basic-prelude-0.7.0: An enhanced core prelude; a common foundation for alternate preludes.

Safe HaskellNone
LanguageHaskell2010

CorePrelude

Contents

Synopsis

Standard

Operators

($) :: (a -> b) -> a -> b infixr 0 #

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

    f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

($!) :: (a -> b) -> a -> b infixr 0 #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

(&&) :: Bool -> Bool -> Bool infixr 3 #

Boolean "and"

(||) :: Bool -> Bool -> Bool infixr 2 #

Boolean "or"

(.) :: Category k cat => forall b c a. cat b c -> cat a b -> cat a c #

morphism composition

Functions

not :: Bool -> Bool #

Boolean "not"

otherwise :: Bool #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

fst :: (a, b) -> a #

Extract the first component of a pair.

snd :: (a, b) -> b #

Extract the second component of a pair.

id :: Category k cat => forall a. cat a a #

the identity morphism

maybe :: b -> (a -> b) -> Maybe a -> b #

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

Basic usage:

>>> maybe False odd (Just 3)
True
>>> maybe False odd Nothing
False

Read an integer from a string using readMaybe. If we succeed, return twice the integer; that is, apply (*2) to it. If instead we fail to parse an integer, return 0 by default:

>>> import Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

Apply show to a Maybe Int. If we have Just n, we want to show the underlying Int n. But if we have Nothing, we return the empty string instead of (for example) "Nothing":

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

either :: (a -> c) -> (b -> c) -> Either a b -> c #

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

We create two values of type Either String Int, one using the Left constructor and another using the Right constructor. Then we apply "either" the length function (if we have a String) or the "times-two" function (if we have an Int):

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

flip :: (a -> b -> c) -> b -> a -> c #

flip f takes its (first) two arguments in the reverse order of f.

const :: a -> b -> a #

const x is a unary function which evaluates to x for all inputs.

For instance,

>>> map (const 42) [0..3]
[42,42,42,42]

error :: HasCallStack => [Char] -> a #

error stops execution and displays an error message.

putStr :: MonadIO m => Text -> m () Source #

putStrLn :: MonadIO m => Text -> m () Source #

print :: (MonadIO m, Show a) => a -> m () Source #

terror :: HasCallStack => Text -> a Source #

error applied to Text

Since 0.4.1

odd :: Integral a => a -> Bool #

even :: Integral a => a -> Bool #

uncurry :: (a -> b -> c) -> (a, b) -> c #

uncurry converts a curried function to a function on pairs.

curry :: ((a, b) -> c) -> a -> b -> c #

curry converts an uncurried function to a curried function.

swap :: (a, b) -> (b, a) #

Swap the components of a pair.

until :: (a -> Bool) -> (a -> a) -> a -> a #

until p f yields the result of applying f until p holds.

asTypeOf :: a -> a -> a #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

undefined :: HasCallStack => a #

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

seq :: a -> b -> b #

The value of seq a b is bottom if a is bottom, and otherwise equal to b. 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.

Type classes

class Eq a => Ord a where #

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.

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Minimal complete definition

compare | (<=)

Methods

compare :: a -> a -> Ordering #

(<) :: a -> a -> Bool infix 4 #

(<=) :: a -> a -> Bool infix 4 #

(>) :: a -> a -> Bool infix 4 #

(>=) :: a -> a -> Bool infix 4 #

max :: a -> a -> a #

min :: a -> a -> a #

Instances

Ord Bool 

Methods

compare :: Bool -> Bool -> Ordering #

(<) :: Bool -> Bool -> Bool #

(<=) :: Bool -> Bool -> Bool #

(>) :: Bool -> Bool -> Bool #

(>=) :: Bool -> Bool -> Bool #

max :: Bool -> Bool -> Bool #

min :: Bool -> Bool -> Bool #

Ord Char 

Methods

compare :: Char -> Char -> Ordering #

(<) :: Char -> Char -> Bool #

(<=) :: Char -> Char -> Bool #

(>) :: Char -> Char -> Bool #

(>=) :: Char -> Char -> Bool #

max :: Char -> Char -> Char #

min :: Char -> Char -> Char #

Ord Double 
Ord Float 

Methods

compare :: Float -> Float -> Ordering #

(<) :: Float -> Float -> Bool #

(<=) :: Float -> Float -> Bool #

(>) :: Float -> Float -> Bool #

(>=) :: Float -> Float -> Bool #

max :: Float -> Float -> Float #

min :: Float -> Float -> Float #

Ord Int 

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Ord Int8 

Methods

compare :: Int8 -> Int8 -> Ordering #

(<) :: Int8 -> Int8 -> Bool #

(<=) :: Int8 -> Int8 -> Bool #

(>) :: Int8 -> Int8 -> Bool #

(>=) :: Int8 -> Int8 -> Bool #

max :: Int8 -> Int8 -> Int8 #

min :: Int8 -> Int8 -> Int8 #

Ord Int16 

Methods

compare :: Int16 -> Int16 -> Ordering #

(<) :: Int16 -> Int16 -> Bool #

(<=) :: Int16 -> Int16 -> Bool #

(>) :: Int16 -> Int16 -> Bool #

(>=) :: Int16 -> Int16 -> Bool #

max :: Int16 -> Int16 -> Int16 #

min :: Int16 -> Int16 -> Int16 #

Ord Int32 

Methods

compare :: Int32 -> Int32 -> Ordering #

(<) :: Int32 -> Int32 -> Bool #

(<=) :: Int32 -> Int32 -> Bool #

(>) :: Int32 -> Int32 -> Bool #

(>=) :: Int32 -> Int32 -> Bool #

max :: Int32 -> Int32 -> Int32 #

min :: Int32 -> Int32 -> Int32 #

Ord Int64 

Methods

compare :: Int64 -> Int64 -> Ordering #

(<) :: Int64 -> Int64 -> Bool #

(<=) :: Int64 -> Int64 -> Bool #

(>) :: Int64 -> Int64 -> Bool #

(>=) :: Int64 -> Int64 -> Bool #

max :: Int64 -> Int64 -> Int64 #

min :: Int64 -> Int64 -> Int64 #

Ord Integer 
Ord Ordering 
Ord Word 

Methods

compare :: Word -> Word -> Ordering #

(<) :: Word -> Word -> Bool #

(<=) :: Word -> Word -> Bool #

(>) :: Word -> Word -> Bool #

(>=) :: Word -> Word -> Bool #

max :: Word -> Word -> Word #

min :: Word -> Word -> Word #

Ord Word8 

Methods

compare :: Word8 -> Word8 -> Ordering #

(<) :: Word8 -> Word8 -> Bool #

(<=) :: Word8 -> Word8 -> Bool #

(>) :: Word8 -> Word8 -> Bool #

(>=) :: Word8 -> Word8 -> Bool #

max :: Word8 -> Word8 -> Word8 #

min :: Word8 -> Word8 -> Word8 #

Ord Word16 
Ord Word32 
Ord Word64 
Ord TypeRep 
Ord () 

Methods

compare :: () -> () -> Ordering #

(<) :: () -> () -> Bool #

(<=) :: () -> () -> Bool #

(>) :: () -> () -> Bool #

(>=) :: () -> () -> Bool #

max :: () -> () -> () #

min :: () -> () -> () #

Ord TyCon 

Methods

compare :: TyCon -> TyCon -> Ordering #

(<) :: TyCon -> TyCon -> Bool #

(<=) :: TyCon -> TyCon -> Bool #

(>) :: TyCon -> TyCon -> Bool #

(>=) :: TyCon -> TyCon -> Bool #

max :: TyCon -> TyCon -> TyCon #

min :: TyCon -> TyCon -> TyCon #

Ord BigNat 
Ord Void 

Methods

compare :: Void -> Void -> Ordering #

(<) :: Void -> Void -> Bool #

(<=) :: Void -> Void -> Bool #

(>) :: Void -> Void -> Bool #

(>=) :: Void -> Void -> Bool #

max :: Void -> Void -> Void #

min :: Void -> Void -> Void #

Ord Version 
Ord AsyncException 
Ord ArrayException 
Ord ExitCode 
Ord BufferMode 
Ord Newline 
Ord NewlineMode 
Ord CChar 

Methods

compare :: CChar -> CChar -> Ordering #

(<) :: CChar -> CChar -> Bool #

(<=) :: CChar -> CChar -> Bool #

(>) :: CChar -> CChar -> Bool #

(>=) :: CChar -> CChar -> Bool #

max :: CChar -> CChar -> CChar #

min :: CChar -> CChar -> CChar #

Ord CSChar 
Ord CUChar 
Ord CShort 
Ord CUShort 
Ord CInt 

Methods

compare :: CInt -> CInt -> Ordering #

(<) :: CInt -> CInt -> Bool #

(<=) :: CInt -> CInt -> Bool #

(>) :: CInt -> CInt -> Bool #

(>=) :: CInt -> CInt -> Bool #

max :: CInt -> CInt -> CInt #

min :: CInt -> CInt -> CInt #

Ord CUInt 

Methods

compare :: CUInt -> CUInt -> Ordering #

(<) :: CUInt -> CUInt -> Bool #

(<=) :: CUInt -> CUInt -> Bool #

(>) :: CUInt -> CUInt -> Bool #

(>=) :: CUInt -> CUInt -> Bool #

max :: CUInt -> CUInt -> CUInt #

min :: CUInt -> CUInt -> CUInt #

Ord CLong 

Methods

compare :: CLong -> CLong -> Ordering #

(<) :: CLong -> CLong -> Bool #

(<=) :: CLong -> CLong -> Bool #

(>) :: CLong -> CLong -> Bool #

(>=) :: CLong -> CLong -> Bool #

max :: CLong -> CLong -> CLong #

min :: CLong -> CLong -> CLong #

Ord CULong 
Ord CLLong 
Ord CULLong 
Ord CFloat 
Ord CDouble 
Ord CPtrdiff 
Ord CSize 

Methods

compare :: CSize -> CSize -> Ordering #

(<) :: CSize -> CSize -> Bool #

(<=) :: CSize -> CSize -> Bool #

(>) :: CSize -> CSize -> Bool #

(>=) :: CSize -> CSize -> Bool #

max :: CSize -> CSize -> CSize #

min :: CSize -> CSize -> CSize #

Ord CWchar 
Ord CSigAtomic 
Ord CClock 
Ord CTime 

Methods

compare :: CTime -> CTime -> Ordering #

(<) :: CTime -> CTime -> Bool #

(<=) :: CTime -> CTime -> Bool #

(>) :: CTime -> CTime -> Bool #

(>=) :: CTime -> CTime -> Bool #

max :: CTime -> CTime -> CTime #

min :: CTime -> CTime -> CTime #

Ord CUSeconds 
Ord CSUSeconds 
Ord CIntPtr 
Ord CUIntPtr 
Ord CIntMax 
Ord CUIntMax 
Ord All 

Methods

compare :: All -> All -> Ordering #

(<) :: All -> All -> Bool #

(<=) :: All -> All -> Bool #

(>) :: All -> All -> Bool #

(>=) :: All -> All -> Bool #

max :: All -> All -> All #

min :: All -> All -> All #

Ord Any 

Methods

compare :: Any -> Any -> Ordering #

(<) :: Any -> Any -> Bool #

(<=) :: Any -> Any -> Bool #

(>) :: Any -> Any -> Bool #

(>=) :: Any -> Any -> Bool #

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

Ord Fixity 
Ord Associativity 
Ord SourceUnpackedness 
Ord SourceStrictness 
Ord DecidedStrictness 
Ord ErrorCall 
Ord ArithException 
Ord SomeNat 
Ord SomeSymbol 
Ord ByteString 
Ord ByteString 
Ord IntSet 
Ord a => Ord [a] 

Methods

compare :: [a] -> [a] -> Ordering #

(<) :: [a] -> [a] -> Bool #

(<=) :: [a] -> [a] -> Bool #

(>) :: [a] -> [a] -> Bool #

(>=) :: [a] -> [a] -> Bool #

max :: [a] -> [a] -> [a] #

min :: [a] -> [a] -> [a] #

Ord a => Ord (Maybe a) 

Methods

compare :: Maybe a -> Maybe a -> Ordering #

(<) :: Maybe a -> Maybe a -> Bool #

(<=) :: Maybe a -> Maybe a -> Bool #

(>) :: Maybe a -> Maybe a -> Bool #

(>=) :: Maybe a -> Maybe a -> Bool #

max :: Maybe a -> Maybe a -> Maybe a #

min :: Maybe a -> Maybe a -> Maybe a #

Integral a => Ord (Ratio a) 

Methods

compare :: Ratio a -> Ratio a -> Ordering #

(<) :: Ratio a -> Ratio a -> Bool #

(<=) :: Ratio a -> Ratio a -> Bool #

(>) :: Ratio a -> Ratio a -> Bool #

(>=) :: Ratio a -> Ratio a -> Bool #

max :: Ratio a -> Ratio a -> Ratio a #

min :: Ratio a -> Ratio a -> Ratio a #

Ord (Ptr a) 

Methods

compare :: Ptr a -> Ptr a -> Ordering #

(<) :: Ptr a -> Ptr a -> Bool #

(<=) :: Ptr a -> Ptr a -> Bool #

(>) :: Ptr a -> Ptr a -> Bool #

(>=) :: Ptr a -> Ptr a -> Bool #

max :: Ptr a -> Ptr a -> Ptr a #

min :: Ptr a -> Ptr a -> Ptr a #

Ord (FunPtr a) 

Methods

compare :: FunPtr a -> FunPtr a -> Ordering #

(<) :: FunPtr a -> FunPtr a -> Bool #

(<=) :: FunPtr a -> FunPtr a -> Bool #

(>) :: FunPtr a -> FunPtr a -> Bool #

(>=) :: FunPtr a -> FunPtr a -> Bool #

max :: FunPtr a -> FunPtr a -> FunPtr a #

min :: FunPtr a -> FunPtr a -> FunPtr a #

Ord (V1 p) 

Methods

compare :: V1 p -> V1 p -> Ordering #

(<) :: V1 p -> V1 p -> Bool #

(<=) :: V1 p -> V1 p -> Bool #

(>) :: V1 p -> V1 p -> Bool #

(>=) :: V1 p -> V1 p -> Bool #

max :: V1 p -> V1 p -> V1 p #

min :: V1 p -> V1 p -> V1 p #

Ord (U1 p) 

Methods

compare :: U1 p -> U1 p -> Ordering #

(<) :: U1 p -> U1 p -> Bool #

(<=) :: U1 p -> U1 p -> Bool #

(>) :: U1 p -> U1 p -> Bool #

(>=) :: U1 p -> U1 p -> Bool #

max :: U1 p -> U1 p -> U1 p #

min :: U1 p -> U1 p -> U1 p #

Ord p => Ord (Par1 p) 

Methods

compare :: Par1 p -> Par1 p -> Ordering #

(<) :: Par1 p -> Par1 p -> Bool #

(<=) :: Par1 p -> Par1 p -> Bool #

(>) :: Par1 p -> Par1 p -> Bool #

(>=) :: Par1 p -> Par1 p -> Bool #

max :: Par1 p -> Par1 p -> Par1 p #

min :: Par1 p -> Par1 p -> Par1 p #

Ord (ForeignPtr a) 
Ord a => Ord (Identity a) 

Methods

compare :: Identity a -> Identity a -> Ordering #

(<) :: Identity a -> Identity a -> Bool #

(<=) :: Identity a -> Identity a -> Bool #

(>) :: Identity a -> Identity a -> Bool #

(>=) :: Identity a -> Identity a -> Bool #

max :: Identity a -> Identity a -> Identity a #

min :: Identity a -> Identity a -> Identity a #

Ord a => Ord (Min a) 

Methods

compare :: Min a -> Min a -> Ordering #

(<) :: Min a -> Min a -> Bool #

(<=) :: Min a -> Min a -> Bool #

(>) :: Min a -> Min a -> Bool #

(>=) :: Min a -> Min a -> Bool #

max :: Min a -> Min a -> Min a #

min :: Min a -> Min a -> Min a #

Ord a => Ord (Max a) 

Methods

compare :: Max a -> Max a -> Ordering #

(<) :: Max a -> Max a -> Bool #

(<=) :: Max a -> Max a -> Bool #

(>) :: Max a -> Max a -> Bool #

(>=) :: Max a -> Max a -> Bool #

max :: Max a -> Max a -> Max a #

min :: Max a -> Max a -> Max a #

Ord a => Ord (First a) 

Methods

compare :: First a -> First a -> Ordering #

(<) :: First a -> First a -> Bool #

(<=) :: First a -> First a -> Bool #

(>) :: First a -> First a -> Bool #

(>=) :: First a -> First a -> Bool #

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Ord a => Ord (Last a) 

Methods

compare :: Last a -> Last a -> Ordering #

(<) :: Last a -> Last a -> Bool #

(<=) :: Last a -> Last a -> Bool #

(>) :: Last a -> Last a -> Bool #

(>=) :: Last a -> Last a -> Bool #

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Ord m => Ord (WrappedMonoid m) 
Ord a => Ord (Option a) 

Methods

compare :: Option a -> Option a -> Ordering #

(<) :: Option a -> Option a -> Bool #

(<=) :: Option a -> Option a -> Bool #

(>) :: Option a -> Option a -> Bool #

(>=) :: Option a -> Option a -> Bool #

max :: Option a -> Option a -> Option a #

min :: Option a -> Option a -> Option a #

Ord a => Ord (NonEmpty a) 

Methods

compare :: NonEmpty a -> NonEmpty a -> Ordering #

(<) :: NonEmpty a -> NonEmpty a -> Bool #

(<=) :: NonEmpty a -> NonEmpty a -> Bool #

(>) :: NonEmpty a -> NonEmpty a -> Bool #

(>=) :: NonEmpty a -> NonEmpty a -> Bool #

max :: NonEmpty a -> NonEmpty a -> NonEmpty a #

min :: NonEmpty a -> NonEmpty a -> NonEmpty a #

Ord a => Ord (ZipList a) 

Methods

compare :: ZipList a -> ZipList a -> Ordering #

(<) :: ZipList a -> ZipList a -> Bool #

(<=) :: ZipList a -> ZipList a -> Bool #

(>) :: ZipList a -> ZipList a -> Bool #

(>=) :: ZipList a -> ZipList a -> Bool #

max :: ZipList a -> ZipList a -> ZipList a #

min :: ZipList a -> ZipList a -> ZipList a #

Ord a => Ord (Dual a) 

Methods

compare :: Dual a -> Dual a -> Ordering #

(<) :: Dual a -> Dual a -> Bool #

(<=) :: Dual a -> Dual a -> Bool #

(>) :: Dual a -> Dual a -> Bool #

(>=) :: Dual a -> Dual a -> Bool #

max :: Dual a -> Dual a -> Dual a #

min :: Dual a -> Dual a -> Dual a #

Ord a => Ord (Sum a) 

Methods

compare :: Sum a -> Sum a -> Ordering #

(<) :: Sum a -> Sum a -> Bool #

(<=) :: Sum a -> Sum a -> Bool #

(>) :: Sum a -> Sum a -> Bool #

(>=) :: Sum a -> Sum a -> Bool #

max :: Sum a -> Sum a -> Sum a #

min :: Sum a -> Sum a -> Sum a #

Ord a => Ord (Product a) 

Methods

compare :: Product a -> Product a -> Ordering #

(<) :: Product a -> Product a -> Bool #

(<=) :: Product a -> Product a -> Bool #

(>) :: Product a -> Product a -> Bool #

(>=) :: Product a -> Product a -> Bool #

max :: Product a -> Product a -> Product a #

min :: Product a -> Product a -> Product a #

Ord a => Ord (First a) 

Methods

compare :: First a -> First a -> Ordering #

(<) :: First a -> First a -> Bool #

(<=) :: First a -> First a -> Bool #

(>) :: First a -> First a -> Bool #

(>=) :: First a -> First a -> Bool #

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Ord a => Ord (Last a) 

Methods

compare :: Last a -> Last a -> Ordering #

(<) :: Last a -> Last a -> Bool #

(<=) :: Last a -> Last a -> Bool #

(>) :: Last a -> Last a -> Bool #

(>=) :: Last a -> Last a -> Bool #

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Ord a => Ord (Down a) 

Methods

compare :: Down a -> Down a -> Ordering #

(<) :: Down a -> Down a -> Bool #

(<=) :: Down a -> Down a -> Bool #

(>) :: Down a -> Down a -> Bool #

(>=) :: Down a -> Down a -> Bool #

max :: Down a -> Down a -> Down a #

min :: Down a -> Down a -> Down a #

Ord a => Ord (IntMap a) 

Methods

compare :: IntMap a -> IntMap a -> Ordering #

(<) :: IntMap a -> IntMap a -> Bool #

(<=) :: IntMap a -> IntMap a -> Bool #

(>) :: IntMap a -> IntMap a -> Bool #

(>=) :: IntMap a -> IntMap a -> Bool #

max :: IntMap a -> IntMap a -> IntMap a #

min :: IntMap a -> IntMap a -> IntMap a #

Ord a => Ord (Seq a) 

Methods

compare :: Seq a -> Seq a -> Ordering #

(<) :: Seq a -> Seq a -> Bool #

(<=) :: Seq a -> Seq a -> Bool #

(>) :: Seq a -> Seq a -> Bool #

(>=) :: Seq a -> Seq a -> Bool #

max :: Seq a -> Seq a -> Seq a #

min :: Seq a -> Seq a -> Seq a #

Ord a => Ord (ViewL a) 

Methods

compare :: ViewL a -> ViewL a -> Ordering #

(<) :: ViewL a -> ViewL a -> Bool #

(<=) :: ViewL a -> ViewL a -> Bool #

(>) :: ViewL a -> ViewL a -> Bool #

(>=) :: ViewL a -> ViewL a -> Bool #

max :: ViewL a -> ViewL a -> ViewL a #

min :: ViewL a -> ViewL a -> ViewL a #

Ord a => Ord (ViewR a) 

Methods

compare :: ViewR a -> ViewR a -> Ordering #

(<) :: ViewR a -> ViewR a -> Bool #

(<=) :: ViewR a -> ViewR a -> Bool #

(>) :: ViewR a -> ViewR a -> Bool #

(>=) :: ViewR a -> ViewR a -> Bool #

max :: ViewR a -> ViewR a -> ViewR a #

min :: ViewR a -> ViewR a -> ViewR a #

Ord a => Ord (Set a) 

Methods

compare :: Set a -> Set a -> Ordering #

(<) :: Set a -> Set a -> Bool #

(<=) :: Set a -> Set a -> Bool #

(>) :: Set a -> Set a -> Bool #

(>=) :: Set a -> Set a -> Bool #

max :: Set a -> Set a -> Set a #

min :: Set a -> Set a -> Set a #

Ord a => Ord (Hashed a) 

Methods

compare :: Hashed a -> Hashed a -> Ordering #

(<) :: Hashed a -> Hashed a -> Bool #

(<=) :: Hashed a -> Hashed a -> Bool #

(>) :: Hashed a -> Hashed a -> Bool #

(>=) :: Hashed a -> Hashed a -> Bool #

max :: Hashed a -> Hashed a -> Hashed a #

min :: Hashed a -> Hashed a -> Hashed a #

Ord a => Ord (Array a) 

Methods

compare :: Array a -> Array a -> Ordering #

(<) :: Array a -> Array a -> Bool #

(<=) :: Array a -> Array a -> Bool #

(>) :: Array a -> Array a -> Bool #

(>=) :: Array a -> Array a -> Bool #

max :: Array a -> Array a -> Array a #

min :: Array a -> Array a -> Array a #

Ord a => Ord (Vector a) 

Methods

compare :: Vector a -> Vector a -> Ordering #

(<) :: Vector a -> Vector a -> Bool #

(<=) :: Vector a -> Vector a -> Bool #

(>) :: Vector a -> Vector a -> Bool #

(>=) :: Vector a -> Vector a -> Bool #

max :: Vector a -> Vector a -> Vector a #

min :: Vector a -> Vector a -> Vector a #

(Storable a, Ord a) => Ord (Vector a) 

Methods

compare :: Vector a -> Vector a -> Ordering #

(<) :: Vector a -> Vector a -> Bool #

(<=) :: Vector a -> Vector a -> Bool #

(>) :: Vector a -> Vector a -> Bool #

(>=) :: Vector a -> Vector a -> Bool #

max :: Vector a -> Vector a -> Vector a #

min :: Vector a -> Vector a -> Vector a #

(Prim a, Ord a) => Ord (Vector a) 

Methods

compare :: Vector a -> Vector a -> Ordering #

(<) :: Vector a -> Vector a -> Bool #

(<=) :: Vector a -> Vector a -> Bool #

(>) :: Vector a -> Vector a -> Bool #

(>=) :: Vector a -> Vector a -> Bool #

max :: Vector a -> Vector a -> Vector a #

min :: Vector a -> Vector a -> Vector a #

(Ord b, Ord a) => Ord (Either a b) 

Methods

compare :: Either a b -> Either a b -> Ordering #

(<) :: Either a b -> Either a b -> Bool #

(<=) :: Either a b -> Either a b -> Bool #

(>) :: Either a b -> Either a b -> Bool #

(>=) :: Either a b -> Either a b -> Bool #

max :: Either a b -> Either a b -> Either a b #

min :: Either a b -> Either a b -> Either a b #

Ord (f p) => Ord (Rec1 f p) 

Methods

compare :: Rec1 f p -> Rec1 f p -> Ordering #

(<) :: Rec1 f p -> Rec1 f p -> Bool #

(<=) :: Rec1 f p -> Rec1 f p -> Bool #

(>) :: Rec1 f p -> Rec1 f p -> Bool #

(>=) :: Rec1 f p -> Rec1 f p -> Bool #

max :: Rec1 f p -> Rec1 f p -> Rec1 f p #

min :: Rec1 f p -> Rec1 f p -> Rec1 f p #

Ord (URec Char p) 

Methods

compare :: URec Char p -> URec Char p -> Ordering #

(<) :: URec Char p -> URec Char p -> Bool #

(<=) :: URec Char p -> URec Char p -> Bool #

(>) :: URec Char p -> URec Char p -> Bool #

(>=) :: URec Char p -> URec Char p -> Bool #

max :: URec Char p -> URec Char p -> URec Char p #

min :: URec Char p -> URec Char p -> URec Char p #

Ord (URec Double p) 

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

Ord (URec Float p) 

Methods

compare :: URec Float p -> URec Float p -> Ordering #

(<) :: URec Float p -> URec Float p -> Bool #

(<=) :: URec Float p -> URec Float p -> Bool #

(>) :: URec Float p -> URec Float p -> Bool #

(>=) :: URec Float p -> URec Float p -> Bool #

max :: URec Float p -> URec Float p -> URec Float p #

min :: URec Float p -> URec Float p -> URec Float p #

Ord (URec Int p) 

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

Ord (URec Word p) 

Methods

compare :: URec Word p -> URec Word p -> Ordering #

(<) :: URec Word p -> URec Word p -> Bool #

(<=) :: URec Word p -> URec Word p -> Bool #

(>) :: URec Word p -> URec Word p -> Bool #

(>=) :: URec Word p -> URec Word p -> Bool #

max :: URec Word p -> URec Word p -> URec Word p #

min :: URec Word p -> URec Word p -> URec Word p #

Ord (URec (Ptr ()) p) 

Methods

compare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering #

(<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #

min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #

(Ord a, Ord b) => Ord (a, b) 

Methods

compare :: (a, b) -> (a, b) -> Ordering #

(<) :: (a, b) -> (a, b) -> Bool #

(<=) :: (a, b) -> (a, b) -> Bool #

(>) :: (a, b) -> (a, b) -> Bool #

(>=) :: (a, b) -> (a, b) -> Bool #

max :: (a, b) -> (a, b) -> (a, b) #

min :: (a, b) -> (a, b) -> (a, b) #

Ord a => Ord (Arg a b) 

Methods

compare :: Arg a b -> Arg a b -> Ordering #

(<) :: Arg a b -> Arg a b -> Bool #

(<=) :: Arg a b -> Arg a b -> Bool #

(>) :: Arg a b -> Arg a b -> Bool #

(>=) :: Arg a b -> Arg a b -> Bool #

max :: Arg a b -> Arg a b -> Arg a b #

min :: Arg a b -> Arg a b -> Arg a b #

Ord (Proxy k s) 

Methods

compare :: Proxy k s -> Proxy k s -> Ordering #

(<) :: Proxy k s -> Proxy k s -> Bool #

(<=) :: Proxy k s -> Proxy k s -> Bool #

(>) :: Proxy k s -> Proxy k s -> Bool #

(>=) :: Proxy k s -> Proxy k s -> Bool #

max :: Proxy k s -> Proxy k s -> Proxy k s #

min :: Proxy k s -> Proxy k s -> Proxy k s #

(Ord k, Ord v) => Ord (Map k v) 

Methods

compare :: Map k v -> Map k v -> Ordering #

(<) :: Map k v -> Map k v -> Bool #

(<=) :: Map k v -> Map k v -> Bool #

(>) :: Map k v -> Map k v -> Bool #

(>=) :: Map k v -> Map k v -> Bool #

max :: Map k v -> Map k v -> Map k v #

min :: Map k v -> Map k v -> Map k v #

(Ord1 m, Ord a) => Ord (MaybeT m a) 

Methods

compare :: MaybeT m a -> MaybeT m a -> Ordering #

(<) :: MaybeT m a -> MaybeT m a -> Bool #

(<=) :: MaybeT m a -> MaybeT m a -> Bool #

(>) :: MaybeT m a -> MaybeT m a -> Bool #

(>=) :: MaybeT m a -> MaybeT m a -> Bool #

max :: MaybeT m a -> MaybeT m a -> MaybeT m a #

min :: MaybeT m a -> MaybeT m a -> MaybeT m a #

(Ord1 m, Ord a) => Ord (ListT m a) 

Methods

compare :: ListT m a -> ListT m a -> Ordering #

(<) :: ListT m a -> ListT m a -> Bool #

(<=) :: ListT m a -> ListT m a -> Bool #

(>) :: ListT m a -> ListT m a -> Bool #

(>=) :: ListT m a -> ListT m a -> Bool #

max :: ListT m a -> ListT m a -> ListT m a #

min :: ListT m a -> ListT m a -> ListT m a #

Ord c => Ord (K1 i c p) 

Methods

compare :: K1 i c p -> K1 i c p -> Ordering #

(<) :: K1 i c p -> K1 i c p -> Bool #

(<=) :: K1 i c p -> K1 i c p -> Bool #

(>) :: K1 i c p -> K1 i c p -> Bool #

(>=) :: K1 i c p -> K1 i c p -> Bool #

max :: K1 i c p -> K1 i c p -> K1 i c p #

min :: K1 i c p -> K1 i c p -> K1 i c p #

(Ord (g p), Ord (f p)) => Ord ((:+:) f g p) 

Methods

compare :: (f :+: g) p -> (f :+: g) p -> Ordering #

(<) :: (f :+: g) p -> (f :+: g) p -> Bool #

(<=) :: (f :+: g) p -> (f :+: g) p -> Bool #

(>) :: (f :+: g) p -> (f :+: g) p -> Bool #

(>=) :: (f :+: g) p -> (f :+: g) p -> Bool #

max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #

min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #

(Ord (g p), Ord (f p)) => Ord ((:*:) f g p) 

Methods

compare :: (f :*: g) p -> (f :*: g) p -> Ordering #

(<) :: (f :*: g) p -> (f :*: g) p -> Bool #

(<=) :: (f :*: g) p -> (f :*: g) p -> Bool #

(>) :: (f :*: g) p -> (f :*: g) p -> Bool #

(>=) :: (f :*: g) p -> (f :*: g) p -> Bool #

max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #

Ord (f (g p)) => Ord ((:.:) f g p) 

Methods

compare :: (f :.: g) p -> (f :.: g) p -> Ordering #

(<) :: (f :.: g) p -> (f :.: g) p -> Bool #

(<=) :: (f :.: g) p -> (f :.: g) p -> Bool #

(>) :: (f :.: g) p -> (f :.: g) p -> Bool #

(>=) :: (f :.: g) p -> (f :.: g) p -> Bool #

max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #

(Ord a, Ord b, Ord c) => Ord (a, b, c) 

Methods

compare :: (a, b, c) -> (a, b, c) -> Ordering #

(<) :: (a, b, c) -> (a, b, c) -> Bool #

(<=) :: (a, b, c) -> (a, b, c) -> Bool #

(>) :: (a, b, c) -> (a, b, c) -> Bool #

(>=) :: (a, b, c) -> (a, b, c) -> Bool #

max :: (a, b, c) -> (a, b, c) -> (a, b, c) #

min :: (a, b, c) -> (a, b, c) -> (a, b, c) #

Ord a => Ord (Const k a b) 

Methods

compare :: Const k a b -> Const k a b -> Ordering #

(<) :: Const k a b -> Const k a b -> Bool #

(<=) :: Const k a b -> Const k a b -> Bool #

(>) :: Const k a b -> Const k a b -> Bool #

(>=) :: Const k a b -> Const k a b -> Bool #

max :: Const k a b -> Const k a b -> Const k a b #

min :: Const k a b -> Const k a b -> Const k a b #

Ord (f a) => Ord (Alt k f a) 

Methods

compare :: Alt k f a -> Alt k f a -> Ordering #

(<) :: Alt k f a -> Alt k f a -> Bool #

(<=) :: Alt k f a -> Alt k f a -> Bool #

(>) :: Alt k f a -> Alt k f a -> Bool #

(>=) :: Alt k f a -> Alt k f a -> Bool #

max :: Alt k f a -> Alt k f a -> Alt k f a #

min :: Alt k f a -> Alt k f a -> Alt k f a #

Ord ((:~:) k a b) 

Methods

compare :: (k :~: a) b -> (k :~: a) b -> Ordering #

(<) :: (k :~: a) b -> (k :~: a) b -> Bool #

(<=) :: (k :~: a) b -> (k :~: a) b -> Bool #

(>) :: (k :~: a) b -> (k :~: a) b -> Bool #

(>=) :: (k :~: a) b -> (k :~: a) b -> Bool #

max :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b #

min :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b #

(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) 

Methods

compare :: WriterT w m a -> WriterT w m a -> Ordering #

(<) :: WriterT w m a -> WriterT w m a -> Bool #

(<=) :: WriterT w m a -> WriterT w m a -> Bool #

(>) :: WriterT w m a -> WriterT w m a -> Bool #

(>=) :: WriterT w m a -> WriterT w m a -> Bool #

max :: WriterT w m a -> WriterT w m a -> WriterT w m a #

min :: WriterT w m a -> WriterT w m a -> WriterT w m a #

(Ord w, Ord1 m, Ord a) => Ord (WriterT w m a) 

Methods

compare :: WriterT w m a -> WriterT w m a -> Ordering #

(<) :: WriterT w m a -> WriterT w m a -> Bool #

(<=) :: WriterT w m a -> WriterT w m a -> Bool #

(>) :: WriterT w m a -> WriterT w m a -> Bool #

(>=) :: WriterT w m a -> WriterT w m a -> Bool #

max :: WriterT w m a -> WriterT w m a -> WriterT w m a #

min :: WriterT w m a -> WriterT w m a -> WriterT w m a #

(Ord1 f, Ord a) => Ord (IdentityT * f a) 

Methods

compare :: IdentityT * f a -> IdentityT * f a -> Ordering #

(<) :: IdentityT * f a -> IdentityT * f a -> Bool #

(<=) :: IdentityT * f a -> IdentityT * f a -> Bool #

(>) :: IdentityT * f a -> IdentityT * f a -> Bool #

(>=) :: IdentityT * f a -> IdentityT * f a -> Bool #

max :: IdentityT * f a -> IdentityT * f a -> IdentityT * f a #

min :: IdentityT * f a -> IdentityT * f a -> IdentityT * f a #

(Ord e, Ord1 m, Ord a) => Ord (ExceptT e m a) 

Methods

compare :: ExceptT e m a -> ExceptT e m a -> Ordering #

(<) :: ExceptT e m a -> ExceptT e m a -> Bool #

(<=) :: ExceptT e m a -> ExceptT e m a -> Bool #

(>) :: ExceptT e m a -> ExceptT e m a -> Bool #

(>=) :: ExceptT e m a -> ExceptT e m a -> Bool #

max :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #

min :: ExceptT e m a -> ExceptT e m a -> ExceptT e m a #

(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a) 

Methods

compare :: ErrorT e m a -> ErrorT e m a -> Ordering #

(<) :: ErrorT e m a -> ErrorT e m a -> Bool #

(<=) :: ErrorT e m a -> ErrorT e m a -> Bool #

(>) :: ErrorT e m a -> ErrorT e m a -> Bool #

(>=) :: ErrorT e m a -> ErrorT e m a -> Bool #

max :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #

min :: ErrorT e m a -> ErrorT e m a -> ErrorT e m a #

Ord (f p) => Ord (M1 i c f p) 

Methods

compare :: M1 i c f p -> M1 i c f p -> Ordering #

(<) :: M1 i c f p -> M1 i c f p -> Bool #

(<=) :: M1 i c f p -> M1 i c f p -> Bool #

(>) :: M1 i c f p -> M1 i c f p -> Bool #

(>=) :: M1 i c f p -> M1 i c f p -> Bool #

max :: M1 i c f p -> M1 i c f p -> M1 i c f p #

min :: M1 i c f p -> M1 i c f p -> M1 i c f p #

(Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) 

Methods

compare :: (a, b, c, d) -> (a, b, c, d) -> Ordering #

(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

(Ord1 f, Ord1 g, Ord a) => Ord (Sum * f g a) 

Methods

compare :: Sum * f g a -> Sum * f g a -> Ordering #

(<) :: Sum * f g a -> Sum * f g a -> Bool #

(<=) :: Sum * f g a -> Sum * f g a -> Bool #

(>) :: Sum * f g a -> Sum * f g a -> Bool #

(>=) :: Sum * f g a -> Sum * f g a -> Bool #

max :: Sum * f g a -> Sum * f g a -> Sum * f g a #

min :: Sum * f g a -> Sum * f g a -> Sum * f g a #

(Ord1 f, Ord1 g, Ord a) => Ord (Product * f g a) 

Methods

compare :: Product * f g a -> Product * f g a -> Ordering #

(<) :: Product * f g a -> Product * f g a -> Bool #

(<=) :: Product * f g a -> Product * f g a -> Bool #

(>) :: Product * f g a -> Product * f g a -> Bool #

(>=) :: Product * f g a -> Product * f g a -> Bool #

max :: Product * f g a -> Product * f g a -> Product * f g a #

min :: Product * f g a -> Product * f g a -> Product * f g a #

(Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) 

Methods

compare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering #

(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

(Ord1 f, Ord1 g, Ord a) => Ord (Compose * * f g a) 

Methods

compare :: Compose * * f g a -> Compose * * f g a -> Ordering #

(<) :: Compose * * f g a -> Compose * * f g a -> Bool #

(<=) :: Compose * * f g a -> Compose * * f g a -> Bool #

(>) :: Compose * * f g a -> Compose * * f g a -> Bool #

(>=) :: Compose * * f g a -> Compose * * f g a -> Bool #

max :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a #

min :: Compose * * f g a -> Compose * * f g a -> Compose * * f g a #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) 

Methods

compare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering #

(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #

min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) 

Methods

compare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering #

(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #

min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) 

Methods

compare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #

min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) 

Methods

compare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #

min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #

min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #

min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #

min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

(Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Methods

compare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering #

(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Eq a where #

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.

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

(==) :: a -> a -> Bool infix 4 #

(/=) :: a -> a -> Bool infix 4 #

Instances

Eq Bool 

Methods

(==) :: Bool -> Bool -> Bool #

(/=) :: Bool -> Bool -> Bool #

Eq Char 

Methods

(==) :: Char -> Char -> Bool #

(/=) :: Char -> Char -> Bool #

Eq Double 

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Eq Float 

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Eq Int 

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Eq Int8 

Methods

(==) :: Int8 -> Int8 -> Bool #

(/=) :: Int8 -> Int8 -> Bool #

Eq Int16 

Methods

(==) :: Int16 -> Int16 -> Bool #

(/=) :: Int16 -> Int16 -> Bool #

Eq Int32 

Methods

(==) :: Int32 -> Int32 -> Bool #

(/=) :: Int32 -> Int32 -> Bool #

Eq Int64 

Methods

(==) :: Int64 -> Int64 -> Bool #

(/=) :: Int64 -> Int64 -> Bool #

Eq Integer 

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Eq Ordering 
Eq Word 

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Eq Word8 

Methods

(==) :: Word8 -> Word8 -> Bool #

(/=) :: Word8 -> Word8 -> Bool #

Eq Word16 

Methods

(==) :: Word16 -> Word16 -> Bool #

(/=) :: Word16 -> Word16 -> Bool #

Eq Word32 

Methods

(==) :: Word32 -> Word32 -> Bool #

(/=) :: Word32 -> Word32 -> Bool #

Eq Word64 

Methods

(==) :: Word64 -> Word64 -> Bool #

(/=) :: Word64 -> Word64 -> Bool #

Eq TypeRep 

Methods

(==) :: TypeRep -> TypeRep -> Bool #

(/=) :: TypeRep -> TypeRep -> Bool #

Eq () 

Methods

(==) :: () -> () -> Bool #

(/=) :: () -> () -> Bool #

Eq TyCon 

Methods

(==) :: TyCon -> TyCon -> Bool #

(/=) :: TyCon -> TyCon -> Bool #

Eq Handle 

Methods

(==) :: Handle -> Handle -> Bool #

(/=) :: Handle -> Handle -> Bool #

Eq BigNat 

Methods

(==) :: BigNat -> BigNat -> Bool #

(/=) :: BigNat -> BigNat -> Bool #

Eq SpecConstrAnnotation 
Eq Void 

Methods

(==) :: Void -> Void -> Bool #

(/=) :: Void -> Void -> Bool #

Eq Version 

Methods

(==) :: Version -> Version -> Bool #

(/=) :: Version -> Version -> Bool #

Eq AsyncException 
Eq ArrayException 
Eq ExitCode 
Eq IOErrorType 
Eq BufferMode 
Eq Newline 

Methods

(==) :: Newline -> Newline -> Bool #

(/=) :: Newline -> Newline -> Bool #

Eq NewlineMode 
Eq CChar 

Methods

(==) :: CChar -> CChar -> Bool #

(/=) :: CChar -> CChar -> Bool #

Eq CSChar 

Methods

(==) :: CSChar -> CSChar -> Bool #

(/=) :: CSChar -> CSChar -> Bool #

Eq CUChar 

Methods

(==) :: CUChar -> CUChar -> Bool #

(/=) :: CUChar -> CUChar -> Bool #

Eq CShort 

Methods

(==) :: CShort -> CShort -> Bool #

(/=) :: CShort -> CShort -> Bool #

Eq CUShort 

Methods

(==) :: CUShort -> CUShort -> Bool #

(/=) :: CUShort -> CUShort -> Bool #

Eq CInt 

Methods

(==) :: CInt -> CInt -> Bool #

(/=) :: CInt -> CInt -> Bool #

Eq CUInt 

Methods

(==) :: CUInt -> CUInt -> Bool #

(/=) :: CUInt -> CUInt -> Bool #

Eq CLong 

Methods

(==) :: CLong -> CLong -> Bool #

(/=) :: CLong -> CLong -> Bool #

Eq CULong 

Methods

(==) :: CULong -> CULong -> Bool #

(/=) :: CULong -> CULong -> Bool #

Eq CLLong 

Methods

(==) :: CLLong -> CLLong -> Bool #

(/=) :: CLLong -> CLLong -> Bool #

Eq CULLong 

Methods

(==) :: CULLong -> CULLong -> Bool #

(/=) :: CULLong -> CULLong -> Bool #

Eq CFloat 

Methods

(==) :: CFloat -> CFloat -> Bool #

(/=) :: CFloat -> CFloat -> Bool #

Eq CDouble 

Methods

(==) :: CDouble -> CDouble -> Bool #

(/=) :: CDouble -> CDouble -> Bool #

Eq CPtrdiff 
Eq CSize 

Methods

(==) :: CSize -> CSize -> Bool #

(/=) :: CSize -> CSize -> Bool #

Eq CWchar 

Methods

(==) :: CWchar -> CWchar -> Bool #

(/=) :: CWchar -> CWchar -> Bool #

Eq CSigAtomic 
Eq CClock 

Methods

(==) :: CClock -> CClock -> Bool #

(/=) :: CClock -> CClock -> Bool #

Eq CTime 

Methods

(==) :: CTime -> CTime -> Bool #

(/=) :: CTime -> CTime -> Bool #

Eq CUSeconds 
Eq CSUSeconds 
Eq CIntPtr 

Methods

(==) :: CIntPtr -> CIntPtr -> Bool #

(/=) :: CIntPtr -> CIntPtr -> Bool #

Eq CUIntPtr 
Eq CIntMax 

Methods

(==) :: CIntMax -> CIntMax -> Bool #

(/=) :: CIntMax -> CIntMax -> Bool #

Eq CUIntMax 
Eq All 

Methods

(==) :: All -> All -> Bool #

(/=) :: All -> All -> Bool #

Eq Any 

Methods

(==) :: Any -> Any -> Bool #

(/=) :: Any -> Any -> Bool #

Eq Fixity 

Methods

(==) :: Fixity -> Fixity -> Bool #

(/=) :: Fixity -> Fixity -> Bool #

Eq Associativity 
Eq SourceUnpackedness 
Eq SourceStrictness 
Eq DecidedStrictness 
Eq MaskingState 
Eq IOException 
Eq ErrorCall 
Eq ArithException 
Eq SomeNat 

Methods

(==) :: SomeNat -> SomeNat -> Bool #

(/=) :: SomeNat -> SomeNat -> Bool #

Eq SomeSymbol 
Eq SrcLoc 

Methods

(==) :: SrcLoc -> SrcLoc -> Bool #

(/=) :: SrcLoc -> SrcLoc -> Bool #

Eq ByteString 
Eq ByteString 
Eq IntSet 

Methods

(==) :: IntSet -> IntSet -> Bool #

(/=) :: IntSet -> IntSet -> Bool #

Eq CodePoint 

Methods

(==) :: CodePoint -> CodePoint -> Bool #

(/=) :: CodePoint -> CodePoint -> Bool #

Eq DecoderState 

Methods

(==) :: DecoderState -> DecoderState -> Bool #

(/=) :: DecoderState -> DecoderState -> Bool #

Eq UnicodeException 
Eq a => Eq [a] 

Methods

(==) :: [a] -> [a] -> Bool #

(/=) :: [a] -> [a] -> Bool #

Eq a => Eq (Maybe a) 

Methods

(==) :: Maybe a -> Maybe a -> Bool #

(/=) :: Maybe a -> Maybe a -> Bool #

Eq a => Eq (Ratio a) 

Methods

(==) :: Ratio a -> Ratio a -> Bool #

(/=) :: Ratio a -> Ratio a -> Bool #

Eq (Ptr a) 

Methods

(==) :: Ptr a -> Ptr a -> Bool #

(/=) :: Ptr a -> Ptr a -> Bool #

Eq (FunPtr a) 

Methods

(==) :: FunPtr a -> FunPtr a -> Bool #

(/=) :: FunPtr a -> FunPtr a -> Bool #

Eq (V1 p) 

Methods

(==) :: V1 p -> V1 p -> Bool #

(/=) :: V1 p -> V1 p -> Bool #

Eq (U1 p) 

Methods

(==) :: U1 p -> U1 p -> Bool #

(/=) :: U1 p -> U1 p -> Bool #

Eq p => Eq (Par1 p) 

Methods

(==) :: Par1 p -> Par1 p -> Bool #

(/=) :: Par1 p -> Par1 p -> Bool #

Eq (ForeignPtr a) 

Methods

(==) :: ForeignPtr a -> ForeignPtr a -> Bool #

(/=) :: ForeignPtr a -> ForeignPtr a -> Bool #

Eq a => Eq (Identity a) 

Methods

(==) :: Identity a -> Identity a -> Bool #

(/=) :: Identity a -> Identity a -> Bool #

Eq a => Eq (Min a) 

Methods

(==) :: Min a -> Min a -> Bool #

(/=) :: Min a -> Min a -> Bool #

Eq a => Eq (Max a) 

Methods

(==) :: Max a -> Max a -> Bool #

(/=) :: Max a -> Max a -> Bool #

Eq a => Eq (First a) 

Methods

(==) :: First a -> First a -> Bool #

(/=) :: First a -> First a -> Bool #

Eq a => Eq (Last a) 

Methods

(==) :: Last a -> Last a -> Bool #

(/=) :: Last a -> Last a -> Bool #

Eq m => Eq (WrappedMonoid m) 
Eq a => Eq (Option a) 

Methods

(==) :: Option a -> Option a -> Bool #

(/=) :: Option a -> Option a -> Bool #

Eq a => Eq (NonEmpty a) 

Methods

(==) :: NonEmpty a -> NonEmpty a -> Bool #

(/=) :: NonEmpty a -> NonEmpty a -> Bool #

Eq a => Eq (Complex a) 

Methods

(==) :: Complex a -> Complex a -> Bool #

(/=) :: Complex a -> Complex a -> Bool #

Eq a => Eq (ZipList a) 

Methods

(==) :: ZipList a -> ZipList a -> Bool #

(/=) :: ZipList a -> ZipList a -> Bool #

Eq a => Eq (Dual a) 

Methods

(==) :: Dual a -> Dual a -> Bool #

(/=) :: Dual a -> Dual a -> Bool #

Eq a => Eq (Sum a) 

Methods

(==) :: Sum a -> Sum a -> Bool #

(/=) :: Sum a -> Sum a -> Bool #

Eq a => Eq (Product a) 

Methods

(==) :: Product a -> Product a -> Bool #

(/=) :: Product a -> Product a -> Bool #

Eq a => Eq (First a) 

Methods

(==) :: First a -> First a -> Bool #

(/=) :: First a -> First a -> Bool #

Eq a => Eq (Last a) 

Methods

(==) :: Last a -> Last a -> Bool #

(/=) :: Last a -> Last a -> Bool #

Eq a => Eq (Down a) 

Methods

(==) :: Down a -> Down a -> Bool #

(/=) :: Down a -> Down a -> Bool #

Eq a => Eq (IntMap a) 

Methods

(==) :: IntMap a -> IntMap a -> Bool #

(/=) :: IntMap a -> IntMap a -> Bool #

Eq a => Eq (Seq a) 

Methods

(==) :: Seq a -> Seq a -> Bool #

(/=) :: Seq a -> Seq a -> Bool #

Eq a => Eq (ViewL a) 

Methods

(==) :: ViewL a -> ViewL a -> Bool #

(/=) :: ViewL a -> ViewL a -> Bool #

Eq a => Eq (ViewR a) 

Methods

(==) :: ViewR a -> ViewR a -> Bool #

(/=) :: ViewR a -> ViewR a -> Bool #

Eq a => Eq (Set a) 

Methods

(==) :: Set a -> Set a -> Bool #

(/=) :: Set a -> Set a -> Bool #

Eq a => Eq (Hashed a)

Uses precomputed hash to detect inequality faster

Methods

(==) :: Hashed a -> Hashed a -> Bool #

(/=) :: Hashed a -> Hashed a -> Bool #

Eq a => Eq (Array a) 

Methods

(==) :: Array a -> Array a -> Bool #

(/=) :: Array a -> Array a -> Bool #

Eq a => Eq (HashSet a) 

Methods

(==) :: HashSet a -> HashSet a -> Bool #

(/=) :: HashSet a -> HashSet a -> Bool #

Eq a => Eq (Vector a) 

Methods

(==) :: Vector a -> Vector a -> Bool #

(/=) :: Vector a -> Vector a -> Bool #

(Storable a, Eq a) => Eq (Vector a) 

Methods

(==) :: Vector a -> Vector a -> Bool #

(/=) :: Vector a -> Vector a -> Bool #

(Prim a, Eq a) => Eq (Vector a) 

Methods

(==) :: Vector a -> Vector a -> Bool #

(/=) :: Vector a -> Vector a -> Bool #

(Eq b, Eq a) => Eq (Either a b) 

Methods

(==) :: Either a b -> Either a b -> Bool #

(/=) :: Either a b -> Either a b -> Bool #

Eq (f p) => Eq (Rec1 f p) 

Methods

(==) :: Rec1 f p -> Rec1 f p -> Bool #

(/=) :: Rec1 f p -> Rec1 f p -> Bool #

Eq (URec Char p) 

Methods

(==) :: URec Char p -> URec Char p -> Bool #

(/=) :: URec Char p -> URec Char p -> Bool #

Eq (URec Double p) 

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Eq (URec Float p) 

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Eq (URec Int p) 

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Eq (URec Word p) 

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

Eq (URec (Ptr ()) p) 

Methods

(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #

(Eq a, Eq b) => Eq (a, b) 

Methods

(==) :: (a, b) -> (a, b) -> Bool #

(/=) :: (a, b) -> (a, b) -> Bool #

Eq a => Eq (Arg a b) 

Methods

(==) :: Arg a b -> Arg a b -> Bool #

(/=) :: Arg a b -> Arg a b -> Bool #

Eq (Proxy k s) 

Methods

(==) :: Proxy k s -> Proxy k s -> Bool #

(/=) :: Proxy k s -> Proxy k s -> Bool #

(Eq k, Eq a) => Eq (Map k a) 

Methods

(==) :: Map k a -> Map k a -> Bool #

(/=) :: Map k a -> Map k a -> Bool #

Eq (MutableArray s a) 

Methods

(==) :: MutableArray s a -> MutableArray s a -> Bool #

(/=) :: MutableArray s a -> MutableArray s a -> Bool #

(Eq1 m, Eq a) => Eq (MaybeT m a) 

Methods

(==) :: MaybeT m a -> MaybeT m a -> Bool #

(/=) :: MaybeT m a -> MaybeT m a -> Bool #

(Eq1 m, Eq a) => Eq (ListT m a) 

Methods

(==) :: ListT m a -> ListT m a -> Bool #

(/=) :: ListT m a -> ListT m a -> Bool #

(Eq v, Eq k) => Eq (Leaf k v) 

Methods

(==) :: Leaf k v -> Leaf k v -> Bool #

(/=) :: Leaf k v -> Leaf k v -> Bool #

(Eq k, Eq v) => Eq (HashMap k v) 

Methods

(==) :: HashMap k v -> HashMap k v -> Bool #

(/=) :: HashMap k v -> HashMap k v -> Bool #

Eq c => Eq (K1 i c p) 

Methods

(==) :: K1 i c p -> K1 i c p -> Bool #

(/=) :: K1 i c p -> K1 i c p -> Bool #

(Eq (g p), Eq (f p)) => Eq ((:+:) f g p) 

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool #

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool #

(Eq (g p), Eq (f p)) => Eq ((:*:) f g p) 

Methods

(==) :: (f :*: g) p -> (f :*: g) p -> Bool #

(/=) :: (f :*: g) p -> (f :*: g) p -> Bool #

Eq (f (g p)) => Eq ((:.:) f g p) 

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool #

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool #

(Eq a, Eq b, Eq c) => Eq (a, b, c) 

Methods

(==) :: (a, b, c) -> (a, b, c) -> Bool #

(/=) :: (a, b, c) -> (a, b, c) -> Bool #

Eq a => Eq (Const k a b) 

Methods

(==) :: Const k a b -> Const k a b -> Bool #

(/=) :: Const k a b -> Const k a b -> Bool #

Eq (f a) => Eq (Alt k f a) 

Methods

(==) :: Alt k f a -> Alt k f a -> Bool #

(/=) :: Alt k f a -> Alt k f a -> Bool #

Eq ((:~:) k a b) 

Methods

(==) :: (k :~: a) b -> (k :~: a) b -> Bool #

(/=) :: (k :~: a) b -> (k :~: a) b -> Bool #

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) 

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool #

(/=) :: WriterT w m a -> WriterT w m a -> Bool #

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a) 

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool #

(/=) :: WriterT w m a -> WriterT w m a -> Bool #

(Eq1 f, Eq a) => Eq (IdentityT * f a) 

Methods

(==) :: IdentityT * f a -> IdentityT * f a -> Bool #

(/=) :: IdentityT * f a -> IdentityT * f a -> Bool #

(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a) 

Methods

(==) :: ExceptT e m a -> ExceptT e m a -> Bool #

(/=) :: ExceptT e m a -> ExceptT e m a -> Bool #

(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) 

Methods

(==) :: ErrorT e m a -> ErrorT e m a -> Bool #

(/=) :: ErrorT e m a -> ErrorT e m a -> Bool #

Eq (f p) => Eq (M1 i c f p) 

Methods

(==) :: M1 i c f p -> M1 i c f p -> Bool #

(/=) :: M1 i c f p -> M1 i c f p -> Bool #

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 

Methods

(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Sum * f g a) 

Methods

(==) :: Sum * f g a -> Sum * f g a -> Bool #

(/=) :: Sum * f g a -> Sum * f g a -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Product * f g a) 

Methods

(==) :: Product * f g a -> Product * f g a -> Bool #

(/=) :: Product * f g a -> Product * f g a -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 

Methods

(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #

(Eq1 f, Eq1 g, Eq a) => Eq (Compose * * f g a) 

Methods

(==) :: Compose * * f g a -> Compose * * f g a -> Bool #

(/=) :: Compose * * f g a -> Compose * * f g a -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 

Methods

(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) 

Methods

(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) 

Methods

(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Methods

(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #

class Bounded a where #

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.

Minimal complete definition

minBound, maxBound

Methods

minBound :: a #

maxBound :: a #

Instances

Bounded Bool 
Bounded Char 
Bounded Int 

Methods

minBound :: Int #

maxBound :: Int #

Bounded Int8 
Bounded Int16 
Bounded Int32 
Bounded Int64 
Bounded Ordering 
Bounded Word 
Bounded Word8 
Bounded Word16 
Bounded Word32 
Bounded Word64 
Bounded () 

Methods

minBound :: () #

maxBound :: () #

Bounded CChar 
Bounded CSChar 
Bounded CUChar 
Bounded CShort 
Bounded CUShort 
Bounded CInt 
Bounded CUInt 
Bounded CLong 
Bounded CULong 
Bounded CLLong 
Bounded CULLong 
Bounded CPtrdiff 
Bounded CSize 
Bounded CWchar 
Bounded CSigAtomic 
Bounded CIntPtr 
Bounded CUIntPtr 
Bounded CIntMax 
Bounded CUIntMax 
Bounded All 

Methods

minBound :: All #

maxBound :: All #

Bounded Any 

Methods

minBound :: Any #

maxBound :: Any #

Bounded Associativity 
Bounded SourceUnpackedness 
Bounded SourceStrictness 
Bounded DecidedStrictness 
Bounded a => Bounded (Identity a) 
Bounded a => Bounded (Min a) 

Methods

minBound :: Min a #

maxBound :: Min a #

Bounded a => Bounded (Max a) 

Methods

minBound :: Max a #

maxBound :: Max a #

Bounded a => Bounded (First a) 

Methods

minBound :: First a #

maxBound :: First a #

Bounded a => Bounded (Last a) 

Methods

minBound :: Last a #

maxBound :: Last a #

Bounded a => Bounded (WrappedMonoid a) 
Bounded a => Bounded (Dual a) 

Methods

minBound :: Dual a #

maxBound :: Dual a #

Bounded a => Bounded (Sum a) 

Methods

minBound :: Sum a #

maxBound :: Sum a #

Bounded a => Bounded (Product a) 
(Bounded a, Bounded b) => Bounded (a, b) 

Methods

minBound :: (a, b) #

maxBound :: (a, b) #

Bounded (Proxy k s) 

Methods

minBound :: Proxy k s #

maxBound :: Proxy k s #

(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) 

Methods

minBound :: (a, b, c) #

maxBound :: (a, b, c) #

Bounded a => Bounded (Const k a b) 

Methods

minBound :: Const k a b #

maxBound :: Const k a b #

(~) k a b => Bounded ((:~:) k a b) 

Methods

minBound :: (k :~: a) b #

maxBound :: (k :~: a) b #

(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) 

Methods

minBound :: (a, b, c, d) #

maxBound :: (a, b, c, d) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) 

Methods

minBound :: (a, b, c, d, e) #

maxBound :: (a, b, c, d, e) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) 

Methods

minBound :: (a, b, c, d, e, f) #

maxBound :: (a, b, c, d, e, f) #

(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) 

Methods

minBound :: (a, b, c, d, e, f, g) #

maxBound :: (a, b, c, d, e, f, g) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h) #

maxBound :: (a, b, c, d, e, f, g, h) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i) #

maxBound :: (a, b, c, d, e, f, g, h, i) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j) #

maxBound :: (a, b, c, d, e, f, g, h, i, j) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

(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) 

Methods

minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

class Enum a where #

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:

   enumFrom     x   = enumFromTo     x maxBound
   enumFromThen x y = enumFromThenTo x y bound
     where
       bound | fromEnum y >= fromEnum x = maxBound
             | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a #

the successor of a value. For numeric types, succ adds 1.

pred :: a -> a #

the predecessor of a value. For numeric types, pred subtracts 1.

toEnum :: Int -> a #

Convert from an Int.

fromEnum :: a -> 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.

enumFrom :: a -> [a] #

Used in Haskell's translation of [n..].

enumFromThen :: a -> a -> [a] #

Used in Haskell's translation of [n,n'..].

enumFromTo :: a -> a -> [a] #

Used in Haskell's translation of [n..m].

enumFromThenTo :: a -> a -> a -> [a] #

Used in Haskell's translation of [n,n'..m].

Instances

Enum Bool 

Methods

succ :: Bool -> Bool #

pred :: Bool -> Bool #

toEnum :: Int -> Bool #

fromEnum :: Bool -> Int #

enumFrom :: Bool -> [Bool] #

enumFromThen :: Bool -> Bool -> [Bool] #

enumFromTo :: Bool -> Bool -> [Bool] #

enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #

Enum Char 

Methods

succ :: Char -> Char #

pred :: Char -> Char #

toEnum :: Int -> Char #

fromEnum :: Char -> Int #

enumFrom :: Char -> [Char] #

enumFromThen :: Char -> Char -> [Char] #

enumFromTo :: Char -> Char -> [Char] #

enumFromThenTo :: Char -> Char -> Char -> [Char] #

Enum Int 

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Enum Int8 

Methods

succ :: Int8 -> Int8 #

pred :: Int8 -> Int8 #

toEnum :: Int -> Int8 #

fromEnum :: Int8 -> Int #

enumFrom :: Int8 -> [Int8] #

enumFromThen :: Int8 -> Int8 -> [Int8] #

enumFromTo :: Int8 -> Int8 -> [Int8] #

enumFromThenTo :: Int8 -> Int8 -> Int8 -> [Int8] #

Enum Int16 
Enum Int32 
Enum Int64 
Enum Integer 
Enum Ordering 
Enum Word 

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Enum Word8 
Enum Word16 
Enum Word32 
Enum Word64 
Enum () 

Methods

succ :: () -> () #

pred :: () -> () #

toEnum :: Int -> () #

fromEnum :: () -> Int #

enumFrom :: () -> [()] #

enumFromThen :: () -> () -> [()] #

enumFromTo :: () -> () -> [()] #

enumFromThenTo :: () -> () -> () -> [()] #

Enum CChar 
Enum CSChar 
Enum CUChar 
Enum CShort 
Enum CUShort 
Enum CInt 

Methods

succ :: CInt -> CInt #

pred :: CInt -> CInt #

toEnum :: Int -> CInt #

fromEnum :: CInt -> Int #

enumFrom :: CInt -> [CInt] #

enumFromThen :: CInt -> CInt -> [CInt] #

enumFromTo :: CInt -> CInt -> [CInt] #

enumFromThenTo :: CInt -> CInt -> CInt -> [CInt] #

Enum CUInt 
Enum CLong 
Enum CULong 
Enum CLLong 
Enum CULLong 
Enum CFloat 
Enum CDouble 
Enum CPtrdiff 
Enum CSize 
Enum CWchar 
Enum CSigAtomic 
Enum CClock 
Enum CTime 
Enum CUSeconds 
Enum CSUSeconds 
Enum CIntPtr 
Enum CUIntPtr 
Enum CIntMax 
Enum CUIntMax 
Enum Associativity 
Enum SourceUnpackedness 
Enum SourceStrictness 
Enum DecidedStrictness 
Integral a => Enum (Ratio a) 

Methods

succ :: Ratio a -> Ratio a #

pred :: Ratio a -> Ratio a #

toEnum :: Int -> Ratio a #

fromEnum :: Ratio a -> Int #

enumFrom :: Ratio a -> [Ratio a] #

enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #

enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #

enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] #

Enum a => Enum (Identity a) 
Enum a => Enum (Min a) 

Methods

succ :: Min a -> Min a #

pred :: Min a -> Min a #

toEnum :: Int -> Min a #

fromEnum :: Min a -> Int #

enumFrom :: Min a -> [Min a] #

enumFromThen :: Min a -> Min a -> [Min a] #

enumFromTo :: Min a -> Min a -> [Min a] #

enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] #

Enum a => Enum (Max a) 

Methods

succ :: Max a -> Max a #

pred :: Max a -> Max a #

toEnum :: Int -> Max a #

fromEnum :: Max a -> Int #

enumFrom :: Max a -> [Max a] #

enumFromThen :: Max a -> Max a -> [Max a] #

enumFromTo :: Max a -> Max a -> [Max a] #

enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] #

Enum a => Enum (First a) 

Methods

succ :: First a -> First a #

pred :: First a -> First a #

toEnum :: Int -> First a #

fromEnum :: First a -> Int #

enumFrom :: First a -> [First a] #

enumFromThen :: First a -> First a -> [First a] #

enumFromTo :: First a -> First a -> [First a] #

enumFromThenTo :: First a -> First a -> First a -> [First a] #

Enum a => Enum (Last a) 

Methods

succ :: Last a -> Last a #

pred :: Last a -> Last a #

toEnum :: Int -> Last a #

fromEnum :: Last a -> Int #

enumFrom :: Last a -> [Last a] #

enumFromThen :: Last a -> Last a -> [Last a] #

enumFromTo :: Last a -> Last a -> [Last a] #

enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] #

Enum a => Enum (WrappedMonoid a) 
Enum (Proxy k s) 

Methods

succ :: Proxy k s -> Proxy k s #

pred :: Proxy k s -> Proxy k s #

toEnum :: Int -> Proxy k s #

fromEnum :: Proxy k s -> Int #

enumFrom :: Proxy k s -> [Proxy k s] #

enumFromThen :: Proxy k s -> Proxy k s -> [Proxy k s] #

enumFromTo :: Proxy k s -> Proxy k s -> [Proxy k s] #

enumFromThenTo :: Proxy k s -> Proxy k s -> Proxy k s -> [Proxy k s] #

Enum a => Enum (Const k a b) 

Methods

succ :: Const k a b -> Const k a b #

pred :: Const k a b -> Const k a b #

toEnum :: Int -> Const k a b #

fromEnum :: Const k a b -> Int #

enumFrom :: Const k a b -> [Const k a b] #

enumFromThen :: Const k a b -> Const k a b -> [Const k a b] #

enumFromTo :: Const k a b -> Const k a b -> [Const k a b] #

enumFromThenTo :: Const k a b -> Const k a b -> Const k a b -> [Const k a b] #

Enum (f a) => Enum (Alt k f a) 

Methods

succ :: Alt k f a -> Alt k f a #

pred :: Alt k f a -> Alt k f a #

toEnum :: Int -> Alt k f a #

fromEnum :: Alt k f a -> Int #

enumFrom :: Alt k f a -> [Alt k f a] #

enumFromThen :: Alt k f a -> Alt k f a -> [Alt k f a] #

enumFromTo :: Alt k f a -> Alt k f a -> [Alt k f a] #

enumFromThenTo :: Alt k f a -> Alt k f a -> Alt k f a -> [Alt k f a] #

(~) k a b => Enum ((:~:) k a b) 

Methods

succ :: (k :~: a) b -> (k :~: a) b #

pred :: (k :~: a) b -> (k :~: a) b #

toEnum :: Int -> (k :~: a) b #

fromEnum :: (k :~: a) b -> Int #

enumFrom :: (k :~: a) b -> [(k :~: a) b] #

enumFromThen :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #

enumFromTo :: (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #

enumFromThenTo :: (k :~: a) b -> (k :~: a) b -> (k :~: a) b -> [(k :~: a) b] #

class Show a #

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

  • The result of show is 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 showsPrec will produce infix applications of the constructor.
  • the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
  • If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

  • show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Instances

Show Bool 

Methods

showsPrec :: Int -> Bool -> ShowS #

show :: Bool -> String #

showList :: [Bool] -> ShowS #

Show Char 

Methods

showsPrec :: Int -> Char -> ShowS #

show :: Char -> String #

showList :: [Char] -> ShowS #

Show Int 

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Show Int8 

Methods

showsPrec :: Int -> Int8 -> ShowS #

show :: Int8 -> String #

showList :: [Int8] -> ShowS #

Show Int16 

Methods

showsPrec :: Int -> Int16 -> ShowS #

show :: Int16 -> String #

showList :: [Int16] -> ShowS #

Show Int32 

Methods

showsPrec :: Int -> Int32 -> ShowS #

show :: Int32 -> String #

showList :: [Int32] -> ShowS #

Show Int64 

Methods

showsPrec :: Int -> Int64 -> ShowS #

show :: Int64 -> String #

showList :: [Int64] -> ShowS #

Show Integer 
Show Ordering 
Show Word 

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Show Word8 

Methods

showsPrec :: Int -> Word8 -> ShowS #

show :: Word8 -> String #

showList :: [Word8] -> ShowS #

Show Word16 
Show Word32 
Show Word64 
Show CallStack 
Show TypeRep 
Show () 

Methods

showsPrec :: Int -> () -> ShowS #

show :: () -> String #

showList :: [()] -> ShowS #

Show TyCon 

Methods

showsPrec :: Int -> TyCon -> ShowS #

show :: TyCon -> String #

showList :: [TyCon] -> ShowS #

Show Module 
Show TrName 
Show Handle 
Show HandleType 

Methods

showsPrec :: Int -> HandleType -> ShowS #

show :: HandleType -> String #

showList :: [HandleType] -> ShowS #

Show Void 

Methods

showsPrec :: Int -> Void -> ShowS #

show :: Void -> String #

showList :: [Void] -> ShowS #

Show Version 
Show PatternMatchFail 
Show RecSelError 
Show RecConError 
Show RecUpdError 
Show NoMethodError 
Show TypeError 
Show NonTermination 
Show NestedAtomically 
Show BlockedIndefinitelyOnMVar 
Show BlockedIndefinitelyOnSTM 
Show Deadlock 
Show AllocationLimitExceeded 
Show AssertionFailed 
Show SomeAsyncException 
Show AsyncException 
Show ArrayException 
Show ExitCode 
Show IOErrorType 
Show BufferMode 
Show Newline 
Show NewlineMode 
Show CChar 

Methods

showsPrec :: Int -> CChar -> ShowS #

show :: CChar -> String #

showList :: [CChar] -> ShowS #

Show CSChar 
Show CUChar 
Show CShort 
Show CUShort 
Show CInt 

Methods

showsPrec :: Int -> CInt -> ShowS #

show :: CInt -> String #

showList :: [CInt] -> ShowS #

Show CUInt 

Methods

showsPrec :: Int -> CUInt -> ShowS #

show :: CUInt -> String #

showList :: [CUInt] -> ShowS #

Show CLong 

Methods

showsPrec :: Int -> CLong -> ShowS #

show :: CLong -> String #

showList :: [CLong] -> ShowS #

Show CULong 
Show CLLong 
Show CULLong 
Show CFloat 
Show CDouble 
Show CPtrdiff 
Show CSize 

Methods

showsPrec :: Int -> CSize -> ShowS #

show :: CSize -> String #

showList :: [CSize] -> ShowS #

Show CWchar 
Show CSigAtomic 
Show CClock 
Show CTime 

Methods

showsPrec :: Int -> CTime -> ShowS #

show :: CTime -> String #

showList :: [CTime] -> ShowS #

Show CUSeconds 
Show CSUSeconds 
Show CIntPtr 
Show CUIntPtr 
Show CIntMax 
Show CUIntMax 
Show All 

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Show Any 

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Show Fixity 
Show Associativity 
Show SourceUnpackedness 
Show SourceStrictness 
Show DecidedStrictness 
Show MaskingState 
Show IOException 
Show ErrorCall 
Show ArithException 
Show SomeNat 
Show SomeSymbol 
Show SomeException 
Show SrcLoc 
Show ByteString 
Show ByteString 
Show IntSet 
Show CodePoint 

Methods

showsPrec :: Int -> CodePoint -> ShowS #

show :: CodePoint -> String #

showList :: [CodePoint] -> ShowS #

Show DecoderState 

Methods

showsPrec :: Int -> DecoderState -> ShowS #

show :: DecoderState -> String #

showList :: [DecoderState] -> ShowS #

Show Decoding 
Show UnicodeException 
Show a => Show [a] 

Methods

showsPrec :: Int -> [a] -> ShowS #

show :: [a] -> String #

showList :: [[a]] -> ShowS #

Show a => Show (Maybe a) 

Methods

showsPrec :: Int -> Maybe a -> ShowS #

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Show a => Show (Ratio a) 

Methods

showsPrec :: Int -> Ratio a -> ShowS #

show :: Ratio a -> String #

showList :: [Ratio a] -> ShowS #

Show (Ptr a) 

Methods

showsPrec :: Int -> Ptr a -> ShowS #

show :: Ptr a -> String #

showList :: [Ptr a] -> ShowS #

Show (FunPtr a) 

Methods

showsPrec :: Int -> FunPtr a -> ShowS #

show :: FunPtr a -> String #

showList :: [FunPtr a] -> ShowS #

Show (V1 p) 

Methods

showsPrec :: Int -> V1 p -> ShowS #

show :: V1 p -> String #

showList :: [V1 p] -> ShowS #

Show (U1 p) 

Methods

showsPrec :: Int -> U1 p -> ShowS #

show :: U1 p -> String #

showList :: [U1 p] -> ShowS #

Show p => Show (Par1 p) 

Methods

showsPrec :: Int -> Par1 p -> ShowS #

show :: Par1 p -> String #

showList :: [Par1 p] -> ShowS #

Show (ForeignPtr a) 
Show a => Show (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Methods

showsPrec :: Int -> Identity a -> ShowS #

show :: Identity a -> String #

showList :: [Identity a] -> ShowS #

Show a => Show (Min a) 

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Show a => Show (Max a) 

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Show a => Show (First a) 

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a) 

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show m => Show (WrappedMonoid m) 
Show a => Show (Option a) 

Methods

showsPrec :: Int -> Option a -> ShowS #

show :: Option a -> String #

showList :: [Option a] -> ShowS #

Show a => Show (NonEmpty a) 

Methods

showsPrec :: Int -> NonEmpty a -> ShowS #

show :: NonEmpty a -> String #

showList :: [NonEmpty a] -> ShowS #

Show a => Show (Complex a) 

Methods

showsPrec :: Int -> Complex a -> ShowS #

show :: Complex a -> String #

showList :: [Complex a] -> ShowS #

Show a => Show (ZipList a) 

Methods

showsPrec :: Int -> ZipList a -> ShowS #

show :: ZipList a -> String #

showList :: [ZipList a] -> ShowS #

Show a => Show (Dual a) 

Methods

showsPrec :: Int -> Dual a -> ShowS #

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Show a => Show (Sum a) 

Methods

showsPrec :: Int -> Sum a -> ShowS #

show :: Sum a -> String #

showList :: [Sum a] -> ShowS #

Show a => Show (Product a) 

Methods

showsPrec :: Int -> Product a -> ShowS #

show :: Product a -> String #

showList :: [Product a] -> ShowS #

Show a => Show (First a) 

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a) 

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show a => Show (Down a) 

Methods

showsPrec :: Int -> Down a -> ShowS #

show :: Down a -> String #

showList :: [Down a] -> ShowS #

Show a => Show (IntMap a) 

Methods

showsPrec :: Int -> IntMap a -> ShowS #

show :: IntMap a -> String #

showList :: [IntMap a] -> ShowS #

Show a => Show (Seq a) 

Methods

showsPrec :: Int -> Seq a -> ShowS #

show :: Seq a -> String #

showList :: [Seq a] -> ShowS #

Show a => Show (ViewL a) 

Methods

showsPrec :: Int -> ViewL a -> ShowS #

show :: ViewL a -> String #

showList :: [ViewL a] -> ShowS #

Show a => Show (ViewR a) 

Methods

showsPrec :: Int -> ViewR a -> ShowS #

show :: ViewR a -> String #

showList :: [ViewR a] -> ShowS #

Show a => Show (Set a) 

Methods

showsPrec :: Int -> Set a -> ShowS #

show :: Set a -> String #

showList :: [Set a] -> ShowS #

Show a => Show (Hashed a) 

Methods

showsPrec :: Int -> Hashed a -> ShowS #

show :: Hashed a -> String #

showList :: [Hashed a] -> ShowS #

Show a => Show (Array a) 

Methods

showsPrec :: Int -> Array a -> ShowS #

show :: Array a -> String #

showList :: [Array a] -> ShowS #

Show a => Show (Array a) 

Methods

showsPrec :: Int -> Array a -> ShowS #

show :: Array a -> String #

showList :: [Array a] -> ShowS #

Show a => Show (HashSet a) 

Methods

showsPrec :: Int -> HashSet a -> ShowS #

show :: HashSet a -> String #

showList :: [HashSet a] -> ShowS #

Show a => Show (Vector a) 

Methods

showsPrec :: Int -> Vector a -> ShowS #

show :: Vector a -> String #

showList :: [Vector a] -> ShowS #

(Show a, Storable a) => Show (Vector a) 

Methods

showsPrec :: Int -> Vector a -> ShowS #

show :: Vector a -> String #

showList :: [Vector a] -> ShowS #

(Show a, Prim a) => Show (Vector a) 

Methods

showsPrec :: Int -> Vector a -> ShowS #

show :: Vector a -> String #

showList :: [Vector a] -> ShowS #

(Show b, Show a) => Show (Either a b) 

Methods

showsPrec :: Int -> Either a b -> ShowS #

show :: Either a b -> String #

showList :: [Either a b] -> ShowS #

Show (f p) => Show (Rec1 f p) 

Methods

showsPrec :: Int -> Rec1 f p -> ShowS #

show :: Rec1 f p -> String #

showList :: [Rec1 f p] -> ShowS #

Show (URec Char p) 

Methods

showsPrec :: Int -> URec Char p -> ShowS #

show :: URec Char p -> String #

showList :: [URec Char p] -> ShowS #

Show (URec Double p) 

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Show (URec Float p) 

Methods

showsPrec :: Int -> URec Float p -> ShowS #

show :: URec Float p -> String #

showList :: [URec Float p] -> ShowS #

Show (URec Int p) 

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Show (URec Word p) 

Methods

showsPrec :: Int -> URec Word p -> ShowS #

show :: URec Word p -> String #

showList :: [URec Word p] -> ShowS #

(Show a, Show b) => Show (a, b) 

Methods

showsPrec :: Int -> (a, b) -> ShowS #

show :: (a, b) -> String #

showList :: [(a, b)] -> ShowS #

Show (ST s a) 

Methods

showsPrec :: Int -> ST s a -> ShowS #

show :: ST s a -> String #

showList :: [ST s a] -> ShowS #

(Show b, Show a) => Show (Arg a b) 

Methods

showsPrec :: Int -> Arg a b -> ShowS #

show :: Arg a b -> String #

showList :: [Arg a b] -> ShowS #

Show (Proxy k s) 

Methods

showsPrec :: Int -> Proxy k s -> ShowS #

show :: Proxy k s -> String #

showList :: [Proxy k s] -> ShowS #

(Show k, Show a) => Show (Map k a) 

Methods

showsPrec :: Int -> Map k a -> ShowS #

show :: Map k a -> String #

showList :: [Map k a] -> ShowS #

(Show1 m, Show a) => Show (MaybeT m a) 

Methods

showsPrec :: Int -> MaybeT m a -> ShowS #

show :: MaybeT m a -> String #

showList :: [MaybeT m a] -> ShowS #

(Show1 m, Show a) => Show (ListT m a) 

Methods

showsPrec :: Int -> ListT m a -> ShowS #

show :: ListT m a -> String #

showList :: [ListT m a] -> ShowS #

(Show k, Show v) => Show (HashMap k v) 

Methods

showsPrec :: Int -> HashMap k v -> ShowS #

show :: HashMap k v -> String #

showList :: [HashMap k v] -> ShowS #

Show c => Show (K1 i c p) 

Methods

showsPrec :: Int -> K1 i c p -> ShowS #

show :: K1 i c p -> String #

showList :: [K1 i c p] -> ShowS #

(Show (g p), Show (f p)) => Show ((:+:) f g p) 

Methods

showsPrec :: Int -> (f :+: g) p -> ShowS #

show :: (f :+: g) p -> String #

showList :: [(f :+: g) p] -> ShowS #

(Show (g p), Show (f p)) => Show ((:*:) f g p) 

Methods

showsPrec :: Int -> (f :*: g) p -> ShowS #

show :: (f :*: g) p -> String #

showList :: [(f :*: g) p] -> ShowS #

Show (f (g p)) => Show ((:.:) f g p) 

Methods

showsPrec :: Int -> (f :.: g) p -> ShowS #

show :: (f :.: g) p -> String #

showList :: [(f :.: g) p] -> ShowS #

(Show a, Show b, Show c) => Show (a, b, c) 

Methods

showsPrec :: Int -> (a, b, c) -> ShowS #

show :: (a, b, c) -> String #

showList :: [(a, b, c)] -> ShowS #

Show a => Show (Const k a b)

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Methods

showsPrec :: Int -> Const k a b -> ShowS #

show :: Const k a b -> String #

showList :: [Const k a b] -> ShowS #

Show (f a) => Show (Alt k f a) 

Methods

showsPrec :: Int -> Alt k f a -> ShowS #

show :: Alt k f a -> String #

showList :: [Alt k f a] -> ShowS #

Show ((:~:) k a b) 

Methods

showsPrec :: Int -> (k :~: a) b -> ShowS #

show :: (k :~: a) b -> String #

showList :: [(k :~: a) b] -> ShowS #

(Show w, Show1 m, Show a) => Show (WriterT w m a) 

Methods

showsPrec :: Int -> WriterT w m a -> ShowS #

show :: WriterT w m a -> String #

showList :: [WriterT w m a] -> ShowS #

(Show w, Show1 m, Show a) => Show (WriterT w m a) 

Methods

showsPrec :: Int -> WriterT w m a -> ShowS #

show :: WriterT w m a -> String #

showList :: [WriterT w m a] -> ShowS #

(Show1 f, Show a) => Show (IdentityT * f a) 

Methods

showsPrec :: Int -> IdentityT * f a -> ShowS #

show :: IdentityT * f a -> String #

showList :: [IdentityT * f a] -> ShowS #

(Show e, Show1 m, Show a) => Show (ExceptT e m a) 

Methods

showsPrec :: Int -> ExceptT e m a -> ShowS #

show :: ExceptT e m a -> String #

showList :: [ExceptT e m a] -> ShowS #

(Show e, Show1 m, Show a) => Show (ErrorT e m a) 

Methods

showsPrec :: Int -> ErrorT e m a -> ShowS #

show :: ErrorT e m a -> String #

showList :: [ErrorT e m a] -> ShowS #

Show (f p) => Show (M1 i c f p) 

Methods

showsPrec :: Int -> M1 i c f p -> ShowS #

show :: M1 i c f p -> String #

showList :: [M1 i c f p] -> ShowS #

(Show a, Show b, Show c, Show d) => Show (a, b, c, d) 

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS #

show :: (a, b, c, d) -> String #

showList :: [(a, b, c, d)] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Sum * f g a) 

Methods

showsPrec :: Int -> Sum * f g a -> ShowS #

show :: Sum * f g a -> String #

showList :: [Sum * f g a] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Product * f g a) 

Methods

showsPrec :: Int -> Product * f g a -> ShowS #

show :: Product * f g a -> String #

showList :: [Product * f g a] -> ShowS #

(Show a, Show b, Show c, Show d, Show e) => Show (a, b, c, d, e) 

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS #

show :: (a, b, c, d, e) -> String #

showList :: [(a, b, c, d, e)] -> ShowS #

(Show1 f, Show1 g, Show a) => Show (Compose * * f g a) 

Methods

showsPrec :: Int -> Compose * * f g a -> ShowS #

show :: Compose * * f g a -> String #

showList :: [Compose * * f g a] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f) => Show (a, b, c, d, e, f) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f) -> ShowS #

show :: (a, b, c, d, e, f) -> String #

showList :: [(a, b, c, d, e, f)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g) => Show (a, b, c, d, e, f, g) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g) -> ShowS #

show :: (a, b, c, d, e, f, g) -> String #

showList :: [(a, b, c, d, e, f, g)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h) => Show (a, b, c, d, e, f, g, h) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h) -> ShowS #

show :: (a, b, c, d, e, f, g, h) -> String #

showList :: [(a, b, c, d, e, f, g, h)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i) => Show (a, b, c, d, e, f, g, h, i) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i) -> String #

showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j) => Show (a, b, c, d, e, f, g, h, i, j) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k) => Show (a, b, c, d, e, f, g, h, i, j, k) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l) => Show (a, b, c, d, e, f, g, h, i, j, k, l) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS #

(Show a, Show b, Show c, Show d, Show e, Show f, Show g, Show h, Show i, Show j, Show k, Show l, Show m, Show n, Show o) => Show (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) 

Methods

showsPrec :: Int -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> ShowS #

show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String #

showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS #

class Read a #

Parsing of Strings, producing values.

Derived instances of Read make the following assumptions, which derived instances of Show obey:

  • If the constructor is defined to be an infix operator, then the derived Read instance 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 Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration.
  • The derived Read instance 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

Minimal complete definition

readsPrec | readPrec

Instances

Read Bool 
Read Char 
Read Double 
Read Float 
Read Int 
Read Int8 
Read Int16 
Read Int32 
Read Int64 
Read Integer 
Read Ordering 
Read Word 
Read Word8 
Read Word16 
Read Word32 
Read Word64 
Read () 

Methods

readsPrec :: Int -> ReadS () #

readList :: ReadS [()] #

readPrec :: ReadPrec () #

readListPrec :: ReadPrec [()] #

Read Void

Reading a Void value is always a parse error, considering Void as a data type with no constructors.

Read Version 
Read ExitCode 
Read BufferMode 
Read Newline 
Read NewlineMode 
Read CChar 
Read CSChar 
Read CUChar 
Read CShort 
Read CUShort 
Read CInt 
Read CUInt 
Read CLong 
Read CULong 
Read CLLong 
Read CULLong 
Read CFloat 
Read CDouble 
Read CPtrdiff 
Read CSize 
Read CWchar 
Read CSigAtomic 
Read CClock 
Read CTime 
Read CUSeconds 
Read CSUSeconds 
Read CIntPtr 
Read CUIntPtr 
Read CIntMax 
Read CUIntMax 
Read All 
Read Any 
Read Fixity 
Read Associativity 
Read SourceUnpackedness 
Read SourceStrictness 
Read DecidedStrictness 
Read SomeNat 
Read SomeSymbol 
Read Lexeme 
Read GeneralCategory 
Read ByteString 
Read ByteString 
Read IntSet 
Read a => Read [a] 

Methods

readsPrec :: Int -> ReadS [a] #

readList :: ReadS [[a]] #

readPrec :: ReadPrec [a] #

readListPrec :: ReadPrec [[a]] #

Read a => Read (Maybe a) 
(Integral a, Read a) => Read (Ratio a) 
Read (V1 p) 
Read (U1 p) 
Read p => Read (Par1 p) 
Read a => Read (Identity a)

This instance would be equivalent to the derived instances of the Identity newtype if the runIdentity field were removed

Read a => Read (Min a) 
Read a => Read (Max a) 
Read a => Read (First a) 
Read a => Read (Last a) 
Read m => Read (WrappedMonoid m) 
Read a => Read (Option a) 
Read a => Read (NonEmpty a) 
Read a => Read (Complex a) 
Read a => Read (ZipList a) 
Read a => Read (Dual a) 
Read a => Read (Sum a) 
Read a => Read (Product a) 
Read a => Read (First a) 
Read a => Read (Last a) 
Read a => Read (Down a) 
Read e => Read (IntMap e) 
Read a => Read (Seq a) 
Read a => Read (ViewL a) 
Read a => Read (ViewR a) 
(Read a, Ord a) => Read (Set a) 
Read a => Read (Array a) 
(Eq a, Hashable a, Read a) => Read (HashSet a) 
Read a => Read (Vector a) 
(Read a, Storable a) => Read (Vector a) 
(Read a, Prim a) => Read (Vector a) 
(Read b, Read a) => Read (Either a b) 
Read (f p) => Read (Rec1 f p) 

Methods

readsPrec :: Int -> ReadS (Rec1 f p) #

readList :: ReadS [Rec1 f p] #

readPrec :: ReadPrec (Rec1 f p) #

readListPrec :: ReadPrec [Rec1 f p] #

(Read a, Read b) => Read (a, b) 

Methods

readsPrec :: Int -> ReadS (a, b) #

readList :: ReadS [(a, b)] #

readPrec :: ReadPrec (a, b) #

readListPrec :: ReadPrec [(a, b)] #

(Ix a, Read a, Read b) => Read (Array a b) 
(Read b, Read a) => Read (Arg a b) 

Methods

readsPrec :: Int -> ReadS (Arg a b) #

readList :: ReadS [Arg a b] #

readPrec :: ReadPrec (Arg a b) #

readListPrec :: ReadPrec [Arg a b] #

Read (Proxy k s) 
(Ord k, Read k, Read e) => Read (Map k e) 

Methods

readsPrec :: Int -> ReadS (Map k e) #

readList :: ReadS [Map k e] #

readPrec :: ReadPrec (Map k e) #

readListPrec :: ReadPrec [Map k e] #

(Read1 m, Read a) => Read (MaybeT m a) 
(Read1 m, Read a) => Read (ListT m a) 
(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) 
Read c => Read (K1 i c p) 

Methods

readsPrec :: Int -> ReadS (K1 i c p) #

readList :: ReadS [K1 i c p] #

readPrec :: ReadPrec (K1 i c p) #

readListPrec :: ReadPrec [K1 i c p] #

(Read (g p), Read (f p)) => Read ((:+:) f g p) 

Methods

readsPrec :: Int -> ReadS ((f :+: g) p) #

readList :: ReadS [(f :+: g) p] #

readPrec :: ReadPrec ((f :+: g) p) #

readListPrec :: ReadPrec [(f :+: g) p] #

(Read (g p), Read (f p)) => Read ((:*:) f g p) 

Methods

readsPrec :: Int -> ReadS ((f :*: g) p) #

readList :: ReadS [(f :*: g) p] #

readPrec :: ReadPrec ((f :*: g) p) #

readListPrec :: ReadPrec [(f :*: g) p] #

Read (f (g p)) => Read ((:.:) f g p) 

Methods

readsPrec :: Int -> ReadS ((f :.: g) p) #

readList :: ReadS [(f :.: g) p] #

readPrec :: ReadPrec ((f :.: g) p) #

readListPrec :: ReadPrec [(f :.: g) p] #

(Read a, Read b, Read c) => Read (a, b, c) 

Methods

readsPrec :: Int -> ReadS (a, b, c) #

readList :: ReadS [(a, b, c)] #

readPrec :: ReadPrec (a, b, c) #

readListPrec :: ReadPrec [(a, b, c)] #

Read a => Read (Const k a b)

This instance would be equivalent to the derived instances of the Const newtype if the runConst field were removed

Methods

readsPrec :: Int -> ReadS (Const k a b) #

readList :: ReadS [Const k a b] #

readPrec :: ReadPrec (Const k a b) #

readListPrec :: ReadPrec [Const k a b] #

Read (f a) => Read (Alt k f a) 

Methods

readsPrec :: Int -> ReadS (Alt k f a) #

readList :: ReadS [Alt k f a] #

readPrec :: ReadPrec (Alt k f a) #

readListPrec :: ReadPrec [Alt k f a] #

(~) k a b => Read ((:~:) k a b) 

Methods

readsPrec :: Int -> ReadS ((k :~: a) b) #

readList :: ReadS [(k :~: a) b] #

readPrec :: ReadPrec ((k :~: a) b) #

readListPrec :: ReadPrec [(k :~: a) b] #

(Read w, Read1 m, Read a) => Read (WriterT w m a) 

Methods

readsPrec :: Int -> ReadS (WriterT w m a) #

readList :: ReadS [WriterT w m a] #

readPrec :: ReadPrec (WriterT w m a) #

readListPrec :: ReadPrec [WriterT w m a] #

(Read w, Read1 m, Read a) => Read (WriterT w m a) 

Methods

readsPrec :: Int -> ReadS (WriterT w m a) #

readList :: ReadS [WriterT w m a] #

readPrec :: ReadPrec (WriterT w m a) #

readListPrec :: ReadPrec [WriterT w m a] #

(Read1 f, Read a) => Read (IdentityT * f a) 
(Read e, Read1 m, Read a) => Read (ExceptT e m a) 

Methods

readsPrec :: Int -> ReadS (ExceptT e m a) #

readList :: ReadS [ExceptT e m a] #

readPrec :: ReadPrec (ExceptT e m a) #

readListPrec :: ReadPrec [ExceptT e m a] #

(Read e, Read1 m, Read a) => Read (ErrorT e m a) 

Methods

readsPrec :: Int -> ReadS (ErrorT e m a) #

readList :: ReadS [ErrorT e m a] #

readPrec :: ReadPrec (ErrorT e m a) #

readListPrec :: ReadPrec [ErrorT e m a] #

Read (f p) => Read (M1 i c f p) 

Methods

readsPrec :: Int -> ReadS (M1 i c f p) #

readList :: ReadS [M1 i c f p] #

readPrec :: ReadPrec (M1 i c f p) #

readListPrec :: ReadPrec [M1 i c f p] #

(Read a, Read b, Read c, Read d) => Read (a, b, c, d) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d) #

readList :: ReadS [(a, b, c, d)] #

readPrec :: ReadPrec (a, b, c, d) #

readListPrec :: ReadPrec [(a, b, c, d)] #

(Read1 f, Read1 g, Read a) => Read (Sum * f g a) 

Methods

readsPrec :: Int -> ReadS (Sum * f g a) #

readList :: ReadS [Sum * f g a] #

readPrec :: ReadPrec (Sum * f g a) #

readListPrec :: ReadPrec [Sum * f g a] #

(Read1 f, Read1 g, Read a) => Read (Product * f g a) 

Methods

readsPrec :: Int -> ReadS (Product * f g a) #

readList :: ReadS [Product * f g a] #

readPrec :: ReadPrec (Product * f g a) #

readListPrec :: ReadPrec [Product * f g a] #

(Read a, Read b, Read c, Read d, Read e) => Read (a, b, c, d, e) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e) #

readList :: ReadS [(a, b, c, d, e)] #

readPrec :: ReadPrec (a, b, c, d, e) #

readListPrec :: ReadPrec [(a, b, c, d, e)] #

(Read1 f, Read1 g, Read a) => Read (Compose * * f g a) 

Methods

readsPrec :: Int -> ReadS (Compose * * f g a) #

readList :: ReadS [Compose * * f g a] #

readPrec :: ReadPrec (Compose * * f g a) #

readListPrec :: ReadPrec [Compose * * f g a] #

(Read a, Read b, Read c, Read d, Read e, Read f) => Read (a, b, c, d, e, f) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f) #

readList :: ReadS [(a, b, c, d, e, f)] #

readPrec :: ReadPrec (a, b, c, d, e, f) #

readListPrec :: ReadPrec [(a, b, c, d, e, f)] #

(Read a, Read b, Read c, Read d, Read e, Read f, Read g) => Read (a, b, c, d, e, f, g) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g) #

readList :: ReadS [(a, b, c, d, e, f, g)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h) #

readList :: ReadS [(a, b, c, d, e, f, g, h)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] #

(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) 

Methods

readsPrec :: Int -> ReadS (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #

readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] #

class Functor f where #

The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws:

fmap id  ==  id
fmap (f . g)  ==  fmap f . fmap g

The instances of Functor for lists, Maybe and IO satisfy these laws.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b #

(<$) :: a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances

Functor [] 

Methods

fmap :: (a -> b) -> [a] -> [b] #

(<$) :: a -> [b] -> [a] #

Functor Maybe 

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b #

(<$) :: a -> Maybe b -> Maybe a #

Functor IO 

Methods

fmap :: (a -> b) -> IO a -> IO b #

(<$) :: a -> IO b -> IO a #

Functor V1 

Methods

fmap :: (a -> b) -> V1 a -> V1 b #

(<$) :: a -> V1 b -> V1 a #

Functor U1 

Methods

fmap :: (a -> b) -> U1 a -> U1 b #

(<$) :: a -> U1 b -> U1 a #

Functor Par1 

Methods

fmap :: (a -> b) -> Par1 a -> Par1 b #

(<$) :: a -> Par1 b -> Par1 a #

Functor Id 

Methods

fmap :: (a -> b) -> Id a -> Id b #

(<$) :: a -> Id b -> Id a #

Functor P 

Methods

fmap :: (a -> b) -> P a -> P b #

(<$) :: a -> P b -> P a #

Functor Identity 

Methods

fmap :: (a -> b) -> Identity a -> Identity b #

(<$) :: a -> Identity b -> Identity a #

Functor Min 

Methods

fmap :: (a -> b) -> Min a -> Min b #

(<$) :: a -> Min b -> Min a #

Functor Max 

Methods

fmap :: (a -> b) -> Max a -> Max b #

(<$) :: a -> Max b -> Max a #

Functor First 

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last 

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor Option 

Methods

fmap :: (a -> b) -> Option a -> Option b #

(<$) :: a -> Option b -> Option a #

Functor NonEmpty 

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b #

(<$) :: a -> NonEmpty b -> NonEmpty a #

Functor Complex 

Methods

fmap :: (a -> b) -> Complex a -> Complex b #

(<$) :: a -> Complex b -> Complex a #

Functor ZipList 

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b #

(<$) :: a -> ZipList b -> ZipList a #

Functor Handler 

Methods

fmap :: (a -> b) -> Handler a -> Handler b #

(<$) :: a -> Handler b -> Handler a #

Functor Dual 

Methods

fmap :: (a -> b) -> Dual a -> Dual b #

(<$) :: a -> Dual b -> Dual a #

Functor Sum 

Methods

fmap :: (a -> b) -> Sum a -> Sum b #

(<$) :: a -> Sum b -> Sum a #

Functor Product 

Methods

fmap :: (a -> b) -> Product a -> Product b #

(<$) :: a -> Product b -> Product a #

Functor First 

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last 

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor ReadP 

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b #

(<$) :: a -> ReadP b -> ReadP a #

Functor Digit 

Methods

fmap :: (a -> b) -> Digit a -> Digit b #

(<$) :: a -> Digit b -> Digit a #

Functor Node 

Methods

fmap :: (a -> b) -> Node a -> Node b #

(<$) :: a -> Node b -> Node a #

Functor Elem 

Methods

fmap :: (a -> b) -> Elem a -> Elem b #

(<$) :: a -> Elem b -> Elem a #

Functor FingerTree 

Methods

fmap :: (a -> b) -> FingerTree a -> FingerTree b #

(<$) :: a -> FingerTree b -> FingerTree a #

Functor IntMap 

Methods

fmap :: (a -> b) -> IntMap a -> IntMap b #

(<$) :: a -> IntMap b -> IntMap a #

Functor Seq 

Methods

fmap :: (a -> b) -> Seq a -> Seq b #

(<$) :: a -> Seq b -> Seq a #

Functor ViewL 

Methods

fmap :: (a -> b) -> ViewL a -> ViewL b #

(<$) :: a -> ViewL b -> ViewL a #

Functor ViewR 

Methods

fmap :: (a -> b) -> ViewR a -> ViewR b #

(<$) :: a -> ViewR b -> ViewR a #

Functor Array 

Methods

fmap :: (a -> b) -> Array a -> Array b #

(<$) :: a -> Array b -> Array a #

Functor Vector 

Methods

fmap :: (a -> b) -> Vector a -> Vector b #

(<$) :: a -> Vector b -> Vector a #

Functor ((->) r) 

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b #

(<$) :: a -> (r -> b) -> r -> a #

Functor (Either a) 

Methods

fmap :: (a -> b) -> Either a a -> Either a b #

(<$) :: a -> Either a b -> Either a a #

Functor f => Functor (Rec1 f) 

Methods

fmap :: (a -> b) -> Rec1 f a -> Rec1 f b #

(<$) :: a -> Rec1 f b -> Rec1 f a #

Functor (URec Char) 

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b #

(<$) :: a -> URec Char b -> URec Char a #

Functor (URec Double) 

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Functor (URec Float) 

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b #

(<$) :: a -> URec Float b -> URec Float a #

Functor (URec Int) 

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Functor (URec Word) 

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b #

(<$) :: a -> URec Word b -> URec Word a #

Functor (URec (Ptr ())) 

Methods

fmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #

(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a #

Functor ((,) a) 

Methods

fmap :: (a -> b) -> (a, a) -> (a, b) #

(<$) :: a -> (a, b) -> (a, a) #

Functor (ST s) 

Methods

fmap :: (a -> b) -> ST s a -> ST s b #

(<$) :: a -> ST s b -> ST s a #

Functor (StateL s) 

Methods

fmap :: (a -> b) -> StateL s a -> StateL s b #

(<$) :: a -> StateL s b -> StateL s a #

Functor (StateR s) 

Methods

fmap :: (a -> b) -> StateR s a -> StateR s b #

(<$) :: a -> StateR s b -> StateR s a #

Functor (Arg a) 

Methods

fmap :: (a -> b) -> Arg a a -> Arg a b #

(<$) :: a -> Arg a b -> Arg a a #

Monad m => Functor (WrappedMonad m) 

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a #

Arrow a => Functor (ArrowMonad a) 

Methods

fmap :: (a -> b) -> ArrowMonad a a -> ArrowMonad a b #

(<$) :: a -> ArrowMonad a b -> ArrowMonad a a #

Functor (Proxy *) 

Methods

fmap :: (a -> b) -> Proxy * a -> Proxy * b #

(<$) :: a -> Proxy * b -> Proxy * a #

Functor (State s) 

Methods

fmap :: (a -> b) -> State s a -> State s b #

(<$) :: a -> State s b -> State s a #

Functor (Map k) 

Methods

fmap :: (a -> b) -> Map k a -> Map k b #

(<$) :: a -> Map k b -> Map k a #

Functor m => Functor (MaybeT m) 

Methods

fmap :: (a -> b) -> MaybeT m a -> MaybeT m b #

(<$) :: a -> MaybeT m b -> MaybeT m a #

Functor m => Functor (ListT m) 

Methods

fmap :: (a -> b) -> ListT m a -> ListT m b #

(<$) :: a -> ListT m b -> ListT m a #

Functor (HashMap k) 

Methods

fmap :: (a -> b) -> HashMap k a -> HashMap k b #

(<$) :: a -> HashMap k b -> HashMap k a #

Functor (K1 i c) 

Methods

fmap :: (a -> b) -> K1 i c a -> K1 i c b #

(<$) :: a -> K1 i c b -> K1 i c a #

(Functor g, Functor f) => Functor ((:+:) f g) 

Methods

fmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #

(<$) :: a -> (f :+: g) b -> (f :+: g) a #

(Functor g, Functor f) => Functor ((:*:) f g) 

Methods

fmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #

(<$) :: a -> (f :*: g) b -> (f :*: g) a #

(Functor g, Functor f) => Functor ((:.:) f g) 

Methods

fmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #

(<$) :: a -> (f :.: g) b -> (f :.: g) a #

Arrow a => Functor (WrappedArrow a b) 

Methods

fmap :: (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b #

(<$) :: a -> WrappedArrow a b b -> WrappedArrow a b a #

Functor (Const * m) 

Methods

fmap :: (a -> b) -> Const * m a -> Const * m b #

(<$) :: a -> Const * m b -> Const * m a #

Functor f => Functor (Alt * f) 

Methods

fmap :: (a -> b) -> Alt * f a -> Alt * f b #

(<$) :: a -> Alt * f b -> Alt * f a #

Functor m => Functor (WriterT w m) 

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b #

(<$) :: a -> WriterT w m b -> WriterT w m a #

Functor m => Functor (WriterT w m) 

Methods

fmap :: (a -> b) -> WriterT w m a -> WriterT w m b #

(<$) :: a -> WriterT w m b -> WriterT w m a #

Functor m => Functor (StateT s m) 

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b #

(<$) :: a -> StateT s m b -> StateT s m a #

Functor m => Functor (StateT s m) 

Methods

fmap :: (a -> b) -> StateT s m a -> StateT s m b #

(<$) :: a -> StateT s m b -> StateT s m a #

Functor m => Functor (IdentityT * m) 

Methods

fmap :: (a -> b) -> IdentityT * m a -> IdentityT * m b #

(<$) :: a -> IdentityT * m b -> IdentityT * m a #

Functor m => Functor (ExceptT e m) 

Methods

fmap :: (a -> b) -> ExceptT e m a -> ExceptT e m b #

(<$) :: a -> ExceptT e m b -> ExceptT e m a #

Functor m => Functor (ErrorT e m) 

Methods

fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b #

(<$) :: a -> ErrorT e m b -> ErrorT e m a #

Functor f => Functor (M1 i c f) 

Methods

fmap :: (a -> b) -> M1 i c f a -> M1 i c f b #

(<$) :: a -> M1 i c f b -> M1 i c f a #

(Functor f, Functor g) => Functor (Sum * f g) 

Methods

fmap :: (a -> b) -> Sum * f g a -> Sum * f g b #

(<$) :: a -> Sum * f g b -> Sum * f g a #

(Functor f, Functor g) => Functor (Product * f g) 

Methods

fmap :: (a -> b) -> Product * f g a -> Product * f g b #

(<$) :: a -> Product * f g b -> Product * f g a #

Functor m => Functor (ReaderT * r m) 

Methods

fmap :: (a -> b) -> ReaderT * r m a -> ReaderT * r m b #

(<$) :: a -> ReaderT * r m b -> ReaderT * r m a #

(Functor f, Functor g) => Functor (Compose * * f g) 

Methods

fmap :: (a -> b) -> Compose * * f g a -> Compose * * f g b #

(<$) :: a -> Compose * * f g b -> Compose * * f g a #

Functor m => Functor (RWST r w s m) 

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b #

(<$) :: a -> RWST r w s m b -> RWST r w s m a #

Functor m => Functor (RWST r w s m) 

Methods

fmap :: (a -> b) -> RWST r w s m a -> RWST r w s m b #

(<$) :: a -> RWST r w s m b -> RWST r w s m a #

class Applicative m => Monad m where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

Furthermore, the Monad and Applicative operations should relate as follows:

The above laws imply:

and that pure and (<*>) satisfy the applicative functor laws.

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1 #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a #

Inject a value into the monadic type.

fail :: String -> m a #

Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression.

As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release.

Instances

Monad [] 

Methods

(>>=) :: [a] -> (a -> [b]) -> [b] #

(>>) :: [a] -> [b] -> [b] #

return :: a -> [a] #

fail :: String -> [a] #

Monad Maybe 

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #

(>>) :: Maybe a -> Maybe b -> Maybe b #

return :: a -> Maybe a #

fail :: String -> Maybe a #

Monad IO 

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b #

(>>) :: IO a -> IO b -> IO b #

return :: a -> IO a #

fail :: String -> IO a #

Monad U1 

Methods

(>>=) :: U1 a -> (a -> U1 b) -> U1 b #

(>>) :: U1 a -> U1 b -> U1 b #

return :: a -> U1 a #

fail :: String -> U1 a #

Monad Par1 

Methods

(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b #

(>>) :: Par1 a -> Par1 b -> Par1 b #

return :: a -> Par1 a #

fail :: String -> Par1 a #

Monad P 

Methods

(>>=) :: P a -> (a -> P b) -> P b #

(>>) :: P a -> P b -> P b #

return :: a -> P a #

fail :: String -> P a #

Monad Identity 

Methods

(>>=) :: Identity a -> (a -> Identity b) -> Identity b #

(>>) :: Identity a -> Identity b -> Identity b #

return :: a -> Identity a #

fail :: String -> Identity a #

Monad Min 

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b #

(>>) :: Min a -> Min b -> Min b #

return :: a -> Min a #

fail :: String -> Min a #

Monad Max 

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b #

(>>) :: Max a -> Max b -> Max b #

return :: a -> Max a #

fail :: String -> Max a #

Monad First 

Methods

(>>=) :: First a -> (a -> First b) -> First b #

(>>) :: First a -> First b -> First b #

return :: a -> First a #

fail :: String -> First a #

Monad Last 

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

(>>) :: Last a -> Last b -> Last b #

return :: a -> Last a #

fail :: String -> Last a #

Monad Option 

Methods

(>>=) :: Option a -> (a -> Option b) -> Option b #

(>>) :: Option a -> Option b -> Option b #

return :: a -> Option a #

fail :: String -> Option a #

Monad NonEmpty 

Methods

(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b #

(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b #

return :: a -> NonEmpty a #

fail :: String -> NonEmpty a #

Monad Complex 

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b #

(>>) :: Complex a -> Complex b -> Complex b #

return :: a -> Complex a #

fail :: String -> Complex a #

Monad Dual 

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b #

(>>) :: Dual a -> Dual b -> Dual b #

return :: a -> Dual a #

fail :: String -> Dual a #

Monad Sum 

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b #

(>>) :: Sum a -> Sum b -> Sum b #

return :: a -> Sum a #

fail :: String -> Sum a #

Monad Product 

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b #

(>>) :: Product a -> Product b -> Product b #

return :: a -> Product a #

fail :: String -> Product a #

Monad First 

Methods

(>>=) :: First a -> (a -> First b) -> First b #

(>>) :: First a -> First b -> First b #

return :: a -> First a #

fail :: String -> First a #

Monad Last 

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b #

(>>) :: Last a -> Last b -> Last b #

return :: a -> Last a #

fail :: String -> Last a #

Monad ReadP 

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b #

(>>) :: ReadP a -> ReadP b -> ReadP b #

return :: a -> ReadP a #

fail :: String -> ReadP a #

Monad Seq 

Methods

(>>=) :: Seq a -> (a -> Seq b) -> Seq b #

(>>) :: Seq a -> Seq b -> Seq b #

return :: a -> Seq a #

fail :: String -> Seq a #

Monad Array 

Methods

(>>=) :: Array a -> (a -> Array b) -> Array b #

(>>) :: Array a -> Array b -> Array b #

return :: a -> Array a #

fail :: String -> Array a #

Monad Vector 

Methods

(>>=) :: Vector a -> (a -> Vector b) -> Vector b #

(>>) :: Vector a -> Vector b -> Vector b #

return :: a -> Vector a #

fail :: String -> Vector a #

Monad ((->) r) 

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b #

(>>) :: (r -> a) -> (r -> b) -> r -> b #

return :: a -> r -> a #

fail :: String -> r -> a #

Monad (Either e) 

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b #

(>>) :: Either e a -> Either e b -> Either e b #

return :: a -> Either e a #

fail :: String -> Either e a #

Monad f => Monad (Rec1 f) 

Methods

(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b #

(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b #

return :: a -> Rec1 f a #

fail :: String -> Rec1 f a #

Monoid a => Monad ((,) a) 

Methods

(>>=) :: (a, a) -> (a -> (a, b)) -> (a, b) #

(>>) :: (a, a) -> (a, b) -> (a, b) #

return :: a -> (a, a) #

fail :: String -> (a, a) #

Monad (ST s) 

Methods

(>>=) :: ST s a -> (a -> ST s b) -> ST s b #

(>>) :: ST s a -> ST s b -> ST s b #

return :: a -> ST s a #

fail :: String -> ST s a #

Monad m => Monad (WrappedMonad m) 

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b #

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #

return :: a -> WrappedMonad m a #

fail :: String -> WrappedMonad m a #

ArrowApply a => Monad (ArrowMonad a) 

Methods

(>>=) :: ArrowMonad a a -> (a -> ArrowMonad a b) -> ArrowMonad a b #

(>>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b #

return :: a -> ArrowMonad a a #

fail :: String -> ArrowMonad a a #

Monad (Proxy *) 

Methods

(>>=) :: Proxy * a -> (a -> Proxy * b) -> Proxy * b #

(>>) :: Proxy * a -> Proxy * b -> Proxy * b #

return :: a -> Proxy * a #

fail :: String -> Proxy * a #

Monad (State s) 

Methods

(>>=) :: State s a -> (a -> State s b) -> State s b #

(>>) :: State s a -> State s b -> State s b #

return :: a -> State s a #

fail :: String -> State s a #

Monad m => Monad (MaybeT m) 

Methods

(>>=) :: MaybeT m a -> (a -> MaybeT m b) -> MaybeT m b #

(>>) :: MaybeT m a -> MaybeT m b -> MaybeT m b #

return :: a -> MaybeT m a #

fail :: String -> MaybeT m a #

Monad m => Monad (ListT m) 

Methods

(>>=) :: ListT m a -> (a -> ListT m b) -> ListT m b #

(>>) :: ListT m a -> ListT m b -> ListT m b #

return :: a -> ListT m a #

fail :: String -> ListT m a #

(Monad f, Monad g) => Monad ((:*:) f g) 

Methods

(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b #

(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b #

return :: a -> (f :*: g) a #

fail :: String -> (f :*: g) a #

Monad f => Monad (Alt * f) 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b #

(>>) :: Alt * f a -> Alt * f b -> Alt * f b #

return :: a -> Alt * f a #

fail :: String -> Alt * f a #

(Monoid w, Monad m) => Monad (WriterT w m) 

Methods

(>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b #

(>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

return :: a -> WriterT w m a #

fail :: String -> WriterT w m a #

(Monoid w, Monad m) => Monad (WriterT w m) 

Methods

(>>=) :: WriterT w m a -> (a -> WriterT w m b) -> WriterT w m b #

(>>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

return :: a -> WriterT w m a #

fail :: String -> WriterT w m a #

Monad m => Monad (StateT s m) 

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b #

(>>) :: StateT s m a -> StateT s m b -> StateT s m b #

return :: a -> StateT s m a #

fail :: String -> StateT s m a #

Monad m => Monad (StateT s m) 

Methods

(>>=) :: StateT s m a -> (a -> StateT s m b) -> StateT s m b #

(>>) :: StateT s m a -> StateT s m b -> StateT s m b #

return :: a -> StateT s m a #

fail :: String -> StateT s m a #

Monad m => Monad (IdentityT * m) 

Methods

(>>=) :: IdentityT * m a -> (a -> IdentityT * m b) -> IdentityT * m b #

(>>) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m b #

return :: a -> IdentityT * m a #

fail :: String -> IdentityT * m a #

Monad m => Monad (ExceptT e m) 

Methods

(>>=) :: ExceptT e m a -> (a -> ExceptT e m b) -> ExceptT e m b #

(>>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b #

return :: a -> ExceptT e m a #

fail :: String -> ExceptT e m a #

(Monad m, Error e) => Monad (ErrorT e m) 

Methods

(>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b #

(>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b #

return :: a -> ErrorT e m a #

fail :: String -> ErrorT e m a #

Monad f => Monad (M1 i c f) 

Methods

(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b #

(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b #

return :: a -> M1 i c f a #

fail :: String -> M1 i c f a #

(Monad f, Monad g) => Monad (Product * f g) 

Methods

(>>=) :: Product * f g a -> (a -> Product * f g b) -> Product * f g b #

(>>) :: Product * f g a -> Product * f g b -> Product * f g b #

return :: a -> Product * f g a #

fail :: String -> Product * f g a #

Monad m => Monad (ReaderT * r m) 

Methods

(>>=) :: ReaderT * r m a -> (a -> ReaderT * r m b) -> ReaderT * r m b #

(>>) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m b #

return :: a -> ReaderT * r m a #

fail :: String -> ReaderT * r m a #

(Monoid w, Monad m) => Monad (RWST r w s m) 

Methods

(>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b #

(>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

return :: a -> RWST r w s m a #

fail :: String -> RWST r w s m a #

(Monoid w, Monad m) => Monad (RWST r w s m) 

Methods

(>>=) :: RWST r w s m a -> (a -> RWST r w s m b) -> RWST r w s m b #

(>>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

return :: a -> RWST r w s m a #

fail :: String -> RWST r w s m a #

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 #

Same as >>=, but with the arguments interchanged.

class IsString a where #

Class for string-like datastructures; used by the overloaded string extension (-XOverloadedStrings in GHC).

Minimal complete definition

fromString

Methods

fromString :: String -> a #

Instances

IsString ByteString 
IsString ByteString 
(~) * a Char => IsString [a] 

Methods

fromString :: String -> [a] #

IsString a => IsString (Identity a) 

Methods

fromString :: String -> Identity a #

IsString (Seq Char) 

Methods

fromString :: String -> Seq Char #

(IsString a, Hashable a) => IsString (Hashed a) 

Methods

fromString :: String -> Hashed a #

IsString a => IsString (Const * a b) 

Methods

fromString :: String -> Const * a b #

Numeric type classes

class Num a where #

Basic numeric class.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Methods

(+) :: a -> a -> a infixl 6 #

(-) :: a -> a -> a infixl 6 #

(*) :: a -> a -> a infixl 7 #

negate :: a -> a #

Unary negation.

abs :: a -> a #

Absolute value.

signum :: a -> a #

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

fromInteger :: Integer -> a #

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

Instances

Num Int 

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Num Int8 

Methods

(+) :: Int8 -> Int8 -> Int8 #

(-) :: Int8 -> Int8 -> Int8 #

(*) :: Int8 -> Int8 -> Int8 #

negate :: Int8 -> Int8 #

abs :: Int8 -> Int8 #

signum :: Int8 -> Int8 #

fromInteger :: Integer -> Int8 #

Num Int16 
Num Int32 
Num Int64 
Num Integer 
Num Word 

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Num Word8 
Num Word16 
Num Word32 
Num Word64 
Num CChar 
Num CSChar 
Num CUChar 
Num CShort 
Num CUShort 
Num CInt 

Methods

(+) :: CInt -> CInt -> CInt #

(-) :: CInt -> CInt -> CInt #

(*) :: CInt -> CInt -> CInt #

negate :: CInt -> CInt #

abs :: CInt -> CInt #

signum :: CInt -> CInt #

fromInteger :: Integer -> CInt #

Num CUInt 
Num CLong 
Num CULong 
Num CLLong 
Num CULLong 
Num CFloat 
Num CDouble 
Num CPtrdiff 
Num CSize 
Num CWchar 
Num CSigAtomic 
Num CClock 
Num CTime 
Num CUSeconds 
Num CSUSeconds 
Num CIntPtr 
Num CUIntPtr 
Num CIntMax 
Num CUIntMax 
Num CodePoint 

Methods

(+) :: CodePoint -> CodePoint -> CodePoint #

(-) :: CodePoint -> CodePoint -> CodePoint #

(*) :: CodePoint -> CodePoint -> CodePoint #

negate :: CodePoint -> CodePoint #

abs :: CodePoint -> CodePoint #

signum :: CodePoint -> CodePoint #

fromInteger :: Integer -> CodePoint #

Num DecoderState 

Methods

(+) :: DecoderState -> DecoderState -> DecoderState #

(-) :: DecoderState -> DecoderState -> DecoderState #

(*) :: DecoderState -> DecoderState -> DecoderState #

negate :: DecoderState -> DecoderState #

abs :: DecoderState -> DecoderState #

signum :: DecoderState -> DecoderState #

fromInteger :: Integer -> DecoderState #

Integral a => Num (Ratio a) 

Methods

(+) :: Ratio a -> Ratio a -> Ratio a #

(-) :: Ratio a -> Ratio a -> Ratio a #

(*) :: Ratio a -> Ratio a -> Ratio a #

negate :: Ratio a -> Ratio a #

abs :: Ratio a -> Ratio a #

signum :: Ratio a -> Ratio a #

fromInteger :: Integer -> Ratio a #

Num a => Num (Identity a) 
Num a => Num (Min a) 

Methods

(+) :: Min a -> Min a -> Min a #

(-) :: Min a -> Min a -> Min a #

(*) :: Min a -> Min a -> Min a #

negate :: Min a -> Min a #

abs :: Min a -> Min a #

signum :: Min a -> Min a #

fromInteger :: Integer -> Min a #

Num a => Num (Max a) 

Methods

(+) :: Max a -> Max a -> Max a #

(-) :: Max a -> Max a -> Max a #

(*) :: Max a -> Max a -> Max a #

negate :: Max a -> Max a #

abs :: Max a -> Max a #

signum :: Max a -> Max a #

fromInteger :: Integer -> Max a #

RealFloat a => Num (Complex a) 

Methods

(+) :: Complex a -> Complex a -> Complex a #

(-) :: Complex a -> Complex a -> Complex a #

(*) :: Complex a -> Complex a -> Complex a #

negate :: Complex a -> Complex a #

abs :: Complex a -> Complex a #

signum :: Complex a -> Complex a #

fromInteger :: Integer -> Complex a #

Num a => Num (Sum a) 

Methods

(+) :: Sum a -> Sum a -> Sum a #

(-) :: Sum a -> Sum a -> Sum a #

(*) :: Sum a -> Sum a -> Sum a #

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Num a => Num (Product a) 

Methods

(+) :: Product a -> Product a -> Product a #

(-) :: Product a -> Product a -> Product a #

(*) :: Product a -> Product a -> Product a #

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Num a => Num (Const k a b) 

Methods

(+) :: Const k a b -> Const k a b -> Const k a b #

(-) :: Const k a b -> Const k a b -> Const k a b #

(*) :: Const k a b -> Const k a b -> Const k a b #

negate :: Const k a b -> Const k a b #

abs :: Const k a b -> Const k a b #

signum :: Const k a b -> Const k a b #

fromInteger :: Integer -> Const k a b #

Num (f a) => Num (Alt k f a) 

Methods

(+) :: Alt k f a -> Alt k f a -> Alt k f a #

(-) :: Alt k f a -> Alt k f a -> Alt k f a #

(*) :: Alt k f a -> Alt k f a -> Alt k f a #

negate :: Alt k f a -> Alt k f a #

abs :: Alt k f a -> Alt k f a #

signum :: Alt k f a -> Alt k f a #

fromInteger :: Integer -> Alt k f a #

class (Num a, Ord a) => Real a where #

Minimal complete definition

toRational

Methods

toRational :: a -> Rational #

the rational equivalent of its real argument with full precision

Instances

Real Int 

Methods

toRational :: Int -> Rational #

Real Int8 

Methods

toRational :: Int8 -> Rational #

Real Int16 

Methods

toRational :: Int16 -> Rational #

Real Int32 

Methods

toRational :: Int32 -> Rational #

Real Int64 

Methods

toRational :: Int64 -> Rational #

Real Integer 
Real Word 

Methods

toRational :: Word -> Rational #

Real Word8 

Methods

toRational :: Word8 -> Rational #

Real Word16 
Real Word32 
Real Word64 
Real CChar 

Methods

toRational :: CChar -> Rational #

Real CSChar 
Real CUChar 
Real CShort 
Real CUShort 
Real CInt 

Methods

toRational :: CInt -> Rational #

Real CUInt 

Methods

toRational :: CUInt -> Rational #

Real CLong 

Methods

toRational :: CLong -> Rational #

Real CULong 
Real CLLong 
Real CULLong 
Real CFloat 
Real CDouble 
Real CPtrdiff 
Real CSize 

Methods

toRational :: CSize -> Rational #

Real CWchar 
Real CSigAtomic 
Real CClock 
Real CTime 

Methods

toRational :: CTime -> Rational #

Real CUSeconds 
Real CSUSeconds 
Real CIntPtr 
Real CUIntPtr 
Real CIntMax 
Real CUIntMax 
Integral a => Real (Ratio a) 

Methods

toRational :: Ratio a -> Rational #

Real a => Real (Identity a) 

Methods

toRational :: Identity a -> Rational #

Real a => Real (Const k a b) 

Methods

toRational :: Const k a b -> Rational #

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

Minimal complete definition

quotRem, toInteger

Methods

quot :: a -> a -> a infixl 7 #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 #

integer remainder, satisfying

(x `quot` y)*y + (x `rem` y) == x

div :: a -> a -> a infixl 7 #

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 #

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

quotRem :: a -> a -> (a, a) #

simultaneous quot and rem

divMod :: a -> a -> (a, a) #

simultaneous div and mod

toInteger :: a -> Integer #

conversion to Integer

Instances

Integral Int 

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Integral Int8 

Methods

quot :: Int8 -> Int8 -> Int8 #

rem :: Int8 -> Int8 -> Int8 #

div :: Int8 -> Int8 -> Int8 #

mod :: Int8 -> Int8 -> Int8 #

quotRem :: Int8 -> Int8 -> (Int8, Int8) #

divMod :: Int8 -> Int8 -> (Int8, Int8) #

toInteger :: Int8 -> Integer #

Integral Int16 
Integral Int32 
Integral Int64 
Integral Integer 
Integral Word 

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

quotRem :: Word -> Word -> (Word, Word) #

divMod :: Word -> Word -> (Word, Word) #

toInteger :: Word -> Integer #

Integral Word8 
Integral Word16 
Integral Word32 
Integral Word64 
Integral CChar 
Integral CSChar 
Integral CUChar 
Integral CShort 
Integral CUShort 
Integral CInt 

Methods

quot :: CInt -> CInt -> CInt #

rem :: CInt -> CInt -> CInt #

div :: CInt -> CInt -> CInt #

mod :: CInt -> CInt -> CInt #

quotRem :: CInt -> CInt -> (CInt, CInt) #

divMod :: CInt -> CInt -> (CInt, CInt) #

toInteger :: CInt -> Integer #

Integral CUInt 
Integral CLong 
Integral CULong 
Integral CLLong 
Integral CULLong 
Integral CPtrdiff 
Integral CSize 
Integral CWchar 
Integral CSigAtomic 
Integral CIntPtr 
Integral CUIntPtr 
Integral CIntMax 
Integral CUIntMax 
Integral a => Integral (Identity a) 
Integral a => Integral (Const k a b) 

Methods

quot :: Const k a b -> Const k a b -> Const k a b #

rem :: Const k a b -> Const k a b -> Const k a b #

div :: Const k a b -> Const k a b -> Const k a b #

mod :: Const k a b -> Const k a b -> Const k a b #

quotRem :: Const k a b -> Const k a b -> (Const k a b, Const k a b) #

divMod :: Const k a b -> Const k a b -> (Const k a b, Const k a b) #

toInteger :: Const k a b -> Integer #

class Num a => Fractional a where #

Fractional numbers, supporting real division.

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 #

fractional division

recip :: a -> a #

reciprocal fraction

fromRational :: Rational -> a #

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

Instances

Fractional CFloat 
Fractional CDouble 
Integral a => Fractional (Ratio a) 

Methods

(/) :: Ratio a -> Ratio a -> Ratio a #

recip :: Ratio a -> Ratio a #

fromRational :: Rational -> Ratio a #

Fractional a => Fractional (Identity a) 
RealFloat a => Fractional (Complex a) 

Methods

(/) :: Complex a -> Complex a -> Complex a #

recip :: Complex a -> Complex a #

fromRational :: Rational -> Complex a #

Fractional a => Fractional (Const k a b) 

Methods

(/) :: Const k a b -> Const k a b -> Const k a b #

recip :: Const k a b -> Const k a b #

fromRational :: Rational -> Const k a b #

class Fractional a => Floating a where #

Trigonometric and hyperbolic functions and related functions.

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a #

exp :: a -> a #

log :: a -> a #

sqrt :: a -> a #

(**) :: a -> a -> a infixr 8 #

logBase :: a -> a -> a #

sin :: a -> a #

cos :: a -> a #

tan :: a -> a #

asin :: a -> a #

acos :: a -> a #

atan :: a -> a #

sinh :: a -> a #

cosh :: a -> a #

tanh :: a -> a #

asinh :: a -> a #

acosh :: a -> a #

atanh :: a -> a #

Instances

Floating Double 
Floating Float 
Floating CFloat 
Floating CDouble 
Floating a => Floating (Identity a) 
RealFloat a => Floating (Complex a) 

Methods

pi :: Complex a #

exp :: Complex a -> Complex a #

log :: Complex a -> Complex a #

sqrt :: Complex a -> Complex a #

(**) :: Complex a -> Complex a -> Complex a #

logBase :: Complex a -> Complex a -> Complex a #

sin :: Complex a -> Complex a #

cos :: Complex a -> Complex a #

tan :: Complex a -> Complex a #

asin :: Complex a -> Complex a #

acos :: Complex a -> Complex a #

atan :: Complex a -> Complex a #

sinh :: Complex a -> Complex a #

cosh :: Complex a -> Complex a #

tanh :: Complex a -> Complex a #

asinh :: Complex a -> Complex a #

acosh :: Complex a -> Complex a #

atanh :: Complex a -> Complex a #

log1p :: Complex a -> Complex a #

expm1 :: Complex a -> Complex a #

log1pexp :: Complex a -> Complex a #

log1mexp :: Complex a -> Complex a #

Floating a => Floating (Const k a b) 

Methods

pi :: Const k a b #

exp :: Const k a b -> Const k a b #

log :: Const k a b -> Const k a b #

sqrt :: Const k a b -> Const k a b #

(**) :: Const k a b -> Const k a b -> Const k a b #

logBase :: Const k a b -> Const k a b -> Const k a b #

sin :: Const k a b -> Const k a b #

cos :: Const k a b -> Const k a b #

tan :: Const k a b -> Const k a b #

asin :: Const k a b -> Const k a b #

acos :: Const k a b -> Const k a b #

atan :: Const k a b -> Const k a b #

sinh :: Const k a b -> Const k a b #

cosh :: Const k a b -> Const k a b #

tanh :: Const k a b -> Const k a b #

asinh :: Const k a b -> Const k a b #

acosh :: Const k a b -> Const k a b #

atanh :: Const k a b -> Const k a b #

log1p :: Const k a b -> Const k a b #

expm1 :: Const k a b -> Const k a b #

log1pexp :: Const k a b -> Const k a b #

log1mexp :: Const k a b -> Const k a b #

class (Real a, Fractional a) => RealFrac a where #

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) #

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

  • n is an integral number with the same sign as x; and
  • f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate :: Integral b => a -> b #

truncate x returns the integer nearest x between zero and x

round :: Integral b => a -> b #

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling :: Integral b => a -> b #

ceiling x returns the least integer not less than x

floor :: Integral b => a -> b #

floor x returns the greatest integer not greater than x

Instances

RealFrac CFloat 

Methods

properFraction :: Integral b => CFloat -> (b, CFloat) #

truncate :: Integral b => CFloat -> b #

round :: Integral b => CFloat -> b #

ceiling :: Integral b => CFloat -> b #

floor :: Integral b => CFloat -> b #

RealFrac CDouble 

Methods

properFraction :: Integral b => CDouble -> (b, CDouble) #

truncate :: Integral b => CDouble -> b #

round :: Integral b => CDouble -> b #

ceiling :: Integral b => CDouble -> b #

floor :: Integral b => CDouble -> b #

Integral a => RealFrac (Ratio a) 

Methods

properFraction :: Integral b => Ratio a -> (b, Ratio a) #

truncate :: Integral b => Ratio a -> b #

round :: Integral b => Ratio a -> b #

ceiling :: Integral b => Ratio a -> b #

floor :: Integral b => Ratio a -> b #

RealFrac a => RealFrac (Identity a) 

Methods

properFraction :: Integral b => Identity a -> (b, Identity a) #

truncate :: Integral b => Identity a -> b #

round :: Integral b => Identity a -> b #

ceiling :: Integral b => Identity a -> b #

floor :: Integral b => Identity a -> b #

RealFrac a => RealFrac (Const k a b) 

Methods

properFraction :: Integral b => Const k a b -> (b, Const k a b) #

truncate :: Integral b => Const k a b -> b #

round :: Integral b => Const k a b -> b #

ceiling :: Integral b => Const k a b -> b #

floor :: Integral b => Const k a b -> b #

class (RealFrac a, Floating a) => RealFloat a where #

Efficient, machine-independent access to the components of a floating-point number.

Methods

floatRadix :: a -> Integer #

a constant function, returning the radix of the representation (often 2)

floatDigits :: a -> Int #

a constant function, returning the number of digits of floatRadix in the significand

floatRange :: a -> (Int, Int) #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) #

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat :: Integer -> Int -> a #

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int #

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

significand :: a -> a #

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

scaleFloat :: Int -> a -> a #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool #

True if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool #

True if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool #

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a #

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Instances

RealFloat Double 
RealFloat Float 
RealFloat CFloat 
RealFloat CDouble 
RealFloat a => RealFloat (Identity a) 
RealFloat a => RealFloat (Const k a b) 

Methods

floatRadix :: Const k a b -> Integer #

floatDigits :: Const k a b -> Int #

floatRange :: Const k a b -> (Int, Int) #

decodeFloat :: Const k a b -> (Integer, Int) #

encodeFloat :: Integer -> Int -> Const k a b #

exponent :: Const k a b -> Int #

significand :: Const k a b -> Const k a b #

scaleFloat :: Int -> Const k a b -> Const k a b #

isNaN :: Const k a b -> Bool #

isInfinite :: Const k a b -> Bool #

isDenormalized :: Const k a b -> Bool #

isNegativeZero :: Const k a b -> Bool #

isIEEE :: Const k a b -> Bool #

atan2 :: Const k a b -> Const k a b -> Const k a b #

Data types

data Maybe a :: * -> * #

The Maybe type encapsulates an optional value. A value of type Maybe a either contains a value of type a (represented as Just a), or it is empty (represented as Nothing). Using Maybe is a good way to deal with errors or exceptional cases without resorting to drastic measures such as error.

The Maybe type is also a monad. It is a simple kind of error monad, where all errors are represented by Nothing. A richer error monad can be built using the Either type.

Constructors

Nothing 
Just a 

Instances

Monad Maybe 

Methods

(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #

(>>) :: Maybe a -> Maybe b -> Maybe b #

return :: a -> Maybe a #

fail :: String -> Maybe a #

Functor Maybe 

Methods

fmap :: (a -> b) -> Maybe a -> Maybe b #

(<$) :: a -> Maybe b -> Maybe a #

Applicative Maybe 

Methods

pure :: a -> Maybe a #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b #

(*>) :: Maybe a -> Maybe b -> Maybe b #

(<*) :: Maybe a -> Maybe b -> Maybe a #

Foldable Maybe 

Methods

fold :: Monoid m => Maybe m -> m #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m #

foldr :: (a -> b -> b) -> b -> Maybe a -> b #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b #

foldl :: (b -> a -> b) -> b -> Maybe a -> b #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b #

foldr1 :: (a -> a -> a) -> Maybe a -> a #

foldl1 :: (a -> a -> a) -> Maybe a -> a #

toList :: Maybe a -> [a] #

null :: Maybe a -> Bool #

length :: Maybe a -> Int #

elem :: Eq a => a -> Maybe a -> Bool #

maximum :: Ord a => Maybe a -> a #

minimum :: Ord a => Maybe a -> a #

sum :: Num a => Maybe a -> a #

product :: Num a => Maybe a -> a #

Traversable Maybe 

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) #

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) #

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) #

sequence :: Monad m => Maybe (m a) -> m (Maybe a) #

Generic1 Maybe 

Associated Types

type Rep1 (Maybe :: * -> *) :: * -> * #

Methods

from1 :: Maybe a -> Rep1 Maybe a #

to1 :: Rep1 Maybe a -> Maybe a #

Alternative Maybe 

Methods

empty :: Maybe a #

(<|>) :: Maybe a -> Maybe a -> Maybe a #

some :: Maybe a -> Maybe [a] #

many :: Maybe a -> Maybe [a] #

MonadPlus Maybe 

Methods

mzero :: Maybe a #

mplus :: Maybe a -> Maybe a -> Maybe a #

Hashable1 Maybe 

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Maybe a -> Int #

Eq a => Eq (Maybe a) 

Methods

(==) :: Maybe a -> Maybe a -> Bool #

(/=) :: Maybe a -> Maybe a -> Bool #

Ord a => Ord (Maybe a) 

Methods

compare :: Maybe a -> Maybe a -> Ordering #

(<) :: Maybe a -> Maybe a -> Bool #

(<=) :: Maybe a -> Maybe a -> Bool #

(>) :: Maybe a -> Maybe a -> Bool #

(>=) :: Maybe a -> Maybe a -> Bool #

max :: Maybe a -> Maybe a -> Maybe a #

min :: Maybe a -> Maybe a -> Maybe a #

Read a => Read (Maybe a) 
Show a => Show (Maybe a) 

Methods

showsPrec :: Int -> Maybe a -> ShowS #

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Generic (Maybe a) 

Associated Types

type Rep (Maybe a) :: * -> * #

Methods

from :: Maybe a -> Rep (Maybe a) x #

to :: Rep (Maybe a) x -> Maybe a #

Semigroup a => Semigroup (Maybe a) 

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a #

sconcat :: NonEmpty (Maybe a) -> Maybe a #

stimes :: Integral b => b -> Maybe a -> Maybe a #

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

mconcat :: [Maybe a] -> Maybe a #

Hashable a => Hashable (Maybe a) 

Methods

hashWithSalt :: Int -> Maybe a -> Int #

hash :: Maybe a -> Int #

SingI (Maybe a) (Nothing a) 

Methods

sing :: Sing (Nothing a) a

SingKind a (KProxy a) => SingKind (Maybe a) (KProxy (Maybe a)) 

Associated Types

type DemoteRep (KProxy (Maybe a)) (kparam :: KProxy (KProxy (Maybe a))) :: *

Methods

fromSing :: Sing (KProxy (Maybe a)) a -> DemoteRep (KProxy (Maybe a)) kparam

SingI a a1 => SingI (Maybe a) (Just a a1) 

Methods

sing :: Sing (Just a a1) a

type Rep1 Maybe 
type Rep (Maybe a) 
data Sing (Maybe a) 
data Sing (Maybe a) where
type (==) (Maybe k) a b 
type (==) (Maybe k) a b = EqMaybe k a b
type DemoteRep (Maybe a) (KProxy (Maybe a)) 
type DemoteRep (Maybe a) (KProxy (Maybe a)) = Maybe (DemoteRep a (KProxy a))

data Ordering :: * #

Constructors

LT 
EQ 
GT 

Instances

Bounded Ordering 
Enum Ordering 
Eq Ordering 
Ord Ordering 
Read Ordering 
Show Ordering 
Generic Ordering 

Associated Types

type Rep Ordering :: * -> * #

Methods

from :: Ordering -> Rep Ordering x #

to :: Rep Ordering x -> Ordering #

Semigroup Ordering 
Monoid Ordering 
Hashable Ordering 

Methods

hashWithSalt :: Int -> Ordering -> Int #

hash :: Ordering -> Int #

type Rep Ordering 
type Rep Ordering = D1 (MetaData "Ordering" "GHC.Types" "ghc-prim" False) ((:+:) (C1 (MetaCons "LT" PrefixI False) U1) ((:+:) (C1 (MetaCons "EQ" PrefixI False) U1) (C1 (MetaCons "GT" PrefixI False) U1)))
type (==) Ordering a b 
type (==) Ordering a b = EqOrdering a b

data Bool :: * #

Constructors

False 
True 

Instances

Bounded Bool 
Enum Bool 

Methods

succ :: Bool -> Bool #

pred :: Bool -> Bool #

toEnum :: Int -> Bool #

fromEnum :: Bool -> Int #

enumFrom :: Bool -> [Bool] #

enumFromThen :: Bool -> Bool -> [Bool] #

enumFromTo :: Bool -> Bool -> [Bool] #

enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] #

Eq Bool 

Methods

(==) :: Bool -> Bool -> Bool #

(/=) :: Bool -> Bool -> Bool #

Ord Bool 

Methods

compare :: Bool -> Bool -> Ordering #

(<) :: Bool -> Bool -> Bool #

(<=) :: Bool -> Bool -> Bool #

(>) :: Bool -> Bool -> Bool #

(>=) :: Bool -> Bool -> Bool #

max :: Bool -> Bool -> Bool #

min :: Bool -> Bool -> Bool #

Read Bool 
Show Bool 

Methods

showsPrec :: Int -> Bool -> ShowS #

show :: Bool -> String #

showList :: [Bool] -> ShowS #

Generic Bool 

Associated Types

type Rep Bool :: * -> * #

Methods

from :: Bool -> Rep Bool x #

to :: Rep Bool x -> Bool #

Storable Bool 

Methods

sizeOf :: Bool -> Int #

alignment :: Bool -> Int #

peekElemOff :: Ptr Bool -> Int -> IO Bool #

pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () #

peekByteOff :: Ptr b -> Int -> IO Bool #

pokeByteOff :: Ptr b -> Int -> Bool -> IO () #

peek :: Ptr Bool -> IO Bool #

poke :: Ptr Bool -> Bool -> IO () #

Hashable Bool 

Methods

hashWithSalt :: Int -> Bool -> Int #

hash :: Bool -> Int #

Unbox Bool 
SingI Bool False 

Methods

sing :: Sing False a

SingI Bool True 

Methods

sing :: Sing True a

Vector Vector Bool 
MVector MVector Bool 
SingKind Bool (KProxy Bool) 

Associated Types

type DemoteRep (KProxy Bool) (kparam :: KProxy (KProxy Bool)) :: *

Methods

fromSing :: Sing (KProxy Bool) a -> DemoteRep (KProxy Bool) kparam

type Rep Bool 
type Rep Bool = D1 (MetaData "Bool" "GHC.Types" "ghc-prim" False) ((:+:) (C1 (MetaCons "False" PrefixI False) U1) (C1 (MetaCons "True" PrefixI False) U1))
data Sing Bool 
data Sing Bool where
data Vector Bool 
data MVector s Bool 
type (==) Bool a b 
type (==) Bool a b = EqBool a b
type DemoteRep Bool (KProxy Bool) 
type DemoteRep Bool (KProxy Bool) = Bool

data Char :: * #

The character type Char is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) 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 
Enum Char 

Methods

succ :: Char -> Char #

pred :: Char -> Char #

toEnum :: Int -> Char #

fromEnum :: Char -> Int #

enumFrom :: Char -> [Char] #

enumFromThen :: Char -> Char -> [Char] #

enumFromTo :: Char -> Char -> [Char] #

enumFromThenTo :: Char -> Char -> Char -> [Char] #

Eq Char 

Methods

(==) :: Char -> Char -> Bool #

(/=) :: Char -> Char -> Bool #

Ord Char 

Methods

compare :: Char -> Char -> Ordering #

(<) :: Char -> Char -> Bool #

(<=) :: Char -> Char -> Bool #

(>) :: Char -> Char -> Bool #

(>=) :: Char -> Char -> Bool #

max :: Char -> Char -> Char #

min :: Char -> Char -> Char #

Read Char 
Show Char 

Methods

showsPrec :: Int -> Char -> ShowS #

show :: Char -> String #

showList :: [Char] -> ShowS #

Storable Char 

Methods

sizeOf :: Char -> Int #

alignment :: Char -> Int #

peekElemOff :: Ptr Char -> Int -> IO Char #

pokeElemOff :: Ptr Char -> Int -> Char -> IO () #

peekByteOff :: Ptr b -> Int -> IO Char #

pokeByteOff :: Ptr b -> Int -> Char -> IO () #

peek :: Ptr Char -> IO Char #

poke :: Ptr Char -> Char -> IO () #

Hashable Char 

Methods

hashWithSalt :: Int -> Char -> Int #

hash :: Char -> Int #

ErrorList Char 

Methods

listMsg :: String -> [Char] #

Unbox Char 
Vector Vector Char 
MVector MVector Char 
Functor (URec Char) 

Methods

fmap :: (a -> b) -> URec Char a -> URec Char b #

(<$) :: a -> URec Char b -> URec Char a #

IsString (Seq Char) 

Methods

fromString :: String -> Seq Char #

Foldable (URec Char) 

Methods

fold :: Monoid m => URec Char m -> m #

foldMap :: Monoid m => (a -> m) -> URec Char a -> m #

foldr :: (a -> b -> b) -> b -> URec Char a -> b #

foldr' :: (a -> b -> b) -> b -> URec Char a -> b #

foldl :: (b -> a -> b) -> b -> URec Char a -> b #

foldl' :: (b -> a -> b) -> b -> URec Char a -> b #

foldr1 :: (a -> a -> a) -> URec Char a -> a #

foldl1 :: (a -> a -> a) -> URec Char a -> a #

toList :: URec Char a -> [a] #

null :: URec Char a -> Bool #

length :: URec Char a -> Int #

elem :: Eq a => a -> URec Char a -> Bool #

maximum :: Ord a => URec Char a -> a #

minimum :: Ord a => URec Char a -> a #

sum :: Num a => URec Char a -> a #

product :: Num a => URec Char a -> a #

Traversable (URec Char) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) #

sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) #

mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) #

sequence :: Monad m => URec Char (m a) -> m (URec Char a) #

Generic1 (URec Char) 

Associated Types

type Rep1 (URec Char :: * -> *) :: * -> * #

Methods

from1 :: URec Char a -> Rep1 (URec Char) a #

to1 :: Rep1 (URec Char) a -> URec Char a #

Eq (URec Char p) 

Methods

(==) :: URec Char p -> URec Char p -> Bool #

(/=) :: URec Char p -> URec Char p -> Bool #

Ord (URec Char p) 

Methods

compare :: URec Char p -> URec Char p -> Ordering #

(<) :: URec Char p -> URec Char p -> Bool #

(<=) :: URec Char p -> URec Char p -> Bool #

(>) :: URec Char p -> URec Char p -> Bool #

(>=) :: URec Char p -> URec Char p -> Bool #

max :: URec Char p -> URec Char p -> URec Char p #

min :: URec Char p -> URec Char p -> URec Char p #

Show (URec Char p) 

Methods

showsPrec :: Int -> URec Char p -> ShowS #

show :: URec Char p -> String #

showList :: [URec Char p] -> ShowS #

Generic (URec Char p) 

Associated Types

type Rep (URec Char p) :: * -> * #

Methods

from :: URec Char p -> Rep (URec Char p) x #

to :: Rep (URec Char p) x -> URec Char p #

data URec Char

Used for marking occurrences of Char#

data URec Char = UChar {}
data Vector Char 
data MVector s Char 
type Rep1 (URec Char) 
type Rep1 (URec Char) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UChar))
type Rep (URec Char p) 
type Rep (URec Char p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UChar" PrefixI True) (S1 (MetaSel (Just Symbol "uChar#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UChar))

data IO a :: * -> * #

A value of type IO a is a computation which, when performed, does some I/O before returning a value of type a.

There is really only one way to "perform" an I/O action: bind it to Main.main in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the IO monad and called at some point, directly or indirectly, from Main.main.

IO is a monad, so IO actions can be combined using either the do-notation or the >> and >>= operations from the Monad class.

Instances

Monad IO 

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b #

(>>) :: IO a -> IO b -> IO b #

return :: a -> IO a #

fail :: String -> IO a #

Functor IO 

Methods

fmap :: (a -> b) -> IO a -> IO b #

(<$) :: a -> IO b -> IO a #

Applicative IO 

Methods

pure :: a -> IO a #

(<*>) :: IO (a -> b) -> IO a -> IO b #

(*>) :: IO a -> IO b -> IO b #

(<*) :: IO a -> IO b -> IO a #

MonadIO IO 

Methods

liftIO :: IO a -> IO a #

Alternative IO 

Methods

empty :: IO a #

(<|>) :: IO a -> IO a -> IO a #

some :: IO a -> IO [a] #

many :: IO a -> IO [a] #

MonadPlus IO 

Methods

mzero :: IO a #

mplus :: IO a -> IO a -> IO a #

PrimMonad IO 

Associated Types

type PrimState (IO :: * -> *) :: * #

PrimBase IO 
Monoid a => Monoid (IO a) 

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

mconcat :: [IO a] -> IO a #

type PrimState IO 

data Either a b :: * -> * -> * #

The Either type represents values with two possibilities: a value of type Either a b is either Left a or Right b.

The Either type is sometimes used to represent a value which is either correct or an error; by convention, the Left constructor is used to hold an error value and the Right constructor is used to hold a correct value (mnemonic: "right" also means "correct").

Examples

The type Either String Int is the type of values which can be either a String or an Int. The Left constructor can be used only on Strings, and the Right constructor can be used only on Ints:

>>> let s = Left "foo" :: Either String Int
>>> s
Left "foo"
>>> let n = Right 3 :: Either String Int
>>> n
Right 3
>>> :type s
s :: Either String Int
>>> :type n
n :: Either String Int

The fmap from our Functor instance will ignore Left values, but will apply the supplied function to values contained in a Right:

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> fmap (*2) s
Left "foo"
>>> fmap (*2) n
Right 6

The Monad instance for Either allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an Int from a Char, or fail.

>>> import Data.Char ( digitToInt, isDigit )
>>> :{
    let parseEither :: Char -> Either String Int
        parseEither c
          | isDigit c = Right (digitToInt c)
          | otherwise = Left "parse error"
>>> :}

The following should work, since both '1' and '2' can be parsed as Ints.

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither '1'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Right 3

But the following should fail overall, since the first operation where we attempt to parse 'm' as an Int will fail:

>>> :{
    let parseMultiple :: Either String Int
        parseMultiple = do
          x <- parseEither 'm'
          y <- parseEither '2'
          return (x + y)
>>> :}
>>> parseMultiple
Left "parse error"

Constructors

Left a 
Right b 

Instances

Hashable2 Either 

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Either a b -> Int #

Monad (Either e) 

Methods

(>>=) :: Either e a -> (a -> Either e b) -> Either e b #

(>>) :: Either e a -> Either e b -> Either e b #

return :: a -> Either e a #

fail :: String -> Either e a #

Functor (Either a) 

Methods

fmap :: (a -> b) -> Either a a -> Either a b #

(<$) :: a -> Either a b -> Either a a #

Applicative (Either e) 

Methods

pure :: a -> Either e a #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b #

(*>) :: Either e a -> Either e b -> Either e b #

(<*) :: Either e a -> Either e b -> Either e a #

Foldable (Either a) 

Methods

fold :: Monoid m => Either a m -> m #

foldMap :: Monoid m => (a -> m) -> Either a a -> m #

foldr :: (a -> b -> b) -> b -> Either a a -> b #

foldr' :: (a -> b -> b) -> b -> Either a a -> b #

foldl :: (b -> a -> b) -> b -> Either a a -> b #

foldl' :: (b -> a -> b) -> b -> Either a a -> b #

foldr1 :: (a -> a -> a) -> Either a a -> a #

foldl1 :: (a -> a -> a) -> Either a a -> a #

toList :: Either a a -> [a] #

null :: Either a a -> Bool #

length :: Either a a -> Int #

elem :: Eq a => a -> Either a a -> Bool #

maximum :: Ord a => Either a a -> a #

minimum :: Ord a => Either a a -> a #

sum :: Num a => Either a a -> a #

product :: Num a => Either a a -> a #

Traversable (Either a) 

Methods

traverse :: Applicative f => (a -> f b) -> Either a a -> f (Either a b) #

sequenceA :: Applicative f => Either a (f a) -> f (Either a a) #

mapM :: Monad m => (a -> m b) -> Either a a -> m (Either a b) #

sequence :: Monad m => Either a (m a) -> m (Either a a) #

Generic1 (Either a) 

Associated Types

type Rep1 (Either a :: * -> *) :: * -> * #

Methods

from1 :: Either a a -> Rep1 (Either a) a #

to1 :: Rep1 (Either a) a -> Either a a #

Hashable a => Hashable1 (Either a) 

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Either a a -> Int #

(Eq b, Eq a) => Eq (Either a b) 

Methods

(==) :: Either a b -> Either a b -> Bool #

(/=) :: Either a b -> Either a b -> Bool #

(Ord b, Ord a) => Ord (Either a b) 

Methods

compare :: Either a b -> Either a b -> Ordering #

(<) :: Either a b -> Either a b -> Bool #

(<=) :: Either a b -> Either a b -> Bool #

(>) :: Either a b -> Either a b -> Bool #

(>=) :: Either a b -> Either a b -> Bool #

max :: Either a b -> Either a b -> Either a b #

min :: Either a b -> Either a b -> Either a b #

(Read b, Read a) => Read (Either a b) 
(Show b, Show a) => Show (Either a b) 

Methods

showsPrec :: Int -> Either a b -> ShowS #

show :: Either a b -> String #

showList :: [Either a b] -> ShowS #

Generic (Either a b) 

Associated Types

type Rep (Either a b) :: * -> * #

Methods

from :: Either a b -> Rep (Either a b) x #

to :: Rep (Either a b) x -> Either a b #

Semigroup (Either a b) 

Methods

(<>) :: Either a b -> Either a b -> Either a b #

sconcat :: NonEmpty (Either a b) -> Either a b #

stimes :: Integral b => b -> Either a b -> Either a b #

(Hashable a, Hashable b) => Hashable (Either a b) 

Methods

hashWithSalt :: Int -> Either a b -> Int #

hash :: Either a b -> Int #

type Rep1 (Either a) 
type Rep (Either a b) 
type (==) (Either k k1) a b 
type (==) (Either k k1) a b = EqEither k k1 a b

Re-exports

Packed reps

data ByteString :: * #

A space-efficient representation of a Word8 vector, supporting many efficient operations.

A ByteString contains 8-bit bytes, or by using the operations from Data.ByteString.Char8 it can be interpreted as containing 8-bit characters.

Instances

Eq ByteString 
Data ByteString 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ByteString -> c ByteString #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ByteString #

toConstr :: ByteString -> Constr #

dataTypeOf :: ByteString -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c ByteString) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ByteString) #

gmapT :: (forall b. Data b => b -> b) -> ByteString -> ByteString #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ByteString -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ByteString -> r #

gmapQ :: (forall d. Data d => d -> u) -> ByteString -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> ByteString -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ByteString -> m ByteString #

Ord ByteString 
Read ByteString 
Show ByteString 
IsString ByteString 
Semigroup ByteString 
Monoid ByteString 
NFData ByteString 

Methods

rnf :: ByteString -> () #

Hashable ByteString 

data Text :: * #

A space efficient, packed, unboxed Unicode text type.

Instances

Hashable Text 

Methods

hashWithSalt :: Int -> Text -> Int #

hash :: Text -> Int #

type Item Text 
type Item Text = Char

Containers

data Map k a :: * -> * -> * #

A Map from keys k to values a.

Instances

Functor (Map k) 

Methods

fmap :: (a -> b) -> Map k a -> Map k b #

(<$) :: a -> Map k b -> Map k a #

Foldable (Map k) 

Methods

fold :: Monoid m => Map k m -> m #

foldMap :: Monoid m => (a -> m) -> Map k a -> m #

foldr :: (a -> b -> b) -> b -> Map k a -> b #

foldr' :: (a -> b -> b) -> b -> Map k a -> b #

foldl :: (b -> a -> b) -> b -> Map k a -> b #

foldl' :: (b -> a -> b) -> b -> Map k a -> b #

foldr1 :: (a -> a -> a) -> Map k a -> a #

foldl1 :: (a -> a -> a) -> Map k a -> a #

toList :: Map k a -> [a] #

null :: Map k a -> Bool #

length :: Map k a -> Int #

elem :: Eq a => a -> Map k a -> Bool #

maximum :: Ord a => Map k a -> a #

minimum :: Ord a => Map k a -> a #

sum :: Num a => Map k a -> a #

product :: Num a => Map k a -> a #

Traversable (Map k) 

Methods

traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) #

sequenceA :: Applicative f => Map k (f a) -> f (Map k a) #

mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) #

sequence :: Monad m => Map k (m a) -> m (Map k a) #

Ord k => IsList (Map k v) 

Associated Types

type Item (Map k v) :: * #

Methods

fromList :: [Item (Map k v)] -> Map k v #

fromListN :: Int -> [Item (Map k v)] -> Map k v #

toList :: Map k v -> [Item (Map k v)] #

(Eq k, Eq a) => Eq (Map k a) 

Methods

(==) :: Map k a -> Map k a -> Bool #

(/=) :: Map k a -> Map k a -> Bool #

(Data k, Data a, Ord k) => Data (Map k a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Map k a -> c (Map k a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Map k a) #

toConstr :: Map k a -> Constr #

dataTypeOf :: Map k a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Map k a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Map k a)) #

gmapT :: (forall b. Data b => b -> b) -> Map k a -> Map k a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Map k a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Map k a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Map k a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Map k a -> m (Map k a) #

(Ord k, Ord v) => Ord (Map k v) 

Methods

compare :: Map k v -> Map k v -> Ordering #

(<) :: Map k v -> Map k v -> Bool #

(<=) :: Map k v -> Map k v -> Bool #

(>) :: Map k v -> Map k v -> Bool #

(>=) :: Map k v -> Map k v -> Bool #

max :: Map k v -> Map k v -> Map k v #

min :: Map k v -> Map k v -> Map k v #

(Ord k, Read k, Read e) => Read (Map k e) 

Methods

readsPrec :: Int -> ReadS (Map k e) #

readList :: ReadS [Map k e] #

readPrec :: ReadPrec (Map k e) #

readListPrec :: ReadPrec [Map k e] #

(Show k, Show a) => Show (Map k a) 

Methods

showsPrec :: Int -> Map k a -> ShowS #

show :: Map k a -> String #

showList :: [Map k a] -> ShowS #

Ord k => Semigroup (Map k v) 

Methods

(<>) :: Map k v -> Map k v -> Map k v #

sconcat :: NonEmpty (Map k v) -> Map k v #

stimes :: Integral b => b -> Map k v -> Map k v #

Ord k => Monoid (Map k v) 

Methods

mempty :: Map k v #

mappend :: Map k v -> Map k v -> Map k v #

mconcat :: [Map k v] -> Map k v #

(NFData k, NFData a) => NFData (Map k a) 

Methods

rnf :: Map k a -> () #

type Item (Map k v) 
type Item (Map k v) = (k, v)

data HashMap k v :: * -> * -> * #

A map from keys to values. A map cannot contain duplicate keys; each key can map to at most one value.

Instances

Eq2 HashMap 

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> HashMap a c -> HashMap b d -> Bool #

Show2 HashMap 

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> HashMap a b -> ShowS #

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [HashMap a b] -> ShowS #

Hashable2 HashMap 

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> HashMap a b -> Int #

Functor (HashMap k) 

Methods

fmap :: (a -> b) -> HashMap k a -> HashMap k b #

(<$) :: a -> HashMap k b -> HashMap k a #

Foldable (HashMap k) 

Methods

fold :: Monoid m => HashMap k m -> m #

foldMap :: Monoid m => (a -> m) -> HashMap k a -> m #

foldr :: (a -> b -> b) -> b -> HashMap k a -> b #

foldr' :: (a -> b -> b) -> b -> HashMap k a -> b #

foldl :: (b -> a -> b) -> b -> HashMap k a -> b #

foldl' :: (b -> a -> b) -> b -> HashMap k a -> b #

foldr1 :: (a -> a -> a) -> HashMap k a -> a #

foldl1 :: (a -> a -> a) -> HashMap k a -> a #

toList :: HashMap k a -> [a] #

null :: HashMap k a -> Bool #

length :: HashMap k a -> Int #

elem :: Eq a => a -> HashMap k a -> Bool #

maximum :: Ord a => HashMap k a -> a #

minimum :: Ord a => HashMap k a -> a #

sum :: Num a => HashMap k a -> a #

product :: Num a => HashMap k a -> a #

Traversable (HashMap k) 

Methods

traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) #

sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) #

mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) #

sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #

Eq k => Eq1 (HashMap k) 

Methods

liftEq :: (a -> b -> Bool) -> HashMap k a -> HashMap k b -> Bool #

(Eq k, Hashable k, Read k) => Read1 (HashMap k) 

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (HashMap k a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [HashMap k a] #

Show k => Show1 (HashMap k) 

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashMap k a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashMap k a] -> ShowS #

Hashable k => Hashable1 (HashMap k) 

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashMap k a -> Int #

(Eq k, Hashable k) => IsList (HashMap k v) 

Associated Types

type Item (HashMap k v) :: * #

Methods

fromList :: [Item (HashMap k v)] -> HashMap k v #

fromListN :: Int -> [Item (HashMap k v)] -> HashMap k v #

toList :: HashMap k v -> [Item (HashMap k v)] #

(Eq k, Eq v) => Eq (HashMap k v) 

Methods

(==) :: HashMap k v -> HashMap k v -> Bool #

(/=) :: HashMap k v -> HashMap k v -> Bool #

(Data k, Data v, Eq k, Hashable k) => Data (HashMap k v) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashMap k v -> c (HashMap k v) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashMap k v) #

toConstr :: HashMap k v -> Constr #

dataTypeOf :: HashMap k v -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (HashMap k v)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashMap k v)) #

gmapT :: (forall b. Data b => b -> b) -> HashMap k v -> HashMap k v #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashMap k v -> r #

gmapQ :: (forall d. Data d => d -> u) -> HashMap k v -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> HashMap k v -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashMap k v -> m (HashMap k v) #

(Eq k, Hashable k, Read k, Read e) => Read (HashMap k e) 
(Show k, Show v) => Show (HashMap k v) 

Methods

showsPrec :: Int -> HashMap k v -> ShowS #

show :: HashMap k v -> String #

showList :: [HashMap k v] -> ShowS #

(Eq k, Hashable k) => Semigroup (HashMap k v) 

Methods

(<>) :: HashMap k v -> HashMap k v -> HashMap k v #

sconcat :: NonEmpty (HashMap k v) -> HashMap k v #

stimes :: Integral b => b -> HashMap k v -> HashMap k v #

(Eq k, Hashable k) => Monoid (HashMap k v) 

Methods

mempty :: HashMap k v #

mappend :: HashMap k v -> HashMap k v -> HashMap k v #

mconcat :: [HashMap k v] -> HashMap k v #

(NFData k, NFData v) => NFData (HashMap k v) 

Methods

rnf :: HashMap k v -> () #

(Hashable k, Hashable v) => Hashable (HashMap k v) 

Methods

hashWithSalt :: Int -> HashMap k v -> Int #

hash :: HashMap k v -> Int #

type Item (HashMap k v) 
type Item (HashMap k v) = (k, v)

data IntMap a :: * -> * #

A map of integers to values a.

Instances

Functor IntMap 

Methods

fmap :: (a -> b) -> IntMap a -> IntMap b #

(<$) :: a -> IntMap b -> IntMap a #

Foldable IntMap 

Methods

fold :: Monoid m => IntMap m -> m #

foldMap :: Monoid m => (a -> m) -> IntMap a -> m #

foldr :: (a -> b -> b) -> b -> IntMap a -> b #

foldr' :: (a -> b -> b) -> b -> IntMap a -> b #

foldl :: (b -> a -> b) -> b -> IntMap a -> b #

foldl' :: (b -> a -> b) -> b -> IntMap a -> b #

foldr1 :: (a -> a -> a) -> IntMap a -> a #

foldl1 :: (a -> a -> a) -> IntMap a -> a #

toList :: IntMap a -> [a] #

null :: IntMap a -> Bool #

length :: IntMap a -> Int #

elem :: Eq a => a -> IntMap a -> Bool #

maximum :: Ord a => IntMap a -> a #

minimum :: Ord a => IntMap a -> a #

sum :: Num a => IntMap a -> a #

product :: Num a => IntMap a -> a #

Traversable IntMap 

Methods

traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) #

sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) #

mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) #

sequence :: Monad m => IntMap (m a) -> m (IntMap a) #

IsList (IntMap a) 

Associated Types

type Item (IntMap a) :: * #

Methods

fromList :: [Item (IntMap a)] -> IntMap a #

fromListN :: Int -> [Item (IntMap a)] -> IntMap a #

toList :: IntMap a -> [Item (IntMap a)] #

Eq a => Eq (IntMap a) 

Methods

(==) :: IntMap a -> IntMap a -> Bool #

(/=) :: IntMap a -> IntMap a -> Bool #

Data a => Data (IntMap a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IntMap a -> c (IntMap a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (IntMap a) #

toConstr :: IntMap a -> Constr #

dataTypeOf :: IntMap a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (IntMap a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (IntMap a)) #

gmapT :: (forall b. Data b => b -> b) -> IntMap a -> IntMap a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IntMap a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IntMap a -> r #

gmapQ :: (forall d. Data d => d -> u) -> IntMap a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> IntMap a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IntMap a -> m (IntMap a) #

Ord a => Ord (IntMap a) 

Methods

compare :: IntMap a -> IntMap a -> Ordering #

(<) :: IntMap a -> IntMap a -> Bool #

(<=) :: IntMap a -> IntMap a -> Bool #

(>) :: IntMap a -> IntMap a -> Bool #

(>=) :: IntMap a -> IntMap a -> Bool #

max :: IntMap a -> IntMap a -> IntMap a #

min :: IntMap a -> IntMap a -> IntMap a #

Read e => Read (IntMap e) 
Show a => Show (IntMap a) 

Methods

showsPrec :: Int -> IntMap a -> ShowS #

show :: IntMap a -> String #

showList :: [IntMap a] -> ShowS #

Semigroup (IntMap a) 

Methods

(<>) :: IntMap a -> IntMap a -> IntMap a #

sconcat :: NonEmpty (IntMap a) -> IntMap a #

stimes :: Integral b => b -> IntMap a -> IntMap a #

Monoid (IntMap a) 

Methods

mempty :: IntMap a #

mappend :: IntMap a -> IntMap a -> IntMap a #

mconcat :: [IntMap a] -> IntMap a #

NFData a => NFData (IntMap a) 

Methods

rnf :: IntMap a -> () #

type Item (IntMap a) 
type Item (IntMap a) = (Key, a)

data Set a :: * -> * #

A set of values a.

Instances

Foldable Set 

Methods

fold :: Monoid m => Set m -> m #

foldMap :: Monoid m => (a -> m) -> Set a -> m #

foldr :: (a -> b -> b) -> b -> Set a -> b #

foldr' :: (a -> b -> b) -> b -> Set a -> b #

foldl :: (b -> a -> b) -> b -> Set a -> b #

foldl' :: (b -> a -> b) -> b -> Set a -> b #

foldr1 :: (a -> a -> a) -> Set a -> a #

foldl1 :: (a -> a -> a) -> Set a -> a #

toList :: Set a -> [a] #

null :: Set a -> Bool #

length :: Set a -> Int #

elem :: Eq a => a -> Set a -> Bool #

maximum :: Ord a => Set a -> a #

minimum :: Ord a => Set a -> a #

sum :: Num a => Set a -> a #

product :: Num a => Set a -> a #

Ord a => IsList (Set a) 

Associated Types

type Item (Set a) :: * #

Methods

fromList :: [Item (Set a)] -> Set a #

fromListN :: Int -> [Item (Set a)] -> Set a #

toList :: Set a -> [Item (Set a)] #

Eq a => Eq (Set a) 

Methods

(==) :: Set a -> Set a -> Bool #

(/=) :: Set a -> Set a -> Bool #

(Data a, Ord a) => Data (Set a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Set a -> c (Set a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Set a) #

toConstr :: Set a -> Constr #

dataTypeOf :: Set a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Set a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Set a)) #

gmapT :: (forall b. Data b => b -> b) -> Set a -> Set a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Set a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Set a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Set a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Set a -> m (Set a) #

Ord a => Ord (Set a) 

Methods

compare :: Set a -> Set a -> Ordering #

(<) :: Set a -> Set a -> Bool #

(<=) :: Set a -> Set a -> Bool #

(>) :: Set a -> Set a -> Bool #

(>=) :: Set a -> Set a -> Bool #

max :: Set a -> Set a -> Set a #

min :: Set a -> Set a -> Set a #

(Read a, Ord a) => Read (Set a) 
Show a => Show (Set a) 

Methods

showsPrec :: Int -> Set a -> ShowS #

show :: Set a -> String #

showList :: [Set a] -> ShowS #

Ord a => Semigroup (Set a) 

Methods

(<>) :: Set a -> Set a -> Set a #

sconcat :: NonEmpty (Set a) -> Set a #

stimes :: Integral b => b -> Set a -> Set a #

Ord a => Monoid (Set a) 

Methods

mempty :: Set a #

mappend :: Set a -> Set a -> Set a #

mconcat :: [Set a] -> Set a #

NFData a => NFData (Set a) 

Methods

rnf :: Set a -> () #

type Item (Set a) 
type Item (Set a) = a

data HashSet a :: * -> * #

A set of values. A set cannot contain duplicate values.

Instances

Foldable HashSet 

Methods

fold :: Monoid m => HashSet m -> m #

foldMap :: Monoid m => (a -> m) -> HashSet a -> m #

foldr :: (a -> b -> b) -> b -> HashSet a -> b #

foldr' :: (a -> b -> b) -> b -> HashSet a -> b #

foldl :: (b -> a -> b) -> b -> HashSet a -> b #

foldl' :: (b -> a -> b) -> b -> HashSet a -> b #

foldr1 :: (a -> a -> a) -> HashSet a -> a #

foldl1 :: (a -> a -> a) -> HashSet a -> a #

toList :: HashSet a -> [a] #

null :: HashSet a -> Bool #

length :: HashSet a -> Int #

elem :: Eq a => a -> HashSet a -> Bool #

maximum :: Ord a => HashSet a -> a #

minimum :: Ord a => HashSet a -> a #

sum :: Num a => HashSet a -> a #

product :: Num a => HashSet a -> a #

Eq1 HashSet 

Methods

liftEq :: (a -> b -> Bool) -> HashSet a -> HashSet b -> Bool #

Show1 HashSet 

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> HashSet a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [HashSet a] -> ShowS #

Hashable1 HashSet 

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> HashSet a -> Int #

(Eq a, Hashable a) => IsList (HashSet a) 

Associated Types

type Item (HashSet a) :: * #

Methods

fromList :: [Item (HashSet a)] -> HashSet a #

fromListN :: Int -> [Item (HashSet a)] -> HashSet a #

toList :: HashSet a -> [Item (HashSet a)] #

Eq a => Eq (HashSet a) 

Methods

(==) :: HashSet a -> HashSet a -> Bool #

(/=) :: HashSet a -> HashSet a -> Bool #

(Data a, Eq a, Hashable a) => Data (HashSet a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> HashSet a -> c (HashSet a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (HashSet a) #

toConstr :: HashSet a -> Constr #

dataTypeOf :: HashSet a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (HashSet a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (HashSet a)) #

gmapT :: (forall b. Data b => b -> b) -> HashSet a -> HashSet a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> HashSet a -> r #

gmapQ :: (forall d. Data d => d -> u) -> HashSet a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> HashSet a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> HashSet a -> m (HashSet a) #

(Eq a, Hashable a, Read a) => Read (HashSet a) 
Show a => Show (HashSet a) 

Methods

showsPrec :: Int -> HashSet a -> ShowS #

show :: HashSet a -> String #

showList :: [HashSet a] -> ShowS #

(Hashable a, Eq a) => Semigroup (HashSet a) 

Methods

(<>) :: HashSet a -> HashSet a -> HashSet a #

sconcat :: NonEmpty (HashSet a) -> HashSet a #

stimes :: Integral b => b -> HashSet a -> HashSet a #

(Hashable a, Eq a) => Monoid (HashSet a) 

Methods

mempty :: HashSet a #

mappend :: HashSet a -> HashSet a -> HashSet a #

mconcat :: [HashSet a] -> HashSet a #

NFData a => NFData (HashSet a) 

Methods

rnf :: HashSet a -> () #

Hashable a => Hashable (HashSet a) 

Methods

hashWithSalt :: Int -> HashSet a -> Int #

hash :: HashSet a -> Int #

type Item (HashSet a) 
type Item (HashSet a) = a

data IntSet :: * #

A set of integers.

Instances

IsList IntSet 

Associated Types

type Item IntSet :: * #

Eq IntSet 

Methods

(==) :: IntSet -> IntSet -> Bool #

(/=) :: IntSet -> IntSet -> Bool #

Data IntSet 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> IntSet -> c IntSet #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c IntSet #

toConstr :: IntSet -> Constr #

dataTypeOf :: IntSet -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c IntSet) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c IntSet) #

gmapT :: (forall b. Data b => b -> b) -> IntSet -> IntSet #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> IntSet -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> IntSet -> r #

gmapQ :: (forall d. Data d => d -> u) -> IntSet -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> IntSet -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> IntSet -> m IntSet #

Ord IntSet 
Read IntSet 
Show IntSet 
Semigroup IntSet 
Monoid IntSet 
NFData IntSet 

Methods

rnf :: IntSet -> () #

type Item IntSet 
type Item IntSet = Key

data Seq a :: * -> * #

General-purpose finite sequences.

Instances

Monad Seq 

Methods

(>>=) :: Seq a -> (a -> Seq b) -> Seq b #

(>>) :: Seq a -> Seq b -> Seq b #

return :: a -> Seq a #

fail :: String -> Seq a #

Functor Seq 

Methods

fmap :: (a -> b) -> Seq a -> Seq b #

(<$) :: a -> Seq b -> Seq a #

Applicative Seq 

Methods

pure :: a -> Seq a #

(<*>) :: Seq (a -> b) -> Seq a -> Seq b #

(*>) :: Seq a -> Seq b -> Seq b #

(<*) :: Seq a -> Seq b -> Seq a #

Foldable Seq 

Methods

fold :: Monoid m => Seq m -> m #

foldMap :: Monoid m => (a -> m) -> Seq a -> m #

foldr :: (a -> b -> b) -> b -> Seq a -> b #

foldr' :: (a -> b -> b) -> b -> Seq a -> b #

foldl :: (b -> a -> b) -> b -> Seq a -> b #

foldl' :: (b -> a -> b) -> b -> Seq a -> b #

foldr1 :: (a -> a -> a) -> Seq a -> a #

foldl1 :: (a -> a -> a) -> Seq a -> a #

toList :: Seq a -> [a] #

null :: Seq a -> Bool #

length :: Seq a -> Int #

elem :: Eq a => a -> Seq a -> Bool #

maximum :: Ord a => Seq a -> a #

minimum :: Ord a => Seq a -> a #

sum :: Num a => Seq a -> a #

product :: Num a => Seq a -> a #

Traversable Seq 

Methods

traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) #

sequenceA :: Applicative f => Seq (f a) -> f (Seq a) #

mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) #

sequence :: Monad m => Seq (m a) -> m (Seq a) #

Alternative Seq 

Methods

empty :: Seq a #

(<|>) :: Seq a -> Seq a -> Seq a #

some :: Seq a -> Seq [a] #

many :: Seq a -> Seq [a] #

MonadPlus Seq 

Methods

mzero :: Seq a #

mplus :: Seq a -> Seq a -> Seq a #

IsList (Seq a) 

Associated Types

type Item (Seq a) :: * #

Methods

fromList :: [Item (Seq a)] -> Seq a #

fromListN :: Int -> [Item (Seq a)] -> Seq a #

toList :: Seq a -> [Item (Seq a)] #

Eq a => Eq (Seq a) 

Methods

(==) :: Seq a -> Seq a -> Bool #

(/=) :: Seq a -> Seq a -> Bool #

Data a => Data (Seq a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Seq a -> c (Seq a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Seq a) #

toConstr :: Seq a -> Constr #

dataTypeOf :: Seq a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Seq a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Seq a)) #

gmapT :: (forall b. Data b => b -> b) -> Seq a -> Seq a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Seq a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Seq a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Seq a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Seq a -> m (Seq a) #

Ord a => Ord (Seq a) 

Methods

compare :: Seq a -> Seq a -> Ordering #

(<) :: Seq a -> Seq a -> Bool #

(<=) :: Seq a -> Seq a -> Bool #

(>) :: Seq a -> Seq a -> Bool #

(>=) :: Seq a -> Seq a -> Bool #

max :: Seq a -> Seq a -> Seq a #

min :: Seq a -> Seq a -> Seq a #

Read a => Read (Seq a) 
Show a => Show (Seq a) 

Methods

showsPrec :: Int -> Seq a -> ShowS #

show :: Seq a -> String #

showList :: [Seq a] -> ShowS #

IsString (Seq Char) 

Methods

fromString :: String -> Seq Char #

Semigroup (Seq a) 

Methods

(<>) :: Seq a -> Seq a -> Seq a #

sconcat :: NonEmpty (Seq a) -> Seq a #

stimes :: Integral b => b -> Seq a -> Seq a #

Monoid (Seq a) 

Methods

mempty :: Seq a #

mappend :: Seq a -> Seq a -> Seq a #

mconcat :: [Seq a] -> Seq a #

NFData a => NFData (Seq a) 

Methods

rnf :: Seq a -> () #

type Item (Seq a) 
type Item (Seq a) = a

data Vector a :: * -> * #

Boxed vectors, supporting efficient slicing.

Instances

Monad Vector 

Methods

(>>=) :: Vector a -> (a -> Vector b) -> Vector b #

(>>) :: Vector a -> Vector b -> Vector b #

return :: a -> Vector a #

fail :: String -> Vector a #

Functor Vector 

Methods

fmap :: (a -> b) -> Vector a -> Vector b #

(<$) :: a -> Vector b -> Vector a #

Applicative Vector 

Methods

pure :: a -> Vector a #

(<*>) :: Vector (a -> b) -> Vector a -> Vector b #

(*>) :: Vector a -> Vector b -> Vector b #

(<*) :: Vector a -> Vector b -> Vector a #

Foldable Vector 

Methods

fold :: Monoid m => Vector m -> m #

foldMap :: Monoid m => (a -> m) -> Vector a -> m #

foldr :: (a -> b -> b) -> b -> Vector a -> b #

foldr' :: (a -> b -> b) -> b -> Vector a -> b #

foldl :: (b -> a -> b) -> b -> Vector a -> b #

foldl' :: (b -> a -> b) -> b -> Vector a -> b #

foldr1 :: (a -> a -> a) -> Vector a -> a #

foldl1 :: (a -> a -> a) -> Vector a -> a #

toList :: Vector a -> [a] #

null :: Vector a -> Bool #

length :: Vector a -> Int #

elem :: Eq a => a -> Vector a -> Bool #

maximum :: Ord a => Vector a -> a #

minimum :: Ord a => Vector a -> a #

sum :: Num a => Vector a -> a #

product :: Num a => Vector a -> a #

Traversable Vector 

Methods

traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) #

sequenceA :: Applicative f => Vector (f a) -> f (Vector a) #

mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) #

sequence :: Monad m => Vector (m a) -> m (Vector a) #

Eq1 Vector 

Methods

liftEq :: (a -> b -> Bool) -> Vector a -> Vector b -> Bool #

Ord1 Vector 

Methods

liftCompare :: (a -> b -> Ordering) -> Vector a -> Vector b -> Ordering #

Read1 Vector 

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Vector a) #

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Vector a] #

Show1 Vector 

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Vector a -> ShowS #

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Vector a] -> ShowS #

MonadZip Vector 

Methods

mzip :: Vector a -> Vector b -> Vector (a, b) #

mzipWith :: (a -> b -> c) -> Vector a -> Vector b -> Vector c #

munzip :: Vector (a, b) -> (Vector a, Vector b) #

Alternative Vector 

Methods

empty :: Vector a #

(<|>) :: Vector a -> Vector a -> Vector a #

some :: Vector a -> Vector [a] #

many :: Vector a -> Vector [a] #

MonadPlus Vector 

Methods

mzero :: Vector a #

mplus :: Vector a -> Vector a -> Vector a #

Vector Vector a 

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) a -> m (Vector a) #

basicUnsafeThaw :: PrimMonad m => Vector a -> m (Mutable Vector (PrimState m) a) #

basicLength :: Vector a -> Int #

basicUnsafeSlice :: Int -> Int -> Vector a -> Vector a #

basicUnsafeIndexM :: Monad m => Vector a -> Int -> m a #

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) a -> Vector a -> m () #

elemseq :: Vector a -> a -> b -> b #

IsList (Vector a) 

Associated Types

type Item (Vector a) :: * #

Methods

fromList :: [Item (Vector a)] -> Vector a #

fromListN :: Int -> [Item (Vector a)] -> Vector a #

toList :: Vector a -> [Item (Vector a)] #

Eq a => Eq (Vector a) 

Methods

(==) :: Vector a -> Vector a -> Bool #

(/=) :: Vector a -> Vector a -> Bool #

Data a => Data (Vector a) 

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Vector a -> c (Vector a) #

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Vector a) #

toConstr :: Vector a -> Constr #

dataTypeOf :: Vector a -> DataType #

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Vector a)) #

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Vector a)) #

gmapT :: (forall b. Data b => b -> b) -> Vector a -> Vector a #

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r #

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Vector a -> r #

gmapQ :: (forall d. Data d => d -> u) -> Vector a -> [u] #

gmapQi :: Int -> (forall d. Data d => d -> u) -> Vector a -> u #

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Vector a -> m (Vector a) #

Ord a => Ord (Vector a) 

Methods

compare :: Vector a -> Vector a -> Ordering #

(<) :: Vector a -> Vector a -> Bool #

(<=) :: Vector a -> Vector a -> Bool #

(>) :: Vector a -> Vector a -> Bool #

(>=) :: Vector a -> Vector a -> Bool #

max :: Vector a -> Vector a -> Vector a #

min :: Vector a -> Vector a -> Vector a #

Read a => Read (Vector a) 
Show a => Show (Vector a) 

Methods

showsPrec :: Int -> Vector a -> ShowS #

show :: Vector a -> String #

showList :: [Vector a] -> ShowS #

Semigroup (Vector a) 

Methods

(<>) :: Vector a -> Vector a -> Vector a #

sconcat :: NonEmpty (Vector a) -> Vector a #

stimes :: Integral b => b -> Vector a -> Vector a #

Monoid (Vector a) 

Methods

mempty :: Vector a #

mappend :: Vector a -> Vector a -> Vector a #

mconcat :: [Vector a] -> Vector a #

NFData a => NFData (Vector a) 

Methods

rnf :: Vector a -> () #

type Mutable Vector 
type Item (Vector a) 
type Item (Vector a) = a

class (Vector Vector a, MVector MVector a) => Unbox a #

Instances

Unbox Bool 
Unbox Char 
Unbox Double 
Unbox Float 
Unbox Int 
Unbox Int8 
Unbox Int16 
Unbox Int32 
Unbox Int64 
Unbox Word 
Unbox Word8 
Unbox Word16 
Unbox Word32 
Unbox Word64 
Unbox () 
Unbox a => Unbox (Complex a) 
(Unbox a, Unbox b) => Unbox (a, b) 
(Unbox a, Unbox b, Unbox c) => Unbox (a, b, c) 
(Unbox a, Unbox b, Unbox c, Unbox d) => Unbox (a, b, c, d) 
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e) => Unbox (a, b, c, d, e) 
(Unbox a, Unbox b, Unbox c, Unbox d, Unbox e, Unbox f) => Unbox (a, b, c, d, e, f) 

class Storable a #

The member functions of this class facilitate writing values of primitive types to raw memory (which may have been allocated with the above mentioned routines) and reading values from blocks of raw memory. The class, furthermore, includes support for computing the storage requirements and alignment restrictions of storable types.

Memory addresses are represented as values of type Ptr a, for some a which is an instance of class Storable. The type argument to Ptr helps provide some valuable type safety in FFI code (you can't mix pointers of different types without an explicit cast), while helping the Haskell type system figure out which marshalling method is needed for a given pointer.

All marshalling between Haskell and a foreign language ultimately boils down to translating Haskell data structures into the binary representation of a corresponding data structure of the foreign language and vice versa. To code this marshalling in Haskell, it is necessary to manipulate primitive data types stored in unstructured memory blocks. The class Storable facilitates this manipulation on all types for which it is instantiated, which are the standard basic types of Haskell, the fixed size Int types (Int8, Int16, Int32, Int64), the fixed size Word types (Word8, Word16, Word32, Word64), StablePtr, all types from Foreign.C.Types, as well as Ptr.

Minimal complete definition

sizeOf, alignment, (peek | peekElemOff | peekByteOff), (poke | pokeElemOff | pokeByteOff)

Instances

Storable Bool 

Methods

sizeOf :: Bool -> Int #

alignment :: Bool -> Int #

peekElemOff :: Ptr Bool -> Int -> IO Bool #

pokeElemOff :: Ptr Bool -> Int -> Bool -> IO () #

peekByteOff :: Ptr b -> Int -> IO Bool #

pokeByteOff :: Ptr b -> Int -> Bool -> IO () #

peek :: Ptr Bool -> IO Bool #

poke :: Ptr Bool -> Bool -> IO () #

Storable Char 

Methods

sizeOf :: Char -> Int #

alignment :: Char -> Int #

peekElemOff :: Ptr Char -> Int -> IO Char #

pokeElemOff :: Ptr Char -> Int -> Char -> IO () #

peekByteOff :: Ptr b -> Int -> IO Char #

pokeByteOff :: Ptr b -> Int -> Char -> IO () #

peek :: Ptr Char -> IO Char #

poke :: Ptr Char -> Char -> IO () #

Storable Double 
Storable Float 

Methods

sizeOf :: Float -> Int #

alignment :: Float -> Int #

peekElemOff :: Ptr Float -> Int -> IO Float #

pokeElemOff :: Ptr Float -> Int -> Float -> IO () #

peekByteOff :: Ptr b -> Int -> IO Float #

pokeByteOff :: Ptr b -> Int -> Float -> IO () #

peek :: Ptr Float -> IO Float #

poke :: Ptr Float -> Float -> IO () #

Storable Int 

Methods

sizeOf :: Int -> Int #

alignment :: Int -> Int #

peekElemOff :: Ptr Int -> Int -> IO Int #

pokeElemOff :: Ptr Int -> Int -> Int -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int #

pokeByteOff :: Ptr b -> Int -> Int -> IO () #

peek :: Ptr Int -> IO Int #

poke :: Ptr Int -> Int -> IO () #

Storable Int8 

Methods

sizeOf :: Int8 -> Int #

alignment :: Int8 -> Int #

peekElemOff :: Ptr Int8 -> Int -> IO Int8 #

pokeElemOff :: Ptr Int8 -> Int -> Int8 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int8 #

pokeByteOff :: Ptr b -> Int -> Int8 -> IO () #

peek :: Ptr Int8 -> IO Int8 #

poke :: Ptr Int8 -> Int8 -> IO () #

Storable Int16 

Methods

sizeOf :: Int16 -> Int #

alignment :: Int16 -> Int #

peekElemOff :: Ptr Int16 -> Int -> IO Int16 #

pokeElemOff :: Ptr Int16 -> Int -> Int16 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int16 #

pokeByteOff :: Ptr b -> Int -> Int16 -> IO () #

peek :: Ptr Int16 -> IO Int16 #

poke :: Ptr Int16 -> Int16 -> IO () #

Storable Int32 

Methods

sizeOf :: Int32 -> Int #

alignment :: Int32 -> Int #

peekElemOff :: Ptr Int32 -> Int -> IO Int32 #

pokeElemOff :: Ptr Int32 -> Int -> Int32 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int32 #

pokeByteOff :: Ptr b -> Int -> Int32 -> IO () #

peek :: Ptr Int32 -> IO Int32 #

poke :: Ptr Int32 -> Int32 -> IO () #

Storable Int64 

Methods

sizeOf :: Int64 -> Int #

alignment :: Int64 -> Int #

peekElemOff :: Ptr Int64 -> Int -> IO Int64 #

pokeElemOff :: Ptr Int64 -> Int -> Int64 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int64 #

pokeByteOff :: Ptr b -> Int -> Int64 -> IO () #

peek :: Ptr Int64 -> IO Int64 #

poke :: Ptr Int64 -> Int64 -> IO () #

Storable Word 

Methods

sizeOf :: Word -> Int #

alignment :: Word -> Int #

peekElemOff :: Ptr Word -> Int -> IO Word #

pokeElemOff :: Ptr Word -> Int -> Word -> IO () #

peekByteOff :: Ptr b -> Int -> IO Word #

pokeByteOff :: Ptr b -> Int -> Word -> IO () #

peek :: Ptr Word -> IO Word #

poke :: Ptr Word -> Word -> IO () #

Storable Word8 

Methods

sizeOf :: Word8 -> Int #

alignment :: Word8 -> Int #

peekElemOff :: Ptr Word8 -> Int -> IO Word8 #

pokeElemOff :: Ptr Word8 -> Int -> Word8 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Word8 #

pokeByteOff :: Ptr b -> Int -> Word8 -> IO () #

peek :: Ptr Word8 -> IO Word8 #

poke :: Ptr Word8 -> Word8 -> IO () #

Storable Word16 
Storable Word32 
Storable Word64 
Storable () 

Methods

sizeOf :: () -> Int #

alignment :: () -> Int #

peekElemOff :: Ptr () -> Int -> IO () #

pokeElemOff :: Ptr () -> Int -> () -> IO () #

peekByteOff :: Ptr b -> Int -> IO () #

pokeByteOff :: Ptr b -> Int -> () -> IO () #

peek :: Ptr () -> IO () #

poke :: Ptr () -> () -> IO () #

Storable CChar 

Methods

sizeOf :: CChar -> Int #

alignment :: CChar -> Int #

peekElemOff :: Ptr CChar -> Int -> IO CChar #

pokeElemOff :: Ptr CChar -> Int -> CChar -> IO () #

peekByteOff :: Ptr b -> Int -> IO CChar #

pokeByteOff :: Ptr b -> Int -> CChar -> IO () #

peek :: Ptr CChar -> IO CChar #

poke :: Ptr CChar -> CChar -> IO () #

Storable CSChar 
Storable CUChar 
Storable CShort 
Storable CUShort 
Storable CInt 

Methods

sizeOf :: CInt -> Int #

alignment :: CInt -> Int #

peekElemOff :: Ptr CInt -> Int -> IO CInt #

pokeElemOff :: Ptr CInt -> Int -> CInt -> IO () #

peekByteOff :: Ptr b -> Int -> IO CInt #

pokeByteOff :: Ptr b -> Int -> CInt -> IO () #

peek :: Ptr CInt -> IO CInt #

poke :: Ptr CInt -> CInt -> IO () #

Storable CUInt 

Methods

sizeOf :: CUInt -> Int #

alignment :: CUInt -> Int #

peekElemOff :: Ptr CUInt -> Int -> IO CUInt #

pokeElemOff :: Ptr CUInt -> Int -> CUInt -> IO () #

peekByteOff :: Ptr b -> Int -> IO CUInt #

pokeByteOff :: Ptr b -> Int -> CUInt -> IO () #

peek :: Ptr CUInt -> IO CUInt #

poke :: Ptr CUInt -> CUInt -> IO () #

Storable CLong 

Methods

sizeOf :: CLong -> Int #

alignment :: CLong -> Int #

peekElemOff :: Ptr CLong -> Int -> IO CLong #

pokeElemOff :: Ptr CLong -> Int -> CLong -> IO () #

peekByteOff :: Ptr b -> Int -> IO CLong #

pokeByteOff :: Ptr b -> Int -> CLong -> IO () #

peek :: Ptr CLong -> IO CLong #

poke :: Ptr CLong -> CLong -> IO () #

Storable CULong 
Storable CLLong 
Storable CULLong 
Storable CFloat 
Storable CDouble 
Storable CPtrdiff 
Storable CSize 

Methods

sizeOf :: CSize -> Int #

alignment :: CSize -> Int #

peekElemOff :: Ptr CSize -> Int -> IO CSize #

pokeElemOff :: Ptr CSize -> Int -> CSize -> IO () #

peekByteOff :: Ptr b -> Int -> IO CSize #

pokeByteOff :: Ptr b -> Int -> CSize -> IO () #

peek :: Ptr CSize -> IO CSize #

poke :: Ptr CSize -> CSize -> IO () #

Storable CWchar 
Storable CSigAtomic 
Storable CClock 
Storable CTime 

Methods

sizeOf :: CTime -> Int #

alignment :: CTime -> Int #

peekElemOff :: Ptr CTime -> Int -> IO CTime #

pokeElemOff :: Ptr CTime -> Int -> CTime -> IO () #

peekByteOff :: Ptr b -> Int -> IO CTime #

pokeByteOff :: Ptr b -> Int -> CTime -> IO () #

peek :: Ptr CTime -> IO CTime #

poke :: Ptr CTime -> CTime -> IO () #

Storable CUSeconds 
Storable CSUSeconds 
Storable CIntPtr 
Storable CUIntPtr 
Storable CIntMax 
Storable CUIntMax 
Storable Fingerprint 
Storable CodePoint 

Methods

sizeOf :: CodePoint -> Int #

alignment :: CodePoint -> Int #

peekElemOff :: Ptr CodePoint -> Int -> IO CodePoint #

pokeElemOff :: Ptr CodePoint -> Int -> CodePoint -> IO () #

peekByteOff :: Ptr b -> Int -> IO CodePoint #

pokeByteOff :: Ptr b -> Int -> CodePoint -> IO () #

peek :: Ptr CodePoint -> IO CodePoint #

poke :: Ptr CodePoint -> CodePoint -> IO () #

Storable DecoderState 

Methods

sizeOf :: DecoderState -> Int #

alignment :: DecoderState -> Int #

peekElemOff :: Ptr DecoderState -> Int -> IO DecoderState #

pokeElemOff :: Ptr DecoderState -> Int -> DecoderState -> IO () #

peekByteOff :: Ptr b -> Int -> IO DecoderState #

pokeByteOff :: Ptr b -> Int -> DecoderState -> IO () #

peek :: Ptr DecoderState -> IO DecoderState #

poke :: Ptr DecoderState -> DecoderState -> IO () #

(Storable a, Integral a) => Storable (Ratio a) 

Methods

sizeOf :: Ratio a -> Int #

alignment :: Ratio a -> Int #

peekElemOff :: Ptr (Ratio a) -> Int -> IO (Ratio a) #

pokeElemOff :: Ptr (Ratio a) -> Int -> Ratio a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Ratio a) #

pokeByteOff :: Ptr b -> Int -> Ratio a -> IO () #

peek :: Ptr (Ratio a) -> IO (Ratio a) #

poke :: Ptr (Ratio a) -> Ratio a -> IO () #

Storable (StablePtr a) 

Methods

sizeOf :: StablePtr a -> Int #

alignment :: StablePtr a -> Int #

peekElemOff :: Ptr (StablePtr a) -> Int -> IO (StablePtr a) #

pokeElemOff :: Ptr (StablePtr a) -> Int -> StablePtr a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (StablePtr a) #

pokeByteOff :: Ptr b -> Int -> StablePtr a -> IO () #

peek :: Ptr (StablePtr a) -> IO (StablePtr a) #

poke :: Ptr (StablePtr a) -> StablePtr a -> IO () #

Storable (Ptr a) 

Methods

sizeOf :: Ptr a -> Int #

alignment :: Ptr a -> Int #

peekElemOff :: Ptr (Ptr a) -> Int -> IO (Ptr a) #

pokeElemOff :: Ptr (Ptr a) -> Int -> Ptr a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Ptr a) #

pokeByteOff :: Ptr b -> Int -> Ptr a -> IO () #

peek :: Ptr (Ptr a) -> IO (Ptr a) #

poke :: Ptr (Ptr a) -> Ptr a -> IO () #

Storable (FunPtr a) 

Methods

sizeOf :: FunPtr a -> Int #

alignment :: FunPtr a -> Int #

peekElemOff :: Ptr (FunPtr a) -> Int -> IO (FunPtr a) #

pokeElemOff :: Ptr (FunPtr a) -> Int -> FunPtr a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (FunPtr a) #

pokeByteOff :: Ptr b -> Int -> FunPtr a -> IO () #

peek :: Ptr (FunPtr a) -> IO (FunPtr a) #

poke :: Ptr (FunPtr a) -> FunPtr a -> IO () #

Storable a => Storable (Identity a) 

Methods

sizeOf :: Identity a -> Int #

alignment :: Identity a -> Int #

peekElemOff :: Ptr (Identity a) -> Int -> IO (Identity a) #

pokeElemOff :: Ptr (Identity a) -> Int -> Identity a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Identity a) #

pokeByteOff :: Ptr b -> Int -> Identity a -> IO () #

peek :: Ptr (Identity a) -> IO (Identity a) #

poke :: Ptr (Identity a) -> Identity a -> IO () #

Storable a => Storable (Complex a) 

Methods

sizeOf :: Complex a -> Int #

alignment :: Complex a -> Int #

peekElemOff :: Ptr (Complex a) -> Int -> IO (Complex a) #

pokeElemOff :: Ptr (Complex a) -> Int -> Complex a -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Complex a) #

pokeByteOff :: Ptr b -> Int -> Complex a -> IO () #

peek :: Ptr (Complex a) -> IO (Complex a) #

poke :: Ptr (Complex a) -> Complex a -> IO () #

Storable a => Storable (Const k a b) 

Methods

sizeOf :: Const k a b -> Int #

alignment :: Const k a b -> Int #

peekElemOff :: Ptr (Const k a b) -> Int -> IO (Const k a b) #

pokeElemOff :: Ptr (Const k a b) -> Int -> Const k a b -> IO () #

peekByteOff :: Ptr b -> Int -> IO (Const k a b) #

pokeByteOff :: Ptr b -> Int -> Const k a b -> IO () #

peek :: Ptr (Const k a b) -> IO (Const k a b) #

poke :: Ptr (Const k a b) -> Const k a b -> IO () #

class Hashable a where #

The class of types that can be converted to a hash value.

Minimal implementation: hashWithSalt.

Methods

hashWithSalt :: Int -> a -> Int infixl 0 #

Return a hash value for the argument, using the given salt.

The general contract of hashWithSalt is:

  • If two values are equal according to the == method, then applying the hashWithSalt method on each of the two values must produce the same integer result if the same salt is used in each case.
  • It is not required that if two values are unequal according to the == method, then applying the hashWithSalt method on each of the two values must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal values may improve the performance of hashing-based data structures.
  • This method can be used to compute different hash values for the same input by providing a different salt in each application of the method. This implies that any instance that defines hashWithSalt must make use of the salt in its implementation.

hash :: a -> Int #

Like hashWithSalt, but no salt is used. The default implementation uses hashWithSalt with some default salt. Instances might want to implement this method to provide a more efficient implementation than the default implementation.

Instances

Hashable Bool 

Methods

hashWithSalt :: Int -> Bool -> Int #

hash :: Bool -> Int #

Hashable Char 

Methods

hashWithSalt :: Int -> Char -> Int #

hash :: Char -> Int #

Hashable Double 

Methods

hashWithSalt :: Int -> Double -> Int #

hash :: Double -> Int #

Hashable Float 

Methods

hashWithSalt :: Int -> Float -> Int #

hash :: Float -> Int #

Hashable Int 

Methods

hashWithSalt :: Int -> Int -> Int #

hash :: Int -> Int #

Hashable Int8 

Methods

hashWithSalt :: Int -> Int8 -> Int #

hash :: Int8 -> Int #

Hashable Int16 

Methods

hashWithSalt :: Int -> Int16 -> Int #

hash :: Int16 -> Int #

Hashable Int32 

Methods

hashWithSalt :: Int -> Int32 -> Int #

hash :: Int32 -> Int #

Hashable Int64 

Methods

hashWithSalt :: Int -> Int64 -> Int #

hash :: Int64 -> Int #

Hashable Integer 

Methods

hashWithSalt :: Int -> Integer -> Int #

hash :: Integer -> Int #

Hashable Ordering 

Methods

hashWithSalt :: Int -> Ordering -> Int #

hash :: Ordering -> Int #

Hashable Word 

Methods

hashWithSalt :: Int -> Word -> Int #

hash :: Word -> Int #

Hashable Word8 

Methods

hashWithSalt :: Int -> Word8 -> Int #

hash :: Word8 -> Int #

Hashable Word16 

Methods

hashWithSalt :: Int -> Word16 -> Int #

hash :: Word16 -> Int #

Hashable Word32 

Methods

hashWithSalt :: Int -> Word32 -> Int #

hash :: Word32 -> Int #

Hashable Word64 

Methods

hashWithSalt :: Int -> Word64 -> Int #

hash :: Word64 -> Int #

Hashable TypeRep 

Methods

hashWithSalt :: Int -> TypeRep -> Int #

hash :: TypeRep -> Int #

Hashable () 

Methods

hashWithSalt :: Int -> () -> Int #

hash :: () -> Int #

Hashable BigNat 

Methods

hashWithSalt :: Int -> BigNat -> Int #

hash :: BigNat -> Int #

Hashable Natural 

Methods

hashWithSalt :: Int -> Natural -> Int #

hash :: Natural -> Int #

Hashable Void 

Methods

hashWithSalt :: Int -> Void -> Int #

hash :: Void -> Int #

Hashable Version 

Methods

hashWithSalt :: Int -> Version -> Int #

hash :: Version -> Int #

Hashable Unique 

Methods

hashWithSalt :: Int -> Unique -> Int #

hash :: Unique -> Int #

Hashable ThreadId 

Methods

hashWithSalt :: Int -> ThreadId -> Int #

hash :: ThreadId -> Int #

Hashable WordPtr 

Methods

hashWithSalt :: Int -> WordPtr -> Int #

hash :: WordPtr -> Int #

Hashable IntPtr 

Methods

hashWithSalt :: Int -> IntPtr -> Int #

hash :: IntPtr -> Int #

Hashable ShortByteString 
Hashable ByteString 
Hashable ByteString 
Hashable Text 

Methods

hashWithSalt :: Int -> Text -> Int #

hash :: Text -> Int #

Hashable Text 

Methods

hashWithSalt :: Int -> Text -> Int #

hash :: Text -> Int #

Hashable a => Hashable [a] 

Methods

hashWithSalt :: Int -> [a] -> Int #

hash :: [a] -> Int #

Hashable a => Hashable (Maybe a) 

Methods

hashWithSalt :: Int -> Maybe a -> Int #

hash :: Maybe a -> Int #

Hashable a => Hashable (Ratio a) 

Methods

hashWithSalt :: Int -> Ratio a -> Int #

hash :: Ratio a -> Int #

Hashable (Ptr a) 

Methods

hashWithSalt :: Int -> Ptr a -> Int #

hash :: Ptr a -> Int #

Hashable (FunPtr a) 

Methods

hashWithSalt :: Int -> FunPtr a -> Int #

hash :: FunPtr a -> Int #

Hashable a => Hashable (Identity a) 

Methods

hashWithSalt :: Int -> Identity a -> Int #

hash :: Identity a -> Int #

Hashable a => Hashable (Min a) 

Methods

hashWithSalt :: Int -> Min a -> Int #

hash :: Min a -> Int #

Hashable a => Hashable (Max a) 

Methods

hashWithSalt :: Int -> Max a -> Int #

hash :: Max a -> Int #

Hashable a => Hashable (First a) 

Methods

hashWithSalt :: Int -> First a -> Int #

hash :: First a -> Int #

Hashable a => Hashable (Last a) 

Methods

hashWithSalt :: Int -> Last a -> Int #

hash :: Last a -> Int #

Hashable a => Hashable (WrappedMonoid a) 
Hashable a => Hashable (Option a) 

Methods

hashWithSalt :: Int -> Option a -> Int #

hash :: Option a -> Int #

Hashable a => Hashable (NonEmpty a) 

Methods

hashWithSalt :: Int -> NonEmpty a -> Int #

hash :: NonEmpty a -> Int #

Hashable (Fixed a) 

Methods

hashWithSalt :: Int -> Fixed a -> Int #

hash :: Fixed a -> Int #

Hashable (StableName a) 

Methods

hashWithSalt :: Int -> StableName a -> Int #

hash :: StableName a -> Int #

Hashable (Hashed a) 

Methods

hashWithSalt :: Int -> Hashed a -> Int #

hash :: Hashed a -> Int #

Hashable a => Hashable (HashSet a) 

Methods

hashWithSalt :: Int -> HashSet a -> Int #

hash :: HashSet a -> Int #

(Hashable a, Hashable b) => Hashable (Either a b) 

Methods

hashWithSalt :: Int -> Either a b -> Int #

hash :: Either a b -> Int #

(Hashable a1, Hashable a2) => Hashable (a1, a2) 

Methods

hashWithSalt :: Int -> (a1, a2) -> Int #

hash :: (a1, a2) -> Int #

(Hashable a, Hashable b) => Hashable (Arg a b) 

Methods

hashWithSalt :: Int -> Arg a b -> Int #

hash :: Arg a b -> Int #

Hashable (Proxy * a) 

Methods

hashWithSalt :: Int -> Proxy * a -> Int #

hash :: Proxy * a -> Int #

(Hashable k, Hashable v) => Hashable (HashMap k v) 

Methods

hashWithSalt :: Int -> HashMap k v -> Int #

hash :: HashMap k v -> Int #

(Hashable a1, Hashable a2, Hashable a3) => Hashable (a1, a2, a3) 

Methods

hashWithSalt :: Int -> (a1, a2, a3) -> Int #

hash :: (a1, a2, a3) -> Int #

Hashable a => Hashable (Const * a b) 

Methods

hashWithSalt :: Int -> Const * a b -> Int #

hash :: Const * a b -> Int #

(Hashable a1, Hashable a2, Hashable a3, Hashable a4) => Hashable (a1, a2, a3, a4) 

Methods

hashWithSalt :: Int -> (a1, a2, a3, a4) -> Int #

hash :: (a1, a2, a3, a4) -> Int #

(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Sum * f g a) 

Methods

hashWithSalt :: Int -> Sum * f g a -> Int #

hash :: Sum * f g a -> Int #

(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Product * f g a) 

Methods

hashWithSalt :: Int -> Product * f g a -> Int #

hash :: Product * f g a -> Int #

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5) => Hashable (a1, a2, a3, a4, a5) 

Methods

hashWithSalt :: Int -> (a1, a2, a3, a4, a5) -> Int #

hash :: (a1, a2, a3, a4, a5) -> Int #

(Hashable1 f, Hashable1 g, Hashable a) => Hashable (Compose * * f g a)

In general, hash (Compose x) ≠ hash x. However, hashWithSalt satisfies its variant of this equivalence.

Methods

hashWithSalt :: Int -> Compose * * f g a -> Int #

hash :: Compose * * f g a -> Int #

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6) => Hashable (a1, a2, a3, a4, a5, a6) 

Methods

hashWithSalt :: Int -> (a1, a2, a3, a4, a5, a6) -> Int #

hash :: (a1, a2, a3, a4, a5, a6) -> Int #

(Hashable a1, Hashable a2, Hashable a3, Hashable a4, Hashable a5, Hashable a6, Hashable a7) => Hashable (a1, a2, a3, a4, a5, a6, a7) 

Methods

hashWithSalt :: Int -> (a1, a2, a3, a4, a5, a6, a7) -> Int #

hash :: (a1, a2, a3, a4, a5, a6, a7) -> Int #

Numbers

data Word :: * #

A Word is an unsigned integral type, with the same size as Int.

Instances

Bounded Word 
Enum Word 

Methods

succ :: Word -> Word #

pred :: Word -> Word #

toEnum :: Int -> Word #

fromEnum :: Word -> Int #

enumFrom :: Word -> [Word] #

enumFromThen :: Word -> Word -> [Word] #

enumFromTo :: Word -> Word -> [Word] #

enumFromThenTo :: Word -> Word -> Word -> [Word] #

Eq Word 

Methods

(==) :: Word -> Word -> Bool #

(/=) :: Word -> Word -> Bool #

Integral Word 

Methods

quot :: Word -> Word -> Word #

rem :: Word -> Word -> Word #

div :: Word -> Word -> Word #

mod :: Word -> Word -> Word #

quotRem :: Word -> Word -> (Word, Word) #

divMod :: Word -> Word -> (Word, Word) #

toInteger :: Word -> Integer #

Num Word 

Methods

(+) :: Word -> Word -> Word #

(-) :: Word -> Word -> Word #

(*) :: Word -> Word -> Word #

negate :: Word -> Word #

abs :: Word -> Word #

signum :: Word -> Word #

fromInteger :: Integer -> Word #

Ord Word 

Methods

compare :: Word -> Word -> Ordering #

(<) :: Word -> Word -> Bool #

(<=) :: Word -> Word -> Bool #

(>) :: Word -> Word -> Bool #

(>=) :: Word -> Word -> Bool #

max :: Word -> Word -> Word #

min :: Word -> Word -> Word #

Read Word 
Real Word 

Methods

toRational :: Word -> Rational #

Show Word 

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Storable Word 

Methods

sizeOf :: Word -> Int #

alignment :: Word -> Int #

peekElemOff :: Ptr Word -> Int -> IO Word #

pokeElemOff :: Ptr Word -> Int -> Word -> IO () #

peekByteOff :: Ptr b -> Int -> IO Word #

pokeByteOff :: Ptr b -> Int -> Word -> IO () #

peek :: Ptr Word -> IO Word #

poke :: Ptr Word -> Word -> IO () #

Hashable Word 

Methods

hashWithSalt :: Int -> Word -> Int #

hash :: Word -> Int #

Unbox Word 
Vector Vector Word 
MVector MVector Word 
Functor (URec Word) 

Methods

fmap :: (a -> b) -> URec Word a -> URec Word b #

(<$) :: a -> URec Word b -> URec Word a #

Foldable (URec Word) 

Methods

fold :: Monoid m => URec Word m -> m #

foldMap :: Monoid m => (a -> m) -> URec Word a -> m #

foldr :: (a -> b -> b) -> b -> URec Word a -> b #

foldr' :: (a -> b -> b) -> b -> URec Word a -> b #

foldl :: (b -> a -> b) -> b -> URec Word a -> b #

foldl' :: (b -> a -> b) -> b -> URec Word a -> b #

foldr1 :: (a -> a -> a) -> URec Word a -> a #

foldl1 :: (a -> a -> a) -> URec Word a -> a #

toList :: URec Word a -> [a] #

null :: URec Word a -> Bool #

length :: URec Word a -> Int #

elem :: Eq a => a -> URec Word a -> Bool #

maximum :: Ord a => URec Word a -> a #

minimum :: Ord a => URec Word a -> a #

sum :: Num a => URec Word a -> a #

product :: Num a => URec Word a -> a #

Traversable (URec Word) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) #

sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) #

mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) #

sequence :: Monad m => URec Word (m a) -> m (URec Word a) #

Generic1 (URec Word) 

Associated Types

type Rep1 (URec Word :: * -> *) :: * -> * #

Methods

from1 :: URec Word a -> Rep1 (URec Word) a #

to1 :: Rep1 (URec Word) a -> URec Word a #

Eq (URec Word p) 

Methods

(==) :: URec Word p -> URec Word p -> Bool #

(/=) :: URec Word p -> URec Word p -> Bool #

Ord (URec Word p) 

Methods

compare :: URec Word p -> URec Word p -> Ordering #

(<) :: URec Word p -> URec Word p -> Bool #

(<=) :: URec Word p -> URec Word p -> Bool #

(>) :: URec Word p -> URec Word p -> Bool #

(>=) :: URec Word p -> URec Word p -> Bool #

max :: URec Word p -> URec Word p -> URec Word p #

min :: URec Word p -> URec Word p -> URec Word p #

Show (URec Word p) 

Methods

showsPrec :: Int -> URec Word p -> ShowS #

show :: URec Word p -> String #

showList :: [URec Word p] -> ShowS #

Generic (URec Word p) 

Associated Types

type Rep (URec Word p) :: * -> * #

Methods

from :: URec Word p -> Rep (URec Word p) x #

to :: Rep (URec Word p) x -> URec Word p #

data URec Word

Used for marking occurrences of Word#

data URec Word = UWord {}
data Vector Word 
data MVector s Word 
type Rep1 (URec Word) 
type Rep1 (URec Word) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UWord" PrefixI True) (S1 (MetaSel (Just Symbol "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UWord))
type Rep (URec Word p) 
type Rep (URec Word p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UWord" PrefixI True) (S1 (MetaSel (Just Symbol "uWord#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UWord))

data Word8 :: * #

8-bit unsigned integer type

Instances

Bounded Word8 
Enum Word8 
Eq Word8 

Methods

(==) :: Word8 -> Word8 -> Bool #

(/=) :: Word8 -> Word8 -> Bool #

Integral Word8 
Num Word8 
Ord Word8 

Methods

compare :: Word8 -> Word8 -> Ordering #

(<) :: Word8 -> Word8 -> Bool #

(<=) :: Word8 -> Word8 -> Bool #

(>) :: Word8 -> Word8 -> Bool #

(>=) :: Word8 -> Word8 -> Bool #

max :: Word8 -> Word8 -> Word8 #

min :: Word8 -> Word8 -> Word8 #

Read Word8 
Real Word8 

Methods

toRational :: Word8 -> Rational #

Show Word8 

Methods

showsPrec :: Int -> Word8 -> ShowS #

show :: Word8 -> String #

showList :: [Word8] -> ShowS #

Ix Word8 
Storable Word8 

Methods

sizeOf :: Word8 -> Int #

alignment :: Word8 -> Int #

peekElemOff :: Ptr Word8 -> Int -> IO Word8 #

pokeElemOff :: Ptr Word8 -> Int -> Word8 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Word8 #

pokeByteOff :: Ptr b -> Int -> Word8 -> IO () #

peek :: Ptr Word8 -> IO Word8 #

poke :: Ptr Word8 -> Word8 -> IO () #

Bits Word8 
FiniteBits Word8 
Hashable Word8 

Methods

hashWithSalt :: Int -> Word8 -> Int #

hash :: Word8 -> Int #

Unbox Word8 
Vector Vector Word8 
MVector MVector Word8 
data Vector Word8 
data MVector s Word8 

data Word32 :: * #

32-bit unsigned integer type

Instances

Bounded Word32 
Enum Word32 
Eq Word32 

Methods

(==) :: Word32 -> Word32 -> Bool #

(/=) :: Word32 -> Word32 -> Bool #

Integral Word32 
Num Word32 
Ord Word32 
Read Word32 
Real Word32 
Show Word32 
Ix Word32 
Storable Word32 
Bits Word32 
FiniteBits Word32 
Hashable Word32 

Methods

hashWithSalt :: Int -> Word32 -> Int #

hash :: Word32 -> Int #

Unbox Word32 
Vector Vector Word32 
MVector MVector Word32 
data Vector Word32 
data MVector s Word32 

data Word64 :: * #

64-bit unsigned integer type

Instances

Bounded Word64 
Enum Word64 
Eq Word64 

Methods

(==) :: Word64 -> Word64 -> Bool #

(/=) :: Word64 -> Word64 -> Bool #

Integral Word64 
Num Word64 
Ord Word64 
Read Word64 
Real Word64 
Show Word64 
Ix Word64 
Storable Word64 
Bits Word64 
FiniteBits Word64 
Hashable Word64 

Methods

hashWithSalt :: Int -> Word64 -> Int #

hash :: Word64 -> Int #

Unbox Word64 
Vector Vector Word64 
MVector MVector Word64 
data Vector Word64 
data MVector s Word64 

data Int :: * #

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 

Methods

minBound :: Int #

maxBound :: Int #

Enum Int 

Methods

succ :: Int -> Int #

pred :: Int -> Int #

toEnum :: Int -> Int #

fromEnum :: Int -> Int #

enumFrom :: Int -> [Int] #

enumFromThen :: Int -> Int -> [Int] #

enumFromTo :: Int -> Int -> [Int] #

enumFromThenTo :: Int -> Int -> Int -> [Int] #

Eq Int 

Methods

(==) :: Int -> Int -> Bool #

(/=) :: Int -> Int -> Bool #

Integral Int 

Methods

quot :: Int -> Int -> Int #

rem :: Int -> Int -> Int #

div :: Int -> Int -> Int #

mod :: Int -> Int -> Int #

quotRem :: Int -> Int -> (Int, Int) #

divMod :: Int -> Int -> (Int, Int) #

toInteger :: Int -> Integer #

Num Int 

Methods

(+) :: Int -> Int -> Int #

(-) :: Int -> Int -> Int #

(*) :: Int -> Int -> Int #

negate :: Int -> Int #

abs :: Int -> Int #

signum :: Int -> Int #

fromInteger :: Integer -> Int #

Ord Int 

Methods

compare :: Int -> Int -> Ordering #

(<) :: Int -> Int -> Bool #

(<=) :: Int -> Int -> Bool #

(>) :: Int -> Int -> Bool #

(>=) :: Int -> Int -> Bool #

max :: Int -> Int -> Int #

min :: Int -> Int -> Int #

Read Int 
Real Int 

Methods

toRational :: Int -> Rational #

Show Int 

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Storable Int 

Methods

sizeOf :: Int -> Int #

alignment :: Int -> Int #

peekElemOff :: Ptr Int -> Int -> IO Int #

pokeElemOff :: Ptr Int -> Int -> Int -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int #

pokeByteOff :: Ptr b -> Int -> Int -> IO () #

peek :: Ptr Int -> IO Int #

poke :: Ptr Int -> Int -> IO () #

Hashable Int 

Methods

hashWithSalt :: Int -> Int -> Int #

hash :: Int -> Int #

Unbox Int 
Vector Vector Int 
MVector MVector Int 
Functor (URec Int) 

Methods

fmap :: (a -> b) -> URec Int a -> URec Int b #

(<$) :: a -> URec Int b -> URec Int a #

Foldable (URec Int) 

Methods

fold :: Monoid m => URec Int m -> m #

foldMap :: Monoid m => (a -> m) -> URec Int a -> m #

foldr :: (a -> b -> b) -> b -> URec Int a -> b #

foldr' :: (a -> b -> b) -> b -> URec Int a -> b #

foldl :: (b -> a -> b) -> b -> URec Int a -> b #

foldl' :: (b -> a -> b) -> b -> URec Int a -> b #

foldr1 :: (a -> a -> a) -> URec Int a -> a #

foldl1 :: (a -> a -> a) -> URec Int a -> a #

toList :: URec Int a -> [a] #

null :: URec Int a -> Bool #

length :: URec Int a -> Int #

elem :: Eq a => a -> URec Int a -> Bool #

maximum :: Ord a => URec Int a -> a #

minimum :: Ord a => URec Int a -> a #

sum :: Num a => URec Int a -> a #

product :: Num a => URec Int a -> a #

Traversable (URec Int) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) #

sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) #

mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) #

sequence :: Monad m => URec Int (m a) -> m (URec Int a) #

Generic1 (URec Int) 

Associated Types

type Rep1 (URec Int :: * -> *) :: * -> * #

Methods

from1 :: URec Int a -> Rep1 (URec Int) a #

to1 :: Rep1 (URec Int) a -> URec Int a #

Eq (URec Int p) 

Methods

(==) :: URec Int p -> URec Int p -> Bool #

(/=) :: URec Int p -> URec Int p -> Bool #

Ord (URec Int p) 

Methods

compare :: URec Int p -> URec Int p -> Ordering #

(<) :: URec Int p -> URec Int p -> Bool #

(<=) :: URec Int p -> URec Int p -> Bool #

(>) :: URec Int p -> URec Int p -> Bool #

(>=) :: URec Int p -> URec Int p -> Bool #

max :: URec Int p -> URec Int p -> URec Int p #

min :: URec Int p -> URec Int p -> URec Int p #

Show (URec Int p) 

Methods

showsPrec :: Int -> URec Int p -> ShowS #

show :: URec Int p -> String #

showList :: [URec Int p] -> ShowS #

Generic (URec Int p) 

Associated Types

type Rep (URec Int p) :: * -> * #

Methods

from :: URec Int p -> Rep (URec Int p) x #

to :: Rep (URec Int p) x -> URec Int p #

data URec Int

Used for marking occurrences of Int#

data URec Int = UInt {}
data Vector Int 
data MVector s Int 
type Rep1 (URec Int) 
type Rep1 (URec Int) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt))
type Rep (URec Int p) 
type Rep (URec Int p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UInt" PrefixI True) (S1 (MetaSel (Just Symbol "uInt#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UInt))

data Int32 :: * #

32-bit signed integer type

Instances

Bounded Int32 
Enum Int32 
Eq Int32 

Methods

(==) :: Int32 -> Int32 -> Bool #

(/=) :: Int32 -> Int32 -> Bool #

Integral Int32 
Num Int32 
Ord Int32 

Methods

compare :: Int32 -> Int32 -> Ordering #

(<) :: Int32 -> Int32 -> Bool #

(<=) :: Int32 -> Int32 -> Bool #

(>) :: Int32 -> Int32 -> Bool #

(>=) :: Int32 -> Int32 -> Bool #

max :: Int32 -> Int32 -> Int32 #

min :: Int32 -> Int32 -> Int32 #

Read Int32 
Real Int32 

Methods

toRational :: Int32 -> Rational #

Show Int32 

Methods

showsPrec :: Int -> Int32 -> ShowS #

show :: Int32 -> String #

showList :: [Int32] -> ShowS #

Ix Int32 
Storable Int32 

Methods

sizeOf :: Int32 -> Int #

alignment :: Int32 -> Int #

peekElemOff :: Ptr Int32 -> Int -> IO Int32 #

pokeElemOff :: Ptr Int32 -> Int -> Int32 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int32 #

pokeByteOff :: Ptr b -> Int -> Int32 -> IO () #

peek :: Ptr Int32 -> IO Int32 #

poke :: Ptr Int32 -> Int32 -> IO () #

Bits Int32 
FiniteBits Int32 
Hashable Int32 

Methods

hashWithSalt :: Int -> Int32 -> Int #

hash :: Int32 -> Int #

Unbox Int32 
Vector Vector Int32 
MVector MVector Int32 
data Vector Int32 
data MVector s Int32 

data Int64 :: * #

64-bit signed integer type

Instances

Bounded Int64 
Enum Int64 
Eq Int64 

Methods

(==) :: Int64 -> Int64 -> Bool #

(/=) :: Int64 -> Int64 -> Bool #

Integral Int64 
Num Int64 
Ord Int64 

Methods

compare :: Int64 -> Int64 -> Ordering #

(<) :: Int64 -> Int64 -> Bool #

(<=) :: Int64 -> Int64 -> Bool #

(>) :: Int64 -> Int64 -> Bool #

(>=) :: Int64 -> Int64 -> Bool #

max :: Int64 -> Int64 -> Int64 #

min :: Int64 -> Int64 -> Int64 #

Read Int64 
Real Int64 

Methods

toRational :: Int64 -> Rational #

Show Int64 

Methods

showsPrec :: Int -> Int64 -> ShowS #

show :: Int64 -> String #

showList :: [Int64] -> ShowS #

Ix Int64 
Storable Int64 

Methods

sizeOf :: Int64 -> Int #

alignment :: Int64 -> Int #

peekElemOff :: Ptr Int64 -> Int -> IO Int64 #

pokeElemOff :: Ptr Int64 -> Int -> Int64 -> IO () #

peekByteOff :: Ptr b -> Int -> IO Int64 #

pokeByteOff :: Ptr b -> Int -> Int64 -> IO () #

peek :: Ptr Int64 -> IO Int64 #

poke :: Ptr Int64 -> Int64 -> IO () #

Bits Int64 
FiniteBits Int64 
Hashable Int64 

Methods

hashWithSalt :: Int -> Int64 -> Int #

hash :: Int64 -> Int #

Unbox Int64 
Vector Vector Int64 
MVector MVector Int64 
data Vector Int64 
data MVector s Int64 

data Integer :: * #

Invariant: Jn# and Jp# are used iff value doesn't fit in S#

Useful properties resulting from the invariants:

Instances

Enum Integer 
Eq Integer 

Methods

(==) :: Integer -> Integer -> Bool #

(/=) :: Integer -> Integer -> Bool #

Integral Integer 
Num Integer 
Ord Integer 
Read Integer 
Real Integer 
Show Integer 
Hashable Integer 

Methods

hashWithSalt :: Int -> Integer -> Int #

hash :: Integer -> Int #

type Rational = Ratio Integer #

Arbitrary-precision rational numbers, represented as a ratio of two Integer values. A rational number may be constructed using the % operator.

data Float :: * #

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 

Methods

(==) :: Float -> Float -> Bool #

(/=) :: Float -> Float -> Bool #

Floating Float 
Ord Float 

Methods

compare :: Float -> Float -> Ordering #

(<) :: Float -> Float -> Bool #

(<=) :: Float -> Float -> Bool #

(>) :: Float -> Float -> Bool #

(>=) :: Float -> Float -> Bool #

max :: Float -> Float -> Float #

min :: Float -> Float -> Float #

Read Float 
RealFloat Float 
Storable Float 

Methods

sizeOf :: Float -> Int #

alignment :: Float -> Int #

peekElemOff :: Ptr Float -> Int -> IO Float #

pokeElemOff :: Ptr Float -> Int -> Float -> IO () #

peekByteOff :: Ptr b -> Int -> IO Float #

pokeByteOff :: Ptr b -> Int -> Float -> IO () #

peek :: Ptr Float -> IO Float #

poke :: Ptr Float -> Float -> IO () #

Hashable Float 

Methods

hashWithSalt :: Int -> Float -> Int #

hash :: Float -> Int #

Unbox Float 
Vector Vector Float 
MVector MVector Float 
Functor (URec Float) 

Methods

fmap :: (a -> b) -> URec Float a -> URec Float b #

(<$) :: a -> URec Float b -> URec Float a #

Foldable (URec Float) 

Methods

fold :: Monoid m => URec Float m -> m #

foldMap :: Monoid m => (a -> m) -> URec Float a -> m #

foldr :: (a -> b -> b) -> b -> URec Float a -> b #

foldr' :: (a -> b -> b) -> b -> URec Float a -> b #

foldl :: (b -> a -> b) -> b -> URec Float a -> b #

foldl' :: (b -> a -> b) -> b -> URec Float a -> b #

foldr1 :: (a -> a -> a) -> URec Float a -> a #

foldl1 :: (a -> a -> a) -> URec Float a -> a #

toList :: URec Float a -> [a] #

null :: URec Float a -> Bool #

length :: URec Float a -> Int #

elem :: Eq a => a -> URec Float a -> Bool #

maximum :: Ord a => URec Float a -> a #

minimum :: Ord a => URec Float a -> a #

sum :: Num a => URec Float a -> a #

product :: Num a => URec Float a -> a #

Traversable (URec Float) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) #

sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) #

mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) #

sequence :: Monad m => URec Float (m a) -> m (URec Float a) #

Generic1 (URec Float) 

Associated Types

type Rep1 (URec Float :: * -> *) :: * -> * #

Methods

from1 :: URec Float a -> Rep1 (URec Float) a #

to1 :: Rep1 (URec Float) a -> URec Float a #

Eq (URec Float p) 

Methods

(==) :: URec Float p -> URec Float p -> Bool #

(/=) :: URec Float p -> URec Float p -> Bool #

Ord (URec Float p) 

Methods

compare :: URec Float p -> URec Float p -> Ordering #

(<) :: URec Float p -> URec Float p -> Bool #

(<=) :: URec Float p -> URec Float p -> Bool #

(>) :: URec Float p -> URec Float p -> Bool #

(>=) :: URec Float p -> URec Float p -> Bool #

max :: URec Float p -> URec Float p -> URec Float p #

min :: URec Float p -> URec Float p -> URec Float p #

Show (URec Float p) 

Methods

showsPrec :: Int -> URec Float p -> ShowS #

show :: URec Float p -> String #

showList :: [URec Float p] -> ShowS #

Generic (URec Float p) 

Associated Types

type Rep (URec Float p) :: * -> * #

Methods

from :: URec Float p -> Rep (URec Float p) x #

to :: Rep (URec Float p) x -> URec Float p #

data URec Float

Used for marking occurrences of Float#

data Vector Float 
data MVector s Float 
type Rep1 (URec Float) 
type Rep1 (URec Float) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat))
type Rep (URec Float p) 
type Rep (URec Float p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UFloat" PrefixI True) (S1 (MetaSel (Just Symbol "uFloat#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UFloat))

data Double :: * #

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 

Methods

(==) :: Double -> Double -> Bool #

(/=) :: Double -> Double -> Bool #

Floating Double 
Ord Double 
Read Double 
RealFloat Double 
Storable Double 
Hashable Double 

Methods

hashWithSalt :: Int -> Double -> Int #

hash :: Double -> Int #

Unbox Double 
Vector Vector Double 
MVector MVector Double 
Functor (URec Double) 

Methods

fmap :: (a -> b) -> URec Double a -> URec Double b #

(<$) :: a -> URec Double b -> URec Double a #

Foldable (URec Double) 

Methods

fold :: Monoid m => URec Double m -> m #

foldMap :: Monoid m => (a -> m) -> URec Double a -> m #

foldr :: (a -> b -> b) -> b -> URec Double a -> b #

foldr' :: (a -> b -> b) -> b -> URec Double a -> b #

foldl :: (b -> a -> b) -> b -> URec Double a -> b #

foldl' :: (b -> a -> b) -> b -> URec Double a -> b #

foldr1 :: (a -> a -> a) -> URec Double a -> a #

foldl1 :: (a -> a -> a) -> URec Double a -> a #

toList :: URec Double a -> [a] #

null :: URec Double a -> Bool #

length :: URec Double a -> Int #

elem :: Eq a => a -> URec Double a -> Bool #

maximum :: Ord a => URec Double a -> a #

minimum :: Ord a => URec Double a -> a #

sum :: Num a => URec Double a -> a #

product :: Num a => URec Double a -> a #

Traversable (URec Double) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) #

sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) #

mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) #

sequence :: Monad m => URec Double (m a) -> m (URec Double a) #

Generic1 (URec Double) 

Associated Types

type Rep1 (URec Double :: * -> *) :: * -> * #

Methods

from1 :: URec Double a -> Rep1 (URec Double) a #

to1 :: Rep1 (URec Double) a -> URec Double a #

Eq (URec Double p) 

Methods

(==) :: URec Double p -> URec Double p -> Bool #

(/=) :: URec Double p -> URec Double p -> Bool #

Ord (URec Double p) 

Methods

compare :: URec Double p -> URec Double p -> Ordering #

(<) :: URec Double p -> URec Double p -> Bool #

(<=) :: URec Double p -> URec Double p -> Bool #

(>) :: URec Double p -> URec Double p -> Bool #

(>=) :: URec Double p -> URec Double p -> Bool #

max :: URec Double p -> URec Double p -> URec Double p #

min :: URec Double p -> URec Double p -> URec Double p #

Show (URec Double p) 

Methods

showsPrec :: Int -> URec Double p -> ShowS #

show :: URec Double p -> String #

showList :: [URec Double p] -> ShowS #

Generic (URec Double p) 

Associated Types

type Rep (URec Double p) :: * -> * #

Methods

from :: URec Double p -> Rep (URec Double p) x #

to :: Rep (URec Double p) x -> URec Double p #

data URec Double

Used for marking occurrences of Double#

data Vector Double 
data MVector s Double 
type Rep1 (URec Double) 
type Rep1 (URec Double) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble))
type Rep (URec Double p) 
type Rep (URec Double p) = D1 (MetaData "URec" "GHC.Generics" "base" False) (C1 (MetaCons "UDouble" PrefixI True) (S1 (MetaSel (Just Symbol "uDouble#") NoSourceUnpackedness NoSourceStrictness DecidedLazy) UDouble))

Numeric functions

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 #

raise a number to a non-negative integral power

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 #

raise a number to an integral power

subtract :: Num a => a -> a -> a #

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b #

general coercion to fractional types

Monoids

class Monoid a where #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

  • mappend mempty x = x
  • mappend x mempty = x
  • mappend x (mappend y z) = mappend (mappend x y) z
  • mconcat = foldr mappend mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

Minimal complete definition

mempty, mappend

Methods

mempty :: a #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

mconcat :: [a] -> a #

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.

Instances

Monoid Ordering 
Monoid () 

Methods

mempty :: () #

mappend :: () -> () -> () #

mconcat :: [()] -> () #

Monoid All 

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Monoid Any 

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Monoid ByteString 
Monoid ByteString 
Monoid IntSet 
Monoid [a] 

Methods

mempty :: [a] #

mappend :: [a] -> [a] -> [a] #

mconcat :: [[a]] -> [a] #

Monoid a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there is no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Methods

mempty :: Maybe a #

mappend :: Maybe a -> Maybe a -> Maybe a #

mconcat :: [Maybe a] -> Maybe a #

Monoid a => Monoid (IO a) 

Methods

mempty :: IO a #

mappend :: IO a -> IO a -> IO a #

mconcat :: [IO a] -> IO a #

Ord a => Monoid (Max a) 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

mconcat :: [Max a] -> Max a #

Ord a => Monoid (Min a) 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

mconcat :: [Min a] -> Min a #

Monoid a => Monoid (Identity a) 

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

mconcat :: [Identity a] -> Identity a #

(Ord a, Bounded a) => Monoid (Min a) 

Methods

mempty :: Min a #

mappend :: Min a -> Min a -> Min a #

mconcat :: [Min a] -> Min a #

(Ord a, Bounded a) => Monoid (Max a) 

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

mconcat :: [Max a] -> Max a #

Monoid m => Monoid (WrappedMonoid m) 
Semigroup a => Monoid (Option a) 

Methods

mempty :: Option a #

mappend :: Option a -> Option a -> Option a #

mconcat :: [Option a] -> Option a #

Monoid a => Monoid (Dual a) 

Methods

mempty :: Dual a #

mappend :: Dual a -> Dual a -> Dual a #

mconcat :: [Dual a] -> Dual a #

Monoid (Endo a) 

Methods

mempty :: Endo a #

mappend :: Endo a -> Endo a -> Endo a #

mconcat :: [Endo a] -> Endo a #

Num a => Monoid (Sum a) 

Methods

mempty :: Sum a #

mappend :: Sum a -> Sum a -> Sum a #

mconcat :: [Sum a] -> Sum a #

Num a => Monoid (Product a) 

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

mconcat :: [Product a] -> Product a #

Monoid (First a) 

Methods

mempty :: First a #

mappend :: First a -> First a -> First a #

mconcat :: [First a] -> First a #

Monoid (Last a) 

Methods

mempty :: Last a #

mappend :: Last a -> Last a -> Last a #

mconcat :: [Last a] -> Last a #

Monoid (IntMap a) 

Methods

mempty :: IntMap a #

mappend :: IntMap a -> IntMap a -> IntMap a #

mconcat :: [IntMap a] -> IntMap a #

Monoid (Seq a) 

Methods

mempty :: Seq a #

mappend :: Seq a -> Seq a -> Seq a #

mconcat :: [Seq a] -> Seq a #

Ord a => Monoid (Set a) 

Methods

mempty :: Set a #

mappend :: Set a -> Set a -> Set a #

mconcat :: [Set a] -> Set a #

Monoid (Array a) 

Methods

mempty :: Array a #

mappend :: Array a -> Array a -> Array a #

mconcat :: [Array a] -> Array a #

(Hashable a, Eq a) => Monoid (HashSet a) 

Methods

mempty :: HashSet a #

mappend :: HashSet a -> HashSet a -> HashSet a #

mconcat :: [HashSet a] -> HashSet a #

Monoid (Vector a) 

Methods

mempty :: Vector a #

mappend :: Vector a -> Vector a -> Vector a #

mconcat :: [Vector a] -> Vector a #

Storable a => Monoid (Vector a) 

Methods

mempty :: Vector a #

mappend :: Vector a -> Vector a -> Vector a #

mconcat :: [Vector a] -> Vector a #

Prim a => Monoid (Vector a) 

Methods

mempty :: Vector a #

mappend :: Vector a -> Vector a -> Vector a #

mconcat :: [Vector a] -> Vector a #

Monoid b => Monoid (a -> b) 

Methods

mempty :: a -> b #

mappend :: (a -> b) -> (a -> b) -> a -> b #

mconcat :: [a -> b] -> a -> b #

(Monoid a, Monoid b) => Monoid (a, b) 

Methods

mempty :: (a, b) #

mappend :: (a, b) -> (a, b) -> (a, b) #

mconcat :: [(a, b)] -> (a, b) #

Monoid (Proxy k s) 

Methods

mempty :: Proxy k s #

mappend :: Proxy k s -> Proxy k s -> Proxy k s #

mconcat :: [Proxy k s] -> Proxy k s #

Ord k => Monoid (Map k v) 

Methods

mempty :: Map k v #

mappend :: Map k v -> Map k v -> Map k v #

mconcat :: [Map k v] -> Map k v #

(Eq k, Hashable k) => Monoid (HashMap k v) 

Methods

mempty :: HashMap k v #

mappend :: HashMap k v -> HashMap k v -> HashMap k v #

mconcat :: [HashMap k v] -> HashMap k v #

(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) 

Methods

mempty :: (a, b, c) #

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) #

mconcat :: [(a, b, c)] -> (a, b, c) #

Monoid a => Monoid (Const k a b) 

Methods

mempty :: Const k a b #

mappend :: Const k a b -> Const k a b -> Const k a b #

mconcat :: [Const k a b] -> Const k a b #

Alternative f => Monoid (Alt * f a) 

Methods

mempty :: Alt * f a #

mappend :: Alt * f a -> Alt * f a -> Alt * f a #

mconcat :: [Alt * f a] -> Alt * f a #

(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) 

Methods

mempty :: (a, b, c, d) #

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #

mconcat :: [(a, b, c, d)] -> (a, b, c, d) #

(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) 

Methods

mempty :: (a, b, c, d, e) #

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) #

(<>) :: Monoid m => m -> m -> m infixr 6 #

An infix synonym for mappend.

Since: 4.5.0.0

Folds and traversals

class Foldable t #

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

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)

Minimal complete definition

foldMap | foldr

Instances

Foldable [] 

Methods

fold :: Monoid m => [m] -> m #

foldMap :: Monoid m => (a -> m) -> [a] -> m #

foldr :: (a -> b -> b) -> b -> [a] -> b #

foldr' :: (a -> b -> b) -> b -> [a] -> b #

foldl :: (b -> a -> b) -> b -> [a] -> b #

foldl' :: (b -> a -> b) -> b -> [a] -> b #

foldr1 :: (a -> a -> a) -> [a] -> a #

foldl1 :: (a -> a -> a) -> [a] -> a #

toList :: [a] -> [a] #

null :: [a] -> Bool #

length :: [a] -> Int #

elem :: Eq a => a -> [a] -> Bool #

maximum :: Ord a => [a] -> a #

minimum :: Ord a => [a] -> a #

sum :: Num a => [a] -> a #

product :: Num a => [a] -> a #

Foldable Maybe 

Methods

fold :: Monoid m => Maybe m -> m #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m #

foldr :: (a -> b -> b) -> b -> Maybe a -> b #

foldr' :: (a -> b -> b) -> b -> Maybe a -> b #

foldl :: (b -> a -> b) -> b -> Maybe a -> b #

foldl' :: (b -> a -> b) -> b -> Maybe a -> b #

foldr1 :: (a -> a -> a) -> Maybe a -> a #

foldl1 :: (a -> a -> a) -> Maybe a -> a #

toList :: Maybe a -> [a] #

null :: Maybe a -> Bool #

length :: Maybe a -> Int #

elem :: Eq a => a -> Maybe a -> Bool #

maximum :: Ord a => Maybe a -> a #

minimum :: Ord a => Maybe a -> a #

sum :: Num a => Maybe a -> a #

product :: Num a => Maybe a -> a #

Foldable V1 

Methods

fold :: Monoid m => V1 m -> m #

foldMap :: Monoid m => (a -> m) -> V1 a -> m #

foldr :: (a -> b -> b) -> b -> V1 a -> b #

foldr' :: (a -> b -> b) -> b -> V1 a -> b #

foldl :: (b -> a -> b) -> b -> V1 a -> b #

foldl' :: (b -> a -> b) -> b -> V1 a -> b #

foldr1 :: (a -> a -> a) -> V1 a -> a #

foldl1 :: (a -> a -> a) -> V1 a -> a #

toList :: V1 a -> [a] #

null :: V1 a -> Bool #

length :: V1 a -> Int #

elem :: Eq a => a -> V1 a -> Bool #

maximum :: Ord a => V1 a -> a #

minimum :: Ord a => V1 a -> a #

sum :: Num a => V1 a -> a #

product :: Num a => V1 a -> a #

Foldable U1 

Methods

fold :: Monoid m => U1 m -> m #

foldMap :: Monoid m => (a -> m) -> U1 a -> m #

foldr :: (a -> b -> b) -> b -> U1 a -> b #

foldr' :: (a -> b -> b) -> b -> U1 a -> b #

foldl :: (b -> a -> b) -> b -> U1 a -> b #

foldl' :: (b -> a -> b) -> b -> U1 a -> b #

foldr1 :: (a -> a -> a) -> U1 a -> a #

foldl1 :: (a -> a -> a) -> U1 a -> a #

toList :: U1 a -> [a] #

null :: U1 a -> Bool #

length :: U1 a -> Int #

elem :: Eq a => a -> U1 a -> Bool #

maximum :: Ord a => U1 a -> a #

minimum :: Ord a => U1 a -> a #

sum :: Num a => U1 a -> a #

product :: Num a => U1 a -> a #

Foldable Par1 

Methods

fold :: Monoid m => Par1 m -> m #

foldMap :: Monoid m => (a -> m) -> Par1 a -> m #

foldr :: (a -> b -> b) -> b -> Par1 a -> b #

foldr' :: (a -> b -> b) -> b -> Par1 a -> b #

foldl :: (b -> a -> b) -> b -> Par1 a -> b #

foldl' :: (b -> a -> b) -> b -> Par1 a -> b #

foldr1 :: (a -> a -> a) -> Par1 a -> a #

foldl1 :: (a -> a -> a) -> Par1 a -> a #

toList :: Par1 a -> [a] #

null :: Par1 a -> Bool #

length :: Par1 a -> Int #

elem :: Eq a => a -> Par1 a -> Bool #

maximum :: Ord a => Par1 a -> a #

minimum :: Ord a => Par1 a -> a #

sum :: Num a => Par1 a -> a #

product :: Num a => Par1 a -> a #

Foldable Identity 

Methods

fold :: Monoid m => Identity m -> m #

foldMap :: Monoid m => (a -> m) -> Identity a -> m #

foldr :: (a -> b -> b) -> b -> Identity a -> b #

foldr' :: (a -> b -> b) -> b -> Identity a -> b #

foldl :: (b -> a -> b) -> b -> Identity a -> b #

foldl' :: (b -> a -> b) -> b -> Identity a -> b #

foldr1 :: (a -> a -> a) -> Identity a -> a #

foldl1 :: (a -> a -> a) -> Identity a -> a #

toList :: Identity a -> [a] #

null :: Identity a -> Bool #

length :: Identity a -> Int #

elem :: Eq a => a -> Identity a -> Bool #

maximum :: Ord a => Identity a -> a #

minimum :: Ord a => Identity a -> a #

sum :: Num a => Identity a -> a #

product :: Num a => Identity a -> a #

Foldable Min 

Methods

fold :: Monoid m => Min m -> m #

foldMap :: Monoid m => (a -> m) -> Min a -> m #

foldr :: (a -> b -> b) -> b -> Min a -> b #

foldr' :: (a -> b -> b) -> b -> Min a -> b #

foldl :: (b -> a -> b) -> b -> Min a -> b #

foldl' :: (b -> a -> b) -> b -> Min a -> b #

foldr1 :: (a -> a -> a) -> Min a -> a #

foldl1 :: (a -> a -> a) -> Min a -> a #

toList :: Min a -> [a] #

null :: Min a -> Bool #

length :: Min a -> Int #

elem :: Eq a => a -> Min a -> Bool #

maximum :: Ord a => Min a -> a #

minimum :: Ord a => Min a -> a #

sum :: Num a => Min a -> a #

product :: Num a => Min a -> a #

Foldable Max 

Methods

fold :: Monoid m => Max m -> m #

foldMap :: Monoid m => (a -> m) -> Max a -> m #

foldr :: (a -> b -> b) -> b -> Max a -> b #

foldr' :: (a -> b -> b) -> b -> Max a -> b #

foldl :: (b -> a -> b) -> b -> Max a -> b #

foldl' :: (b -> a -> b) -> b -> Max a -> b #

foldr1 :: (a -> a -> a) -> Max a -> a #

foldl1 :: (a -> a -> a) -> Max a -> a #

toList :: Max a -> [a] #

null :: Max a -> Bool #

length :: Max a -> Int #

elem :: Eq a => a -> Max a -> Bool #

maximum :: Ord a => Max a -> a #

minimum :: Ord a => Max a -> a #

sum :: Num a => Max a -> a #

product :: Num a => Max a -> a #

Foldable First 

Methods

fold :: Monoid m => First m -> m #

foldMap :: Monoid m => (a -> m) -> First a -> m #

foldr :: (a -> b -> b) -> b -> First a -> b #

foldr' :: (a -> b -> b) -> b -> First a -> b #

foldl :: (b -> a -> b) -> b -> First a -> b #

foldl' :: (b -> a -> b) -> b -> First a -> b #

foldr1 :: (a -> a -> a) -> First a -> a #

foldl1 :: (a -> a -> a) -> First a -> a #

toList :: First a -> [a] #

null :: First a -> Bool #

length :: First a -> Int #

elem :: Eq a => a -> First a -> Bool #

maximum :: Ord a => First a -> a #

minimum :: Ord a => First a -> a #

sum :: Num a => First a -> a #

product :: Num a => First a -> a #

Foldable Last 

Methods

fold :: Monoid m => Last m -> m #

foldMap :: Monoid m => (a -> m) -> Last a -> m #

foldr :: (a -> b -> b) -> b -> Last a -> b #

foldr' :: (a -> b -> b) -> b -> Last a -> b #

foldl :: (b -> a -> b) -> b -> Last a -> b #

foldl' :: (b -> a -> b) -> b -> Last a -> b #

foldr1 :: (a -> a -> a) -> Last a -> a #

foldl1 :: (a -> a -> a) -> Last a -> a #

toList :: Last a -> [a] #

null :: Last a -> Bool #

length :: Last a -> Int #

elem :: Eq a => a -> Last a -> Bool #

maximum :: Ord a => Last a -> a #

minimum :: Ord a => Last a -> a #

sum :: Num a => Last a -> a #

product :: Num a => Last a -> a #

Foldable Option 

Methods

fold :: Monoid m => Option m -> m #

foldMap :: Monoid m => (a -> m) -> Option a -> m #

foldr :: (a -> b -> b) -> b -> Option a -> b #

foldr' :: (a -> b -> b) -> b -> Option a -> b #

foldl :: (b -> a -> b) -> b -> Option a -> b #

foldl' :: (b -> a -> b) -> b -> Option a -> b #

foldr1 :: (a -> a -> a) -> Option a -> a #

foldl1 :: (a -> a -> a) -> Option a -> a #

toList :: Option a -> [a] #

null :: Option a -> Bool #

length :: Option a -> Int #

elem :: Eq a => a -> Option a -> Bool #

maximum :: Ord a => Option a -> a #

minimum :: Ord a => Option a -> a #

sum :: Num a => Option a -> a #

product :: Num a => Option a -> a #

Foldable NonEmpty 

Methods

fold :: Monoid m => NonEmpty m -> m #

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m #

foldr :: (a -> b -> b) -> b -> NonEmpty a -> b #

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b #

foldl :: (b -> a -> b) -> b -> NonEmpty a -> b #

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b #

foldr1 :: (a -> a -> a) -> NonEmpty a -> a #

foldl1 :: (a -> a -> a) -> NonEmpty a -> a #

toList :: NonEmpty a -> [a] #

null :: NonEmpty a -> Bool #

length :: NonEmpty a -> Int #

elem :: Eq a => a -> NonEmpty a -> Bool #

maximum :: Ord a => NonEmpty a -> a #

minimum :: Ord a => NonEmpty a -> a #

sum :: Num a => NonEmpty a -> a #

product :: Num a => NonEmpty a -> a #

Foldable Complex 

Methods

fold :: Monoid m => Complex m -> m #

foldMap :: Monoid m => (a -> m) -> Complex a -> m #

foldr :: (a -> b -> b) -> b -> Complex a -> b #

foldr' :: (a -> b -> b) -> b -> Complex a -> b #

foldl :: (b -> a -> b) -> b -> Complex a -> b #

foldl' :: (b -> a -> b) -> b -> Complex a -> b #

foldr1 :: (a -> a -> a) -> Complex a -> a #

foldl1 :: (a -> a -> a) -> Complex a -> a #

toList :: Complex a -> [a] #

null :: Complex a -> Bool #

length :: Complex a -> Int #

elem :: Eq a => a -> Complex a -> Bool #

maximum :: Ord a => Complex a -> a #

minimum :: Ord a => Complex a -> a #

sum :: Num a => Complex a -> a #

product :: Num a => Complex a -> a #

Foldable ZipList 

Methods

fold :: Monoid m => ZipList m -> m #

foldMap :: Monoid m => (a -> m) -> ZipList a -> m #

foldr :: (a -> b -> b) -> b -> ZipList a -> b #

foldr' :: (a -> b -> b) -> b -> ZipList a -> b #

foldl :: (b -> a -> b) -> b -> ZipList a -> b #

foldl' :: (b -> a -> b) -> b -> ZipList a -> b #

foldr1 :: (a -> a -> a) -> ZipList a -> a #

foldl1 :: (a -> a -> a) -> ZipList a -> a #

toList :: ZipList a -> [a] #

null :: ZipList a -> Bool #

length :: ZipList a -> Int #

elem :: Eq a => a -> ZipList a -> Bool #

maximum :: Ord a => ZipList a -> a #

minimum :: Ord a => ZipList a -> a #

sum :: Num a => ZipList a -> a #

product :: Num a => ZipList a -> a #

Foldable Dual 

Methods

fold :: Monoid m => Dual m -> m #

foldMap :: Monoid m => (a -> m) -> Dual a -> m #

foldr :: (a -> b -> b) -> b -> Dual a -> b #

foldr' :: (a -> b -> b) -> b -> Dual a -> b #

foldl :: (b -> a -> b) -> b -> Dual a -> b #

foldl' :: (b -> a -> b) -> b -> Dual a -> b #

foldr1 :: (a -> a -> a) -> Dual a -> a #

foldl1 :: (a -> a -> a) -> Dual a -> a #

toList :: Dual a -> [a] #

null :: Dual a -> Bool #

length :: Dual a -> Int #

elem :: Eq a => a -> Dual a -> Bool #

maximum :: Ord a => Dual a -> a #

minimum :: Ord a => Dual a -> a #

sum :: Num a => Dual a -> a #

product :: Num a => Dual a -> a #

Foldable Sum 

Methods

fold :: Monoid m => Sum m -> m #

foldMap :: Monoid m => (a -> m) -> Sum a -> m #

foldr :: (a -> b -> b) -> b -> Sum a -> b #

foldr' :: (a -> b -> b) -> b -> Sum a -> b #

foldl :: (b -> a -> b) -> b -> Sum a -> b #

foldl' :: (b -> a -> b) -> b -> Sum a -> b #

foldr1 :: (a -> a -> a) -> Sum a -> a #

foldl1 :: (a -> a -> a) -> Sum a -> a #

toList :: Sum a -> [a] #

null :: Sum a -> Bool #

length :: Sum a -> Int #

elem :: Eq a => a -> Sum a -> Bool #

maximum :: Ord a => Sum a -> a #

minimum :: Ord a => Sum a -> a #

sum :: Num a => Sum a -> a #

product :: Num a => Sum a -> a #

Foldable Product 

Methods

fold :: Monoid m => Product m -> m #

foldMap :: Monoid m => (a -> m) -> Product a -> m #

foldr :: (a -> b -> b) -> b -> Product a -> b #

foldr' :: (a -> b -> b) -> b -> Product a -> b #

foldl :: (b -> a -> b) -> b -> Product a -> b #

foldl' :: (b -> a -> b) -> b -> Product a -> b #

foldr1 :: (a -> a -> a) -> Product a -> a #

foldl1 :: (a -> a -> a) -> Product a -> a #

toList :: Product a -> [a] #

null :: Product a -> Bool #

length :: Product a -> Int #

elem :: Eq a => a -> Product a -> Bool #

maximum :: Ord a => Product a -> a #

minimum :: Ord a => Product a -> a #

sum :: Num a => Product a -> a #

product :: Num a => Product a -> a #

Foldable First 

Methods

fold :: Monoid m => First m -> m #

foldMap :: Monoid m => (a -> m) -> First a -> m #

foldr :: (a -> b -> b) -> b -> First a -> b #

foldr' :: (a -> b -> b) -> b -> First a -> b #

foldl :: (b -> a -> b) -> b -> First a -> b #

foldl' :: (b -> a -> b) -> b -> First a -> b #

foldr1 :: (a -> a -> a) -> First a -> a #

foldl1 :: (a -> a -> a) -> First a -> a #

toList :: First a -> [a] #

null :: First a -> Bool #

length :: First a -> Int #

elem :: Eq a => a -> First a -> Bool #

maximum :: Ord a => First a -> a #

minimum :: Ord a => First a -> a #

sum :: Num a => First a -> a #

product :: Num a => First a -> a #

Foldable Last 

Methods

fold :: Monoid m => Last m -> m #

foldMap :: Monoid m => (a -> m) -> Last a -> m #

foldr :: (a -> b -> b) -> b -> Last a -> b #

foldr' :: (a -> b -> b) -> b -> Last a -> b #

foldl :: (b -> a -> b) -> b -> Last a -> b #

foldl' :: (b -> a -> b) -> b -> Last a -> b #

foldr1 :: (a -> a -> a) -> Last a -> a #

foldl1 :: (a -> a -> a) -> Last a -> a #

toList :: Last a -> [a] #

null :: Last a -> Bool #

length :: Last a -> Int #

elem :: Eq a => a -> Last a -> Bool #

maximum :: Ord a => Last a -> a #

minimum :: Ord a => Last a -> a #

sum :: Num a => Last a -> a #

product :: Num a => Last a -> a #

Foldable Digit 

Methods

fold :: Monoid m => Digit m -> m #

foldMap :: Monoid m => (a -> m) -> Digit a -> m #

foldr :: (a -> b -> b) -> b -> Digit a -> b #

foldr' :: (a -> b -> b) -> b -> Digit a -> b #

foldl :: (b -> a -> b) -> b -> Digit a -> b #

foldl' :: (b -> a -> b) -> b -> Digit a -> b #

foldr1 :: (a -> a -> a) -> Digit a -> a #

foldl1 :: (a -> a -> a) -> Digit a -> a #

toList :: Digit a -> [a] #

null :: Digit a -> Bool #

length :: Digit a -> Int #

elem :: Eq a => a -> Digit a -> Bool #

maximum :: Ord a => Digit a -> a #

minimum :: Ord a => Digit a -> a #

sum :: Num a => Digit a -> a #

product :: Num a => Digit a -> a #

Foldable Node 

Methods

fold :: Monoid m => Node m -> m #

foldMap :: Monoid m => (a -> m) -> Node a -> m #

foldr :: (a -> b -> b) -> b -> Node a -> b #

foldr' :: (a -> b -> b) -> b -> Node a -> b #

foldl :: (b -> a -> b) -> b -> Node a -> b #

foldl' :: (b -> a -> b) -> b -> Node a -> b #

foldr1 :: (a -> a -> a) -> Node a -> a #

foldl1 :: (a -> a -> a) -> Node a -> a #

toList :: Node a -> [a] #

null :: Node a -> Bool #

length :: Node a -> Int #

elem :: Eq a => a -> Node a -> Bool #

maximum :: Ord a => Node a -> a #

minimum :: Ord a => Node a -> a #

sum :: Num a => Node a -> a #

product :: Num a => Node a -> a #

Foldable Elem 

Methods

fold :: Monoid m => Elem m -> m #

foldMap :: Monoid m => (a -> m) -> Elem a -> m #

foldr :: (a -> b -> b) -> b -> Elem a -> b #

foldr' :: (a -> b -> b) -> b -> Elem a -> b #

foldl :: (b -> a -> b) -> b -> Elem a -> b #

foldl' :: (b -> a -> b) -> b -> Elem a -> b #

foldr1 :: (a -> a -> a) -> Elem a -> a #

foldl1 :: (a -> a -> a) -> Elem a -> a #

toList :: Elem a -> [a] #

null :: Elem a -> Bool #

length :: Elem a -> Int #

elem :: Eq a => a -> Elem a -> Bool #

maximum :: Ord a => Elem a -> a #

minimum :: Ord a => Elem a -> a #

sum :: Num a => Elem a -> a #

product :: Num a => Elem a -> a #

Foldable FingerTree 

Methods

fold :: Monoid m => FingerTree m -> m #

foldMap :: Monoid m => (a -> m) -> FingerTree a -> m #

foldr :: (a -> b -> b) -> b -> FingerTree a -> b #

foldr' :: (a -> b -> b) -> b -> FingerTree a -> b #

foldl :: (b -> a -> b) -> b -> FingerTree a -> b #

foldl' :: (b -> a -> b) -> b -> FingerTree a -> b #

foldr1 :: (a -> a -> a) -> FingerTree a -> a #

foldl1 :: (a -> a -> a) -> FingerTree a -> a #

toList :: FingerTree a -> [a] #

null :: FingerTree a -> Bool #

length :: FingerTree a -> Int #

elem :: Eq a => a -> FingerTree a -> Bool #

maximum :: Ord a => FingerTree a -> a #

minimum :: Ord a => FingerTree a -> a #

sum :: Num a => FingerTree a -> a #

product :: Num a => FingerTree a -> a #

Foldable IntMap 

Methods

fold :: Monoid m => IntMap m -> m #

foldMap :: Monoid m => (a -> m) -> IntMap a -> m #

foldr :: (a -> b -> b) -> b -> IntMap a -> b #

foldr' :: (a -> b -> b) -> b -> IntMap a -> b #

foldl :: (b -> a -> b) -> b -> IntMap a -> b #

foldl' :: (b -> a -> b) -> b -> IntMap a -> b #

foldr1 :: (a -> a -> a) -> IntMap a -> a #

foldl1 :: (a -> a -> a) -> IntMap a -> a #

toList :: IntMap a -> [a] #

null :: IntMap a -> Bool #

length :: IntMap a -> Int #

elem :: Eq a => a -> IntMap a -> Bool #

maximum :: Ord a => IntMap a -> a #

minimum :: Ord a => IntMap a -> a #

sum :: Num a => IntMap a -> a #

product :: Num a => IntMap a -> a #

Foldable Seq 

Methods

fold :: Monoid m => Seq m -> m #

foldMap :: Monoid m => (a -> m) -> Seq a -> m #

foldr :: (a -> b -> b) -> b -> Seq a -> b #

foldr' :: (a -> b -> b) -> b -> Seq a -> b #

foldl :: (b -> a -> b) -> b -> Seq a -> b #

foldl' :: (b -> a -> b) -> b -> Seq a -> b #

foldr1 :: (a -> a -> a) -> Seq a -> a #

foldl1 :: (a -> a -> a) -> Seq a -> a #

toList :: Seq a -> [a] #

null :: Seq a -> Bool #

length :: Seq a -> Int #

elem :: Eq a => a -> Seq a -> Bool #

maximum :: Ord a => Seq a -> a #

minimum :: Ord a => Seq a -> a #

sum :: Num a => Seq a -> a #

product :: Num a => Seq a -> a #

Foldable ViewL 

Methods

fold :: Monoid m => ViewL m -> m #

foldMap :: Monoid m => (a -> m) -> ViewL a -> m #

foldr :: (a -> b -> b) -> b -> ViewL a -> b #

foldr' :: (a -> b -> b) -> b -> ViewL a -> b #

foldl :: (b -> a -> b) -> b -> ViewL a -> b #

foldl' :: (b -> a -> b) -> b -> ViewL a -> b #

foldr1 :: (a -> a -> a) -> ViewL a -> a #

foldl1 :: (a -> a -> a) -> ViewL a -> a #

toList :: ViewL a -> [a] #

null :: ViewL a -> Bool #

length :: ViewL a -> Int #

elem :: Eq a => a -> ViewL a -> Bool #

maximum :: Ord a => ViewL a -> a #

minimum :: Ord a => ViewL a -> a #

sum :: Num a => ViewL a -> a #

product :: Num a => ViewL a -> a #

Foldable ViewR 

Methods

fold :: Monoid m => ViewR m -> m #

foldMap :: Monoid m => (a -> m) -> ViewR a -> m #

foldr :: (a -> b -> b) -> b -> ViewR a -> b #

foldr' :: (a -> b -> b) -> b -> ViewR a -> b #

foldl :: (b -> a -> b) -> b -> ViewR a -> b #

foldl' :: (b -> a -> b) -> b -> ViewR a -> b #

foldr1 :: (a -> a -> a) -> ViewR a -> a #

foldl1 :: (a -> a -> a) -> ViewR a -> a #

toList :: ViewR a -> [a] #

null :: ViewR a -> Bool #

length :: ViewR a -> Int #

elem :: Eq a => a -> ViewR a -> Bool #

maximum :: Ord a => ViewR a -> a #

minimum :: Ord a => ViewR a -> a #

sum :: Num a => ViewR a -> a #

product :: Num a => ViewR a -> a #

Foldable Set 

Methods

fold :: Monoid m => Set m -> m #

foldMap :: Monoid m => (a -> m) -> Set a -> m #

foldr :: (a -> b -> b) -> b -> Set a -> b #

foldr' :: (a -> b -> b) -> b -> Set a -> b #

foldl :: (b -> a -> b) -> b -> Set a -> b #

foldl' :: (b -> a -> b) -> b -> Set a -> b #

foldr1 :: (a -> a -> a) -> Set a -> a #

foldl1 :: (a -> a -> a) -> Set a -> a #

toList :: Set a -> [a] #

null :: Set a -> Bool #

length :: Set a -> Int #

elem :: Eq a => a -> Set a -> Bool #

maximum :: Ord a => Set a -> a #

minimum :: Ord a => Set a -> a #

sum :: Num a => Set a -> a #

product :: Num a => Set a -> a #

Foldable Hashed 

Methods

fold :: Monoid m => Hashed m -> m #

foldMap :: Monoid m => (a -> m) -> Hashed a -> m #

foldr :: (a -> b -> b) -> b -> Hashed a -> b #

foldr' :: (a -> b -> b) -> b -> Hashed a -> b #

foldl :: (b -> a -> b) -> b -> Hashed a -> b #

foldl' :: (b -> a -> b) -> b -> Hashed a -> b #

foldr1 :: (a -> a -> a) -> Hashed a -> a #

foldl1 :: (a -> a -> a) -> Hashed a -> a #

toList :: Hashed a -> [a] #

null :: Hashed a -> Bool #

length :: Hashed a -> Int #

elem :: Eq a => a -> Hashed a -> Bool #

maximum :: Ord a => Hashed a -> a #

minimum :: Ord a => Hashed a -> a #

sum :: Num a => Hashed a -> a #

product :: Num a => Hashed a -> a #

Foldable Array 

Methods

fold :: Monoid m => Array m -> m #

foldMap :: Monoid m => (a -> m) -> Array a -> m #

foldr :: (a -> b -> b) -> b -> Array a -> b #

foldr' :: (a -> b -> b) -> b -> Array a -> b #

foldl :: (b -> a -> b) -> b -> Array a -> b #

foldl' :: (b -> a -> b) -> b -> Array a -> b #

foldr1 :: (a -> a -> a) -> Array a -> a #

foldl1 :: (a -> a -> a) -> Array a -> a #

toList :: Array a -> [a] #

null :: Array a -> Bool #

length :: Array a -> Int #

elem :: Eq a => a -> Array a -> Bool #

maximum :: Ord a => Array a -> a #

minimum :: Ord a => Array a -> a #

sum :: Num a => Array a -> a #

product :: Num a => Array a -> a #

Foldable HashSet 

Methods

fold :: Monoid m => HashSet m -> m #

foldMap :: Monoid m => (a -> m) -> HashSet a -> m #

foldr :: (a -> b -> b) -> b -> HashSet a -> b #

foldr' :: (a -> b -> b) -> b -> HashSet a -> b #

foldl :: (b -> a -> b) -> b -> HashSet a -> b #

foldl' :: (b -> a -> b) -> b -> HashSet a -> b #

foldr1 :: (a -> a -> a) -> HashSet a -> a #

foldl1 :: (a -> a -> a) -> HashSet a -> a #

toList :: HashSet a -> [a] #

null :: HashSet a -> Bool #

length :: HashSet a -> Int #

elem :: Eq a => a -> HashSet a -> Bool #

maximum :: Ord a => HashSet a -> a #

minimum :: Ord a => HashSet a -> a #

sum :: Num a => HashSet a -> a #

product :: Num a => HashSet a -> a #

Foldable Vector 

Methods

fold :: Monoid m => Vector m -> m #

foldMap :: Monoid m => (a -> m) -> Vector a -> m #

foldr :: (a -> b -> b) -> b -> Vector a -> b #

foldr' :: (a -> b -> b) -> b -> Vector a -> b #

foldl :: (b -> a -> b) -> b -> Vector a -> b #

foldl' :: (b -> a -> b) -> b -> Vector a -> b #

foldr1 :: (a -> a -> a) -> Vector a -> a #

foldl1 :: (a -> a -> a) -> Vector a -> a #

toList :: Vector a -> [a] #

null :: Vector a -> Bool #

length :: Vector a -> Int #

elem :: Eq a => a -> Vector a -> Bool #

maximum :: Ord a => Vector a -> a #

minimum :: Ord a => Vector a -> a #

sum :: Num a => Vector a -> a #

product :: Num a => Vector a -> a #

Foldable (Either a) 

Methods

fold :: Monoid m => Either a m -> m #

foldMap :: Monoid m => (a -> m) -> Either a a -> m #

foldr :: (a -> b -> b) -> b -> Either a a -> b #

foldr' :: (a -> b -> b) -> b -> Either a a -> b #

foldl :: (b -> a -> b) -> b -> Either a a -> b #

foldl' :: (b -> a -> b) -> b -> Either a a -> b #

foldr1 :: (a -> a -> a) -> Either a a -> a #

foldl1 :: (a -> a -> a) -> Either a a -> a #

toList :: Either a a -> [a] #

null :: Either a a -> Bool #

length :: Either a a -> Int #

elem :: Eq a => a -> Either a a -> Bool #

maximum :: Ord a => Either a a -> a #

minimum :: Ord a => Either a a -> a #

sum :: Num a => Either a a -> a #

product :: Num a => Either a a -> a #

Foldable f => Foldable (Rec1 f) 

Methods

fold :: Monoid m => Rec1 f m -> m #

foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m #

foldr :: (a -> b -> b) -> b -> Rec1 f a -> b #

foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b #

foldl :: (b -> a -> b) -> b -> Rec1 f a -> b #

foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b #

foldr1 :: (a -> a -> a) -> Rec1 f a -> a #

foldl1 :: (a -> a -> a) -> Rec1 f a -> a #

toList :: Rec1 f a -> [a] #

null :: Rec1 f a -> Bool #

length :: Rec1 f a -> Int #

elem :: Eq a => a -> Rec1 f a -> Bool #

maximum :: Ord a => Rec1 f a -> a #

minimum :: Ord a => Rec1 f a -> a #

sum :: Num a => Rec1 f a -> a #

product :: Num a => Rec1 f a -> a #

Foldable (URec Char) 

Methods

fold :: Monoid m => URec Char m -> m #

foldMap :: Monoid m => (a -> m) -> URec Char a -> m #

foldr :: (a -> b -> b) -> b -> URec Char a -> b #

foldr' :: (a -> b -> b) -> b -> URec Char a -> b #

foldl :: (b -> a -> b) -> b -> URec Char a -> b #

foldl' :: (b -> a -> b) -> b -> URec Char a -> b #

foldr1 :: (a -> a -> a) -> URec Char a -> a #

foldl1 :: (a -> a -> a) -> URec Char a -> a #

toList :: URec Char a -> [a] #

null :: URec Char a -> Bool #

length :: URec Char a -> Int #

elem :: Eq a => a -> URec Char a -> Bool #

maximum :: Ord a => URec Char a -> a #

minimum :: Ord a => URec Char a -> a #

sum :: Num a => URec Char a -> a #

product :: Num a => URec Char a -> a #

Foldable (URec Double) 

Methods

fold :: Monoid m => URec Double m -> m #

foldMap :: Monoid m => (a -> m) -> URec Double a -> m #

foldr :: (a -> b -> b) -> b -> URec Double a -> b #

foldr' :: (a -> b -> b) -> b -> URec Double a -> b #

foldl :: (b -> a -> b) -> b -> URec Double a -> b #

foldl' :: (b -> a -> b) -> b -> URec Double a -> b #

foldr1 :: (a -> a -> a) -> URec Double a -> a #

foldl1 :: (a -> a -> a) -> URec Double a -> a #

toList :: URec Double a -> [a] #

null :: URec Double a -> Bool #

length :: URec Double a -> Int #

elem :: Eq a => a -> URec Double a -> Bool #

maximum :: Ord a => URec Double a -> a #

minimum :: Ord a => URec Double a -> a #

sum :: Num a => URec Double a -> a #

product :: Num a => URec Double a -> a #

Foldable (URec Float) 

Methods

fold :: Monoid m => URec Float m -> m #

foldMap :: Monoid m => (a -> m) -> URec Float a -> m #

foldr :: (a -> b -> b) -> b -> URec Float a -> b #

foldr' :: (a -> b -> b) -> b -> URec Float a -> b #

foldl :: (b -> a -> b) -> b -> URec Float a -> b #

foldl' :: (b -> a -> b) -> b -> URec Float a -> b #

foldr1 :: (a -> a -> a) -> URec Float a -> a #

foldl1 :: (a -> a -> a) -> URec Float a -> a #

toList :: URec Float a -> [a] #

null :: URec Float a -> Bool #

length :: URec Float a -> Int #

elem :: Eq a => a -> URec Float a -> Bool #

maximum :: Ord a => URec Float a -> a #

minimum :: Ord a => URec Float a -> a #

sum :: Num a => URec Float a -> a #

product :: Num a => URec Float a -> a #

Foldable (URec Int) 

Methods

fold :: Monoid m => URec Int m -> m #

foldMap :: Monoid m => (a -> m) -> URec Int a -> m #

foldr :: (a -> b -> b) -> b -> URec Int a -> b #

foldr' :: (a -> b -> b) -> b -> URec Int a -> b #

foldl :: (b -> a -> b) -> b -> URec Int a -> b #

foldl' :: (b -> a -> b) -> b -> URec Int a -> b #

foldr1 :: (a -> a -> a) -> URec Int a -> a #

foldl1 :: (a -> a -> a) -> URec Int a -> a #

toList :: URec Int a -> [a] #

null :: URec Int a -> Bool #

length :: URec Int a -> Int #

elem :: Eq a => a -> URec Int a -> Bool #

maximum :: Ord a => URec Int a -> a #

minimum :: Ord a => URec Int a -> a #

sum :: Num a => URec Int a -> a #

product :: Num a => URec Int a -> a #

Foldable (URec Word) 

Methods

fold :: Monoid m => URec Word m -> m #

foldMap :: Monoid m => (a -> m) -> URec Word a -> m #

foldr :: (a -> b -> b) -> b -> URec Word a -> b #

foldr' :: (a -> b -> b) -> b -> URec Word a -> b #

foldl :: (b -> a -> b) -> b -> URec Word a -> b #

foldl' :: (b -> a -> b) -> b -> URec Word a -> b #

foldr1 :: (a -> a -> a) -> URec Word a -> a #

foldl1 :: (a -> a -> a) -> URec Word a -> a #

toList :: URec Word a -> [a] #

null :: URec Word a -> Bool #

length :: URec Word a -> Int #

elem :: Eq a => a -> URec Word a -> Bool #

maximum :: Ord a => URec Word a -> a #

minimum :: Ord a => URec Word a -> a #

sum :: Num a => URec Word a -> a #

product :: Num a => URec Word a -> a #

Foldable (URec (Ptr ())) 

Methods

fold :: Monoid m => URec (Ptr ()) m -> m #

foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m #

foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b #

foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b #

foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b #

foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b #

foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a #

foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a #

toList :: URec (Ptr ()) a -> [a] #

null :: URec (Ptr ()) a -> Bool #

length :: URec (Ptr ()) a -> Int #

elem :: Eq a => a -> URec (Ptr ()) a -> Bool #

maximum :: Ord a => URec (Ptr ()) a -> a #

minimum :: Ord a => URec (Ptr ()) a -> a #

sum :: Num a => URec (Ptr ()) a -> a #

product :: Num a => URec (Ptr ()) a -> a #

Foldable ((,) a) 

Methods

fold :: Monoid m => (a, m) -> m #

foldMap :: Monoid m => (a -> m) -> (a, a) -> m #

foldr :: (a -> b -> b) -> b -> (a, a) -> b #

foldr' :: (a -> b -> b) -> b -> (a, a) -> b #

foldl :: (b -> a -> b) -> b -> (a, a) -> b #

foldl' :: (b -> a -> b) -> b -> (a, a) -> b #

foldr1 :: (a -> a -> a) -> (a, a) -> a #

foldl1 :: (a -> a -> a) -> (a, a) -> a #

toList :: (a, a) -> [a] #

null :: (a, a) -> Bool #

length :: (a, a) -> Int #

elem :: Eq a => a -> (a, a) -> Bool #

maximum :: Ord a => (a, a) -> a #

minimum :: Ord a => (a, a) -> a #

sum :: Num a => (a, a) -> a #

product :: Num a => (a, a) -> a #

Foldable (Array i) 

Methods

fold :: Monoid m => Array i m -> m #

foldMap :: Monoid m => (a -> m) -> Array i a -> m #

foldr :: (a -> b -> b) -> b -> Array i a -> b #

foldr' :: (a -> b -> b) -> b -> Array i a -> b #

foldl :: (b -> a -> b) -> b -> Array i a -> b #

foldl' :: (b -> a -> b) -> b -> Array i a -> b #

foldr1 :: (a -> a -> a) -> Array i a -> a #

foldl1 :: (a -> a -> a) -> Array i a -> a #

toList :: Array i a -> [a] #

null :: Array i a -> Bool #

length :: Array i a -> Int #

elem :: Eq a => a -> Array i a -> Bool #

maximum :: Ord a => Array i a -> a #

minimum :: Ord a => Array i a -> a #

sum :: Num a => Array i a -> a #

product :: Num a => Array i a -> a #

Foldable (Arg a) 

Methods

fold :: Monoid m => Arg a m -> m #

foldMap :: Monoid m => (a -> m) -> Arg a a -> m #

foldr :: (a -> b -> b) -> b -> Arg a a -> b #

foldr' :: (a -> b -> b) -> b -> Arg a a -> b #

foldl :: (b -> a -> b) -> b -> Arg a a -> b #

foldl' :: (b -> a -> b) -> b -> Arg a a -> b #

foldr1 :: (a -> a -> a) -> Arg a a -> a #

foldl1 :: (a -> a -> a) -> Arg a a -> a #

toList :: Arg a a -> [a] #

null :: Arg a a -> Bool #

length :: Arg a a -> Int #

elem :: Eq a => a -> Arg a a -> Bool #

maximum :: Ord a => Arg a a -> a #

minimum :: Ord a => Arg a a -> a #

sum :: Num a => Arg a a -> a #

product :: Num a => Arg a a -> a #

Foldable (Proxy *) 

Methods

fold :: Monoid m => Proxy * m -> m #

foldMap :: Monoid m => (a -> m) -> Proxy * a -> m #

foldr :: (a -> b -> b) -> b -> Proxy * a -> b #

foldr' :: (a -> b -> b) -> b -> Proxy * a -> b #

foldl :: (b -> a -> b) -> b -> Proxy * a -> b #

foldl' :: (b -> a -> b) -> b -> Proxy * a -> b #

foldr1 :: (a -> a -> a) -> Proxy * a -> a #

foldl1 :: (a -> a -> a) -> Proxy * a -> a #

toList :: Proxy * a -> [a] #

null :: Proxy * a -> Bool #

length :: Proxy * a -> Int #

elem :: Eq a => a -> Proxy * a -> Bool #

maximum :: Ord a => Proxy * a -> a #

minimum :: Ord a => Proxy * a -> a #

sum :: Num a => Proxy * a -> a #

product :: Num a => Proxy * a -> a #

Foldable (Map k) 

Methods

fold :: Monoid m => Map k m -> m #

foldMap :: Monoid m => (a -> m) -> Map k a -> m #

foldr :: (a -> b -> b) -> b -> Map k a -> b #

foldr' :: (a -> b -> b) -> b -> Map k a -> b #

foldl :: (b -> a -> b) -> b -> Map k a -> b #

foldl' :: (b -> a -> b) -> b -> Map k a -> b #

foldr1 :: (a -> a -> a) -> Map k a -> a #

foldl1 :: (a -> a -> a) -> Map k a -> a #

toList :: Map k a -> [a] #

null :: Map k a -> Bool #

length :: Map k a -> Int #

elem :: Eq a => a -> Map k a -> Bool #

maximum :: Ord a => Map k a -> a #

minimum :: Ord a => Map k a -> a #

sum :: Num a => Map k a -> a #

product :: Num a => Map k a -> a #

Foldable f => Foldable (MaybeT f) 

Methods

fold :: Monoid m => MaybeT f m -> m #

foldMap :: Monoid m => (a -> m) -> MaybeT f a -> m #

foldr :: (a -> b -> b) -> b -> MaybeT f a -> b #

foldr' :: (a -> b -> b) -> b -> MaybeT f a -> b #

foldl :: (b -> a -> b) -> b -> MaybeT f a -> b #

foldl' :: (b -> a -> b) -> b -> MaybeT f a -> b #

foldr1 :: (a -> a -> a) -> MaybeT f a -> a #

foldl1 :: (a -> a -> a) -> MaybeT f a -> a #

toList :: MaybeT f a -> [a] #

null :: MaybeT f a -> Bool #

length :: MaybeT f a -> Int #

elem :: Eq a => a -> MaybeT f a -> Bool #

maximum :: Ord a => MaybeT f a -> a #

minimum :: Ord a => MaybeT f a -> a #

sum :: Num a => MaybeT f a -> a #

product :: Num a => MaybeT f a -> a #

Foldable f => Foldable (ListT f) 

Methods

fold :: Monoid m => ListT f m -> m #

foldMap :: Monoid m => (a -> m) -> ListT f a -> m #

foldr :: (a -> b -> b) -> b -> ListT f a -> b #

foldr' :: (a -> b -> b) -> b -> ListT f a -> b #

foldl :: (b -> a -> b) -> b -> ListT f a -> b #

foldl' :: (b -> a -> b) -> b -> ListT f a -> b #

foldr1 :: (a -> a -> a) -> ListT f a -> a #

foldl1 :: (a -> a -> a) -> ListT f a -> a #

toList :: ListT f a -> [a] #

null :: ListT f a -> Bool #

length :: ListT f a -> Int #

elem :: Eq a => a -> ListT f a -> Bool #

maximum :: Ord a => ListT f a -> a #

minimum :: Ord a => ListT f a -> a #

sum :: Num a => ListT f a -> a #

product :: Num a => ListT f a -> a #

Foldable (HashMap k) 

Methods

fold :: Monoid m => HashMap k m -> m #

foldMap :: Monoid m => (a -> m) -> HashMap k a -> m #

foldr :: (a -> b -> b) -> b -> HashMap k a -> b #

foldr' :: (a -> b -> b) -> b -> HashMap k a -> b #

foldl :: (b -> a -> b) -> b -> HashMap k a -> b #

foldl' :: (b -> a -> b) -> b -> HashMap k a -> b #

foldr1 :: (a -> a -> a) -> HashMap k a -> a #

foldl1 :: (a -> a -> a) -> HashMap k a -> a #

toList :: HashMap k a -> [a] #

null :: HashMap k a -> Bool #

length :: HashMap k a -> Int #

elem :: Eq a => a -> HashMap k a -> Bool #

maximum :: Ord a => HashMap k a -> a #

minimum :: Ord a => HashMap k a -> a #

sum :: Num a => HashMap k a -> a #

product :: Num a => HashMap k a -> a #

Foldable (K1 i c) 

Methods

fold :: Monoid m => K1 i c m -> m #

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m #

foldr :: (a -> b -> b) -> b -> K1 i c a -> b #

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b #

foldl :: (b -> a -> b) -> b -> K1 i c a -> b #

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b #

foldr1 :: (a -> a -> a) -> K1 i c a -> a #

foldl1 :: (a -> a -> a) -> K1 i c a -> a #

toList :: K1 i c a -> [a] #

null :: K1 i c a -> Bool #

length :: K1 i c a -> Int #

elem :: Eq a => a -> K1 i c a -> Bool #

maximum :: Ord a => K1 i c a -> a #

minimum :: Ord a => K1 i c a -> a #

sum :: Num a => K1 i c a -> a #

product :: Num a => K1 i c a -> a #

(Foldable f, Foldable g) => Foldable ((:+:) f g) 

Methods

fold :: Monoid m => (f :+: g) m -> m #

foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a #

toList :: (f :+: g) a -> [a] #

null :: (f :+: g) a -> Bool #

length :: (f :+: g) a -> Int #

elem :: Eq a => a -> (f :+: g) a -> Bool #

maximum :: Ord a => (f :+: g) a -> a #

minimum :: Ord a => (f :+: g) a -> a #

sum :: Num a => (f :+: g) a -> a #

product :: Num a => (f :+: g) a -> a #

(Foldable f, Foldable g) => Foldable ((:*:) f g) 

Methods

fold :: Monoid m => (f :*: g) m -> m #

foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a #

toList :: (f :*: g) a -> [a] #

null :: (f :*: g) a -> Bool #

length :: (f :*: g) a -> Int #

elem :: Eq a => a -> (f :*: g) a -> Bool #

maximum :: Ord a => (f :*: g) a -> a #

minimum :: Ord a => (f :*: g) a -> a #

sum :: Num a => (f :*: g) a -> a #

product :: Num a => (f :*: g) a -> a #

(Foldable f, Foldable g) => Foldable ((:.:) f g) 

Methods

fold :: Monoid m => (f :.: g) m -> m #

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m #

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b #

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b #

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a #

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a #

toList :: (f :.: g) a -> [a] #

null :: (f :.: g) a -> Bool #

length :: (f :.: g) a -> Int #

elem :: Eq a => a -> (f :.: g) a -> Bool #

maximum :: Ord a => (f :.: g) a -> a #

minimum :: Ord a => (f :.: g) a -> a #

sum :: Num a => (f :.: g) a -> a #

product :: Num a => (f :.: g) a -> a #

Foldable (Const * m) 

Methods

fold :: Monoid m => Const * m m -> m #

foldMap :: Monoid m => (a -> m) -> Const * m a -> m #

foldr :: (a -> b -> b) -> b -> Const * m a -> b #

foldr' :: (a -> b -> b) -> b -> Const * m a -> b #

foldl :: (b -> a -> b) -> b -> Const * m a -> b #

foldl' :: (b -> a -> b) -> b -> Const * m a -> b #

foldr1 :: (a -> a -> a) -> Const * m a -> a #

foldl1 :: (a -> a -> a) -> Const * m a -> a #

toList :: Const * m a -> [a] #

null :: Const * m a -> Bool #

length :: Const * m a -> Int #

elem :: Eq a => a -> Const * m a -> Bool #

maximum :: Ord a => Const * m a -> a #

minimum :: Ord a => Const * m a -> a #

sum :: Num a => Const * m a -> a #

product :: Num a => Const * m a -> a #

Foldable f => Foldable (WriterT w f) 

Methods

fold :: Monoid m => WriterT w f m -> m #

foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m #

foldr :: (a -> b -> b) -> b -> WriterT w f a -> b #

foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b #

foldl :: (b -> a -> b) -> b -> WriterT w f a -> b #

foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b #

foldr1 :: (a -> a -> a) -> WriterT w f a -> a #

foldl1 :: (a -> a -> a) -> WriterT w f a -> a #

toList :: WriterT w f a -> [a] #

null :: WriterT w f a -> Bool #

length :: WriterT w f a -> Int #

elem :: Eq a => a -> WriterT w f a -> Bool #

maximum :: Ord a => WriterT w f a -> a #

minimum :: Ord a => WriterT w f a -> a #

sum :: Num a => WriterT w f a -> a #

product :: Num a => WriterT w f a -> a #

Foldable f => Foldable (WriterT w f) 

Methods

fold :: Monoid m => WriterT w f m -> m #

foldMap :: Monoid m => (a -> m) -> WriterT w f a -> m #

foldr :: (a -> b -> b) -> b -> WriterT w f a -> b #

foldr' :: (a -> b -> b) -> b -> WriterT w f a -> b #

foldl :: (b -> a -> b) -> b -> WriterT w f a -> b #

foldl' :: (b -> a -> b) -> b -> WriterT w f a -> b #

foldr1 :: (a -> a -> a) -> WriterT w f a -> a #

foldl1 :: (a -> a -> a) -> WriterT w f a -> a #

toList :: WriterT w f a -> [a] #

null :: WriterT w f a -> Bool #

length :: WriterT w f a -> Int #

elem :: Eq a => a -> WriterT w f a -> Bool #

maximum :: Ord a => WriterT w f a -> a #

minimum :: Ord a => WriterT w f a -> a #

sum :: Num a => WriterT w f a -> a #

product :: Num a => WriterT w f a -> a #

Foldable f => Foldable (IdentityT * f) 

Methods

fold :: Monoid m => IdentityT * f m -> m #

foldMap :: Monoid m => (a -> m) -> IdentityT * f a -> m #

foldr :: (a -> b -> b) -> b -> IdentityT * f a -> b #

foldr' :: (a -> b -> b) -> b -> IdentityT * f a -> b #

foldl :: (b -> a -> b) -> b -> IdentityT * f a -> b #

foldl' :: (b -> a -> b) -> b -> IdentityT * f a -> b #

foldr1 :: (a -> a -> a) -> IdentityT * f a -> a #

foldl1 :: (a -> a -> a) -> IdentityT * f a -> a #

toList :: IdentityT * f a -> [a] #

null :: IdentityT * f a -> Bool #

length :: IdentityT * f a -> Int #

elem :: Eq a => a -> IdentityT * f a -> Bool #

maximum :: Ord a => IdentityT * f a -> a #

minimum :: Ord a => IdentityT * f a -> a #

sum :: Num a => IdentityT * f a -> a #

product :: Num a => IdentityT * f a -> a #

Foldable f => Foldable (ExceptT e f) 

Methods

fold :: Monoid m => ExceptT e f m -> m #

foldMap :: Monoid m => (a -> m) -> ExceptT e f a -> m #

foldr :: (a -> b -> b) -> b -> ExceptT e f a -> b #

foldr' :: (a -> b -> b) -> b -> ExceptT e f a -> b #

foldl :: (b -> a -> b) -> b -> ExceptT e f a -> b #

foldl' :: (b -> a -> b) -> b -> ExceptT e f a -> b #

foldr1 :: (a -> a -> a) -> ExceptT e f a -> a #

foldl1 :: (a -> a -> a) -> ExceptT e f a -> a #

toList :: ExceptT e f a -> [a] #

null :: ExceptT e f a -> Bool #

length :: ExceptT e f a -> Int #

elem :: Eq a => a -> ExceptT e f a -> Bool #

maximum :: Ord a => ExceptT e f a -> a #

minimum :: Ord a => ExceptT e f a -> a #

sum :: Num a => ExceptT e f a -> a #

product :: Num a => ExceptT e f a -> a #

Foldable f => Foldable (ErrorT e f) 

Methods

fold :: Monoid m => ErrorT e f m -> m #

foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m #

foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b #

foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b #

foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b #

foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b #

foldr1 :: (a -> a -> a) -> ErrorT e f a -> a #

foldl1 :: (a -> a -> a) -> ErrorT e f a -> a #

toList :: ErrorT e f a -> [a] #

null :: ErrorT e f a -> Bool #

length :: ErrorT e f a -> Int #

elem :: Eq a => a -> ErrorT e f a -> Bool #

maximum :: Ord a => ErrorT e f a -> a #

minimum :: Ord a => ErrorT e f a -> a #

sum :: Num a => ErrorT e f a -> a #

product :: Num a => ErrorT e f a -> a #

Foldable f => Foldable (M1 i c f) 

Methods

fold :: Monoid m => M1 i c f m -> m #

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m #

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b #

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b #

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b #

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b #

foldr1 :: (a -> a -> a) -> M1 i c f a -> a #

foldl1 :: (a -> a -> a) -> M1 i c f a -> a #

toList :: M1 i c f a -> [a] #

null :: M1 i c f a -> Bool #

length :: M1 i c f a -> Int #

elem :: Eq a => a -> M1 i c f a -> Bool #

maximum :: Ord a => M1 i c f a -> a #

minimum :: Ord a => M1 i c f a -> a #

sum :: Num a => M1 i c f a -> a #

product :: Num a => M1 i c f a -> a #

(Foldable f, Foldable g) => Foldable (Sum * f g) 

Methods

fold :: Monoid m => Sum * f g m -> m #

foldMap :: Monoid m => (a -> m) -> Sum * f g a -> m #

foldr :: (a -> b -> b) -> b -> Sum * f g a -> b #

foldr' :: (a -> b -> b) -> b -> Sum * f g a -> b #

foldl :: (b -> a -> b) -> b -> Sum * f g a -> b #

foldl' :: (b -> a -> b) -> b -> Sum * f g a -> b #

foldr1 :: (a -> a -> a) -> Sum * f g a -> a #

foldl1 :: (a -> a -> a) -> Sum * f g a -> a #

toList :: Sum * f g a -> [a] #

null :: Sum * f g a -> Bool #

length :: Sum * f g a -> Int #

elem :: Eq a => a -> Sum * f g a -> Bool #

maximum :: Ord a => Sum * f g a -> a #

minimum :: Ord a => Sum * f g a -> a #

sum :: Num a => Sum * f g a -> a #

product :: Num a => Sum * f g a -> a #

(Foldable f, Foldable g) => Foldable (Product * f g) 

Methods

fold :: Monoid m => Product * f g m -> m #

foldMap :: Monoid m => (a -> m) -> Product * f g a -> m #

foldr :: (a -> b -> b) -> b -> Product * f g a -> b #

foldr' :: (a -> b -> b) -> b -> Product * f g a -> b #

foldl :: (b -> a -> b) -> b -> Product * f g a -> b #

foldl' :: (b -> a -> b) -> b -> Product * f g a -> b #

foldr1 :: (a -> a -> a) -> Product * f g a -> a #

foldl1 :: (a -> a -> a) -> Product * f g a -> a #

toList :: Product * f g a -> [a] #

null :: Product * f g a -> Bool #

length :: Product * f g a -> Int #

elem :: Eq a => a -> Product * f g a -> Bool #

maximum :: Ord a => Product * f g a -> a #

minimum :: Ord a => Product * f g a -> a #

sum :: Num a => Product * f g a -> a #

product :: Num a => Product * f g a -> a #

(Foldable f, Foldable g) => Foldable (Compose * * f g) 

Methods

fold :: Monoid m => Compose * * f g m -> m #

foldMap :: Monoid m => (a -> m) -> Compose * * f g a -> m #

foldr :: (a -> b -> b) -> b -> Compose * * f g a -> b #

foldr' :: (a -> b -> b) -> b -> Compose * * f g a -> b #

foldl :: (b -> a -> b) -> b -> Compose * * f g a -> b #

foldl' :: (b -> a -> b) -> b -> Compose * * f g a -> b #

foldr1 :: (a -> a -> a) -> Compose * * f g a -> a #

foldl1 :: (a -> a -> a) -> Compose * * f g a -> a #

toList :: Compose * * f g a -> [a] #

null :: Compose * * f g a -> Bool #

length :: Compose * * f g a -> Int #

elem :: Eq a => a -> Compose * * f g a -> Bool #

maximum :: Ord a => Compose * * f g a -> a #

minimum :: Ord a => Compose * * f g a -> a #

sum :: Num a => Compose * * f g a -> a #

product :: Num a => Compose * * f g a -> a #

asum :: (Foldable t, Alternative f) => t (f a) -> f a #

The sum of a collection of actions, generalizing concat.

class (Functor t, Foldable t) => Traversable t #

Functors representing data structures that can be traversed from left to right.

A definition of traverse must satisfy the following laws:

naturality
t . traverse f = traverse (t . f) for every applicative transformation t
identity
traverse Identity = Identity
composition
traverse (Compose . fmap g . f) = Compose . fmap (traverse g) . traverse f

A definition of sequenceA must satisfy the following laws:

naturality
t . sequenceA = sequenceA . fmap t for every applicative transformation t
identity
sequenceA . fmap Identity = Identity
composition
sequenceA . fmap Compose = Compose . fmap sequenceA . sequenceA

where an applicative transformation is a function

t :: (Applicative f, Applicative g) => f a -> g a

preserving the Applicative operations, i.e.

and the identity functor Identity and composition of functors Compose are defined as

  newtype Identity a = Identity a

  instance Functor Identity where
    fmap f (Identity x) = Identity (f x)

  instance Applicative Identity where
    pure x = Identity x
    Identity f <*> Identity x = Identity (f x)

  newtype Compose f g a = Compose (f (g a))

  instance (Functor f, Functor g) => Functor (Compose f g) where
    fmap f (Compose x) = Compose (fmap (fmap f) x)

  instance (Applicative f, Applicative g) => Applicative (Compose f g) where
    pure x = Compose (pure (pure x))
    Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

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:

Minimal complete definition

traverse | sequenceA

Instances

Traversable [] 

Methods

traverse :: Applicative f => (a -> f b) -> [a] -> f [b] #

sequenceA :: Applicative f => [f a] -> f [a] #

mapM :: Monad m => (a -> m b) -> [a] -> m [b] #

sequence :: Monad m => [m a] -> m [a] #

Traversable Maybe 

Methods

traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) #

sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) #

mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) #

sequence :: Monad m => Maybe (m a) -> m (Maybe a) #

Traversable V1 

Methods

traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) #

sequenceA :: Applicative f => V1 (f a) -> f (V1 a) #

mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) #

sequence :: Monad m => V1 (m a) -> m (V1 a) #

Traversable U1 

Methods

traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) #

sequenceA :: Applicative f => U1 (f a) -> f (U1 a) #

mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) #

sequence :: Monad m => U1 (m a) -> m (U1 a) #

Traversable Par1 

Methods

traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) #

sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) #

mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) #

sequence :: Monad m => Par1 (m a) -> m (Par1 a) #

Traversable Identity 

Methods

traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) #

sequenceA :: Applicative f => Identity (f a) -> f (Identity a) #

mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) #

sequence :: Monad m => Identity (m a) -> m (Identity a) #

Traversable Min 

Methods

traverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) #

sequenceA :: Applicative f => Min (f a) -> f (Min a) #

mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) #

sequence :: Monad m => Min (m a) -> m (Min a) #

Traversable Max 

Methods

traverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) #

sequenceA :: Applicative f => Max (f a) -> f (Max a) #

mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) #

sequence :: Monad m => Max (m a) -> m (Max a) #

Traversable First 

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) #

sequenceA :: Applicative f => First (f a) -> f (First a) #

mapM :: Monad m => (a -> m b) -> First a -> m (First b) #

sequence :: Monad m => First (m a) -> m (First a) #

Traversable Last 

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) #

sequenceA :: Applicative f => Last (f a) -> f (Last a) #

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) #

sequence :: Monad m => Last (m a) -> m (Last a) #

Traversable Option 

Methods

traverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) #

sequenceA :: Applicative f => Option (f a) -> f (Option a) #

mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) #

sequence :: Monad m => Option (m a) -> m (Option a) #

Traversable NonEmpty 

Methods

traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) #

sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) #

mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) #

sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) #

Traversable Complex 

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) #

sequenceA :: Applicative f => Complex (f a) -> f (Complex a) #

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) #

sequence :: Monad m => Complex (m a) -> m (Complex a) #

Traversable ZipList 

Methods

traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) #

sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) #

mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) #

sequence :: Monad m => ZipList (m a) -> m (ZipList a) #

Traversable Dual 

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) #

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) #

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) #

sequence :: Monad m => Dual (m a) -> m (Dual a) #

Traversable Sum 

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) #

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) #

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) #

sequence :: Monad m => Sum (m a) -> m (Sum a) #

Traversable Product 

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) #

sequenceA :: Applicative f => Product (f a) -> f (Product a) #

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) #

sequence :: Monad m => Product (m a) -> m (Product a) #

Traversable First 

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) #

sequenceA :: Applicative f => First (f a) -> f (First a) #

mapM :: Monad m => (a -> m b) -> First a -> m (First b) #

sequence :: Monad m => First (m a) -> m (First a) #

Traversable Last 

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) #

sequenceA :: Applicative f => Last (f a) -> f (Last a) #

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) #

sequence :: Monad m => Last (m a) -> m (Last a) #

Traversable Digit 

Methods

traverse :: Applicative f => (a -> f b) -> Digit a -> f (Digit b) #

sequenceA :: Applicative f => Digit (f a) -> f (Digit a) #

mapM :: Monad m => (a -> m b) -> Digit a -> m (Digit b) #

sequence :: Monad m => Digit (m a) -> m (Digit a) #

Traversable Node 

Methods

traverse :: Applicative f => (a -> f b) -> Node a -> f (Node b) #

sequenceA :: Applicative f => Node (f a) -> f (Node a) #

mapM :: Monad m => (a -> m b) -> Node a -> m (Node b) #

sequence :: Monad m => Node (m a) -> m (Node a) #

Traversable Elem 

Methods

traverse :: Applicative f => (a -> f b) -> Elem a -> f (Elem b) #

sequenceA :: Applicative f => Elem (f a) -> f (Elem a) #

mapM :: Monad m => (a -> m b) -> Elem a -> m (Elem b) #

sequence :: Monad m => Elem (m a) -> m (Elem a) #

Traversable FingerTree 

Methods

traverse :: Applicative f => (a -> f b) -> FingerTree a -> f (FingerTree b) #

sequenceA :: Applicative f => FingerTree (f a) -> f (FingerTree a) #

mapM :: Monad m => (a -> m b) -> FingerTree a -> m (FingerTree b) #

sequence :: Monad m => FingerTree (m a) -> m (FingerTree a) #

Traversable IntMap 

Methods

traverse :: Applicative f => (a -> f b) -> IntMap a -> f (IntMap b) #

sequenceA :: Applicative f => IntMap (f a) -> f (IntMap a) #

mapM :: Monad m => (a -> m b) -> IntMap a -> m (IntMap b) #

sequence :: Monad m => IntMap (m a) -> m (IntMap a) #

Traversable Seq 

Methods

traverse :: Applicative f => (a -> f b) -> Seq a -> f (Seq b) #

sequenceA :: Applicative f => Seq (f a) -> f (Seq a) #

mapM :: Monad m => (a -> m b) -> Seq a -> m (Seq b) #

sequence :: Monad m => Seq (m a) -> m (Seq a) #

Traversable ViewL 

Methods

traverse :: Applicative f => (a -> f b) -> ViewL a -> f (ViewL b) #

sequenceA :: Applicative f => ViewL (f a) -> f (ViewL a) #

mapM :: Monad m => (a -> m b) -> ViewL a -> m (ViewL b) #

sequence :: Monad m => ViewL (m a) -> m (ViewL a) #

Traversable ViewR 

Methods

traverse :: Applicative f => (a -> f b) -> ViewR a -> f (ViewR b) #

sequenceA :: Applicative f => ViewR (f a) -> f (ViewR a) #

mapM :: Monad m => (a -> m b) -> ViewR a -> m (ViewR b) #

sequence :: Monad m => ViewR (m a) -> m (ViewR a) #

Traversable Array 

Methods

traverse :: Applicative f => (a -> f b) -> Array a -> f (Array b) #

sequenceA :: Applicative f => Array (f a) -> f (Array a) #

mapM :: Monad m => (a -> m b) -> Array a -> m (Array b) #

sequence :: Monad m => Array (m a) -> m (Array a) #

Traversable Vector 

Methods

traverse :: Applicative f => (a -> f b) -> Vector a -> f (Vector b) #

sequenceA :: Applicative f => Vector (f a) -> f (Vector a) #

mapM :: Monad m => (a -> m b) -> Vector a -> m (Vector b) #

sequence :: Monad m => Vector (m a) -> m (Vector a) #

Traversable (Either a) 

Methods

traverse :: Applicative f => (a -> f b) -> Either a a -> f (Either a b) #

sequenceA :: Applicative f => Either a (f a) -> f (Either a a) #

mapM :: Monad m => (a -> m b) -> Either a a -> m (Either a b) #

sequence :: Monad m => Either a (m a) -> m (Either a a) #

Traversable f => Traversable (Rec1 f) 

Methods

traverse :: Applicative f => (a -> f b) -> Rec1 f a -> f (Rec1 f b) #

sequenceA :: Applicative f => Rec1 f (f a) -> f (Rec1 f a) #

mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) #

sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) #

Traversable (URec Char) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) #

sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) #

mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) #

sequence :: Monad m => URec Char (m a) -> m (URec Char a) #

Traversable (URec Double) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) #

sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) #

mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) #

sequence :: Monad m => URec Double (m a) -> m (URec Double a) #

Traversable (URec Float) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) #

sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) #

mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) #

sequence :: Monad m => URec Float (m a) -> m (URec Float a) #

Traversable (URec Int) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) #

sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) #

mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) #

sequence :: Monad m => URec Int (m a) -> m (URec Int a) #

Traversable (URec Word) 

Methods

traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) #

sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) #

mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) #

sequence :: Monad m => URec Word (m a) -> m (URec Word a) #

Traversable (URec (Ptr ())) 

Methods

traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) #

sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) #

mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) #

sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) #

Traversable ((,) a) 

Methods

traverse :: Applicative f => (a -> f b) -> (a, a) -> f (a, b) #

sequenceA :: Applicative f => (a, f a) -> f (a, a) #

mapM :: Monad m => (a -> m b) -> (a, a) -> m (a, b) #

sequence :: Monad m => (a, m a) -> m (a, a) #

Ix i => Traversable (Array i) 

Methods

traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) #

sequenceA :: Applicative f => Array i (f a) -> f (Array i a) #

mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) #

sequence :: Monad m => Array i (m a) -> m (Array i a) #

Traversable (Arg a) 

Methods

traverse :: Applicative f => (a -> f b) -> Arg a a -> f (Arg a b) #

sequenceA :: Applicative f => Arg a (f a) -> f (Arg a a) #

mapM :: Monad m => (a -> m b) -> Arg a a -> m (Arg a b) #

sequence :: Monad m => Arg a (m a) -> m (Arg a a) #

Traversable (Proxy *) 

Methods

traverse :: Applicative f => (a -> f b) -> Proxy * a -> f (Proxy * b) #

sequenceA :: Applicative f => Proxy * (f a) -> f (Proxy * a) #

mapM :: Monad m => (a -> m b) -> Proxy * a -> m (Proxy * b) #

sequence :: Monad m => Proxy * (m a) -> m (Proxy * a) #

Traversable (Map k) 

Methods

traverse :: Applicative f => (a -> f b) -> Map k a -> f (Map k b) #

sequenceA :: Applicative f => Map k (f a) -> f (Map k a) #

mapM :: Monad m => (a -> m b) -> Map k a -> m (Map k b) #

sequence :: Monad m => Map k (m a) -> m (Map k a) #

Traversable f => Traversable (MaybeT f) 

Methods

traverse :: Applicative f => (a -> f b) -> MaybeT f a -> f (MaybeT f b) #

sequenceA :: Applicative f => MaybeT f (f a) -> f (MaybeT f a) #

mapM :: Monad m => (a -> m b) -> MaybeT f a -> m (MaybeT f b) #

sequence :: Monad m => MaybeT f (m a) -> m (MaybeT f a) #

Traversable f => Traversable (ListT f) 

Methods

traverse :: Applicative f => (a -> f b) -> ListT f a -> f (ListT f b) #

sequenceA :: Applicative f => ListT f (f a) -> f (ListT f a) #

mapM :: Monad m => (a -> m b) -> ListT f a -> m (ListT f b) #

sequence :: Monad m => ListT f (m a) -> m (ListT f a) #

Traversable (HashMap k) 

Methods

traverse :: Applicative f => (a -> f b) -> HashMap k a -> f (HashMap k b) #

sequenceA :: Applicative f => HashMap k (f a) -> f (HashMap k a) #

mapM :: Monad m => (a -> m b) -> HashMap k a -> m (HashMap k b) #

sequence :: Monad m => HashMap k (m a) -> m (HashMap k a) #

Traversable (K1 i c) 

Methods

traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) #

sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) #

mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) #

sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) #

(Traversable f, Traversable g) => Traversable ((:+:) f g) 

Methods

traverse :: Applicative f => (a -> f b) -> (f :+: g) a -> f ((f :+: g) b) #

sequenceA :: Applicative f => (f :+: g) (f a) -> f ((f :+: g) a) #

mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) #

sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) #

(Traversable f, Traversable g) => Traversable ((:*:) f g) 

Methods

traverse :: Applicative f => (a -> f b) -> (f :*: g) a -> f ((f :*: g) b) #

sequenceA :: Applicative f => (f :*: g) (f a) -> f ((f :*: g) a) #

mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) #

sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) #

(Traversable f, Traversable g) => Traversable ((:.:) f g) 

Methods

traverse :: Applicative f => (a -> f b) -> (f :.: g) a -> f ((f :.: g) b) #

sequenceA :: Applicative f => (f :.: g) (f a) -> f ((f :.: g) a) #

mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) #

sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) #

Traversable (Const * m) 

Methods

traverse :: Applicative f => (a -> f b) -> Const * m a -> f (Const * m b) #

sequenceA :: Applicative f => Const * m (f a) -> f (Const * m a) #

mapM :: Monad m => (a -> m b) -> Const * m a -> m (Const * m b) #

sequence :: Monad m => Const * m (m a) -> m (Const * m a) #

Traversable f => Traversable (WriterT w f) 

Methods

traverse :: Applicative f => (a -> f b) -> WriterT w f a -> f (WriterT w f b) #

sequenceA :: Applicative f => WriterT w f (f a) -> f (WriterT w f a) #

mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) #

sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #

Traversable f => Traversable (WriterT w f) 

Methods

traverse :: Applicative f => (a -> f b) -> WriterT w f a -> f (WriterT w f b) #

sequenceA :: Applicative f => WriterT w f (f a) -> f (WriterT w f a) #

mapM :: Monad m => (a -> m b) -> WriterT w f a -> m (WriterT w f b) #

sequence :: Monad m => WriterT w f (m a) -> m (WriterT w f a) #

Traversable f => Traversable (IdentityT * f) 

Methods

traverse :: Applicative f => (a -> f b) -> IdentityT * f a -> f (IdentityT * f b) #

sequenceA :: Applicative f => IdentityT * f (f a) -> f (IdentityT * f a) #

mapM :: Monad m => (a -> m b) -> IdentityT * f a -> m (IdentityT * f b) #

sequence :: Monad m => IdentityT * f (m a) -> m (IdentityT * f a) #

Traversable f => Traversable (ExceptT e f) 

Methods

traverse :: Applicative f => (a -> f b) -> ExceptT e f a -> f (ExceptT e f b) #

sequenceA :: Applicative f => ExceptT e f (f a) -> f (ExceptT e f a) #

mapM :: Monad m => (a -> m b) -> ExceptT e f a -> m (ExceptT e f b) #

sequence :: Monad m => ExceptT e f (m a) -> m (ExceptT e f a) #

Traversable f => Traversable (ErrorT e f) 

Methods

traverse :: Applicative f => (a -> f b) -> ErrorT e f a -> f (ErrorT e f b) #

sequenceA :: Applicative f => ErrorT e f (f a) -> f (ErrorT e f a) #

mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) #

sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) #

Traversable f => Traversable (M1 i c f) 

Methods

traverse :: Applicative f => (a -> f b) -> M1 i c f a -> f (M1 i c f b) #

sequenceA :: Applicative f => M1 i c f (f a) -> f (M1 i c f a) #

mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) #

sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) #

(Traversable f, Traversable g) => Traversable (Sum * f g) 

Methods

traverse :: Applicative f => (a -> f b) -> Sum * f g a -> f (Sum * f g b) #

sequenceA :: Applicative f => Sum * f g (f a) -> f (Sum * f g a) #

mapM :: Monad m => (a -> m b) -> Sum * f g a -> m (Sum * f g b) #

sequence :: Monad m => Sum * f g (m a) -> m (Sum * f g a) #

(Traversable f, Traversable g) => Traversable (Product * f g) 

Methods

traverse :: Applicative f => (a -> f b) -> Product * f g a -> f (Product * f g b) #

sequenceA :: Applicative f => Product * f g (f a) -> f (Product * f g a) #

mapM :: Monad m => (a -> m b) -> Product * f g a -> m (Product * f g b) #

sequence :: Monad m => Product * f g (m a) -> m (Product * f g a) #

(Traversable f, Traversable g) => Traversable (Compose * * f g) 

Methods

traverse :: Applicative f => (a -> f b) -> Compose * * f g a -> f (Compose * * f g b) #

sequenceA :: Applicative f => Compose * * f g (f a) -> f (Compose * * f g a) #

mapM :: Monad m => (a -> m b) -> Compose * * f g a -> m (Compose * * f g b) #

sequence :: Monad m => Compose * * f g (m a) -> m (Compose * * f g a) #

arrow

first :: Arrow a => forall b c d. a b c -> a (b, d) (c, d) #

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

second :: Arrow a => forall b c d. a b c -> a (d, b) (d, c) #

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

(***) :: Arrow a => forall b c b' c'. a b c -> a b' c' -> a (b, b') (c, c') #

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

(&&&) :: Arrow a => forall b c c'. a b c -> a b c' -> a b (c, c') #

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

Bool

bool :: a -> a -> Bool -> a #

Case analysis for the Bool type. bool x y p evaluates to x when p is False, and evaluates to y when p is True.

This is equivalent to if p then y else x; that is, one can think of it as an if-then-else construct with its arguments reordered.

Examples

Basic usage:

>>> bool "foo" "bar" True
"bar"
>>> bool "foo" "bar" False
"foo"

Confirm that bool x y p and if p then y else x are equivalent:

>>> let p = True; x = "bar"; y = "foo"
>>> bool x y p == if p then y else x
True
>>> let p = False
>>> bool x y p == if p then y else x
True

Since: 4.7.0.0

Maybe

mapMaybe :: (a -> Maybe b) -> [a] -> [b] #

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

Examples

Using mapMaybe f x is a shortcut for catMaybes $ map f x in most cases:

>>> import Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

If we map the Just constructor, the entire list should be returned:

>>> mapMaybe Just [1,2,3]
[1,2,3]

catMaybes :: [Maybe a] -> [a] #

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

Examples

Basic usage:

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

When constructing a list of Maybe values, catMaybes can be used to return all of the "success" results (if the list is the result of a map, then mapMaybe would be more appropriate):

>>> import Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

fromMaybe :: a -> Maybe a -> a #

The fromMaybe function takes a default value and and Maybe value. If the Maybe is Nothing, it returns the default values; otherwise, it returns the value contained in the Maybe.

Examples

Basic usage:

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"
>>> fromMaybe "" Nothing
""

Read an integer from a string using readMaybe. If we fail to parse an integer, we want to return 0 by default:

>>> import Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

isJust :: Maybe a -> Bool #

The isJust function returns True iff its argument is of the form Just _.

Examples

Basic usage:

>>> isJust (Just 3)
True
>>> isJust (Just ())
True
>>> isJust Nothing
False

Only the outer constructor is taken into consideration:

>>> isJust (Just Nothing)
True

isNothing :: Maybe a -> Bool #

The isNothing function returns True iff its argument is Nothing.

Examples

Basic usage:

>>> isNothing (Just 3)
False
>>> isNothing (Just ())
False
>>> isNothing Nothing
True

Only the outer constructor is taken into consideration:

>>> isNothing (Just Nothing)
False

listToMaybe :: [a] -> Maybe a #

The listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

Examples

Basic usage:

>>> listToMaybe []
Nothing
>>> listToMaybe [9]
Just 9
>>> listToMaybe [1,2,3]
Just 1

Composing maybeToList with listToMaybe should be the identity on singleton/empty lists:

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

But not on lists with more than one element:

>>> maybeToList $ listToMaybe [1,2,3]
[1]

maybeToList :: Maybe a -> [a] #

The maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.

Examples

Basic usage:

>>> maybeToList (Just 7)
[7]
>>> maybeToList Nothing
[]

One can use maybeToList to avoid pattern matching when combined with a function that (safely) works on lists:

>>> import Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

Either

partitionEithers :: [Either a b] -> ([a], [b]) #

Partitions a list of Either into two lists. All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list
(["foo","bar","baz"],[3,7])

The pair returned by partitionEithers x should be the same pair as (lefts x, rights x):

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list == (lefts list, rights list)
True

lefts :: [Either a b] -> [a] #

Extracts from a list of Either all the Left elements. All the Left elements are extracted in order.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> lefts list
["foo","bar","baz"]

rights :: [Either a b] -> [b] #

Extracts from a list of Either all the Right elements. All the Right elements are extracted in order.

Examples

Basic usage:

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> rights list
[3,7]

Ord

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0 #

(*) `on` f = \x y -> f x * f y.

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

  • (*) `on` id = (*) (if (*) ∉ {⊥, const ⊥})
  • ((*) `on` f) `on` g = (*) `on` (f . g)
  • flip on f . flip on g = flip on (g . f)

comparing :: Ord a => (b -> a) -> b -> b -> Ordering #

comparing p x y = compare (p x) (p y)

Useful combinator for use in conjunction with the xxxBy family of functions from Data.List, for example:

  ... sortBy (comparing fst) ...

equating :: Eq a => (b -> a) -> b -> b -> Bool Source #

newtype Down a :: * -> * #

The Down type allows you to reverse sort order conveniently. A value of type Down a contains a value of type a (represented as Down a). If a has an Ord instance associated with it then comparing two values thus wrapped will give you the opposite of their normal sort order. This is particularly useful when sorting in generalised list comprehensions, as in: then sortWith by Down x

Provides Show and Read instances (since: 4.7.0.0).

Since: 4.6.0.0

Constructors

Down a 

Instances

Eq a => Eq (Down a) 

Methods

(==) :: Down a -> Down a -> Bool #

(/=) :: Down a -> Down a -> Bool #

Ord a => Ord (Down a) 

Methods

compare :: Down a -> Down a -> Ordering #

(<) :: Down a -> Down a -> Bool #

(<=) :: Down a -> Down a -> Bool #

(>) :: Down a -> Down a -> Bool #

(>=) :: Down a -> Down a -> Bool #

max :: Down a -> Down a -> Down a #

min :: Down a -> Down a -> Down a #

Read a => Read (Down a) 
Show a => Show (Down a) 

Methods

showsPrec :: Int -> Down a -> ShowS #

show :: Down a -> String #

showList :: [Down a] -> ShowS #

Applicative

class Functor f => Applicative f where #

A functor with application, providing operations to

  • embed pure expressions (pure), and
  • sequence computations and combine their results (<*>).

A minimal complete definition must include implementations of these functions satisfying the following laws:

identity
pure id <*> v = v
composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
homomorphism
pure f <*> pure x = pure (f x)
interchange
u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the Functor instance for f will satisfy

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, (<*>)

Methods

pure :: a -> f a #

Lift a value.

(<*>) :: f (a -> b) -> f a -> f b infixl 4 #

Sequential application.

(*>) :: f a -> f b -> f b infixl 4 #

Sequence actions, discarding the value of the first argument.

(<*) :: f a -> f b -> f a infixl 4 #

Sequence actions, discarding the value of the second argument.

Instances

Applicative [] 

Methods

pure :: a -> [a] #

(<*>) :: [a -> b] -> [a] -> [b] #

(*>) :: [a] -> [b] -> [b] #

(<*) :: [a] -> [b] -> [a] #

Applicative Maybe 

Methods

pure :: a -> Maybe a #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b #

(*>) :: Maybe a -> Maybe b -> Maybe b #

(<*) :: Maybe a -> Maybe b -> Maybe a #

Applicative IO 

Methods

pure :: a -> IO a #

(<*>) :: IO (a -> b) -> IO a -> IO b #

(*>) :: IO a -> IO b -> IO b #

(<*) :: IO a -> IO b -> IO a #

Applicative U1 

Methods

pure :: a -> U1 a #

(<*>) :: U1 (a -> b) -> U1 a -> U1 b #

(*>) :: U1 a -> U1 b -> U1 b #

(<*) :: U1 a -> U1 b -> U1 a #

Applicative Par1 

Methods

pure :: a -> Par1 a #

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b #

(*>) :: Par1 a -> Par1 b -> Par1 b #

(<*) :: Par1 a -> Par1 b -> Par1 a #

Applicative Id 

Methods

pure :: a -> Id a #

(<*>) :: Id (a -> b) -> Id a -> Id b #

(*>) :: Id a -> Id b -> Id b #

(<*) :: Id a -> Id b -> Id a #

Applicative P 

Methods

pure :: a -> P a #

(<*>) :: P (a -> b) -> P a -> P b #

(*>) :: P a -> P b -> P b #

(<*) :: P a -> P b -> P a #

Applicative Identity 

Methods

pure :: a -> Identity a #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b #

(*>) :: Identity a -> Identity b -> Identity b #

(<*) :: Identity a -> Identity b -> Identity a #

Applicative Min 

Methods

pure :: a -> Min a #

(<*>) :: Min (a -> b) -> Min a -> Min b #

(*>) :: Min a -> Min b -> Min b #

(<*) :: Min a -> Min b -> Min a #

Applicative Max 

Methods

pure :: a -> Max a #

(<*>) :: Max (a -> b) -> Max a -> Max b #

(*>) :: Max a -> Max b -> Max b #

(<*) :: Max a -> Max b -> Max a #

Applicative First 

Methods

pure :: a -> First a #

(<*>) :: First (a -> b) -> First a -> First b #

(*>) :: First a -> First b -> First b #

(<*) :: First a -> First b -> First a #

Applicative Last 

Methods

pure :: a -> Last a #

(<*>) :: Last (a -> b) -> Last a -> Last b #

(*>) :: Last a -> Last b -> Last b #

(<*) :: Last a -> Last b -> Last a #

Applicative Option 

Methods

pure :: a -> Option a #

(<*>) :: Option (a -> b) -> Option a -> Option b #

(*>) :: Option a -> Option b -> Option b #

(<*) :: Option a -> Option b -> Option a #

Applicative NonEmpty 

Methods

pure :: a -> NonEmpty a #

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b #

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b #

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a #

Applicative Complex 

Methods

pure :: a -> Complex a #

(<*>) :: Complex (a -> b) -> Complex a -> Complex b #

(*>) :: Complex a -> Complex b -> Complex b #

(<*) :: Complex a -> Complex b -> Complex a #

Applicative ZipList 

Methods

pure :: a -> ZipList a #

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b #

(*>) :: ZipList a -> ZipList b -> ZipList b #

(<*) :: ZipList a -> ZipList b -> ZipList a #

Applicative Dual 

Methods

pure :: a -> Dual a #

(<*>) :: Dual (a -> b) -> Dual a -> Dual b #

(*>) :: Dual a -> Dual b -> Dual b #

(<*) :: Dual a -> Dual b -> Dual a #

Applicative Sum 

Methods

pure :: a -> Sum a #

(<*>) :: Sum (a -> b) -> Sum a -> Sum b #

(*>) :: Sum a -> Sum b -> Sum b #

(<*) :: Sum a -> Sum b -> Sum a #

Applicative Product 

Methods

pure :: a -> Product a #

(<*>) :: Product (a -> b) -> Product a -> Product b #

(*>) :: Product a -> Product b -> Product b #

(<*) :: Product a -> Product b -> Product a #

Applicative First 

Methods

pure :: a -> First a #

(<*>) :: First (a -> b) -> First a -> First b #

(*>) :: First a -> First b -> First b #

(<*) :: First a -> First b -> First a #

Applicative Last 

Methods

pure :: a -> Last a #

(<*>) :: Last (a -> b) -> Last a -> Last b #

(*>) :: Last a -> Last b -> Last b #

(<*) :: Last a -> Last b -> Last a #

Applicative ReadP 

Methods

pure :: a -> ReadP a #

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b #

(*>) :: ReadP a -> ReadP b -> ReadP b #

(<*) :: ReadP a -> ReadP b -> ReadP a #

Applicative Seq 

Methods

pure :: a -> Seq a #

(<*>) :: Seq (a -> b) -> Seq a -> Seq b #

(*>) :: Seq a -> Seq b -> Seq b #

(<*) :: Seq a -> Seq b -> Seq a #

Applicative Array 

Methods

pure :: a -> Array a #

(<*>) :: Array (a -> b) -> Array a -> Array b #

(*>) :: Array a -> Array b -> Array b #

(<*) :: Array a -> Array b -> Array a #

Applicative Vector 

Methods

pure :: a -> Vector a #

(<*>) :: Vector (a -> b) -> Vector a -> Vector b #

(*>) :: Vector a -> Vector b -> Vector b #

(<*) :: Vector a -> Vector b -> Vector a #

Applicative ((->) a) 

Methods

pure :: a -> a -> a #

(<*>) :: (a -> a -> b) -> (a -> a) -> a -> b #

(*>) :: (a -> a) -> (a -> b) -> a -> b #

(<*) :: (a -> a) -> (a -> b) -> a -> a #

Applicative (Either e) 

Methods

pure :: a -> Either e a #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b #

(*>) :: Either e a -> Either e b -> Either e b #

(<*) :: Either e a -> Either e b -> Either e a #

Applicative f => Applicative (Rec1 f) 

Methods

pure :: a -> Rec1 f a #

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b #

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b #

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a #

Monoid a => Applicative ((,) a) 

Methods

pure :: a -> (a, a) #

(<*>) :: (a, a -> b) -> (a, a) -> (a, b) #

(*>) :: (a, a) -> (a, b) -> (a, b) #

(<*) :: (a, a) -> (a, b) -> (a, a) #

Applicative (ST s) 

Methods

pure :: a -> ST s a #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b #

(*>) :: ST s a -> ST s b -> ST s b #

(<*) :: ST s a -> ST s b -> ST s a #

Applicative (StateL s) 

Methods

pure :: a -> StateL s a #

(<*>) :: StateL s (a -> b) -> StateL s a -> StateL s b #

(*>) :: StateL s a -> StateL s b -> StateL s b #

(<*) :: StateL s a -> StateL s b -> StateL s a #

Applicative (StateR s) 

Methods

pure :: a -> StateR s a #

(<*>) :: StateR s (a -> b) -> StateR s a -> StateR s b #

(*>) :: StateR s a -> StateR s b -> StateR s b #

(<*) :: StateR s a -> StateR s b -> StateR s a #

Monad m => Applicative (WrappedMonad m) 

Methods

pure :: a -> WrappedMonad m a #

(<*>) :: WrappedMonad m (a -> b) -> WrappedMonad m a -> WrappedMonad m b #

(*>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #

(<*) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m a #

Arrow a => Applicative (ArrowMonad a) 

Methods

pure :: a -> ArrowMonad a a #

(<*>) :: ArrowMonad a (a -> b) -> ArrowMonad a a -> ArrowMonad a b #

(*>) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a b #

(<*) :: ArrowMonad a a -> ArrowMonad a b -> ArrowMonad a a #

Applicative (Proxy *) 

Methods

pure :: a -> Proxy * a #

(<*>) :: Proxy * (a -> b) -> Proxy * a -> Proxy * b #

(*>) :: Proxy * a -> Proxy * b -> Proxy * b #

(<*) :: Proxy * a -> Proxy * b -> Proxy * a #

Applicative (State s) 

Methods

pure :: a -> State s a #

(<*>) :: State s (a -> b) -> State s a -> State s b #

(*>) :: State s a -> State s b -> State s b #

(<*) :: State s a -> State s b -> State s a #

(Functor m, Monad m) => Applicative (MaybeT m) 

Methods

pure :: a -> MaybeT m a #

(<*>) :: MaybeT m (a -> b) -> MaybeT m a -> MaybeT m b #

(*>) :: MaybeT m a -> MaybeT m b -> MaybeT m b #

(<*) :: MaybeT m a -> MaybeT m b -> MaybeT m a #

Applicative m => Applicative (ListT m) 

Methods

pure :: a -> ListT m a #

(<*>) :: ListT m (a -> b) -> ListT m a -> ListT m b #

(*>) :: ListT m a -> ListT m b -> ListT m b #

(<*) :: ListT m a -> ListT m b -> ListT m a #

(Applicative f, Applicative g) => Applicative ((:*:) f g) 

Methods

pure :: a -> (f :*: g) a #

(<*>) :: (f :*: g) (a -> b) -> (f :*: g) a -> (f :*: g) b #

(*>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b #

(<*) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) a #

(Applicative f, Applicative g) => Applicative ((:.:) f g) 

Methods

pure :: a -> (f :.: g) a #

(<*>) :: (f :.: g) (a -> b) -> (f :.: g) a -> (f :.: g) b #

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b #

(<*) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) a #

Arrow a => Applicative (WrappedArrow a b) 

Methods

pure :: a -> WrappedArrow a b a #

(<*>) :: WrappedArrow a b (a -> b) -> WrappedArrow a b a -> WrappedArrow a b b #

(*>) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b b #

(<*) :: WrappedArrow a b a -> WrappedArrow a b b -> WrappedArrow a b a #

Monoid m => Applicative (Const * m) 

Methods

pure :: a -> Const * m a #

(<*>) :: Const * m (a -> b) -> Const * m a -> Const * m b #

(*>) :: Const * m a -> Const * m b -> Const * m b #

(<*) :: Const * m a -> Const * m b -> Const * m a #

Applicative f => Applicative (Alt * f) 

Methods

pure :: a -> Alt * f a #

(<*>) :: Alt * f (a -> b) -> Alt * f a -> Alt * f b #

(*>) :: Alt * f a -> Alt * f b -> Alt * f b #

(<*) :: Alt * f a -> Alt * f b -> Alt * f a #

(Monoid w, Applicative m) => Applicative (WriterT w m) 

Methods

pure :: a -> WriterT w m a #

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b #

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #

(Monoid w, Applicative m) => Applicative (WriterT w m) 

Methods

pure :: a -> WriterT w m a #

(<*>) :: WriterT w m (a -> b) -> WriterT w m a -> WriterT w m b #

(*>) :: WriterT w m a -> WriterT w m b -> WriterT w m b #

(<*) :: WriterT w m a -> WriterT w m b -> WriterT w m a #

(Functor m, Monad m) => Applicative (StateT s m) 

Methods

pure :: a -> StateT s m a #

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b #

(*>) :: StateT s m a -> StateT s m b -> StateT s m b #

(<*) :: StateT s m a -> StateT s m b -> StateT s m a #

(Functor m, Monad m) => Applicative (StateT s m) 

Methods

pure :: a -> StateT s m a #

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b #

(*>) :: StateT s m a -> StateT s m b -> StateT s m b #

(<*) :: StateT s m a -> StateT s m b -> StateT s m a #

Applicative m => Applicative (IdentityT * m) 

Methods

pure :: a -> IdentityT * m a #

(<*>) :: IdentityT * m (a -> b) -> IdentityT * m a -> IdentityT * m b #

(*>) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m b #

(<*) :: IdentityT * m a -> IdentityT * m b -> IdentityT * m a #

(Functor m, Monad m) => Applicative (ExceptT e m) 

Methods

pure :: a -> ExceptT e m a #

(<*>) :: ExceptT e m (a -> b) -> ExceptT e m a -> ExceptT e m b #

(*>) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m b #

(<*) :: ExceptT e m a -> ExceptT e m b -> ExceptT e m a #

(Functor m, Monad m) => Applicative (ErrorT e m) 

Methods

pure :: a -> ErrorT e m a #

(<*>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b #

(*>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b #

(<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a #

Applicative f => Applicative (M1 i c f) 

Methods

pure :: a -> M1 i c f a #

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b #

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b #

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a #

(Applicative f, Applicative g) => Applicative (Product * f g) 

Methods

pure :: a -> Product * f g a #

(<*>) :: Product * f g (a -> b) -> Product * f g a -> Product * f g b #

(*>) :: Product * f g a -> Product * f g b -> Product * f g b #

(<*) :: Product * f g a -> Product * f g b -> Product * f g a #

Applicative m => Applicative (ReaderT * r m) 

Methods

pure :: a -> ReaderT * r m a #

(<*>) :: ReaderT * r m (a -> b) -> ReaderT * r m a -> ReaderT * r m b #

(*>) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m b #

(<*) :: ReaderT * r m a -> ReaderT * r m b -> ReaderT * r m a #

(Applicative f, Applicative g) => Applicative (Compose * * f g) 

Methods

pure :: a -> Compose * * f g a #

(<*>) :: Compose * * f g (a -> b) -> Compose * * f g a -> Compose * * f g b #

(*>) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g b #

(<*) :: Compose * * f g a -> Compose * * f g b -> Compose * * f g a #

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) 

Methods

pure :: a -> RWST r w s m a #

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b #

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #

(Monoid w, Functor m, Monad m) => Applicative (RWST r w s m) 

Methods

pure :: a -> RWST r w s m a #

(<*>) :: RWST r w s m (a -> b) -> RWST r w s m a -> RWST r w s m b #

(*>) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m b #

(<*) :: RWST r w s m a -> RWST r w s m b -> RWST r w s m a #

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 #

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

 ($)  ::              (a -> b) ->   a ->   b
(<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

Convert from a Maybe Int to a Maybe String using show:

>>> show <$> Nothing
Nothing
>>> show <$> Just 3
Just "3"

Convert from an Either Int Int to an Either Int String using show:

>>> show <$> Left 17
Left 17
>>> show <$> Right 17
Right "17"

Double each element of a list:

>>> (*2) <$> [1,2,3]
[2,4,6]

Apply even to the second element of a pair:

>>> even <$> (2,2)
(2,True)

(<|>) :: Alternative f => forall a. f a -> f a -> f a #

An associative binary operation

Monad

(>=>) :: Monad m => (a -> m b) -> (b -> m c) -> a -> m c infixr 1 #

Left-to-right Kleisli composition of monads.

Transformers

lift :: MonadTrans t => forall m a. Monad m => m a -> t m a #

Lift a computation from the argument monad to the constructed monad.

class Monad m => MonadIO m where #

Monads in which IO computations may be embedded. Any monad built by applying a sequence of monad transformers to the IO monad will be an instance of this class.

Instances should satisfy the following laws, which state that liftIO is a transformer of monads:

Minimal complete definition

liftIO

Methods

liftIO :: IO a -> m a #

Lift a computation from the IO monad.

Instances

MonadIO IO 

Methods

liftIO :: IO a -> IO a #

MonadIO m => MonadIO (MaybeT m) 

Methods

liftIO :: IO a -> MaybeT m a #

MonadIO m => MonadIO (ListT m) 

Methods

liftIO :: IO a -> ListT m a #

(Monoid w, MonadIO m) => MonadIO (WriterT w m) 

Methods

liftIO :: IO a -> WriterT w m a #

(Monoid w, MonadIO m) => MonadIO (WriterT w m) 

Methods

liftIO :: IO a -> WriterT w m a #

MonadIO m => MonadIO (StateT s m) 

Methods

liftIO :: IO a -> StateT s m a #

MonadIO m => MonadIO (StateT s m) 

Methods

liftIO :: IO a -> StateT s m a #

MonadIO m => MonadIO (IdentityT * m) 

Methods

liftIO :: IO a -> IdentityT * m a #

MonadIO m => MonadIO (ExceptT e m) 

Methods

liftIO :: IO a -> ExceptT e m a #

(Error e, MonadIO m) => MonadIO (ErrorT e m) 

Methods

liftIO :: IO a -> ErrorT e m a #

MonadIO m => MonadIO (ReaderT * r m) 

Methods

liftIO :: IO a -> ReaderT * r m a #

(Monoid w, MonadIO m) => MonadIO (RWST r w s m) 

Methods

liftIO :: IO a -> RWST r w s m a #

(Monoid w, MonadIO m) => MonadIO (RWST r w s m) 

Methods

liftIO :: IO a -> RWST r w s m a #

liftIO :: MonadIO m => forall a. IO a -> m a #

Lift a computation from the IO monad.

Exceptions

class (Typeable * e, Show e) => Exception e where #

Any type that you wish to throw or catch as an exception must be an instance of the Exception class. The simplest case is a new exception type directly below the root:

data MyException = ThisException | ThatException
    deriving (Show, Typeable)

instance Exception MyException

The default method definitions in the Exception class do what we need in this case. You can now throw and catch ThisException and ThatException as exceptions:

*Main> throw ThisException `catch` \e -> putStrLn ("Caught " ++ show (e :: MyException))
Caught ThisException

In more complicated examples, you may wish to define a whole hierarchy of exceptions:

---------------------------------------------------------------------
-- Make the root exception type for all the exceptions in a compiler

data SomeCompilerException = forall e . Exception e => SomeCompilerException e
    deriving Typeable

instance Show SomeCompilerException where
    show (SomeCompilerException e) = show e

instance Exception SomeCompilerException

compilerExceptionToException :: Exception e => e -> SomeException
compilerExceptionToException = toException . SomeCompilerException

compilerExceptionFromException :: Exception e => SomeException -> Maybe e
compilerExceptionFromException x = do
    SomeCompilerException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make a subhierarchy for exceptions in the frontend of the compiler

data SomeFrontendException = forall e . Exception e => SomeFrontendException e
    deriving Typeable

instance Show SomeFrontendException where
    show (SomeFrontendException e) = show e

instance Exception SomeFrontendException where
    toException = compilerExceptionToException
    fromException = compilerExceptionFromException

frontendExceptionToException :: Exception e => e -> SomeException
frontendExceptionToException = toException . SomeFrontendException

frontendExceptionFromException :: Exception e => SomeException -> Maybe e
frontendExceptionFromException x = do
    SomeFrontendException a <- fromException x
    cast a

---------------------------------------------------------------------
-- Make an exception type for a particular frontend compiler exception

data MismatchedParentheses = MismatchedParentheses
    deriving (Typeable, Show)

instance Exception MismatchedParentheses where
    toException   = frontendExceptionToException
    fromException = frontendExceptionFromException

We can now catch a MismatchedParentheses exception as MismatchedParentheses, SomeFrontendException or SomeCompilerException, but not other types, e.g. IOException:

*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: MismatchedParentheses))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeFrontendException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: SomeCompilerException))
Caught MismatchedParentheses
*Main> throw MismatchedParentheses catch e -> putStrLn ("Caught " ++ show (e :: IOException))
*** Exception: MismatchedParentheses

Methods

toException :: e -> SomeException #

fromException :: SomeException -> Maybe e #

displayException :: e -> String #

Render this exception value in a human-friendly manner.

Default implementation: show.

Since: 4.8.0.0

Instances

Exception Void 
Exception PatternMatchFail 
Exception RecSelError 
Exception RecConError 
Exception RecUpdError 
Exception NoMethodError 
Exception TypeError 
Exception NonTermination 
Exception NestedAtomically 
Exception BlockedIndefinitelyOnMVar 
Exception BlockedIndefinitelyOnSTM 
Exception Deadlock 
Exception AllocationLimitExceeded 
Exception AssertionFailed 
Exception SomeAsyncException 
Exception AsyncException 
Exception ArrayException 
Exception ExitCode 
Exception IOException 
Exception ErrorCall 
Exception ArithException 
Exception SomeException 
Exception UnicodeException 

class Typeable k a #

The class Typeable allows a concrete representation of a type to be calculated.

Minimal complete definition

typeRep#

data SomeException :: * #

The SomeException type is the root of the exception type hierarchy. When an exception of type e is thrown, behind the scenes it is encapsulated in a SomeException.

data IOException :: * #

Exceptions that occur in the IO monad. An IOException records a more specific error type, a descriptive string and maybe the handle that was used when the error was flagged.

Files

type FilePath = String #

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.

(</>) :: FilePath -> FilePath -> FilePath infixr 5 #

Combine two paths with a path separator. If the second path starts with a path separator or a drive letter, then it returns the second. The intention is that readFile (dir </> file) will access the same file as setCurrentDirectory dir; readFile file.

Posix:   "/directory" </> "file.ext" == "/directory/file.ext"
Windows: "/directory" </> "file.ext" == "/directory\\file.ext"
         "directory" </> "/file.ext" == "/file.ext"
Valid x => (takeDirectory x </> takeFileName x) `equalFilePath` x

Combined:

Posix:   "/" </> "test" == "/test"
Posix:   "home" </> "bob" == "home/bob"
Posix:   "x:" </> "foo" == "x:/foo"
Windows: "C:\\foo" </> "bar" == "C:\\foo\\bar"
Windows: "home" </> "bob" == "home\\bob"

Not combined:

Posix:   "home" </> "/bob" == "/bob"
Windows: "home" </> "C:\\bob" == "C:\\bob"

Not combined (tricky):

On Windows, if a filepath starts with a single slash, it is relative to the root of the current drive. In [1], this is (confusingly) referred to as an absolute path. The current behavior of </> is to never combine these forms.

Windows: "home" </> "/bob" == "/bob"
Windows: "home" </> "\\bob" == "\\bob"
Windows: "C:\\home" </> "\\bob" == "\\bob"

On Windows, from [1]: "If a file name begins with only a disk designator but not the backslash after the colon, it is interpreted as a relative path to the current directory on the drive with the specified letter." The current behavior of </> is to never combine these forms.

Windows: "D:\\foo" </> "C:bar" == "C:bar"
Windows: "C:\\foo" </> "C:bar" == "C:bar"

(<.>) :: FilePath -> String -> FilePath infixr 7 #

Add an extension, even if there is already one there, equivalent to addExtension.

"/directory/path" <.> "ext" == "/directory/path.ext"
"/directory/path" <.> ".ext" == "/directory/path.ext"

Strings

type String = [Char] #

A String is a list of characters. String constants in Haskell are values of type String.

Hashing

hash :: Hashable a => a -> Int #

Like hashWithSalt, but no salt is used. The default implementation uses hashWithSalt with some default salt. Instances might want to implement this method to provide a more efficient implementation than the default implementation.

hashWithSalt :: Hashable a => Int -> a -> Int #

Return a hash value for the argument, using the given salt.

The general contract of hashWithSalt is:

  • If two values are equal according to the == method, then applying the hashWithSalt method on each of the two values must produce the same integer result if the same salt is used in each case.
  • It is not required that if two values are unequal according to the == method, then applying the hashWithSalt method on each of the two values must produce distinct integer results. However, the programmer should be aware that producing distinct integer results for unequal values may improve the performance of hashing-based data structures.
  • This method can be used to compute different hash values for the same input by providing a different salt in each application of the method. This implies that any instance that defines hashWithSalt must make use of the salt in its implementation.