BNFC-2.8.2: A compiler front-end generator.

Algebra.RingUtils

Synopsis

# Documentation

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

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 #

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] #

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)] #

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 () #

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

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

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

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

Extract the first component of a pair.

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

Extract the second component of a pair.

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

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

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

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, ...]

($) :: (a -> b) -> a -> b infixr 0 # Application operator. This operator is redundant, since ordinary application (f x) means the same as (f$ x). However, $has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example: f$ g $h x = f (g (h x)) It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs. Note that ($) is levity-polymorphic in its result type, so that foo $True where foo :: Bool -> Int# is well-typed fromIntegral :: (Integral a, Num b) => a -> b # general coercion from integral types realToFrac :: (Real a, Fractional b) => a -> b # general coercion to fractional types class Bounded a where # The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds. The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded. Methods minBound :: a # maxBound :: a # Instances  Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-2.1 Instance detailsDefined in GHC.Enum Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum Methods Bounded () Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: () #maxBound :: () # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Bounded a => Bounded (Dual a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Bounded a => Bounded (Sum a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsminBound :: Sum a #maxBound :: Sum a # Bounded a => Bounded (Product a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods (Bounded a, Bounded b) => Bounded (a, b) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b) #maxBound :: (a, b) # Bounded (Proxy t) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methods (Bounded a, Bounded b, Bounded c) => Bounded (a, b, c) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c) #maxBound :: (a, b, c) # Bounded a => Bounded (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsminBound :: Const a b #maxBound :: Const a b # (Applicative f, Bounded a) => Bounded (Ap f a) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid MethodsminBound :: Ap f a #maxBound :: Ap f a # (Bounded a, Bounded b, Bounded c, Bounded d) => Bounded (a, b, c, d) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d) #maxBound :: (a, b, c, d) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e) => Bounded (a, b, c, d, e) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e) #maxBound :: (a, b, c, d, e) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f) => Bounded (a, b, c, d, e, f) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f) #maxBound :: (a, b, c, d, e, f) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g) => Bounded (a, b, c, d, e, f, g) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g) #maxBound :: (a, b, c, d, e, f, g) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h) => Bounded (a, b, c, d, e, f, g, h) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h) #maxBound :: (a, b, c, d, e, f, g, h) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i) => Bounded (a, b, c, d, e, f, g, h, i) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i) #maxBound :: (a, b, c, d, e, f, g, h, i) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j) => Bounded (a, b, c, d, e, f, g, h, i, j) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j) #maxBound :: (a, b, c, d, e, f, g, h, i, j) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k) => Bounded (a, b, c, d, e, f, g, h, i, j, k) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # (Bounded a, Bounded b, Bounded c, Bounded d, Bounded e, Bounded f, Bounded g, Bounded h, Bounded i, Bounded j, Bounded k, Bounded l, Bounded m, Bounded n, Bounded o) => Bounded (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsminBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #maxBound :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # class Enum a where # Class Enum defines operations on sequentially ordered types. The enumFrom... methods are used in Haskell's translation of arithmetic sequences. Instances of Enum may be derived for any enumeration type (types whose constructors have no fields). The nullary constructors are assumed to be numbered left-to-right by fromEnum from 0 through n-1. See Chapter 10 of the Haskell Report for more details. For any type that is an instance of class Bounded as well as Enum, the following should hold: enumFrom x = enumFromTo x maxBound enumFromThen x y = enumFromThenTo x y bound where bound | fromEnum y >= fromEnum x = maxBound | otherwise = minBound Minimal complete definition Methods succ :: a -> a # the successor of a value. For numeric types, succ adds 1. pred :: a -> a # the predecessor of a value. For numeric types, pred subtracts 1. toEnum :: Int -> a # Convert from an Int. fromEnum :: a -> Int # Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int. enumFrom :: a -> [a] # Used in Haskell's translation of [n..] with [n..] = enumFrom n, a possible implementation being enumFrom n = n : enumFrom (succ n). For example: • enumFrom 4 :: [Integer] = [4,5,6,7,...] • enumFrom 6 :: [Int] = [6,7,8,9,...,maxBound :: Int] enumFromThen :: a -> a -> [a] # Used in Haskell's translation of [n,n'..] with [n,n'..] = enumFromThen n n', a possible implementation being enumFromThen n n' = n : n' : worker (f x) (f x n'), worker s v = v : worker s (s v), x = fromEnum n' - fromEnum n and f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y For example: • enumFromThen 4 6 :: [Integer] = [4,6,8,10...] • enumFromThen 6 2 :: [Int] = [6,2,-2,-6,...,minBound :: Int] enumFromTo :: a -> a -> [a] # Used in Haskell's translation of [n..m] with [n..m] = enumFromTo n m, a possible implementation being enumFromTo n m | n <= m = n : enumFromTo (succ n) m | otherwise = []. For example: • enumFromTo 6 10 :: [Int] = [6,7,8,9,10] • enumFromTo 42 1 :: [Integer] = [] enumFromThenTo :: a -> a -> a -> [a] # Used in Haskell's translation of [n,n'..m] with [n,n'..m] = enumFromThenTo n n' m, a possible implementation being enumFromThenTo n n' m = worker (f x) (c x) n m, x = fromEnum n' - fromEnum n, c x = bool (>=) ((x 0) f n y | n > 0 = f (n - 1) (succ y) | n < 0 = f (n + 1) (pred y) | otherwise = y and worker s c v m | c v m = v : worker s c (s v) m | otherwise = [] For example: • enumFromThenTo 4 2 -6 :: [Integer] = [4,2,0,-2,-4,-6] • enumFromThenTo 6 8 2 :: [Int] = [] Instances  Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Bool -> Bool #pred :: Bool -> Bool #toEnum :: Int -> Bool #fromEnum :: Bool -> Int #enumFrom :: Bool -> [Bool] #enumFromThen :: Bool -> Bool -> [Bool] #enumFromTo :: Bool -> Bool -> [Bool] #enumFromThenTo :: Bool -> Bool -> Bool -> [Bool] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Char -> Char #pred :: Char -> Char #toEnum :: Int -> Char #fromEnum :: Char -> Int #enumFrom :: Char -> [Char] #enumFromThen :: Char -> Char -> [Char] #enumFromTo :: Char -> Char -> [Char] #enumFromThenTo :: Char -> Char -> Char -> [Char] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Int -> Int #pred :: Int -> Int #toEnum :: Int -> Int #fromEnum :: Int -> Int #enumFrom :: Int -> [Int] #enumFromThen :: Int -> Int -> [Int] #enumFromTo :: Int -> Int -> [Int] #enumFromThenTo :: Int -> Int -> Int -> [Int] # Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Integer -> [Integer] #enumFromThen :: Integer -> Integer -> [Integer] #enumFromTo :: Integer -> Integer -> [Integer] #enumFromThenTo :: Integer -> Integer -> Integer -> [Integer] # Since: base-4.8.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Natural -> [Natural] #enumFromThen :: Natural -> Natural -> [Natural] #enumFromTo :: Natural -> Natural -> [Natural] #enumFromThenTo :: Natural -> Natural -> Natural -> [Natural] # Since: base-2.1 Instance detailsDefined in GHC.Enum MethodsenumFrom :: Ordering -> [Ordering] #enumFromTo :: Ordering -> Ordering -> [Ordering] # Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: Word -> Word #pred :: Word -> Word #toEnum :: Int -> Word #fromEnum :: Word -> Int #enumFrom :: Word -> [Word] #enumFromThen :: Word -> Word -> [Word] #enumFromTo :: Word -> Word -> [Word] #enumFromThenTo :: Word -> Word -> Word -> [Word] # Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: VecCount -> [VecCount] #enumFromTo :: VecCount -> VecCount -> [VecCount] # Since: base-4.10.0.0 Instance detailsDefined in GHC.Enum MethodsenumFrom :: VecElem -> [VecElem] #enumFromThen :: VecElem -> VecElem -> [VecElem] #enumFromTo :: VecElem -> VecElem -> [VecElem] #enumFromThenTo :: VecElem -> VecElem -> VecElem -> [VecElem] # Enum () Since: base-2.1 Instance detailsDefined in GHC.Enum Methodssucc :: () -> () #pred :: () -> () #toEnum :: Int -> () #fromEnum :: () -> Int #enumFrom :: () -> [()] #enumFromThen :: () -> () -> [()] #enumFromTo :: () -> () -> [()] #enumFromThenTo :: () -> () -> () -> [()] # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Integral a => Enum (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodssucc :: Ratio a -> Ratio a #pred :: Ratio a -> Ratio a #toEnum :: Int -> Ratio a #fromEnum :: Ratio a -> Int #enumFrom :: Ratio a -> [Ratio a] #enumFromThen :: Ratio a -> Ratio a -> [Ratio a] #enumFromTo :: Ratio a -> Ratio a -> [Ratio a] #enumFromThenTo :: Ratio a -> Ratio a -> Ratio a -> [Ratio a] # Enum (Proxy s) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodssucc :: Proxy s -> Proxy s #pred :: Proxy s -> Proxy s #toEnum :: Int -> Proxy s #fromEnum :: Proxy s -> Int #enumFrom :: Proxy s -> [Proxy s] #enumFromThen :: Proxy s -> Proxy s -> [Proxy s] #enumFromTo :: Proxy s -> Proxy s -> [Proxy s] #enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [Proxy s] # Enum a => Enum (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodssucc :: Const a b -> Const a b #pred :: Const a b -> Const a b #toEnum :: Int -> Const a b #fromEnum :: Const a b -> Int #enumFrom :: Const a b -> [Const a b] #enumFromThen :: Const a b -> Const a b -> [Const a b] #enumFromTo :: Const a b -> Const a b -> [Const a b] #enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b] # Enum (f a) => Enum (Ap f a) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodssucc :: Ap f a -> Ap f a #pred :: Ap f a -> Ap f a #toEnum :: Int -> Ap f a #fromEnum :: Ap f a -> Int #enumFrom :: Ap f a -> [Ap f a] #enumFromThen :: Ap f a -> Ap f a -> [Ap f a] #enumFromTo :: Ap f a -> Ap f a -> [Ap f a] #enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] # Enum (f a) => Enum (Alt f a) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodssucc :: Alt f a -> Alt f a #pred :: Alt f a -> Alt f a #toEnum :: Int -> Alt f a #fromEnum :: Alt f a -> Int #enumFrom :: Alt f a -> [Alt f a] #enumFromThen :: Alt f a -> Alt f a -> [Alt f a] #enumFromTo :: Alt f a -> Alt f a -> [Alt f a] #enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] # class Eq a where # The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq. The Haskell Report defines no laws for Eq. However, == is customarily expected to implement an equivalence relationship where two values comparing equal are indistinguishable by "public" functions, with a "public" function being one not allowing to see implementation details. For example, for a type representing non-normalised natural numbers modulo 100, a "public" function doesn't make the difference between 1 and 201. It is expected to have the following properties: Reflexivity x == x = True Symmetry x == y = y == x Transitivity if x == y && y == z = True, then x == z = True Substitutivity if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True Negation x /= y = not (x == y) Minimal complete definition: either == or /=. Minimal complete definition Methods (==) :: a -> a -> Bool infix 4 # (/=) :: a -> a -> Bool infix 4 # Instances  Instance detailsDefined in GHC.Classes Methods(==) :: Bool -> Bool -> Bool #(/=) :: Bool -> Bool -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Char -> Char -> Bool #(/=) :: Char -> Char -> Bool # 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 detailsDefined in GHC.Classes Methods(==) :: Double -> Double -> Bool #(/=) :: Double -> Double -> Bool # 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 detailsDefined in GHC.Classes Methods(==) :: Float -> Float -> Bool #(/=) :: Float -> Float -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Int -> Int -> Bool #(/=) :: Int -> Int -> Bool # Instance detailsDefined in GHC.Integer.Type Methods(==) :: Integer -> Integer -> Bool #(/=) :: Integer -> Integer -> Bool # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods(==) :: Natural -> Natural -> Bool #(/=) :: Natural -> Natural -> Bool # Instance detailsDefined in GHC.Classes Methods Instance detailsDefined in GHC.Classes Methods(==) :: Word -> Word -> Bool #(/=) :: Word -> Word -> Bool # Eq () Instance detailsDefined in GHC.Classes Methods(==) :: () -> () -> Bool #(/=) :: () -> () -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: TyCon -> TyCon -> Bool #(/=) :: TyCon -> TyCon -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: Module -> Module -> Bool #(/=) :: Module -> Module -> Bool # Instance detailsDefined in GHC.Classes Methods(==) :: TrName -> TrName -> Bool #(/=) :: TrName -> TrName -> Bool # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods(==) :: Handle -> Handle -> Bool #(/=) :: Handle -> Handle -> Bool # Instance detailsDefined in GHC.Integer.Type Methods(==) :: BigNat -> BigNat -> Bool #(/=) :: BigNat -> BigNat -> Bool # Since: base-4.3.0.0 Instance detailsDefined in GHC.Exts Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods(==) :: Newline -> Newline -> Bool #(/=) :: Newline -> Newline -> Bool # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods Since: base-4.3.0.0 Instance detailsDefined in GHC.IO Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: All -> All -> Bool #(/=) :: All -> All -> Bool # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Any -> Any -> Bool #(/=) :: Any -> Any -> Bool # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: Fixity -> Fixity -> Bool #(/=) :: Fixity -> Fixity -> Bool # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Stack.Types Methods(==) :: SrcLoc -> SrcLoc -> Bool #(/=) :: SrcLoc -> SrcLoc -> Bool # Source # Instance detailsDefined in Data.Matrix.Class Methods Eq a => Eq [a] Instance detailsDefined in GHC.Classes Methods(==) :: [a] -> [a] -> Bool #(/=) :: [a] -> [a] -> Bool # Eq a => Eq (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methods(==) :: Maybe a -> Maybe a -> Bool #(/=) :: Maybe a -> Maybe a -> Bool # Eq a => Eq (Ratio a) Since: base-2.1 Instance detailsDefined in GHC.Real Methods(==) :: Ratio a -> Ratio a -> Bool #(/=) :: Ratio a -> Ratio a -> Bool # Eq (Ptr a) Since: base-2.1 Instance detailsDefined in GHC.Ptr Methods(==) :: Ptr a -> Ptr a -> Bool #(/=) :: Ptr a -> Ptr a -> Bool # Eq (FunPtr a) Instance detailsDefined in GHC.Ptr Methods(==) :: FunPtr a -> FunPtr a -> Bool #(/=) :: FunPtr a -> FunPtr a -> Bool # Eq p => Eq (Par1 p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: Par1 p -> Par1 p -> Bool #(/=) :: Par1 p -> Par1 p -> Bool # Eq a => Eq (ZipList a) Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methods(==) :: ZipList a -> ZipList a -> Bool #(/=) :: ZipList a -> ZipList a -> Bool # Eq a => Eq (First a) Since: base-2.1 Instance detailsDefined in Data.Monoid Methods(==) :: First a -> First a -> Bool #(/=) :: First a -> First a -> Bool # Eq a => Eq (Last a) Since: base-2.1 Instance detailsDefined in Data.Monoid Methods(==) :: Last a -> Last a -> Bool #(/=) :: Last a -> Last a -> Bool # Eq a => Eq (Dual a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Dual a -> Dual a -> Bool #(/=) :: Dual a -> Dual a -> Bool # Eq a => Eq (Sum a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Sum a -> Sum a -> Bool #(/=) :: Sum a -> Sum a -> Bool # Eq a => Eq (Product a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Product a -> Product a -> Bool #(/=) :: Product a -> Product a -> Bool # Eq a => Eq (Down a) Since: base-4.6.0.0 Instance detailsDefined in Data.Ord Methods(==) :: Down a -> Down a -> Bool #(/=) :: Down a -> Down a -> Bool # Eq a => Eq (NonEmpty a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(==) :: NonEmpty a -> NonEmpty a -> Bool #(/=) :: NonEmpty a -> NonEmpty a -> Bool # (Eq a, Eq b) => Eq (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methods(==) :: Either a b -> Either a b -> Bool #(/=) :: Either a b -> Either a b -> Bool # Eq (V1 p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: V1 p -> V1 p -> Bool #(/=) :: V1 p -> V1 p -> Bool # Eq (U1 p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: U1 p -> U1 p -> Bool #(/=) :: U1 p -> U1 p -> Bool # (Eq a, Eq b) => Eq (a, b) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b) -> (a, b) -> Bool #(/=) :: (a, b) -> (a, b) -> Bool # (Ix i, Eq e) => Eq (Array i e) Since: base-2.1 Instance detailsDefined in GHC.Arr Methods(==) :: Array i e -> Array i e -> Bool #(/=) :: Array i e -> Array i e -> Bool # Eq (Proxy s) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methods(==) :: Proxy s -> Proxy s -> Bool #(/=) :: Proxy s -> Proxy s -> Bool # Eq (f p) => Eq (Rec1 f p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: Rec1 f p -> Rec1 f p -> Bool #(/=) :: Rec1 f p -> Rec1 f p -> Bool # Eq (URec (Ptr ()) p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(/=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool # Eq (URec Char p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: URec Char p -> URec Char p -> Bool #(/=) :: URec Char p -> URec Char p -> Bool # Eq (URec Double p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: URec Double p -> URec Double p -> Bool #(/=) :: URec Double p -> URec Double p -> Bool # Eq (URec Float p) Instance detailsDefined in GHC.Generics Methods(==) :: URec Float p -> URec Float p -> Bool #(/=) :: URec Float p -> URec Float p -> Bool # Eq (URec Int p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: URec Int p -> URec Int p -> Bool #(/=) :: URec Int p -> URec Int p -> Bool # Eq (URec Word p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: URec Word p -> URec Word p -> Bool #(/=) :: URec Word p -> URec Word p -> Bool # (Eq a, Eq b, Eq c) => Eq (a, b, c) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c) -> (a, b, c) -> Bool #(/=) :: (a, b, c) -> (a, b, c) -> Bool # Eq (STArray s i e) Since: base-2.1 Instance detailsDefined in GHC.Arr Methods(==) :: STArray s i e -> STArray s i e -> Bool #(/=) :: STArray s i e -> STArray s i e -> Bool # Eq a => Eq (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(==) :: Const a b -> Const a b -> Bool #(/=) :: Const a b -> Const a b -> Bool # Eq (f a) => Eq (Ap f a) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methods(==) :: Ap f a -> Ap f a -> Bool #(/=) :: Ap f a -> Ap f a -> Bool # Eq (f a) => Eq (Alt f a) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Alt f a -> Alt f a -> Bool #(/=) :: Alt f a -> Alt f a -> Bool # Eq c => Eq (K1 i c p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: K1 i c p -> K1 i c p -> Bool #(/=) :: K1 i c p -> K1 i c p -> Bool # (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: (f :+: g) p -> (f :+: g) p -> Bool #(/=) :: (f :+: g) p -> (f :+: g) p -> Bool # (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: (f :*: g) p -> (f :*: g) p -> Bool #(/=) :: (f :*: g) p -> (f :*: g) p -> Bool # (Eq a, Eq b, Eq c, Eq d) => Eq (a, b, c, d) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(/=) :: (a, b, c, d) -> (a, b, c, d) -> Bool # Eq (f p) => Eq (M1 i c f p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: M1 i c f p -> M1 i c f p -> Bool #(/=) :: M1 i c f p -> M1 i c f p -> Bool # Eq (f (g p)) => Eq ((f :.: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methods(==) :: (f :.: g) p -> (f :.: g) p -> Bool #(/=) :: (f :.: g) p -> (f :.: g) p -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e) => Eq (a, b, c, d, e) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(/=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f) => Eq (a, b, c, d, e, f) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(/=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g) => Eq (a, b, c, d, e, f, g) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(/=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h) => Eq (a, b, c, d, e, f, g, h) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(/=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i) => Eq (a, b, c, d, e, f, g, h, i) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j) => Eq (a, b, c, d, e, f, g, h, i, j) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k) => Eq (a, b, c, d, e, f, g, h, i, j, k) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l) => Eq (a, b, c, d, e, f, g, h, i, j, k, l) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool # (Eq a, Eq b, Eq c, Eq d, Eq e, Eq f, Eq g, Eq h, Eq i, Eq j, Eq k, Eq l, Eq m, Eq n, Eq o) => Eq (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Instance detailsDefined in GHC.Classes Methods(==) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(/=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool # class Fractional a => Floating a where # 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 Methods pi :: a # exp :: a -> a # log :: a -> a # sqrt :: a -> a # (**) :: a -> a -> a infixr 8 # logBase :: a -> a -> a # sin :: a -> a # cos :: a -> a # tan :: a -> a # asin :: a -> a # acos :: a -> a # atan :: a -> a # sinh :: a -> a # cosh :: a -> a # tanh :: a -> a # asinh :: a -> a # acosh :: a -> a # atanh :: a -> a # Instances  Since: base-2.1 Instance detailsDefined in GHC.Float Methodsexp :: Double -> Double #log :: Double -> Double #(**) :: Double -> Double -> Double #sin :: Double -> Double #cos :: Double -> Double #tan :: Double -> Double # Since: base-2.1 Instance detailsDefined in GHC.Float Methodspi :: Float #exp :: Float -> Float #log :: Float -> Float #sqrt :: Float -> Float #(**) :: Float -> Float -> Float #logBase :: Float -> Float -> Float #sin :: Float -> Float #cos :: Float -> Float #tan :: Float -> Float #asin :: Float -> Float #acos :: Float -> Float #atan :: Float -> Float #sinh :: Float -> Float #cosh :: Float -> Float #tanh :: Float -> Float #asinh :: Float -> Float #acosh :: Float -> Float #atanh :: Float -> Float #log1p :: Float -> Float #expm1 :: Float -> Float # Floating a => Floating (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodspi :: Const a b #exp :: Const a b -> Const a b #log :: Const a b -> Const a b #sqrt :: Const a b -> Const a b #(**) :: Const a b -> Const a b -> Const a b #logBase :: Const a b -> Const a b -> Const a b #sin :: Const a b -> Const a b #cos :: Const a b -> Const a b #tan :: Const a b -> Const a b #asin :: Const a b -> Const a b #acos :: Const a b -> Const a b #atan :: Const a b -> Const a b #sinh :: Const a b -> Const a b #cosh :: Const a b -> Const a b #tanh :: Const a b -> Const a b #asinh :: Const a b -> Const a b #acosh :: Const a b -> Const a b #atanh :: Const a b -> Const a b #log1p :: Const a b -> Const a b #expm1 :: Const a b -> Const a b #log1pexp :: Const a b -> Const a b #log1mexp :: Const a b -> Const a b # class Num a => Fractional a where # 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 # fractional division recip :: a -> a # reciprocal fraction fromRational :: Rational -> a # Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a. Instances  Integral a => Fractional (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(/) :: Ratio a -> Ratio a -> Ratio a #recip :: Ratio a -> Ratio a # Fractional a => Fractional (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(/) :: Const a b -> Const a b -> Const a b #recip :: Const a b -> Const a b #fromRational :: Rational -> Const a b # class (Real a, Enum a) => Integral a where # Integral numbers, supporting integer division. The Haskell Report defines no laws for Integral. However, Integral instances are customarily expected to define a Euclidean domain and have the following properties for the 'div'/'mod' and 'quot'/'rem' pairs, given suitable Euclidean functions f and g: • x = y * quot x y + rem x y with rem x y = fromInteger 0 or g (rem x y) < g y • x = y * div x y + mod x y with mod x y = fromInteger 0 or f (mod x y) < f y An example of a suitable Euclidean function, for Integer's instance, is abs. Minimal complete definition Methods quot :: a -> a -> a infixl 7 # integer division truncated toward zero rem :: a -> a -> a infixl 7 # integer remainder, satisfying (x quot y)*y + (x rem y) == x div :: a -> a -> a infixl 7 # integer division truncated toward negative infinity mod :: a -> a -> a infixl 7 # integer modulus, satisfying (x div y)*y + (x mod y) == x quotRem :: a -> a -> (a, a) # simultaneous quot and rem divMod :: a -> a -> (a, a) # simultaneous div and mod toInteger :: a -> Integer # conversion to Integer Instances  Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodsquot :: Int -> Int -> Int #rem :: Int -> Int -> Int #div :: Int -> Int -> Int #mod :: Int -> Int -> Int #quotRem :: Int -> Int -> (Int, Int) #divMod :: Int -> Int -> (Int, Int) # Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsquotRem :: Integer -> Integer -> (Integer, Integer) #divMod :: Integer -> Integer -> (Integer, Integer) # Since: base-4.8.0.0 Instance detailsDefined in GHC.Real MethodsquotRem :: Natural -> Natural -> (Natural, Natural) #divMod :: Natural -> Natural -> (Natural, Natural) # Since: base-2.1 Instance detailsDefined in GHC.Real Methodsquot :: Word -> Word -> Word #rem :: Word -> Word -> Word #div :: Word -> Word -> Word #mod :: Word -> Word -> Word #quotRem :: Word -> Word -> (Word, Word) #divMod :: Word -> Word -> (Word, Word) # Integral a => Integral (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodsquot :: Const a b -> Const a b -> Const a b #rem :: Const a b -> Const a b -> Const a b #div :: Const a b -> Const a b -> Const a b #mod :: Const a b -> Const a b -> Const a b #quotRem :: Const a b -> Const a b -> (Const a b, Const a b) #divMod :: Const a b -> Const a b -> (Const a b, Const a b) #toInteger :: Const a b -> Integer # class Applicative m => Monad (m :: Type -> Type) where # The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions. Instances of Monad should satisfy the following laws: Furthermore, the Monad and Applicative operations should relate as follows: The above laws imply: and that pure and (<*>) satisfy the applicative functor laws. The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws. Minimal complete definition (>>=) Methods (>>=) :: m a -> (a -> m b) -> m b infixl 1 # Sequentially compose two actions, passing any value produced by the first as an argument to the second. (>>) :: m a -> m b -> m b infixl 1 # Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages. return :: a -> m a # Inject a value into the monadic type. fail :: String -> m a # Fail with a message. This operation is not part of the mathematical definition of a monad, but is invoked on pattern-match failure in a do expression. As part of the MonadFail proposal (MFP), this function is moved to its own class MonadFail (see Control.Monad.Fail for more details). The definition here will be removed in a future release. Instances  Monad [] Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: [a] -> (a -> [b]) -> [b] #(>>) :: [a] -> [b] -> [b] #return :: a -> [a] #fail :: String -> [a] # Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b #(>>) :: Maybe a -> Maybe b -> Maybe b #return :: a -> Maybe a #fail :: String -> Maybe a # Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: IO a -> (a -> IO b) -> IO b #(>>) :: IO a -> IO b -> IO b #return :: a -> IO a #fail :: String -> IO a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: Par1 a -> (a -> Par1 b) -> Par1 b #(>>) :: Par1 a -> Par1 b -> Par1 b #return :: a -> Par1 a #fail :: String -> Par1 a # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methods(>>=) :: First a -> (a -> First b) -> First b #(>>) :: First a -> First b -> First b #return :: a -> First a #fail :: String -> First a # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methods(>>=) :: Last a -> (a -> Last b) -> Last b #(>>) :: Last a -> Last b -> Last b #return :: a -> Last a #fail :: String -> Last a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Dual a -> (a -> Dual b) -> Dual b #(>>) :: Dual a -> Dual b -> Dual b #return :: a -> Dual a #fail :: String -> Dual a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Sum a -> (a -> Sum b) -> Sum b #(>>) :: Sum a -> Sum b -> Sum b #return :: a -> Sum a #fail :: String -> Sum a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Product a -> (a -> Product b) -> Product b #(>>) :: Product a -> Product b -> Product b #return :: a -> Product a #fail :: String -> Product a # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methods(>>=) :: Down a -> (a -> Down b) -> Down b #(>>) :: Down a -> Down b -> Down b #return :: a -> Down a #fail :: String -> Down a # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methods(>>=) :: ReadP a -> (a -> ReadP b) -> ReadP b #(>>) :: ReadP a -> ReadP b -> ReadP b #return :: a -> ReadP a #fail :: String -> ReadP a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(>>=) :: NonEmpty a -> (a -> NonEmpty b) -> NonEmpty b #(>>) :: NonEmpty a -> NonEmpty b -> NonEmpty b #return :: a -> NonEmpty a #fail :: String -> NonEmpty a # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methods(>>=) :: P a -> (a -> P b) -> P b #(>>) :: P a -> P b -> P b #return :: a -> P a #fail :: String -> P a # Monad (Either e) Since: base-4.4.0.0 Instance detailsDefined in Data.Either Methods(>>=) :: Either e a -> (a -> Either e b) -> Either e b #(>>) :: Either e a -> Either e b -> Either e b #return :: a -> Either e a #fail :: String -> Either e a # Monad (U1 :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: U1 a -> (a -> U1 b) -> U1 b #(>>) :: U1 a -> U1 b -> U1 b #return :: a -> U1 a #fail :: String -> U1 a # Monoid a => Monad ((,) a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(>>=) :: (a, a0) -> (a0 -> (a, b)) -> (a, b) #(>>) :: (a, a0) -> (a, b) -> (a, b) #return :: a0 -> (a, a0) #fail :: String -> (a, a0) # Monad m => Monad (WrappedMonad m) Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methods(>>=) :: WrappedMonad m a -> (a -> WrappedMonad m b) -> WrappedMonad m b #(>>) :: WrappedMonad m a -> WrappedMonad m b -> WrappedMonad m b #return :: a -> WrappedMonad m a #fail :: String -> WrappedMonad m a # ArrowApply a => Monad (ArrowMonad a) Since: base-2.1 Instance detailsDefined in Control.Arrow Methods(>>=) :: ArrowMonad a a0 -> (a0 -> ArrowMonad a b) -> ArrowMonad a b #(>>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b #return :: a0 -> ArrowMonad a a0 #fail :: String -> ArrowMonad a a0 # Monad (Proxy :: Type -> Type) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methods(>>=) :: Proxy a -> (a -> Proxy b) -> Proxy b #(>>) :: Proxy a -> Proxy b -> Proxy b #return :: a -> Proxy a #fail :: String -> Proxy a # Monad f => Monad (Rec1 f) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: Rec1 f a -> (a -> Rec1 f b) -> Rec1 f b #(>>) :: Rec1 f a -> Rec1 f b -> Rec1 f b #return :: a -> Rec1 f a #fail :: String -> Rec1 f a # Monad f => Monad (Ap f) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methods(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b #(>>) :: Ap f a -> Ap f b -> Ap f b #return :: a -> Ap f a #fail :: String -> Ap f a # Monad f => Monad (Alt f) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b #(>>) :: Alt f a -> Alt f b -> Alt f b #return :: a -> Alt f a #fail :: String -> Alt f a # Monad ((->) r :: Type -> Type) Since: base-2.1 Instance detailsDefined in GHC.Base Methods(>>=) :: (r -> a) -> (a -> r -> b) -> r -> b #(>>) :: (r -> a) -> (r -> b) -> r -> b #return :: a -> r -> a #fail :: String -> r -> a # (Monad f, Monad g) => Monad (f :*: g) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: (f :*: g) a -> (a -> (f :*: g) b) -> (f :*: g) b #(>>) :: (f :*: g) a -> (f :*: g) b -> (f :*: g) b #return :: a -> (f :*: g) a #fail :: String -> (f :*: g) a # Monad f => Monad (M1 i c f) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods(>>=) :: M1 i c f a -> (a -> M1 i c f b) -> M1 i c f b #(>>) :: M1 i c f a -> M1 i c f b -> M1 i c f b #return :: a -> M1 i c f a #fail :: String -> M1 i c f a # class Functor (f :: Type -> Type) where # The Functor class is used for types that can be mapped over. Instances of Functor should satisfy the following laws: fmap id == id fmap (f . g) == fmap f . fmap g The instances of Functor for lists, Maybe and IO satisfy these laws. Minimal complete definition fmap Methods fmap :: (a -> b) -> f a -> f b # (<$) :: a -> f b -> f a infixl 4 #

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

Instances
 Functor [] Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> [a] -> [b] #(<$) :: a -> [b] -> [a] # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> Maybe a -> Maybe b #(<$) :: a -> Maybe b -> Maybe a # Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> IO a -> IO b #(<$) :: a -> IO b -> IO a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Par1 a -> Par1 b #(<$) :: a -> Par1 b -> Par1 a # Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> ZipList a -> ZipList b #(<$) :: a -> ZipList b -> ZipList a # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # Since: base-4.8.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b #(<$) :: a -> Dual b -> Dual a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b #(<$) :: a -> Sum b -> Sum a # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b #(<$) :: a -> Product b -> Product a # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methodsfmap :: (a -> b) -> Down a -> Down b #(<$) :: a -> Down b -> Down a # Since: base-2.1 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> ReadP a -> ReadP b #(<$) :: a -> ReadP b -> ReadP a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> NonEmpty a -> NonEmpty b #(<$) :: a -> NonEmpty b -> NonEmpty a # Source # Instance detailsDefined in Data.Pair Methodsfmap :: (a -> b) -> Pair a -> Pair b #(<$) :: a -> Pair b -> Pair a # Since: base-4.8.0.0 Instance detailsDefined in Text.ParserCombinators.ReadP Methodsfmap :: (a -> b) -> P a -> P b #(<$) :: a -> P b -> P a # Since: base-3.0 Instance detailsDefined in Data.Either Methodsfmap :: (a0 -> b) -> Either a a0 -> Either a b #(<$) :: a0 -> Either a b -> Either a a0 # Functor (V1 :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> V1 a -> V1 b #(<$) :: a -> V1 b -> V1 a # Functor (U1 :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> U1 a -> U1 b #(<$) :: a -> U1 b -> U1 a # Functor ((,) a) Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a0 -> b) -> (a, a0) -> (a, b) #(<$) :: a0 -> (a, b) -> (a, a0) # Functor (Array i) Since: base-2.1 Instance detailsDefined in GHC.Arr Methodsfmap :: (a -> b) -> Array i a -> Array i b #(<$) :: a -> Array i b -> Array i a # Monad m => Functor (WrappedMonad m) Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a -> b) -> WrappedMonad m a -> WrappedMonad m b #(<$) :: a -> WrappedMonad m b -> WrappedMonad m a # Arrow a => Functor (ArrowMonad a) Since: base-4.6.0.0 Instance detailsDefined in Control.Arrow Methodsfmap :: (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b #(<$) :: a0 -> ArrowMonad a b -> ArrowMonad a a0 # Functor (Proxy :: Type -> Type) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodsfmap :: (a -> b) -> Proxy a -> Proxy b #(<$) :: a -> Proxy b -> Proxy a # Functor f => Functor (Rec1 f) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> Rec1 f a -> Rec1 f b #(<$) :: a -> Rec1 f b -> Rec1 f a # Functor (URec Char :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Char a -> URec Char b #(<$) :: a -> URec Char b -> URec Char a # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Double a -> URec Double b #(<$) :: a -> URec Double b -> URec Double a # Functor (URec Float :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Float a -> URec Float b #(<$) :: a -> URec Float b -> URec Float a # Functor (URec Int :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Int a -> URec Int b #(<$) :: a -> URec Int b -> URec Int a # Functor (URec Word :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec Word a -> URec Word b #(<$) :: a -> URec Word b -> URec Word a # Functor (URec (Ptr ()) :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> URec (Ptr ()) a -> URec (Ptr ()) b #(<$) :: a -> URec (Ptr ()) b -> URec (Ptr ()) a # Arrow a => Functor (WrappedArrow a b) Since: base-2.1 Instance detailsDefined in Control.Applicative Methodsfmap :: (a0 -> b0) -> WrappedArrow a b a0 -> WrappedArrow a b b0 #(<$) :: a0 -> WrappedArrow a b b0 -> WrappedArrow a b a0 # Functor (Const m :: Type -> Type) Since: base-2.1 Instance detailsDefined in Data.Functor.Const Methodsfmap :: (a -> b) -> Const m a -> Const m b #(<$) :: a -> Const m b -> Const m a # Functor f => Functor (Ap f) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodsfmap :: (a -> b) -> Ap f a -> Ap f b #(<$) :: a -> Ap f b -> Ap f a # Functor f => Functor (Alt f) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Alt f a -> Alt f b #(<$) :: a -> Alt f b -> Alt f a # (Functor f, Functor g) => Functor (O f g) Source # Instance detailsDefined in Algebra.RingUtils Methodsfmap :: (a -> b) -> O f g a -> O f g b #(<$) :: a -> O f g b -> O f g a # Functor ((->) r :: Type -> Type) Since: base-2.1 Instance detailsDefined in GHC.Base Methodsfmap :: (a -> b) -> (r -> a) -> r -> b #(<$) :: a -> (r -> b) -> r -> a # Functor (K1 i c :: Type -> Type) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> K1 i c a -> K1 i c b #(<$) :: a -> K1 i c b -> K1 i c a # (Functor f, Functor g) => Functor (f :+: g) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :+: g) a -> (f :+: g) b #(<$) :: a -> (f :+: g) b -> (f :+: g) a # (Functor f, Functor g) => Functor (f :*: g) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :*: g) a -> (f :*: g) b #(<$) :: a -> (f :*: g) b -> (f :*: g) a # Functor f => Functor (M1 i c f) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> M1 i c f a -> M1 i c f b #(<$) :: a -> M1 i c f b -> M1 i c f a # (Functor f, Functor g) => Functor (f :.: g) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodsfmap :: (a -> b) -> (f :.: g) a -> (f :.: g) b #(<$) :: a -> (f :.: g) b -> (f :.: g) a # class Num a where # 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 # negate :: a -> a # Unary negation. abs :: a -> a # Absolute value. signum :: a -> a # Sign of a number. The functions abs and signum should satisfy the law: abs x * signum x == x For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive). fromInteger :: Integer -> a # Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a. Instances  Since: base-2.1 Instance detailsDefined in GHC.Num Methods(+) :: Int -> Int -> Int #(-) :: Int -> Int -> Int #(*) :: Int -> Int -> Int #negate :: Int -> Int #abs :: Int -> Int #signum :: Int -> Int # Since: base-2.1 Instance detailsDefined in GHC.Num Methods 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 detailsDefined in GHC.Num Methods Since: base-2.1 Instance detailsDefined in GHC.Num Methods(+) :: Word -> Word -> Word #(-) :: Word -> Word -> Word #(*) :: Word -> Word -> Word #negate :: Word -> Word #abs :: Word -> Word #signum :: Word -> Word # Integral a => Num (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods(+) :: Ratio a -> Ratio a -> Ratio a #(-) :: Ratio a -> Ratio a -> Ratio a #(*) :: Ratio a -> Ratio a -> Ratio a #negate :: Ratio a -> Ratio a #abs :: Ratio a -> Ratio a #signum :: Ratio a -> Ratio a # Num a => Num (Sum a) Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(+) :: Sum a -> Sum a -> Sum a #(-) :: Sum a -> Sum a -> Sum a #(*) :: Sum a -> Sum a -> Sum a #negate :: Sum a -> Sum a #abs :: Sum a -> Sum a #signum :: Sum a -> Sum a # Num a => Num (Product a) Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(+) :: Product a -> Product a -> Product a #(-) :: Product a -> Product a -> Product a #(*) :: Product a -> Product a -> Product a #negate :: Product a -> Product a #abs :: Product a -> Product a #signum :: Product a -> Product a # Num a => Num (Down a) Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methods(+) :: Down a -> Down a -> Down a #(-) :: Down a -> Down a -> Down a #(*) :: Down a -> Down a -> Down a #negate :: Down a -> Down a #abs :: Down a -> Down a #signum :: Down a -> Down a # Num a => Num (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(+) :: Const a b -> Const a b -> Const a b #(-) :: Const a b -> Const a b -> Const a b #(*) :: Const a b -> Const a b -> Const a b #negate :: Const a b -> Const a b #abs :: Const a b -> Const a b #signum :: Const a b -> Const a b #fromInteger :: Integer -> Const a b # (Applicative f, Num a) => Num (Ap f a) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methods(+) :: Ap f a -> Ap f a -> Ap f a #(-) :: Ap f a -> Ap f a -> Ap f a #(*) :: Ap f a -> Ap f a -> Ap f a #negate :: Ap f a -> Ap f a #abs :: Ap f a -> Ap f a #signum :: Ap f a -> Ap f a #fromInteger :: Integer -> Ap f a # Num (f a) => Num (Alt f a) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(+) :: Alt f a -> Alt f a -> Alt f a #(-) :: Alt f a -> Alt f a -> Alt f a #(*) :: Alt f a -> Alt f a -> Alt f a #negate :: Alt f a -> Alt f a #abs :: Alt f a -> Alt f a #signum :: Alt f a -> Alt f a #fromInteger :: Integer -> Alt f a # class Eq a => Ord a where # The Ord class is used for totally ordered datatypes. Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects. The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties: Transitivity if x <= y && y <= z = True, then x <= z = True Reflexivity x <= x = True Antisymmetry if x <= y && y <= x = True, then x == y = True Note that the following operator interactions are expected to hold: 1. x >= y = y <= x 2. x < y = x <= y && x /= y 3. x > y = y < x 4. x < y = compare x y == LT 5. x > y = compare x y == GT 6. x == y = compare x y == EQ 7. min x y == if x <= y then x else y = True 8. max x y == if x >= y then x else y = True Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types. Minimal complete definition Methods compare :: a -> a -> Ordering # (<) :: a -> a -> Bool infix 4 # (<=) :: a -> a -> Bool infix 4 # (>) :: a -> a -> Bool infix 4 # (>=) :: a -> a -> Bool infix 4 # max :: a -> a -> a # min :: a -> a -> a # Instances  Instance detailsDefined in GHC.Classes Methodscompare :: Bool -> Bool -> Ordering #(<) :: Bool -> Bool -> Bool #(<=) :: Bool -> Bool -> Bool #(>) :: Bool -> Bool -> Bool #(>=) :: Bool -> Bool -> Bool #max :: Bool -> Bool -> Bool #min :: Bool -> Bool -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Char -> Char -> Ordering #(<) :: Char -> Char -> Bool #(<=) :: Char -> Char -> Bool #(>) :: Char -> Char -> Bool #(>=) :: Char -> Char -> Bool #max :: Char -> Char -> Char #min :: Char -> Char -> Char # 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 detailsDefined in GHC.Classes Methods(<) :: Double -> Double -> Bool #(<=) :: Double -> Double -> Bool #(>) :: Double -> Double -> Bool #(>=) :: Double -> Double -> Bool #max :: Double -> Double -> Double #min :: Double -> Double -> Double # 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 detailsDefined in GHC.Classes Methods(<) :: Float -> Float -> Bool #(<=) :: Float -> Float -> Bool #(>) :: Float -> Float -> Bool #(>=) :: Float -> Float -> Bool #max :: Float -> Float -> Float #min :: Float -> Float -> Float # Instance detailsDefined in GHC.Classes Methodscompare :: Int -> Int -> Ordering #(<) :: Int -> Int -> Bool #(<=) :: Int -> Int -> Bool #(>) :: Int -> Int -> Bool #(>=) :: Int -> Int -> Bool #max :: Int -> Int -> Int #min :: Int -> Int -> Int # Instance detailsDefined in GHC.Integer.Type Methods(<) :: Integer -> Integer -> Bool #(<=) :: Integer -> Integer -> Bool #(>) :: Integer -> Integer -> Bool #(>=) :: Integer -> Integer -> Bool # Since: base-4.8.0.0 Instance detailsDefined in GHC.Natural Methods(<) :: Natural -> Natural -> Bool #(<=) :: Natural -> Natural -> Bool #(>) :: Natural -> Natural -> Bool #(>=) :: Natural -> Natural -> Bool # Instance detailsDefined in GHC.Classes Methods(<) :: Ordering -> Ordering -> Bool #(>) :: Ordering -> Ordering -> Bool # Instance detailsDefined in GHC.Classes Methodscompare :: Word -> Word -> Ordering #(<) :: Word -> Word -> Bool #(<=) :: Word -> Word -> Bool #(>) :: Word -> Word -> Bool #(>=) :: Word -> Word -> Bool #max :: Word -> Word -> Word #min :: Word -> Word -> Word # Ord () Instance detailsDefined in GHC.Classes Methodscompare :: () -> () -> Ordering #(<) :: () -> () -> Bool #(<=) :: () -> () -> Bool #(>) :: () -> () -> Bool #(>=) :: () -> () -> Bool #max :: () -> () -> () #min :: () -> () -> () # Instance detailsDefined in GHC.Classes Methods(<) :: TyCon -> TyCon -> Bool #(<=) :: TyCon -> TyCon -> Bool #(>) :: TyCon -> TyCon -> Bool #(>=) :: TyCon -> TyCon -> Bool #max :: TyCon -> TyCon -> TyCon #min :: TyCon -> TyCon -> TyCon # Instance detailsDefined in GHC.Integer.Type Methods(<) :: BigNat -> BigNat -> Bool #(<=) :: BigNat -> BigNat -> Bool #(>) :: BigNat -> BigNat -> Bool #(>=) :: BigNat -> BigNat -> Bool #max :: BigNat -> BigNat -> BigNat #min :: BigNat -> BigNat -> BigNat # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Exception Methods Instance detailsDefined in GHC.IO.Exception Methods(<) :: ExitCode -> ExitCode -> Bool #(>) :: ExitCode -> ExitCode -> Bool # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods Since: base-4.3.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods(<) :: Newline -> Newline -> Bool #(<=) :: Newline -> Newline -> Bool #(>) :: Newline -> Newline -> Bool #(>=) :: Newline -> Newline -> Bool # Since: base-4.3.0.0 Instance detailsDefined in GHC.IO.Handle.Types Methods Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: All -> All -> Ordering #(<) :: All -> All -> Bool #(<=) :: All -> All -> Bool #(>) :: All -> All -> Bool #(>=) :: All -> All -> Bool #max :: All -> All -> All #min :: All -> All -> All # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Any -> Any -> Ordering #(<) :: Any -> Any -> Bool #(<=) :: Any -> Any -> Bool #(>) :: Any -> Any -> Bool #(>=) :: Any -> Any -> Bool #max :: Any -> Any -> Any #min :: Any -> Any -> Any # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics Methods(<) :: Fixity -> Fixity -> Bool #(<=) :: Fixity -> Fixity -> Bool #(>) :: Fixity -> Fixity -> Bool #(>=) :: Fixity -> Fixity -> Bool #max :: Fixity -> Fixity -> Fixity #min :: Fixity -> Fixity -> Fixity # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methods Ord a => Ord [a] Instance detailsDefined in GHC.Classes Methodscompare :: [a] -> [a] -> Ordering #(<) :: [a] -> [a] -> Bool #(<=) :: [a] -> [a] -> Bool #(>) :: [a] -> [a] -> Bool #(>=) :: [a] -> [a] -> Bool #max :: [a] -> [a] -> [a] #min :: [a] -> [a] -> [a] # Ord a => Ord (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Maybe Methodscompare :: Maybe a -> Maybe a -> Ordering #(<) :: Maybe a -> Maybe a -> Bool #(<=) :: Maybe a -> Maybe a -> Bool #(>) :: Maybe a -> Maybe a -> Bool #(>=) :: Maybe a -> Maybe a -> Bool #max :: Maybe a -> Maybe a -> Maybe a #min :: Maybe a -> Maybe a -> Maybe a # Integral a => Ord (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real Methodscompare :: Ratio a -> Ratio a -> Ordering #(<) :: Ratio a -> Ratio a -> Bool #(<=) :: Ratio a -> Ratio a -> Bool #(>) :: Ratio a -> Ratio a -> Bool #(>=) :: Ratio a -> Ratio a -> Bool #max :: Ratio a -> Ratio a -> Ratio a #min :: Ratio a -> Ratio a -> Ratio a # Ord (Ptr a) Since: base-2.1 Instance detailsDefined in GHC.Ptr Methodscompare :: Ptr a -> Ptr a -> Ordering #(<) :: Ptr a -> Ptr a -> Bool #(<=) :: Ptr a -> Ptr a -> Bool #(>) :: Ptr a -> Ptr a -> Bool #(>=) :: Ptr a -> Ptr a -> Bool #max :: Ptr a -> Ptr a -> Ptr a #min :: Ptr a -> Ptr a -> Ptr a # Ord (FunPtr a) Instance detailsDefined in GHC.Ptr Methodscompare :: FunPtr a -> FunPtr a -> Ordering #(<) :: FunPtr a -> FunPtr a -> Bool #(<=) :: FunPtr a -> FunPtr a -> Bool #(>) :: FunPtr a -> FunPtr a -> Bool #(>=) :: FunPtr a -> FunPtr a -> Bool #max :: FunPtr a -> FunPtr a -> FunPtr a #min :: FunPtr a -> FunPtr a -> FunPtr a # Ord p => Ord (Par1 p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: Par1 p -> Par1 p -> Ordering #(<) :: Par1 p -> Par1 p -> Bool #(<=) :: Par1 p -> Par1 p -> Bool #(>) :: Par1 p -> Par1 p -> Bool #(>=) :: Par1 p -> Par1 p -> Bool #max :: Par1 p -> Par1 p -> Par1 p #min :: Par1 p -> Par1 p -> Par1 p # Ord a => Ord (ZipList a) Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative Methodscompare :: ZipList a -> ZipList a -> Ordering #(<) :: ZipList a -> ZipList a -> Bool #(<=) :: ZipList a -> ZipList a -> Bool #(>) :: ZipList a -> ZipList a -> Bool #(>=) :: ZipList a -> ZipList a -> Bool #max :: ZipList a -> ZipList a -> ZipList a #min :: ZipList a -> ZipList a -> ZipList a # Ord a => Ord (First a) Since: base-2.1 Instance detailsDefined in Data.Monoid Methodscompare :: First a -> First a -> Ordering #(<) :: First a -> First a -> Bool #(<=) :: First a -> First a -> Bool #(>) :: First a -> First a -> Bool #(>=) :: First a -> First a -> Bool #max :: First a -> First a -> First a #min :: First a -> First a -> First a # Ord a => Ord (Last a) Since: base-2.1 Instance detailsDefined in Data.Monoid Methodscompare :: Last a -> Last a -> Ordering #(<) :: Last a -> Last a -> Bool #(<=) :: Last a -> Last a -> Bool #(>) :: Last a -> Last a -> Bool #(>=) :: Last a -> Last a -> Bool #max :: Last a -> Last a -> Last a #min :: Last a -> Last a -> Last a # Ord a => Ord (Dual a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Dual a -> Dual a -> Ordering #(<) :: Dual a -> Dual a -> Bool #(<=) :: Dual a -> Dual a -> Bool #(>) :: Dual a -> Dual a -> Bool #(>=) :: Dual a -> Dual a -> Bool #max :: Dual a -> Dual a -> Dual a #min :: Dual a -> Dual a -> Dual a # Ord a => Ord (Sum a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Sum a -> Sum a -> Ordering #(<) :: Sum a -> Sum a -> Bool #(<=) :: Sum a -> Sum a -> Bool #(>) :: Sum a -> Sum a -> Bool #(>=) :: Sum a -> Sum a -> Bool #max :: Sum a -> Sum a -> Sum a #min :: Sum a -> Sum a -> Sum a # Ord a => Ord (Product a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Product a -> Product a -> Ordering #(<) :: Product a -> Product a -> Bool #(<=) :: Product a -> Product a -> Bool #(>) :: Product a -> Product a -> Bool #(>=) :: Product a -> Product a -> Bool #max :: Product a -> Product a -> Product a #min :: Product a -> Product a -> Product a # Ord a => Ord (Down a) Since: base-4.6.0.0 Instance detailsDefined in Data.Ord Methodscompare :: Down a -> Down a -> Ordering #(<) :: Down a -> Down a -> Bool #(<=) :: Down a -> Down a -> Bool #(>) :: Down a -> Down a -> Bool #(>=) :: Down a -> Down a -> Bool #max :: Down a -> Down a -> Down a #min :: Down a -> Down a -> Down a # Ord a => Ord (NonEmpty a) Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodscompare :: NonEmpty a -> NonEmpty a -> Ordering #(<) :: NonEmpty a -> NonEmpty a -> Bool #(<=) :: NonEmpty a -> NonEmpty a -> Bool #(>) :: NonEmpty a -> NonEmpty a -> Bool #(>=) :: NonEmpty a -> NonEmpty a -> Bool #max :: NonEmpty a -> NonEmpty a -> NonEmpty a #min :: NonEmpty a -> NonEmpty a -> NonEmpty a # (Ord a, Ord b) => Ord (Either a b) Since: base-2.1 Instance detailsDefined in Data.Either Methodscompare :: Either a b -> Either a b -> Ordering #(<) :: Either a b -> Either a b -> Bool #(<=) :: Either a b -> Either a b -> Bool #(>) :: Either a b -> Either a b -> Bool #(>=) :: Either a b -> Either a b -> Bool #max :: Either a b -> Either a b -> Either a b #min :: Either a b -> Either a b -> Either a b # Ord (V1 p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: V1 p -> V1 p -> Ordering #(<) :: V1 p -> V1 p -> Bool #(<=) :: V1 p -> V1 p -> Bool #(>) :: V1 p -> V1 p -> Bool #(>=) :: V1 p -> V1 p -> Bool #max :: V1 p -> V1 p -> V1 p #min :: V1 p -> V1 p -> V1 p # Ord (U1 p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: U1 p -> U1 p -> Ordering #(<) :: U1 p -> U1 p -> Bool #(<=) :: U1 p -> U1 p -> Bool #(>) :: U1 p -> U1 p -> Bool #(>=) :: U1 p -> U1 p -> Bool #max :: U1 p -> U1 p -> U1 p #min :: U1 p -> U1 p -> U1 p # (Ord a, Ord b) => Ord (a, b) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b) -> (a, b) -> Ordering #(<) :: (a, b) -> (a, b) -> Bool #(<=) :: (a, b) -> (a, b) -> Bool #(>) :: (a, b) -> (a, b) -> Bool #(>=) :: (a, b) -> (a, b) -> Bool #max :: (a, b) -> (a, b) -> (a, b) #min :: (a, b) -> (a, b) -> (a, b) # (Ix i, Ord e) => Ord (Array i e) Since: base-2.1 Instance detailsDefined in GHC.Arr Methodscompare :: Array i e -> Array i e -> Ordering #(<) :: Array i e -> Array i e -> Bool #(<=) :: Array i e -> Array i e -> Bool #(>) :: Array i e -> Array i e -> Bool #(>=) :: Array i e -> Array i e -> Bool #max :: Array i e -> Array i e -> Array i e #min :: Array i e -> Array i e -> Array i e # Ord (Proxy s) Since: base-4.7.0.0 Instance detailsDefined in Data.Proxy Methodscompare :: Proxy s -> Proxy s -> Ordering #(<) :: Proxy s -> Proxy s -> Bool #(<=) :: Proxy s -> Proxy s -> Bool #(>) :: Proxy s -> Proxy s -> Bool #(>=) :: Proxy s -> Proxy s -> Bool #max :: Proxy s -> Proxy s -> Proxy s #min :: Proxy s -> Proxy s -> Proxy s # Ord (f p) => Ord (Rec1 f p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: Rec1 f p -> Rec1 f p -> Ordering #(<) :: Rec1 f p -> Rec1 f p -> Bool #(<=) :: Rec1 f p -> Rec1 f p -> Bool #(>) :: Rec1 f p -> Rec1 f p -> Bool #(>=) :: Rec1 f p -> Rec1 f p -> Bool #max :: Rec1 f p -> Rec1 f p -> Rec1 f p #min :: Rec1 f p -> Rec1 f p -> Rec1 f p # Ord (URec (Ptr ()) p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: URec (Ptr ()) p -> URec (Ptr ()) p -> Ordering #(<) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(<=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(>) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #(>=) :: URec (Ptr ()) p -> URec (Ptr ()) p -> Bool #max :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p #min :: URec (Ptr ()) p -> URec (Ptr ()) p -> URec (Ptr ()) p # Ord (URec Char p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: URec Char p -> URec Char p -> Ordering #(<) :: URec Char p -> URec Char p -> Bool #(<=) :: URec Char p -> URec Char p -> Bool #(>) :: URec Char p -> URec Char p -> Bool #(>=) :: URec Char p -> URec Char p -> Bool #max :: URec Char p -> URec Char p -> URec Char p #min :: URec Char p -> URec Char p -> URec Char p # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: URec Double p -> URec Double p -> Ordering #(<) :: URec Double p -> URec Double p -> Bool #(<=) :: URec Double p -> URec Double p -> Bool #(>) :: URec Double p -> URec Double p -> Bool #(>=) :: URec Double p -> URec Double p -> Bool #max :: URec Double p -> URec Double p -> URec Double p #min :: URec Double p -> URec Double p -> URec Double p # Ord (URec Float p) Instance detailsDefined in GHC.Generics Methodscompare :: URec Float p -> URec Float p -> Ordering #(<) :: URec Float p -> URec Float p -> Bool #(<=) :: URec Float p -> URec Float p -> Bool #(>) :: URec Float p -> URec Float p -> Bool #(>=) :: URec Float p -> URec Float p -> Bool #max :: URec Float p -> URec Float p -> URec Float p #min :: URec Float p -> URec Float p -> URec Float p # Ord (URec Int p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: URec Int p -> URec Int p -> Ordering #(<) :: URec Int p -> URec Int p -> Bool #(<=) :: URec Int p -> URec Int p -> Bool #(>) :: URec Int p -> URec Int p -> Bool #(>=) :: URec Int p -> URec Int p -> Bool #max :: URec Int p -> URec Int p -> URec Int p #min :: URec Int p -> URec Int p -> URec Int p # Ord (URec Word p) Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: URec Word p -> URec Word p -> Ordering #(<) :: URec Word p -> URec Word p -> Bool #(<=) :: URec Word p -> URec Word p -> Bool #(>) :: URec Word p -> URec Word p -> Bool #(>=) :: URec Word p -> URec Word p -> Bool #max :: URec Word p -> URec Word p -> URec Word p #min :: URec Word p -> URec Word p -> URec Word p # (Ord a, Ord b, Ord c) => Ord (a, b, c) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c) -> (a, b, c) -> Ordering #(<) :: (a, b, c) -> (a, b, c) -> Bool #(<=) :: (a, b, c) -> (a, b, c) -> Bool #(>) :: (a, b, c) -> (a, b, c) -> Bool #(>=) :: (a, b, c) -> (a, b, c) -> Bool #max :: (a, b, c) -> (a, b, c) -> (a, b, c) #min :: (a, b, c) -> (a, b, c) -> (a, b, c) # Ord a => Ord (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methodscompare :: Const a b -> Const a b -> Ordering #(<) :: Const a b -> Const a b -> Bool #(<=) :: Const a b -> Const a b -> Bool #(>) :: Const a b -> Const a b -> Bool #(>=) :: Const a b -> Const a b -> Bool #max :: Const a b -> Const a b -> Const a b #min :: Const a b -> Const a b -> Const a b # Ord (f a) => Ord (Ap f a) Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methodscompare :: Ap f a -> Ap f a -> Ordering #(<) :: Ap f a -> Ap f a -> Bool #(<=) :: Ap f a -> Ap f a -> Bool #(>) :: Ap f a -> Ap f a -> Bool #(>=) :: Ap f a -> Ap f a -> Bool #max :: Ap f a -> Ap f a -> Ap f a #min :: Ap f a -> Ap f a -> Ap f a # Ord (f a) => Ord (Alt f a) Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Alt f a -> Alt f a -> Ordering #(<) :: Alt f a -> Alt f a -> Bool #(<=) :: Alt f a -> Alt f a -> Bool #(>) :: Alt f a -> Alt f a -> Bool #(>=) :: Alt f a -> Alt f a -> Bool #max :: Alt f a -> Alt f a -> Alt f a #min :: Alt f a -> Alt f a -> Alt f a # Ord c => Ord (K1 i c p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: K1 i c p -> K1 i c p -> Ordering #(<) :: K1 i c p -> K1 i c p -> Bool #(<=) :: K1 i c p -> K1 i c p -> Bool #(>) :: K1 i c p -> K1 i c p -> Bool #(>=) :: K1 i c p -> K1 i c p -> Bool #max :: K1 i c p -> K1 i c p -> K1 i c p #min :: K1 i c p -> K1 i c p -> K1 i c p # (Ord (f p), Ord (g p)) => Ord ((f :+: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: (f :+: g) p -> (f :+: g) p -> Ordering #(<) :: (f :+: g) p -> (f :+: g) p -> Bool #(<=) :: (f :+: g) p -> (f :+: g) p -> Bool #(>) :: (f :+: g) p -> (f :+: g) p -> Bool #(>=) :: (f :+: g) p -> (f :+: g) p -> Bool #max :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p #min :: (f :+: g) p -> (f :+: g) p -> (f :+: g) p # (Ord (f p), Ord (g p)) => Ord ((f :*: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: (f :*: g) p -> (f :*: g) p -> Ordering #(<) :: (f :*: g) p -> (f :*: g) p -> Bool #(<=) :: (f :*: g) p -> (f :*: g) p -> Bool #(>) :: (f :*: g) p -> (f :*: g) p -> Bool #(>=) :: (f :*: g) p -> (f :*: g) p -> Bool #max :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #min :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p # (Ord a, Ord b, Ord c, Ord d) => Ord (a, b, c, d) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d) -> (a, b, c, d) -> Ordering #(<) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(<=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(>) :: (a, b, c, d) -> (a, b, c, d) -> Bool #(>=) :: (a, b, c, d) -> (a, b, c, d) -> Bool #max :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #min :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # Ord (f p) => Ord (M1 i c f p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: M1 i c f p -> M1 i c f p -> Ordering #(<) :: M1 i c f p -> M1 i c f p -> Bool #(<=) :: M1 i c f p -> M1 i c f p -> Bool #(>) :: M1 i c f p -> M1 i c f p -> Bool #(>=) :: M1 i c f p -> M1 i c f p -> Bool #max :: M1 i c f p -> M1 i c f p -> M1 i c f p #min :: M1 i c f p -> M1 i c f p -> M1 i c f p # Ord (f (g p)) => Ord ((f :.: g) p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics Methodscompare :: (f :.: g) p -> (f :.: g) p -> Ordering #(<) :: (f :.: g) p -> (f :.: g) p -> Bool #(<=) :: (f :.: g) p -> (f :.: g) p -> Bool #(>) :: (f :.: g) p -> (f :.: g) p -> Bool #(>=) :: (f :.: g) p -> (f :.: g) p -> Bool #max :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #min :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p # (Ord a, Ord b, Ord c, Ord d, Ord e) => Ord (a, b, c, d, e) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e) -> (a, b, c, d, e) -> Ordering #(<) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(<=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #(>=) :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool #max :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) #min :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f) => Ord (a, b, c, d, e, f) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Ordering #(<) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(<=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(>) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #(>=) :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> Bool #max :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) #min :: (a, b, c, d, e, f) -> (a, b, c, d, e, f) -> (a, b, c, d, e, f) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g) => Ord (a, b, c, d, e, f, g) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Ordering #(<) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(<=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(>) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #(>=) :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> Bool #max :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) #min :: (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) -> (a, b, c, d, e, f, g) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h) => Ord (a, b, c, d, e, f, g, h) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Ordering #(<) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(<=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(>) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #(>=) :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> Bool #max :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) #min :: (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) -> (a, b, c, d, e, f, g, h) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i) => Ord (a, b, c, d, e, f, g, h, i) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> Bool #max :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) #min :: (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) -> (a, b, c, d, e, f, g, h, i) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j) => Ord (a, b, c, d, e, f, g, h, i, j) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) #min :: (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) -> (a, b, c, d, e, f, g, h, i, j) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k) => Ord (a, b, c, d, e, f, g, h, i, j, k) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) #min :: (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) -> (a, b, c, d, e, f, g, h, i, j, k) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l) => Ord (a, b, c, d, e, f, g, h, i, j, k, l) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) #min :: (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) -> (a, b, c, d, e, f, g, h, i, j, k, l) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) -> (a, b, c, d, e, f, g, h, i, j, k, l, m) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n) # (Ord a, Ord b, Ord c, Ord d, Ord e, Ord f, Ord g, Ord h, Ord i, Ord j, Ord k, Ord l, Ord m, Ord n, Ord o) => Ord (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Instance detailsDefined in GHC.Classes Methodscompare :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Ordering #(<) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(<=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(>) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #(>=) :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> Bool #max :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) #min :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) # class Read a where # Parsing of Strings, producing values. Derived instances of Read make the following assumptions, which derived instances of Show obey: • If the constructor is defined to be an infix operator, then the derived Read instance will parse only infix applications of the constructor (not the prefix form). • Associativity is not used to reduce the occurrence of parentheses, although precedence may be. • If the constructor is defined using record syntax, the derived Read will parse only the record-syntax form, and furthermore, the fields must be given in the same order as the original declaration. • The derived Read instance allows arbitrary Haskell whitespace between tokens of the input string. Extra parentheses are also allowed. For example, given the declarations infixr 5 :^: data Tree a = Leaf a | Tree a :^: Tree a the derived instance of Read in Haskell 2010 is equivalent to instance (Read a) => Read (Tree a) where readsPrec d r = readParen (d > app_prec) (\r -> [(Leaf m,t) | ("Leaf",s) <- lex r, (m,t) <- readsPrec (app_prec+1) s]) r ++ readParen (d > up_prec) (\r -> [(u:^:v,w) | (u,s) <- readsPrec (up_prec+1) r, (":^:",t) <- lex s, (v,w) <- readsPrec (up_prec+1) t]) r where app_prec = 10 up_prec = 5 Note that right-associativity of :^: is unused. The derived instance in GHC is equivalent to instance (Read a) => Read (Tree a) where readPrec = parens$ (prec app_prec $do Ident "Leaf" <- lexP m <- step readPrec return (Leaf m)) +++ (prec up_prec$ do
u <- step readPrec
Symbol ":^:" <- lexP
v <- step readPrec
return (u :^: v))

where app_prec = 10
up_prec = 5

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

Minimal complete definition

Methods

Arguments

 :: Int the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10. -> ReadS a

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

Derived instances of Read and Show satisfy the following:

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

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

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

Methods

toRational :: a -> Rational #

the rational equivalent of its real argument with full precision

Instances
 Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-2.0.1 Instance detailsDefined in GHC.Real Methods Since: base-4.8.0.0 Instance detailsDefined in GHC.Real Methods Since: base-2.1 Instance detailsDefined in GHC.Real Methods Integral a => Real (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodstoRational :: Ratio a -> Rational # Real a => Real (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodstoRational :: Const a b -> Rational #

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

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

Minimal complete definition

Methods

floatRadix :: a -> Integer #

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

floatDigits :: a -> Int #

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

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

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

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

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

encodeFloat :: Integer -> Int -> a #

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

exponent :: a -> Int #

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

significand :: a -> a #

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

scaleFloat :: Int -> a -> a #

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

isNaN :: a -> Bool #

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

isInfinite :: a -> Bool #

True if the argument is an IEEE infinity or negative infinity

isDenormalized :: a -> Bool #

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

isNegativeZero :: a -> Bool #

True if the argument is an IEEE negative zero

isIEEE :: a -> Bool #

True if the argument is an IEEE floating point number

atan2 :: a -> a -> a #

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

Instances
 Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Double -> (Int, Int) #decodeFloat :: Double -> (Integer, Int) #isNaN :: Double -> Bool #atan2 :: Double -> Double -> Double # Since: base-2.1 Instance detailsDefined in GHC.Float MethodsfloatRange :: Float -> (Int, Int) #decodeFloat :: Float -> (Integer, Int) #scaleFloat :: Int -> Float -> Float #isNaN :: Float -> Bool #isIEEE :: Float -> Bool #atan2 :: Float -> Float -> Float # RealFloat a => RealFloat (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsfloatRadix :: Const a b -> Integer #floatDigits :: Const a b -> Int #floatRange :: Const a b -> (Int, Int) #decodeFloat :: Const a b -> (Integer, Int) #encodeFloat :: Integer -> Int -> Const a b #exponent :: Const a b -> Int #significand :: Const a b -> Const a b #scaleFloat :: Int -> Const a b -> Const a b #isNaN :: Const a b -> Bool #isInfinite :: Const a b -> Bool #isDenormalized :: Const a b -> Bool #isNegativeZero :: Const a b -> Bool #isIEEE :: Const a b -> Bool #atan2 :: Const a b -> Const a b -> Const a b #

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

Extracting components of fractions.

Minimal complete definition

properFraction

Methods

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

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

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

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

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

truncate x returns the integer nearest x between zero and x

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

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

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

ceiling x returns the least integer not less than x

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

floor x returns the greatest integer not greater than x

Instances
 Integral a => RealFrac (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsproperFraction :: Integral b => Ratio a -> (b, Ratio a) #truncate :: Integral b => Ratio a -> b #round :: Integral b => Ratio a -> b #ceiling :: Integral b => Ratio a -> b #floor :: Integral b => Ratio a -> b # RealFrac a => RealFrac (Const a b) Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const MethodsproperFraction :: Integral b0 => Const a b -> (b0, Const a b) #truncate :: Integral b0 => Const a b -> b0 #round :: Integral b0 => Const a b -> b0 #ceiling :: Integral b0 => Const a b -> b0 #floor :: Integral b0 => Const a b -> b0 #

class Show a where #

Conversion of values to readable Strings.

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

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

For example, given the declarations

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

the derived instance of Show is equivalent to

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

showsPrec d (Leaf m) = showParen (d > app_prec) $showString "Leaf " . showsPrec (app_prec+1) m where app_prec = 10 showsPrec d (u :^: v) = showParen (d > up_prec)$
showsPrec (up_prec+1) u .
showString " :^: "      .
showsPrec (up_prec+1) v
where up_prec = 5

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

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

Minimal complete definition

Methods

Arguments

 :: Int the operator precedence of the enclosing context (a number from 0 to 11). Function application has precedence 10. -> a the value to be converted to a String -> ShowS

Convert a value to a readable String.

showsPrec should satisfy the law

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

Derived instances of Read and Show satisfy the following:

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

show :: a -> String #

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

showList :: [a] -> ShowS #

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

Instances
 Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Bool -> ShowS #show :: Bool -> String #showList :: [Bool] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Char -> ShowS #show :: Char -> String #showList :: [Char] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Int -> ShowS #show :: Int -> String #showList :: [Int] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Integer] -> ShowS # Since: base-4.8.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [Natural] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowList :: [Ordering] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Word -> ShowS #show :: Word -> String #showList :: [Word] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [RuntimeRep] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [VecCount] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [VecElem] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [CallStack] -> ShowS # Show () Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> () -> ShowS #show :: () -> String #showList :: [()] -> ShowS # Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> TyCon -> ShowS #show :: TyCon -> String #showList :: [TyCon] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Module -> ShowS #showList :: [Module] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> TrName -> ShowS #showList :: [TrName] -> ShowS # Instance detailsDefined in GHC.Show MethodsshowList :: [KindRep] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowList :: [TypeLitSort] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Handle.Types MethodsshowsPrec :: Int -> Handle -> ShowS #showList :: [Handle] -> ShowS # Show HandleType Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Handle.Types MethodsshowsPrec :: Int -> HandleType -> ShowS #show :: HandleType -> String #showList :: [HandleType] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [Deadlock] -> ShowS # Since: base-4.7.1.0 Instance detailsDefined in GHC.IO.Exception Methods Since: base-4.10.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [CompactionFailed] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [AssertionFailed] -> ShowS # Since: base-4.7.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [SomeAsyncException] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [AsyncException] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [ArrayException] -> ShowS # Since: base-4.11.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [FixIOException] -> ShowS # Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [ExitCode] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [IOErrorType] -> ShowS # Since: base-4.2.0.0 Instance detailsDefined in GHC.IO.Handle.Types MethodsshowList :: [BufferMode] -> ShowS # Since: base-4.3.0.0 Instance detailsDefined in GHC.IO.Handle.Types MethodsshowList :: [Newline] -> ShowS # Since: base-4.3.0.0 Instance detailsDefined in GHC.IO.Handle.Types MethodsshowList :: [NewlineMode] -> ShowS # Since: base-4.3.0.0 Instance detailsDefined in GHC.IO MethodsshowList :: [MaskingState] -> ShowS # Since: base-4.1.0.0 Instance detailsDefined in GHC.IO.Exception MethodsshowList :: [IOException] -> ShowS # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> All -> ShowS #show :: All -> String #showList :: [All] -> ShowS # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Any -> ShowS #show :: Any -> String #showList :: [Any] -> ShowS # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics MethodsshowsPrec :: Int -> Fixity -> ShowS #showList :: [Fixity] -> ShowS # Since: base-4.6.0.0 Instance detailsDefined in GHC.Generics MethodsshowList :: [Associativity] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics MethodsshowList :: [SourceUnpackedness] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics MethodsshowList :: [SourceStrictness] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Generics MethodsshowList :: [DecidedStrictness] -> ShowS # Since: base-4.9.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> SrcLoc -> ShowS #showList :: [SrcLoc] -> ShowS # Source # Instance detailsDefined in Data.Matrix.Class MethodsshowList :: [Dimension] -> ShowS # Show a => Show [a] Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> [a] -> ShowS #show :: [a] -> String #showList :: [[a]] -> ShowS # Show a => Show (Maybe a) Since: base-2.1 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int -> Maybe a -> ShowS #show :: Maybe a -> String #showList :: [Maybe a] -> ShowS # Show a => Show (Ratio a) Since: base-2.0.1 Instance detailsDefined in GHC.Real MethodsshowsPrec :: Int -> Ratio a -> ShowS #show :: Ratio a -> String #showList :: [Ratio a] -> ShowS # Show (Ptr a) Since: base-2.1 Instance detailsDefined in GHC.Ptr MethodsshowsPrec :: Int -> Ptr a -> ShowS #show :: Ptr a -> String #showList :: [Ptr a] -> ShowS # Show (FunPtr a) Since: base-2.1 Instance detailsDefined in GHC.Ptr MethodsshowsPrec :: Int -> FunPtr a -> ShowS #show :: FunPtr a -> String #showList :: [FunPtr a] -> ShowS # Show p => Show (Par1 p) Since: base-4.7.0.0 Instance detailsDefined in GHC.Generics MethodsshowsPrec :: Int -> Par1 p -> ShowS #show :: Par1 p -> String #showList :: [Par1 p] -> ShowS # Show a => Show (ZipList a) Since: base-4.7.0.0 Instance detailsDefined in Control.Applicative MethodsshowsPrec :: Int -> ZipList a -> ShowS #show :: ZipList a -> String #showList :: [ZipList a] -> ShowS # Show a => Show (First a) Since: base-2.1 Instance detailsDefined in Data.Monoid MethodsshowsPrec :: Int -> First a -> ShowS #show :: First a -> String #showList :: [First a] -> ShowS # Show a => Show (Last a) Since: base-2.1 Instance detailsDefined in Data.Monoid MethodsshowsPrec :: Int -> Last a -> ShowS #show :: Last a -> String #showList :: [Last a] -> ShowS # Show a => Show (Dual a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Dual a -> ShowS #show :: Dual a -> String #showList :: [Dual a] -> ShowS # Show a => Show (Sum a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Sum a -> ShowS #show :: Sum a -> String #showList :: [Sum a] -> ShowS # Show a => Show (Product a) Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Product a -> ShowS #show :: Product a -> String #showList :: [Product a] -> ShowS # Show a => Show (Down a) Since: base-4.7.0.0 Instance detailsDefined in Data.Ord MethodsshowsPrec :: Int -> Down a -> ShowS #show :: Down a -> String #showList :: [Down a] -> ShowS # Show a => Show (NonEmpty a) Since: base-4.11.0.0 Instance detailsDefined in GHC.Show MethodsshowsPrec :: Int ->