loc-0.1.3.4: Types representing line and column positions and ranges in text files.

Safe HaskellSafe
LanguageHaskell2010

Data.Loc.Internal.Prelude

Synopsis

Documentation

print :: Show a => a -> IO () #

The print function outputs a value of any printable type to the standard output device. Printable types are those that are instances of class Show; print converts values to strings for output using the show operation and adds a newline.

For example, a program to print the first 20 integers and their powers of 2 could be written as:

main = print ([(n, 2^n) | n <- [0..19]])

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

Extract the first component of a pair.

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

Extract the second component of a pair.

otherwise :: Bool #

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

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

($) :: (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.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed

fromIntegral :: (Integral a, Num b) => a -> b #

general coercion from integral types

guard :: Alternative f => Bool -> f () #

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

Expand

Common uses of guard include conditionally signaling an error in an error monad and conditionally rejecting the current choice in an Alternative-based parser.

As an example of signaling an error in the error monad Maybe, consider a safe division function safeDiv x y that returns Nothing when the denominator y is zero and Just (x `div` y) otherwise. For example:

>>> safeDiv 4 0
Nothing
>>> safeDiv 4 2
Just 2

A definition of safeDiv using guards, but not guard:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0    = Just (x `div` y)
            | otherwise = Nothing

A definition of safeDiv using guard and Monad do-notation:

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y = do
  guard (y /= 0)
  return (x `div` y)

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..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example:

  • enumFrom 4 :: [Integer] = [4,5,6,7,...]
  • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

enumFromThen :: a -> a -> [a] #

Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example:

  • enumFromThen 4 6 :: [Integer] = [4,6,8,10...]
  • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

enumFromTo :: a -> a -> [a] #

Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example:

  • enumFromTo 6 10 :: [Int] = [6,7,8,9,10]
  • enumFromTo 42 1 :: [Integer] = []

enumFromThenTo :: a -> a -> a -> [a] #

Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example:

  • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]
  • enumFromThenTo 6 8 2 :: [Int] = []
Instances
Enum Bool

Since: base-2.1

Instance details

Defined in GHC.Enum

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

Since: base-2.1

Instance details

Defined in GHC.Enum

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

Since: base-2.1

Instance details

Defined in GHC.Enum

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 Integer

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Enum Ordering

Since: base-2.1

Instance details

Defined in GHC.Enum

Enum Word

Since: base-2.1

Instance details

Defined in GHC.Enum

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

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Enum Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Enum VecCount

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum VecElem

Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Enum ()

Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: () -> () #

pred :: () -> () #

toEnum :: Int -> () #

fromEnum :: () -> Int #

enumFrom :: () -> [()] #

enumFromThen :: () -> () -> [()] #

enumFromTo :: () -> () -> [()] #

enumFromThenTo :: () -> () -> () -> [()] #

Enum GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Enum Column Source # 
Instance details

Defined in Data.Loc.Pos

Enum Line Source # 
Instance details

Defined in Data.Loc.Pos

Methods

succ :: Line -> Line #

pred :: Line -> Line #

toEnum :: Int -> Line #

fromEnum :: Line -> Int #

enumFrom :: Line -> [Line] #

enumFromThen :: Line -> Line -> [Line] #

enumFromTo :: Line -> Line -> [Line] #

enumFromThenTo :: Line -> Line -> Line -> [Line] #

Enum Pos Source #
>>> toEnum 3 :: Pos
3
>>> toEnum 0 :: Pos
*** Exception: arithmetic underflow
>>> fromEnum (3 :: Pos)
3
Instance details

Defined in Data.Loc.Pos

Methods

succ :: Pos -> Pos #

pred :: Pos -> Pos #

toEnum :: Int -> Pos #

fromEnum :: Pos -> Int #

enumFrom :: Pos -> [Pos] #

enumFromThen :: Pos -> Pos -> [Pos] #

enumFromTo :: Pos -> Pos -> [Pos] #

enumFromThenTo :: Pos -> Pos -> Pos -> [Pos] #

Integral a => Enum (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

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 (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Enum (f a) => Enum (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

succ :: Ap f a -> Ap f a #

pred :: Ap f a -> Ap f a #

toEnum :: Int -> Ap f a #

fromEnum :: Ap f a -> Int #

enumFrom :: Ap f a -> [Ap f a] #

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] #

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] #

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] #

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.

The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties:

Reflexivity
x == x = True
Symmetry
x == y = y == x
Transitivity
if x == y && y == z = True, then x == z = True
Substitutivity
if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True
Negation
x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances
Eq Bool 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Char 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Double

Note that due to the presence of NaN, Double's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Double)
False

Also note that Double's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Double)
True
>>> recip 0 == recip (-0 :: Double)
False
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Float

Note that due to the presence of NaN, Float's Eq instance does not satisfy reflexivity.

>>> 0/0 == (0/0 :: Float)
False

Also note that Float's Eq instance does not satisfy substitutivity:

>>> 0 == (-0 :: Float)
True
>>> recip 0 == recip (-0 :: Float)
False
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Int 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Integer 
Instance details

Defined in GHC.Integer.Type

Methods

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

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

Eq Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Methods

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

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

Eq Ordering 
Instance details

Defined in GHC.Classes

Eq Word 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq SomeTypeRep 
Instance details

Defined in Data.Typeable.Internal

Eq () 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq TyCon 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Module 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq TrName 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq BigNat 
Instance details

Defined in GHC.Integer.Type

Methods

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

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

Eq ErrorCall

Since: base-4.7.0.0

Instance details

Defined in GHC.Exception

Eq ArithException

Since: base-3.0

Instance details

Defined in GHC.Exception.Type

Eq Lexeme

Since: base-2.1

Instance details

Defined in Text.Read.Lex

Methods

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

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

Eq Number

Since: base-4.6.0.0

Instance details

Defined in Text.Read.Lex

Methods

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

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

Eq GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Eq SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Stack.Types

Methods

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

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

Eq LocException Source # 
Instance details

Defined in Data.Loc.Exception

Eq Column Source # 
Instance details

Defined in Data.Loc.Pos

Methods

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

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

Eq Line Source # 
Instance details

Defined in Data.Loc.Pos

Methods

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

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

Eq Pos Source # 
Instance details

Defined in Data.Loc.Pos

Methods

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

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

Eq Loc Source # 
Instance details

Defined in Data.Loc.Loc

Methods

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

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

Eq Span Source # 
Instance details

Defined in Data.Loc.Span

Methods

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

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

Eq Area Source # 
Instance details

Defined in Data.Loc.Area

Methods

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

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

Eq a => Eq [a] 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

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

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

Eq a => Eq (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

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

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

Eq a => Eq (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Eq a => Eq (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

Eq a => Eq (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Down a)

Since: base-4.6.0.0

Instance details

Defined in Data.Ord

Methods

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

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

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Eq a => Eq (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

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

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

Eq a => Eq (OneToTwo a) Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Methods

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

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

Eq a => Eq (ZeroToTwo a) Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

Methods

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

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

Eq (TypeRep a)

Since: base-2.1

Instance details

Defined in Data.Typeable.Internal

Methods

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

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

(Eq a, Eq b) => Eq (a, b) 
Instance details

Defined in GHC.Classes

Methods

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

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

(Ix i, Eq e) => Eq (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: Array i e -> Array i e -> Bool #

(/=) :: Array i e -> Array i e -> Bool #

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

(Eq k, Eq a) => Eq (Map k a) 
Instance details

Defined in Data.Map.Internal

Methods

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

(/=) :: Map k a -> Map k a -> Bool #

(Eq a, Eq b, Eq c) => Eq (a, b, c) 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq (STArray s i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: STArray s i e -> STArray s i e -> Bool #

(/=) :: STArray s i e -> STArray s i e -> Bool #

Eq (f a) => Eq (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool #

(/=) :: Ap f a -> Ap f a -> Bool #

(Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) 
Instance details

Defined in GHC.Classes

Methods

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

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

(Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) 
Instance details

Defined in GHC.Classes

Methods

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

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

(Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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) 
Instance details

Defined in GHC.Classes

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 #

sqrt :: Floating a => a -> a #

(/) :: Fractional a => a -> a -> a infixl 7 #

fractional division

class (Real a, Enum a) => Integral a where #

Integral numbers, supporting integer division.

The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given suitable Euclidean functions f and g:

  • x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y
  • x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y

An example of a suitable Euclidean function, for Integer's instance, is abs.

Minimal complete definition

quotRem, toInteger

Methods

div :: a -> a -> a infixl 7 #

integer division truncated toward negative infinity

quotRem :: a -> a -> (a, a) #

simultaneous quot and rem

toInteger :: a -> Integer #

conversion to Integer

Instances
Integral Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

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 Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Integral Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Integral Word

Since: base-2.1

Instance details

Defined in GHC.Real

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

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Integral Word64

Since: base-2.1

Instance details

Defined in GHC.Word

class Applicative m => Monad (m :: Type -> Type) where #

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following 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 []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> [a] #

fail :: String -> [a] #

Monad Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> Maybe a #

fail :: String -> Maybe a #

Monad IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: IO a -> (a -> IO b) -> IO b #

(>>) :: IO a -> IO b -> IO b #

return :: a -> IO a #

fail :: String -> IO a #

Monad Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Min a #

fail :: String -> Min a #

Monad Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Max a #

fail :: String -> Max a #

Monad First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Monad Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Monad Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

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

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

return :: a -> Option a #

fail :: String -> Option a #

Monad First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Monad Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Monad Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

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

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

return :: a -> Down a #

fail :: String -> Down a #

Monad ReadPrec

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

(>>=) :: ReadPrec a -> (a -> ReadPrec b) -> ReadPrec b #

(>>) :: ReadPrec a -> ReadPrec b -> ReadPrec b #

return :: a -> ReadPrec a #

fail :: String -> ReadPrec a #

Monad ReadP

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b #

(>>) :: ReadP a -> ReadP b -> ReadP b #

return :: a -> ReadP a #

fail :: String -> ReadP a #

Monad NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

return :: a -> NonEmpty a #

fail :: String -> NonEmpty a #

Monad P

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

(>>=) :: P a -> (a -> P b) -> P b #

(>>) :: P a -> P b -> P b #

return :: a -> P a #

fail :: String -> P a #

Monoid a => Monad ((,) a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) #

(>>) :: (a, a0) -> (a, b) -> (a, b) #

return :: a0 -> (a, a0) #

fail :: String -> (a, a0) #

Monad m => Monad (WrappedMonad m)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b #

(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #

return :: a -> WrappedMonad m a #

fail :: String -> WrappedMonad m a #

ArrowApply a => Monad (ArrowMonad a)

Since: base-2.1

Instance details

Defined in Control.Arrow

Methods

(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b #

(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b #

return :: a0 -> ArrowMonad a a0 #

fail :: String -> ArrowMonad a a0 #

Monad f => Monad (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b #

(>>) :: Ap f a -> Ap f b -> Ap f b #

return :: a -> Ap f a #

fail :: String -> Ap f a #

Monad ((->) r :: Type -> Type)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b #

(>>) :: (r -> a) -> (r -> b) -> r -> b #

return :: a -> r -> a #

fail :: String -> r -> a #

(Applicative f, Monad f) => Monad (WhenMissing f k x)

Equivalent to ReaderT k (ReaderT x (MaybeT f)) .

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

(>>=) :: WhenMissing f k x a -> (a -> WhenMissing f k x b) -> WhenMissing f k x b #

(>>) :: WhenMissing f k x a -> WhenMissing f k x b -> WhenMissing f k x b #

return :: a -> WhenMissing f k x a #

fail :: String -> WhenMissing f k x a #

(Monad f, Applicative f) => Monad (WhenMatched f k x y)

Equivalent to ReaderT k (ReaderT x (ReaderT y (MaybeT f)))

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

(>>=) :: WhenMatched f k x y a -> (a -> WhenMatched f k x y b) -> WhenMatched f k x y b #

(>>) :: WhenMatched f k x y a -> WhenMatched f k x y b -> WhenMatched f k x y b #

return :: a -> WhenMatched f k x y a #

fail :: String -> WhenMatched f k x y a #

class Functor (f :: Type -> Type) 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 []

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> [a] -> [b] #

(<$) :: a -> [b] -> [a] #

Functor Maybe

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

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

(<$) :: a -> Maybe b -> Maybe a #

Functor IO

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> IO a -> IO b #

(<$) :: a -> IO b -> IO a #

Functor Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b #

(<$) :: a -> Min b -> Min a #

Functor Max

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b #

(<$) :: a -> Max b -> Max a #

Functor First

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor Option

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Option a -> Option b #

(<$) :: a -> Option b -> Option a #

Functor ZipList

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> ZipList a -> ZipList b #

(<$) :: a -> ZipList b -> ZipList a #

Functor Handler

Since: base-4.6.0.0

Instance details

Defined in Control.Exception

Methods

fmap :: (a -> b) -> Handler a -> Handler b #

(<$) :: a -> Handler b -> Handler a #

Functor First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> First a -> First b #

(<$) :: a -> First b -> First a #

Functor Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b #

(<$) :: a -> Last b -> Last a #

Functor Down

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

fmap :: (a -> b) -> Down a -> Down b #

(<$) :: a -> Down b -> Down a #

Functor ReadPrec

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadPrec

Methods

fmap :: (a -> b) -> ReadPrec a -> ReadPrec b #

(<$) :: a -> ReadPrec b -> ReadPrec a #

Functor ReadP

Since: base-2.1

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> ReadP a -> ReadP b #

(<$) :: a -> ReadP b -> ReadP a #

Functor NonEmpty

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> NonEmpty a -> NonEmpty b #

(<$) :: a -> NonEmpty b -> NonEmpty a #

Functor P

Since: base-4.8.0.0

Instance details

Defined in Text.ParserCombinators.ReadP

Methods

fmap :: (a -> b) -> P a -> P b #

(<$) :: a -> P b -> P a #

Functor OneToTwo Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Methods

fmap :: (a -> b) -> OneToTwo a -> OneToTwo b #

(<$) :: a -> OneToTwo b -> OneToTwo a #

Functor ZeroToTwo Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

Methods

fmap :: (a -> b) -> ZeroToTwo a -> ZeroToTwo b #

(<$) :: a -> ZeroToTwo b -> ZeroToTwo a #

Functor ((,) a)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a0 -> b) -> (a, a0) -> (a, b) #

(<$) :: a0 -> (a, b) -> (a, a0) #

Functor (Array i)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b #

(<$) :: a -> Array i b -> Array i a #

Functor (Arg a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b #

(<$) :: a0 -> Arg a b -> Arg a a0 #

Monad m => Functor (WrappedMonad m)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #

(<$) :: a -> WrappedMonad m b -> WrappedMonad m a #

Arrow a => Functor (ArrowMonad a)

Since: base-4.6.0.0

Instance details

Defined in Control.Arrow

Methods

fmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b #

(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 #

Functor (Map k) 
Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> Map k a -> Map k b #

(<$) :: a -> Map k b -> Map k a #

Arrow a => Functor (WrappedArrow a b)

Since: base-2.1

Instance details

Defined in Control.Applicative

Methods

fmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 #

(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 #

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b #

(<$) :: a -> Ap f b -> Ap f a #

Functor ((->) r :: Type -> Type)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

fmap :: (a -> b) -> (r -> a) -> r -> b #

(<$) :: a -> (r -> b) -> r -> a #

(Applicative f, Monad f) => Functor (WhenMissing f k x)

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMissing f k x a -> WhenMissing f k x b #

(<$) :: a -> WhenMissing f k x b -> WhenMissing f k x a #

Functor f => Functor (WhenMatched f k x y)

Since: containers-0.5.9

Instance details

Defined in Data.Map.Internal

Methods

fmap :: (a -> b) -> WhenMatched f k x y a -> WhenMatched f k x y b #

(<$) :: a -> WhenMatched f k x y b -> WhenMatched f k x y a #

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.

The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

Transitivity
if x <= y && y <= z = True, then x <= z = True
Reflexivity
x <= x = True
Antisymmetry
if x <= y && y <= x = True, then x == y = True

Note that the following operator interactions are expected to hold:

  1. x >= y = y <= x
  2. x < y = x <= y && x /= y
  3. x > y = y < x
  4. x < y = compare x y == LT
  5. x > y = compare x y == GT
  6. x == y = compare x y == EQ
  7. min x y == if x <= y then x else y = True
  8. max x y == if x >= y then x else y = True

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 
Instance details

Defined in GHC.Classes

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 
Instance details

Defined in GHC.Classes

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

Note that due to the presence of NaN, Double's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Double)
False

Also note that, due to the same, Ord's operator interactions are not respected by Double's instance:

>>> (0/0 :: Double) > 1
False
>>> compare (0/0 :: Double) 1
GT
Instance details

Defined in GHC.Classes

Ord Float

Note that due to the presence of NaN, Float's Ord instance does not satisfy reflexivity.

>>> 0/0 <= (0/0 :: Float)
False

Also note that, due to the same, Ord's operator interactions are not respected by Float's instance:

>>> (0/0 :: Float) > 1
False
>>> compare (0/0 :: Float) 1
GT
Instance details

Defined in GHC.Classes

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 
Instance details

Defined in GHC.Classes

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 Integer 
Instance details

Defined in GHC.Integer.Type

Ord Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Natural

Ord Ordering 
Instance details

Defined in GHC.Classes

Ord Word 
Instance details

Defined in GHC.Classes

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

Since: base-2.1

Instance details

Defined in GHC.Word

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

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Ord Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Ord SomeTypeRep 
Instance details

Defined in Data.Typeable.Internal

Ord () 
Instance details

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

Ord TyCon 
Instance details

Defined in GHC.Classes

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 
Instance details

Defined in GHC.Integer.Type

Ord ErrorCall

Since: base-4.7.0.0

Instance details

Defined in GHC.Exception

Ord ArithException

Since: base-3.0

Instance details

Defined in GHC.Exception.Type

Ord GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Ord LocException Source # 
Instance details

Defined in Data.Loc.Exception

Ord Column Source # 
Instance details

Defined in Data.Loc.Pos

Ord Line Source # 
Instance details

Defined in Data.Loc.Pos

Methods

compare :: Line -> Line -> Ordering #

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

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

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

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

max :: Line -> Line -> Line #

min :: Line -> Line -> Line #

Ord Pos Source # 
Instance details

Defined in Data.Loc.Pos

Methods

compare :: Pos -> Pos -> Ordering #

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

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

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

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

max :: Pos -> Pos -> Pos #

min :: Pos -> Pos -> Pos #

Ord Loc Source # 
Instance details

Defined in Data.Loc.Loc

Methods

compare :: Loc -> Loc -> Ordering #

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

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

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

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

max :: Loc -> Loc -> Loc #

min :: Loc -> Loc -> Loc #

Ord Span Source # 
Instance details

Defined in Data.Loc.Span

Methods

compare :: Span -> Span -> Ordering #

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

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

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

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

max :: Span -> Span -> Span #

min :: Span -> Span -> Span #

Ord Area Source # 
Instance details

Defined in Data.Loc.Area

Methods

compare :: Area -> Area -> Ordering #

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

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

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

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

max :: Area -> Area -> Area #

min :: Area -> Area -> Area #

Ord a => Ord [a] 
Instance details

Defined in GHC.Classes

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)

Since: base-2.1

Instance details

Defined in GHC.Maybe

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)

Since: base-2.0.1

Instance details

Defined in GHC.Real

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 a => Ord (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Ord a => Ord (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

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 (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

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)

Since: base-2.1

Instance details

Defined in Data.Monoid

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)

Since: base-4.6.0.0

Instance details

Defined in Data.Ord

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 (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

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 (Set a) 
Instance details

Defined in Data.Set.Internal

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 (OneToTwo a) Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Methods

compare :: OneToTwo a -> OneToTwo a -> Ordering #

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

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

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

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

max :: OneToTwo a -> OneToTwo a -> OneToTwo a #

min :: OneToTwo a -> OneToTwo a -> OneToTwo a #

Ord a => Ord (ZeroToTwo a) Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

Ord (TypeRep a)

Since: base-4.4.0.0

Instance details

Defined in Data.Typeable.Internal

Methods

compare :: TypeRep a -> TypeRep a -> Ordering #

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

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

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

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

max :: TypeRep a -> TypeRep a -> TypeRep a #

min :: TypeRep a -> TypeRep a -> TypeRep a #

(Ord a, Ord b) => Ord (a, b) 
Instance details

Defined in GHC.Classes

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) #

(Ix i, Ord e) => Ord (Array i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

compare :: Array i e -> Array i e -> Ordering #

(<) :: Array i e -> Array i e -> Bool #

(<=) :: Array i e -> Array i e -> Bool #

(>) :: Array i e -> Array i e -> Bool #

(>=) :: Array i e -> Array i e -> Bool #

max :: Array i e -> Array i e -> Array i e #

min :: Array i e -> Array i e -> Array i e #

Ord a => Ord (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 k, Ord v) => Ord (Map k v) 
Instance details

Defined in Data.Map.Internal

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

Defined in GHC.Classes

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 (f a) => Ord (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering #

(<) :: Ap f a -> Ap f a -> Bool #

(<=) :: Ap f a -> Ap f a -> Bool #

(>) :: Ap f a -> Ap f a -> Bool #

(>=) :: Ap f a -> Ap f a -> Bool #

max :: Ap f a -> Ap f a -> Ap f a #

min :: Ap f a -> Ap f a -> Ap f a #

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

Defined in GHC.Classes

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) #

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

class Read a where #

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

Why do both readsPrec and readPrec exist, and why does GHC opt to implement readPrec in derived Read instances instead of readsPrec? The reason is that readsPrec is based on the ReadS type, and although ReadS is mentioned in the Haskell 2010 Report, it is not a very efficient parser data structure.

readPrec, on the other hand, is based on a much more efficient ReadPrec datatype (a.k.a "new-style parsers"), but its definition relies on the use of the RankNTypes language extension. Therefore, readPrec (and its cousin, readListPrec) are marked as GHC-only. Nevertheless, it is recommended to use readPrec instead of readsPrec whenever possible for the efficiency improvements it brings.

As mentioned above, derived Read instances in GHC will implement readPrec instead of readsPrec. The default implementations of readsPrec (and its cousin, readList) will simply use readPrec under the hood. If you are writing a Read instance by hand, it is recommended to write it like so:

instance Read T where
  readPrec     = ...
  readListPrec = readListPrecDefault

Minimal complete definition

readsPrec | readPrec

Methods

readsPrec #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> ReadS a 

attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty.

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

readList :: ReadS [a] #

The method readList is provided to allow the programmer to give a specialised way of parsing lists of values. For example, this is used by the predefined Read instance of the Char type, where values of type String should be are expected to use double quotes, rather than square brackets.

readPrec :: ReadPrec a #

Proposed replacement for readsPrec using new-style parsers (GHC only).

readListPrec :: ReadPrec [a] #

Proposed replacement for readList using new-style parsers (GHC only). The default definition uses readList. Instances that define readPrec should also define readListPrec as readListPrecDefault.

Instances
Read Bool

Since: base-2.1

Instance details

Defined in GHC.Read

Read Char

Since: base-2.1

Instance details

Defined in GHC.Read

Read Double

Since: base-2.1

Instance details

Defined in GHC.Read

Read Float

Since: base-2.1

Instance details

Defined in GHC.Read

Read Int

Since: base-2.1

Instance details

Defined in GHC.Read

Read Integer

Since: base-2.1

Instance details

Defined in GHC.Read

Read Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Read

Read Ordering

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word

Since: base-4.5.0.0

Instance details

Defined in GHC.Read

Read Word8

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word16

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word32

Since: base-2.1

Instance details

Defined in GHC.Read

Read Word64

Since: base-2.1

Instance details

Defined in GHC.Read

Read ()

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS () #

readList :: ReadS [()] #

readPrec :: ReadPrec () #

readListPrec :: ReadPrec [()] #

Read Lexeme

Since: base-2.1

Instance details

Defined in GHC.Read

Read GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Read

Read Column Source # 
Instance details

Defined in Data.Loc.Pos

Read Line Source # 
Instance details

Defined in Data.Loc.Pos

Read Pos Source # 
Instance details

Defined in Data.Loc.Pos

Read Loc Source #

readPrec = locReadPrec

Instance details

Defined in Data.Loc.Loc

Read Span Source #

readPrec = spanReadPrec

Instance details

Defined in Data.Loc.Span

Read Area Source #

readPrec = areaReadPrec

Instance details

Defined in Data.Loc.Area

Read a => Read [a]

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS [a] #

readList :: ReadS [[a]] #

readPrec :: ReadPrec [a] #

readListPrec :: ReadPrec [[a]] #

Read a => Read (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Read

(Integral a, Read a) => Read (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Read

Read a => Read (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read m => Read (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Read a => Read (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Read a => Read (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Read a => Read (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Read a => Read (Down a)

Since: base-4.7.0.0

Instance details

Defined in Data.Ord

Read a => Read (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Read

(Read a, Ord a) => Read (Set a) 
Instance details

Defined in Data.Set.Internal

Read a => Read (OneToTwo a) Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Read a => Read (ZeroToTwo a) Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

(Read a, Read b) => Read (a, b)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

(Read a, Read b) => Read (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Arg a b) #

readList :: ReadS [Arg a b] #

readPrec :: ReadPrec (Arg a b) #

readListPrec :: ReadPrec [Arg a b] #

(Ord k, Read k, Read e) => Read (Map k e) 
Instance details

Defined in Data.Map.Internal

Methods

readsPrec :: Int -> ReadS (Map k e) #

readList :: ReadS [Map k e] #

readPrec :: ReadPrec (Map k e) #

readListPrec :: ReadPrec [Map k e] #

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

Since: base-2.1

Instance details

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (a, b, c) #

readList :: ReadS [(a, b, c)] #

readPrec :: ReadPrec (a, b, c) #

readListPrec :: ReadPrec [(a, b, c)] #

Read (f a) => Read (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

readsPrec :: Int -> ReadS (Ap f a) #

readList :: ReadS [Ap f a] #

readPrec :: ReadPrec (Ap f a) #

readListPrec :: ReadPrec [Ap f a] #

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

Since: base-2.1

Instance details

Defined in GHC.Read

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)] #

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

Since: base-2.1

Instance details

Defined in GHC.Read

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)] #

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

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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)

Since: base-2.1

Instance details

Defined in GHC.Read

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 (Num a, Ord a) => Real a where #

Methods

toRational :: a -> Rational #

the rational equivalent of its real argument with full precision

Instances
Real Int

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Int -> Rational #

Real Integer

Since: base-2.0.1

Instance details

Defined in GHC.Real

Real Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Real

Real Word

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

toRational :: Word -> Rational #

Real Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

toRational :: Word8 -> Rational #

Real Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Real Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Real Column Source # 
Instance details

Defined in Data.Loc.Pos

Real Line Source # 
Instance details

Defined in Data.Loc.Pos

Methods

toRational :: Line -> Rational #

Real Pos Source # 
Instance details

Defined in Data.Loc.Pos

Methods

toRational :: Pos -> Rational #

Integral a => Real (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

toRational :: Ratio a -> Rational #

round :: (RealFrac a, Integral b) => a -> b #

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

class Show a where #

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

Methods

showsPrec #

Arguments

:: Int

the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10.

-> a

the value to be converted to a String

-> ShowS 

Convert a value to a readable String.

showsPrec should satisfy the law

showsPrec d x r ++ s  ==  showsPrec d x (r ++ s)

Derived instances of Read and Show satisfy the following:

That is, readsPrec parses the string produced by showsPrec, and delivers the value that showsPrec started with.

show :: a -> String #

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

showList :: [a] -> ShowS #

The method showList is provided to allow the programmer to give a specialised way of showing lists of values. For example, this is used by the predefined Show instance of the Char type, where values of type String should be shown in double quotes, rather than between square brackets.

Instances
Show Bool

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS #

show :: Bool -> String #

showList :: [Bool] -> ShowS #

Show Char

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Char -> ShowS #

show :: Char -> String #

showList :: [Char] -> ShowS #

Show Int

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS #

show :: Int -> String #

showList :: [Int] -> ShowS #

Show Integer

Since: base-2.1

Instance details

Defined in GHC.Show

Show Natural

Since: base-4.8.0.0

Instance details

Defined in GHC.Show

Show Ordering

Since: base-2.1

Instance details

Defined in GHC.Show

Show Word

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS #

show :: Word -> String #

showList :: [Word] -> ShowS #

Show Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

showsPrec :: Int -> Word8 -> ShowS #

show :: Word8 -> String #

showList :: [Word8] -> ShowS #

Show Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Show Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Show RuntimeRep

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show VecCount

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show VecElem

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show CallStack

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show SomeTypeRep

Since: base-4.10.0.0

Instance details

Defined in Data.Typeable.Internal

Show ()

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> () -> ShowS #

show :: () -> String #

showList :: [()] -> ShowS #

Show TyCon

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> TyCon -> ShowS #

show :: TyCon -> String #

showList :: [TyCon] -> ShowS #

Show Module

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show TrName

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show KindRep 
Instance details

Defined in GHC.Show

Show TypeLitSort

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Show ErrorCall

Since: base-4.0.0.0

Instance details

Defined in GHC.Exception

Show ArithException

Since: base-4.0.0.0

Instance details

Defined in GHC.Exception.Type

Show Lexeme

Since: base-2.1

Instance details

Defined in Text.Read.Lex

Show Number

Since: base-4.6.0.0

Instance details

Defined in Text.Read.Lex

Show GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Show SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Show

Show SomeException

Since: base-3.0

Instance details

Defined in GHC.Exception.Type

Show LocException Source # 
Instance details

Defined in Data.Loc.Exception

Show Column Source # 
Instance details

Defined in Data.Loc.Pos

Show Line Source # 
Instance details

Defined in Data.Loc.Pos

Methods

showsPrec :: Int -> Line -> ShowS #

show :: Line -> String #

showList :: [Line] -> ShowS #

Show Pos Source # 
Instance details

Defined in Data.Loc.Pos

Methods

showsPrec :: Int -> Pos -> ShowS #

show :: Pos -> String #

showList :: [Pos] -> ShowS #

Show Loc Source #

showsPrec = locShowsPrec

Instance details

Defined in Data.Loc.Loc

Methods

showsPrec :: Int -> Loc -> ShowS #

show :: Loc -> String #

showList :: [Loc] -> ShowS #

Show Span Source #

showsPrec = spanShowsPrec

Instance details

Defined in Data.Loc.Span

Methods

showsPrec :: Int -> Span -> ShowS #

show :: Span -> String #

showList :: [Span] -> ShowS #

Show Area Source #

showsPrec = areaShowsPrec

Instance details

Defined in Data.Loc.Area

Methods

showsPrec :: Int -> Area -> ShowS #

show :: Area -> String #

showList :: [Area] -> ShowS #

Show a => Show [a]

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> [a] -> ShowS #

show :: [a] -> String #

showList :: [[a]] -> ShowS #

Show a => Show (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS #

show :: Maybe a -> String #

showList :: [Maybe a] -> ShowS #

Show a => Show (Ratio a)

Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS #

show :: Ratio a -> String #

showList :: [Ratio a] -> ShowS #

Show a => Show (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Min a -> ShowS #

show :: Min a -> String #

showList :: [Min a] -> ShowS #

Show a => Show (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Max a -> ShowS #

show :: Max a -> String #

showList :: [Max a] -> ShowS #

Show a => Show (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Show a => Show (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Option a -> ShowS #

show :: Option a -> String #

showList :: [Option a] -> ShowS #

Show a => Show (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

showsPrec :: Int -> ZipList a -> ShowS #

show :: ZipList a -> String #

showList :: [ZipList a] -> ShowS #

Show a => Show (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS #

show :: First a -> String #

showList :: [First a] -> ShowS #

Show a => Show (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS #

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Show a => Show (Down a)

Since: base-4.7.0.0

Instance details

Defined in Data.Ord

Methods

showsPrec :: Int -> Down a -> ShowS #

show :: Down a -> String #

showList :: [Down a] -> ShowS #

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS #

show :: NonEmpty a -> String #

showList :: [NonEmpty a] -> ShowS #

Show a => Show (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

showsPrec :: Int -> Set a -> ShowS #

show :: Set a -> String #

showList :: [Set a] -> ShowS #

Show a => Show (OneToTwo a) Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Methods

showsPrec :: Int -> OneToTwo a -> ShowS #

show :: OneToTwo a -> String #

showList :: [OneToTwo a] -> ShowS #

Show a => Show (ZeroToTwo a) Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

Show (TypeRep a) 
Instance details

Defined in Data.Typeable.Internal

Methods

showsPrec :: Int -> TypeRep a -> ShowS #

show :: TypeRep a -> String #

showList :: [TypeRep a] -> ShowS #

(Show a, Show b) => Show (a, b)

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b) -> ShowS #

show :: (a, b) -> String #

showList :: [(a, b)] -> ShowS #

(Ix a, Show a, Show b) => Show (Array a b)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

showsPrec :: Int -> Array a b -> ShowS #

show :: Array a b -> String #

showList :: [Array a b] -> ShowS #

(Show a, Show b) => Show (Arg a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS #

show :: Arg a b -> String #

showList :: [Arg a b] -> ShowS #

(Show k, Show a) => Show (Map k a) 
Instance details

Defined in Data.Map.Internal

Methods

showsPrec :: Int -> Map k a -> ShowS #

show :: Map k a -> String #

showList :: [Map k a] -> ShowS #

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

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c) -> ShowS #

show :: (a, b, c) -> String #

showList :: [(a, b, c)] -> ShowS #

Show (f a) => Show (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS #

show :: Ap f a -> String #

showList :: [Ap f a] -> ShowS #

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

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d) -> ShowS #

show :: (a, b, c, d) -> String #

showList :: [(a, b, c, d)] -> ShowS #

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

Since: base-2.1

Instance details

Defined in GHC.Show

Methods

showsPrec :: Int -> (a, b, c, d, e) -> ShowS #

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

showList :: [(a, b, c, d, e)] -> ShowS #

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

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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)

Since: base-2.1

Instance details

Defined in GHC.Show

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 #

pure :: Applicative f => a -> f a #

Lift a value.

(<*>) :: Applicative f => f (a -> b) -> f a -> f b infixl 4 #

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

(*>) :: Applicative f => f a -> f b -> f b infixl 4 #

Sequence actions, discarding the value of the first argument.

(<*) :: Applicative f => f a -> f b -> f a infixl 4 #

Sequence actions, discarding the value of the second argument.

class Foldable (t :: Type -> Type) where #

Data structures that can be folded.

For example, given a data type

data Tree a = Empty | Leaf a | Node (Tree a) a (Tree a)

a suitable instance would be

instance Foldable Tree where
   foldMap f Empty = mempty
   foldMap f (Leaf x) = f x
   foldMap f (Node l k r) = foldMap f l `mappend` f k `mappend` foldMap f r

This is suitable even for abstract types, as the monoid is assumed to satisfy the monoid laws. Alternatively, one could define foldr:

instance Foldable Tree where
   foldr f z Empty = z
   foldr f z (Leaf x) = f x z
   foldr f z (Node l k r) = foldr f (f k (foldr f z r)) l

Foldable instances are expected to satisfy the following laws:

foldr f z t = appEndo (foldMap (Endo . f) t ) z
foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z
fold = foldMap id
length = getSum . foldMap (Sum . const  1)

sum, product, maximum, and minimum should all be essentially equivalent to foldMap forms, such as

sum = getSum . foldMap Sum

but may be less defined.

If the type is also a Functor instance, it should satisfy

foldMap f = fold . fmap f

which implies that

foldMap f . fmap g = foldMap (f . g)

Minimal complete definition

foldMap | foldr

Methods

fold :: Monoid m => t m -> m #

Combine the elements of a structure using a monoid.

foldMap :: Monoid m => (a -> m) -> t a -> m #

Map each element of the structure to a monoid, and combine the results.

foldr :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure.

In the case of lists, foldr, when applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

foldr' :: (a -> b -> b) -> b -> t a -> b #

Right-associative fold of a structure, but with strict application of the operator.

foldl :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure.

In the case of lists, foldl, when applied to a binary operator, a starting value (typically the left-identity of the operator), and a list, reduces the list using the binary operator, from left to right:

foldl f z [x1, x2, ..., xn] == (...((z `f` x1) `f` x2) `f`...) `f` xn

Note that to produce the outermost application of the operator the entire input list must be traversed. This means that foldl' will diverge if given an infinite list.

Also note that if you want an efficient left-fold, you probably want to use foldl' instead of foldl. The reason for this is that latter does not force the "inner" results (e.g. z f x1 in the above example) before applying them to the operator (e.g. to (f x2)). This results in a thunk chain O(n) elements long, which then must be evaluated from the outside-in.

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl f z . toList

foldl' :: (b -> a -> b) -> b -> t a -> b #

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite list to a single, monolithic result (e.g. length).

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl' f z . toList

foldr1 :: (a -> a -> a) -> t a -> a #

A variant of foldr that has no base case, and thus may only be applied to non-empty structures.

foldr1 f = foldr1 f . toList

foldl1 :: (a -> a -> a) -> t a -> a #

A variant of foldl that has no base case, and thus may only be applied to non-empty structures.

foldl1 f = foldl1 f . toList

toList :: t a -> [a] #

List of elements of a structure, from left to right.

null :: t a -> Bool #

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

length :: t a -> Int #

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

elem :: Eq a => a -> t a -> Bool infix 4 #

Does the element occur in the structure?

maximum :: Ord a => t a -> a #

The largest element of a non-empty structure.

minimum :: Ord a => t a -> a #

The least element of a non-empty structure.

sum :: Num a => t a -> a #

The sum function computes the sum of the numbers of a structure.

product :: Num a => t a -> a #

The product function computes the product of the numbers of a structure.

Instances
Foldable []

Since: base-2.1

Instance details

Defined in Data.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

Since: base-2.1

Instance details

Defined in Data.Foldable

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 Par1

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 Min

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

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 ZipList

Since: base-4.9.0.0

Instance details

Defined in Control.Applicative

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 First

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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 Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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 Down

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Down m -> m #

foldMap :: Monoid m => (a -> m) -> Down a -> m #

foldr :: (a -> b -> b) -> b -> Down a -> b #

foldr' :: (a -> b -> b) -> b -> Down a -> b #

foldl :: (b -> a -> b) -> b -> Down a -> b #

foldl' :: (b -> a -> b) -> b -> Down a -> b #

foldr1 :: (a -> a -> a) -> Down a -> a #

foldl1 :: (a -> a -> a) -> Down a -> a #

toList :: Down a -> [a] #

null :: Down a -> Bool #

length :: Down a -> Int #

elem :: Eq a => a -> Down a -> Bool #

maximum :: Ord a => Down a -> a #

minimum :: Ord a => Down a -> a #

sum :: Num a => Down a -> a #

product :: Num a => Down a -> a #

Foldable NonEmpty

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 Set 
Instance details

Defined in Data.Set.Internal

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 OneToTwo Source # 
Instance details

Defined in Data.Loc.List.OneToTwo

Methods

fold :: Monoid m => OneToTwo m -> m #

foldMap :: Monoid m => (a -> m) -> OneToTwo a -> m #

foldr :: (a -> b -> b) -> b -> OneToTwo a -> b #

foldr' :: (a -> b -> b) -> b -> OneToTwo a -> b #

foldl :: (b -> a -> b) -> b -> OneToTwo a -> b #

foldl' :: (b -> a -> b) -> b -> OneToTwo a -> b #

foldr1 :: (a -> a -> a) -> OneToTwo a -> a #

foldl1 :: (a -> a -> a) -> OneToTwo a -> a #

toList :: OneToTwo a -> [a] #

null :: OneToTwo a -> Bool #

length :: OneToTwo a -> Int #

elem :: Eq a => a -> OneToTwo a -> Bool #

maximum :: Ord a => OneToTwo a -> a #

minimum :: Ord a => OneToTwo a -> a #

sum :: Num a => OneToTwo a -> a #

product :: Num a => OneToTwo a -> a #

Foldable ZeroToTwo Source # 
Instance details

Defined in Data.Loc.List.ZeroToTwo

Methods

fold :: Monoid m => ZeroToTwo m -> m #

foldMap :: Monoid m => (a -> m) -> ZeroToTwo a -> m #

foldr :: (a -> b -> b) -> b -> ZeroToTwo a -> b #

foldr' :: (a -> b -> b) -> b -> ZeroToTwo a -> b #

foldl :: (b -> a -> b) -> b -> ZeroToTwo a -> b #

foldl' :: (b -> a -> b) -> b -> ZeroToTwo a -> b #

foldr1 :: (a -> a -> a) -> ZeroToTwo a -> a #

foldl1 :: (a -> a -> a) -> ZeroToTwo a -> a #

toList :: ZeroToTwo a -> [a] #

null :: ZeroToTwo a -> Bool #

length :: ZeroToTwo a -> Int #

elem :: Eq a => a -> ZeroToTwo a -> Bool #

maximum :: Ord a => ZeroToTwo a -> a #

minimum :: Ord a => ZeroToTwo a -> a #

sum :: Num a => ZeroToTwo a -> a #

product :: Num a => ZeroToTwo a -> a #

Foldable (Either a)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Either a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Either a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Either a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Either a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Either a a0 -> a0 #

toList :: Either a a0 -> [a0] #

null :: Either a a0 -> Bool #

length :: Either a a0 -> Int #

elem :: Eq a0 => a0 -> Either a a0 -> Bool #

maximum :: Ord a0 => Either a a0 -> a0 #

minimum :: Ord a0 => Either a a0 -> a0 #

sum :: Num a0 => Either a a0 -> a0 #

product :: Num a0 => Either a a0 -> a0 #

Foldable (V1 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 ((,) a)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (a, m) -> m #

foldMap :: Monoid m => (a0 -> m) -> (a, a0) -> m #

foldr :: (a0 -> b -> b) -> b -> (a, a0) -> b #

foldr' :: (a0 -> b -> b) -> b -> (a, a0) -> b #

foldl :: (b -> a0 -> b) -> b -> (a, a0) -> b #

foldl' :: (b -> a0 -> b) -> b -> (a, a0) -> b #

foldr1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> (a, a0) -> a0 #

toList :: (a, a0) -> [a0] #

null :: (a, a0) -> Bool #

length :: (a, a0) -> Int #

elem :: Eq a0 => a0 -> (a, a0) -> Bool #

maximum :: Ord a0 => (a, a0) -> a0 #

minimum :: Ord a0 => (a, a0) -> a0 #

sum :: Num a0 => (a, a0) -> a0 #

product :: Num a0 => (a, a0) -> a0 #

Foldable (Array i)

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

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)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m #

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m #

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b #

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b #

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b #

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b #

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #

toList :: Arg a a0 -> [a0] #

null :: Arg a a0 -> Bool #

length :: Arg a a0 -> Int #

elem :: Eq a0 => a0 -> Arg a a0 -> Bool #

maximum :: Ord a0 => Arg a a0 -> a0 #

minimum :: Ord a0 => Arg a a0 -> a0 #

sum :: Num a0 => Arg a a0 -> a0 #

product :: Num a0 => Arg a a0 -> a0 #

Foldable (Proxy :: Type -> Type)

Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

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) 
Instance details

Defined in Data.Map.Internal

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 (Rec1 f)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 :: Type -> Type)

Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

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 #

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