AOPPrelude

Documentation

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9

const :: a -> b -> a

id :: a -> a

outl :: (a, b) -> a

outr :: (a, b) -> b

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

assocl :: (a, (b, c)) -> ((a, b), c)

assocr :: ((a, b), c) -> (a, (b, c))

dupl :: (a, (b, c)) -> ((a, b), (a, c))

dupr :: ((a, b), c) -> ((a, c), (b, c))

pair :: (a -> b, a -> c) -> a -> (b, c)

cross :: (a -> c, b -> d) -> (a, b) -> (c, d)

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

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

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

false :: a -> Bool

true :: a -> Bool

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

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

not :: Bool -> Bool

otherwise :: Bool

leq :: Ord a => (a, a) -> Bool

less :: Ord a => (a, a) -> Bool

eql :: Ord a => (a, a) -> Bool

neq :: Ord a => (a, a) -> Bool

gtr :: Ord a => (a, a) -> Bool

geq :: Ord a => (a, a) -> Bool

meet :: (a -> Bool, a -> Bool) -> a -> Bool

join :: (a -> Bool, a -> Bool) -> a -> Bool

wok :: ((b, a) -> c) -> (a, b) -> c

zero :: Num a => t -> a

succ :: Num a => a -> a

pred :: Num a => a -> a

plus :: Num a => (a, a) -> a

minus :: Num a => (a, a) -> a

times :: Num a => (a, a) -> a

divide :: Fractional a => (a, a) -> a

negative :: (Ord a, Num a) => a -> Bool

positive :: (Ord a, Num a) => a -> Bool

(++) :: [a] -> [a] -> [a] infixr 5

null :: [a] -> Bool

nil :: t -> [a]

wrap :: a -> [a]

cons :: (a, [a]) -> [a]

cat :: ([a], [a]) -> [a]

concat :: [[a]] -> [a]

snoc :: ([a], a) -> [a]

head :: [a] -> a

tail :: [a] -> [a]

split :: [a] -> (a, [a])

last :: [a] -> a

init :: [a] -> [a]

inits :: [a] -> [[a]]

tails :: [a] -> [[a]]

splits :: [a] -> [([a], [a])]

cpp :: ([a], [b]) -> [(a, b)]

cpl :: ([a], b) -> [(a, b)]

cpr :: (a, [b]) -> [(a, b)]

cplist :: [[a]] -> [[a]]

minlist :: ((a, a) -> Bool) -> [a] -> a

bmin :: ((a, a) -> Bool) -> (a, a) -> a

maxlist :: ((a, a) -> Bool) -> [a] -> a

bmax :: ((a, a) -> Bool) -> (a, a) -> a

thinlist :: ((a, a) -> Bool) -> [a] -> [a]

length :: Num a => [t] -> a

sum :: Num a => [a] -> a

trans :: [[a]] -> [[a]]

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

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

catalist :: (b, (a, b) -> b) -> [a] -> b

cata1list :: (a -> b, (a, b) -> b) -> [a] -> b

cata2list :: ((a, a) -> b, (a, b) -> b) -> [a] -> b

loop :: ((a, b) -> a) -> (a, [b]) -> a

merge :: ((a, a) -> Bool) -> ([a], [a]) -> [a]

zip :: ([a], [b]) -> [(a, b)]

unzip :: [(a, b)] -> ([a], [b])

words :: String -> [String]

lines :: String -> [String]

unwords :: [String] -> String

unlines :: [String] -> String

ord :: Char -> Int

The fromEnum method restricted to the type Char.

chr :: Int -> Char

The toEnum method restricted to the type Char.

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

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

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

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

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

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

(+) :: Num a => a -> a -> a infixl 6

(-) :: Num a => a -> a -> a infixl 6

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

Fractional division.

div :: Integral a => a -> a -> a infixl 7

integer division truncated toward negative infinity

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

mod :: Integral a => a -> a -> a infixl 7

integer modulus, satisfying

(x `div` y)*y + (x `mod` y) == x

WARNING: This function is partial (because it throws when 0 is passed as the divisor) for all the integer types in base.

(*) :: Num a => a -> a -> a infixl 7

negate :: Num a => a -> a

Unary negation.

primPrint :: Show a => a -> IO ()

strict :: (a -> b) -> a -> b

error :: forall (r :: RuntimeRep) (a :: TYPE r). HasCallStack => [Char] -> a

error stops execution and displays an error message.

show :: Show a => a -> String

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

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

type String = [Char]

String is an alias for a list of characters.

String constants in Haskell are values of type String. That means if you write a string literal like "hello world", it will have the type [Char], which is the same as String.

Note: You can ask the compiler to automatically infer different types with the -XOverloadedStrings language extension, for example "hello world" :: Text. See IsString for more information.

Because String is just a list of characters, you can use normal list functions to do basic string manipulation. See Data.List for operations on lists.

Performance considerations

[Char] is a relatively memory-inefficient type. It is a linked list of boxed word-size characters, internally it looks something like:

╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭─────┬───┬──╮  ╭────╮
│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ (:) │   │ ─┼─>│ [] │
╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰─────┴─┼─┴──╯  ╰────╯
        v               v               v
       'a'             'b'             'c'

The String "abc" will use 5*3+1 = 16 (in general 5n+1) words of space in memory.

Furthermore, operations like (++) (string concatenation) are O(n) (in the left argument).

For historical reasons, the base library uses String in a lot of places for the conceptual simplicity, but library code dealing with user-data should use the text package for Unicode text, or the the bytestring package for binary data.

class Eq a

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, instances are encouraged to follow these properties:

Reflexivity

x == x = True

Symmetry

x == y = y == x

Transitivity

if x == y && y == z = True, then x == z = True

Extensionality

if x == y = True and f is a 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

(==) | (/=)

Instances

Eq Void

Since: base-4.8.0.0

Defined in GHC.Base

Methods

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

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

Eq SrcLoc

Since: base-4.9.0.0

Defined in GHC.Stack.Types

Methods

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

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

Eq Module

Defined in GHC.Classes

Methods

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

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

Eq Ordering

Defined in GHC.Classes

Methods

(==) :: Ordering -> Ordering -> Bool

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

Eq TrName

Defined in GHC.Classes

Methods

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

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

Eq TyCon

Defined in GHC.Classes

Methods

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

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

Eq Integer

Defined in GHC.Num.Integer

Methods

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

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

Eq Natural

Defined in GHC.Num.Natural

Methods

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

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

Eq ()

Defined in GHC.Classes

Methods

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

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

Eq Bool

Defined in GHC.Classes

Methods

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

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

Eq Char

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

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 extensionality:

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

Defined in GHC.Classes

Methods

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

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

Eq Int

Defined in GHC.Classes

Methods

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

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

Eq Word

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

Eq a => Eq (Ratio a)

Since: base-2.1

Defined in GHC.Real

Methods

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

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

Eq a => Eq (a)

Defined in GHC.Classes

Methods

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

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

Eq a => Eq [a]

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

class Eq a => Ord a

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.

Ord, as defined by the Haskell report, implements a total order and has the following properties:

Comparability

x <= y || y <= x = True

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

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

Note that (7.) and (8.) do not require min and max to return either of their arguments. The result is merely required to equal one of the arguments in terms of (==).

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

Minimal complete definition

compare | (<=)

Instances

Ord Void

Since: base-4.8.0.0

Defined in GHC.Base

Methods

compare :: Void -> Void -> Ordering

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

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

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

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

max :: Void -> Void -> Void

min :: Void -> Void -> Void

Ord Ordering

Defined in GHC.Classes

Methods

compare :: Ordering -> Ordering -> Ordering

(<) :: Ordering -> Ordering -> Bool

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

(>) :: Ordering -> Ordering -> Bool

(>=) :: Ordering -> Ordering -> Bool

max :: Ordering -> Ordering -> Ordering

min :: Ordering -> Ordering -> Ordering

Ord TyCon

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 Integer

Defined in GHC.Num.Integer

Methods

compare :: Integer -> Integer -> Ordering

(<) :: Integer -> Integer -> Bool

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

(>) :: Integer -> Integer -> Bool

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

max :: Integer -> Integer -> Integer

min :: Integer -> Integer -> Integer

Ord Natural

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering

(<) :: Natural -> Natural -> Bool

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

(>) :: Natural -> Natural -> Bool

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

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

Ord ()

Defined in GHC.Classes

Methods

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

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

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

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

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

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

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

Ord Bool

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

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

Defined in GHC.Classes

Methods

compare :: Double -> Double -> Ordering

(<) :: Double -> Double -> Bool

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

(>) :: Double -> Double -> Bool

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

max :: Double -> Double -> Double

min :: Double -> Double -> Double

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

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

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 Word

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 a => Ord (NonEmpty a)

Since: base-4.9.0.0

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

Integral a => Ord (Ratio a)

Since: base-2.0.1

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 (a)

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 [a]

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 b) => Ord (a, b)

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)

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 Num a

Basic numeric class.

The Haskell Report defines no laws for Num. However, (+) and (*) are customarily expected to define a ring and have the following properties:

Associativity of (+)

(x + y) + z = x + (y + z)

Commutativity of (+)

x + y = y + x

fromInteger 0 is the additive identity

x + fromInteger 0 = x

negate gives the additive inverse

x + negate x = fromInteger 0

Associativity of (*)

(x * y) * z = x * (y * z)

fromInteger 1 is the multiplicative identity

x * fromInteger 1 = x and fromInteger 1 * x = x

Distributivity of (*) with respect to (+)

a * (b + c) = (a * b) + (a * c) and (b + c) * a = (b * a) + (c * a)

Coherence with toInteger

if the type also implements Integral, then fromInteger is a left inverse for toInteger, i.e. fromInteger (toInteger i) == i

Note that it isn't customarily expected that a type instance of both Num and Ord implement an ordered ring. Indeed, in base only Integer and Rational do.

Minimal complete definition

(+), (*), abs, signum, fromInteger, (negate | (-))

Instances

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Integer -> Integer -> Integer

(-) :: Integer -> Integer -> Integer

(*) :: Integer -> Integer -> Integer

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

Num Natural

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Num Int

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Int -> Int -> Int

(-) :: Int -> Int -> Int

(*) :: Int -> Int -> Int

negate :: Int -> Int

abs :: Int -> Int

signum :: Int -> Int

fromInteger :: Integer -> Int

Num Word

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Word -> Word -> Word

(-) :: Word -> Word -> Word

(*) :: Word -> Word -> Word

negate :: Word -> Word

abs :: Word -> Word

signum :: Word -> Word

fromInteger :: Integer -> Word

Integral a => Num (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

(+) :: Ratio a -> Ratio a -> Ratio a

(-) :: Ratio a -> Ratio a -> Ratio a

(*) :: Ratio a -> Ratio a -> Ratio a

negate :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

signum :: Ratio a -> Ratio a

fromInteger :: Integer -> Ratio a

class Num a => Fractional a

Fractional numbers, supporting real division.

The Haskell Report defines no laws for Fractional. However, (+) and (*) are customarily expected to define a division ring and have the following properties:

recip gives the multiplicative inverse

x * recip x = recip x * x = fromInteger 1

Totality of toRational

toRational is total

Coherence with toRational

if the type also implements Real, then fromRational is a left inverse for toRational, i.e. fromRational (toRational i) = i

Note that it isn't customarily expected that a type instance of Fractional implement a field. However, all instances in base do.

Minimal complete definition

fromRational, (recip | (/))

Instances

Integral a => Fractional (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

(/) :: Ratio a -> Ratio a -> Ratio a

recip :: Ratio a -> Ratio a

fromRational :: Rational -> Ratio a

class Show a

Conversion of values to readable Strings.

Derived instances of Show have the following properties, which are compatible with derived instances of Read:

• The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used.
• If the constructor is defined to be an infix operator, then showsPrec will produce infix applications of the constructor.
• the representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d (associativity is ignored). Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression.
• If the constructor is defined using record syntax, then show will produce the record-syntax form, with the fields given in the same order as the original declaration.

For example, given the declarations

infixr 5 :^:
data Tree a =  Leaf a  |  Tree a :^: Tree a

the derived instance of Show is equivalent to

instance (Show a) => Show (Tree a) where

       showsPrec d (Leaf m) = showParen (d > app_prec) $
            showString "Leaf " . showsPrec (app_prec+1) m
         where app_prec = 10

       showsPrec d (u :^: v) = showParen (d > up_prec) $
            showsPrec (up_prec+1) u .
            showString " :^: "      .
            showsPrec (up_prec+1) v
         where up_prec = 5

Note that right-associativity of :^: is ignored. For example,

• show (Leaf 1 :^: Leaf 2 :^: Leaf 3) produces the string "Leaf 1 :^: (Leaf 2 :^: Leaf 3)".

Minimal complete definition

showsPrec | show

Instances

Show Void

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Void -> ShowS

show :: Void -> String

showList :: [Void] -> ShowS

Show FractionalExponentBase

Defined in GHC.Real

Methods

showsPrec :: Int -> FractionalExponentBase -> ShowS

show :: FractionalExponentBase -> String

showList :: [FractionalExponentBase] -> ShowS

Show CallStack

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> CallStack -> ShowS

show :: CallStack -> String

showList :: [CallStack] -> ShowS

Show SrcLoc

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> SrcLoc -> ShowS

show :: SrcLoc -> String

showList :: [SrcLoc] -> ShowS

Show KindRep

Defined in GHC.Show

Methods

showsPrec :: Int -> KindRep -> ShowS

show :: KindRep -> String

showList :: [KindRep] -> ShowS

Show Module

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Module -> ShowS

show :: Module -> String

showList :: [Module] -> ShowS

Show Ordering

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Ordering -> ShowS

show :: Ordering -> String

showList :: [Ordering] -> ShowS

Show TrName

Since: base-4.9.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> TrName -> ShowS

show :: TrName -> String

showList :: [TrName] -> ShowS

Show TyCon

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> TyCon -> ShowS

show :: TyCon -> String

showList :: [TyCon] -> ShowS

Show TypeLitSort

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> TypeLitSort -> ShowS

show :: TypeLitSort -> String

showList :: [TypeLitSort] -> ShowS

Show Integer

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Integer -> ShowS

show :: Integer -> String

showList :: [Integer] -> ShowS

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Show ()

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> () -> ShowS

show :: () -> String

showList :: [()] -> ShowS

Show Bool

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Bool -> ShowS

show :: Bool -> String

showList :: [Bool] -> ShowS

Show Char

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Char -> ShowS

show :: Char -> String

showList :: [Char] -> ShowS

Show Int

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Int -> ShowS

show :: Int -> String

showList :: [Int] -> ShowS

Show Levity

Since: base-4.15.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Levity -> ShowS

show :: Levity -> String

showList :: [Levity] -> ShowS

Show RuntimeRep

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> RuntimeRep -> ShowS

show :: RuntimeRep -> String

showList :: [RuntimeRep] -> ShowS

Show VecCount

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> VecCount -> ShowS

show :: VecCount -> String

showList :: [VecCount] -> ShowS

Show VecElem

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> VecElem -> ShowS

show :: VecElem -> String

showList :: [VecElem] -> ShowS

Show Word

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Word -> ShowS

show :: Word -> String

showList :: [Word] -> ShowS

Show a => Show (NonEmpty a)

Since: base-4.11.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> NonEmpty a -> ShowS

show :: NonEmpty a -> String

showList :: [NonEmpty a] -> ShowS

Show a => Show (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

showsPrec :: Int -> Ratio a -> ShowS

show :: Ratio a -> String

showList :: [Ratio a] -> ShowS

Show a => Show (Maybe a)

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Maybe a -> ShowS

show :: Maybe a -> String

showList :: [Maybe a] -> ShowS

Show a => Show (a)

Since: base-4.15

Defined in GHC.Show

Methods

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

show :: (a) -> String

showList :: [(a)] -> ShowS

Show a => Show [a]

Since: base-2.1

Defined in GHC.Show

Methods

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

show :: [a] -> String

showList :: [[a]] -> ShowS

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

Since: base-2.1

Defined in GHC.Show

Methods

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

show :: (a, b) -> String

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

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

Since: base-2.1

Defined in GHC.Show

Methods

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

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

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

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

Since: base-2.1

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

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

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

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

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

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

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

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

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

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

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

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

data Integer

Arbitrary precision integers. In contrast with fixed-size integral types such as Int, the Integer type represents the entire infinite range of integers.

Integers are stored in a kind of sign-magnitude form, hence do not expect two's complement form when using bit operations.

If the value is small (fit into an Int), IS constructor is used. Otherwise Integer and IN constructors are used to store a BigNat representing respectively the positive or the negative value magnitude.

Invariant: Integer and IN are used iff value doesn't fit in IS

Instances

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

(+) :: Integer -> Integer -> Integer

(-) :: Integer -> Integer -> Integer

(*) :: Integer -> Integer -> Integer

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

Integral Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

quot :: Integer -> Integer -> Integer

rem :: Integer -> Integer -> Integer

div :: Integer -> Integer -> Integer

mod :: Integer -> Integer -> Integer

quotRem :: Integer -> Integer -> (Integer, Integer)

divMod :: Integer -> Integer -> (Integer, Integer)

toInteger :: Integer -> Integer

Real Integer

Since: base-2.0.1

Defined in GHC.Real

Methods

toRational :: Integer -> Rational

Show Integer

Since: base-2.1

Defined in GHC.Show

Methods

showsPrec :: Int -> Integer -> ShowS

show :: Integer -> String

showList :: [Integer] -> ShowS

Eq Integer

Defined in GHC.Num.Integer

Methods

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

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

Ord Integer

Defined in GHC.Num.Integer

Methods

compare :: Integer -> Integer -> Ordering

(<) :: Integer -> Integer -> Bool

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

(>) :: Integer -> Integer -> Bool

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

max :: Integer -> Integer -> Integer

min :: Integer -> Integer -> Integer

data Natural

Natural number

Invariant: numbers <= 0xffffffffffffffff use the NS constructor

Instances

Num Natural

Note that Natural's Num instance isn't a ring: no element but 0 has an additive inverse. It is a semiring though.

Since: base-4.8.0.0

Defined in GHC.Num

Methods

(+) :: Natural -> Natural -> Natural

(-) :: Natural -> Natural -> Natural

(*) :: Natural -> Natural -> Natural

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Integral Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

quot :: Natural -> Natural -> Natural

rem :: Natural -> Natural -> Natural

div :: Natural -> Natural -> Natural

mod :: Natural -> Natural -> Natural

quotRem :: Natural -> Natural -> (Natural, Natural)

divMod :: Natural -> Natural -> (Natural, Natural)

toInteger :: Natural -> Integer

Real Natural

Since: base-4.8.0.0

Defined in GHC.Real

Methods

toRational :: Natural -> Rational

Show Natural

Since: base-4.8.0.0

Defined in GHC.Show

Methods

showsPrec :: Int -> Natural -> ShowS

show :: Natural -> String

showList :: [Natural] -> ShowS

Eq Natural

Defined in GHC.Num.Natural

Methods

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

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

Ord Natural

Defined in GHC.Num.Natural

Methods

compare :: Natural -> Natural -> Ordering

(<) :: Natural -> Natural -> Bool

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

(>) :: Natural -> Natural -> Bool

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

max :: Natural -> Natural -> Natural

min :: Natural -> Natural -> Natural

module GHC.Types