumT w m b -> AccumT w m c Source # (*>) :: AccumT w m a -> AccumT w m b -> AccumT w m b Source # (<*) :: AccumT w m a -> AccumT w m b -> AccumT w m a Source # |
|
| ( Functor m, Monad m) => Applicative ( WriterT w m) | |
|
Defined in Control.Monad.Trans.Writer.CPS Methods pure :: a -> WriterT w m a Source # (<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b Source # liftA2 :: (a -> b -> c) -> WriterT w m a -> WriterT w m b -> WriterT w m c Source # (*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b Source # (<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a Source # |
|
| ( Functor m, Monad m) => Applicative ( SelectT r m) | |
|
Defined in Control.Monad.Trans.Select Methods pure :: a -> SelectT r m a Source # (<*>) :: SelectT r m (a -> b) -> SelectT r m a -> SelectT r m b Source # liftA2 :: (a -> b -> c) -> SelectT r m a -> SelectT r m b -> SelectT r m c Source # (*>) :: SelectT r m a -> SelectT r m b -> SelectT r m b Source # (<*) :: SelectT r m a -> SelectT r m b -> SelectT r m a Source # |
|
| Applicative ((->) r :: Type -> Type ) |
Since: base-2.1 |
| Monoid c => Applicative ( K1 i c :: Type -> Type ) |
Since: base-4.12.0.0 |
| ( Applicative f, Applicative g) => Applicative (f :*: g) |
Since: base-4.9.0.0 |
| ( Monoid a, Monoid b, Monoid c) => Applicative ( (,,,) a b c) |
Since: base-4.14.0.0 |
|
Defined in GHC.Base Methods pure :: a0 -> (a, b, c, a0) Source # (<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source # liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source # (*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source # (<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source # |
|
| ( Applicative f, Applicative g) => Applicative ( Product f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Product Methods pure :: a -> Product f g a Source # (<*>) :: Product f g (a -> b) -> Product f g a -> Product f g b Source # liftA2 :: (a -> b -> c) -> Product f g a -> Product f g b -> Product f g c Source # (*>) :: Product f g a -> Product f g b -> Product f g b Source # (<*) :: Product f g a -> Product f g b -> Product f g a Source # |
|
| ( Monad f, Applicative f) => Applicative ( WhenMatched f x y) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.IntMap.Internal Methods pure :: a -> WhenMatched f x y a Source # (<*>) :: WhenMatched f x y (a -> b) -> WhenMatched f x y a -> WhenMatched f x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y c Source # (*>) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y b Source # (<*) :: WhenMatched f x y a -> WhenMatched f x y b -> WhenMatched f x y a Source # |
|
| ( Applicative f, Monad f) => Applicative ( WhenMissing f k x) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods pure :: a -> WhenMissing f k x a Source # (<*>) :: WhenMissing f k x (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b Source # liftA2 :: (a -> b -> c) -> WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x c Source # (*>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b Source # (<*) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x a Source # |
|
| Applicative ( ContT r m) | |
| Applicative f => Applicative ( M1 i c f) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| ( Applicative f, Applicative g) => Applicative (f :.: g) |
Since: base-4.9.0.0 |
| ( Applicative f, Applicative g) => Applicative ( Compose f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Compose Methods pure :: a -> Compose f g a Source # (<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source # liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source # (*>) :: Compose f g a -> Compose f g b -> Compose f g b Source # (<*) :: Compose f g a -> Compose f g b -> Compose f g a Source # |
|
| ( Monad f, Applicative f) => Applicative ( WhenMatched f k x y) |
Equivalent to
Since: containers-0.5.9 |
|
Defined in Data.Map.Internal Methods pure :: a -> WhenMatched f k x y a Source # (<*>) :: WhenMatched f k x y (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b Source # liftA2 :: (a -> b -> c) -> WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y c Source # (*>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b Source # (<*) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y a Source # |
|
| ( Monoid w, Functor m, Monad m) => Applicative ( RWST r w s m) | |
|
Defined in Control.Monad.Trans.RWS.Lazy Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # |
|
| ( Monoid w, Functor m, Monad m) => Applicative ( RWST r w s m) | |
|
Defined in Control.Monad.Trans.RWS.Strict Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # |
|
| ( Functor m, Monad m) => Applicative ( RWST r w s m) | |
|
Defined in Control.Monad.Trans.RWS.CPS Methods pure :: a -> RWST r w s m a Source # (<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b Source # liftA2 :: (a -> b -> c) -> RWST r w s m a -> RWST r w s m b -> RWST r w s m c Source # (*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b Source # (<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a Source # |
|
class Foldable (t :: Type -> Type ) where Source #
Data structures that can be folded.
For example, given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Foldable Tree where foldMap f Empty = mempty foldMap f (Leaf x) = f x foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r
This is suitable even for abstract types, as the monoid is assumed
to satisfy the monoid laws. Alternatively, one could define
foldr
:
instance Foldable Tree where foldr f z Empty = z foldr f z (Leaf x) = f x z foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l
Foldable
instances are expected to satisfy the following laws:
foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
length = getSum . foldMap (Sum . const 1)
sum
,
product
,
maximum
, and
minimum
should all be essentially
equivalent to
foldMap
forms, such as
sum = getSum . foldMap Sum
but may be less defined.
If the type is also a
Functor
instance, it should satisfy
foldMap f = fold . fmap f
which implies that
foldMap f . fmap g = foldMap (f . g)
Methods
foldMap :: Monoid m => (a -> m) -> t a -> m Source #
Map each element of the structure to a monoid, and combine the results.
foldr :: (a -> b -> b) -> b -> t a -> b Source #
Right-associative fold of a structure.
In the case of lists,
foldr
, when applied to a binary operator, a
starting value (typically the right-identity of the operator), and a
list, reduces the list using the binary operator, from right to left:
foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)
Note that, since the head of the resulting expression is produced by
an application of the operator to the first element of the list,
foldr
can produce a terminating expression from an infinite list.
For a general
Foldable
structure this should be semantically identical
to,
foldr f z =foldrf z .toList
foldl :: (b -> a -> b) -> b -> t a -> b Source #
Left-associative fold of a structure.
In the case of lists,
foldl
, when applied to a binary
operator, a starting value (typically the left-identity of the operator),
and a list, reduces the list using the binary operator, from left to
right:
foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn
Note that to produce the outermost application of the operator the
entire input list must be traversed. This means that
foldl'
will
diverge if given an infinite list.
Also note that if you want an efficient left-fold, you probably want to
use
foldl'
instead of
foldl
. The reason for this is that latter does
not force the "inner" results (e.g.
z `f` x1
in the above example)
before applying them to the operator (e.g. to
(`f` x2)
). This results
in a thunk chain
\(\mathcal{O}(n)\)
elements long, which then must be
evaluated from the outside-in.
For a general
Foldable
structure this should be semantically identical
to,
foldl f z =foldlf z .toList
foldr1 :: (a -> a -> a) -> t a -> a Source #
A variant of
foldr
that has no base case,
and thus may only be applied to non-empty structures.
foldr1f =foldr1f .toList
foldl1 :: (a -> a -> a) -> t a -> a Source #
A variant of
foldl
that has no base case,
and thus may only be applied to non-empty structures.
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 Source #
Does the element occur in the structure?
Since: base-4.8.0.0
maximum :: Ord a => t a -> a Source #
The largest element of a non-empty structure.
Since: base-4.8.0.0
minimum :: Ord a => t a -> a Source #
The least element of a non-empty structure.
Since: base-4.8.0.0
sum :: Num a => t a -> a Source #
The
sum
function computes the sum of the numbers of a structure.
Since: base-4.8.0.0
product :: Num a => t a -> a Source #
The
product
function computes the product of the numbers of a
structure.
Since: base-4.8.0.0
Instances
| Foldable [] |
Since: base-2.1 |
|
Defined in Data.Foldable Methods fold :: Monoid m => [m] -> m Source # foldMap :: Monoid m => (a -> m) -> [a] -> m Source # foldMap' :: Monoid m => (a -> m) -> [a] -> m Source # foldr :: (a -> b -> b) -> b -> [a] -> b Source # foldr' :: (a -> b -> b) -> b -> [a] -> b Source # foldl :: (b -> a -> b) -> b -> [a] -> b Source # foldl' :: (b -> a -> b) -> b -> [a] -> b Source # foldr1 :: (a -> a -> a) -> [a] -> a Source # foldl1 :: (a -> a -> a) -> [a] -> a Source # elem :: Eq a => a -> [a] -> Bool Source # maximum :: Ord a => [a] -> a Source # minimum :: Ord a => [a] -> a Source # |
|
| Foldable Maybe |
Since: base-2.1 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # |
|
| Foldable Par1 |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Par1 m -> m Source # foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> Par1 a -> m Source # foldr :: (a -> b -> b) -> b -> Par1 a -> b Source # foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source # foldl :: (b -> a -> b) -> b -> Par1 a -> b Source # foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source # foldr1 :: (a -> a -> a) -> Par1 a -> a Source # foldl1 :: (a -> a -> a) -> Par1 a -> a Source # toList :: Par1 a -> [a] Source # null :: Par1 a -> Bool Source # length :: Par1 a -> Int Source # elem :: Eq a => a -> Par1 a -> Bool Source # maximum :: Ord a => Par1 a -> a Source # minimum :: Ord a => Par1 a -> a Source # |
|
| Foldable Identity |
Since: base-4.8.0.0 |
|
Defined in Data.Functor.Identity Methods fold :: Monoid m => Identity m -> m Source # foldMap :: Monoid m => (a -> m) -> Identity a -> m Source # foldMap' :: Monoid m => (a -> m) -> Identity a -> m Source # foldr :: (a -> b -> b) -> b -> Identity a -> b Source # foldr' :: (a -> b -> b) -> b -> Identity a -> b Source # foldl :: (b -> a -> b) -> b -> Identity a -> b Source # foldl' :: (b -> a -> b) -> b -> Identity a -> b Source # foldr1 :: (a -> a -> a) -> Identity a -> a Source # foldl1 :: (a -> a -> a) -> Identity a -> a Source # toList :: Identity a -> [a] Source # null :: Identity a -> Bool Source # length :: Identity a -> Int Source # elem :: Eq a => a -> Identity a -> Bool Source # maximum :: Ord a => Identity a -> a Source # minimum :: Ord a => Identity a -> a Source # |
|
| Foldable Complex |
Since: base-4.9.0.0 |
|
Defined in Data.Complex Methods fold :: Monoid m => Complex m -> m Source # foldMap :: Monoid m => (a -> m) -> Complex a -> m Source # foldMap' :: Monoid m => (a -> m) -> Complex a -> m Source # foldr :: (a -> b -> b) -> b -> Complex a -> b Source # foldr' :: (a -> b -> b) -> b -> Complex a -> b Source # foldl :: (b -> a -> b) -> b -> Complex a -> b Source # foldl' :: (b -> a -> b) -> b -> Complex a -> b Source # foldr1 :: (a -> a -> a) -> Complex a -> a Source # foldl1 :: (a -> a -> a) -> Complex a -> a Source # toList :: Complex a -> [a] Source # null :: Complex a -> Bool Source # length :: Complex a -> Int Source # elem :: Eq a => a -> Complex a -> Bool Source # maximum :: Ord a => Complex a -> a Source # minimum :: Ord a => Complex a -> a Source # |
|
| Foldable Min |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldMap' :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # |
|
| Foldable Max |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldMap' :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # |
|
| Foldable First |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # |
|
| Foldable Last |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # |
|
| Foldable Option |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m Source # foldMap :: Monoid m => (a -> m) -> Option a -> m Source # foldMap' :: Monoid m => (a -> m) -> Option a -> m Source # foldr :: (a -> b -> b) -> b -> Option a -> b Source # foldr' :: (a -> b -> b) -> b -> Option a -> b Source # foldl :: (b -> a -> b) -> b -> Option a -> b Source # foldl' :: (b -> a -> b) -> b -> Option a -> b Source # foldr1 :: (a -> a -> a) -> Option a -> a Source # foldl1 :: (a -> a -> a) -> Option a -> a Source # toList :: Option a -> [a] Source # null :: Option a -> Bool Source # length :: Option a -> Int Source # elem :: Eq a => a -> Option a -> Bool Source # maximum :: Ord a => Option a -> a Source # minimum :: Ord a => Option a -> a Source # |
|
| Foldable ZipList |
Since: base-4.9.0.0 |
|
Defined in Control.Applicative Methods fold :: Monoid m => ZipList m -> m Source # foldMap :: Monoid m => (a -> m) -> ZipList a -> m Source # foldMap' :: Monoid m => (a -> m) -> ZipList a -> m Source # foldr :: (a -> b -> b) -> b -> ZipList a -> b Source # foldr' :: (a -> b -> b) -> b -> ZipList a -> b Source # foldl :: (b -> a -> b) -> b -> ZipList a -> b Source # foldl' :: (b -> a -> b) -> b -> ZipList a -> b Source # foldr1 :: (a -> a -> a) -> ZipList a -> a Source # foldl1 :: (a -> a -> a) -> ZipList a -> a Source # toList :: ZipList a -> [a] Source # null :: ZipList a -> Bool Source # length :: ZipList a -> Int Source # elem :: Eq a => a -> ZipList a -> Bool Source # maximum :: Ord a => ZipList a -> a Source # minimum :: Ord a => ZipList a -> a Source # |
|
| Foldable First |
Since: base-4.8.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldMap' :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # |
|
| Foldable Last |
Since: base-4.8.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldMap' :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # |
|
| Foldable Dual |
Since: base-4.8.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # |
|
| Foldable Sum |
Since: base-4.8.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # |
|
| Foldable Product |
Since: base-4.8.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # |
|
| Foldable Down |
Since: base-4.12.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Down m -> m Source # foldMap :: Monoid m => (a -> m) -> Down a -> m Source # foldMap' :: Monoid m => (a -> m) -> Down a -> m Source # foldr :: (a -> b -> b) -> b -> Down a -> b Source # foldr' :: (a -> b -> b) -> b -> Down a -> b Source # foldl :: (b -> a -> b) -> b -> Down a -> b Source # foldl' :: (b -> a -> b) -> b -> Down a -> b Source # foldr1 :: (a -> a -> a) -> Down a -> a Source # foldl1 :: (a -> a -> a) -> Down a -> a Source # toList :: Down a -> [a] Source # null :: Down a -> Bool Source # length :: Down a -> Int Source # elem :: Eq a => a -> Down a -> Bool Source # maximum :: Ord a => Down a -> a Source # minimum :: Ord a => Down a -> a Source # |
|
| Foldable NonEmpty |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => NonEmpty m -> m Source # foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldMap' :: Monoid m => (a -> m) -> NonEmpty a -> m Source # foldr :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source # foldl :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source # foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source # foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source # toList :: NonEmpty a -> [a] Source # null :: NonEmpty a -> Bool Source # length :: NonEmpty a -> Int Source # elem :: Eq a => a -> NonEmpty a -> Bool Source # maximum :: Ord a => NonEmpty a -> a Source # minimum :: Ord a => NonEmpty a -> a Source # |
|
| Foldable IntMap |
Folds in order of increasing key. |
|
Defined in Data.IntMap.Internal Methods fold :: Monoid m => IntMap m -> m Source # foldMap :: Monoid m => (a -> m) -> IntMap a -> m Source # foldMap' :: Monoid m => (a -> m) -> IntMap a -> m Source # foldr :: (a -> b -> b) -> b -> IntMap a -> b Source # foldr' :: (a -> b -> b) -> b -> IntMap a -> b Source # foldl :: (b -> a -> b) -> b -> IntMap a -> b Source # foldl' :: (b -> a -> b) -> b -> IntMap a -> b Source # foldr1 :: (a -> a -> a) -> IntMap a -> a Source # foldl1 :: (a -> a -> a) -> IntMap a -> a Source # toList :: IntMap a -> [a] Source # null :: IntMap a -> Bool Source # length :: IntMap a -> Int Source # elem :: Eq a => a -> IntMap a -> Bool Source # maximum :: Ord a => IntMap a -> a Source # minimum :: Ord a => IntMap a -> a Source # |
|
| Foldable Tree | |
|
Defined in Data.Tree Methods fold :: Monoid m => Tree m -> m Source # foldMap :: Monoid m => (a -> m) -> Tree a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source # foldr :: (a -> b -> b) -> b -> Tree a -> b Source # foldr' :: (a -> b -> b) -> b -> Tree a -> b Source # foldl :: (b -> a -> b) -> b -> Tree a -> b Source # foldl' :: (b -> a -> b) -> b -> Tree a -> b Source # foldr1 :: (a -> a -> a) -> Tree a -> a Source # foldl1 :: (a -> a -> a) -> Tree a -> a Source # toList :: Tree a -> [a] Source # null :: Tree a -> Bool Source # length :: Tree a -> Int Source # elem :: Eq a => a -> Tree a -> Bool Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # |
|
| Foldable Seq | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Seq m -> m Source # foldMap :: Monoid m => (a -> m) -> Seq a -> m Source # foldMap' :: Monoid m => (a -> m) -> Seq a -> m Source # foldr :: (a -> b -> b) -> b -> Seq a -> b Source # foldr' :: (a -> b -> b) -> b -> Seq a -> b Source # foldl :: (b -> a -> b) -> b -> Seq a -> b Source # foldl' :: (b -> a -> b) -> b -> Seq a -> b Source # foldr1 :: (a -> a -> a) -> Seq a -> a Source # foldl1 :: (a -> a -> a) -> Seq a -> a Source # toList :: Seq a -> [a] Source # null :: Seq a -> Bool Source # length :: Seq a -> Int Source # elem :: Eq a => a -> Seq a -> Bool Source # maximum :: Ord a => Seq a -> a Source # minimum :: Ord a => Seq a -> a Source # |
|
| Foldable FingerTree | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => FingerTree m -> m Source # foldMap :: Monoid m => (a -> m) -> FingerTree a -> m Source # foldMap' :: Monoid m => (a -> m) -> FingerTree a -> m Source # foldr :: (a -> b -> b) -> b -> FingerTree a -> b Source # foldr' :: (a -> b -> b) -> b -> FingerTree a -> b Source # foldl :: (b -> a -> b) -> b -> FingerTree a -> b Source # foldl' :: (b -> a -> b) -> b -> FingerTree a -> b Source # foldr1 :: (a -> a -> a) -> FingerTree a -> a Source # foldl1 :: (a -> a -> a) -> FingerTree a -> a Source # toList :: FingerTree a -> [a] Source # null :: FingerTree a -> Bool Source # length :: FingerTree a -> Int Source # elem :: Eq a => a -> FingerTree a -> Bool Source # maximum :: Ord a => FingerTree a -> a Source # minimum :: Ord a => FingerTree a -> a Source # sum :: Num a => FingerTree a -> a Source # product :: Num a => FingerTree a -> a Source # |
|
| Foldable Digit | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Digit m -> m Source # foldMap :: Monoid m => (a -> m) -> Digit a -> m Source # foldMap' :: Monoid m => (a -> m) -> Digit a -> m Source # foldr :: (a -> b -> b) -> b -> Digit a -> b Source # foldr' :: (a -> b -> b) -> b -> Digit a -> b Source # foldl :: (b -> a -> b) -> b -> Digit a -> b Source # foldl' :: (b -> a -> b) -> b -> Digit a -> b Source # foldr1 :: (a -> a -> a) -> Digit a -> a Source # foldl1 :: (a -> a -> a) -> Digit a -> a Source # toList :: Digit a -> [a] Source # null :: Digit a -> Bool Source # length :: Digit a -> Int Source # elem :: Eq a => a -> Digit a -> Bool Source # maximum :: Ord a => Digit a -> a Source # minimum :: Ord a => Digit a -> a Source # |
|
| Foldable Node | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Node m -> m Source # foldMap :: Monoid m => (a -> m) -> Node a -> m Source # foldMap' :: Monoid m => (a -> m) -> Node a -> m Source # foldr :: (a -> b -> b) -> b -> Node a -> b Source # foldr' :: (a -> b -> b) -> b -> Node a -> b Source # foldl :: (b -> a -> b) -> b -> Node a -> b Source # foldl' :: (b -> a -> b) -> b -> Node a -> b Source # foldr1 :: (a -> a -> a) -> Node a -> a Source # foldl1 :: (a -> a -> a) -> Node a -> a Source # toList :: Node a -> [a] Source # null :: Node a -> Bool Source # length :: Node a -> Int Source # elem :: Eq a => a -> Node a -> Bool Source # maximum :: Ord a => Node a -> a Source # minimum :: Ord a => Node a -> a Source # |
|
| Foldable Elem | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => Elem m -> m Source # foldMap :: Monoid m => (a -> m) -> Elem a -> m Source # foldMap' :: Monoid m => (a -> m) -> Elem a -> m Source # foldr :: (a -> b -> b) -> b -> Elem a -> b Source # foldr' :: (a -> b -> b) -> b -> Elem a -> b Source # foldl :: (b -> a -> b) -> b -> Elem a -> b Source # foldl' :: (b -> a -> b) -> b -> Elem a -> b Source # foldr1 :: (a -> a -> a) -> Elem a -> a Source # foldl1 :: (a -> a -> a) -> Elem a -> a Source # toList :: Elem a -> [a] Source # null :: Elem a -> Bool Source # length :: Elem a -> Int Source # elem :: Eq a => a -> Elem a -> Bool Source # maximum :: Ord a => Elem a -> a Source # minimum :: Ord a => Elem a -> a Source # |
|
| Foldable ViewL | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewL m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewL a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewL a -> m Source # foldr :: (a -> b -> b) -> b -> ViewL a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewL a -> b Source # foldl :: (b -> a -> b) -> b -> ViewL a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewL a -> b Source # foldr1 :: (a -> a -> a) -> ViewL a -> a Source # foldl1 :: (a -> a -> a) -> ViewL a -> a Source # toList :: ViewL a -> [a] Source # null :: ViewL a -> Bool Source # length :: ViewL a -> Int Source # elem :: Eq a => a -> ViewL a -> Bool Source # maximum :: Ord a => ViewL a -> a Source # minimum :: Ord a => ViewL a -> a Source # |
|
| Foldable ViewR | |
|
Defined in Data.Sequence.Internal Methods fold :: Monoid m => ViewR m -> m Source # foldMap :: Monoid m => (a -> m) -> ViewR a -> m Source # foldMap' :: Monoid m => (a -> m) -> ViewR a -> m Source # foldr :: (a -> b -> b) -> b -> ViewR a -> b Source # foldr' :: (a -> b -> b) -> b -> ViewR a -> b Source # foldl :: (b -> a -> b) -> b -> ViewR a -> b Source # foldl' :: (b -> a -> b) -> b -> ViewR a -> b Source # foldr1 :: (a -> a -> a) -> ViewR a -> a Source # foldl1 :: (a -> a -> a) -> ViewR a -> a Source # toList :: ViewR a -> [a] Source # null :: ViewR a -> Bool Source # length :: ViewR a -> Int Source # elem :: Eq a => a -> ViewR a -> Bool Source # maximum :: Ord a => ViewR a -> a Source # minimum :: Ord a => ViewR a -> a Source # |
|
| Foldable Set |
Folds in order of increasing key. |
|
Defined in Data.Set.Internal Methods fold :: Monoid m => Set m -> m Source # foldMap :: Monoid m => (a -> m) -> Set a -> m Source # foldMap' :: Monoid m => (a -> m) -> Set a -> m Source # foldr :: (a -> b -> b) -> b -> Set a -> b Source # foldr' :: (a -> b -> b) -> b -> Set a -> b Source # foldl :: (b -> a -> b) -> b -> Set a -> b Source # foldl' :: (b -> a -> b) -> b -> Set a -> b Source # foldr1 :: (a -> a -> a) -> Set a -> a Source # foldl1 :: (a -> a -> a) -> Set a -> a Source # toList :: Set a -> [a] Source # null :: Set a -> Bool Source # length :: Set a -> Int Source # elem :: Eq a => a -> Set a -> Bool Source # maximum :: Ord a => Set a -> a Source # minimum :: Ord a => Set a -> a Source # |
|
| Foldable Hashed | |
|
Defined in Data.Hashable.Class Methods fold :: Monoid m => Hashed m -> m Source # foldMap :: Monoid m => (a -> m) -> Hashed a -> m Source # foldMap' :: Monoid m => (a -> m) -> Hashed a -> m Source # foldr :: (a -> b -> b) -> b -> Hashed a -> b Source # foldr' :: (a -> b -> b) -> b -> Hashed a -> b Source # foldl :: (b -> a -> b) -> b -> Hashed a -> b Source # foldl' :: (b -> a -> b) -> b -> Hashed a -> b Source # foldr1 :: (a -> a -> a) -> Hashed a -> a Source # foldl1 :: (a -> a -> a) -> Hashed a -> a Source # toList :: Hashed a -> [a] Source # null :: Hashed a -> Bool Source # length :: Hashed a -> Int Source # elem :: Eq a => a -> Hashed a -> Bool Source # maximum :: Ord a => Hashed a -> a Source # minimum :: Ord a => Hashed a -> a Source # |
|
| Foldable Window | |
|
Defined in System.Console.Terminal.Common Methods fold :: Monoid m => Window m -> m Source # foldMap :: Monoid m => (a -> m) -> Window a -> m Source # foldMap' :: Monoid m => (a -> m) -> Window a -> m Source # foldr :: (a -> b -> b) -> b -> Window a -> b Source # foldr' :: (a -> b -> b) -> b -> Window a -> b Source # foldl :: (b -> a -> b) -> b -> Window a -> b Source # foldl' :: (b -> a -> b) -> b -> Window a -> b Source # foldr1 :: (a -> a -> a) -> Window a -> a Source # foldl1 :: (a -> a -> a) -> Window a -> a Source # toList :: Window a -> [a] Source # null :: Window a -> Bool Source # length :: Window a -> Int Source # elem :: Eq a => a -> Window a -> Bool Source # maximum :: Ord a => Window a -> a Source # minimum :: Ord a => Window a -> a Source # |
|
| Foldable SimpleDoc | |
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Defined in Text.PrettyPrint.Annotated.WL Methods fold :: Monoid m => SimpleDoc m -> m Source # foldMap :: Monoid m => (a -> m) -> SimpleDoc a -> m Source # foldMap' :: Monoid m => (a -> m) -> SimpleDoc a -> m Source # foldr :: (a -> b -> b) -> b -> SimpleDoc a -> b Source # foldr' :: (a -> b -> b) -> b -> SimpleDoc a -> b Source # foldl :: (b -> a -> b) -> b -> SimpleDoc a -> b Source # foldl' :: (b -> a -> b) -> b -> SimpleDoc a -> b Source # foldr1 :: (a -> a -> a) -> SimpleDoc a -> a Source # foldl1 :: (a -> a -> a) -> SimpleDoc a -> a Source # toList :: SimpleDoc a -> [a] Source # null :: SimpleDoc a -> Bool Source # length :: SimpleDoc a -> Int Source # elem :: Eq a => a -> SimpleDoc a -> Bool Source # maximum :: Ord a => SimpleDoc a -> a Source # minimum :: Ord a => SimpleDoc a -> a Source # |
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| Foldable Node Source # | |
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Defined in Hedgehog.Internal.Tree Methods fold :: Monoid m => Node m -> m Source # foldMap :: Monoid m => (a -> m) -> Node a -> m Source # foldMap' :: Monoid m => (a -> m) -> Node a -> m Source # foldr :: (a -> b -> b) -> b -> Node a -> b Source # foldr' :: (a -> b -> b) -> b -> Node a -> b Source # foldl :: (b -> a -> b) -> b -> Node a -> b Source # foldl' :: (b -> a -> b) -> b -> Node a -> b Source # foldr1 :: (a -> a -> a) -> Node a -> a Source # foldl1 :: (a -> a -> a) -> Node a -> a Source # toList :: Node a -> [a] Source # null :: Node a -> Bool Source # length :: Node a -> Int Source # elem :: Eq a => a -> Node a -> Bool Source # maximum :: Ord a => Node a -> a Source # minimum :: Ord a => Node a -> a Source # |
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| Foldable Tree Source # | |
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Defined in Hedgehog.Internal.Tree Methods fold :: Monoid m => Tree m -> m Source # foldMap :: Monoid m => (a -> m) -> Tree a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tree a -> m Source # foldr :: (a -> b -> b) -> b -> Tree a -> b Source # foldr' :: (a -> b -> b) -> b -> Tree a -> b Source # foldl :: (b -> a -> b) -> b -> Tree a -> b Source # foldl' :: (b -> a -> b) -> b -> Tree a -> b Source # foldr1 :: (a -> a -> a) -> Tree a -> a Source # foldl1 :: (a -> a -> a) -> Tree a -> a Source # toList :: Tree a -> [a] Source # null :: Tree a -> Bool Source # length :: Tree a -> Int Source # elem :: Eq a => a -> Tree a -> Bool Source # maximum :: Ord a => Tree a -> a Source # minimum :: Ord a => Tree a -> a Source # |
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| Foldable Coverage Source # | |
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Defined in Hedgehog.Internal.Property Methods fold :: Monoid m => Coverage m -> m Source # foldMap :: Monoid m => (a -> m) -> Coverage a -> m Source # foldMap' :: Monoid m => (a -> m) -> Coverage a -> m Source # foldr :: (a -> b -> b) -> b -> Coverage a -> b Source # foldr' :: (a -> b -> b) -> b -> Coverage a -> b Source # foldl :: (b -> a -> b) -> b -> Coverage a -> b Source # foldl' :: (b -> a -> b) -> b -> Coverage a -> b Source # foldr1 :: (a -> a -> a) -> Coverage a -> a Source # foldl1 :: (a -> a -> a) -> Coverage a -> a Source # toList :: Coverage a -> [a] Source # null :: Coverage a -> Bool Source # length :: Coverage a -> Int Source # elem :: Eq a => a -> Coverage a -> Bool Source # maximum :: Ord a => Coverage a -> a Source # minimum :: Ord a => Coverage a -> a Source # |
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| Foldable Label Source # | |
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Defined in Hedgehog.Internal.Property Methods fold :: Monoid m => Label m -> m Source # foldMap :: Monoid m => (a -> m) -> Label a -> m Source # foldMap' :: Monoid m => (a -> m) -> Label a -> m Source # foldr :: (a -> b -> b) -> b -> Label a -> b Source # foldr' :: (a -> b -> b) -> b -> Label a -> b Source # foldl :: (b -> a -> b) -> b -> Label a -> b Source # foldl' :: (b -> a -> b) -> b -> Label a -> b Source # foldr1 :: (a -> a -> a) -> Label a -> a Source # foldl1 :: (a -> a -> a) -> Label a -> a Source # toList :: Label a -> [a] Source # null :: Label a -> Bool Source # length :: Label a -> Int Source # elem :: Eq a => a -> Label a -> Bool Source # maximum :: Ord a => Label a -> a Source # minimum :: Ord a => Label a -> a Source # |
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| Foldable Concrete Source # | |
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Defined in Hedgehog.Internal.State Methods fold :: Monoid m => Concrete m -> m Source # foldMap :: Monoid m => (a -> m) -> Concrete a -> m Source # foldMap' :: Monoid m => (a -> m) -> Concrete a -> m Source # foldr :: (a -> b -> b) -> b -> Concrete a -> b Source # foldr' :: (a -> b -> b) -> b -> Concrete a -> b Source # foldl :: (b -> a -> b) -> b -> Concrete a -> b Source # foldl' :: (b -> a -> b) -> b -> Concrete a -> b Source # foldr1 :: (a -> a -> a) -> Concrete a -> a Source # foldl1 :: (a -> a -> a) -> Concrete a -> a Source # toList :: Concrete a -> [a] Source # null :: Concrete a -> Bool Source # length :: Concrete a -> Int Source # elem :: Eq a => a -> Concrete a -> Bool Source # maximum :: Ord a => Concrete a -> a Source # minimum :: Ord a => Concrete a -> a Source # |
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| Foldable Report Source # | |
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Defined in Hedgehog.Internal.Report Methods fold :: Monoid m => Report m -> m Source # foldMap :: Monoid m => (a -> m) -> Report a -> m Source # foldMap' :: Monoid m => (a -> m) -> Report a -> m Source # foldr :: (a -> b -> b) -> b -> Report a -> b Source # foldr' :: (a -> b -> b) -> b -> Report a -> b Source # foldl :: (b -> a -> b) -> b -> Report a -> b Source # foldl' :: (b -> a -> b) -> b -> Report a -> b Source # foldr1 :: (a -> a -> a) -> Report a -> a Source # foldl1 :: (a -> a -> a) -> Report a -> a Source # toList :: Report a -> [a] Source # null :: Report a -> Bool Source # length :: Report a -> Int Source # elem :: Eq a => a -> Report a -> Bool Source # maximum :: Ord a => Report a -> a Source # minimum :: Ord a => Report a -> a Source # |
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| Foldable ( Either a) |
Since: base-4.7.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # |
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| Foldable ( V1 :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m Source # foldMap :: Monoid m => (a -> m) -> V1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> V1 a -> m Source # foldr :: (a -> b -> b) -> b -> V1 a -> b Source # foldr' :: (a -> b -> b) -> b -> V1 a -> b Source # foldl :: (b -> a -> b) -> b -> V1 a -> b Source # foldl' :: (b -> a -> b) -> b -> V1 a -> b Source # foldr1 :: (a -> a -> a) -> V1 a -> a Source # foldl1 :: (a -> a -> a) -> V1 a -> a Source # toList :: V1 a -> [a] Source # length :: V1 a -> Int Source # elem :: Eq a => a -> V1 a -> Bool Source # maximum :: Ord a => V1 a -> a Source # minimum :: Ord a => V1 a -> a Source # |
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| Foldable ( U1 :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => U1 m -> m Source # foldMap :: Monoid m => (a -> m) -> U1 a -> m Source # foldMap' :: Monoid m => (a -> m) -> U1 a -> m Source # foldr :: (a -> b -> b) -> b -> U1 a -> b Source # foldr' :: (a -> b -> b) -> b -> U1 a -> b Source # foldl :: (b -> a -> b) -> b -> U1 a -> b Source # foldl' :: (b -> a -> b) -> b -> U1 a -> b Source # foldr1 :: (a -> a -> a) -> U1 a -> a Source # foldl1 :: (a -> a -> a) -> U1 a -> a Source # toList :: U1 a -> [a] Source # length :: U1 a -> Int Source # elem :: Eq a => a -> U1 a -> Bool Source # maximum :: Ord a => U1 a -> a Source # minimum :: Ord a => U1 a -> a Source # |
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| Foldable ( UAddr :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UAddr m -> m Source # foldMap :: Monoid m => (a -> m) -> UAddr a -> m Source # foldMap' :: Monoid m => (a -> m) -> UAddr a -> m Source # foldr :: (a -> b -> b) -> b -> UAddr a -> b Source # foldr' :: (a -> b -> b) -> b -> UAddr a -> b Source # foldl :: (b -> a -> b) -> b -> UAddr a -> b Source # foldl' :: (b -> a -> b) -> b -> UAddr a -> b Source # foldr1 :: (a -> a -> a) -> UAddr a -> a Source # foldl1 :: (a -> a -> a) -> UAddr a -> a Source # toList :: UAddr a -> [a] Source # null :: UAddr a -> Bool Source # length :: UAddr a -> Int Source # elem :: Eq a => a -> UAddr a -> Bool Source # maximum :: Ord a => UAddr a -> a Source # minimum :: Ord a => UAddr a -> a Source # |
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| Foldable ( UChar :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # |
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| Foldable ( UDouble :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # |
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| Foldable ( UFloat :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # |
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| Foldable ( UInt :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # |
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| Foldable ( UWord :: Type -> Type ) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # |
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| Foldable ( (,) a) |
Since: base-4.7.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => (a, m) -> m Source # foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldMap' :: Monoid m => (a0 -> m) -> (a, a0) -> m Source # foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b Source # foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b Source # foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 Source # toList :: (a, a0) -> [a0] Source # null :: (a, a0) -> Bool Source # length :: (a, a0) -> Int Source # elem :: Eq a0 => a0 -> (a, a0) -> Bool Source # maximum :: Ord a0 => (a, a0) -> a0 Source # minimum :: Ord a0 => (a, a0) -> a0 Source # |
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| Foldable ( Array i) |
Since: base-4.8.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Array i m -> m Source # foldMap :: Monoid m => (a -> m) -> Array i a -> m Source # foldMap' :: Monoid m => (a -> m) -> Array i a -> m Source # foldr :: (a -> b -> b) -> b -> Array i a -> b Source # foldr' :: (a -> b -> b) -> b -> Array i a -> b Source # foldl :: (b -> a -> b) -> b -> Array i a -> b Source # foldl' :: (b -> a -> b) -> b -> Array i a -> b Source # foldr1 :: (a -> a -> a) -> Array i a -> a Source # foldl1 :: (a -> a -> a) -> Array i a -> a Source # toList :: Array i a -> [a] Source # null :: Array i a -> Bool Source # length :: Array i a -> Int Source # elem :: Eq a => a -> Array i a -> Bool Source # maximum :: Ord a => Array i a -> a Source # minimum :: Ord a => Array i a -> a Source # |
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| Foldable ( Arg a) |
Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # |
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| Foldable ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # |
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| Foldable ( Map k) |
Folds in order of increasing key. |
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Defined in Data.Map.Internal Methods fold :: Monoid m => Map k m -> m Source # foldMap :: Monoid m => (a -> m) -> Map k a -> m Source # foldMap' :: Monoid m => (a -> m) -> Map k a -> m Source # foldr :: (a -> b -> b) -> b -> Map k a -> b Source # foldr' :: (a -> b -> b) -> b -> Map k a -> b Source # foldl :: (b -> a -> b) -> b -> Map k a -> b Source # foldl' :: (b -> a -> b) -> b -> Map k a -> b Source # foldr1 :: (a -> a -> a) -> Map k a -> a Source # foldl1 :: (a -> a -> a) -> Map k a -> a Source # toList :: Map k a -> [a] Source # null :: Map k a -> Bool Source # length :: Map k a -> Int Source # elem :: Eq a => a -> Map k a -> Bool Source # maximum :: Ord a => Map k a -> a Source # minimum :: Ord a => Map k a -> a Source # |
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| Foldable f => Foldable ( MaybeT f) | |
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Defined in Control.Monad.Trans.Maybe Methods fold :: Monoid m => MaybeT f m -> m Source # foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> MaybeT f a -> m Source # foldr :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b Source # foldl :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b Source # foldr1 :: (a -> a -> a) -> MaybeT f a -> a Source # foldl1 :: (a -> a -> a) -> MaybeT f a -> a Source # toList :: MaybeT f a -> [a] Source # null :: MaybeT f a -> Bool Source # length :: MaybeT f a -> Int Source # elem :: Eq a => a -> MaybeT f a -> Bool Source # maximum :: Ord a => MaybeT f a -> a Source # minimum :: Ord a => MaybeT f a -> a Source # |
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| Foldable f => Foldable ( ListT f) | |
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Defined in Control.Monad.Trans.List Methods fold :: Monoid m => ListT f m -> m Source # foldMap :: Monoid m => (a -> m) -> ListT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ListT f a -> m Source # foldr :: (a -> b -> b) -> b -> ListT f a -> b Source # foldr' :: (a -> b -> b) -> b -> ListT f a -> b Source # foldl :: (b -> a -> b) -> b -> ListT f a -> b Source # foldl' :: (b -> a -> b) -> b -> ListT f a -> b Source # foldr1 :: (a -> a -> a) -> ListT f a -> a Source # foldl1 :: (a -> a -> a) -> ListT f a -> a Source # toList :: ListT f a -> [a] Source # null :: ListT f a -> Bool Source # length :: ListT f a -> Int Source # elem :: Eq a => a -> ListT f a -> Bool Source # maximum :: Ord a => ListT f a -> a Source # minimum :: Ord a => ListT f a -> a Source # |
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| Foldable ( Vec n) Source # | |
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Defined in Hedgehog.Internal.Gen Methods fold :: Monoid m => Vec n m -> m Source # foldMap :: Monoid m => (a -> m) -> Vec n a -> m Source # foldMap' :: Monoid m => (a -> m) -> Vec n a -> m Source # foldr :: (a -> b -> b) -> b -> Vec n a -> b Source # foldr' :: (a -> b -> b) -> b -> Vec n a -> b Source # foldl :: (b -> a -> b) -> b -> Vec n a -> b Source # foldl' :: (b -> a -> b) -> b -> Vec n a -> b Source # foldr1 :: (a -> a -> a) -> Vec n a -> a Source # foldl1 :: (a -> a -> a) -> Vec n a -> a Source # toList :: Vec n a -> [a] Source # null :: Vec n a -> Bool Source # length :: Vec n a -> Int Source # elem :: Eq a => a -> Vec n a -> Bool Source # maximum :: Ord a => Vec n a -> a Source # minimum :: Ord a => Vec n a -> a Source # |
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| Foldable f => Foldable ( Rec1 f) |
Since: base-4.9.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Rec1 f m -> m Source # foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Rec1 f a -> m Source # foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source # foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source # foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source # foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source # toList :: Rec1 f a -> [a] Source # null :: Rec1 f a -> Bool Source # length :: Rec1 f a -> Int Source # elem :: Eq a => a -> Rec1 f a -> Bool Source # maximum :: Ord a => Rec1 f a -> a Source # minimum :: Ord a => Rec1 f a -> a Source # |
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| Foldable ( Const m :: Type -> Type ) |
Since: base-4.7.0.0 |
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Defined in Data.Functor.Const Methods fold :: Monoid m0 => Const m m0 -> m0 Source # foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0 Source # foldr :: (a -> b -> b) -> b -> Const m a -> b Source # foldr' :: (a -> b -> b) -> b -> Const m a -> b Source # foldl :: (b -> a -> b) -> b -> Const m a -> b Source # foldl' :: (b -> a -> b) -> b -> Const m a -> b Source # foldr1 :: (a -> a -> a) -> Const m a -> a Source # foldl1 :: (a -> a -> a) -> Const m a -> a Source # toList :: Const m a -> [a] Source # null :: Const m a -> Bool Source # length :: Const m a -> Int Source # elem :: Eq a => a -> Const m a -> Bool Source # maximum :: Ord a => Const m a -> a Source # minimum :: Ord a => Const m a -> a Source # |
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| Foldable f => Foldable ( Ap f) |
Since: base-4.12.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source # foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source # foldr :: (a -> b -> b) -> b -> Ap f a -> b Source # foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source # foldl :: (b -> a -> b) -> b -> Ap f a -> b Source # foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source # foldr1 :: (a -> a -> a) -> Ap f a -> a Source # foldl1 :: (a -> a -> a) -> Ap f a -> a Source # toList :: Ap f a -> [a] Source # null :: Ap f a -> Bool Source # length :: Ap f a -> Int Source # elem :: Eq a => a -> Ap f a -> Bool Source # maximum :: Ord a => Ap f a -> a Source # minimum :: Ord a => Ap f a -> a Source # |
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| Foldable f => Foldable ( Alt f) |
Since: base-4.12.0.0 |
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Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source # foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source # foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source # foldr :: (a -> b -> b) -> b -> Alt f a -> b Source # foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source # foldl :: (b -> a -> b) -> b -> Alt f a -> b Source # foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source # foldr1 :: (a -> a -> a) -> Alt f a -> a Source # foldl1 :: (a -> a -> a) -> Alt f a -> a Source # toList :: Alt f a -> [a] Source # null :: Alt f a -> Bool Source # length :: Alt f a -> Int Source # elem :: Eq a => a -> Alt f a -> Bool Source # maximum :: Ord a => Alt f a -> a Source # minimum :: Ord a => Alt f a -> a Source # |
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| Foldable f => Foldable ( ExceptT e f) | |
|
Defined in Control.Monad.Trans.Except Methods fold :: Monoid m => ExceptT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ExceptT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b Source # foldr1 :: (a -> a -> a) -> ExceptT e f a -> a Source # foldl1 :: (a -> a -> a) -> ExceptT e f a -> a Source # toList :: ExceptT e f a -> [a] Source # null :: ExceptT e f a -> Bool Source # length :: ExceptT e f a -> Int Source # elem :: Eq a => a -> ExceptT e f a -> Bool Source # maximum :: Ord a => ExceptT e f a -> a Source # minimum :: Ord a => ExceptT e f a -> a Source # |
|
| Foldable f => Foldable ( WriterT w f) | |
|
Defined in Control.Monad.Trans.Writer.Lazy Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # |
|
| Foldable f => Foldable ( ErrorT e f) | |
|
Defined in Control.Monad.Trans.Error Methods fold :: Monoid m => ErrorT e f m -> m Source # foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldMap' :: Monoid m => (a -> m) -> ErrorT e f a -> m Source # foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b Source # foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b Source # foldr1 :: (a -> a -> a) -> ErrorT e f a -> a Source # foldl1 :: (a -> a -> a) -> ErrorT e f a -> a Source # toList :: ErrorT e f a -> [a] Source # null :: ErrorT e f a -> Bool Source # length :: ErrorT e f a -> Int Source # elem :: Eq a => a -> ErrorT e f a -> Bool Source # maximum :: Ord a => ErrorT e f a -> a Source # minimum :: Ord a => ErrorT e f a -> a Source # |
|
| Foldable f => Foldable ( IdentityT f) | |
|
Defined in Control.Monad.Trans.Identity Methods fold :: Monoid m => IdentityT f m -> m Source # foldMap :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldMap' :: Monoid m => (a -> m) -> IdentityT f a -> m Source # foldr :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldr' :: (a -> b -> b) -> b -> IdentityT f a -> b Source # foldl :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldl' :: (b -> a -> b) -> b -> IdentityT f a -> b Source # foldr1 :: (a -> a -> a) -> IdentityT f a -> a Source # foldl1 :: (a -> a -> a) -> IdentityT f a -> a Source # toList :: IdentityT f a -> [a] Source # null :: IdentityT f a -> Bool Source # length :: IdentityT f a -> Int Source # elem :: Eq a => a -> IdentityT f a -> Bool Source # maximum :: Ord a => IdentityT f a -> a Source # minimum :: Ord a => IdentityT f a -> a Source # |
|
| Foldable f => Foldable ( WriterT w f) | |
|
Defined in Control.Monad.Trans.Writer.Strict Methods fold :: Monoid m => WriterT w f m -> m Source # foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldMap' :: Monoid m => (a -> m) -> WriterT w f a -> m Source # foldr :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b Source # foldl :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b Source # foldr1 :: (a -> a -> a) -> WriterT w f a -> a Source # foldl1 :: (a -> a -> a) -> WriterT w f a -> a Source # toList :: WriterT w f a -> [a] Source # null :: WriterT w f a -> Bool Source # length :: WriterT w f a -> Int Source # elem :: Eq a => a -> WriterT w f a -> Bool Source # maximum :: Ord a => WriterT w f a -> a Source # minimum :: Ord a => WriterT w f a -> a Source # |
|
| Foldable ( Tagged s) | |
|
Defined in Data.Tagged Methods fold :: Monoid m => Tagged s m -> m Source # foldMap :: Monoid m => (a -> m) -> Tagged s a -> m Source # foldMap' :: Monoid m => (a -> m) -> Tagged s a -> m Source # foldr :: (a -> b -> b) -> b -> Tagged s a -> b Source # foldr' :: (a -> b -> b) -> b -> Tagged s a -> b Source # foldl :: (b -> a -> b) -> b -> Tagged s a -> b Source # foldl' :: (b -> a -> b) -> b -> Tagged s a -> b Source # foldr1 :: (a -> a -> a) -> Tagged s a -> a Source # foldl1 :: (a -> a -> a) -> Tagged s a -> a Source # toList :: Tagged s a -> [a] Source # null :: Tagged s a -> Bool Source # length :: Tagged s a -> Int Source # elem :: Eq a => a -> Tagged s a -> Bool Source # maximum :: Ord a => Tagged s a -> a Source # minimum :: Ord a => Tagged s a -> a Source # |
|
| Foldable ( K1 i c :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => K1 i c m -> m Source # foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldMap' :: Monoid m => (a -> m) -> K1 i c a -> m Source # foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source # foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source # foldr1 :: (a -> a -> a) -> K1 i c a -> a Source # foldl1 :: (a -> a -> a) -> K1 i c a -> a Source # toList :: K1 i c a -> [a] Source # null :: K1 i c a -> Bool Source # length :: K1 i c a -> Int Source # elem :: Eq a => a -> K1 i c a -> Bool Source # maximum :: Ord a => K1 i c a -> a Source # minimum :: Ord a => K1 i c a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable (f :+: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :+: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source # toList :: (f :+: g) a -> [a] Source # null :: (f :+: g) a -> Bool Source # length :: (f :+: g) a -> Int Source # elem :: Eq a => a -> (f :+: g) a -> Bool Source # maximum :: Ord a => (f :+: g) a -> a Source # minimum :: Ord a => (f :+: g) a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable (f :*: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :*: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source # toList :: (f :*: g) a -> [a] Source # null :: (f :*: g) a -> Bool Source # length :: (f :*: g) a -> Int Source # elem :: Eq a => a -> (f :*: g) a -> Bool Source # maximum :: Ord a => (f :*: g) a -> a Source # minimum :: Ord a => (f :*: g) a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable ( Product f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Product Methods fold :: Monoid m => Product f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Product f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Product f g a -> m Source # foldr :: (a -> b -> b) -> b -> Product f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Product f g a -> b Source # foldl :: (b -> a -> b) -> b -> Product f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Product f g a -> b Source # foldr1 :: (a -> a -> a) -> Product f g a -> a Source # foldl1 :: (a -> a -> a) -> Product f g a -> a Source # toList :: Product f g a -> [a] Source # null :: Product f g a -> Bool Source # length :: Product f g a -> Int Source # elem :: Eq a => a -> Product f g a -> Bool Source # maximum :: Ord a => Product f g a -> a Source # minimum :: Ord a => Product f g a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable ( Sum f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Sum Methods fold :: Monoid m => Sum f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Sum f g a -> m Source # foldr :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum f g a -> b Source # foldl :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum f g a -> b Source # foldr1 :: (a -> a -> a) -> Sum f g a -> a Source # foldl1 :: (a -> a -> a) -> Sum f g a -> a Source # toList :: Sum f g a -> [a] Source # null :: Sum f g a -> Bool Source # length :: Sum f g a -> Int Source # elem :: Eq a => a -> Sum f g a -> Bool Source # maximum :: Ord a => Sum f g a -> a Source # minimum :: Ord a => Sum f g a -> a Source # |
|
| Foldable f => Foldable ( M1 i c f) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => M1 i c f m -> m Source # foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldMap' :: Monoid m => (a -> m) -> M1 i c f a -> m Source # foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source # foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source # foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source # foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source # toList :: M1 i c f a -> [a] Source # null :: M1 i c f a -> Bool Source # length :: M1 i c f a -> Int Source # elem :: Eq a => a -> M1 i c f a -> Bool Source # maximum :: Ord a => M1 i c f a -> a Source # minimum :: Ord a => M1 i c f a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable (f :.: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # |
|
| ( Foldable f, Foldable g) => Foldable ( Compose f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Compose Methods fold :: Monoid m => Compose f g m -> m Source # foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source # foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source # foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source # foldr1 :: (a -> a -> a) -> Compose f g a -> a Source # foldl1 :: (a -> a -> a) -> Compose f g a -> a Source # toList :: Compose f g a -> [a] Source # null :: Compose f g a -> Bool Source # length :: Compose f g a -> Int Source # elem :: Eq a => a -> Compose f g a -> Bool Source # maximum :: Ord a => Compose f g a -> a Source # minimum :: Ord a => Compose f g a -> a Source # |
|
class ( Functor t, Foldable t) => Traversable (t :: Type -> Type ) where Source #
Functors representing data structures that can be traversed from left to right.
A definition of
traverse
must satisfy the following laws:
- Naturality
-
t .for every applicative transformationtraversef =traverse(t . f)t - Identity
-
traverseIdentity=Identity - Composition
-
traverse(Compose.fmapg . f) =Compose.fmap(traverseg) .traversef
A definition of
sequenceA
must satisfy the following laws:
- Naturality
-
t .for every applicative transformationsequenceA=sequenceA.fmaptt - Identity
-
sequenceA.fmapIdentity=Identity - Composition
-
sequenceA.fmapCompose=Compose.fmapsequenceA.sequenceA
where an applicative transformation is a function
t :: (Applicative f, Applicative g) => f a -> g a
preserving the
Applicative
operations, i.e.
t (purex) =purex t (f<*>x) = t f<*>t x
and the identity functor
Identity
and composition functors
Compose
are from
Data.Functor.Identity
and
Data.Functor.Compose
.
A result of the naturality law is a purity law for
traverse
traversepure=pure
(The naturality law is implied by parametricity and thus so is the purity law [1, p15].)
Instances are similar to
Functor
, e.g. given a data type
data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)
a suitable instance would be
instance Traversable Tree where traverse f Empty = pure Empty traverse f (Leaf x) = Leaf <$> f x traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r
This is suitable even for abstract types, as the laws for
<*>
imply a form of associativity.
The superclass instances should satisfy the following:
-
In the
Functorinstance,fmapshould be equivalent to traversal with the identity applicative functor (fmapDefault). -
In the
Foldableinstance,foldMapshould be equivalent to traversal with a constant applicative functor (foldMapDefault).
References: [1] The Essence of the Iterator Pattern, Jeremy Gibbons and Bruno C. d. S. Oliveira
Methods
traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #
Map each element of a structure to an action, evaluate these actions
from left to right, and collect the results. For a version that ignores
the results see
traverse_
.
sequenceA :: Applicative f => t (f a) -> f (t a) Source #
Evaluate each action in the structure from left to right, and
collect the results. For a version that ignores the results
see
sequenceA_
.
mapM :: Monad m => (a -> m b) -> t a -> m (t b) Source #
Map each element of a structure to a monadic action, evaluate
these actions from left to right, and collect the results. For
a version that ignores the results see
mapM_
.
sequence :: Monad m => t (m a) -> m (t a) Source #
Evaluate each monadic action in the structure from left to
right, and collect the results. For a version that ignores the
results see
sequence_
.
Instances
| Traversable [] |
Since: base-2.1 |
| Traversable Maybe |
Since: base-2.1 |
|
Defined in Data.Traversable |
|
| Traversable Par1 |
Since: base-4.9.0.0 |
| Traversable Identity |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f ( Identity b) Source # sequenceA :: Applicative f => Identity (f a) -> f ( Identity a) Source # mapM :: Monad m => (a -> m b) -> Identity a -> m ( Identity b) Source # sequence :: Monad m => Identity (m a) -> m ( Identity a) Source # |
|
| Traversable Complex |
Since: base-4.9.0.0 |
|
Defined in Data.Complex |
|
| Traversable Min |
Since: base-4.9.0.0 |
| Traversable Max |
Since: base-4.9.0.0 |
| Traversable First |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup |
|
| Traversable Last |
Since: base-4.9.0.0 |
| Traversable Option |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup |
|
| Traversable ZipList |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable First |
Since: base-4.8.0.0 |
|
Defined in Data.Traversable |
|
| Traversable Last |
Since: base-4.8.0.0 |
| Traversable Dual |
Since: base-4.8.0.0 |
| Traversable Sum |
Since: base-4.8.0.0 |
| Traversable Product |
Since: base-4.8.0.0 |
|
Defined in Data.Traversable |
|
| Traversable Down |
Since: base-4.12.0.0 |
| Traversable NonEmpty |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f ( NonEmpty b) Source # sequenceA :: Applicative f => NonEmpty (f a) -> f ( NonEmpty a) Source # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m ( NonEmpty b) Source # sequence :: Monad m => NonEmpty (m a) -> m ( NonEmpty a) Source # |
|
| Traversable IntMap |
Traverses in order of increasing key. |
|
Defined in Data.IntMap.Internal |
|
| Traversable Tree | |
| Traversable Seq | |
| Traversable FingerTree | |
|
Defined in Data.Sequence.Internal Methods traverse :: Applicative f => (a -> f b) -> FingerTree a -> f ( FingerTree b) Source # sequenceA :: Applicative f => FingerTree (f a) -> f ( FingerTree a) Source # mapM :: Monad m => (a -> m b) -> FingerTree a -> m ( FingerTree b) Source # sequence :: Monad m => FingerTree (m a) -> m ( FingerTree a) Source # |
|
| Traversable Digit | |
|
Defined in Data.Sequence.Internal |
|
| Traversable Node | |
|
Defined in Data.Sequence.Internal |
|
| Traversable Elem | |
|
Defined in Data.Sequence.Internal |
|
| Traversable ViewL | |
|
Defined in Data.Sequence.Internal |
|
| Traversable ViewR | |
|
Defined in Data.Sequence.Internal |
|
| Traversable Window | |
|
Defined in System.Console.Terminal.Common |
|
| Traversable SimpleDoc | |
|
Defined in Text.PrettyPrint.Annotated.WL Methods traverse :: Applicative f => (a -> f b) -> SimpleDoc a -> f ( SimpleDoc b) Source # sequenceA :: Applicative f => SimpleDoc (f a) -> f ( SimpleDoc a) Source # mapM :: Monad m => (a -> m b) -> SimpleDoc a -> m ( SimpleDoc b) Source # sequence :: Monad m => SimpleDoc (m a) -> m ( SimpleDoc a) Source # |
|
| Traversable Node Source # | |
|
Defined in Hedgehog.Internal.Tree |
|
| Traversable Tree Source # | |
|
Defined in Hedgehog.Internal.Tree |
|
| Traversable Coverage Source # | |
|
Defined in Hedgehog.Internal.Property Methods traverse :: Applicative f => (a -> f b) -> Coverage a -> f ( Coverage b) Source # sequenceA :: Applicative f => Coverage (f a) -> f ( Coverage a) Source # mapM :: Monad m => (a -> m b) -> Coverage a -> m ( Coverage b) Source # sequence :: Monad m => Coverage (m a) -> m ( Coverage a) Source # |
|
| Traversable Label Source # | |
|
Defined in Hedgehog.Internal.Property |
|
| Traversable Concrete Source # | |
|
Defined in Hedgehog.Internal.State Methods traverse :: Applicative f => (a -> f b) -> Concrete a -> f ( Concrete b) Source # sequenceA :: Applicative f => Concrete (f a) -> f ( Concrete a) Source # mapM :: Monad m => (a -> m b) -> Concrete a -> m ( Concrete b) Source # sequence :: Monad m => Concrete (m a) -> m ( Concrete a) Source # |
|
| Traversable Report Source # | |
|
Defined in Hedgehog.Internal.Report |
|
| Traversable ( Either a) |
Since: base-4.7.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f ( Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f ( Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m ( Either a b) Source # sequence :: Monad m => Either a (m a0) -> m ( Either a a0) Source # |
|
| Traversable ( V1 :: Type -> Type ) |
Since: base-4.9.0.0 |
| Traversable ( U1 :: Type -> Type ) |
Since: base-4.9.0.0 |
| Traversable ( UAddr :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( UChar :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( UDouble :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( UFloat :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( UInt :: Type -> Type ) |
Since: base-4.9.0.0 |
| Traversable ( UWord :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( (,) a) |
Since: base-4.7.0.0 |
| Ix i => Traversable ( Array i) |
Since: base-2.1 |
|
Defined in Data.Traversable |
|
| Traversable ( Arg a) |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup |
|
| Traversable ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( Map k) |
Traverses in order of increasing key. |
|
Defined in Data.Map.Internal |
|
| Traversable f => Traversable ( MaybeT f) | |
|
Defined in Control.Monad.Trans.Maybe Methods traverse :: Applicative f0 => (a -> f0 b) -> MaybeT f a -> f0 ( MaybeT f b) Source # sequenceA :: Applicative f0 => MaybeT f (f0 a) -> f0 ( MaybeT f a) Source # mapM :: Monad m => (a -> m b) -> MaybeT f a -> m ( MaybeT f b) Source # sequence :: Monad m => MaybeT f (m a) -> m ( MaybeT f a) Source # |
|
| Traversable f => Traversable ( ListT f) | |
|
Defined in Control.Monad.Trans.List |
|
| Traversable ( Vec n) Source # | |
|
Defined in Hedgehog.Internal.Gen |
|
| Traversable f => Traversable ( Rec1 f) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Traversable ( Const m :: Type -> Type ) |
Since: base-4.7.0.0 |
|
Defined in Data.Traversable |
|
| Traversable f => Traversable ( Ap f) |
Since: base-4.12.0.0 |
|
Defined in Data.Traversable |
|
| Traversable f => Traversable ( Alt f) |
Since: base-4.12.0.0 |
|
Defined in Data.Traversable |
|
| Traversable f => Traversable ( ExceptT e f) | |
|
Defined in Control.Monad.Trans.Except Methods traverse :: Applicative f0 => (a -> f0 b) -> ExceptT e f a -> f0 ( ExceptT e f b) Source # sequenceA :: Applicative f0 => ExceptT e f (f0 a) -> f0 ( ExceptT e f a) Source # mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m ( ExceptT e f b) Source # sequence :: Monad m => ExceptT e f (m a) -> m ( ExceptT e f a) Source # |
|
| Traversable f => Traversable ( WriterT w f) | |
|
Defined in Control.Monad.Trans.Writer.Lazy Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 ( WriterT w f b) Source # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 ( WriterT w f a) Source # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m ( WriterT w f b) Source # sequence :: Monad m => WriterT w f (m a) -> m ( WriterT w f a) Source # |
|
| Traversable f => Traversable ( ErrorT e f) | |
|
Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 ( ErrorT e f b) Source # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 ( ErrorT e f a) Source # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m ( ErrorT e f b) Source # sequence :: Monad m => ErrorT e f (m a) -> m ( ErrorT e f a) Source # |
|
| Traversable f => Traversable ( IdentityT f) | |
|
Defined in Control.Monad.Trans.Identity Methods traverse :: Applicative f0 => (a -> f0 b) -> IdentityT f a -> f0 ( IdentityT f b) Source # sequenceA :: Applicative f0 => IdentityT f (f0 a) -> f0 ( IdentityT f a) Source # mapM :: Monad m => (a -> m b) -> IdentityT f a -> m ( IdentityT f b) Source # sequence :: Monad m => IdentityT f (m a) -> m ( IdentityT f a) Source # |
|
| Traversable f => Traversable ( WriterT w f) | |
|
Defined in Control.Monad.Trans.Writer.Strict Methods traverse :: Applicative f0 => (a -> f0 b) -> WriterT w f a -> f0 ( WriterT w f b) Source # sequenceA :: Applicative f0 => WriterT w f (f0 a) -> f0 ( WriterT w f a) Source # mapM :: Monad m => (a -> m b) -> WriterT w f a -> m ( WriterT w f b) Source # sequence :: Monad m => WriterT w f (m a) -> m ( WriterT w f a) Source # |
|
| Traversable ( Tagged s) | |
|
Defined in Data.Tagged Methods traverse :: Applicative f => (a -> f b) -> Tagged s a -> f ( Tagged s b) Source # sequenceA :: Applicative f => Tagged s (f a) -> f ( Tagged s a) Source # mapM :: Monad m => (a -> m b) -> Tagged s a -> m ( Tagged s b) Source # sequence :: Monad m => Tagged s (m a) -> m ( Tagged s a) Source # |
|
| Traversable ( K1 i c :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| ( Traversable f, Traversable g) => Traversable (f :+: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) Source # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) Source # |
|
| ( Traversable f, Traversable g) => Traversable (f :*: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source # sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) Source # sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) Source # |
|
| ( Traversable f, Traversable g) => Traversable ( Product f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Product Methods traverse :: Applicative f0 => (a -> f0 b) -> Product f g a -> f0 ( Product f g b) Source # sequenceA :: Applicative f0 => Product f g (f0 a) -> f0 ( Product f g a) Source # mapM :: Monad m => (a -> m b) -> Product f g a -> m ( Product f g b) Source # sequence :: Monad m => Product f g (m a) -> m ( Product f g a) Source # |
|
| ( Traversable f, Traversable g) => Traversable ( Sum f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Sum |
|
| Traversable f => Traversable ( M1 i c f) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 ( M1 i c f b) Source # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 ( M1 i c f a) Source # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m ( M1 i c f b) Source # sequence :: Monad m => M1 i c f (m a) -> m ( M1 i c f a) Source # |
|
| ( Traversable f, Traversable g) => Traversable (f :.: g) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source # |
|
| ( Traversable f, Traversable g) => Traversable ( Compose f g) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 ( Compose f g b) Source # sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 ( Compose f g a) Source # mapM :: Monad m => (a -> m b) -> Compose f g a -> m ( Compose f g b) Source # sequence :: Monad m => Compose f g (m a) -> m ( Compose f g a) Source # |
|
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 Source #
An associative operation.
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
Instances
class Semigroup a => Monoid a where Source #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
- Right identity
-
x<>mempty= x - Left identity
-
mempty<>x = x - Associativity
-
x(<>(y<>z) = (x<>y)<>zSemigrouplaw) - Concatenation
-
mconcat=foldr(<>)mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define
newtype
s and make those instances
of
Monoid
, e.g.
Sum
and
Product
.
NOTE
:
Semigroup
is a superclass of
Monoid
since
base-4.11.0.0
.
Minimal complete definition
Methods
Identity of
mappend
>>>"Hello world" <> mempty"Hello world"
mappend :: a -> a -> a Source #
An associative operation
NOTE
: This method is redundant and has the default
implementation
since
base-4.11.0.0
.
Should it be implemented manually, since
mappend
= (
<>
)
mappend
is a synonym for
(
<>
), it is expected that the two functions are defined the same
way. In a future GHC release
mappend
will be removed from
Monoid
.
Fold a list using the monoid.
For most types, the default definition for
mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>mconcat ["Hello", " ", "Haskell", "!"]"Hello Haskell!"
Instances
| Monoid Ordering |
Since: base-2.1 |
| Monoid () |
Since: base-2.1 |
| Monoid All |
Since: base-2.1 |
| Monoid Any |
Since: base-2.1 |
| Monoid ShortByteString | |
|
Defined in Data.ByteString.Short.Internal Methods mempty :: ShortByteString Source # mappend :: ShortByteString -> ShortByteString -> ShortByteString Source # mconcat :: [ ShortByteString ] -> ShortByteString Source # |
|
| Monoid ByteString | |
|
Defined in Data.ByteString.Lazy.Internal Methods mempty :: ByteString Source # mappend :: ByteString -> ByteString -> ByteString Source # mconcat :: [ ByteString ] -> ByteString Source # |
|
| Monoid ByteString | |
|
Defined in Data.ByteString.Internal Methods mempty :: ByteString Source # mappend :: ByteString -> ByteString -> ByteString Source # mconcat :: [ ByteString ] -> ByteString Source # |
|
| Monoid Builder | |
| Monoid IntSet | |
| Monoid Doc | |
| Monoid LabelName Source # | |
| Monoid CoverCount Source # | |
|
Defined in Hedgehog.Internal.Property Methods mempty :: CoverCount Source # mappend :: CoverCount -> CoverCount -> CoverCount Source # mconcat :: [ CoverCount ] -> CoverCount Source # |
|
| Monoid Cover Source # | |
| Monoid Journal Source # | |
| Monoid Summary Source # | |
| Monoid [a] |
Since: base-2.1 |
| Semigroup a => Monoid ( Maybe a) |
Lift a semigroup into
Since 4.11.0
: constraint on inner
Since: base-2.1 |
| Monoid a => Monoid ( IO a) |
Since: base-4.9.0.0 |
| Monoid p => Monoid ( Par1 p) |
Since: base-4.12.0.0 |
| ( Semigroup a, Monoid a) => Monoid ( Concurrently a) |
Since: async-2.1.0 |
|
Defined in Control.Concurrent.Async Methods mempty :: Concurrently a Source # mappend :: Concurrently a -> Concurrently a -> Concurrently a Source # mconcat :: [ Concurrently a] -> Concurrently a Source # |
|
| Monoid a => Monoid ( Identity a) |
Since: base-4.9.0.0 |
| ( Ord a, Bounded a) => Monoid ( Min a) |
Since: base-4.9.0.0 |
| ( Ord a, Bounded a) => Monoid ( Max a) |
Since: base-4.9.0.0 |
| Monoid m => Monoid ( WrappedMonoid m) |
Since: base-4.9.0.0 |
|
Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # mconcat :: [ WrappedMonoid m] -> WrappedMonoid m Source # |
|
| Semigroup a => Monoid ( Option a) |
Since: base-4.9.0.0 |
| Monoid ( First a) |
Since: base-2.1 |
| Monoid ( Last a) |
Since: base-2.1 |
| Monoid a => Monoid ( Dual a) |
Since: base-2.1 |
| Monoid ( Endo a) |
Since: base-2.1 |
| Num a => Monoid ( Sum a) |
Since: base-2.1 |
| Num a => Monoid ( Product a) |
Since: base-2.1 |
| Monoid a => Monoid ( Down a) |
Since: base-4.11.0.0 |
| Num a => Monoid ( Colour a) | |
| Num a => Monoid ( AlphaColour a) | |
|
Defined in Data.Colour.Internal Methods mempty :: AlphaColour a Source # mappend :: AlphaColour a -> AlphaColour a -> AlphaColour a Source # mconcat :: [ AlphaColour a] -> AlphaColour a Source # |
|
| Monoid ( IntMap a) | |
| Monoid ( Seq a) | |
| Ord a => Monoid ( Set a) | |
| Monoid ( Doc a) | |
| Monoid ( Doc a) | |
| Monoid (MergeSet a) | |
| ( Semigroup a, Monoid a) => Monoid ( Coverage a) Source # | |
| Monoid b => Monoid (a -> b) |
Since: base-2.1 |
| Monoid ( U1 p) |
Since: base-4.12.0.0 |
| ( Monoid a, Monoid b) => Monoid (a, b) |
Since: base-2.1 |
| Monoid a => Monoid ( ST s a) |
Since: base-4.11.0.0 |
| Monoid ( Proxy s) |
Since: base-4.7.0.0 |
| Ord k => Monoid ( Map k v) | |
| ( MonadBaseControl IO m, Semigroup a, Monoid a) => Monoid ( Concurrently m a) | |
|
Defined in Control.Concurrent.Async.Lifted Methods mempty :: Concurrently m a Source # mappend :: Concurrently m a -> Concurrently m a -> Concurrently m a Source # mconcat :: [ Concurrently m a] -> Concurrently m a Source # |
|
| ( Monad m, Monoid a) => Monoid ( GenT m a) Source # | |
| Monoid (f p) => Monoid ( Rec1 f p) |
Since: base-4.12.0.0 |
| ( Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) |
Since: base-2.1 |
| Monoid a => Monoid ( Const a b) |
Since: base-4.9.0.0 |
| ( Applicative f, Monoid a) => Monoid ( Ap f a) |
Since: base-4.12.0.0 |
| Alternative f => Monoid ( Alt f a) |
Since: base-4.8.0.0 |
| ( Semigroup a, Monoid a) => Monoid ( Tagged s a) | |
| Monoid c => Monoid ( K1 i c p) |
Since: base-4.12.0.0 |
| ( Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) |
Since: base-4.12.0.0 |
| ( Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) |
Since: base-2.1 |
| Monoid (f p) => Monoid ( M1 i c f p) |
Since: base-4.12.0.0 |
| Monoid (f (g p)) => Monoid ((f :.: g) p) |
Since: base-4.12.0.0 |
| ( Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) |
Since: base-2.1 |
Instances
The character type
Char
is an enumeration whose values represent
Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see
http://www.unicode.org/
for details). This set extends the ISO 8859-1
(Latin-1) character set (the first 256 characters), which is itself an extension
of the ASCII character set (the first 128 characters). A character literal in
Haskell has type
Char
.
To convert a
Char
to or from the corresponding
Int
value defined
by Unicode, use
toEnum
and
fromEnum
from the
Enum
class respectively (or equivalently
ord
and
chr
).
Instances
| Bounded Char |
Since: base-2.1 |
| Enum Char |
Since: base-2.1 |
| Eq Char | |
| Ord Char | |
| Read Char |
Since: base-2.1 |
| Show Char |
Since: base-2.1 |
| Ix Char |
Since: base-2.1 |
| PrintfArg Char |
Since: base-2.1 |
|
Defined in Text.Printf |
|
| IsChar Char |
Since: base-2.1 |
| ToRegionContent String | |
|
Defined in System.Console.Regions Methods |
|
| Outputable String | |
| NFData Char | |
|
Defined in Control.DeepSeq |
|
| Hashable Char | |
| Random Char | |
| Uniform Char | |
|
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Char Source # |
|
| UniformRange Char | |
|
Defined in System.Random.Internal |
|
| ErrorList Char | |
| Pretty Char | |
| Lift Char | |
| Generic1 ( URec Char :: k -> Type ) |
Since: base-4.9.0.0 |
| Foldable ( UChar :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => UChar m -> m Source # foldMap :: Monoid m => (a -> m) -> UChar a -> m Source # foldMap' :: Monoid m => (a -> m) -> UChar a -> m Source # foldr :: (a -> b -> b) -> b -> UChar a -> b Source # foldr' :: (a -> b -> b) -> b -> UChar a -> b Source # foldl :: (b -> a -> b) -> b -> UChar a -> b Source # foldl' :: (b -> a -> b) -> b -> UChar a -> b Source # foldr1 :: (a -> a -> a) -> UChar a -> a Source # foldl1 :: (a -> a -> a) -> UChar a -> a Source # toList :: UChar a -> [a] Source # null :: UChar a -> Bool Source # length :: UChar a -> Int Source # elem :: Eq a => a -> UChar a -> Bool Source # maximum :: Ord a => UChar a -> a Source # minimum :: Ord a => UChar a -> a Source # |
|
| Traversable ( UChar :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Functor ( URec Char :: Type -> Type ) |
Since: base-4.9.0.0 |
| Eq ( URec Char p) |
Since: base-4.9.0.0 |
| Ord ( URec Char p) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods compare :: URec Char p -> URec Char p -> Ordering Source # (<) :: URec Char p -> URec Char p -> Bool Source # (<=) :: URec Char p -> URec Char p -> Bool Source # (>) :: URec Char p -> URec Char p -> Bool Source # (>=) :: URec Char p -> URec Char p -> Bool Source # |
|
| Show ( URec Char p) |
Since: base-4.9.0.0 |
| Generic ( URec Char p) |
Since: base-4.9.0.0 |
| data URec Char (p :: k) |
Used for marking occurrences of
Since: base-4.9.0.0 |
| type Rep1 ( URec Char :: k -> Type ) | |
|
Defined in GHC.Generics |
|
| type Rep ( URec Char p) | |
|
Defined in GHC.Generics |
|
Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.
Instances
| Eq Double |
Note that due to the presence of
Also note that
|
| Floating Double |
Since: base-2.1 |
|
Defined in GHC.Float Methods exp :: Double -> Double Source # log :: Double -> Double Source # sqrt :: Double -> Double Source # (**) :: Double -> Double -> Double Source # logBase :: Double -> Double -> Double Source # sin :: Double -> Double Source # cos :: Double -> Double Source # tan :: Double -> Double Source # asin :: Double -> Double Source # acos :: Double -> Double Source # atan :: Double -> Double Source # sinh :: Double -> Double Source # cosh :: Double -> Double Source # tanh :: Double -> Double Source # asinh :: Double -> Double Source # acosh :: Double -> Double Source # atanh :: Double -> Double Source # log1p :: Double -> Double Source # expm1 :: Double -> Double Source # |
|
| Ord Double |
Note that due to the presence of
Also note that, due to the same,
|
| Read Double |
Since: base-2.1 |
| RealFloat Double |
Since: base-2.1 |
|
Defined in GHC.Float Methods floatRadix :: Double -> Integer Source # floatDigits :: Double -> Int Source # floatRange :: Double -> ( Int , Int ) Source # decodeFloat :: Double -> ( Integer , Int ) Source # encodeFloat :: Integer -> Int -> Double Source # exponent :: Double -> Int Source # significand :: Double -> Double Source # scaleFloat :: Int -> Double -> Double Source # isNaN :: Double -> Bool Source # isInfinite :: Double -> Bool Source # isDenormalized :: Double -> Bool Source # isNegativeZero :: Double -> Bool Source # |
|
| PrintfArg Double |
Since: base-2.1 |
|
Defined in Text.Printf Methods formatArg :: Double -> FieldFormatter Source # parseFormat :: Double -> ModifierParser Source # |
|
| NFData Double | |
|
Defined in Control.DeepSeq |
|
| Erf Double | |
| InvErf Double | |
| Hashable Double |
Note
: prior to
The
Since: hashable-1.3.0.0 |
| Random Double |
Note
-
|
| UniformRange Double | |
|
Defined in System.Random.Internal |
|
| Pretty Double | |
| Lift Double | |
| Generic1 ( URec Double :: k -> Type ) |
Since: base-4.9.0.0 |
| Foldable ( UDouble :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => UDouble m -> m Source # foldMap :: Monoid m => (a -> m) -> UDouble a -> m Source # foldMap' :: Monoid m => (a -> m) -> UDouble a -> m Source # foldr :: (a -> b -> b) -> b -> UDouble a -> b Source # foldr' :: (a -> b -> b) -> b -> UDouble a -> b Source # foldl :: (b -> a -> b) -> b -> UDouble a -> b Source # foldl' :: (b -> a -> b) -> b -> UDouble a -> b Source # foldr1 :: (a -> a -> a) -> UDouble a -> a Source # foldl1 :: (a -> a -> a) -> UDouble a -> a Source # toList :: UDouble a -> [a] Source # null :: UDouble a -> Bool Source # length :: UDouble a -> Int Source # elem :: Eq a => a -> UDouble a -> Bool Source # maximum :: Ord a => UDouble a -> a Source # minimum :: Ord a => UDouble a -> a Source # |
|
| Traversable ( UDouble :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Functor ( URec Double :: Type -> Type ) |
Since: base-4.9.0.0 |
| Eq ( URec Double p) |
Since: base-4.9.0.0 |
| Ord ( URec Double p) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods compare :: URec Double p -> URec Double p -> Ordering Source # (<) :: URec Double p -> URec Double p -> Bool Source # (<=) :: URec Double p -> URec Double p -> Bool Source # (>) :: URec Double p -> URec Double p -> Bool Source # (>=) :: URec Double p -> URec Double p -> Bool Source # max :: URec Double p -> URec Double p -> URec Double p Source # min :: URec Double p -> URec Double p -> URec Double p Source # |
|
| Show ( URec Double p) |
Since: base-4.9.0.0 |
| Generic ( URec Double p) |
Since: base-4.9.0.0 |
| data URec Double (p :: k) |
Used for marking occurrences of
Since: base-4.9.0.0 |
| type Rep1 ( URec Double :: k -> Type ) | |
|
Defined in GHC.Generics |
|
| type Rep ( URec Double p) | |
|
Defined in GHC.Generics |
|
Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.
Instances
| Eq Float |
Note that due to the presence of
Also note that
|
| Floating Float |
Since: base-2.1 |
|
Defined in GHC.Float Methods exp :: Float -> Float Source # log :: Float -> Float Source # sqrt :: Float -> Float Source # (**) :: Float -> Float -> Float Source # logBase :: Float -> Float -> Float Source # sin :: Float -> Float Source # cos :: Float -> Float Source # tan :: Float -> Float Source # asin :: Float -> Float Source # acos :: Float -> Float Source # atan :: Float -> Float Source # sinh :: Float -> Float Source # cosh :: Float -> Float Source # tanh :: Float -> Float Source # asinh :: Float -> Float Source # acosh :: Float -> Float Source # atanh :: Float -> Float Source # log1p :: Float -> Float Source # expm1 :: Float -> Float Source # |
|
| Ord Float |
Note that due to the presence of
Also note that, due to the same,
|
|
Defined in GHC.Classes |
|
| Read Float |
Since: base-2.1 |
| RealFloat Float |
Since: base-2.1 |
|
Defined in GHC.Float Methods floatRadix :: Float -> Integer Source # floatDigits :: Float -> Int Source # floatRange :: Float -> ( Int , Int ) Source # decodeFloat :: Float -> ( Integer , Int ) Source # encodeFloat :: Integer -> Int -> Float Source # exponent :: Float -> Int Source # significand :: Float -> Float Source # scaleFloat :: Int -> Float -> Float Source # isNaN :: Float -> Bool Source # isInfinite :: Float -> Bool Source # isDenormalized :: Float -> Bool Source # isNegativeZero :: Float -> Bool Source # |
|
| PrintfArg Float |
Since: base-2.1 |
|
Defined in Text.Printf Methods formatArg :: Float -> FieldFormatter Source # parseFormat :: Float -> ModifierParser Source # |
|
| NFData Float | |
|
Defined in Control.DeepSeq |
|
| Erf Float | |
| InvErf Float | |
| Hashable Float |
Note
: prior to
The
Since: hashable-1.3.0.0 |
| Random Float |
Note
-
|
| UniformRange Float | |
|
Defined in System.Random.Internal |
|
| Pretty Float | |
| Lift Float | |
| Generic1 ( URec Float :: k -> Type ) |
Since: base-4.9.0.0 |
| Foldable ( UFloat :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => UFloat m -> m Source # foldMap :: Monoid m => (a -> m) -> UFloat a -> m Source # foldMap' :: Monoid m => (a -> m) -> UFloat a -> m Source # foldr :: (a -> b -> b) -> b -> UFloat a -> b Source # foldr' :: (a -> b -> b) -> b -> UFloat a -> b Source # foldl :: (b -> a -> b) -> b -> UFloat a -> b Source # foldl' :: (b -> a -> b) -> b -> UFloat a -> b Source # foldr1 :: (a -> a -> a) -> UFloat a -> a Source # foldl1 :: (a -> a -> a) -> UFloat a -> a Source # toList :: UFloat a -> [a] Source # null :: UFloat a -> Bool Source # length :: UFloat a -> Int Source # elem :: Eq a => a -> UFloat a -> Bool Source # maximum :: Ord a => UFloat a -> a Source # minimum :: Ord a => UFloat a -> a Source # |
|
| Traversable ( UFloat :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Functor ( URec Float :: Type -> Type ) |
Since: base-4.9.0.0 |
| Eq ( URec Float p) | |
| Ord ( URec Float p) | |
|
Defined in GHC.Generics Methods compare :: URec Float p -> URec Float p -> Ordering Source # (<) :: URec Float p -> URec Float p -> Bool Source # (<=) :: URec Float p -> URec Float p -> Bool Source # (>) :: URec Float p -> URec Float p -> Bool Source # (>=) :: URec Float p -> URec Float p -> Bool Source # max :: URec Float p -> URec Float p -> URec Float p Source # min :: URec Float p -> URec Float p -> URec Float p Source # |
|
| Show ( URec Float p) | |
| Generic ( URec Float p) | |
| data URec Float (p :: k) |
Used for marking occurrences of
Since: base-4.9.0.0 |
| type Rep1 ( URec Float :: k -> Type ) | |
|
Defined in GHC.Generics |
|
| type Rep ( URec Float p) | |
|
Defined in GHC.Generics |
|
A fixed-precision integer type with at least the range
[-2^29 .. 2^29-1]
.
The exact range for a given implementation can be determined by using
minBound
and
maxBound
from the
Bounded
class.
Instances
| Bounded Int |
Since: base-2.1 |
| Enum Int |
Since: base-2.1 |
| Eq Int | |
| Integral Int |
Since: base-2.0.1 |
| Num Int |
Since: base-2.1 |
| Ord Int | |
| Read Int |
Since: base-2.1 |
| Real Int |
Since: base-2.0.1 |
| Show Int |
Since: base-2.1 |
| Ix Int |
Since: base-2.1 |
|
Defined in GHC.Ix |
|
| PrintfArg Int |
Since: base-2.1 |
|
Defined in Text.Printf |
|
| Bits Int |
Since: base-2.1 |
|
Defined in Data.Bits Methods (.&.) :: Int -> Int -> Int Source # (.|.) :: Int -> Int -> Int Source # xor :: Int -> Int -> Int Source # complement :: Int -> Int Source # shift :: Int -> Int -> Int Source # rotate :: Int -> Int -> Int Source # setBit :: Int -> Int -> Int Source # clearBit :: Int -> Int -> Int Source # complementBit :: Int -> Int -> Int Source # testBit :: Int -> Int -> Bool Source # bitSizeMaybe :: Int -> Maybe Int Source # bitSize :: Int -> Int Source # isSigned :: Int -> Bool Source # shiftL :: Int -> Int -> Int Source # unsafeShiftL :: Int -> Int -> Int Source # shiftR :: Int -> Int -> Int Source # unsafeShiftR :: Int -> Int -> Int Source # rotateL :: Int -> Int -> Int Source # |
|
| FiniteBits Int |
Since: base-4.6.0.0 |
| NFData Int | |
|
Defined in Control.DeepSeq |
|
| Hashable Int | |
| Random Int | |
| Uniform Int | |
|
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Int Source # |
|
| UniformRange Int | |
|
Defined in System.Random.Internal |
|
| Pretty Int | |
| Lift Int | |
| Generic1 ( URec Int :: k -> Type ) |
Since: base-4.9.0.0 |
| Foldable ( UInt :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => UInt m -> m Source # foldMap :: Monoid m => (a -> m) -> UInt a -> m Source # foldMap' :: Monoid m => (a -> m) -> UInt a -> m Source # foldr :: (a -> b -> b) -> b -> UInt a -> b Source # foldr' :: (a -> b -> b) -> b -> UInt a -> b Source # foldl :: (b -> a -> b) -> b -> UInt a -> b Source # foldl' :: (b -> a -> b) -> b -> UInt a -> b Source # foldr1 :: (a -> a -> a) -> UInt a -> a Source # foldl1 :: (a -> a -> a) -> UInt a -> a Source # toList :: UInt a -> [a] Source # null :: UInt a -> Bool Source # length :: UInt a -> Int Source # elem :: Eq a => a -> UInt a -> Bool Source # maximum :: Ord a => UInt a -> a Source # minimum :: Ord a => UInt a -> a Source # |
|
| Traversable ( UInt :: Type -> Type ) |
Since: base-4.9.0.0 |
| Functor ( URec Int :: Type -> Type ) |
Since: base-4.9.0.0 |
| Eq ( URec Int p) |
Since: base-4.9.0.0 |
| Ord ( URec Int p) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods compare :: URec Int p -> URec Int p -> Ordering Source # (<) :: URec Int p -> URec Int p -> Bool Source # (<=) :: URec Int p -> URec Int p -> Bool Source # (>) :: URec Int p -> URec Int p -> Bool Source # (>=) :: URec Int p -> URec Int p -> Bool Source # |
|
| Show ( URec Int p) |
Since: base-4.9.0.0 |
| Generic ( URec Int p) |
Since: base-4.9.0.0 |
| data URec Int (p :: k) |
Used for marking occurrences of
Since: base-4.9.0.0 |
| type Rep1 ( URec Int :: k -> Type ) | |
|
Defined in GHC.Generics |
|
| type Rep ( URec Int p) | |
|
Defined in GHC.Generics |
|
Arbitrary precision integers. In contrast with fixed-size integral types
such as
Int
, the
Integer
type represents the entire infinite range of
integers.
For more information about this type's representation, see the comments in its implementation.
Instances
The
Maybe
type encapsulates an optional value. A value of type
either contains a value of type
Maybe
a
a
(represented as
),
or it is empty (represented as
Just
a
Nothing
). Using
Maybe
is a good way to
deal with errors or exceptional cases without resorting to drastic
measures such as
error
.
The
Maybe
type is also a monad. It is a simple kind of error
monad, where all errors are represented by
Nothing
. A richer
error monad can be built using the
Either
type.
Instances
| Monad Maybe |
Since: base-2.1 |
| Functor Maybe |
Since: base-2.1 |
| MonadFail Maybe |
Since: base-4.9.0.0 |
| Applicative Maybe |
Since: base-2.1 |
| Foldable Maybe |
Since: base-2.1 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Maybe m -> m Source # foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source # foldMap' :: Monoid m => (a -> m) -> Maybe a -> m Source # foldr :: (a -> b -> b) -> b -> Maybe a -> b Source # foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source # foldl :: (b -> a -> b) -> b -> Maybe a -> b Source # foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source # foldr1 :: (a -> a -> a) -> Maybe a -> a Source # foldl1 :: (a -> a -> a) -> Maybe a -> a Source # toList :: Maybe a -> [a] Source # null :: Maybe a -> Bool Source # length :: Maybe a -> Int Source # elem :: Eq a => a -> Maybe a -> Bool Source # maximum :: Ord a => Maybe a -> a Source # minimum :: Ord a => Maybe a -> a Source # |
|
| Traversable Maybe |
Since: base-2.1 |
|
Defined in Data.Traversable |
|
| Alternative Maybe |
Since: base-2.1 |
| Eq1 Maybe |
Since: base-4.9.0.0 |
| Ord1 Maybe |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes |
|
| Show1 Maybe |
Since: base-4.9.0.0 |
| Read1 Maybe |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes Methods liftReadsPrec :: ( Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ( Maybe a) Source # liftReadList :: ( Int -> ReadS a) -> ReadS [a] -> ReadS [ Maybe a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ( Maybe a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [ Maybe a] Source # |
|
| MonadZip Maybe |
Since: base-4.8.0.0 |
| MonadPlus Maybe |
Since: base-2.1 |
| MonadThrow Maybe | |
| NFData1 Maybe |
Since: deepseq-1.4.3.0 |
|
Defined in Control.DeepSeq |
|
| Hashable1 Maybe | |
|
Defined in Data.Hashable.Class |
|
| MonadBase Maybe Maybe | |
| MonadBaseControl Maybe Maybe | |
| MonadError () Maybe |
Since: mtl-2.2.2 |
|
Defined in Control.Monad.Error.Class Methods throwError :: () -> Maybe a Source # catchError :: Maybe a -> (() -> Maybe a) -> Maybe a Source # |
|
| Lift a => Lift ( Maybe a :: Type ) | |
| Eq a => Eq ( Maybe a) |
Since: base-2.1 |
| Ord a => Ord ( Maybe a) |
Since: base-2.1 |
| Read a => Read ( Maybe a) |
Since: base-2.1 |
| Show a => Show ( Maybe a) |
Since: base-2.1 |
| Generic ( Maybe a) |
Since: base-4.6.0.0 |
| Semigroup a => Semigroup ( Maybe a) |
Since: base-4.9.0.0 |
| Semigroup a => Monoid ( Maybe a) |
Lift a semigroup into
Since 4.11.0
: constraint on inner
Since: base-2.1 |
| NFData a => NFData ( Maybe a) | |
|
Defined in Control.DeepSeq |
|
| Hashable a => Hashable ( Maybe a) | |
| Pretty a => Pretty ( Maybe a) | |
| SingKind a => SingKind ( Maybe a) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Associated Types type DemoteRep ( Maybe a) |
|
| Generic1 Maybe |
Since: base-4.6.0.0 |
| SingI (' Nothing :: Maybe a) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| SingI a2 => SingI (' Just a2 :: Maybe a1) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics |
|
| type StM Maybe a | |
|
Defined in Control.Monad.Trans.Control |
|
| type Rep ( Maybe a) | |
|
Defined in GHC.Generics
type
Rep
(
Maybe
a) =
D1
('
MetaData
"Maybe" "GHC.Maybe" "base" '
False
) (
C1
('
MetaCons
"Nothing" '
PrefixI
'
False
) (
U1
::
Type
->
Type
)
:+:
C1
('
MetaCons
"Just" '
PrefixI
'
False
) (
S1
('
MetaSel
('
Nothing
::
Maybe
Symbol
) '
NoSourceUnpackedness
'
NoSourceStrictness
'
DecidedLazy
) (
Rec0
a)))
|
|
| type DemoteRep ( Maybe a) | |
|
Defined in GHC.Generics |
|
| data Sing (b :: Maybe a) | |
| type Rep1 Maybe | |
|
Defined in GHC.Generics |
|
Instances
A value of type
is a computation which, when performed,
does some I/O before returning a value of type
IO
a
a
.
There is really only one way to "perform" an I/O action: bind it to
Main.main
in your program. When your program is run, the I/O will
be performed. It isn't possible to perform I/O from an arbitrary
function, unless that function is itself in the
IO
monad and called
at some point, directly or indirectly, from
Main.main
.
IO
is a monad, so
IO
actions can be combined using either the do-notation
or the
>>
and
>>=
operations from the
Monad
class.
Instances
Instances
| Bounded Word |
Since: base-2.1 |
| Enum Word |
Since: base-2.1 |
| Eq Word | |
| Integral Word |
Since: base-2.1 |
|
Defined in GHC.Real |
|
| Num Word |
Since: base-2.1 |
| Ord Word | |
| Read Word |
Since: base-4.5.0.0 |
| Real Word |
Since: base-2.1 |
| Show Word |
Since: base-2.1 |
| Ix Word |
Since: base-4.6.0.0 |
| PrintfArg Word |
Since: base-2.1 |
|
Defined in Text.Printf |
|
| Bits Word |
Since: base-2.1 |
|
Defined in Data.Bits Methods (.&.) :: Word -> Word -> Word Source # (.|.) :: Word -> Word -> Word Source # xor :: Word -> Word -> Word Source # complement :: Word -> Word Source # shift :: Word -> Int -> Word Source # rotate :: Word -> Int -> Word Source # setBit :: Word -> Int -> Word Source # clearBit :: Word -> Int -> Word Source # complementBit :: Word -> Int -> Word Source # testBit :: Word -> Int -> Bool Source # bitSizeMaybe :: Word -> Maybe Int Source # bitSize :: Word -> Int Source # isSigned :: Word -> Bool Source # shiftL :: Word -> Int -> Word Source # unsafeShiftL :: Word -> Int -> Word Source # shiftR :: Word -> Int -> Word Source # unsafeShiftR :: Word -> Int -> Word Source # rotateL :: Word -> Int -> Word Source # |
|
| FiniteBits Word |
Since: base-4.6.0.0 |
| NFData Word | |
|
Defined in Control.DeepSeq |
|
| Hashable Word | |
| Random Word | |
| Uniform Word | |
|
Defined in System.Random.Internal Methods uniformM :: StatefulGen g m => g -> m Word Source # |
|
| UniformRange Word | |
|
Defined in System.Random.Internal |
|
| Pretty Word | |
| Lift Word | |
| Generic1 ( URec Word :: k -> Type ) |
Since: base-4.9.0.0 |
| Foldable ( UWord :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => UWord m -> m Source # foldMap :: Monoid m => (a -> m) -> UWord a -> m Source # foldMap' :: Monoid m => (a -> m) -> UWord a -> m Source # foldr :: (a -> b -> b) -> b -> UWord a -> b Source # foldr' :: (a -> b -> b) -> b -> UWord a -> b Source # foldl :: (b -> a -> b) -> b -> UWord a -> b Source # foldl' :: (b -> a -> b) -> b -> UWord a -> b Source # foldr1 :: (a -> a -> a) -> UWord a -> a Source # foldl1 :: (a -> a -> a) -> UWord a -> a Source # toList :: UWord a -> [a] Source # null :: UWord a -> Bool Source # length :: UWord a -> Int Source # elem :: Eq a => a -> UWord a -> Bool Source # maximum :: Ord a => UWord a -> a Source # minimum :: Ord a => UWord a -> a Source # |
|
| Traversable ( UWord :: Type -> Type ) |
Since: base-4.9.0.0 |
|
Defined in Data.Traversable |
|
| Functor ( URec Word :: Type -> Type ) |
Since: base-4.9.0.0 |
| Eq ( URec Word p) |
Since: base-4.9.0.0 |
| Ord ( URec Word p) |
Since: base-4.9.0.0 |
|
Defined in GHC.Generics Methods compare :: URec Word p -> URec Word p -> Ordering Source # (<) :: URec Word p -> URec Word p -> Bool Source # (<=) :: URec Word p -> URec Word p -> Bool Source # (>) :: URec Word p -> URec Word p -> Bool Source # (>=) :: URec Word p -> URec Word p -> Bool Source # |
|
| Show ( URec Word p) |
Since: base-4.9.0.0 |
| Generic ( URec Word p) |
Since: base-4.9.0.0 |
| data URec Word (p :: k) |
Used for marking occurrences of
Since: base-4.9.0.0 |
| type Rep1 ( URec Word :: k -> Type ) | |
|
Defined in GHC.Generics |
|
| type Rep ( URec Word p) | |
|
Defined in GHC.Generics |
|
The
Either
type represents values with two possibilities: a value of
type
is either
Either
a b
or
Left
a
.
Right
b
The
Either
type is sometimes used to represent a value which is
either correct or an error; by convention, the
Left
constructor is
used to hold an error value and the
Right
constructor is used to
hold a correct value (mnemonic: "right" also means "correct").
Examples
The type
is the type of values which can be either
a
Either
String
Int
String
or an
Int
. The
Left
constructor can be used only on
String
s, and the
Right
constructor can be used only on
Int
s:
>>>let s = Left "foo" :: Either String Int>>>sLeft "foo">>>let n = Right 3 :: Either String Int>>>nRight 3>>>:type ss :: Either String Int>>>:type nn :: Either String Int
The
fmap
from our
Functor
instance will ignore
Left
values, but
will apply the supplied function to values contained in a
Right
:
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>fmap (*2) sLeft "foo">>>fmap (*2) nRight 6
The
Monad
instance for
Either
allows us to chain together multiple
actions which may fail, and fail overall if any of the individual
steps failed. First we'll write a function that can either parse an
Int
from a
Char
, or fail.
>>>import Data.Char ( digitToInt, isDigit )>>>:{let parseEither :: Char -> Either String Int parseEither c | isDigit c = Right (digitToInt c) | otherwise = Left "parse error">>>:}
The following should work, since both
'1'
and
'2'
can be
parsed as
Int
s.
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither '1' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleRight 3
But the following should fail overall, since the first operation where
we attempt to parse
'm'
as an
Int
will fail:
>>>:{let parseMultiple :: Either String Int parseMultiple = do x <- parseEither 'm' y <- parseEither '2' return (x + y)>>>:}
>>>parseMultipleLeft "parse error"
Instances
| Bifunctor Either |
Since: base-4.8.0.0 |
| Eq2 Either |
Since: base-4.9.0.0 |
| Ord2 Either |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes |
|
| Read2 Either |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes Methods liftReadsPrec2 :: ( Int -> ReadS a) -> ReadS [a] -> ( Int -> ReadS b) -> ReadS [b] -> Int -> ReadS ( Either a b) Source # liftReadList2 :: ( Int -> ReadS a) -> ReadS [a] -> ( Int -> ReadS b) -> ReadS [b] -> ReadS [ Either a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec ( Either a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [ Either a b] Source # |
|
| Show2 Either |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes |
|
| NFData2 Either |
Since: deepseq-1.4.3.0 |
|
Defined in Control.DeepSeq |
|
| Hashable2 Either | |
| MonadError e ( Either e) | |
|
Defined in Control.Monad.Error.Class Methods throwError :: e -> Either e a Source # catchError :: Either e a -> (e -> Either e a) -> Either e a Source # |
|
| ( Lift a, Lift b) => Lift ( Either a b :: Type ) | |
| Monad ( Either e) |
Since: base-4.4.0.0 |
| Functor ( Either a) |
Since: base-3.0 |
| Applicative ( Either e) |
Since: base-3.0 |
|
Defined in Data.Either |
|
| Foldable ( Either a) |
Since: base-4.7.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Either a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> Either a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 Source # toList :: Either a a0 -> [a0] Source # null :: Either a a0 -> Bool Source # length :: Either a a0 -> Int Source # elem :: Eq a0 => a0 -> Either a a0 -> Bool Source # maximum :: Ord a0 => Either a a0 -> a0 Source # minimum :: Ord a0 => Either a a0 -> a0 Source # |
|
| Traversable ( Either a) |
Since: base-4.7.0.0 |
|
Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f ( Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f ( Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m ( Either a b) Source # sequence :: Monad m => Either a (m a0) -> m ( Either a a0) Source # |
|
| Eq a => Eq1 ( Either a) |
Since: base-4.9.0.0 |
| Ord a => Ord1 ( Either a) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes |
|
| Show a => Show1 ( Either a) |
Since: base-4.9.0.0 |
| Read a => Read1 ( Either a) |
Since: base-4.9.0.0 |
|
Defined in Data.Functor.Classes Methods liftReadsPrec :: ( Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS ( Either a a0) Source # liftReadList :: ( Int -> ReadS a0) -> ReadS [a0] -> ReadS [ Either a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec ( Either a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [ Either a a0] Source # |
|
| e ~ SomeException => MonadMask ( Either e) |
Since: exceptions-0.8.3 |
|
Defined in Control.Monad.Catch Methods mask :: (( forall a. Either e a -> Either e a) -> Either e b) -> Either e b Source # uninterruptibleMask :: (( forall a. Either e a -> Either e a) -> Either e b) -> Either e b Source # generalBracket :: Either e a -> (a -> ExitCase b -> Either e c) -> (a -> Either e b) -> Either e (b, c) Source # |
|
| e ~ SomeException => MonadCatch ( Either e) |
Since: exceptions-0.8.3 |
| e ~ SomeException => MonadThrow ( Either e) | |
| NFData a => NFData1 ( Either a) |
Since: deepseq-1.4.3.0 |
|
Defined in Control.DeepSeq |
|
| Hashable a => Hashable1 ( Either a) | |
|
Defined in Data.Hashable.Class |
|
| Generic1 ( Either a :: Type -> Type ) |
Since: base-4.6.0.0 |
| MonadBase ( Either e) ( Either e) | |
| MonadBaseControl ( Either e) ( Either e) | |
| ( Eq a, Eq b) => Eq ( Either a b) |
Since: base-2.1 |
| ( Ord a, Ord b) => Ord ( Either a b) |
Since: base-2.1 |
|
Defined in Data.Either Methods compare :: Either a b -> Either a b -> Ordering Source # (<) :: Either a b -> Either a b -> Bool Source # (<=) :: Either a b -> Either a b -> Bool Source # (>) :: Either a b -> Either a b -> Bool Source # (>=) :: Either a b -> Either a b -> Bool Source # |
|
| ( Read a, Read b) => Read ( Either a b) |
Since: base-3.0 |
| ( Show a, Show b) => Show ( Either a b) |
Since: base-3.0 |
| Generic ( Either a b) |
Since: base-4.6.0.0 |
| Semigroup ( Either a b) |
Since: base-4.9.0.0 |
| ( NFData a, NFData b) => NFData ( Either a b) | |
|
Defined in Control.DeepSeq |
|
| ( Hashable a, Hashable b) => Hashable ( Either a b) | |
| type StM ( Either e) a | |
|
Defined in Control.Monad.Trans.Control |
|
| type Rep1 ( Either a :: Type -> Type ) | |
|
Defined in GHC.Generics
type
Rep1
(
Either
a ::
Type
->
Type
) =
D1
('
MetaData
"Either" "Data.Either" "base" '
False
) (
C1
('
MetaCons
"Left" '
PrefixI
'
False
) (
S1
('
MetaSel
('
Nothing
::
Maybe
Symbol
) '
NoSourceUnpackedness
'
NoSourceStrictness
'
DecidedLazy
) (
Rec0
a))
:+:
C1
('
MetaCons
"Right" '
PrefixI
'
False
) (
S1
('
MetaSel
('
Nothing
::
Maybe
Symbol
) '
NoSourceUnpackedness
'
NoSourceStrictness
'
DecidedLazy
)
Par1
))
|
|
| type Rep ( Either a b) | |
|
Defined in GHC.Generics
type
Rep
(
Either
a b) =
D1
('
MetaData
"Either" "Data.Either" "base" '
False
) (
C1
('
MetaCons
"Left" '
PrefixI
'
False
) (
S1
('
MetaSel
('
Nothing
::
Maybe
Symbol
) '
NoSourceUnpackedness
'
NoSourceStrictness
'
DecidedLazy
) (
Rec0
a))
:+:
C1
('
MetaCons
"Right" '
PrefixI
'
False
) (
S1
('
MetaSel
('
Nothing
::
Maybe
Symbol
) '
NoSourceUnpackedness
'
NoSourceStrictness
'
DecidedLazy
) (
Rec0
b)))
|
|
unzip :: [(a, b)] -> ([a], [b]) Source #
unzip
transforms a list of pairs into a list of first components
and a list of second components.
uncurry :: (a -> b -> c) -> (a, b) -> c Source #
uncurry
converts a curried function to a function on pairs.
Examples
>>>uncurry (+) (1,2)3
>>>uncurry ($) (show, 1)"1"
>>>map (uncurry max) [(1,2), (3,4), (6,8)][2,4,8]
appendFile :: FilePath -> String -> IO () Source #
The computation
appendFile
file str
function appends the string
str
,
to the file
file
.
Note that
writeFile
and
appendFile
write a literal string
to a file. To write a value of any printable type, as with
print
,
use the
show
function to convert the value to a string first.
main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])
writeFile :: FilePath -> String -> IO () Source #
The computation
writeFile
file str
function writes the string
str
,
to the file
file
.
readFile :: FilePath -> IO String Source #
The
readFile
function reads a file and
returns the contents of the file as a string.
The file is read lazily, on demand, as with
getContents
.
interact :: ( String -> String ) -> IO () Source #
The
interact
function takes a function of type
String->String
as its argument. The entire input from the standard input device is
passed to this function as its argument, and the resulting string is
output on the standard output device.
getContents :: IO String Source #
The
getContents
operation returns all user input as a single string,
which is read lazily as it is needed
(same as
hGetContents
stdin
).
type FilePath = String Source #
File and directory names are values of type
String
, whose precise
meaning is operating system dependent. Files can be opened, yielding a
handle which can then be used to operate on the contents of that file.
type IOError = IOException Source #
all :: Foldable t => (a -> Bool ) -> t a -> Bool Source #
Determines whether all elements of the structure satisfy the predicate.
any :: Foldable t => (a -> Bool ) -> t a -> Bool Source #
Determines whether any element of the structure satisfies the predicate.
concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #
Map a function over all the elements of a container and concatenate the resulting lists.
concat :: Foldable t => t [a] -> [a] Source #
The concatenation of all the elements of a container of lists.
sequence_ :: ( Foldable t, Monad m) => t (m a) -> m () Source #
Evaluate each monadic action in the structure from left to right,
and ignore the results. For a version that doesn't ignore the
results see
sequence
.
As of base 4.8.0.0,
sequence_
is just
sequenceA_
, specialized
to
Monad
.
words :: String -> [ String ] Source #
words
breaks a string up into a list of words, which were delimited
by white space.
>>>words "Lorem ipsum\ndolor"["Lorem","ipsum","dolor"]
lines :: String -> [ String ] Source #
lines
breaks a string up into a list of strings at newline
characters. The resulting strings do not contain newlines.
Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,
>>>lines ""[]
>>>lines "\n"[""]
>>>lines "one"["one"]
>>>lines "one\n"["one"]
>>>lines "one\n\n"["one",""]
>>>lines "one\ntwo"["one","two"]
>>>lines "one\ntwo\n"["one","two"]
Thus
contains at least as many elements as newlines in
lines
s
s
.
read :: Read a => String -> a Source #
The
read
function reads input from a string, which must be
completely consumed by the input process.
read
fails with an
error
if the
parse is unsuccessful, and it is therefore discouraged from being used in
real applications. Use
readMaybe
or
readEither
for safe alternatives.
>>>read "123" :: Int123
>>>read "hello" :: Int*** Exception: Prelude.read: no parse
either :: (a -> c) -> (b -> c) -> Either a b -> c Source #
Case analysis for the
Either
type.
If the value is
, apply the first function to
Left
a
a
;
if it is
, apply the second function to
Right
b
b
.
Examples
We create two values of type
, one using the
Either
String
Int
Left
constructor and another using the
Right
constructor. Then
we apply "either" the
length
function (if we have a
String
)
or the "times-two" function (if we have an
Int
):
>>>let s = Left "foo" :: Either String Int>>>let n = Right 3 :: Either String Int>>>either length (*2) s3>>>either length (*2) n6
The
lex
function reads a single lexeme from the input, discarding
initial white space, and returning the characters that constitute the
lexeme. If the input string contains only white space,
lex
returns a
single successful `lexeme' consisting of the empty string. (Thus
.) If there is no legal lexeme at the
beginning of the input string,
lex
"" = [("","")]
lex
fails (i.e. returns
[]
).
This lexer is not completely faithful to the Haskell lexical syntax in the following respects:
- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly
lcm :: Integral a => a -> a -> a Source #
is the smallest positive integer that both
lcm
x y
x
and
y
divide.
gcd :: Integral a => a -> a -> a Source #
is the non-negative factor of both
gcd
x y
x
and
y
of which
every common factor of
x
and
y
is also a factor; for example
,
gcd
4 2 = 2
,
gcd
(-4) 6 = 2
=
gcd
0 4
4
.
=
gcd
0 0
0
.
(That is, the common divisor that is "greatest" in the divisibility
preordering.)
Note: Since for signed fixed-width integer types,
,
the result may be negative if one of the arguments is
abs
minBound
< 0
(and
necessarily is if the other is
minBound
0
or
) for such types.
minBound
(^^) :: ( Fractional a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to an integral power
(^) :: ( Num a, Integral b) => a -> b -> a infixr 8 Source #
raise a number to a non-negative integral power
showString :: String -> ShowS Source #
utility function converting a
String
to a show function that
simply prepends the string unchanged.
showChar :: Char -> ShowS Source #
utility function converting a
Char
to a show function that
simply prepends the character unchanged.
zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #
\(\mathcal{O}(\min(m,n))\)
.
zipWith
generalises
zip
by zipping with the
function given as the first argument, instead of a tupling function. For
example,
is applied to two lists to produce the list of
corresponding sums:
zipWith
(+)
>>>zipWith (+) [1, 2, 3] [4, 5, 6][5,7,9]
zipWith
is right-lazy:
zipWith f [] _|_ = []
zipWith
is capable of list fusion, but it is restricted to its
first list argument and its resulting list.
(!!) :: [a] -> Int -> a infixl 9 Source #
List index (subscript) operator, starting from 0.
It is an instance of the more general
genericIndex
,
which takes an index of any integral type.
lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #
\(\mathcal{O}(n)\)
.
lookup
key assocs
looks up a key in an association
list.
>>>lookup 2 [(1, "first"), (2, "second"), (3, "third")]Just "second"
reverse :: [a] -> [a] Source #
reverse
xs
returns the elements of
xs
in reverse order.
xs
must be finite.
break :: (a -> Bool ) -> [a] -> ([a], [a]) Source #
break
, applied to a predicate
p
and a list
xs
, returns a tuple where
first element is longest prefix (possibly empty) of
xs
of elements that
do not satisfy
p
and second element is the remainder of the list:
break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4]) break (< 9) [1,2,3] == ([],[1,2,3]) break (> 9) [1,2,3] == ([1,2,3],[])
span :: (a -> Bool ) -> [a] -> ([a], [a]) Source #
span
, applied to a predicate
p
and a list
xs
, returns a tuple where
first element is longest prefix (possibly empty) of
xs
of elements that
satisfy
p
and second element is the remainder of the list:
span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4]) span (< 9) [1,2,3] == ([1,2,3],[]) span (< 0) [1,2,3] == ([],[1,2,3])
span
p xs
is equivalent to
(
takeWhile
p xs,
dropWhile
p xs)
splitAt :: Int -> [a] -> ([a], [a]) Source #
splitAt
n xs
returns a tuple where first element is
xs
prefix of
length
n
and second element is the remainder of the list:
splitAt 6 "Hello World!" == ("Hello ","World!")
splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
splitAt 1 [1,2,3] == ([1],[2,3])
splitAt 3 [1,2,3] == ([1,2,3],[])
splitAt 4 [1,2,3] == ([1,2,3],[])
splitAt 0 [1,2,3] == ([],[1,2,3])
splitAt (-1) [1,2,3] == ([],[1,2,3])
It is equivalent to
(
when
take
n xs,
drop
n xs)
n
is not
_|_
(
splitAt _|_ xs = _|_
).
splitAt
is an instance of the more general
genericSplitAt
,
in which
n
may be of any integral type.
drop :: Int -> [a] -> [a] Source #
drop
n xs
returns the suffix of
xs
after the first
n
elements, or
[]
if
n >
:
length
xs
drop 6 "Hello World!" == "World!" drop 3 [1,2,3,4,5] == [4,5] drop 3 [1,2] == [] drop 3 [] == [] drop (-1) [1,2] == [1,2] drop 0 [1,2] == [1,2]
It is an instance of the more general
genericDrop
,
in which
n
may be of any integral type.
take :: Int -> [a] -> [a] Source #
take
n
, applied to a list
xs
, returns the prefix of
xs
of length
n
, or
xs
itself if
n >
:
length
xs
take 5 "Hello World!" == "Hello" take 3 [1,2,3,4,5] == [1,2,3] take 3 [1,2] == [1,2] take 3 [] == [] take (-1) [1,2] == [] take 0 [1,2] == []
It is an instance of the more general
genericTake
,
in which
n
may be of any integral type.
takeWhile :: (a -> Bool ) -> [a] -> [a] Source #
takeWhile
, applied to a predicate
p
and a list
xs
, returns the
longest prefix (possibly empty) of
xs
of elements that satisfy
p
:
takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2] takeWhile (< 9) [1,2,3] == [1,2,3] takeWhile (< 0) [1,2,3] == []
cycle
ties a finite list into a circular one, or equivalently,
the infinite repetition of the original list. It is the identity
on infinite lists.
replicate :: Int -> a -> [a] Source #
replicate
n x
is a list of length
n
with
x
the value of
every element.
It is an instance of the more general
genericReplicate
,
in which
n
may be of any integral type.
\(\mathcal{O}(n)\) . Return all the elements of a list except the last one. The list must be non-empty.
\(\mathcal{O}(n)\) . Extract the last element of a list, which must be finite and non-empty.
\(\mathcal{O}(1)\) . Extract the elements after the head of a list, which must be non-empty.
\(\mathcal{O}(1)\) . Extract the first element of a list, which must be non-empty.
maybe :: b -> (a -> b) -> Maybe a -> b Source #
The
maybe
function takes a default value, a function, and a
Maybe
value. If the
Maybe
value is
Nothing
, the function returns the
default value. Otherwise, it applies the function to the value inside
the
Just
and returns the result.
Examples
Basic usage:
>>>maybe False odd (Just 3)True
>>>maybe False odd NothingFalse
Read an integer from a string using
readMaybe
. If we succeed,
return twice the integer; that is, apply
(*2)
to it. If instead
we fail to parse an integer, return
0
by default:
>>>import Text.Read ( readMaybe )>>>maybe 0 (*2) (readMaybe "5")10>>>maybe 0 (*2) (readMaybe "")0
Apply
show
to a
Maybe Int
. If we have
Just n
, we want to show
the underlying
Int
n
. But if we have
Nothing
, we return the
empty string instead of (for example) "Nothing":
>>>maybe "" show (Just 5)"5">>>maybe "" show Nothing""
(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #
An infix synonym for
fmap
.
The name of this operator is an allusion to
$
.
Note the similarities between their types:
($) :: (a -> b) -> a -> b (<$>) :: Functor f => (a -> b) -> f a -> f b
Whereas
$
is function application,
<$>
is function
application lifted over a
Functor
.
Examples
Convert from a
to a
Maybe
Int
using
Maybe
String
show
:
>>>show <$> NothingNothing>>>show <$> Just 3Just "3"
Convert from an
to an
Either
Int
Int
Either
Int
String
using
show
:
>>>show <$> Left 17Left 17>>>show <$> Right 17Right "17"
Double each element of a list:
>>>(*2) <$> [1,2,3][2,4,6]
Apply
even
to the second element of a pair:
>>>even <$> (2,2)(2,True)
until :: (a -> Bool ) -> (a -> a) -> a -> a Source #
yields the result of applying
until
p f
f
until
p
holds.
($!) :: forall (r :: RuntimeRep ) a (b :: TYPE r). (a -> b) -> a -> b infixr 0 Source #
Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.
flip :: (a -> b -> c) -> b -> a -> c Source #
takes its (first) two arguments in the reverse order of
flip
f
f
.
>>>flip (++) "hello" "world""worldhello"
const x
is a unary function which evaluates to
x
for all inputs.
>>>const 42 "hello"42
>>>map (const 42) [0..3][42,42,42,42]
(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #
Same as
>>=
, but with the arguments interchanged.
undefined :: forall (r :: RuntimeRep ) (a :: TYPE r). HasCallStack => a Source #
errorWithoutStackTrace :: forall (r :: RuntimeRep ) (a :: TYPE r). [ Char ] -> a Source #
A variant of
error
that does not produce a stack trace.
Since: base-4.9.0.0
error :: forall (r :: RuntimeRep ) (a :: TYPE r). HasCallStack => [ Char ] -> a Source #
error
stops execution and displays an error message.