hspec-2.6.1: A Testing Framework for Haskell

Safe Haskell | None
Language | Haskell2010

Test.Hspec.Discover

Description

Warning: This module is used by `hspec-discover`. It is not part of the public API and may change at any time.

Synopsis

- type Spec = SpecWith ()
- hspec :: Spec -> IO ()
- class IsFormatter a where
  - toFormatter :: a -> IO Formatter
- hspecWithFormatter :: IsFormatter a => a -> Spec -> IO ()
- postProcessSpec :: FilePath -> Spec -> Spec
- describe :: HasCallStack => String -> SpecWith a -> SpecWith a
- (++) :: [a] -> [a] -> [a]
- seq :: a -> b -> b
- filter :: (a -> Bool) -> [a] -> [a]
- zip :: [a] -> [b] -> [(a, b)]
- print :: Show a => a -> IO ()
- fst :: (a, b) -> a
- snd :: (a, b) -> b
- otherwise :: Bool
- map :: (a -> b) -> [a] -> [b]
- ($) :: (a -> b) -> a -> b
- fromIntegral :: (Integral a, Num b) => a -> b
- realToFrac :: (Real a, Fractional b) => a -> b
- class Bounded a where
  - minBound :: a
  - maxBound :: a
- class Enum a where
  - succ :: a -> a
  - pred :: a -> a
  - toEnum :: Int -> a
  - fromEnum :: a -> Int
  - enumFrom :: a -> [a]
  - enumFromThen :: a -> a -> [a]
  - enumFromTo :: a -> a -> [a]
  - enumFromThenTo :: a -> a -> a -> [a]
- class Eq a where
  - (==) :: a -> a -> Bool
  - (/=) :: a -> a -> Bool
- class Fractional a => Floating a where
  - pi :: a
  - exp :: a -> a
  - log :: a -> a
  - sqrt :: a -> a
  - (**) :: a -> a -> a
  - logBase :: a -> a -> a
  - sin :: a -> a
  - cos :: a -> a
  - tan :: a -> a
  - asin :: a -> a
  - acos :: a -> a
  - atan :: a -> a
  - sinh :: a -> a
  - cosh :: a -> a
  - tanh :: a -> a
  - asinh :: a -> a
  - acosh :: a -> a
  - atanh :: a -> a
- class Num a => Fractional a where
  - (/) :: a -> a -> a
  - recip :: a -> a
  - fromRational :: Rational -> a
- class (Real a, Enum a) => Integral a where
  - quot :: a -> a -> a
  - rem :: a -> a -> a
  - div :: a -> a -> a
  - mod :: a -> a -> a
  - quotRem :: a -> a -> (a, a)
  - divMod :: a -> a -> (a, a)
  - toInteger :: a -> Integer
- class Applicative m => Monad (m :: Type -> Type) where
  - (>>=) :: m a -> (a -> m b) -> m b
  - (>>) :: m a -> m b -> m b
  - return :: a -> m a
  - fail :: String -> m a
- class Functor (f :: Type -> Type) where
  - fmap :: (a -> b) -> f a -> f b
  - (<$) :: a -> f b -> f a
- class Num a where
  - (+) :: a -> a -> a
  - (-) :: a -> a -> a
  - (*) :: a -> a -> a
  - negate :: a -> a
  - abs :: a -> a
  - signum :: a -> a
  - fromInteger :: Integer -> a
- class Eq a => Ord a where
  - compare :: a -> a -> Ordering
  - (<) :: a -> a -> Bool
  - (<=) :: a -> a -> Bool
  - (>) :: a -> a -> Bool
  - (>=) :: a -> a -> Bool
  - max :: a -> a -> a
  - min :: a -> a -> a
- class Read a where
  - readsPrec :: Int -> ReadS a
  - readList :: ReadS [a]
- class (Num a, Ord a) => Real a where
  - toRational :: a -> Rational
- class (RealFrac a, Floating a) => RealFloat a where
  - floatRadix :: a -> Integer
  - floatDigits :: a -> Int
  - floatRange :: a -> (Int, Int)
  - decodeFloat :: a -> (Integer, Int)
  - encodeFloat :: Integer -> Int -> a
  - exponent :: a -> Int
  - significand :: a -> a
  - scaleFloat :: Int -> a -> a
  - isNaN :: a -> Bool
  - isInfinite :: a -> Bool
  - isDenormalized :: a -> Bool
  - isNegativeZero :: a -> Bool
  - isIEEE :: a -> Bool
  - atan2 :: a -> a -> a
- class (Real a, Fractional a) => RealFrac a where
  - properFraction :: Integral b => a -> (b, a)
  - truncate :: Integral b => a -> b
  - round :: Integral b => a -> b
  - ceiling :: Integral b => a -> b
  - floor :: Integral b => a -> b
- class Show a where
  - showsPrec :: Int -> a -> ShowS
  - show :: a -> String
  - showList :: [a] -> ShowS
- class Functor f => Applicative (f :: Type -> Type) where
  - pure :: a -> f a
  - (<*>) :: f (a -> b) -> f a -> f b
  - (*>) :: f a -> f b -> f b
  - (<*) :: f a -> f b -> f a
- class Foldable (t :: Type -> Type) where
  - foldMap :: Monoid m => (a -> m) -> t a -> m
  - foldr :: (a -> b -> b) -> b -> t a -> b
  - foldl :: (b -> a -> b) -> b -> t a -> b
  - foldr1 :: (a -> a -> a) -> t a -> a
  - foldl1 :: (a -> a -> a) -> t a -> a
  - null :: t a -> Bool
  - length :: t a -> Int
  - elem :: Eq a => a -> t a -> Bool
  - maximum :: Ord a => t a -> a
  - minimum :: Ord a => t a -> a
  - sum :: Num a => t a -> a
  - product :: Num a => t a -> a
- class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where
  - traverse :: Applicative f => (a -> f b) -> t a -> f (t b)
  - sequenceA :: Applicative f => t (f a) -> f (t a)
  - sequence :: Monad m => t (m a) -> m (t a)
- class Semigroup a where
  - (<>) :: a -> a -> a
- class Semigroup a => Monoid a where
  - mempty :: a
  - mappend :: a -> a -> a
  - mconcat :: [a] -> a
- data Bool
  - = False
  - | True
- data Char
- data Double
- data Float
- data Int
- data Integer
- data Maybe a
  - = Nothing
  - | Just a
- data Ordering
  - = LT
  - | EQ
  - | GT
- type Rational = Ratio Integer
- data IO a
- data Word
- data Either a b
  - = Left a
  - | Right b
- type String = [Char]
- readIO :: Read a => String -> IO a
- readLn :: Read a => IO a
- appendFile :: FilePath -> String -> IO ()
- writeFile :: FilePath -> String -> IO ()
- readFile :: FilePath -> IO String
- interact :: (String -> String) -> IO ()
- getContents :: IO String
- getLine :: IO String
- getChar :: IO Char
- putStrLn :: String -> IO ()
- putStr :: String -> IO ()
- putChar :: Char -> IO ()
- ioError :: IOError -> IO a
- type FilePath = String
- userError :: String -> IOError
- type IOError = IOException
- notElem :: (Foldable t, Eq a) => a -> t a -> Bool
- all :: Foldable t => (a -> Bool) -> t a -> Bool
- any :: Foldable t => (a -> Bool) -> t a -> Bool
- or :: Foldable t => t Bool -> Bool
- and :: Foldable t => t Bool -> Bool
- concatMap :: Foldable t => (a -> [b]) -> t a -> [b]
- concat :: Foldable t => t [a] -> [a]
- sequence_ :: (Foldable t, Monad m) => t (m a) -> m ()
- mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m ()
- unwords :: [String] -> String
- words :: String -> [String]
- unlines :: [String] -> String
- lines :: String -> [String]
- read :: Read a => String -> a
- reads :: Read a => ReadS a
- either :: (a -> c) -> (b -> c) -> Either a b -> c
- lex :: ReadS String
- readParen :: Bool -> ReadS a -> ReadS a
- type ReadS a = String -> [(a, String)]
- (<$>) :: Functor f => (a -> b) -> f a -> f b
- lcm :: Integral a => a -> a -> a
- gcd :: Integral a => a -> a -> a
- (^^) :: (Fractional a, Integral b) => a -> b -> a
- (^) :: (Num a, Integral b) => a -> b -> a
- odd :: Integral a => a -> Bool
- even :: Integral a => a -> Bool
- showParen :: Bool -> ShowS -> ShowS
- showString :: String -> ShowS
- showChar :: Char -> ShowS
- shows :: Show a => a -> ShowS
- type ShowS = String -> String
- unzip3 :: [(a, b, c)] -> ([a], [b], [c])
- unzip :: [(a, b)] -> ([a], [b])
- zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
- zip3 :: [a] -> [b] -> [c] -> [(a, b, c)]
- (!!) :: [a] -> Int -> a
- lookup :: Eq a => a -> [(a, b)] -> Maybe b
- reverse :: [a] -> [a]
- break :: (a -> Bool) -> [a] -> ([a], [a])
- span :: (a -> Bool) -> [a] -> ([a], [a])
- splitAt :: Int -> [a] -> ([a], [a])
- drop :: Int -> [a] -> [a]
- take :: Int -> [a] -> [a]
- dropWhile :: (a -> Bool) -> [a] -> [a]
- takeWhile :: (a -> Bool) -> [a] -> [a]
- cycle :: [a] -> [a]
- replicate :: Int -> a -> [a]
- repeat :: a -> [a]
- iterate :: (a -> a) -> a -> [a]
- scanr1 :: (a -> a -> a) -> [a] -> [a]
- scanr :: (a -> b -> b) -> b -> [a] -> [b]
- scanl1 :: (a -> a -> a) -> [a] -> [a]
- scanl :: (b -> a -> b) -> b -> [a] -> [b]
- init :: [a] -> [a]
- last :: [a] -> a
- tail :: [a] -> [a]
- head :: [a] -> a
- maybe :: b -> (a -> b) -> Maybe a -> b
- uncurry :: (a -> b -> c) -> (a, b) -> c
- curry :: ((a, b) -> c) -> a -> b -> c
- subtract :: Num a => a -> a -> a
- asTypeOf :: a -> a -> a
- until :: (a -> Bool) -> (a -> a) -> a -> a
- ($!) :: (a -> b) -> a -> b
- flip :: (a -> b -> c) -> b -> a -> c
- (.) :: (b -> c) -> (a -> b) -> a -> c
- const :: a -> b -> a
- id :: a -> a
- (=<<) :: Monad m => (a -> m b) -> m a -> m b
- undefined :: HasCallStack => a
- errorWithoutStackTrace :: [Char] -> a
- error :: HasCallStack => [Char] -> a
- (&&) :: Bool -> Bool -> Bool
- (||) :: Bool -> Bool -> Bool
- not :: Bool -> Bool

# Documentation

type Spec = SpecWith () Source #

hspec :: Spec -> IO () Source #

Run a given spec and write a report to `stdout`. Exit with `exitFailure` if at least one spec item fails.

Note: `hspec` handles command-line options and reads config files. This is not always desired. Use `runSpec` if you need more control over these aspects.

class IsFormatter a where Source #

Methods

toFormatter :: a -> IO Formatter Source #

Instances

IsFormatter Formatter Source # |
Instance details Defined in Test.Hspec.Discover Methods toFormatter :: Formatter -> IO Formatter Source #
IsFormatter (IO Formatter) Source # |
Instance details Defined in Test.Hspec.Discover Methods toFormatter :: IO Formatter -> IO Formatter Source #

hspecWithFormatter :: IsFormatter a => a -> Spec -> IO () Source #

postProcessSpec :: FilePath -> Spec -> Spec Source #

describe :: HasCallStack => String -> SpecWith a -> SpecWith a Source #

The `describe` function combines a list of specs into a larger spec.

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

Append two lists, i.e.,

    [x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
    [x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

seq :: a -> b -> b Source #

The value of `seq a b` is bottom if `a` is bottom, and otherwise equal to `b`. In other words, it evaluates the first argument `a` to weak head normal form (WHNF). `seq` is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression `seq a b` does not guarantee that `a` will be evaluated before `b`. The only guarantee given by `seq` is that the both `a` and `b` will be evaluated before `seq` returns a value. In particular, this means that `b` may be evaluated before `a`. If you need to guarantee a specific order of evaluation, you must use the function `pseq` from the "parallel" package.

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

`filter`, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

    filter p xs = [ x | x <- xs, p x]

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

`zip` takes two lists and returns a list of corresponding pairs.

    zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

    zip [1] ['a', 'b'] = [(1, 'a')]
    zip [1, 2] ['a'] = [(1, 'a')]

`zip` is right-lazy:

    zip [] _|_ = []
    zip _|_ [] = _|_

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

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 Source #

Extract the first component of a pair.

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

Extract the second component of a pair.

otherwise :: Bool Source #

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

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

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

`map` `f xs` is the list obtained by applying `f` to each element of `xs`, i.e.,

    map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
    map f [x1, x2, ...] == [f x1, f x2, ...]

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

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 Source #

general coercion from integral types

realToFrac :: (Real a, Fractional b) => a -> b Source #

general coercion to fractional types

class Bounded a where Source #

The `Bounded` class is used to name the upper and lower limits of a type. `Ord` is not a superclass of `Bounded` since types that are not totally ordered may also have upper and lower bounds.

The `Bounded` class may be derived for any enumeration type; `minBound` is the first constructor listed in the `data` declaration and `maxBound` is the last. `Bounded` may also be derived for single-constructor datatypes whose constituent types are in `Bounded`.

Methods

minBound :: a Source #

maxBound :: a Source #

Instances

Bounded Bool | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool Source # maxBound :: Bool Source #
Bounded Char | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char Source # maxBound :: Char Source #
Bounded Int | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int Source # maxBound :: Int Source #
Bounded Ordering | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering Source # maxBound :: Ordering Source #
Bounded Word | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word Source # maxBound :: Word Source #
Bounded VecCount | Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecCount Source # maxBound :: VecCount Source #
Bounded VecElem | Since: base-4.10.0.0
Instance details Defined in GHC.Enum Methods minBound :: VecElem Source # maxBound :: VecElem Source #
Bounded () | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: () Source # maxBound :: () Source #
(Bounded a, Bounded b) => Bounded (a, b) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b) Source # maxBound :: (a, b) Source #
(Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c) Source # maxBound :: (a, b, c) Source #
(Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d) Source # maxBound :: (a, b, c, d) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e) Source # maxBound :: (a, b, c, d, e) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f) Source # maxBound :: (a, b, c, d, e, f) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g) Source # maxBound :: (a, b, c, d, e, f, g) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h) Source # maxBound :: (a, b, c, d, e, f, g, h) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i) Source # maxBound :: (a, b, c, d, e, f, g, h, i) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j, k) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source #
(Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source #

class Enum a where Source #

Class `Enum` defines operations on sequentially ordered types.

The `enumFrom`... methods are used in Haskell's translation of arithmetic sequences.

Instances of `Enum` may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by `fromEnum` from `0` through `n-1`. See Chapter 10 of the Haskell Report for more details.

For any type that is an instance of class `Bounded` as well as `Enum`, the following should hold:

- The calls ``succ` `maxBound`` and ``pred` `minBound`` should result in a runtime error.
- `fromEnum` and `toEnum` should give a runtime error if the result value is not representable in the result type. For example, ``toEnum` 7 :: `Bool`` is an error.
- `enumFrom` and `enumFromThen` should be defined with an implicit bound, thus:

       enumFrom     x   = enumFromTo     x maxBound
       enumFromThen x y = enumFromThenTo x y bound
         where
           bound | fromEnum y >= fromEnum x = maxBound
                 | otherwise                = minBound

Minimal complete definition

toEnum, fromEnum

Methods

succ :: a -> a Source #

the successor of a value. For numeric types, `succ` adds 1.

pred :: a -> a Source #

the predecessor of a value. For numeric types, `pred` subtracts 1.

toEnum :: Int -> a Source #

Convert from an `Int`.

fromEnum :: a -> Int Source #

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] Source #

Used in Haskell's translation of `[n..]` with `[n..] = enumFrom n`, a possible implementation being `enumFrom n = n : enumFrom (succ n)`. For example:

-     enumFrom 4 :: [Integer] = [4,5,6,7,...]

-     enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int]

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

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

-     enumFromThen 4 6 :: [Integer] = [4,6,8,10...]

-     enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int]

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

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

-     enumFromTo 6 10 :: [Int] = [6,7,8,9,10]

-     enumFromTo 42 1 :: [Integer] = []

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

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

-     enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6]

-     enumFromThenTo 6 8 2 :: [Int] = []

Instances

Enum Bool | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool Source # pred :: Bool -> Bool Source # toEnum :: Int -> Bool Source # fromEnum :: Bool -> Int Source # enumFrom :: Bool -> [Bool] Source # enumFromThen :: Bool -> Bool -> [Bool] Source # enumFromTo :: Bool -> Bool -> [Bool] Source # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] Source #
Enum Char | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char Source # pred :: Char -> Char Source # toEnum :: Int -> Char Source # fromEnum :: Char -> Int Source # enumFrom :: Char -> [Char] Source # enumFromThen :: Char -> Char -> [Char] Source # enumFromTo :: Char -> Char -> [Char] Source # enumFromThenTo :: Char -> Char -> Char -> [Char] Source #
Enum Int | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int Source # pred :: Int -> Int Source # toEnum :: Int -> Int Source # fromEnum :: Int -> Int Source # enumFrom :: Int -> [Int] Source # enumFromThen :: Int -> Int -> [Int] Source # enumFromTo :: Int -> Int -> [Int] Source # enumFromThenTo :: Int -> Int -> Int -> [Int] Source #
Enum Integer | Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Integer -> Integer Source #

pred :: Integer -> Integer Source #

toEnum :: Int -> Integer Source #

fromEnum :: Integer -> Int Source #

enumFrom :: Integer -> [Integer] Source #

enumFromThen :: Integer -> Integer -> [Integer] Source #

enumFromTo :: Integer -> Integer -> [Integer] Source #

enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source #

Enum Natural | Since: base-4.8.0.0

Instance details

Defined in GHC.Enum

Methods

succ :: Natural -> Natural Source #

pred :: Natural -> Natural Source #

toEnum :: Int -> Natural Source #

fromEnum :: Natural -> Int Source #

enumFrom :: Natural -> [Natural] Source #

enumFromThen :: Natural -> Natural -> [Natural] Source #

enumFromTo :: Natural -> Natural -> [Natural] Source #

enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] Source #

Enum Ordering | Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Ordering -> Ordering Source #

pred :: Ordering -> Ordering Source #

toEnum :: Int -> Ordering Source #

fromEnum :: Ordering -> Int Source #

enumFrom :: Ordering -> [Ordering] Source #

enumFromThen :: Ordering -> Ordering -> [Ordering] Source #

enumFromTo :: Ordering -> Ordering -> [Ordering] Source #

enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source #

Enum Word | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word Source # pred :: Word -> Word Source # toEnum :: Int -> Word Source # fromEnum :: Word -> Int Source # enumFrom :: Word -> [Word] Source # enumFromThen :: Word -> Word -> [Word] Source # enumFromTo :: Word -> Word -> [Word] Source # enumFromThenTo :: Word -> Word -> Word -> [Word] Source #
Enum VecCount | Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Methods

succ :: VecCount -> VecCount Source #

pred :: VecCount -> VecCount Source #

toEnum :: Int -> VecCount Source #

fromEnum :: VecCount -> Int Source #

enumFrom :: VecCount -> [VecCount] Source #

enumFromThen :: VecCount -> VecCount -> [VecCount] Source #

enumFromTo :: VecCount -> VecCount -> [VecCount] Source #

enumFromThenTo :: VecCount -> VecCount -> VecCount -> [VecCount] Source #

Enum VecElem | Since: base-4.10.0.0

Instance details

Defined in GHC.Enum

Methods

succ :: VecElem -> VecElem Source #

pred :: VecElem -> VecElem Source #

toEnum :: Int -> VecElem Source #

fromEnum :: VecElem -> Int Source #

enumFrom :: VecElem -> [VecElem] Source #

enumFromThen :: VecElem -> VecElem -> [VecElem] Source #

enumFromTo :: VecElem -> VecElem -> [VecElem] Source #

enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] Source #

Enum () | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: () -> () Source # pred :: () -> () Source # toEnum :: Int -> () Source # fromEnum :: () -> Int Source # enumFrom :: () -> [()] Source # enumFromThen :: () -> () -> [()] Source # enumFromTo :: () -> () -> [()] Source # enumFromThenTo :: () -> () -> () -> [()] Source #
Integral a => Enum (Ratio a) | Since: base-2.0.1

Instance details

Defined in GHC.Real

Methods

succ :: Ratio a -> Ratio a Source #

pred :: Ratio a -> Ratio a Source #

toEnum :: Int -> Ratio a Source #

fromEnum :: Ratio a -> Int Source #

enumFrom :: Ratio a -> [Ratio a] Source #

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

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

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

Enum a => Enum (Blind a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Blind a -> Blind a Source #

pred :: Blind a -> Blind a Source #

toEnum :: Int -> Blind a Source #

fromEnum :: Blind a -> Int Source #

enumFrom :: Blind a -> [Blind a] Source #

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

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

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

Enum a => Enum (Fixed a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Fixed a -> Fixed a Source #

pred :: Fixed a -> Fixed a Source #

toEnum :: Int -> Fixed a Source #

fromEnum :: Fixed a -> Int Source #

enumFrom :: Fixed a -> [Fixed a] Source #

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

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

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

Enum a => Enum (Positive a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Positive a -> Positive a Source #

pred :: Positive a -> Positive a Source #

toEnum :: Int -> Positive a Source #

fromEnum :: Positive a -> Int Source #

enumFrom :: Positive a -> [Positive a] Source #

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

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

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

Enum a => Enum (NonZero a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: NonZero a -> NonZero a Source #

pred :: NonZero a -> NonZero a Source #

toEnum :: Int -> NonZero a Source #

fromEnum :: NonZero a -> Int Source #

enumFrom :: NonZero a -> [NonZero a] Source #

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

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

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

Enum a => Enum (NonNegative a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: NonNegative a -> NonNegative a Source #

pred :: NonNegative a -> NonNegative a Source #

toEnum :: Int -> NonNegative a Source #

fromEnum :: NonNegative a -> Int Source #

enumFrom :: NonNegative a -> [NonNegative a] Source #

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

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

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

Enum a => Enum (Large a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Large a -> Large a Source #

pred :: Large a -> Large a Source #

toEnum :: Int -> Large a Source #

fromEnum :: Large a -> Int Source #

enumFrom :: Large a -> [Large a] Source #

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

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

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

Enum a => Enum (Small a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Small a -> Small a Source #

pred :: Small a -> Small a Source #

toEnum :: Int -> Small a Source #

fromEnum :: Small a -> Int Source #

enumFrom :: Small a -> [Small a] Source #

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

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

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

Enum a => Enum (Shrink2 a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

succ :: Shrink2 a -> Shrink2 a Source #

pred :: Shrink2 a -> Shrink2 a Source #

toEnum :: Int -> Shrink2 a Source #

fromEnum :: Shrink2 a -> Int Source #

enumFrom :: Shrink2 a -> [Shrink2 a] Source #

enumFromThen :: Shrink2 a -> Shrink2 a -> [Shrink2 a] Source #

enumFromTo :: Shrink2 a -> Shrink2 a -> [Shrink2 a] Source #

enumFromThenTo :: Shrink2 a -> Shrink2 a -> Shrink2 a -> [Shrink2 a] Source #

class Eq a where Source #

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 Source #

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

Instances

Eq Bool |
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool Source # (/=) :: Bool -> Bool -> Bool Source #
Eq Char |
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool Source # (/=) :: Char -> Char -> Bool Source #

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

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 Source # (/=) :: Float -> Float -> Bool Source #
Eq Int |
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool Source # (/=) :: Int -> Int -> Bool Source #
Eq Integer |
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool Source # (/=) :: Integer -> Integer -> Bool Source #
Eq Ordering |
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool Source # (/=) :: Ordering -> Ordering -> Bool Source #
Eq Word |
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool Source # (/=) :: Word -> Word -> Bool Source #
Eq () |
Instance details Defined in GHC.Classes Methods (==) :: () -> () -> Bool Source # (/=) :: () -> () -> Bool Source #
Eq TyCon |
Instance details Defined in GHC.Classes Methods (==) :: TyCon -> TyCon -> Bool Source # (/=) :: TyCon -> TyCon -> Bool Source #
Eq Module |
Instance details Defined in GHC.Classes Methods (==) :: Module -> Module -> Bool Source # (/=) :: Module -> Module -> Bool Source #
Eq TrName |
Instance details Defined in GHC.Classes Methods (==) :: TrName -> TrName -> Bool Source # (/=) :: TrName -> TrName -> Bool Source #
Eq Version | Since: base-2.1
Instance details Defined in Data.Version Methods (==) :: Version -> Version -> Bool Source # (/=) :: Version -> Version -> Bool Source #
Eq ASCIIString |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: ASCIIString -> ASCIIString -> Bool Source # (/=) :: ASCIIString -> ASCIIString -> Bool Source #
Eq UnicodeString |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: UnicodeString -> UnicodeString -> Bool Source # (/=) :: UnicodeString -> UnicodeString -> Bool Source #
Eq PrintableString |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: PrintableString -> PrintableString -> Bool Source # (/=) :: PrintableString -> PrintableString -> Bool Source #
Eq Handle | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: Handle -> Handle -> Bool Source # (/=) :: Handle -> Handle -> Bool Source #
Eq BigNat |
Instance details Defined in GHC.Integer.Type Methods (==) :: BigNat -> BigNat -> Bool Source # (/=) :: BigNat -> BigNat -> Bool Source #
Eq AsyncException | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: AsyncException -> AsyncException -> Bool Source # (/=) :: AsyncException -> AsyncException -> Bool Source #
Eq ArrayException | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: ArrayException -> ArrayException -> Bool Source # (/=) :: ArrayException -> ArrayException -> Bool Source #
Eq ExitCode |
Instance details Defined in GHC.IO.Exception Methods (==) :: ExitCode -> ExitCode -> Bool Source # (/=) :: ExitCode -> ExitCode -> Bool Source #
Eq IOErrorType | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOErrorType -> IOErrorType -> Bool Source # (/=) :: IOErrorType -> IOErrorType -> Bool Source #
Eq BufferMode | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: BufferMode -> BufferMode -> Bool Source # (/=) :: BufferMode -> BufferMode -> Bool Source #
Eq Newline | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: Newline -> Newline -> Bool Source # (/=) :: Newline -> Newline -> Bool Source #
Eq NewlineMode | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods (==) :: NewlineMode -> NewlineMode -> Bool Source # (/=) :: NewlineMode -> NewlineMode -> Bool Source #
Eq MaskingState | Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods (==) :: MaskingState -> MaskingState -> Bool Source # (/=) :: MaskingState -> MaskingState -> Bool Source #
Eq IOException | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods (==) :: IOException -> IOException -> Bool Source # (/=) :: IOException -> IOException -> Bool Source #
Eq ArithException | Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods (==) :: ArithException -> ArithException -> Bool Source # (/=) :: ArithException -> ArithException -> Bool Source #
Eq SrcLoc | Since: base-4.9.0.0
Instance details Defined in GHC.Stack.Types Methods (==) :: SrcLoc -> SrcLoc -> Bool Source # (/=) :: SrcLoc -> SrcLoc -> Bool Source #
Eq Summary |
Instance details Defined in Test.Hspec.Core.Runner Methods (==) :: Summary -> Summary -> Bool Source # (/=) :: Summary -> Summary -> Bool Source #
Eq ColorMode |
Instance details Defined in Test.Hspec.Core.Config.Options Methods (==) :: ColorMode -> ColorMode -> Bool Source # (/=) :: ColorMode -> ColorMode -> Bool Source #
Eq Location |
Instance details Defined in Test.Hspec.Core.Example.Location Methods (==) :: Location -> Location -> Bool Source # (/=) :: Location -> Location -> Bool Source #
Eq Seconds |
Instance details Defined in Test.Hspec.Core.Clock Methods (==) :: Seconds -> Seconds -> Bool Source # (/=) :: Seconds -> Seconds -> Bool Source #
Eq LocalTime |
Instance details Defined in Data.Time.LocalTime.Internal.LocalTime Methods (==) :: LocalTime -> LocalTime -> Bool Source # (/=) :: LocalTime -> LocalTime -> Bool Source #
Eq HUnitFailure |
Instance details Defined in Test.HUnit.Lang Methods (==) :: HUnitFailure -> HUnitFailure -> Bool Source # (/=) :: HUnitFailure -> HUnitFailure -> Bool Source #
Eq FailureReason |
Instance details Defined in Test.HUnit.Lang Methods (==) :: FailureReason -> FailureReason -> Bool Source # (/=) :: FailureReason -> FailureReason -> Bool Source #
Eq Result |
Instance details Defined in Test.HUnit.Lang Methods (==) :: Result -> Result -> Bool Source # (/=) :: Result -> Result -> Bool Source #
Eq Shrunk |
Instance details Defined in Test.QuickCheck.Function Methods (==) :: Shrunk -> Shrunk -> Bool Source # (/=) :: Shrunk -> Shrunk -> Bool Source #
Eq a => Eq [a] |
Instance details Defined in GHC.Classes Methods (==) :: [a] -> [a] -> Bool Source # (/=) :: [a] -> [a] -> Bool Source #
Eq a => Eq (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool Source # (/=) :: Maybe a -> Maybe a -> Bool Source #
Eq a => Eq (Ratio a) | Since: base-2.1
Instance details Defined in GHC.Real Methods (==) :: Ratio a -> Ratio a -> Bool Source # (/=) :: Ratio a -> Ratio a -> Bool Source #
Eq a => Eq (Blind a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Blind a -> Blind a -> Bool Source # (/=) :: Blind a -> Blind a -> Bool Source #
Eq a => Eq (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Fixed a -> Fixed a -> Bool Source # (/=) :: Fixed a -> Fixed a -> Bool Source #
Eq a => Eq (OrderedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: OrderedList a -> OrderedList a -> Bool Source # (/=) :: OrderedList a -> OrderedList a -> Bool Source #
Eq a => Eq (NonEmptyList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: NonEmptyList a -> NonEmptyList a -> Bool Source # (/=) :: NonEmptyList a -> NonEmptyList a -> Bool Source #
Eq a => Eq (SortedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: SortedList a -> SortedList a -> Bool Source # (/=) :: SortedList a -> SortedList a -> Bool Source #
Eq a => Eq (Positive a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Positive a -> Positive a -> Bool Source # (/=) :: Positive a -> Positive a -> Bool Source #
Eq a => Eq (NonZero a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: NonZero a -> NonZero a -> Bool Source # (/=) :: NonZero a -> NonZero a -> Bool Source #
Eq a => Eq (NonNegative a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: NonNegative a -> NonNegative a -> Bool Source # (/=) :: NonNegative a -> NonNegative a -> Bool Source #
Eq a => Eq (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Large a -> Large a -> Bool Source # (/=) :: Large a -> Large a -> Bool Source #
Eq a => Eq (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Small a -> Small a -> Bool Source # (/=) :: Small a -> Small a -> Bool Source #
Eq a => Eq (Shrink2 a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (==) :: Shrink2 a -> Shrink2 a -> Bool Source # (/=) :: Shrink2 a -> Shrink2 a -> Bool Source #
Eq a => Eq (NonEmpty a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (==) :: NonEmpty a -> NonEmpty a -> Bool Source # (/=) :: NonEmpty a -> NonEmpty a -> Bool Source #
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool Source # (/=) :: Either a b -> Either a b -> Bool Source #
(Eq a, Eq b) => Eq (a, b) |
Instance details Defined in GHC.Classes Methods (==) :: (a, b) -> (a, b) -> Bool Source # (/=) :: (a, b) -> (a, b) -> Bool Source #
(Eq c, Eq a) => Eq (Tree c a) |
Instance details Defined in Test.Hspec.Core.Tree Methods (==) :: Tree c a -> Tree c a -> Bool Source # (/=) :: Tree c a -> Tree c a -> Bool Source #
(Eq a, Eq b, Eq c) => Eq (a, b, c) |
Instance details Defined in GHC.Classes Methods (==) :: (a, b, c) -> (a, b, c) -> Bool Source # (/=) :: (a, b, c) -> (a, b, c) -> Bool Source #
(Eq e, Eq1 m, Eq a) => Eq (ErrorT e m a) |
Instance details Defined in Control.Monad.Trans.Error Methods (==) :: ErrorT e m a -> ErrorT e m a -> Bool Source # (/=) :: ErrorT e m a -> ErrorT e m a -> Bool Source #
(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 Source # (/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool Source #
(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 Source # (/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool Source #
(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 Source # (/=) :: (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 Source #
(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 Source # (/=) :: (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 Source #
(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 Source # (/=) :: (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 Source #
(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 Source # (/=) :: (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 Source #

class Fractional a => Floating a where Source #

Trigonometric and hyperbolic functions and related functions.

The Haskell Report defines no laws for `Floating`. However, '(+)', '(*)' and `exp` are customarily expected to define an exponential field and have the following properties:

- `exp (a + b)` = @exp a * exp b
- `exp (fromInteger 0)` = `fromInteger 1`

Minimal complete definition

pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh, asinh, acosh, atanh

Methods

pi :: a Source #

exp :: a -> a Source #

log :: a -> a Source #

sqrt :: a -> a Source #

(**) :: a -> a -> a infixr 8 Source #

logBase :: a -> a -> a Source #

sin :: a -> a Source #

cos :: a -> a Source #

tan :: a -> a Source #

asin :: a -> a Source #

acos :: a -> a Source #

atan :: a -> a Source #

sinh :: a -> a Source #

cosh :: a -> a Source #

tanh :: a -> a Source #

asinh :: a -> a Source #

acosh :: a -> a Source #

atanh :: a -> a Source #

Instances

Floating Double | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

pi :: Double Source #

exp :: Double -> Double Source #

log :: Double -> Double Source #

sqrt :: Double -> Double Source #

(**) :: Double -> Double -> Double Source #

logBase :: Double -> Double -> Double Source #

sin :: Double -> Double Source #

cos :: Double -> Double Source #

tan :: Double -> Double Source #

asin :: Double -> Double Source #

acos :: Double -> Double Source #

atan :: Double -> Double Source #

sinh :: Double -> Double Source #

cosh :: Double -> Double Source #

tanh :: Double -> Double Source #

asinh :: Double -> Double Source #

acosh :: Double -> Double Source #

atanh :: Double -> Double Source #

log1p :: Double -> Double Source #

expm1 :: Double -> Double Source #

log1pexp :: Double -> Double Source #

log1mexp :: Double -> Double Source #

Floating Float | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

pi :: Float Source #

exp :: Float -> Float Source #

log :: Float -> Float Source #

sqrt :: Float -> Float Source #

(**) :: Float -> Float -> Float Source #

logBase :: Float -> Float -> Float Source #

sin :: Float -> Float Source #

cos :: Float -> Float Source #

tan :: Float -> Float Source #

asin :: Float -> Float Source #

acos :: Float -> Float Source #

atan :: Float -> Float Source #

sinh :: Float -> Float Source #

cosh :: Float -> Float Source #

tanh :: Float -> Float Source #

asinh :: Float -> Float Source #

acosh :: Float -> Float Source #

atanh :: Float -> Float Source #

log1p :: Float -> Float Source #

expm1 :: Float -> Float Source #

log1pexp :: Float -> Float Source #

log1mexp :: Float -> Float Source #

class Num a => Fractional a where Source #

Fractional numbers, supporting real division.

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

`recip` gives the multiplicative inverse
  `x * recip x` = `recip x * x` = `fromInteger 1`

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

Minimal complete definition

fromRational, (recip | (/))

Methods

(/) :: a -> a -> a infixl 7 Source #

fractional division

recip :: a -> a Source #

reciprocal fraction

fromRational :: Rational -> a Source #

Conversion from a `Rational` (that is ``Ratio` `Integer``). A floating literal stands for an application of `fromRational` to a value of type `Rational`, so such literals have type `(`Fractional` a) => a`.

Instances

Fractional Seconds |
Instance details Defined in Test.Hspec.Core.Clock Methods (/) :: Seconds -> Seconds -> Seconds Source # recip :: Seconds -> Seconds Source # fromRational :: Rational -> Seconds Source #
Integral a => Fractional (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods (/) :: Ratio a -> Ratio a -> Ratio a Source # recip :: Ratio a -> Ratio a Source # fromRational :: Rational -> Ratio a Source #

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

Integral numbers, supporting integer division.

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

- `x` = `y * quot x y + rem x 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

quot :: a -> a -> a infixl 7 Source #

integer division truncated toward zero

rem :: a -> a -> a infixl 7 Source #

integer remainder, satisfying

    (x `quot` y)*y + (x `rem` y) == x

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

integer division truncated toward negative infinity

mod :: a -> a -> a infixl 7 Source #

integer modulus, satisfying

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

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

simultaneous `quot` and `rem`

divMod :: a -> a -> (a, a) Source #

simultaneous `div` and `mod`

toInteger :: a -> Integer Source #

conversion to `Integer`

Instances

Integral Int | Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int Source # rem :: Int -> Int -> Int Source # div :: Int -> Int -> Int Source # mod :: Int -> Int -> Int Source # quotRem :: Int -> Int -> (Int, Int) Source # divMod :: Int -> Int -> (Int, Int) Source # toInteger :: Int -> Integer Source #
Integral Integer | Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # divMod :: Integer -> Integer -> (Integer, Integer) Source # toInteger :: Integer -> Integer Source #
Integral Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods quot :: Natural -> Natural -> Natural Source # rem :: Natural -> Natural -> Natural Source # div :: Natural -> Natural -> Natural Source # mod :: Natural -> Natural -> Natural Source # quotRem :: Natural -> Natural -> (Natural, Natural) Source # divMod :: Natural -> Natural -> (Natural, Natural) Source # toInteger :: Natural -> Integer Source #
Integral Word | Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word Source # rem :: Word -> Word -> Word Source # div :: Word -> Word -> Word Source # mod :: Word -> Word -> Word Source # quotRem :: Word -> Word -> (Word, Word) Source # divMod :: Word -> Word -> (Word, Word) Source # toInteger :: Word -> Integer Source #
Integral a => Integral (Blind a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

quot :: Blind a -> Blind a -> Blind a Source #

rem :: Blind a -> Blind a -> Blind a Source #

div :: Blind a -> Blind a -> Blind a Source #

mod :: Blind a -> Blind a -> Blind a Source #

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

divMod :: Blind a -> Blind a -> (Blind a, Blind a) Source #

toInteger :: Blind a -> Integer Source #

Integral a => Integral (Fixed a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

quot :: Fixed a -> Fixed a -> Fixed a Source #

rem :: Fixed a -> Fixed a -> Fixed a Source #

div :: Fixed a -> Fixed a -> Fixed a Source #

mod :: Fixed a -> Fixed a -> Fixed a Source #

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

divMod :: Fixed a -> Fixed a -> (Fixed a, Fixed a) Source #

toInteger :: Fixed a -> Integer Source #

Integral a => Integral (Large a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

quot :: Large a -> Large a -> Large a Source #

rem :: Large a -> Large a -> Large a Source #

div :: Large a -> Large a -> Large a Source #

mod :: Large a -> Large a -> Large a Source #

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

divMod :: Large a -> Large a -> (Large a, Large a) Source #

toInteger :: Large a -> Integer Source #

Integral a => Integral (Small a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

quot :: Small a -> Small a -> Small a Source #

rem :: Small a -> Small a -> Small a Source #

div :: Small a -> Small a -> Small a Source #

mod :: Small a -> Small a -> Small a Source #

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

divMod :: Small a -> Small a -> (Small a, Small a) Source #

toInteger :: Small a -> Integer Source #

Integral a => Integral (Shrink2 a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

quot :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

rem :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

div :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

mod :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

quotRem :: Shrink2 a -> Shrink2 a -> (Shrink2 a, Shrink2 a) Source #

divMod :: Shrink2 a -> Shrink2 a -> (Shrink2 a, Shrink2 a) Source #

toInteger :: Shrink2 a -> Integer Source #

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

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

Instances of `Monad` should satisfy the following laws:

-     return a >>= k  =  k a

-     m >>= return  =  m

-     m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the `Monad` and `Applicative` operations should relate as follows:

-     pure = return

-     (<*>) = ap

The above laws imply:

-     fmap f xs  =  xs >>= return . f

-     (>>) = (*>)

and that `pure` and (`<*>`) satisfy the applicative functor laws.

The instances of `Monad` for lists, `Maybe` and `IO` defined in the Prelude satisfy these laws.

Minimal complete definition

(>>=)

Methods

(>>=) :: m a -> (a -> m b) -> m b infixl 1 Source #

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

(>>) :: m a -> m b -> m b infixl 1 Source #

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

return :: a -> m a Source #

Inject a value into the monadic type.

fail :: String -> m a Source #

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] Source # (>>) :: [a] -> [b] -> [b] Source # return :: a -> [a] Source # fail :: String -> [a] Source #
Monad Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source # (>>) :: Maybe a -> Maybe b -> Maybe b Source # return :: a -> Maybe a Source # fail :: String -> Maybe a Source #
Monad IO | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source # (>>) :: IO a -> IO b -> IO b Source # return :: a -> IO a Source # fail :: String -> IO a Source #
Monad Rose |
Instance details Defined in Test.QuickCheck.Property Methods (>>=) :: Rose a -> (a -> Rose b) -> Rose b Source # (>>) :: Rose a -> Rose b -> Rose b Source # return :: a -> Rose a Source # fail :: String -> Rose a Source #
Monad Gen |
Instance details Defined in Test.QuickCheck.Gen Methods (>>=) :: Gen a -> (a -> Gen b) -> Gen b Source # (>>) :: Gen a -> Gen b -> Gen b Source # return :: a -> Gen a Source # fail :: String -> Gen a Source #
Monad ReadP | Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b Source # (>>) :: ReadP a -> ReadP b -> ReadP b Source # return :: a -> ReadP a Source # fail :: String -> ReadP a Source #
Monad NonEmpty | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b Source # (>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # return :: a -> NonEmpty a Source # fail :: String -> NonEmpty a Source #
Monad P | Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods (>>=) :: P a -> (a -> P b) -> P b Source # (>>) :: P a -> P b -> P b Source # return :: a -> P a Source # fail :: String -> P a Source #
Monad (Either e) | Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source # (>>) :: Either e a -> Either e b -> Either e b Source # return :: a -> Either e a Source # fail :: String -> Either e a Source #
Monoid a => Monad ((,) a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) Source # (>>) :: (a, a0) -> (a, b) -> (a, b) Source # return :: a0 -> (a, a0) Source # fail :: String -> (a, a0) Source #
Monad (SpecM a) |
Instance details Defined in Test.Hspec.Core.Spec.Monad Methods (>>=) :: SpecM a a0 -> (a0 -> SpecM a b) -> SpecM a b Source # (>>) :: SpecM a a0 -> SpecM a b -> SpecM a b Source # return :: a0 -> SpecM a a0 Source # fail :: String -> SpecM a a0 Source #
(Monad m, Error e) => Monad (ErrorT e m) |
Instance details Defined in Control.Monad.Trans.Error Methods (>>=) :: ErrorT e m a -> (a -> ErrorT e m b) -> ErrorT e m b Source # (>>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b Source # return :: a -> ErrorT e m a Source # fail :: String -> ErrorT e m a Source #
Monad ((->) r :: Type -> Type) | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: (r -> a) -> (a -> r -> b) -> r -> b Source # (>>) :: (r -> a) -> (r -> b) -> r -> b Source # return :: a -> r -> a Source # fail :: String -> r -> a Source #

class Functor (f :: Type -> Type) where Source #

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 Source #

(<$) :: a -> f b -> f a infixl 4 Source #

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] Source # (<$) :: a -> [b] -> [a] Source #
Functor Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source # (<$) :: a -> Maybe b -> Maybe a Source #
Functor IO | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source # (<$) :: a -> IO b -> IO a Source #
Functor Rose |
Instance details Defined in Test.QuickCheck.Property Methods fmap :: (a -> b) -> Rose a -> Rose b Source # (<$) :: a -> Rose b -> Rose a Source #
Functor Blind |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Blind a -> Blind b Source # (<$) :: a -> Blind b -> Blind a Source #
Functor Fixed |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Fixed a -> Fixed b Source # (<$) :: a -> Fixed b -> Fixed a Source #
Functor OrderedList |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> OrderedList a -> OrderedList b Source # (<$) :: a -> OrderedList b -> OrderedList a Source #
Functor NonEmptyList |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> NonEmptyList a -> NonEmptyList b Source # (<$) :: a -> NonEmptyList b -> NonEmptyList a Source #
Functor SortedList |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> SortedList a -> SortedList b Source # (<$) :: a -> SortedList b -> SortedList a Source #
Functor Positive |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Positive a -> Positive b Source # (<$) :: a -> Positive b -> Positive a Source #
Functor NonZero |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> NonZero a -> NonZero b Source # (<$) :: a -> NonZero b -> NonZero a Source #
Functor NonNegative |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> NonNegative a -> NonNegative b Source # (<$) :: a -> NonNegative b -> NonNegative a Source #
Functor Large |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Large a -> Large b Source # (<$) :: a -> Large b -> Large a Source #
Functor Small |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Small a -> Small b Source # (<$) :: a -> Small b -> Small a Source #
Functor Shrink2 |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Shrink2 a -> Shrink2 b Source # (<$) :: a -> Shrink2 b -> Shrink2 a Source #
Functor Smart |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Smart a -> Smart b Source # (<$) :: a -> Smart b -> Smart a Source #
Functor Gen |
Instance details Defined in Test.QuickCheck.Gen Methods fmap :: (a -> b) -> Gen a -> Gen b Source # (<$) :: a -> Gen b -> Gen a Source #
Functor Handler | Since: base-4.6.0.0
Instance details Defined in Control.Exception Methods fmap :: (a -> b) -> Handler a -> Handler b Source # (<$) :: a -> Handler b -> Handler a Source #
Functor ReadP | Since: base-2.1
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> ReadP a -> ReadP b Source # (<$) :: a -> ReadP b -> ReadP a Source #
Functor NonEmpty | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> NonEmpty a -> NonEmpty b Source # (<$) :: a -> NonEmpty b -> NonEmpty a Source #
Functor P | Since: base-4.8.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods fmap :: (a -> b) -> P a -> P b Source # (<$) :: a -> P b -> P a Source #
Functor FormatF |
Instance details Defined in Test.Hspec.Core.Formatters.Monad Methods fmap :: (a -> b) -> FormatF a -> FormatF b Source # (<$) :: a -> FormatF b -> FormatF a Source #
Functor (Either a) | Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source # (<$) :: a0 -> Either a b -> Either a a0 Source #
Functor ((,) a) | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a0 -> b) -> (a, a0) -> (a, b) Source # (<$) :: a0 -> (a, b) -> (a, a0) Source #
Functor ((:->) a) |
Instance details Defined in Test.QuickCheck.Function Methods fmap :: (a0 -> b) -> (a :-> a0) -> a :-> b Source # (<$) :: a0 -> (a :-> b) -> a :-> a0 Source #
Functor (Fun a) |
Instance details Defined in Test.QuickCheck.Function Methods fmap :: (a0 -> b) -> Fun a a0 -> Fun a b Source # (<$) :: a0 -> Fun a b -> Fun a a0 Source #
Functor (Shrinking s) |
Instance details Defined in Test.QuickCheck.Modifiers Methods fmap :: (a -> b) -> Shrinking s a -> Shrinking s b Source # (<$) :: a -> Shrinking s b -> Shrinking s a Source #
Functor (SpecM a) |
Instance details Defined in Test.Hspec.Core.Spec.Monad Methods fmap :: (a0 -> b) -> SpecM a a0 -> SpecM a b Source # (<$) :: a0 -> SpecM a b -> SpecM a a0 Source #
Functor (Tree c) |
Instance details Defined in Test.Hspec.Core.Tree Methods fmap :: (a -> b) -> Tree c a -> Tree c b Source # (<$) :: a -> Tree c b -> Tree c a Source #
Functor m => Functor (ErrorT e m) |
Instance details Defined in Control.Monad.Trans.Error Methods fmap :: (a -> b) -> ErrorT e m a -> ErrorT e m b Source # (<$) :: a -> ErrorT e m b -> ErrorT e m a Source #
Functor ((->) r :: Type -> Type) | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> (r -> a) -> r -> b Source # (<$) :: a -> (r -> b) -> r -> a Source #

class Num a where Source #

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)`

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 | (-))

Methods

(+) :: a -> a -> a infixl 6 Source #

(-) :: a -> a -> a infixl 6 Source #

(*) :: a -> a -> a infixl 7 Source #

negate :: a -> a Source #

Unary negation.

abs :: a -> a Source #

Absolute value.

signum :: a -> a Source #

Sign of a number. The functions `abs` and `signum` should satisfy the law:

    abs x * signum x == x

For real numbers, the `signum` is either `-1` (negative), `0` (zero) or `1` (positive).

fromInteger :: Integer -> a Source #

Conversion from an `Integer`. An integer literal represents the application of the function `fromInteger` to the appropriate value of type `Integer`, so such literals have type `(`Num` a) => a`.

Instances

Num Int | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int Source # (-) :: Int -> Int -> Int Source # (*) :: Int -> Int -> Int Source # negate :: Int -> Int Source # abs :: Int -> Int Source # signum :: Int -> Int Source # fromInteger :: Integer -> Int Source #
Num Integer | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # (*) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # abs :: Integer -> Integer Source # signum :: Integer -> Integer Source # fromInteger :: Integer -> Integer Source #
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
Instance details Defined in GHC.Num Methods (+) :: Natural -> Natural -> Natural Source # (-) :: Natural -> Natural -> Natural Source # (*) :: Natural -> Natural -> Natural Source # negate :: Natural -> Natural Source # abs :: Natural -> Natural Source # signum :: Natural -> Natural Source # fromInteger :: Integer -> Natural Source #
Num Word | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word Source # (-) :: Word -> Word -> Word Source # (*) :: Word -> Word -> Word Source # negate :: Word -> Word Source # abs :: Word -> Word Source # signum :: Word -> Word Source # fromInteger :: Integer -> Word Source #
Num Seconds |
Instance details Defined in Test.Hspec.Core.Clock Methods (+) :: Seconds -> Seconds -> Seconds Source # (-) :: Seconds -> Seconds -> Seconds Source # (*) :: Seconds -> Seconds -> Seconds Source # negate :: Seconds -> Seconds Source # abs :: Seconds -> Seconds Source # signum :: Seconds -> Seconds Source # fromInteger :: Integer -> Seconds Source #
Integral a => Num (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods (+) :: Ratio a -> Ratio a -> Ratio a Source # (-) :: Ratio a -> Ratio a -> Ratio a Source # (*) :: Ratio a -> Ratio a -> Ratio a Source # negate :: Ratio a -> Ratio a Source # abs :: Ratio a -> Ratio a Source # signum :: Ratio a -> Ratio a Source # fromInteger :: Integer -> Ratio a Source #
Num a => Num (Blind a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (+) :: Blind a -> Blind a -> Blind a Source # (-) :: Blind a -> Blind a -> Blind a Source # (*) :: Blind a -> Blind a -> Blind a Source # negate :: Blind a -> Blind a Source # abs :: Blind a -> Blind a Source # signum :: Blind a -> Blind a Source # fromInteger :: Integer -> Blind a Source #
Num a => Num (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (+) :: Fixed a -> Fixed a -> Fixed a Source # (-) :: Fixed a -> Fixed a -> Fixed a Source # (*) :: Fixed a -> Fixed a -> Fixed a Source # negate :: Fixed a -> Fixed a Source # abs :: Fixed a -> Fixed a Source # signum :: Fixed a -> Fixed a Source # fromInteger :: Integer -> Fixed a Source #
Num a => Num (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (+) :: Large a -> Large a -> Large a Source # (-) :: Large a -> Large a -> Large a Source # (*) :: Large a -> Large a -> Large a Source # negate :: Large a -> Large a Source # abs :: Large a -> Large a Source # signum :: Large a -> Large a Source # fromInteger :: Integer -> Large a Source #
Num a => Num (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (+) :: Small a -> Small a -> Small a Source # (-) :: Small a -> Small a -> Small a Source # (*) :: Small a -> Small a -> Small a Source # negate :: Small a -> Small a Source # abs :: Small a -> Small a Source # signum :: Small a -> Small a Source # fromInteger :: Integer -> Small a Source #
Num a => Num (Shrink2 a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods (+) :: Shrink2 a -> Shrink2 a -> Shrink2 a Source # (-) :: Shrink2 a -> Shrink2 a -> Shrink2 a Source # (*) :: Shrink2 a -> Shrink2 a -> Shrink2 a Source # negate :: Shrink2 a -> Shrink2 a Source # abs :: Shrink2 a -> Shrink2 a Source # signum :: Shrink2 a -> Shrink2 a Source # fromInteger :: Integer -> Shrink2 a Source #

class Eq a => Ord a where Source #

The `Ord` class is used for totally ordered datatypes.

Instances of `Ord` can be derived for any user-defined datatype whose constituent types are in `Ord`. The declared order of the constructors in the data declaration determines the ordering in derived `Ord` instances. The `Ordering` datatype allows a single comparison to determine the precise ordering of two objects.

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

Transitivity
  if `x <= y && y <= z` = `True`, 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 Source #

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

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

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

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

max :: a -> a -> a Source #

min :: a -> a -> a Source #

Instances

Ord Bool |
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering Source # (<) :: Bool -> Bool -> Bool Source # (<=) :: Bool -> Bool -> Bool Source # (>) :: Bool -> Bool -> Bool Source # (>=) :: Bool -> Bool -> Bool Source # max :: Bool -> Bool -> Bool Source # min :: Bool -> Bool -> Bool Source #
Ord Char |
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering Source # (<) :: Char -> Char -> Bool Source # (<=) :: Char -> Char -> Bool Source # (>) :: Char -> Char -> Bool Source # (>=) :: Char -> Char -> Bool Source # max :: Char -> Char -> Char Source # min :: Char -> Char -> Char Source #

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 Methods compare :: Double -> Double -> Ordering Source # (<) :: Double -> Double -> Bool Source # (<=) :: Double -> Double -> Bool Source # (>) :: Double -> Double -> Bool Source # (>=) :: Double -> Double -> Bool Source # max :: Double -> Double -> Double Source # min :: Double -> Double -> Double Source #

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 Source # (<) :: Float -> Float -> Bool Source # (<=) :: Float -> Float -> Bool Source # (>) :: Float -> Float -> Bool Source # (>=) :: Float -> Float -> Bool Source # max :: Float -> Float -> Float Source # min :: Float -> Float -> Float Source #
Ord Int |
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering Source # (<) :: Int -> Int -> Bool Source # (<=) :: Int -> Int -> Bool Source # (>) :: Int -> Int -> Bool Source # (>=) :: Int -> Int -> Bool Source # max :: Int -> Int -> Int Source # min :: Int -> Int -> Int Source #
Ord Integer |
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering Source # (<) :: Integer -> Integer -> Bool Source # (<=) :: Integer -> Integer -> Bool Source # (>) :: Integer -> Integer -> Bool Source # (>=) :: Integer -> Integer -> Bool Source # max :: Integer -> Integer -> Integer Source # min :: Integer -> Integer -> Integer Source #
Ord Ordering |
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering Source # (<) :: Ordering -> Ordering -> Bool Source # (<=) :: Ordering -> Ordering -> Bool Source # (>) :: Ordering -> Ordering -> Bool Source # (>=) :: Ordering -> Ordering -> Bool Source # max :: Ordering -> Ordering -> Ordering Source # min :: Ordering -> Ordering -> Ordering Source #
Ord Word |
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering Source # (<) :: Word -> Word -> Bool Source # (<=) :: Word -> Word -> Bool Source # (>) :: Word -> Word -> Bool Source # (>=) :: Word -> Word -> Bool Source # max :: Word -> Word -> Word Source # min :: Word -> Word -> Word Source #
Ord () |
Instance details Defined in GHC.Classes Methods compare :: () -> () -> Ordering Source # (<) :: () -> () -> Bool Source # (<=) :: () -> () -> Bool Source # (>) :: () -> () -> Bool Source # (>=) :: () -> () -> Bool Source # max :: () -> () -> () Source # min :: () -> () -> () Source #
Ord TyCon |
Instance details Defined in GHC.Classes Methods compare :: TyCon -> TyCon -> Ordering Source # (<) :: TyCon -> TyCon -> Bool Source # (<=) :: TyCon -> TyCon -> Bool Source # (>) :: TyCon -> TyCon -> Bool Source # (>=) :: TyCon -> TyCon -> Bool Source # max :: TyCon -> TyCon -> TyCon Source # min :: TyCon -> TyCon -> TyCon Source #
Ord Version | Since: base-2.1
Instance details Defined in Data.Version Methods compare :: Version -> Version -> Ordering Source # (<) :: Version -> Version -> Bool Source # (<=) :: Version -> Version -> Bool Source # (>) :: Version -> Version -> Bool Source # (>=) :: Version -> Version -> Bool Source # max :: Version -> Version -> Version Source # min :: Version -> Version -> Version Source #
Ord ASCIIString |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: ASCIIString -> ASCIIString -> Ordering Source #

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

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

(>) :: ASCIIString -> ASCIIString -> Bool Source #

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

max :: ASCIIString -> ASCIIString -> ASCIIString Source #

min :: ASCIIString -> ASCIIString -> ASCIIString Source #

Ord UnicodeString |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: UnicodeString -> UnicodeString -> Ordering Source #

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

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

(>) :: UnicodeString -> UnicodeString -> Bool Source #

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

max :: UnicodeString -> UnicodeString -> UnicodeString Source #

min :: UnicodeString -> UnicodeString -> UnicodeString Source #

Ord PrintableString |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: PrintableString -> PrintableString -> Ordering Source #

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

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

(>) :: PrintableString -> PrintableString -> Bool Source #

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

max :: PrintableString -> PrintableString -> PrintableString Source #

min :: PrintableString -> PrintableString -> PrintableString Source #

Ord BigNat |
Instance details Defined in GHC.Integer.Type Methods compare :: BigNat -> BigNat -> Ordering Source # (<) :: BigNat -> BigNat -> Bool Source # (<=) :: BigNat -> BigNat -> Bool Source # (>) :: BigNat -> BigNat -> Bool Source # (>=) :: BigNat -> BigNat -> Bool Source # max :: BigNat -> BigNat -> BigNat Source # min :: BigNat -> BigNat -> BigNat Source #
Ord AsyncException | Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Methods

compare :: AsyncException -> AsyncException -> Ordering Source #

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

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

(>) :: AsyncException -> AsyncException -> Bool Source #

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

max :: AsyncException -> AsyncException -> AsyncException Source #

min :: AsyncException -> AsyncException -> AsyncException Source #

Ord ArrayException | Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Methods

compare :: ArrayException -> ArrayException -> Ordering Source #

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

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

(>) :: ArrayException -> ArrayException -> Bool Source #

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

max :: ArrayException -> ArrayException -> ArrayException Source #

min :: ArrayException -> ArrayException -> ArrayException Source #

Ord ExitCode |
Instance details Defined in GHC.IO.Exception Methods compare :: ExitCode -> ExitCode -> Ordering Source # (<) :: ExitCode -> ExitCode -> Bool Source # (<=) :: ExitCode -> ExitCode -> Bool Source # (>) :: ExitCode -> ExitCode -> Bool Source # (>=) :: ExitCode -> ExitCode -> Bool Source # max :: ExitCode -> ExitCode -> ExitCode Source # min :: ExitCode -> ExitCode -> ExitCode Source #
Ord BufferMode | Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Handle.Types

Methods

compare :: BufferMode -> BufferMode -> Ordering Source #

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

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

(>) :: BufferMode -> BufferMode -> Bool Source #

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

max :: BufferMode -> BufferMode -> BufferMode Source #

min :: BufferMode -> BufferMode -> BufferMode Source #

Ord Newline | Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods compare :: Newline -> Newline -> Ordering Source # (<) :: Newline -> Newline -> Bool Source # (<=) :: Newline -> Newline -> Bool Source # (>) :: Newline -> Newline -> Bool Source # (>=) :: Newline -> Newline -> Bool Source # max :: Newline -> Newline -> Newline Source # min :: Newline -> Newline -> Newline Source #
Ord NewlineMode | Since: base-4.3.0.0

Instance details

Defined in GHC.IO.Handle.Types

Methods

compare :: NewlineMode -> NewlineMode -> Ordering Source #

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

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

(>) :: NewlineMode -> NewlineMode -> Bool Source #

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

max :: NewlineMode -> NewlineMode -> NewlineMode Source #

min :: NewlineMode -> NewlineMode -> NewlineMode Source #

Ord ArithException | Since: base-3.0

Instance details

Defined in GHC.Exception.Type

Methods

compare :: ArithException -> ArithException -> Ordering Source #

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

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

(>) :: ArithException -> ArithException -> Bool Source #

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

max :: ArithException -> ArithException -> ArithException Source #

min :: ArithException -> ArithException -> ArithException Source #

Ord LocalTime |

Instance details

Defined in Data.Time.LocalTime.Internal.LocalTime

Methods

compare :: LocalTime -> LocalTime -> Ordering Source #

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

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

(>) :: LocalTime -> LocalTime -> Bool Source #

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

max :: LocalTime -> LocalTime -> LocalTime Source #

min :: LocalTime -> LocalTime -> LocalTime Source #

Ord a => Ord [a] |
Instance details Defined in GHC.Classes Methods compare :: [a] -> [a] -> Ordering Source # (<) :: [a] -> [a] -> Bool Source # (<=) :: [a] -> [a] -> Bool Source # (>) :: [a] -> [a] -> Bool Source # (>=) :: [a] -> [a] -> Bool Source # max :: [a] -> [a] -> [a] Source # min :: [a] -> [a] -> [a] Source #
Ord a => Ord (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering Source # (<) :: Maybe a -> Maybe a -> Bool Source # (<=) :: Maybe a -> Maybe a -> Bool Source # (>) :: Maybe a -> Maybe a -> Bool Source # (>=) :: Maybe a -> Maybe a -> Bool Source # max :: Maybe a -> Maybe a -> Maybe a Source # min :: Maybe a -> Maybe a -> Maybe a Source #
Integral a => Ord (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods compare :: Ratio a -> Ratio a -> Ordering Source # (<) :: Ratio a -> Ratio a -> Bool Source # (<=) :: Ratio a -> Ratio a -> Bool Source # (>) :: Ratio a -> Ratio a -> Bool Source # (>=) :: Ratio a -> Ratio a -> Bool Source # max :: Ratio a -> Ratio a -> Ratio a Source # min :: Ratio a -> Ratio a -> Ratio a Source #
Ord a => Ord (Blind a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods compare :: Blind a -> Blind a -> Ordering Source # (<) :: Blind a -> Blind a -> Bool Source # (<=) :: Blind a -> Blind a -> Bool Source # (>) :: Blind a -> Blind a -> Bool Source # (>=) :: Blind a -> Blind a -> Bool Source # max :: Blind a -> Blind a -> Blind a Source # min :: Blind a -> Blind a -> Blind a Source #
Ord a => Ord (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods compare :: Fixed a -> Fixed a -> Ordering Source # (<) :: Fixed a -> Fixed a -> Bool Source # (<=) :: Fixed a -> Fixed a -> Bool Source # (>) :: Fixed a -> Fixed a -> Bool Source # (>=) :: Fixed a -> Fixed a -> Bool Source # max :: Fixed a -> Fixed a -> Fixed a Source # min :: Fixed a -> Fixed a -> Fixed a Source #
Ord a => Ord (OrderedList a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: OrderedList a -> OrderedList a -> Ordering Source #

(<) :: OrderedList a -> OrderedList a -> Bool Source #

(<=) :: OrderedList a -> OrderedList a -> Bool Source #

(>) :: OrderedList a -> OrderedList a -> Bool Source #

(>=) :: OrderedList a -> OrderedList a -> Bool Source #

max :: OrderedList a -> OrderedList a -> OrderedList a Source #

min :: OrderedList a -> OrderedList a -> OrderedList a Source #

Ord a => Ord (NonEmptyList a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: NonEmptyList a -> NonEmptyList a -> Ordering Source #

(<) :: NonEmptyList a -> NonEmptyList a -> Bool Source #

(<=) :: NonEmptyList a -> NonEmptyList a -> Bool Source #

(>) :: NonEmptyList a -> NonEmptyList a -> Bool Source #

(>=) :: NonEmptyList a -> NonEmptyList a -> Bool Source #

max :: NonEmptyList a -> NonEmptyList a -> NonEmptyList a Source #

min :: NonEmptyList a -> NonEmptyList a -> NonEmptyList a Source #

Ord a => Ord (SortedList a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: SortedList a -> SortedList a -> Ordering Source #

(<) :: SortedList a -> SortedList a -> Bool Source #

(<=) :: SortedList a -> SortedList a -> Bool Source #

(>) :: SortedList a -> SortedList a -> Bool Source #

(>=) :: SortedList a -> SortedList a -> Bool Source #

max :: SortedList a -> SortedList a -> SortedList a Source #

min :: SortedList a -> SortedList a -> SortedList a Source #

Ord a => Ord (Positive a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: Positive a -> Positive a -> Ordering Source #

(<) :: Positive a -> Positive a -> Bool Source #

(<=) :: Positive a -> Positive a -> Bool Source #

(>) :: Positive a -> Positive a -> Bool Source #

(>=) :: Positive a -> Positive a -> Bool Source #

max :: Positive a -> Positive a -> Positive a Source #

min :: Positive a -> Positive a -> Positive a Source #

Ord a => Ord (NonZero a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: NonZero a -> NonZero a -> Ordering Source #

(<) :: NonZero a -> NonZero a -> Bool Source #

(<=) :: NonZero a -> NonZero a -> Bool Source #

(>) :: NonZero a -> NonZero a -> Bool Source #

(>=) :: NonZero a -> NonZero a -> Bool Source #

max :: NonZero a -> NonZero a -> NonZero a Source #

min :: NonZero a -> NonZero a -> NonZero a Source #

Ord a => Ord (NonNegative a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: NonNegative a -> NonNegative a -> Ordering Source #

(<) :: NonNegative a -> NonNegative a -> Bool Source #

(<=) :: NonNegative a -> NonNegative a -> Bool Source #

(>) :: NonNegative a -> NonNegative a -> Bool Source #

(>=) :: NonNegative a -> NonNegative a -> Bool Source #

max :: NonNegative a -> NonNegative a -> NonNegative a Source #

min :: NonNegative a -> NonNegative a -> NonNegative a Source #

Ord a => Ord (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods compare :: Large a -> Large a -> Ordering Source # (<) :: Large a -> Large a -> Bool Source # (<=) :: Large a -> Large a -> Bool Source # (>) :: Large a -> Large a -> Bool Source # (>=) :: Large a -> Large a -> Bool Source # max :: Large a -> Large a -> Large a Source # min :: Large a -> Large a -> Large a Source #
Ord a => Ord (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods compare :: Small a -> Small a -> Ordering Source # (<) :: Small a -> Small a -> Bool Source # (<=) :: Small a -> Small a -> Bool Source # (>) :: Small a -> Small a -> Bool Source # (>=) :: Small a -> Small a -> Bool Source # max :: Small a -> Small a -> Small a Source # min :: Small a -> Small a -> Small a Source #
Ord a => Ord (Shrink2 a) |

Instance details

Defined in Test.QuickCheck.Modifiers

Methods

compare :: Shrink2 a -> Shrink2 a -> Ordering Source #

(<) :: Shrink2 a -> Shrink2 a -> Bool Source #

(<=) :: Shrink2 a -> Shrink2 a -> Bool Source #

(>) :: Shrink2 a -> Shrink2 a -> Bool Source #

(>=) :: Shrink2 a -> Shrink2 a -> Bool Source #

max :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

min :: Shrink2 a -> Shrink2 a -> Shrink2 a Source #

Ord a => Ord (NonEmpty a) | Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

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

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

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

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

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

(Ord a, Ord b) => Ord (Either a b) | Since: base-2.1

Instance details

Defined in Data.Either

Methods

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

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

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

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

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

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

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

(Ord a, Ord b) => Ord (a, b) |
Instance details Defined in GHC.Classes Methods compare :: (a, b) -> (a, b) -> Ordering Source # (<) :: (a, b) -> (a, b) -> Bool Source # (<=) :: (a, b) -> (a, b) -> Bool Source # (>) :: (a, b) -> (a, b) -> Bool Source # (>=) :: (a, b) -> (a, b) -> Bool Source # max :: (a, b) -> (a, b) -> (a, b) Source # min :: (a, b) -> (a, b) -> (a, b) Source #
(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 Source # (<) :: (a, b, c) -> (a, b, c) -> Bool Source # (<=) :: (a, b, c) -> (a, b, c) -> Bool Source # (>) :: (a, b, c) -> (a, b, c) -> Bool Source # (>=) :: (a, b, c) -> (a, b, c) -> Bool Source # max :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # min :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #
(Ord e, Ord1 m, Ord a) => Ord (ErrorT e m a) |

Instance details

Defined in Control.Monad.Trans.Error

Methods

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

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

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

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

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

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

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

(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 Source #

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

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

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

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

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

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

(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 Source #

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

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

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

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

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

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

(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 Source #

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

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

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

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

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

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

(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 Source #

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

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

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

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

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

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

(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 Source #

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

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

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

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

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) Source #

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) Source #

(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 Source #

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

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

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

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

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) Source #

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) Source #

(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 Source #

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

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

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

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

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) Source #

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) Source #

(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 Source #

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

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

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

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

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) Source #

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) Source #

(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 Source #

(<) :: (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 Source #

(<=) :: (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 Source #

(>) :: (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 Source #

(>=) :: (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 Source #

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) Source #

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) Source #

(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 Source #

(<) :: (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 Source #

(<=) :: (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 Source #

(>) :: (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 Source #

(>=) :: (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 Source #

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) Source #

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) Source #

(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 Source #

(<) :: (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 Source #

(<=) :: (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 Source #

(>) :: (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 Source #

(>=) :: (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 Source #

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) Source #

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) Source #

(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 Source #

(<) :: (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 Source #

(<=) :: (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 Source #

(>) :: (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 Source #

(>=) :: (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 Source #

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) Source #

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) Source #

class Read a where Source #

Parsing of `String`s, producing values.

Derived instances of `Read` make the following assumptions, which derived instances of `Show` obey:

- If the constructor is defined to be an infix operator, then the derived `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 Source #

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:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

readList :: ReadS [a] Source #

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.

Instances

Read Bool | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool Source # readList :: ReadS [Bool] Source # readPrec :: ReadPrec Bool Source # readListPrec :: ReadPrec [Bool] Source #
Read Char | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char Source # readList :: ReadS [Char] Source # readPrec :: ReadPrec Char Source # readListPrec :: ReadPrec [Char] Source #
Read Double | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double Source # readList :: ReadS [Double] Source # readPrec :: ReadPrec Double Source # readListPrec :: ReadPrec [Double] Source #
Read Float | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float Source # readList :: ReadS [Float] Source # readPrec :: ReadPrec Float Source # readListPrec :: ReadPrec [Float] Source #
Read Int | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int Source # readList :: ReadS [Int] Source # readPrec :: ReadPrec Int Source # readListPrec :: ReadPrec [Int] Source #
Read Integer | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer Source # readList :: ReadS [Integer] Source # readPrec :: ReadPrec Integer Source # readListPrec :: ReadPrec [Integer] Source #
Read Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Natural Source # readList :: ReadS [Natural] Source # readPrec :: ReadPrec Natural Source # readListPrec :: ReadPrec [Natural] Source #
Read Ordering | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering Source # readList :: ReadS [Ordering] Source # readPrec :: ReadPrec Ordering Source # readListPrec :: ReadPrec [Ordering] Source #
Read Word | Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word Source # readList :: ReadS [Word] Source # readPrec :: ReadPrec Word Source # readListPrec :: ReadPrec [Word] Source #
Read Word8 | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word8 Source # readList :: ReadS [Word8] Source # readPrec :: ReadPrec Word8 Source # readListPrec :: ReadPrec [Word8] Source #
Read Word16 | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word16 Source # readList :: ReadS [Word16] Source # readPrec :: ReadPrec Word16 Source # readListPrec :: ReadPrec [Word16] Source #
Read Word32 | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word32 Source # readList :: ReadS [Word32] Source # readPrec :: ReadPrec Word32 Source # readListPrec :: ReadPrec [Word32] Source #
Read Word64 | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word64 Source # readList :: ReadS [Word64] Source # readPrec :: ReadPrec Word64 Source # readListPrec :: ReadPrec [Word64] Source #
Read () | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS () Source # readList :: ReadS [()] Source # readPrec :: ReadPrec () Source # readListPrec :: ReadPrec [()] Source #
Read Version | Since: base-2.1
Instance details Defined in Data.Version Methods readsPrec :: Int -> ReadS Version Source # readList :: ReadS [Version] Source # readPrec :: ReadPrec Version Source # readListPrec :: ReadPrec [Version] Source #
Read Args |
Instance details Defined in Test.QuickCheck.Test Methods readsPrec :: Int -> ReadS Args Source # readList :: ReadS [Args] Source # readPrec :: ReadPrec Args Source # readListPrec :: ReadPrec [Args] Source #
Read ASCIIString |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS ASCIIString Source # readList :: ReadS [ASCIIString] Source # readPrec :: ReadPrec ASCIIString Source # readListPrec :: ReadPrec [ASCIIString] Source #
Read UnicodeString |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS UnicodeString Source # readList :: ReadS [UnicodeString] Source # readPrec :: ReadPrec UnicodeString Source # readListPrec :: ReadPrec [UnicodeString] Source #
Read PrintableString |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS PrintableString Source # readList :: ReadS [PrintableString] Source # readPrec :: ReadPrec PrintableString Source # readListPrec :: ReadPrec [PrintableString] Source #
Read ExitCode |
Instance details Defined in GHC.IO.Exception Methods readsPrec :: Int -> ReadS ExitCode Source # readList :: ReadS [ExitCode] Source # readPrec :: ReadPrec ExitCode Source # readListPrec :: ReadPrec [ExitCode] Source #
Read BufferMode | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS BufferMode Source # readList :: ReadS [BufferMode] Source # readPrec :: ReadPrec BufferMode Source # readListPrec :: ReadPrec [BufferMode] Source #
Read Newline | Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS Newline Source # readList :: ReadS [Newline] Source # readPrec :: ReadPrec Newline Source # readListPrec :: ReadPrec [Newline] Source #
Read NewlineMode | Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods readsPrec :: Int -> ReadS NewlineMode Source # readList :: ReadS [NewlineMode] Source # readPrec :: ReadPrec NewlineMode Source # readListPrec :: ReadPrec [NewlineMode] Source #
Read Lexeme | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Lexeme Source # readList :: ReadS [Lexeme] Source # readPrec :: ReadPrec Lexeme Source # readListPrec :: ReadPrec [Lexeme] Source #
Read GeneralCategory | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS GeneralCategory Source # readList :: ReadS [GeneralCategory] Source # readPrec :: ReadPrec GeneralCategory Source # readListPrec :: ReadPrec [GeneralCategory] Source #
Read Location |
Instance details Defined in Test.Hspec.Core.Example.Location Methods readsPrec :: Int -> ReadS Location Source # readList :: ReadS [Location] Source # readPrec :: ReadPrec Location Source # readListPrec :: ReadPrec [Location] Source #
Read a => Read [a] | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS [a] Source # readList :: ReadS [[a]] Source # readPrec :: ReadPrec [a] Source # readListPrec :: ReadPrec [[a]] Source #
Read a => Read (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) Source # readList :: ReadS [Maybe a] Source # readPrec :: ReadPrec (Maybe a) Source # readListPrec :: ReadPrec [Maybe a] Source #
(Integral a, Read a) => Read (Ratio a) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Ratio a) Source # readList :: ReadS [Ratio a] Source # readPrec :: ReadPrec (Ratio a) Source # readListPrec :: ReadPrec [Ratio a] Source #
Read a => Read (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (Fixed a) Source # readList :: ReadS [Fixed a] Source # readPrec :: ReadPrec (Fixed a) Source # readListPrec :: ReadPrec [Fixed a] Source #
Read a => Read (OrderedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (OrderedList a) Source # readList :: ReadS [OrderedList a] Source # readPrec :: ReadPrec (OrderedList a) Source # readListPrec :: ReadPrec [OrderedList a] Source #
Read a => Read (NonEmptyList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (NonEmptyList a) Source # readList :: ReadS [NonEmptyList a] Source # readPrec :: ReadPrec (NonEmptyList a) Source # readListPrec :: ReadPrec [NonEmptyList a] Source #
Read a => Read (SortedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (SortedList a) Source # readList :: ReadS [SortedList a] Source # readPrec :: ReadPrec (SortedList a) Source # readListPrec :: ReadPrec [SortedList a] Source #
Read a => Read (Positive a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (Positive a) Source # readList :: ReadS [Positive a] Source # readPrec :: ReadPrec (Positive a) Source # readListPrec :: ReadPrec [Positive a] Source #
Read a => Read (NonZero a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (NonZero a) Source # readList :: ReadS [NonZero a] Source # readPrec :: ReadPrec (NonZero a) Source # readListPrec :: ReadPrec [NonZero a] Source #
Read a => Read (NonNegative a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (NonNegative a) Source # readList :: ReadS [NonNegative a] Source # readPrec :: ReadPrec (NonNegative a) Source # readListPrec :: ReadPrec [NonNegative a] Source #
Read a => Read (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (Large a) Source # readList :: ReadS [Large a] Source # readPrec :: ReadPrec (Large a) Source # readListPrec :: ReadPrec [Large a] Source #
Read a => Read (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (Small a) Source # readList :: ReadS [Small a] Source # readPrec :: ReadPrec (Small a) Source # readListPrec :: ReadPrec [Small a] Source #
Read a => Read (Shrink2 a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods readsPrec :: Int -> ReadS (Shrink2 a) Source # readList :: ReadS [Shrink2 a] Source # readPrec :: ReadPrec (Shrink2 a) Source # readListPrec :: ReadPrec [Shrink2 a] Source #
Read a => Read (NonEmpty a) | Since: base-4.11.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (NonEmpty a) Source # readList :: ReadS [NonEmpty a] Source # readPrec :: ReadPrec (NonEmpty a) Source # readListPrec :: ReadPrec [NonEmpty a] Source #
(Read a, Read b) => Read (Either a b) | Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) Source # readList :: ReadS [Either a b] Source # readPrec :: ReadPrec (Either a b) Source # readListPrec :: ReadPrec [Either a b] Source #
(Read a, Read b) => Read (a, b) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (a, b) Source # readList :: ReadS [(a, b)] Source # readPrec :: ReadPrec (a, b) Source # readListPrec :: ReadPrec [(a, b)] Source #
(Ix a, Read a, Read b) => Read (Array a b) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Array a b) Source # readList :: ReadS [Array a b] Source # readPrec :: ReadPrec (Array a b) Source # readListPrec :: ReadPrec [Array a b] Source #
(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) Source # readList :: ReadS [(a, b, c)] Source # readPrec :: ReadPrec (a, b, c) Source # readListPrec :: ReadPrec [(a, b, c)] Source #
(Read e, Read1 m, Read a) => Read (ErrorT e m a) |
Instance details Defined in Control.Monad.Trans.Error Methods readsPrec :: Int -> ReadS (ErrorT e m a) Source # readList :: ReadS [ErrorT e m a] Source # readPrec :: ReadPrec (ErrorT e m a) Source # readListPrec :: ReadPrec [ErrorT e m a] Source #
(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) Source # readList :: ReadS [(a, b, c, d)] Source # readPrec :: ReadPrec (a, b, c, d) Source # readListPrec :: ReadPrec [(a, b, c, d)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e)] Source # readPrec :: ReadPrec (a, b, c, d, e) Source # readListPrec :: ReadPrec [(a, b, c, d, e)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f)] Source # readPrec :: ReadPrec (a, b, c, d, e, f) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f, g)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j)] Source #
(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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k)] Source #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l) => Read (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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l)] Source #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m) => Read (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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m)] Source #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n) => Read (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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] Source #
(Read a, Read b, Read c, Read d, Read e, Read f, Read g, Read h, Read i, Read j, Read k, Read l, Read m, Read n, Read o) => Read (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) | Since: base-2.1
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) Source # readList :: ReadS [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source # readPrec :: ReadPrec (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # readListPrec :: ReadPrec [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] Source #

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

Methods

toRational :: a -> Rational Source #

the rational equivalent of its real argument with full precision

Instances

Real Int | Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational Source #
Real Integer | Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational Source #
Real Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Real Methods toRational :: Natural -> Rational Source #
Real Word | Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational Source #
Integral a => Real (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Ratio a -> Rational Source #
Real a => Real (Blind a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods toRational :: Blind a -> Rational Source #
Real a => Real (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods toRational :: Fixed a -> Rational Source #
Real a => Real (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods toRational :: Large a -> Rational Source #
Real a => Real (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods toRational :: Small a -> Rational Source #
Real a => Real (Shrink2 a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods toRational :: Shrink2 a -> Rational Source #

class (RealFrac a, Floating a) => RealFloat a where Source #

Efficient, machine-independent access to the components of a floating-point number.

Minimal complete definition

floatRadix, floatDigits, floatRange, decodeFloat, encodeFloat, isNaN, isInfinite, isDenormalized, isNegativeZero, isIEEE

Methods

floatRadix :: a -> Integer Source #

a constant function, returning the radix of the representation (often `2`)

floatDigits :: a -> Int Source #

a constant function, returning the number of digits of `floatRadix` in the significand

floatRange :: a -> (Int, Int) Source #

a constant function, returning the lowest and highest values the exponent may assume

decodeFloat :: a -> (Integer, Int) Source #

The function `decodeFloat` applied to a real floating-point number returns the significand expressed as an `Integer` and an appropriately scaled exponent (an `Int`). If ``decodeFloat` x` yields `(m,n)`, then `x` is equal in value to `m*b^^n`, where `b` is the floating-point radix, and furthermore, either `m` and `n` are both zero or else `b^(d-1) <= `abs` m < b^d`, where `d` is the value of ``floatDigits` x`. In particular, ``decodeFloat` 0 = (0,0)`. If the type contains a negative zero, also ``decodeFloat` (-0.0) = (0,0)`. The result of ``decodeFloat` x` is unspecified if either of ``isNaN` x` or ``isInfinite` x` is `True`.

encodeFloat :: Integer -> Int -> a Source #

`encodeFloat` performs the inverse of `decodeFloat` in the sense that for finite `x` with the exception of `-0.0`, ``uncurry` `encodeFloat` (`decodeFloat` x) = x`. ``encodeFloat` m n` is one of the two closest representable floating-point numbers to `m*b^^n` (or `±Infinity` if overflow occurs); usually the closer, but if `m` contains too many bits, the result may be rounded in the wrong direction.

exponent :: a -> Int Source #

`exponent` corresponds to the second component of `decodeFloat`. ``exponent` 0 = 0` and for finite nonzero `x`, ``exponent` x = snd (`decodeFloat` x) + `floatDigits` x`. If `x` is a finite floating-point number, it is equal in value to ``significand` x * b ^^ `exponent` x`, where `b` is the floating-point radix. The behaviour is unspecified on infinite or `NaN` values.

significand :: a -> a Source #

The first component of `decodeFloat`, scaled to lie in the open interval (`-1`,`1`), either `0.0` or of absolute value `>= 1/b`, where `b` is the floating-point radix. The behaviour is unspecified on infinite or `NaN` values.

scaleFloat :: Int -> a -> a Source #

multiplies a floating-point number by an integer power of the radix

isNaN :: a -> Bool Source #

`True` if the argument is an IEEE "not-a-number" (NaN) value

isInfinite :: a -> Bool Source #

`True` if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool Source #

`True` if the argument is too small to be represented in normalized format

isNegativeZero :: a -> Bool Source #

`True` if the argument is an IEEE negative zero

isIEEE :: a -> Bool Source #

`True` if the argument is an IEEE floating point number

atan2 :: a -> a -> a Source #

a version of arctangent taking two real floating-point arguments. For real floating `x` and `y`, ``atan2` y x` computes the angle (from the positive x-axis) of the vector from the origin to the point `(x,y)`. ``atan2` y x` returns a value in the range [`-pi`, `pi`]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. ``atan2` y 1`, with `y` in a type that is `RealFloat`, should return the same value as ``atan` y`. A default definition of `atan2` is provided, but implementors can provide a more accurate implementation.

Instances

RealFloat Double | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer Source #

floatDigits :: Double -> Int Source #

floatRange :: Double -> (Int, Int) Source #

decodeFloat :: Double -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Double Source #

exponent :: Double -> Int Source #

significand :: Double -> Double Source #

scaleFloat :: Int -> Double -> Double Source #

isNaN :: Double -> Bool Source #

isInfinite :: Double -> Bool Source #

isDenormalized :: Double -> Bool Source #

isNegativeZero :: Double -> Bool Source #

isIEEE :: Double -> Bool Source #

atan2 :: Double -> Double -> Double Source #

RealFloat Float | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer Source #

floatDigits :: Float -> Int Source #

floatRange :: Float -> (Int, Int) Source #

decodeFloat :: Float -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Float Source #

exponent :: Float -> Int Source #

significand :: Float -> Float Source #

scaleFloat :: Int -> Float -> Float Source #

isNaN :: Float -> Bool Source #

isInfinite :: Float -> Bool Source #

isDenormalized :: Float -> Bool Source #

isNegativeZero :: Float -> Bool Source #

isIEEE :: Float -> Bool Source #

atan2 :: Float -> Float -> Float Source #

class (Real a, Fractional a) => RealFrac a where Source #

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

properFraction :: Integral b => a -> (b, a) Source #

The function `properFraction` takes a real fractional number `x` and returns a pair `(n,f)` such that `x = n+f`, and:

- `n` is an integral number with the same sign as `x`; and
- `f` is a fraction with the same type and sign as `x`, and with absolute value less than `1`.

The default definitions of the `ceiling`, `floor`, `truncate` and `round` functions are in terms of `properFraction`.

truncate :: Integral b => a -> b Source #

``truncate` x` returns the integer nearest `x` between zero and `x`

round :: Integral b => a -> b Source #

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

ceiling :: Integral b => a -> b Source #

``ceiling` x` returns the least integer not less than `x`

floor :: Integral b => a -> b Source #

``floor` x` returns the greatest integer not greater than `x`

Instances

Integral a => RealFrac (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods properFraction :: Integral b => Ratio a -> (b, Ratio a) Source # truncate :: Integral b => Ratio a -> b Source # round :: Integral b => Ratio a -> b Source # ceiling :: Integral b => Ratio a -> b Source # floor :: Integral b => Ratio a -> b Source #

class Show a where Source #

Conversion of values to readable `String`s.

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

- The result of `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 Source #

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:

- `(x,"")` is an element of `(`readsPrec` d (`showsPrec` d x ""))`.

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

show :: a -> String Source #

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

showList :: [a] -> ShowS Source #

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 Source # show :: Bool -> String Source # showList :: [Bool] -> ShowS Source #
Show Char | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS Source # show :: Char -> String Source # showList :: [Char] -> ShowS Source #
Show Int | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS Source # show :: Int -> String Source # showList :: [Int] -> ShowS Source #
Show Integer | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS Source # show :: Integer -> String Source # showList :: [Integer] -> ShowS Source #
Show Natural | Since: base-4.8.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Natural -> ShowS Source # show :: Natural -> String Source # showList :: [Natural] -> ShowS Source #
Show Ordering | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS Source # show :: Ordering -> String Source # showList :: [Ordering] -> ShowS Source #
Show Word | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS Source # show :: Word -> String Source # showList :: [Word] -> ShowS Source #
Show RuntimeRep | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> RuntimeRep -> ShowS Source # show :: RuntimeRep -> String Source # showList :: [RuntimeRep] -> ShowS Source #
Show VecCount | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecCount -> ShowS Source # show :: VecCount -> String Source # showList :: [VecCount] -> ShowS Source #
Show VecElem | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> VecElem -> ShowS Source # show :: VecElem -> String Source # showList :: [VecElem] -> ShowS Source #
Show CallStack | Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> CallStack -> ShowS Source # show :: CallStack -> String Source # showList :: [CallStack] -> ShowS Source #
Show () | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> () -> ShowS Source # show :: () -> String Source # showList :: [()] -> ShowS Source #
Show TyCon | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TyCon -> ShowS Source # show :: TyCon -> String Source # showList :: [TyCon] -> ShowS Source #
Show Module | Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Module -> ShowS Source # show :: Module -> String Source # showList :: [Module] -> ShowS Source #
Show TrName | Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TrName -> ShowS Source # show :: TrName -> String Source # showList :: [TrName] -> ShowS Source #
Show KindRep |
Instance details Defined in GHC.Show Methods showsPrec :: Int -> KindRep -> ShowS Source # show :: KindRep -> String Source # showList :: [KindRep] -> ShowS Source #
Show TypeLitSort | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> TypeLitSort -> ShowS Source # show :: TypeLitSort -> String Source # showList :: [TypeLitSort] -> ShowS Source #
Show Version | Since: base-2.1
Instance details Defined in Data.Version Methods showsPrec :: Int -> Version -> ShowS Source # show :: Version -> String Source # showList :: [Version] -> ShowS Source #
Show Args |
Instance details Defined in Test.QuickCheck.Test Methods showsPrec :: Int -> Args -> ShowS Source # show :: Args -> String Source # showList :: [Args] -> ShowS Source #
Show Result |
Instance details Defined in Test.QuickCheck.Test Methods showsPrec :: Int -> Result -> ShowS Source # show :: Result -> String Source # showList :: [Result] -> ShowS Source #
Show Confidence |
Instance details Defined in Test.QuickCheck.State Methods showsPrec :: Int -> Confidence -> ShowS Source # show :: Confidence -> String Source # showList :: [Confidence] -> ShowS Source #
Show ASCIIString |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> ASCIIString -> ShowS Source # show :: ASCIIString -> String Source # showList :: [ASCIIString] -> ShowS Source #
Show UnicodeString |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> UnicodeString -> ShowS Source # show :: UnicodeString -> String Source # showList :: [UnicodeString] -> ShowS Source #
Show PrintableString |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> PrintableString -> ShowS Source # show :: PrintableString -> String Source # showList :: [PrintableString] -> ShowS Source #
Show Handle | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> Handle -> ShowS Source # show :: Handle -> String Source # showList :: [Handle] -> ShowS Source #
Show HandleType | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> HandleType -> ShowS Source # show :: HandleType -> String Source # showList :: [HandleType] -> ShowS Source #
Show BlockedIndefinitelyOnMVar | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnMVar -> ShowS Source # show :: BlockedIndefinitelyOnMVar -> String Source # showList :: [BlockedIndefinitelyOnMVar] -> ShowS Source #
Show BlockedIndefinitelyOnSTM | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> BlockedIndefinitelyOnSTM -> ShowS Source # show :: BlockedIndefinitelyOnSTM -> String Source # showList :: [BlockedIndefinitelyOnSTM] -> ShowS Source #
Show Deadlock | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> Deadlock -> ShowS Source # show :: Deadlock -> String Source # showList :: [Deadlock] -> ShowS Source #
Show AllocationLimitExceeded | Since: base-4.7.1.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AllocationLimitExceeded -> ShowS Source # show :: AllocationLimitExceeded -> String Source # showList :: [AllocationLimitExceeded] -> ShowS Source #
Show CompactionFailed | Since: base-4.10.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> CompactionFailed -> ShowS Source # show :: CompactionFailed -> String Source # showList :: [CompactionFailed] -> ShowS Source #
Show AssertionFailed | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AssertionFailed -> ShowS Source # show :: AssertionFailed -> String Source # showList :: [AssertionFailed] -> ShowS Source #
Show SomeAsyncException | Since: base-4.7.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> SomeAsyncException -> ShowS Source # show :: SomeAsyncException -> String Source # showList :: [SomeAsyncException] -> ShowS Source #
Show AsyncException | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> AsyncException -> ShowS Source # show :: AsyncException -> String Source # showList :: [AsyncException] -> ShowS Source #
Show ArrayException | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ArrayException -> ShowS Source # show :: ArrayException -> String Source # showList :: [ArrayException] -> ShowS Source #
Show FixIOException | Since: base-4.11.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> FixIOException -> ShowS Source # show :: FixIOException -> String Source # showList :: [FixIOException] -> ShowS Source #
Show ExitCode |
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> ExitCode -> ShowS Source # show :: ExitCode -> String Source # showList :: [ExitCode] -> ShowS Source #
Show IOErrorType | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOErrorType -> ShowS Source # show :: IOErrorType -> String Source # showList :: [IOErrorType] -> ShowS Source #
Show BufferMode | Since: base-4.2.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> BufferMode -> ShowS Source # show :: BufferMode -> String Source # showList :: [BufferMode] -> ShowS Source #
Show Newline | Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> Newline -> ShowS Source # show :: Newline -> String Source # showList :: [Newline] -> ShowS Source #
Show NewlineMode | Since: base-4.3.0.0
Instance details Defined in GHC.IO.Handle.Types Methods showsPrec :: Int -> NewlineMode -> ShowS Source # show :: NewlineMode -> String Source # showList :: [NewlineMode] -> ShowS Source #
Show MaskingState | Since: base-4.3.0.0
Instance details Defined in GHC.IO Methods showsPrec :: Int -> MaskingState -> ShowS Source # show :: MaskingState -> String Source # showList :: [MaskingState] -> ShowS Source #
Show IOException | Since: base-4.1.0.0
Instance details Defined in GHC.IO.Exception Methods showsPrec :: Int -> IOException -> ShowS Source # show :: IOException -> String Source # showList :: [IOException] -> ShowS Source #
Show ArithException | Since: base-4.0.0.0
Instance details Defined in GHC.Exception.Type Methods showsPrec :: Int -> ArithException -> ShowS Source # show :: ArithException -> String Source # showList :: [ArithException] -> ShowS Source #
Show SrcLoc | Since: base-4.9.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> SrcLoc -> ShowS Source # show :: SrcLoc -> String Source # showList :: [SrcLoc] -> ShowS Source #
Show SomeException | Since: base-3.0
Instance details Defined in GHC.Exception.Type Methods showsPrec :: Int -> SomeException -> ShowS Source # show :: SomeException -> String Source # showList :: [SomeException] -> ShowS Source #
Show Summary |
Instance details Defined in Test.Hspec.Core.Runner Methods showsPrec :: Int -> Summary -> ShowS Source # show :: Summary -> String Source # showList :: [Summary] -> ShowS Source #
Show ColorMode |
Instance details Defined in Test.Hspec.Core.Config.Options Methods showsPrec :: Int -> ColorMode -> ShowS Source # show :: ColorMode -> String Source # showList :: [ColorMode] -> ShowS Source #
Show Params |
Instance details Defined in Test.Hspec.Core.Example Methods showsPrec :: Int -> Params -> ShowS Source # show :: Params -> String Source # showList :: [Params] -> ShowS Source #
Show Result |
Instance details Defined in Test.Hspec.Core.Example Methods showsPrec :: Int -> Result -> ShowS Source # show :: Result -> String Source # showList :: [Result] -> ShowS Source #
Show ResultStatus |
Instance details Defined in Test.Hspec.Core.Example Methods showsPrec :: Int -> ResultStatus -> ShowS Source # show :: ResultStatus -> String Source # showList :: [ResultStatus] -> ShowS Source #
Show FailureReason |
Instance details Defined in Test.Hspec.Core.Example Methods showsPrec :: Int -> FailureReason -> ShowS Source # show :: FailureReason -> String Source # showList :: [FailureReason] -> ShowS Source #
Show Location |
Instance details Defined in Test.Hspec.Core.Example.Location Methods showsPrec :: Int -> Location -> ShowS Source # show :: Location -> String Source # showList :: [Location] -> ShowS Source #
Show Seconds |
Instance details Defined in Test.Hspec.Core.Clock Methods showsPrec :: Int -> Seconds -> ShowS Source # show :: Seconds -> String Source # showList :: [Seconds] -> ShowS Source #
Show ZonedTime |
Instance details Defined in Data.Time.LocalTime.Internal.ZonedTime Methods showsPrec :: Int -> ZonedTime -> ShowS Source # show :: ZonedTime -> String Source # showList :: [ZonedTime] -> ShowS Source #
Show LocalTime |
Instance details Defined in Data.Time.LocalTime.Internal.LocalTime Methods showsPrec :: Int -> LocalTime -> ShowS Source # show :: LocalTime -> String Source # showList :: [LocalTime] -> ShowS Source #
Show HUnitFailure |
Instance details Defined in Test.HUnit.Lang Methods showsPrec :: Int -> HUnitFailure -> ShowS Source # show :: HUnitFailure -> String Source # showList :: [HUnitFailure] -> ShowS Source #
Show DateFormatSpec |
Instance details Defined in Data.Time.Format.Parse Methods showsPrec :: Int -> DateFormatSpec -> ShowS Source # show :: DateFormatSpec -> String Source # showList :: [DateFormatSpec] -> ShowS Source #
Show Padding |
Instance details Defined in Data.Time.Format.Parse Methods showsPrec :: Int -> Padding -> ShowS Source # show :: Padding -> String Source # showList :: [Padding] -> ShowS Source #
Show FailureReason |
Instance details Defined in Test.HUnit.Lang Methods showsPrec :: Int -> FailureReason -> ShowS Source # show :: FailureReason -> String Source # showList :: [FailureReason] -> ShowS Source #
Show Result |
Instance details Defined in Test.HUnit.Lang Methods showsPrec :: Int -> Result -> ShowS Source # show :: Result -> String Source # showList :: [Result] -> ShowS Source #
Show a => Show [a] | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> [a] -> ShowS Source # show :: [a] -> String Source # showList :: [[a]] -> ShowS Source #
Show a => Show (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS Source # show :: Maybe a -> String Source # showList :: [Maybe a] -> ShowS Source #
Show a => Show (Ratio a) | Since: base-2.0.1
Instance details Defined in GHC.Real Methods showsPrec :: Int -> Ratio a -> ShowS Source # show :: Ratio a -> String Source # showList :: [Ratio a] -> ShowS Source #
Show (Blind a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Blind a -> ShowS Source # show :: Blind a -> String Source # showList :: [Blind a] -> ShowS Source #
Show a => Show (Fixed a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Fixed a -> ShowS Source # show :: Fixed a -> String Source # showList :: [Fixed a] -> ShowS Source #
Show a => Show (OrderedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> OrderedList a -> ShowS Source # show :: OrderedList a -> String Source # showList :: [OrderedList a] -> ShowS Source #
Show a => Show (NonEmptyList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> NonEmptyList a -> ShowS Source # show :: NonEmptyList a -> String Source # showList :: [NonEmptyList a] -> ShowS Source #
Show a => Show (InfiniteList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> InfiniteList a -> ShowS Source # show :: InfiniteList a -> String Source # showList :: [InfiniteList a] -> ShowS Source #
Show a => Show (SortedList a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> SortedList a -> ShowS Source # show :: SortedList a -> String Source # showList :: [SortedList a] -> ShowS Source #
Show a => Show (Positive a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Positive a -> ShowS Source # show :: Positive a -> String Source # showList :: [Positive a] -> ShowS Source #
Show a => Show (NonZero a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> NonZero a -> ShowS Source # show :: NonZero a -> String Source # showList :: [NonZero a] -> ShowS Source #
Show a => Show (NonNegative a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> NonNegative a -> ShowS Source # show :: NonNegative a -> String Source # showList :: [NonNegative a] -> ShowS Source #
Show a => Show (Large a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Large a -> ShowS Source # show :: Large a -> String Source # showList :: [Large a] -> ShowS Source #
Show a => Show (Small a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Small a -> ShowS Source # show :: Small a -> String Source # showList :: [Small a] -> ShowS Source #
Show a => Show (Shrink2 a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Shrink2 a -> ShowS Source # show :: Shrink2 a -> String Source # showList :: [Shrink2 a] -> ShowS Source #
Show a => Show (Smart a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Smart a -> ShowS Source # show :: Smart a -> String Source # showList :: [Smart a] -> ShowS Source #
Show a => Show (NonEmpty a) | Since: base-4.11.0.0
Instance details Defined in GHC.Show Methods showsPrec :: Int -> NonEmpty a -> ShowS Source # show :: NonEmpty a -> String Source # showList :: [NonEmpty a] -> ShowS Source #
(Show a, Show b) => Show (Either a b) | Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS Source # show :: Either a b -> String Source # showList :: [Either a b] -> ShowS Source #
(Show a, Show b) => Show (a, b) | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> (a, b) -> ShowS Source # show :: (a, b) -> String Source # showList :: [(a, b)] -> ShowS Source #
(Show a, Show b) => Show (a :-> b) |
Instance details Defined in Test.QuickCheck.Function Methods showsPrec :: Int -> (a :-> b) -> ShowS Source # show :: (a :-> b) -> String Source # showList :: [a :-> b] -> ShowS Source #
(Show a, Show b) => Show (Fun a b) |
Instance details Defined in Test.QuickCheck.Function Methods showsPrec :: Int -> Fun a b -> ShowS Source # show :: Fun a b -> String Source # showList :: [Fun a b] -> ShowS Source #
Show a => Show (Shrinking s a) |
Instance details Defined in Test.QuickCheck.Modifiers Methods showsPrec :: Int -> Shrinking s a -> ShowS Source # show :: Shrinking s a -> String Source # showList :: [Shrinking s a] -> ShowS Source #
(Show c, Show a) => Show (Tree c a) |
Instance details Defined in Test.Hspec.Core.Tree Methods showsPrec :: Int -> Tree c a -> ShowS Source # show :: Tree c a -> String Source # showList :: [Tree c a] -> ShowS Source #
(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 Source # show :: (a, b, c) -> String Source # showList :: [(a, b, c)] -> ShowS Source #
(Show e, Show1 m, Show a) => Show (ErrorT e m a) |
Instance details Defined in Control.Monad.Trans.Error Methods showsPrec :: Int -> ErrorT e m a -> ShowS Source # show :: ErrorT e m a -> String Source # showList :: [ErrorT e m a] -> ShowS Source #
(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 Source # show :: (a, b, c, d) -> String Source # showList :: [(a, b, c, d)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e) -> String Source # showList :: [(a, b, c, d, e)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f) -> String Source # showList :: [(a, b, c, d, e, f)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g) -> String Source # showList :: [(a, b, c, d, e, f, g)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h) -> String Source # showList :: [(a, b, c, d, e, f, g, h)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j, k) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j, k)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j, k, l) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n)] -> ShowS Source #
(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 Source # show :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> String Source # showList :: [(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o)] -> ShowS Source #

class Functor f => Applicative (f :: Type -> Type) where Source #

A functor with application, providing operations to

- embed pure expressions (`pure`), and
- sequence computations and combine their results (`<*>` and `liftA2`).

A minimal complete definition must include implementations of `pure` and of either `<*>` or `liftA2`. If it defines both, then they must behave the same as their default definitions:

    (<*>) = liftA2 id

    liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

identity

      pure id <*> v = v

composition

      pure (.) <*> u <*> v <*> w = u <*> (v <*> w)

homomorphism

      pure f <*> pure x = pure (f x)

interchange

      u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

-     u *> v = (id <$ u) <*> v

-     u <* v = liftA2 const u v

As a consequence of these laws, the `Functor` instance for `f` will satisfy

-     fmap f x = pure f <*> x

It may be useful to note that supposing

    forall x y. p (q x y) = f x . g y

it follows from the above that

    liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If `f` is also a `Monad`, it should satisfy

-     pure = return

-     (<*>) = ap

-     (*>) = (>>)

(which implies that `pure` and `<*>` satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value.

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

Sequential application.

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

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

Sequence actions, discarding the value of the first argument.

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

Sequence actions, discarding the value of the second argument.

Instances

Applicative [] | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> [a] Source # (<*>) :: [a -> b] -> [a] -> [b] Source # liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source # (*>) :: [a] -> [b] -> [b] Source # (<*) :: [a] -> [b] -> [a] Source #
Applicative Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a Source # (<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source # (*>) :: Maybe a -> Maybe b -> Maybe b Source # (<*) :: Maybe a -> Maybe b -> Maybe a Source #
Applicative IO | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a Source # (<*>) :: IO (a -> b) -> IO a -> IO b Source # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source # (*>) :: IO a -> IO b -> IO b Source # (<*) :: IO a -> IO b -> IO a Source #
Applicative Rose |
Instance details Defined in Test.QuickCheck.Property Methods pure :: a -> Rose a Source # (<*>) :: Rose (a -> b) -> Rose a -> Rose b Source # liftA2 :: (a -> b -> c) -> Rose a -> Rose b -> Rose c Source # (*>) :: Rose a -> Rose b -> Rose b Source # (<*) :: Rose a -> Rose b -> Rose a Source #
Applicative Gen |
Instance details Defined in Test.QuickCheck.Gen Methods pure :: a -> Gen a Source # (<*>) :: Gen (a -> b) -> Gen a -> Gen b Source # liftA2 :: (a -> b -> c) -> Gen a -> Gen b -> Gen c Source # (*>) :: Gen a -> Gen b -> Gen b Source # (<*) :: Gen a -> Gen b -> Gen a Source #
Applicative ReadP | Since: base-4.6.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> ReadP a Source # (<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source # liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source # (*>) :: ReadP a -> ReadP b -> ReadP b Source # (<*) :: ReadP a -> ReadP b -> ReadP a Source #
Applicative NonEmpty | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods pure :: a -> NonEmpty a Source # (<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source # liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source # (*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source # (<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #
Applicative P | Since: base-4.5.0.0
Instance details Defined in Text.ParserCombinators.ReadP Methods pure :: a -> P a Source # (<*>) :: P (a -> b) -> P a -> P b Source # liftA2 :: (a -> b -> c) -> P a -> P b -> P c Source # (*>) :: P a -> P b -> P b Source # (<*) :: P a -> P b -> P a Source #
Applicative (Either e) | Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a Source # (<*>) :: Either e (a -> b) -> Either e a -> Either e b Source # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source # (*>) :: Either e a -> Either e b -> Either e b Source # (<*) :: Either e a -> Either e b -> Either e a Source #

Monoid a => Applicative ((,) a)

For tuples, the `Monoid` constraint on `a` determines how the first values merge. For example, `String`s concatenate:

    ("hello ", (+15)) <*> ("world!", 2002)
    ("hello world!",2017)

Since: base-2.1

Instance details Defined in GHC.Base Methods pure :: a0 -> (a, a0) Source # (<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source # liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source # (*>) :: (a, a0) -> (a, b) -> (a, b) Source # (<*) :: (a, a0) -> (a, b) -> (a, a0) Source #
Applicative (SpecM a) |
Instance details Defined in Test.Hspec.Core.Spec.Monad Methods pure :: a0 -> SpecM a a0 Source # (<*>) :: SpecM a (a0 -> b) -> SpecM a a0 -> SpecM a b Source # liftA2 :: (a0 -> b -> c) -> SpecM a a0 -> SpecM a b -> SpecM a c Source # (*>) :: SpecM a a0 -> SpecM a b -> SpecM a b Source # (<*) :: SpecM a a0 -> SpecM a b -> SpecM a a0 Source #
(Functor m, Monad m) => Applicative (ErrorT e m) |
Instance details Defined in Control.Monad.Trans.Error Methods pure :: a -> ErrorT e m a Source # (<*>) :: ErrorT e m (a -> b) -> ErrorT e m a -> ErrorT e m b Source # liftA2 :: (a -> b -> c) -> ErrorT e m a -> ErrorT e m b -> ErrorT e m c Source # (*>) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m b Source # (<*) :: ErrorT e m a -> ErrorT e m b -> ErrorT e m a Source #
Applicative ((->) a :: Type -> Type) | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a0 -> a -> a0 Source # (<*>) :: (a -> (a0 -> b)) -> (a -> a0) -> a -> b Source # liftA2 :: (a0 -> b -> c) -> (a -> a0) -> (a -> b) -> a -> c Source # (*>) :: (a -> a0) -> (a -> b) -> a -> b Source # (<*) :: (a -> a0) -> (a -> b) -> a -> a0 Source #

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

Data structures that can be folded.

For example, given a data type

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

a suitable instance would be

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

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

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

`Foldable` instances are expected to satisfy the following laws:

    foldr f z t = appEndo (foldMap (Endo . f) t ) z

    foldl f z t = appEndo (getDual (foldMap (Dual . Endo . flip f) t)) z

    fold = foldMap id

    length = getSum . foldMap (Sum . const  1)

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

    sum = getSum . foldMap Sum

but may be less defined.

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

    foldMap f = fold . fmap f

which implies that

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

Minimal complete definition

foldMap | foldr

Methods

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

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

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

Right-associative fold of a structure.

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

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

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

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

    foldr f z = foldr f z . toList

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

Left-associative fold of a structure.

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

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

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

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

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

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

    foldr1 f = foldr1 f . toList

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

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

    foldl1 f = foldl1 f . toList

null :: t a -> Bool Source #

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 Source #

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 Source #

Does the element occur in the structure?

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

The largest element of a non-empty structure.

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

The least element of a non-empty structure.

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

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

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

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 Source #

foldMap :: Monoid m => (a -> m) -> [a] -> m Source #

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

foldr' :: (a -> b -> b) -> b -> [a] -> b Source #

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

foldl' :: (b -> a -> b) -> b -> [a] -> b Source #

foldr1 :: (a -> a -> a) -> [a] -> a Source #

foldl1 :: (a -> a -> a) -> [a] -> a Source #

toList :: [a] -> [a] Source #

null :: [a] -> Bool Source #

length :: [a] -> Int Source #

elem :: Eq a => a -> [a] -> Bool Source #

maximum :: Ord a => [a] -> a Source #

minimum :: Ord a => [a] -> a Source #

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

product :: Num a => [a] -> a Source #

Foldable Maybe | Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m Source #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldr1 :: (a -> a -> a) -> Maybe a -> a Source #

foldl1 :: (a -> a -> a) -> Maybe a -> a Source #

toList :: Maybe a -> [a] Source #

null :: Maybe a -> Bool Source #

length :: Maybe a -> Int Source #

elem :: Eq a => a -> Maybe a -> Bool Source #

maximum :: Ord a => Maybe a -> a Source #

minimum :: Ord a => Maybe a -> a Source #

sum :: Num a => Maybe a -> a Source #

product :: Num a => Maybe a -> a Source #

Foldable Par1 | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Par1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> Par1 a -> m Source #

foldr :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> Par1 a -> b Source #

foldl :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> Par1 a -> b Source #

foldr1 :: (a -> a -> a) -> Par1 a -> a Source #

foldl1 :: (a -> a -> a) -> Par1 a -> a Source #

toList :: Par1 a -> [a] Source #

null :: Par1 a -> Bool Source #

length :: Par1 a -> Int Source #

elem :: Eq a => a -> Par1 a -> Bool Source #

maximum :: Ord a => Par1 a -> a Source #

minimum :: Ord a => Par1 a -> a Source #

sum :: Num a => Par1 a -> a Source #

product :: Num a => Par1 a -> a Source #

Foldable First | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => First m -> m Source #

foldMap :: Monoid m => (a -> m) -> First a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> First a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> First a -> b Source #

foldr1 :: (a -> a -> a) -> First a -> a Source #

foldl1 :: (a -> a -> a) -> First a -> a Source #

toList :: First a -> [a] Source #

null :: First a -> Bool Source #

length :: First a -> Int Source #

elem :: Eq a => a -> First a -> Bool Source #

maximum :: Ord a => First a -> a Source #

minimum :: Ord a => First a -> a Source #

sum :: Num a => First a -> a Source #

product :: Num a => First a -> a Source #

Foldable Last | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Last m -> m Source #

foldMap :: Monoid m => (a -> m) -> Last a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> Last a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> Last a -> b Source #

foldr1 :: (a -> a -> a) -> Last a -> a Source #

foldl1 :: (a -> a -> a) -> Last a -> a Source #

toList :: Last a -> [a] Source #

null :: Last a -> Bool Source #

length :: Last a -> Int Source #

elem :: Eq a => a -> Last a -> Bool Source #

maximum :: Ord a => Last a -> a Source #

minimum :: Ord a => Last a -> a Source #

sum :: Num a => Last a -> a Source #

product :: Num a => Last a -> a Source #

Foldable Dual | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m Source #

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #

foldr :: (a -> b -> b) -> b -> Dual a -> b Source #

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #

foldl :: (b -> a -> b) -> b -> Dual a -> b Source #

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #

foldr1 :: (a -> a -> a) -> Dual a -> a Source #

foldl1 :: (a -> a -> a) -> Dual a -> a Source #

toList :: Dual a -> [a] Source #

null :: Dual a -> Bool Source #

length :: Dual a -> Int Source #

elem :: Eq a => a -> Dual a -> Bool Source #

maximum :: Ord a => Dual a -> a Source #

minimum :: Ord a => Dual a -> a Source #

sum :: Num a => Dual a -> a Source #

product :: Num a => Dual a -> a Source #

Foldable Sum | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m Source #

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source #

foldr :: (a -> b -> b) -> b -> Sum a -> b Source #

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source #

foldl :: (b -> a -> b) -> b -> Sum a -> b Source #

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source #

foldr1 :: (a -> a -> a) -> Sum a -> a Source #

foldl1 :: (a -> a -> a) -> Sum a -> a Source #

toList :: Sum a -> [a] Source #

null :: Sum a -> Bool Source #

length :: Sum a -> Int Source #

elem :: Eq a => a -> Sum a -> Bool Source #

maximum :: Ord a => Sum a -> a Source #

minimum :: Ord a => Sum a -> a Source #

sum :: Num a => Sum a -> a Source #

product :: Num a => Sum a -> a Source #

Foldable Product | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m Source #

foldMap :: Monoid m => (a -> m) -> Product a -> m Source #

foldr :: (a -> b -> b) -> b -> Product a -> b Source #

foldr' :: (a -> b -> b) -> b -> Product a -> b Source #

foldl :: (b -> a -> b) -> b -> Product a -> b Source #

foldl' :: (b -> a -> b) -> b -> Product a -> b Source #

foldr1 :: (a -> a -> a) -> Product a -> a Source #

foldl1 :: (a -> a -> a) -> Product a -> a Source #

toList :: Product a -> [a] Source #

null :: Product a -> Bool Source #

length :: Product a -> Int Source #

elem :: Eq a => a -> Product a -> Bool Source #

maximum :: Ord a => Product a -> a Source #

minimum :: Ord a => Product a -> a Source #

sum :: Num a => Product a -> a Source #

product :: Num a => Product a -> a Source #

Foldable Down | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

toList :: Down a -> [a] Source #

null :: Down a -> Bool Source #

length :: Down a -> Int Source #

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

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

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

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

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

Foldable NonEmpty | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => NonEmpty m -> m Source #

foldMap :: Monoid m => (a -> m) -> NonEmpty a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> NonEmpty a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> NonEmpty a -> b Source #

foldr1 :: (a -> a -> a) -> NonEmpty a -> a Source #

foldl1 :: (a -> a -> a) -> NonEmpty a -> a Source #

toList :: NonEmpty a -> [a] Source #

null :: NonEmpty a -> Bool Source #

length :: NonEmpty a -> Int Source #

elem :: Eq a => a -> NonEmpty a -> Bool Source #

maximum :: Ord a => NonEmpty a -> a Source #

minimum :: Ord a => NonEmpty a -> a Source #

sum :: Num a => NonEmpty a -> a Source #

product :: Num a => NonEmpty a -> a Source #

Foldable (Either a) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

null :: Either a a0 -> Bool Source #

length :: Either a a0 -> Int Source #

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

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

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

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

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

Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => V1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> V1 a -> m Source #

foldr :: (a -> b -> b) -> b -> V1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> V1 a -> b Source #

foldl :: (b -> a -> b) -> b -> V1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> V1 a -> b Source #

foldr1 :: (a -> a -> a) -> V1 a -> a Source #

foldl1 :: (a -> a -> a) -> V1 a -> a Source #

toList :: V1 a -> [a] Source #

null :: V1 a -> Bool Source #

length :: V1 a -> Int Source #

elem :: Eq a => a -> V1 a -> Bool Source #

maximum :: Ord a => V1 a -> a Source #

minimum :: Ord a => V1 a -> a Source #

sum :: Num a => V1 a -> a Source #

product :: Num a => V1 a -> a Source #

Foldable (U1 :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => U1 m -> m Source #

foldMap :: Monoid m => (a -> m) -> U1 a -> m Source #

foldr :: (a -> b -> b) -> b -> U1 a -> b Source #

foldr' :: (a -> b -> b) -> b -> U1 a -> b Source #

foldl :: (b -> a -> b) -> b -> U1 a -> b Source #

foldl' :: (b -> a -> b) -> b -> U1 a -> b Source #

foldr1 :: (a -> a -> a) -> U1 a -> a Source #

foldl1 :: (a -> a -> a) -> U1 a -> a Source #

toList :: U1 a -> [a] Source #

null :: U1 a -> Bool Source #

length :: U1 a -> Int Source #

elem :: Eq a => a -> U1 a -> Bool Source #

maximum :: Ord a => U1 a -> a Source #

minimum :: Ord a => U1 a -> a Source #

sum :: Num a => U1 a -> a Source #

product :: Num a => U1 a -> a Source #

Foldable ((,) a) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Foldable (Array i) | Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Array i m -> m Source #

foldMap :: Monoid m => (a -> m) -> Array i a -> m Source #

foldr :: (a -> b -> b) -> b -> Array i a -> b Source #

foldr' :: (a -> b -> b) -> b -> Array i a -> b Source #

foldl :: (b -> a -> b) -> b -> Array i a -> b Source #

foldl' :: (b -> a -> b) -> b -> Array i a -> b Source #

foldr1 :: (a -> a -> a) -> Array i a -> a Source #

foldl1 :: (a -> a -> a) -> Array i a -> a Source #

toList :: Array i a -> [a] Source #

null :: Array i a -> Bool Source #

length :: Array i a -> Int Source #

elem :: Eq a => a -> Array i a -> Bool Source #

maximum :: Ord a => Array i a -> a Source #

minimum :: Ord a => Array i a -> a Source #

sum :: Num a => Array i a -> a Source #

product :: Num a => Array i a -> a Source #

Foldable (Proxy :: Type -> Type) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Proxy m -> m Source #

foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source #

foldr :: (a -> b -> b) -> b -> Proxy a -> b Source #

foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source #

foldl :: (b -> a -> b) -> b -> Proxy a -> b Source #

foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source #

foldr1 :: (a -> a -> a) -> Proxy a -> a Source #

foldl1 :: (a -> a -> a) -> Proxy a -> a Source #

toList :: Proxy a -> [a] Source #

null :: Proxy a -> Bool Source #

length :: Proxy a -> Int Source #

elem :: Eq a => a -> Proxy a -> Bool Source #

maximum :: Ord a => Proxy a -> a Source #

minimum :: Ord a => Proxy a -> a Source #

sum :: Num a => Proxy a -> a Source #

product :: Num a => Proxy a -> a Source #

Foldable (Tree c) |

Instance details

Defined in Test.Hspec.Core.Tree

Methods

fold :: Monoid m => Tree c m -> m Source #

foldMap :: Monoid m => (a -> m) -> Tree c a -> m Source #

foldr :: (a -> b -> b) -> b -> Tree c a -> b Source #

foldr' :: (a -> b -> b) -> b -> Tree c a -> b Source #

foldl :: (b -> a -> b) -> b -> Tree c a -> b Source #

foldl' :: (b -> a -> b) -> b -> Tree c a -> b Source #

foldr1 :: (a -> a -> a) -> Tree c a -> a Source #

foldl1 :: (a -> a -> a) -> Tree c a -> a Source #

toList :: Tree c a -> [a] Source #

null :: Tree c a -> Bool Source #

length :: Tree c a -> Int Source #

elem :: Eq a => a -> Tree c a -> Bool Source #

maximum :: Ord a => Tree c a -> a Source #

minimum :: Ord a => Tree c a -> a Source #

sum :: Num a => Tree c a -> a Source #

product :: Num a => Tree c a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> Rec1 f a -> m Source #

foldr :: (a -> b -> b) -> b -> Rec1 f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Rec1 f a -> b Source #

foldl :: (b -> a -> b) -> b -> Rec1 f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Rec1 f a -> b Source #

foldr1 :: (a -> a -> a) -> Rec1 f a -> a Source #

foldl1 :: (a -> a -> a) -> Rec1 f a -> a Source #

toList :: Rec1 f a -> [a] Source #

null :: Rec1 f a -> Bool Source #

length :: Rec1 f a -> Int Source #

elem :: Eq a => a -> Rec1 f a -> Bool Source #

maximum :: Ord a => Rec1 f a -> a Source #

minimum :: Ord a => Rec1 f a -> a Source #

sum :: Num a => Rec1 f a -> a Source #

product :: Num a => Rec1 f a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> URec Char a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Char a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Char a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Char a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Char a -> b Source #

foldr1 :: (a -> a -> a) -> URec Char a -> a Source #

foldl1 :: (a -> a -> a) -> URec Char a -> a Source #

toList :: URec Char a -> [a] Source #

null :: URec Char a -> Bool Source #

length :: URec Char a -> Int Source #

elem :: Eq a => a -> URec Char a -> Bool Source #

maximum :: Ord a => URec Char a -> a Source #

minimum :: Ord a => URec Char a -> a Source #

sum :: Num a => URec Char a -> a Source #

product :: Num a => URec Char a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> URec Double a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Double a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Double a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Double a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Double a -> b Source #

foldr1 :: (a -> a -> a) -> URec Double a -> a Source #

foldl1 :: (a -> a -> a) -> URec Double a -> a Source #

toList :: URec Double a -> [a] Source #

null :: URec Double a -> Bool Source #

length :: URec Double a -> Int Source #

elem :: Eq a => a -> URec Double a -> Bool Source #

maximum :: Ord a => URec Double a -> a Source #

minimum :: Ord a => URec Double a -> a Source #

sum :: Num a => URec Double a -> a Source #

product :: Num a => URec Double a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> URec Float a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Float a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Float a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Float a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Float a -> b Source #

foldr1 :: (a -> a -> a) -> URec Float a -> a Source #

foldl1 :: (a -> a -> a) -> URec Float a -> a Source #

toList :: URec Float a -> [a] Source #

null :: URec Float a -> Bool Source #

length :: URec Float a -> Int Source #

elem :: Eq a => a -> URec Float a -> Bool Source #

maximum :: Ord a => URec Float a -> a Source #

minimum :: Ord a => URec Float a -> a Source #

sum :: Num a => URec Float a -> a Source #

product :: Num a => URec Float a -> a Source #

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 Source #

foldMap :: Monoid m => (a -> m) -> URec Int a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Int a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Int a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Int a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Int a -> b Source #

foldr1 :: (a -> a -> a) -> URec Int a -> a Source #

foldl1 :: (a -> a -> a) -> URec Int a -> a Source #

toList :: URec Int a -> [a] Source #

null :: URec Int a -> Bool Source #

length :: URec Int a -> Int Source #

elem :: Eq a => a -> URec Int a -> Bool Source #

maximum :: Ord a => URec Int a -> a Source #

minimum :: Ord a => URec Int a -> a Source #

sum :: Num a => URec Int a -> a Source #

product :: Num a => URec Int a -> a Source #

Foldable (URec Word :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Word m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec Word a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Word a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Word a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Word a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Word a -> b Source #

foldr1 :: (a -> a -> a) -> URec Word a -> a Source #

foldl1 :: (a -> a -> a) -> URec Word a -> a Source #

toList :: URec Word a -> [a] Source #

null :: URec Word a -> Bool Source #

length :: URec Word a -> Int Source #

elem :: Eq a => a -> URec Word a -> Bool Source #

maximum :: Ord a => URec Word a -> a Source #

minimum :: Ord a => URec Word a -> a Source #

sum :: Num a => URec Word a -> a Source #

product :: Num a => URec Word a -> a Source #

Foldable (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec (Ptr ()) m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec (Ptr ()) a -> m Source #

foldr :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec (Ptr ()) a -> b Source #

foldl :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec (Ptr ()) a -> b Source #

foldr1 :: (a -> a -> a) -> URec (Ptr ()) a -> a Source #

foldl1 :: (a -> a -> a) -> URec (Ptr ()) a -> a Source #

toList :: URec (Ptr ()) a -> [a] Source #

null :: URec (Ptr ()) a -> Bool Source #

length :: URec (Ptr ()) a -> Int Source #

elem :: Eq a => a -> URec (Ptr ()) a -> Bool Source #

maximum :: Ord a => URec (Ptr ()) a -> a Source #

minimum :: Ord a => URec (Ptr ()) a -> a Source #

sum :: Num a => URec (Ptr ()) a -> a Source #

product :: Num a => URec (Ptr ()) a -> a Source #

Foldable f => Foldable (Ap f) | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source #

foldr1 :: (a -> a -> a) -> Ap f a -> a Source #

foldl1 :: (a -> a -> a) -> Ap f a -> a Source #

toList :: Ap f a -> [a] Source #

null :: Ap f a -> Bool Source #

length :: Ap f a -> Int Source #

elem :: Eq a => a -> Ap f a -> Bool Source #

maximum :: Ord a => Ap f a -> a Source #

minimum :: Ord a => Ap f a -> a Source #

sum :: Num a => Ap f a -> a Source #

product :: Num a => Ap f a -> a Source #

Foldable f => Foldable (Alt f) | Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m Source #

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source #

foldr :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source #

foldl :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source #

foldr1 :: (a -> a -> a) -> Alt f a -> a Source #

foldl1 :: (a -> a -> a) -> Alt f a -> a Source #

toList :: Alt f a -> [a] Source #

null :: Alt f a -> Bool Source #

length :: Alt f a -> Int Source #

elem :: Eq a => a -> Alt f a -> Bool Source #

maximum :: Ord a => Alt f a -> a Source #

minimum :: Ord a => Alt f a -> a Source #

sum :: Num a => Alt f a -> a Source #

product :: Num a => Alt f a -> a Source #

Foldable f => Foldable (ErrorT e f) |

Instance details

Defined in Control.Monad.Trans.Error

Methods

fold :: Monoid m => ErrorT e f m -> m Source #

foldMap :: Monoid m => (a -> m) -> ErrorT e f a -> m Source #

foldr :: (a -> b -> b) -> b -> ErrorT e f a -> b Source #

foldr' :: (a -> b -> b) -> b -> ErrorT e f a -> b Source #

foldl :: (b -> a -> b) -> b -> ErrorT e f a -> b Source #

foldl' :: (b -> a -> b) -> b -> ErrorT e f a -> b Source #

foldr1 :: (a -> a -> a) -> ErrorT e f a -> a Source #

foldl1 :: (a -> a -> a) -> ErrorT e f a -> a Source #

toList :: ErrorT e f a -> [a] Source #

null :: ErrorT e f a -> Bool Source #

length :: ErrorT e f a -> Int Source #

elem :: Eq a => a -> ErrorT e f a -> Bool Source #

maximum :: Ord a => ErrorT e f a -> a Source #

minimum :: Ord a => ErrorT e f a -> a Source #

sum :: Num a => ErrorT e f a -> a Source #

product :: Num a => ErrorT e f a -> a Source #

Foldable (K1 i c :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => K1 i c m -> m Source #

foldMap :: Monoid m => (a -> m) -> K1 i c a -> m Source #

foldr :: (a -> b -> b) -> b -> K1 i c a -> b Source #

foldr' :: (a -> b -> b) -> b -> K1 i c a -> b Source #

foldl :: (b -> a -> b) -> b -> K1 i c a -> b Source #

foldl' :: (b -> a -> b) -> b -> K1 i c a -> b Source #

foldr1 :: (a -> a -> a) -> K1 i c a -> a Source #

foldl1 :: (a -> a -> a) -> K1 i c a -> a Source #

toList :: K1 i c a -> [a] Source #

null :: K1 i c a -> Bool Source #

length :: K1 i c a -> Int Source #

elem :: Eq a => a -> K1 i c a -> Bool Source #

maximum :: Ord a => K1 i c a -> a Source #

minimum :: Ord a => K1 i c a -> a Source #

sum :: Num a => K1 i c a -> a Source #

product :: Num a => K1 i c a -> a Source #

(Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :+: g) m -> m Source #

foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :+: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :+: g) a -> a Source #

toList :: (f :+: g) a -> [a] Source #

null :: (f :+: g) a -> Bool Source #

length :: (f :+: g) a -> Int Source #

elem :: Eq a => a -> (f :+: g) a -> Bool Source #

maximum :: Ord a => (f :+: g) a -> a Source #

minimum :: Ord a => (f :+: g) a -> a Source #

sum :: Num a => (f :+: g) a -> a Source #

product :: Num a => (f :+: g) a -> a Source #

(Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :*: g) m -> m Source #

foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :*: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :*: g) a -> a Source #

toList :: (f :*: g) a -> [a] Source #

null :: (f :*: g) a -> Bool Source #

length :: (f :*: g) a -> Int Source #

elem :: Eq a => a -> (f :*: g) a -> Bool Source #

maximum :: Ord a => (f :*: g) a -> a Source #

minimum :: Ord a => (f :*: g) a -> a Source #

sum :: Num a => (f :*: g) a -> a Source #

product :: Num a => (f :*: g) a -> a Source #

Foldable f => Foldable (M1 i c f) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => M1 i c f m -> m Source #

foldMap :: Monoid m => (a -> m) -> M1 i c f a -> m Source #

foldr :: (a -> b -> b) -> b -> M1 i c f a -> b Source #

foldr' :: (a -> b -> b) -> b -> M1 i c f a -> b Source #

foldl :: (b -> a -> b) -> b -> M1 i c f a -> b Source #

foldl' :: (b -> a -> b) -> b -> M1 i c f a -> b Source #

foldr1 :: (a -> a -> a) -> M1 i c f a -> a Source #

foldl1 :: (a -> a -> a) -> M1 i c f a -> a Source #

toList :: M1 i c f a -> [a] Source #

null :: M1 i c f a -> Bool Source #

length :: M1 i c f a -> Int Source #

elem :: Eq a => a -> M1 i c f a -> Bool Source #

maximum :: Ord a => M1 i c f a -> a Source #

minimum :: Ord a => M1 i c f a -> a Source #

sum :: Num a => M1 i c f a -> a Source #

product :: Num a => M1 i c f a -> a Source #

(Foldable f, Foldable g) => Foldable (f :.: g) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => (f :.: g) m -> m Source #

foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source #

foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source #

foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source #

foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source #

foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source #

foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source #

foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source #

toList :: (f :.: g) a -> [a] Source #

null :: (f :.: g) a -> Bool Source #

length :: (f :.: g) a -> Int Source #

elem :: Eq a => a -> (f :.: g) a -> Bool Source #

maximum :: Ord a => (f :.: g) a -> a Source #

minimum :: Ord a => (f :.: g) a -> a Source #

sum :: Num a => (f :.: g) a -> a Source #

product :: Num a => (f :.: g) a -> a Source #

class (Functor t, Foldable t) => Traversable (t :: Type -> Type) where Source #

Functors representing data structures that can be traversed from left to right.

A definition of `traverse` must satisfy the following laws:

naturality
  `t . `traverse` f = `traverse` (t . f)` for every applicative transformation `t`
identity
  ``traverse` Identity = Identity`
composition
  ``traverse` (Compose . `fmap` g . f) = Compose . `fmap` (`traverse` g) . `traverse` f`

A definition of `sequenceA` must satisfy the following laws:

naturality
  `t . `sequenceA` = `sequenceA` . `fmap` t` for every applicative transformation `t`
identity
  ``sequenceA` . `fmap` Identity = Identity`
composition
  ``sequenceA` . `fmap` Compose = Compose . `fmap` `sequenceA` . `sequenceA``

where an applicative transformation is a function

    t :: (Applicative f, Applicative g) => f a -> g a

preserving the `Applicative` operations, i.e.

-     t (pure x) = pure x

-     t (x <*> y) = t x <*> t y

and the identity functor `Identity` and composition of functors `Compose` are defined as

      newtype Identity a = Identity a

      instance Functor Identity where
        fmap f (Identity x) = Identity (f x)

      instance Applicative Identity where
        pure x = Identity x
        Identity f <*> Identity x = Identity (f x)

      newtype Compose f g a = Compose (f (g a))

      instance (Functor f, Functor g) => Functor (Compose f g) where
        fmap f (Compose x) = Compose (fmap (fmap f) x)

      instance (Applicative f, Applicative g) => Applicative (Compose f g) where
        pure x = Compose (pure (pure x))
        Compose f <*> Compose x = Compose ((<*>) <$> f <*> x)

(The naturality law is implied by parametricity.)

Instances are similar to `Functor`, e.g. given a data type

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

a suitable instance would be

    instance Traversable Tree where
       traverse f Empty = pure Empty
       traverse f (Leaf x) = Leaf <$> f x
       traverse f (Node l k r) = Node <$> traverse f l <*> f k <*> traverse f r

This is suitable even for abstract types, as the laws for `<*>` imply a form of associativity.

The superclass instances should satisfy the following:

- In the `Functor` instance, `fmap` should be equivalent to traversal with the identity applicative functor (`fmapDefault`).
- In the `Foldable` instance, `foldMap` should be equivalent to traversal with a constant applicative functor (`foldMapDefault`).

Minimal complete definition

traverse | sequenceA

Methods

traverse :: Applicative f => (a -> f b) -> t a -> f (t b) Source #

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see `traverse_`.

sequenceA :: Applicative f => t (f a) -> f (t a) Source #

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see `sequenceA_`.

sequence :: Monad m => t (m a) -> m (t a) Source #

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see `sequence_`.

Instances

Traversable [] | Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> [a] -> f [b] Source # sequenceA :: Applicative f => [f a] -> f [a] Source # mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source # sequence :: Monad m => [m a] -> m [a] Source #
Traversable Maybe | Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source # sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source #
Traversable Par1 | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Par1 a -> f (Par1 b) Source # sequenceA :: Applicative f => Par1 (f a) -> f (Par1 a) Source # mapM :: Monad m => (a -> m b) -> Par1 a -> m (Par1 b) Source # sequence :: Monad m => Par1 (m a) -> m (Par1 a) Source #
Traversable ZipList | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> ZipList a -> f (ZipList b) Source # sequenceA :: Applicative f => ZipList (f a) -> f (ZipList a) Source # mapM :: Monad m => (a -> m b) -> ZipList a -> m (ZipList b) Source # sequence :: Monad m => ZipList (m a) -> m (ZipList a) Source #
Traversable Identity | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Identity a -> f (Identity b) Source # sequenceA :: Applicative f => Identity (f a) -> f (Identity a) Source # mapM :: Monad m => (a -> m b) -> Identity a -> m (Identity b) Source # sequence :: Monad m => Identity (m a) -> m (Identity a) Source #
Traversable First | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source # sequenceA :: Applicative f => First (f a) -> f (First a) Source # mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source # sequence :: Monad m => First (m a) -> m (First a) Source #
Traversable Last | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source # sequenceA :: Applicative f => Last (f a) -> f (Last a) Source # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source # sequence :: Monad m => Last (m a) -> m (Last a) Source #
Traversable Dual | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source # sequence :: Monad m => Dual (m a) -> m (Dual a) Source #
Traversable Sum | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source # sequence :: Monad m => Sum (m a) -> m (Sum a) Source #
Traversable Product | Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source # sequenceA :: Applicative f => Product (f a) -> f (Product a) Source # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source # sequence :: Monad m => Product (m a) -> m (Product a) Source #
Traversable Down | Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Down a -> f (Down b) Source # sequenceA :: Applicative f => Down (f a) -> f (Down a) Source # mapM :: Monad m => (a -> m b) -> Down a -> m (Down b) Source # sequence :: Monad m => Down (m a) -> m (Down a) Source #
Traversable NonEmpty | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> NonEmpty a -> f (NonEmpty b) Source # sequenceA :: Applicative f => NonEmpty (f a) -> f (NonEmpty a) Source # mapM :: Monad m => (a -> m b) -> NonEmpty a -> m (NonEmpty b) Source # sequence :: Monad m => NonEmpty (m a) -> m (NonEmpty a) Source #
Traversable (Either a) | Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source #
Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> V1 a -> f (V1 b) Source # sequenceA :: Applicative f => V1 (f a) -> f (V1 a) Source # mapM :: Monad m => (a -> m b) -> V1 a -> m (V1 b) Source # sequence :: Monad m => V1 (m a) -> m (V1 a) Source #
Traversable (U1 :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> U1 a -> f (U1 b) Source # sequenceA :: Applicative f => U1 (f a) -> f (U1 a) Source # mapM :: Monad m => (a -> m b) -> U1 a -> m (U1 b) Source # sequence :: Monad m => U1 (m a) -> m (U1 a) Source #
Traversable ((,) a) | Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> (a, a0) -> f (a, b) Source # sequenceA :: Applicative f => (a, f a0) -> f (a, a0) Source # mapM :: Monad m => (a0 -> m b) -> (a, a0) -> m (a, b) Source # sequence :: Monad m => (a, m a0) -> m (a, a0) Source #
Ix i => Traversable (Array i) | Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b) Source # sequenceA :: Applicative f => Array i (f a) -> f (Array i a) Source # mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b) Source # sequence :: Monad m => Array i (m a) -> m (Array i a) Source #
Traversable (Proxy :: Type -> Type) | Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Proxy a -> f (Proxy b) Source # sequenceA :: Applicative f => Proxy (f a) -> f (Proxy a) Source # mapM :: Monad m => (a -> m b) -> Proxy a -> m (Proxy b) Source # sequence :: Monad m => Proxy (m a) -> m (Proxy a) Source #
Traversable (Tree c) |
Instance details Defined in Test.Hspec.Core.Tree Methods traverse :: Applicative f => (a -> f b) -> Tree c a -> f (Tree c b) Source # sequenceA :: Applicative f => Tree c (f a) -> f (Tree c a) Source # mapM :: Monad m => (a -> m b) -> Tree c a -> m (Tree c b) Source # sequence :: Monad m => Tree c (m a) -> m (Tree c a) Source #
Traversable f => Traversable (Rec1 f) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Rec1 f a -> f0 (Rec1 f b) Source # sequenceA :: Applicative f0 => Rec1 f (f0 a) -> f0 (Rec1 f a) Source # mapM :: Monad m => (a -> m b) -> Rec1 f a -> m (Rec1 f b) Source # sequence :: Monad m => Rec1 f (m a) -> m (Rec1 f a) Source #
Traversable (URec Char :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) Source # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) Source # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) Source # sequence :: Monad m => URec Char (m a) -> m (URec Char a) Source #
Traversable (URec Double :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) Source # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) Source # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) Source # sequence :: Monad m => URec Double (m a) -> m (URec Double a) Source #
Traversable (URec Float :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) Source # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) Source # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) Source # sequence :: Monad m => URec Float (m a) -> m (URec Float a) Source #
Traversable (URec Int :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) Source # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) Source # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) Source # sequence :: Monad m => URec Int (m a) -> m (URec Int a) Source #
Traversable (URec Word :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) Source # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) Source # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) Source # sequence :: Monad m => URec Word (m a) -> m (URec Word a) Source #
Traversable (URec (Ptr ()) :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec (Ptr ()) a -> f (URec (Ptr ()) b) Source # sequenceA :: Applicative f => URec (Ptr ()) (f a) -> f (URec (Ptr ()) a) Source # mapM :: Monad m => (a -> m b) -> URec (Ptr ()) a -> m (URec (Ptr ()) b) Source # sequence :: Monad m => URec (Ptr ()) (m a) -> m (URec (Ptr ()) a) Source #
Traversable (Const m :: Type -> Type) | Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b) Source # sequenceA :: Applicative f => Const m (f a) -> f (Const m a) Source # mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b) Source # sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a) Source #
Traversable f => Traversable (Ap f) | Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source # sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source # mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source # sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source #
Traversable f => Traversable (Alt f) | Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source # sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source # mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source # sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source #
Traversable f => Traversable (ErrorT e f) |
Instance details Defined in Control.Monad.Trans.Error Methods traverse :: Applicative f0 => (a -> f0 b) -> ErrorT e f a -> f0 (ErrorT e f b) Source # sequenceA :: Applicative f0 => ErrorT e f (f0 a) -> f0 (ErrorT e f a) Source # mapM :: Monad m => (a -> m b) -> ErrorT e f a -> m (ErrorT e f b) Source # sequence :: Monad m => ErrorT e f (m a) -> m (ErrorT e f a) Source #
Traversable (K1 i c :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> K1 i c a -> f (K1 i c b) Source # sequenceA :: Applicative f => K1 i c (f a) -> f (K1 i c a) Source # mapM :: Monad m => (a -> m b) -> K1 i c a -> m (K1 i c b) Source # sequence :: Monad m => K1 i c (m a) -> m (K1 i c a) Source #
(Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :+: g) a -> f0 ((f :+: g) b) Source # sequenceA :: Applicative f0 => (f :+: g) (f0 a) -> f0 ((f :+: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :+: g) a -> m ((f :+: g) b) Source # sequence :: Monad m => (f :+: g) (m a) -> m ((f :+: g) a) Source #
(Traversable f, Traversable g) => Traversable (f :*: g) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :*: g) a -> f0 ((f :*: g) b) Source # sequenceA :: Applicative f0 => (f :*: g) (f0 a) -> f0 ((f :*: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :*: g) a -> m ((f :*: g) b) Source # sequence :: Monad m => (f :*: g) (m a) -> m ((f :*: g) a) Source #
Traversable f => Traversable (M1 i c f) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> M1 i c f a -> f0 (M1 i c f b) Source # sequenceA :: Applicative f0 => M1 i c f (f0 a) -> f0 (M1 i c f a) Source # mapM :: Monad m => (a -> m b) -> M1 i c f a -> m (M1 i c f b) Source # sequence :: Monad m => M1 i c f (m a) -> m (M1 i c f a) Source #
(Traversable f, Traversable g) => Traversable (f :.: g) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source #

class Semigroup a where Source #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the associativity law:

-     x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Methods

(<>) :: a -> a -> a infixr 6 Source #

An associative operation.

Instances

Semigroup Ordering | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Semigroup () | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: () -> () -> () Source # sconcat :: NonEmpty () -> () Source # stimes :: Integral b => b -> () -> () Source #
Semigroup Summary |
Instance details Defined in Test.Hspec.Core.Runner Methods (<>) :: Summary -> Summary -> Summary Source # sconcat :: NonEmpty Summary -> Summary Source # stimes :: Integral b => b -> Summary -> Summary Source #
Semigroup [a] | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: [a] -> [a] -> [a] Source # sconcat :: NonEmpty [a] -> [a] Source # stimes :: Integral b => b -> [a] -> [a] Source #
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Semigroup (NonEmpty a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source # sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a Source # stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source #
Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a -> b) -> (a -> b) -> a -> b Source # sconcat :: NonEmpty (a -> b) -> a -> b Source # stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source #
Semigroup (Either a b) | Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
(Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b) -> (a, b) -> (a, b) Source # sconcat :: NonEmpty (a, b) -> (a, b) Source # stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source #
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source # stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source # stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source #
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source # stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source #

class Semigroup a => Monoid a where Source #

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following laws:

-     x <> mempty = x

-     mempty <> x = x

- `x `<>` (y `<>` z) = (x `<>` y) `<>` z` (`Semigroup` law)

-     mconcat = foldr '(<>)' mempty

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define `newtype`s and make those instances of `Monoid`, e.g. `Sum` and `Product`.

NOTE: `Semigroup` is a superclass of `Monoid` since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of `mappend`

mappend :: a -> a -> a Source #

An associative operation

NOTE: This method is redundant and has the default implementation ``mappend` = '(<>)'` since base-4.11.0.0.

mconcat :: [a] -> a Source #

Fold a list using the monoid.

For most types, the default definition for `mconcat` will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

Instances

Monoid Ordering | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid Summary |
Instance details Defined in Test.Hspec.Core.Runner Methods mempty :: Summary Source # mappend :: Summary -> Summary -> Summary Source # mconcat :: [Summary] -> Summary Source #
Monoid [a] | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Semigroup a => Monoid (Maybe a) | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (IO a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid b => Monoid (a -> b) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
(Monoid a, Monoid b) => Monoid (a, b) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

data Bool Source #

Constructors

False |
True |

Instances

Bounded Bool | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Bool Source # maxBound :: Bool Source #
Enum Bool | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Bool -> Bool Source # pred :: Bool -> Bool Source # toEnum :: Int -> Bool Source # fromEnum :: Bool -> Int Source # enumFrom :: Bool -> [Bool] Source # enumFromThen :: Bool -> Bool -> [Bool] Source # enumFromTo :: Bool -> Bool -> [Bool] Source # enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] Source #
Eq Bool |
Instance details Defined in GHC.Classes Methods (==) :: Bool -> Bool -> Bool Source # (/=) :: Bool -> Bool -> Bool Source #
Ord Bool |
Instance details Defined in GHC.Classes Methods compare :: Bool -> Bool -> Ordering Source # (<) :: Bool -> Bool -> Bool Source # (<=) :: Bool -> Bool -> Bool Source # (>) :: Bool -> Bool -> Bool Source # (>=) :: Bool -> Bool -> Bool Source # max :: Bool -> Bool -> Bool Source # min :: Bool -> Bool -> Bool Source #
Read Bool | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Bool Source # readList :: ReadS [Bool] Source # readPrec :: ReadPrec Bool Source # readListPrec :: ReadPrec [Bool] Source #
Show Bool | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Bool -> ShowS Source # show :: Bool -> String Source # showList :: [Bool] -> ShowS Source #
Testable Bool |
Instance details Defined in Test.QuickCheck.Property Methods property :: Bool -> Property Source #
Function Bool |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Bool -> b) -> Bool :-> b Source #
Arbitrary Bool |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Bool Source # shrink :: Bool -> [Bool] Source #
CoArbitrary Bool |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Bool -> Gen b -> Gen b Source #
Example Bool |
Instance details Defined in Test.Hspec.Core.Example Associated Types type Arg Bool :: Type Source # Methods evaluateExample :: Bool -> Params -> (ActionWith (Arg Bool) -> IO ()) -> ProgressCallback -> IO Result Source #
Example (a -> Bool) |
Instance details Defined in Test.Hspec.Core.Example Associated Types type Arg (a -> Bool) :: Type Source # Methods evaluateExample :: (a -> Bool) -> Params -> (ActionWith (Arg (a -> Bool)) -> IO ()) -> ProgressCallback -> IO Result Source #
type Arg Bool |
Instance details Defined in Test.Hspec.Core.Example type Arg Bool = ()
type Arg (a -> Bool) |
Instance details Defined in Test.Hspec.Core.Example type Arg (a -> Bool) = a

data Char Source #

The character type `Char` is an enumeration whose values represent Unicode (or equivalently ISO/IEC 10646) code points (i.e. characters, see http://www.unicode.org/ for details). This set extends the ISO 8859-1 (Latin-1) character set (the first 256 characters), which is itself an extension of the ASCII character set (the first 128 characters). A character literal in Haskell has type `Char`.

To convert a `Char` to or from the corresponding `Int` value defined by Unicode, use `toEnum` and `fromEnum` from the `Enum` class respectively (or equivalently `ord` and `chr`).

Instances

Bounded Char | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Char Source # maxBound :: Char Source #
Enum Char | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Char -> Char Source # pred :: Char -> Char Source # toEnum :: Int -> Char Source # fromEnum :: Char -> Int Source # enumFrom :: Char -> [Char] Source # enumFromThen :: Char -> Char -> [Char] Source # enumFromTo :: Char -> Char -> [Char] Source # enumFromThenTo :: Char -> Char -> Char -> [Char] Source #
Eq Char |
Instance details Defined in GHC.Classes Methods (==) :: Char -> Char -> Bool Source # (/=) :: Char -> Char -> Bool Source #
Ord Char |
Instance details Defined in GHC.Classes Methods compare :: Char -> Char -> Ordering Source # (<) :: Char -> Char -> Bool Source # (<=) :: Char -> Char -> Bool Source # (>) :: Char -> Char -> Bool Source # (>=) :: Char -> Char -> Bool Source # max :: Char -> Char -> Char Source # min :: Char -> Char -> Char Source #
Read Char | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Char Source # readList :: ReadS [Char] Source # readPrec :: ReadPrec Char Source # readListPrec :: ReadPrec [Char] Source #
Show Char | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Char -> ShowS Source # show :: Char -> String Source # showList :: [Char] -> ShowS Source #
Function Char |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Char -> b) -> Char :-> b Source #
Arbitrary Char |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Char Source # shrink :: Char -> [Char] Source #
CoArbitrary Char |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Char -> Gen b -> Gen b Source #
ErrorList Char |
Instance details Defined in Control.Monad.Trans.Error Methods listMsg :: String -> [Char] Source #
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 Source #

foldMap :: Monoid m => (a -> m) -> URec Char a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Char a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Char a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Char a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Char a -> b Source #

foldr1 :: (a -> a -> a) -> URec Char a -> a Source #

foldl1 :: (a -> a -> a) -> URec Char a -> a Source #

toList :: URec Char a -> [a] Source #

null :: URec Char a -> Bool Source #

length :: URec Char a -> Int Source #

elem :: Eq a => a -> URec Char a -> Bool Source #

maximum :: Ord a => URec Char a -> a Source #

minimum :: Ord a => URec Char a -> a Source #

sum :: Num a => URec Char a -> a Source #

product :: Num a => URec Char a -> a Source #

Traversable (URec Char :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Char a -> f (URec Char b) Source # sequenceA :: Applicative f => URec Char (f a) -> f (URec Char a) Source # mapM :: Monad m => (a -> m b) -> URec Char a -> m (URec Char b) Source # sequence :: Monad m => URec Char (m a) -> m (URec Char a) Source #

data Double Source #

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.

Instances

Eq Double

Note that due to the presence of `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 Source # (/=) :: Double -> Double -> Bool Source #
Floating Double | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

pi :: Double Source #

exp :: Double -> Double Source #

log :: Double -> Double Source #

sqrt :: Double -> Double Source #

(**) :: Double -> Double -> Double Source #

logBase :: Double -> Double -> Double Source #

sin :: Double -> Double Source #

cos :: Double -> Double Source #

tan :: Double -> Double Source #

asin :: Double -> Double Source #

acos :: Double -> Double Source #

atan :: Double -> Double Source #

sinh :: Double -> Double Source #

cosh :: Double -> Double Source #

tanh :: Double -> Double Source #

asinh :: Double -> Double Source #

acosh :: Double -> Double Source #

atanh :: Double -> Double Source #

log1p :: Double -> Double Source #

expm1 :: Double -> Double Source #

log1pexp :: Double -> Double Source #

log1mexp :: Double -> Double Source #

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 Methods compare :: Double -> Double -> Ordering Source # (<) :: Double -> Double -> Bool Source # (<=) :: Double -> Double -> Bool Source # (>) :: Double -> Double -> Bool Source # (>=) :: Double -> Double -> Bool Source # max :: Double -> Double -> Double Source # min :: Double -> Double -> Double Source #
Read Double | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Double Source # readList :: ReadS [Double] Source # readPrec :: ReadPrec Double Source # readListPrec :: ReadPrec [Double] Source #
RealFloat Double | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

floatRadix :: Double -> Integer Source #

floatDigits :: Double -> Int Source #

floatRange :: Double -> (Int, Int) Source #

decodeFloat :: Double -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Double Source #

exponent :: Double -> Int Source #

significand :: Double -> Double Source #

scaleFloat :: Int -> Double -> Double Source #

isNaN :: Double -> Bool Source #

isInfinite :: Double -> Bool Source #

isDenormalized :: Double -> Bool Source #

isNegativeZero :: Double -> Bool Source #

isIEEE :: Double -> Bool Source #

atan2 :: Double -> Double -> Double Source #

Function Double |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Double -> b) -> Double :-> b Source #
Arbitrary Double |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Double Source # shrink :: Double -> [Double] Source #
CoArbitrary Double |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Double -> Gen b -> Gen b Source #
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 Source #

foldMap :: Monoid m => (a -> m) -> URec Double a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Double a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Double a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Double a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Double a -> b Source #

foldr1 :: (a -> a -> a) -> URec Double a -> a Source #

foldl1 :: (a -> a -> a) -> URec Double a -> a Source #

toList :: URec Double a -> [a] Source #

null :: URec Double a -> Bool Source #

length :: URec Double a -> Int Source #

elem :: Eq a => a -> URec Double a -> Bool Source #

maximum :: Ord a => URec Double a -> a Source #

minimum :: Ord a => URec Double a -> a Source #

sum :: Num a => URec Double a -> a Source #

product :: Num a => URec Double a -> a Source #

Traversable (URec Double :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Double a -> f (URec Double b) Source # sequenceA :: Applicative f => URec Double (f a) -> f (URec Double a) Source # mapM :: Monad m => (a -> m b) -> URec Double a -> m (URec Double b) Source # sequence :: Monad m => URec Double (m a) -> m (URec Double a) Source #

data Float Source #

Single-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE single-precision type.

Instances

Eq Float

Note that due to the presence of `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 Source # (/=) :: Float -> Float -> Bool Source #
Floating Float | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

pi :: Float Source #

exp :: Float -> Float Source #

log :: Float -> Float Source #

sqrt :: Float -> Float Source #

(**) :: Float -> Float -> Float Source #

logBase :: Float -> Float -> Float Source #

sin :: Float -> Float Source #

cos :: Float -> Float Source #

tan :: Float -> Float Source #

asin :: Float -> Float Source #

acos :: Float -> Float Source #

atan :: Float -> Float Source #

sinh :: Float -> Float Source #

cosh :: Float -> Float Source #

tanh :: Float -> Float Source #

asinh :: Float -> Float Source #

acosh :: Float -> Float Source #

atanh :: Float -> Float Source #

log1p :: Float -> Float Source #

expm1 :: Float -> Float Source #

log1pexp :: Float -> Float Source #

log1mexp :: Float -> Float Source #

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 Source # (<) :: Float -> Float -> Bool Source # (<=) :: Float -> Float -> Bool Source # (>) :: Float -> Float -> Bool Source # (>=) :: Float -> Float -> Bool Source # max :: Float -> Float -> Float Source # min :: Float -> Float -> Float Source #
Read Float | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Float Source # readList :: ReadS [Float] Source # readPrec :: ReadPrec Float Source # readListPrec :: ReadPrec [Float] Source #
RealFloat Float | Since: base-2.1

Instance details

Defined in GHC.Float

Methods

floatRadix :: Float -> Integer Source #

floatDigits :: Float -> Int Source #

floatRange :: Float -> (Int, Int) Source #

decodeFloat :: Float -> (Integer, Int) Source #

encodeFloat :: Integer -> Int -> Float Source #

exponent :: Float -> Int Source #

significand :: Float -> Float Source #

scaleFloat :: Int -> Float -> Float Source #

isNaN :: Float -> Bool Source #

isInfinite :: Float -> Bool Source #

isDenormalized :: Float -> Bool Source #

isNegativeZero :: Float -> Bool Source #

isIEEE :: Float -> Bool Source #

atan2 :: Float -> Float -> Float Source #

Function Float |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Float -> b) -> Float :-> b Source #
Arbitrary Float |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Float Source # shrink :: Float -> [Float] Source #
CoArbitrary Float |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Float -> Gen b -> Gen b Source #
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 Source #

foldMap :: Monoid m => (a -> m) -> URec Float a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Float a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Float a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Float a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Float a -> b Source #

foldr1 :: (a -> a -> a) -> URec Float a -> a Source #

foldl1 :: (a -> a -> a) -> URec Float a -> a Source #

toList :: URec Float a -> [a] Source #

null :: URec Float a -> Bool Source #

length :: URec Float a -> Int Source #

elem :: Eq a => a -> URec Float a -> Bool Source #

maximum :: Ord a => URec Float a -> a Source #

minimum :: Ord a => URec Float a -> a Source #

sum :: Num a => URec Float a -> a Source #

product :: Num a => URec Float a -> a Source #

Traversable (URec Float :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Float a -> f (URec Float b) Source # sequenceA :: Applicative f => URec Float (f a) -> f (URec Float a) Source # mapM :: Monad m => (a -> m b) -> URec Float a -> m (URec Float b) Source # sequence :: Monad m => URec Float (m a) -> m (URec Float a) Source #

data Int Source #

A fixed-precision integer type with at least the range `[-2^29 .. 2^29-1]`. The exact range for a given implementation can be determined by using `minBound` and `maxBound` from the `Bounded` class.

Instances

Bounded Int | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Int Source # maxBound :: Int Source #
Enum Int | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Int -> Int Source # pred :: Int -> Int Source # toEnum :: Int -> Int Source # fromEnum :: Int -> Int Source # enumFrom :: Int -> [Int] Source # enumFromThen :: Int -> Int -> [Int] Source # enumFromTo :: Int -> Int -> [Int] Source # enumFromThenTo :: Int -> Int -> Int -> [Int] Source #
Eq Int |
Instance details Defined in GHC.Classes Methods (==) :: Int -> Int -> Bool Source # (/=) :: Int -> Int -> Bool Source #
Integral Int | Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Int -> Int -> Int Source # rem :: Int -> Int -> Int Source # div :: Int -> Int -> Int Source # mod :: Int -> Int -> Int Source # quotRem :: Int -> Int -> (Int, Int) Source # divMod :: Int -> Int -> (Int, Int) Source # toInteger :: Int -> Integer Source #
Num Int | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Int -> Int -> Int Source # (-) :: Int -> Int -> Int Source # (*) :: Int -> Int -> Int Source # negate :: Int -> Int Source # abs :: Int -> Int Source # signum :: Int -> Int Source # fromInteger :: Integer -> Int Source #
Ord Int |
Instance details Defined in GHC.Classes Methods compare :: Int -> Int -> Ordering Source # (<) :: Int -> Int -> Bool Source # (<=) :: Int -> Int -> Bool Source # (>) :: Int -> Int -> Bool Source # (>=) :: Int -> Int -> Bool Source # max :: Int -> Int -> Int Source # min :: Int -> Int -> Int Source #
Read Int | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Int Source # readList :: ReadS [Int] Source # readPrec :: ReadPrec Int Source # readListPrec :: ReadPrec [Int] Source #
Real Int | Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Int -> Rational Source #
Show Int | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Int -> ShowS Source # show :: Int -> String Source # showList :: [Int] -> ShowS Source #
Function Int |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Int -> b) -> Int :-> b Source #
Arbitrary Int |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Int Source # shrink :: Int -> [Int] Source #
CoArbitrary Int |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Int -> Gen b -> Gen b Source #
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 Source #

foldMap :: Monoid m => (a -> m) -> URec Int a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Int a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Int a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Int a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Int a -> b Source #

foldr1 :: (a -> a -> a) -> URec Int a -> a Source #

foldl1 :: (a -> a -> a) -> URec Int a -> a Source #

toList :: URec Int a -> [a] Source #

null :: URec Int a -> Bool Source #

length :: URec Int a -> Int Source #

elem :: Eq a => a -> URec Int a -> Bool Source #

maximum :: Ord a => URec Int a -> a Source #

minimum :: Ord a => URec Int a -> a Source #

sum :: Num a => URec Int a -> a Source #

product :: Num a => URec Int a -> a Source #

Traversable (URec Int :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Int a -> f (URec Int b) Source # sequenceA :: Applicative f => URec Int (f a) -> f (URec Int a) Source # mapM :: Monad m => (a -> m b) -> URec Int a -> m (URec Int b) Source # sequence :: Monad m => URec Int (m a) -> m (URec Int a) Source #

data Integer Source #

Invariant: `Jn#` and `Jp#` are used iff value doesn't fit in `S#`

Useful properties resulting from the invariants:

-     abs (S# _) <= abs (Jp# _)

-     abs (S# _) <  abs (Jn# _)

Instances

Enum Integer | Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Integer -> Integer Source #

pred :: Integer -> Integer Source #

toEnum :: Int -> Integer Source #

fromEnum :: Integer -> Int Source #

enumFrom :: Integer -> [Integer] Source #

enumFromThen :: Integer -> Integer -> [Integer] Source #

enumFromTo :: Integer -> Integer -> [Integer] Source #

enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] Source #

Eq Integer |
Instance details Defined in GHC.Integer.Type Methods (==) :: Integer -> Integer -> Bool Source # (/=) :: Integer -> Integer -> Bool Source #
Integral Integer | Since: base-2.0.1
Instance details Defined in GHC.Real Methods quot :: Integer -> Integer -> Integer Source # rem :: Integer -> Integer -> Integer Source # div :: Integer -> Integer -> Integer Source # mod :: Integer -> Integer -> Integer Source # quotRem :: Integer -> Integer -> (Integer, Integer) Source # divMod :: Integer -> Integer -> (Integer, Integer) Source # toInteger :: Integer -> Integer Source #
Num Integer | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Integer -> Integer -> Integer Source # (-) :: Integer -> Integer -> Integer Source # (*) :: Integer -> Integer -> Integer Source # negate :: Integer -> Integer Source # abs :: Integer -> Integer Source # signum :: Integer -> Integer Source # fromInteger :: Integer -> Integer Source #
Ord Integer |
Instance details Defined in GHC.Integer.Type Methods compare :: Integer -> Integer -> Ordering Source # (<) :: Integer -> Integer -> Bool Source # (<=) :: Integer -> Integer -> Bool Source # (>) :: Integer -> Integer -> Bool Source # (>=) :: Integer -> Integer -> Bool Source # max :: Integer -> Integer -> Integer Source # min :: Integer -> Integer -> Integer Source #
Read Integer | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Integer Source # readList :: ReadS [Integer] Source # readPrec :: ReadPrec Integer Source # readListPrec :: ReadPrec [Integer] Source #
Real Integer | Since: base-2.0.1
Instance details Defined in GHC.Real Methods toRational :: Integer -> Rational Source #
Show Integer | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Integer -> ShowS Source # show :: Integer -> String Source # showList :: [Integer] -> ShowS Source #
Function Integer |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Integer -> b) -> Integer :-> b Source #
Arbitrary Integer |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Integer Source # shrink :: Integer -> [Integer] Source #
CoArbitrary Integer |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Integer -> Gen b -> Gen b Source #

data Maybe a Source #

The `Maybe` type encapsulates an optional value. A value of type ``Maybe` a` either contains a value of type `a` (represented as ``Just` a`), or it is empty (represented as `Nothing`). Using `Maybe` is a good way to deal with errors or exceptional cases without resorting to drastic measures such as `error`.

The `Maybe` type is also a monad. It is a simple kind of error monad, where all errors are represented by `Nothing`. A richer error monad can be built using the `Either` type.

Constructors

Nothing |
Just a |

Instances

Monad Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b Source # (>>) :: Maybe a -> Maybe b -> Maybe b Source # return :: a -> Maybe a Source # fail :: String -> Maybe a Source #
Functor Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> Maybe a -> Maybe b Source # (<$) :: a -> Maybe b -> Maybe a Source #
Applicative Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> Maybe a Source # (<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source # liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source # (*>) :: Maybe a -> Maybe b -> Maybe b Source # (<*) :: Maybe a -> Maybe b -> Maybe a Source #
Foldable Maybe | Since: base-2.1

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Maybe m -> m Source #

foldMap :: Monoid m => (a -> m) -> Maybe a -> m Source #

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

foldr' :: (a -> b -> b) -> b -> Maybe a -> b Source #

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

foldl' :: (b -> a -> b) -> b -> Maybe a -> b Source #

foldr1 :: (a -> a -> a) -> Maybe a -> a Source #

foldl1 :: (a -> a -> a) -> Maybe a -> a Source #

toList :: Maybe a -> [a] Source #

null :: Maybe a -> Bool Source #

length :: Maybe a -> Int Source #

elem :: Eq a => a -> Maybe a -> Bool Source #

maximum :: Ord a => Maybe a -> a Source #

minimum :: Ord a => Maybe a -> a Source #

sum :: Num a => Maybe a -> a Source #

product :: Num a => Maybe a -> a Source #

Traversable Maybe | Since: base-2.1
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Maybe a -> f (Maybe b) Source # sequenceA :: Applicative f => Maybe (f a) -> f (Maybe a) Source # mapM :: Monad m => (a -> m b) -> Maybe a -> m (Maybe b) Source # sequence :: Monad m => Maybe (m a) -> m (Maybe a) Source #
Arbitrary1 Maybe |
Instance details Defined in Test.QuickCheck.Arbitrary Methods liftArbitrary :: Gen a -> Gen (Maybe a) Source # liftShrink :: (a -> [a]) -> Maybe a -> [Maybe a] Source #
Alternative Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods empty :: Maybe a Source # (<|>) :: Maybe a -> Maybe a -> Maybe a Source # some :: Maybe a -> Maybe [a] Source # many :: Maybe a -> Maybe [a] Source #
MonadPlus Maybe | Since: base-2.1
Instance details Defined in GHC.Base Methods mzero :: Maybe a Source # mplus :: Maybe a -> Maybe a -> Maybe a Source #
Eq a => Eq (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Maybe Methods (==) :: Maybe a -> Maybe a -> Bool Source # (/=) :: Maybe a -> Maybe a -> Bool Source #
Ord a => Ord (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Maybe Methods compare :: Maybe a -> Maybe a -> Ordering Source # (<) :: Maybe a -> Maybe a -> Bool Source # (<=) :: Maybe a -> Maybe a -> Bool Source # (>) :: Maybe a -> Maybe a -> Bool Source # (>=) :: Maybe a -> Maybe a -> Bool Source # max :: Maybe a -> Maybe a -> Maybe a Source # min :: Maybe a -> Maybe a -> Maybe a Source #
Read a => Read (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS (Maybe a) Source # readList :: ReadS [Maybe a] Source # readPrec :: ReadPrec (Maybe a) Source # readListPrec :: ReadPrec [Maybe a] Source #
Show a => Show (Maybe a) | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Maybe a -> ShowS Source # show :: Maybe a -> String Source # showList :: [Maybe a] -> ShowS Source #
Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Maybe a -> Maybe a -> Maybe a Source # sconcat :: NonEmpty (Maybe a) -> Maybe a Source # stimes :: Integral b => b -> Maybe a -> Maybe a Source #
Semigroup a => Monoid (Maybe a) | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Function a => Function (Maybe a) |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Maybe a -> b) -> Maybe a :-> b Source #
Arbitrary a => Arbitrary (Maybe a) |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen (Maybe a) Source # shrink :: Maybe a -> [Maybe a] Source #
CoArbitrary a => CoArbitrary (Maybe a) |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Maybe a -> Gen b -> Gen b Source #

data Ordering Source #

Constructors

LT |
EQ |
GT |

Instances

Bounded Ordering | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Ordering Source # maxBound :: Ordering Source #
Enum Ordering | Since: base-2.1

Instance details

Defined in GHC.Enum

Methods

succ :: Ordering -> Ordering Source #

pred :: Ordering -> Ordering Source #

toEnum :: Int -> Ordering Source #

fromEnum :: Ordering -> Int Source #

enumFrom :: Ordering -> [Ordering] Source #

enumFromThen :: Ordering -> Ordering -> [Ordering] Source #

enumFromTo :: Ordering -> Ordering -> [Ordering] Source #

enumFromThenTo :: Ordering -> Ordering -> Ordering -> [Ordering] Source #

Eq Ordering |
Instance details Defined in GHC.Classes Methods (==) :: Ordering -> Ordering -> Bool Source # (/=) :: Ordering -> Ordering -> Bool Source #
Ord Ordering |
Instance details Defined in GHC.Classes Methods compare :: Ordering -> Ordering -> Ordering Source # (<) :: Ordering -> Ordering -> Bool Source # (<=) :: Ordering -> Ordering -> Bool Source # (>) :: Ordering -> Ordering -> Bool Source # (>=) :: Ordering -> Ordering -> Bool Source # max :: Ordering -> Ordering -> Ordering Source # min :: Ordering -> Ordering -> Ordering Source #
Read Ordering | Since: base-2.1
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Ordering Source # readList :: ReadS [Ordering] Source # readPrec :: ReadPrec Ordering Source # readListPrec :: ReadPrec [Ordering] Source #
Show Ordering | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Ordering -> ShowS Source # show :: Ordering -> String Source # showList :: [Ordering] -> ShowS Source #
Semigroup Ordering | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods (<>) :: Ordering -> Ordering -> Ordering Source # sconcat :: NonEmpty Ordering -> Ordering Source # stimes :: Integral b => b -> Ordering -> Ordering Source #
Monoid Ordering | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Function Ordering |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Ordering -> b) -> Ordering :-> b Source #
Arbitrary Ordering |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Ordering Source # shrink :: Ordering -> [Ordering] Source #
CoArbitrary Ordering |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Ordering -> Gen b -> Gen b Source #

type Rational = Ratio Integer Source #

Arbitrary-precision rational numbers, represented as a ratio of two `Integer` values. A rational number may be constructed using the `%` operator.

data IO a Source #

A value of type ``IO` a` is a computation which, when performed, does some I/O before returning a value of type `a`.

There is really only one way to "perform" an I/O action: bind it to `Main.main` in your program. When your program is run, the I/O will be performed. It isn't possible to perform I/O from an arbitrary function, unless that function is itself in the `IO` monad and called at some point, directly or indirectly, from `Main.main`.

`IO` is a monad, so `IO` actions can be combined using either the do-notation or the `>>` and `>>=` operations from the `Monad` class.

Instances

Monad IO | Since: base-2.1
Instance details Defined in GHC.Base Methods (>>=) :: IO a -> (a -> IO b) -> IO b Source # (>>) :: IO a -> IO b -> IO b Source # return :: a -> IO a Source # fail :: String -> IO a Source #
Functor IO | Since: base-2.1
Instance details Defined in GHC.Base Methods fmap :: (a -> b) -> IO a -> IO b Source # (<$) :: a -> IO b -> IO a Source #
Applicative IO | Since: base-2.1
Instance details Defined in GHC.Base Methods pure :: a -> IO a Source # (<*>) :: IO (a -> b) -> IO a -> IO b Source # liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source # (*>) :: IO a -> IO b -> IO b Source # (<*) :: IO a -> IO b -> IO a Source #
Alternative IO | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods empty :: IO a Source # (<|>) :: IO a -> IO a -> IO a Source # some :: IO a -> IO [a] Source # many :: IO a -> IO [a] Source #
MonadPlus IO | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mzero :: IO a Source # mplus :: IO a -> IO a -> IO a Source #
Example Expectation |
Instance details Defined in Test.Hspec.Core.Example Associated Types type Arg Expectation :: Type Source # Methods evaluateExample :: Expectation -> Params -> (ActionWith (Arg Expectation) -> IO ()) -> ProgressCallback -> IO Result Source #
Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0
Instance details Defined in GHC.Base Methods (<>) :: IO a -> IO a -> IO a Source # sconcat :: NonEmpty (IO a) -> IO a Source # stimes :: Integral b => b -> IO a -> IO a Source #
Monoid a => Monoid (IO a) | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
IsFormatter (IO Formatter) Source # |
Instance details Defined in Test.Hspec.Discover Methods toFormatter :: IO Formatter -> IO Formatter Source #
Example (a -> Expectation) |
Instance details Defined in Test.Hspec.Core.Example Associated Types type Arg (a -> Expectation) :: Type Source # Methods evaluateExample :: (a -> Expectation) -> Params -> (ActionWith (Arg (a -> Expectation)) -> IO ()) -> ProgressCallback -> IO Result Source #
type Arg Expectation |
Instance details Defined in Test.Hspec.Core.Example type Arg Expectation = ()
type Arg (a -> Expectation) |
Instance details Defined in Test.Hspec.Core.Example type Arg (a -> Expectation) = a

data Word Source #

A `Word` is an unsigned integral type, with the same size as `Int`.

Instances

Bounded Word | Since: base-2.1
Instance details Defined in GHC.Enum Methods minBound :: Word Source # maxBound :: Word Source #
Enum Word | Since: base-2.1
Instance details Defined in GHC.Enum Methods succ :: Word -> Word Source # pred :: Word -> Word Source # toEnum :: Int -> Word Source # fromEnum :: Word -> Int Source # enumFrom :: Word -> [Word] Source # enumFromThen :: Word -> Word -> [Word] Source # enumFromTo :: Word -> Word -> [Word] Source # enumFromThenTo :: Word -> Word -> Word -> [Word] Source #
Eq Word |
Instance details Defined in GHC.Classes Methods (==) :: Word -> Word -> Bool Source # (/=) :: Word -> Word -> Bool Source #
Integral Word | Since: base-2.1
Instance details Defined in GHC.Real Methods quot :: Word -> Word -> Word Source # rem :: Word -> Word -> Word Source # div :: Word -> Word -> Word Source # mod :: Word -> Word -> Word Source # quotRem :: Word -> Word -> (Word, Word) Source # divMod :: Word -> Word -> (Word, Word) Source # toInteger :: Word -> Integer Source #
Num Word | Since: base-2.1
Instance details Defined in GHC.Num Methods (+) :: Word -> Word -> Word Source # (-) :: Word -> Word -> Word Source # (*) :: Word -> Word -> Word Source # negate :: Word -> Word Source # abs :: Word -> Word Source # signum :: Word -> Word Source # fromInteger :: Integer -> Word Source #
Ord Word |
Instance details Defined in GHC.Classes Methods compare :: Word -> Word -> Ordering Source # (<) :: Word -> Word -> Bool Source # (<=) :: Word -> Word -> Bool Source # (>) :: Word -> Word -> Bool Source # (>=) :: Word -> Word -> Bool Source # max :: Word -> Word -> Word Source # min :: Word -> Word -> Word Source #
Read Word | Since: base-4.5.0.0
Instance details Defined in GHC.Read Methods readsPrec :: Int -> ReadS Word Source # readList :: ReadS [Word] Source # readPrec :: ReadPrec Word Source # readListPrec :: ReadPrec [Word] Source #
Real Word | Since: base-2.1
Instance details Defined in GHC.Real Methods toRational :: Word -> Rational Source #
Show Word | Since: base-2.1
Instance details Defined in GHC.Show Methods showsPrec :: Int -> Word -> ShowS Source # show :: Word -> String Source # showList :: [Word] -> ShowS Source #
Function Word |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Word -> b) -> Word :-> b Source #
Arbitrary Word |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen Word Source # shrink :: Word -> [Word] Source #
CoArbitrary Word |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Word -> Gen b -> Gen b Source #
Foldable (URec Word :: Type -> Type) | Since: base-4.9.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => URec Word m -> m Source #

foldMap :: Monoid m => (a -> m) -> URec Word a -> m Source #

foldr :: (a -> b -> b) -> b -> URec Word a -> b Source #

foldr' :: (a -> b -> b) -> b -> URec Word a -> b Source #

foldl :: (b -> a -> b) -> b -> URec Word a -> b Source #

foldl' :: (b -> a -> b) -> b -> URec Word a -> b Source #

foldr1 :: (a -> a -> a) -> URec Word a -> a Source #

foldl1 :: (a -> a -> a) -> URec Word a -> a Source #

toList :: URec Word a -> [a] Source #

null :: URec Word a -> Bool Source #

length :: URec Word a -> Int Source #

elem :: Eq a => a -> URec Word a -> Bool Source #

maximum :: Ord a => URec Word a -> a Source #

minimum :: Ord a => URec Word a -> a Source #

sum :: Num a => URec Word a -> a Source #

product :: Num a => URec Word a -> a Source #

Traversable (URec Word :: Type -> Type) | Since: base-4.9.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> URec Word a -> f (URec Word b) Source # sequenceA :: Applicative f => URec Word (f a) -> f (URec Word a) Source # mapM :: Monad m => (a -> m b) -> URec Word a -> m (URec Word b) Source # sequence :: Monad m => URec Word (m a) -> m (URec Word a) Source #

data Either a b Source #

The `Either` type represents values with two possibilities: a value of type ``Either` a b` is either ``Left` a` or ``Right` b`.

The `Either` type is sometimes used to represent a value which is either correct or an error; by convention, the `Left` constructor is used to hold an error value and the `Right` constructor is used to hold a correct value (mnemonic: "right" also means "correct").

#### Examples

Expand

The type ``Either` `String` `Int`` is the type of values which can be either a `String` or an `Int`. The `Left` constructor can be used only on `String`s, and the `Right` constructor can be used only on `Int`s:

    >>> let s = Left "foo" :: Either String Int
    >>> s
    Left "foo"
    >>> let n = Right 3 :: Either String Int
    >>> n
    Right 3
    >>> :type s
    s :: Either String Int
    >>> :type n
    n :: Either String Int

The `fmap` from our `Functor` instance will ignore `Left` values, but will apply the supplied function to values contained in a `Right`:

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

The `Monad` instance for `Either` allows us to chain together multiple actions which may fail, and fail overall if any of the individual steps failed. First we'll write a function that can either parse an `Int` from a `Char`, or fail.

    >>> import Data.Char ( digitToInt, isDigit )
    >>> :{
        let parseEither :: Char -> Either String Int
            parseEither c
              | isDigit c = Right (digitToInt c)
              | otherwise = Left "parse error"
    >>> :}

The following should work, since both `'1'` and `'2'` can be parsed as `Int`s.

    >>> :{
        let parseMultiple :: Either String Int
            parseMultiple = do
              x <- parseEither '1'
              y <- parseEither '2'
              return (x + y)
    >>> :}

    >>> parseMultiple
    Right 3

But the following should fail overall, since the first operation where we attempt to parse `'m'` as an `Int` will fail:

    >>> :{
        let parseMultiple :: Either String Int
            parseMultiple = do
              x <- parseEither 'm'
              y <- parseEither '2'
              return (x + y)
    >>> :}

    >>> parseMultiple
    Left "parse error"

Constructors

Left a |
Right b |

Instances

Arbitrary2 Either |
Instance details Defined in Test.QuickCheck.Arbitrary Methods liftArbitrary2 :: Gen a -> Gen b -> Gen (Either a b) Source # liftShrink2 :: (a -> [a]) -> (b -> [b]) -> Either a b -> [Either a b] Source #
Monad (Either e) | Since: base-4.4.0.0
Instance details Defined in Data.Either Methods (>>=) :: Either e a -> (a -> Either e b) -> Either e b Source # (>>) :: Either e a -> Either e b -> Either e b Source # return :: a -> Either e a Source # fail :: String -> Either e a Source #
Functor (Either a) | Since: base-3.0
Instance details Defined in Data.Either Methods fmap :: (a0 -> b) -> Either a a0 -> Either a b Source # (<$) :: a0 -> Either a b -> Either a a0 Source #
Applicative (Either e) | Since: base-3.0
Instance details Defined in Data.Either Methods pure :: a -> Either e a Source # (<*>) :: Either e (a -> b) -> Either e a -> Either e b Source # liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source # (*>) :: Either e a -> Either e b -> Either e b Source # (<*) :: Either e a -> Either e b -> Either e a Source #
Foldable (Either a) | Since: base-4.7.0.0

Instance details

Defined in Data.Foldable

Methods

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

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

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

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

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

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

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

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

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

null :: Either a a0 -> Bool Source #

length :: Either a a0 -> Int Source #

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

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

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

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

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

Traversable (Either a) | Since: base-4.7.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a0 -> f b) -> Either a a0 -> f (Either a b) Source # sequenceA :: Applicative f => Either a (f a0) -> f (Either a a0) Source # mapM :: Monad m => (a0 -> m b) -> Either a a0 -> m (Either a b) Source # sequence :: Monad m => Either a (m a0) -> m (Either a a0) Source #
Arbitrary a => Arbitrary1 (Either a) |
Instance details Defined in Test.QuickCheck.Arbitrary Methods liftArbitrary :: Gen a0 -> Gen (Either a a0) Source # liftShrink :: (a0 -> [a0]) -> Either a a0 -> [Either a a0] Source #
(Eq a, Eq b) => Eq (Either a b) | Since: base-2.1
Instance details Defined in Data.Either Methods (==) :: Either a b -> Either a b -> Bool Source # (/=) :: Either a b -> Either a b -> Bool Source #
(Ord a, Ord b) => Ord (Either a b) | Since: base-2.1

Instance details

Defined in Data.Either

Methods

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

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

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

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

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

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

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

(Read a, Read b) => Read (Either a b) | Since: base-3.0
Instance details Defined in Data.Either Methods readsPrec :: Int -> ReadS (Either a b) Source # readList :: ReadS [Either a b] Source # readPrec :: ReadPrec (Either a b) Source # readListPrec :: ReadPrec [Either a b] Source #
(Show a, Show b) => Show (Either a b) | Since: base-3.0
Instance details Defined in Data.Either Methods showsPrec :: Int -> Either a b -> ShowS Source # show :: Either a b -> String Source # showList :: [Either a b] -> ShowS Source #
Semigroup (Either a b) | Since: base-4.9.0.0
Instance details Defined in Data.Either Methods (<>) :: Either a b -> Either a b -> Either a b Source # sconcat :: NonEmpty (Either a b) -> Either a b Source # stimes :: Integral b0 => b0 -> Either a b -> Either a b Source #
(Function a, Function b) => Function (Either a b) |
Instance details Defined in Test.QuickCheck.Function Methods function :: (Either a b -> b0) -> Either a b :-> b0 Source #
(Arbitrary a, Arbitrary b) => Arbitrary (Either a b) |
Instance details Defined in Test.QuickCheck.Arbitrary Methods arbitrary :: Gen (Either a b) Source # shrink :: Either a b -> [Either a b] Source #
(CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) |
Instance details Defined in Test.QuickCheck.Arbitrary Methods coarbitrary :: Either a b -> Gen b0 -> Gen b0 Source #

type String = [Char] Source #

A `String` is a list of characters. String constants in Haskell are values of type `String`.

readIO :: Read a => String -> IO a Source #

The `readIO` function is similar to `read` except that it signals parse failure to the `IO` monad instead of terminating the program.

readLn :: Read a => IO a Source #

The `readLn` function combines `getLine` and `readIO`.

appendFile :: FilePath -> String -> IO () Source #

The computation `appendFile` `file str` function appends the string `str`, to the file `file`.

Note that `writeFile` and `appendFile` write a literal string to a file. To write a value of any printable type, as with `print`, use the `show` function to convert the value to a string first.

    main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

writeFile :: FilePath -> String -> IO () Source #

The computation `writeFile` `file str` function writes the string `str`, to the file `file`.

readFile :: FilePath -> IO String Source #

The `readFile` function reads a file and returns the contents of the file as a string. The file is read lazily, on demand, as with `getContents`.

interact :: (String -> String) -> IO () Source #

The `interact` function takes a function of type `String->String` as its argument. The entire input from the standard input device is passed to this function as its argument, and the resulting string is output on the standard output device.

getContents :: IO String Source #

The `getContents` operation returns all user input as a single string, which is read lazily as it is needed (same as `hGetContents` `stdin`).

getLine :: IO String Source #

Read a line from the standard input device (same as `hGetLine` `stdin`).

getChar :: IO Char Source #

Read a character from the standard input device (same as `hGetChar` `stdin`).

putStrLn :: String -> IO () Source #

The same as `putStr`, but adds a newline character.

putStr :: String -> IO () Source #

Write a string to the standard output device (same as `hPutStr` `stdout`).

putChar :: Char -> IO () Source #

Write a character to the standard output device (same as `hPutChar` `stdout`).

ioError :: IOError -> IO a Source #

Raise an `IOException` in the `IO` monad.

type FilePath = String Source #

File and directory names are values of type `String`, whose precise meaning is operating system dependent. Files can be opened, yielding a handle which can then be used to operate on the contents of that file.

userError :: String -> IOError Source #

Construct an `IOException` value with a string describing the error. The `fail` method of the `IO` instance of the `Monad` class raises a `userError`, thus:

    instance Monad IO where
      ...
      fail s = ioError (userError s)

type IOError = IOException Source #

The Haskell 2010 type for exceptions in the `IO` monad. Any I/O operation may raise an `IOException` instead of returning a result. For a more general type of exception, including also those that arise in pure code, see `Exception`.

In Haskell 2010, this is an opaque type.

notElem :: (Foldable t, Eq a) => a -> t a -> Bool infix 4 Source #

`notElem` is the negation of `elem`.

all :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether all elements of the structure satisfy the predicate.

any :: Foldable t => (a -> Bool) -> t a -> Bool Source #

Determines whether any element of the structure satisfies the predicate.

or :: Foldable t => t Bool -> Bool Source #

`or` returns the disjunction of a container of Bools. For the result to be `False`, the container must be finite; `True`, however, results from a `True` value finitely far from the left end.

and :: Foldable t => t Bool -> Bool Source #

`and` returns the conjunction of a container of Bools. For the result to be `True`, the container must be finite; `False`, however, results from a `False` value finitely far from the left end.

concatMap :: Foldable t => (a -> [b]) -> t a -> [b] Source #

Map a function over all the elements of a container and concatenate the resulting lists.

concat :: Foldable t => t [a] -> [a] Source #

The concatenation of all the elements of a container of lists.

sequence_ :: (Foldable t, Monad m) => t (m a) -> m () Source #

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see `sequence`.

As of base 4.8.0.0, `sequence_` is just `sequenceA_`, specialized to `Monad`.

mapM_ :: (Foldable t, Monad m) => (a -> m b) -> t a -> m () Source #

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see `mapM`.

As of base 4.8.0.0, `mapM_` is just `traverse_`, specialized to `Monad`.

unwords :: [String] -> String Source #

`unwords` is an inverse operation to `words`. It joins words with separating spaces.

    >>> unwords ["Lorem", "ipsum", "dolor"]
    "Lorem ipsum dolor"

words :: String -> [String] Source #

`words` breaks a string up into a list of words, which were delimited by white space.

    >>> words "Lorem ipsum\ndolor"
    ["Lorem","ipsum","dolor"]

unlines :: [String] -> String Source #

`unlines` is an inverse operation to `lines`. It joins lines, after appending a terminating newline to each.

    >>> unlines ["Hello", "World", "!"]
    "Hello\nWorld\n!\n"

lines :: String -> [String] Source #

`lines` breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

    >>> lines ""
    []

    >>> lines "\n"
    [""]

    >>> lines "one"
    ["one"]

    >>> lines "one\n"
    ["one"]

    >>> lines "one\n\n"
    ["one",""]

    >>> lines "one\ntwo"
    ["one","two"]

    >>> lines "one\ntwo\n"
    ["one","two"]

Thus ``lines` s` contains at least as many elements as newlines in `s`.

read :: Read a => String -> a Source #

The `read` function reads input from a string, which must be completely consumed by the input process. `read` fails with an `error` if the parse is unsuccessful, and it is therefore discouraged from being used in real applications. Use `readMaybe` or `readEither` for safe alternatives.

    >>> read "123" :: Int
    123

    >>> read "hello" :: Int
    *** Exception: Prelude.read: no parse

reads :: Read a => ReadS a Source #

equivalent to `readsPrec` with a precedence of 0.

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

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

#### Examples

Expand

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

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

lex :: ReadS String Source #

The `lex` function reads a single lexeme from the input, discarding initial white space, and returning the characters that constitute the lexeme. If the input string contains only white space, `lex` returns a single successful `lexeme' consisting of the empty string. (Thus ``lex` "" = [("","")]`.) If there is no legal lexeme at the beginning of the input string, `lex` fails (i.e. returns `[]`).

This lexer is not completely faithful to the Haskell lexical syntax in the following respects:

- Qualified names are not handled properly
- Octal and hexadecimal numerics are not recognized as a single token
- Comments are not treated properly

readParen :: Bool -> ReadS a -> ReadS a Source #

``readParen` `True` p` parses what `p` parses, but surrounded with parentheses.

``readParen` `False` p` parses what `p` parses, but optionally surrounded with parentheses.

type ReadS a = String -> [(a, String)] Source #

A parser for a type `a`, represented as a function that takes a `String` and returns a list of possible parses as `(a,`String`)` pairs.

Note that this kind of backtracking parser is very inefficient; reading a large structure may be quite slow (cf `ReadP`).

(<$>) :: Functor f => (a -> b) -> f a -> f b infixl 4 Source #

An infix synonym for `fmap`.

The name of this operator is an allusion to `$`. Note the similarities between their types:

     ($)  ::              (a -> b) ->   a ->   b
    (<$>) :: Functor f => (a -> b) -> f a -> f b

Whereas `$` is function application, `<$>` is function application lifted over a `Functor`.

#### Examples

Expand

Convert from a ``Maybe` `Int`` to a ``Maybe` `String`` using `show`:

    >>> show <$> Nothing
    Nothing
    >>> show <$> Just 3
    Just "3"

Convert from an ``Either` `Int` `Int`` to an ``Either` `Int`` `String` using `show`:

    >>> show <$> Left 17
    Left 17
    >>> show <$> Right 17
    Right "17"

Double each element of a list:

    >>> (*2) <$> [1,2,3]
    [2,4,6]

Apply `even` to the second element of a pair:

    >>> even <$> (2,2)
    (2,True)

lcm :: Integral a => a -> a -> a Source #

``lcm` x y` is the smallest positive integer that both `x` and `y` divide.

gcd :: Integral a => a -> a -> a Source #

``gcd` x y` is the non-negative factor of both `x` and `y` of which every common factor of `x` and `y` is also a factor; for example ``gcd` 4 2 = 2`, ``gcd` (-4) 6 = 2`, ``gcd` 0 4` = `4`. ``gcd` 0 0` = `0`. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, ``abs` `minBound` < 0`, the result may be negative if one of the arguments is ``minBound`` (and necessarily is if the other is `0` or ``minBound``) for such types.

(^^) :: (Fractional a, Integral b) => a -> b -> a infixr 8 Source #

raise a number to an integral power

(^) :: (Num a, Integral b) => a -> b -> a infixr 8 Source #

raise a number to a non-negative integral power

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

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

showParen :: Bool -> ShowS -> ShowS Source #

utility function that surrounds the inner show function with parentheses when the `Bool` parameter is `True`.

showString :: String -> ShowS Source #

utility function converting a `String` to a show function that simply prepends the string unchanged.

showChar :: Char -> ShowS Source #

utility function converting a `Char` to a show function that simply prepends the character unchanged.

shows :: Show a => a -> ShowS Source #

equivalent to `showsPrec` with a precedence of 0.

type ShowS = String -> String Source #

The `shows` functions return a function that prepends the output `String` to an existing `String`. This allows constant-time concatenation of results using function composition.

unzip3 :: [(a, b, c)] -> ([a], [b], [c]) Source #

The `unzip3` function takes a list of triples and returns three lists, analogous to `unzip`.

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

`unzip` transforms a list of pairs into a list of first components and a list of second components.

zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d] Source #

The `zipWith3` function takes a function which combines three elements, as well as three lists and returns a list of their point-wise combination, analogous to `zipWith`.

zipWith :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

`zipWith` generalises `zip` by zipping with the function given as the first argument, instead of a tupling function. For example, ``zipWith` (+)` is applied to two lists to produce the list of corresponding sums.

`zipWith` is right-lazy:

    zipWith f [] _|_ = []

zip3 :: [a] -> [b] -> [c] -> [(a, b, c)] Source #

`zip3` takes three lists and returns a list of triples, analogous to `zip`.

(!!) :: [a] -> Int -> a infixl 9 Source #

List index (subscript) operator, starting from 0. It is an instance of the more general `genericIndex`, which takes an index of any integral type.

lookup :: Eq a => a -> [(a, b)] -> Maybe b Source #

`lookup` `key assocs` looks up a key in an association list.

reverse :: [a] -> [a] Source #

`reverse` `xs` returns the elements of `xs` in reverse order. `xs` must be finite.

break :: (a -> Bool) -> [a] -> ([a], [a]) Source #

`break`, applied to a predicate `p` and a list `xs`, returns a tuple where first element is longest prefix (possibly empty) of `xs` of elements that do not satisfy `p` and second element is the remainder of the list:

    break (> 3) [1,2,3,4,1,2,3,4] == ([1,2,3],[4,1,2,3,4])
    break (< 9) [1,2,3] == ([],[1,2,3])
    break (> 9) [1,2,3] == ([1,2,3],[])

`break` `p` is equivalent to ``span` (`not` . p)`.

span :: (a -> Bool) -> [a] -> ([a], [a]) Source #

`span`, applied to a predicate `p` and a list `xs`, returns a tuple where first element is longest prefix (possibly empty) of `xs` of elements that satisfy `p` and second element is the remainder of the list:

    span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
    span (< 9) [1,2,3] == ([1,2,3],[])
    span (< 0) [1,2,3] == ([],[1,2,3])

`span` `p xs` is equivalent to `(`takeWhile` p xs, `dropWhile` p xs)`

splitAt :: Int -> [a] -> ([a], [a]) Source #

`splitAt` `n xs` returns a tuple where first element is `xs` prefix of length `n` and second element is the remainder of the list:

    splitAt 6 "Hello World!" == ("Hello ","World!")
    splitAt 3 [1,2,3,4,5] == ([1,2,3],[4,5])
    splitAt 1 [1,2,3] == ([1],[2,3])
    splitAt 3 [1,2,3] == ([1,2,3],[])
    splitAt 4 [1,2,3] == ([1,2,3],[])
    splitAt 0 [1,2,3] == ([],[1,2,3])
    splitAt (-1) [1,2,3] == ([],[1,2,3])

It is equivalent to `(`take` n xs, `drop` n xs)` when `n` is not `_|_` (`splitAt _|_ xs = _|_`). `splitAt` is an instance of the more general `genericSplitAt`, in which `n` may be of any integral type.

drop :: Int -> [a] -> [a] Source #

`drop` `n xs` returns the suffix of `xs` after the first `n` elements, or `[]` if `n > `length` xs`:

    drop 6 "Hello World!" == "World!"
    drop 3 [1,2,3,4,5] == [4,5]
    drop 3 [1,2] == []
    drop 3 [] == []
    drop (-1) [1,2] == [1,2]
    drop 0 [1,2] == [1,2]

It is an instance of the more general `genericDrop`, in which `n` may be of any integral type.

take :: Int -> [a] -> [a] Source #

`take` `n`, applied to a list `xs`, returns the prefix of `xs` of length `n`, or `xs` itself if `n > `length` xs`:

    take 5 "Hello World!" == "Hello"
    take 3 [1,2,3,4,5] == [1,2,3]
    take 3 [1,2] == [1,2]
    take 3 [] == []
    take (-1) [1,2] == []
    take 0 [1,2] == []

It is an instance of the more general `genericTake`, in which `n` may be of any integral type.

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

`dropWhile` `p xs` returns the suffix remaining after `takeWhile` `p xs`:

    dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
    dropWhile (< 9) [1,2,3] == []
    dropWhile (< 0) [1,2,3] == [1,2,3]

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

`takeWhile`, applied to a predicate `p` and a list `xs`, returns the longest prefix (possibly empty) of `xs` of elements that satisfy `p`:

    takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
    takeWhile (< 9) [1,2,3] == [1,2,3]
    takeWhile (< 0) [1,2,3] == []

cycle :: [a] -> [a] Source #

`cycle` ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

replicate :: Int -> a -> [a] Source #

`replicate` `n x` is a list of length `n` with `x` the value of every element. It is an instance of the more general `genericReplicate`, in which `n` may be of any integral type.

repeat :: a -> [a] Source #

`repeat` `x` is an infinite list, with `x` the value of every element.

iterate :: (a -> a) -> a -> [a] Source #

`iterate` `f x` returns an infinite list of repeated applications of `f` to `x`:

    iterate f x == [x, f x, f (f x), ...]

Note that `iterate` is lazy, potentially leading to thunk build-up if the consumer doesn't force each iterate. See 'iterate\'' for a strict variant of this function.

scanr1 :: (a -> a -> a) -> [a] -> [a] Source #

`scanr1` is a variant of `scanr` that has no starting value argument.

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

`scanr` is the right-to-left dual of `scanl`. Note that

    head (scanr f z xs) == foldr f z xs.

scanl1 :: (a -> a -> a) -> [a] -> [a] Source #

`scanl1` is a variant of `scanl` that has no starting value argument:

    scanl1 f [x1, x2, ...] == [x1, x1 `f` x2, ...]

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

`scanl` is similar to `foldl`, but returns a list of successive reduced values from the left:

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

Note that

    last (scanl f z xs) == foldl f z xs.

init :: [a] -> [a] Source #

Return all the elements of a list except the last one. The list must be non-empty.

last :: [a] -> a Source #

Extract the last element of a list, which must be finite and non-empty.

tail :: [a] -> [a] Source #

Extract the elements after the head of a list, which must be non-empty.

head :: [a] -> a Source #

Extract the first element of a list, which must be non-empty.

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

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

#### Examples

Expand

Basic usage:

    >>> maybe False odd (Just 3)
    True

    >>> maybe False odd Nothing
    False

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

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

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

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

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

`uncurry` converts a curried function to a function on pairs.

#### Examples

Expand

    >>> uncurry (+) (1,2)
    3

    >>> uncurry ($) (show, 1)
    "1"

    >>> map (uncurry max) [(1,2), (3,4), (6,8)]
    [2,4,8]

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

`curry` converts an uncurried function to a curried function.

#### Examples

Expand

    >>> curry fst 1 2
    1

subtract :: Num a => a -> a -> a Source #

the same as ``flip` (`-`)`.

Because `-` is treated specially in the Haskell grammar, `(-` e`)` is not a section, but an application of prefix negation. However, `(`subtract`` exp`)` is equivalent to the disallowed section.

asTypeOf :: a -> a -> a Source #

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

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

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

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

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

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

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

    >>> flip (++) "hello" "world"
    "worldhello"

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

Function composition.

const :: a -> b -> a Source #

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

    >>> const 42 "hello"
    42

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

id :: a -> a Source #

Identity function.

    id x = x

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #

Same as `>>=`, but with the arguments interchanged.

undefined :: HasCallStack => a Source #

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

errorWithoutStackTrace :: [Char] -> a Source #

A variant of `error` that does not produce a stack trace.

Since: base-4.9.0.0

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

`error` stops execution and displays an error message.

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

Boolean "and"

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

Boolean "or"

not :: Bool -> Bool Source #

Boolean "not"