Data.Universe.Instances.Eq

Documentation

An Eq instance for functions, given the input is Finite and the output is Eq. Compares pointwise.

class Eq a where

The Eq class defines equality (==) and inequality (/=). All the basic datatypes exported by the Prelude are instances of Eq, and Eq may be derived for any datatype whose constituents are also instances of Eq.

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

Reflexivity

x == x = True

Symmetry

x == y = y == x

Transitivity

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

Substitutivity

if x == y = True and f is a "public" function whose return type is an instance of Eq, then f x == f y = True

Negation

x /= y = not (x == y)

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances

Eq Bool

Defined in GHC.Classes

Methods

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

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

Eq Char

Defined in GHC.Classes

Methods

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

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

Eq Double

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

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

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

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

Defined in GHC.Classes

Methods

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

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

Eq Float

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

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

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

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

Defined in GHC.Classes

Methods

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

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

Eq Int

Defined in GHC.Classes

Methods

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

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

Eq Int8

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Eq Int16

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Eq Int32

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Eq Int64

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Eq Integer

Defined in GHC.Integer.Type

Methods

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

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

Eq Natural

Since: base-4.8.0.0

Defined in GHC.Natural

Methods

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

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

Eq Ordering

Defined in GHC.Classes

Methods

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

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

Eq Word

Defined in GHC.Classes

Methods

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

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

Eq Word8

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Eq Word16

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Eq Word32

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Eq Word64

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Eq ()

Defined in GHC.Classes

Methods

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

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

Eq TyCon

Defined in GHC.Classes

Methods

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

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

Eq Module

Defined in GHC.Classes

Methods

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

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

Eq TrName

Defined in GHC.Classes

Methods

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

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

Eq Void

Since: base-4.8.0.0

Defined in Data.Void

Methods

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

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

Eq AsyncException

Since: base-4.2.0.0

Defined in GHC.IO.Exception

Methods

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

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

Eq ArrayException

Since: base-4.2.0.0

Defined in GHC.IO.Exception

Methods

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

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

Eq ExitCode

Defined in GHC.IO.Exception

Methods

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

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

Eq IOErrorType

Since: base-4.1.0.0

Defined in GHC.IO.Exception

Methods

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

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

Eq MaskingState

Since: base-4.3.0.0

Defined in GHC.IO

Methods

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

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

Eq IOException

Since: base-4.1.0.0

Defined in GHC.IO.Exception

Methods

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

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

Eq All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Eq Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Eq Lexeme

Since: base-2.1

Defined in Text.Read.Lex

Methods

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

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

Eq Number

Since: base-4.6.0.0

Defined in Text.Read.Lex

Methods

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

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

Eq GeneralCategory

Since: base-2.1

Defined in GHC.Unicode

Methods

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

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

Eq SrcLoc

Since: base-4.9.0.0

Defined in GHC.Stack.Types

Methods

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

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

Eq BigNat

Defined in GHC.Integer.Type

Methods

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

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

Eq a => Eq [a]

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (Maybe a)

Since: base-2.1

Defined in GHC.Maybe

Methods

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

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

Eq a => Eq (Ratio a)

Since: base-2.1

Defined in GHC.Real

Methods

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

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

Eq a => Eq (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool

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

Eq a => Eq (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

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

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

Eq a => Eq (Identity a)

Since: base-4.8.0.0

Defined in Data.Functor.Identity

Methods

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

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

Eq a => Eq (First a)

Since: base-2.1

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Last a)

Since: base-2.1

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

(Finite a, Eq a) => Eq (Endo a)

Defined in Data.Universe.Instances.Eq

Methods

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

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

Eq a => Eq (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Eq a => Eq (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

Eq a => Eq (Set a)

Defined in Data.Set.Internal

Methods

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

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

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

Defined in Data.Universe.Instances.Eq

Methods

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

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

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

Since: base-2.1

Defined in Data.Either

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Since: base-2.1

Defined in GHC.Arr

Methods

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

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

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Eq (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

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

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

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

Defined in Data.Map.Internal

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

Eq (STArray s i e)

Since: base-2.1

Defined 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

Defined 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

Defined 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

Defined in Data.Semigroup.Internal

Methods

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

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

Eq b => Eq (Tagged s b)

Defined in Data.Tagged

Methods

(==) :: Tagged s b -> Tagged s b -> Bool

(/=) :: Tagged s b -> Tagged s b -> Bool

(Eq1 f, Eq a) => Eq (IdentityT f a)

Defined in Control.Monad.Trans.Identity

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

(Eq1 f, Eq1 g, Eq a) => Eq (Product f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Product

Methods

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

(/=) :: Product f g a -> Product f g a -> Bool

(Eq1 f, Eq1 g, Eq a) => Eq (Sum f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Sum

Methods

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

(/=) :: Sum f g a -> Sum f g a -> Bool

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

Defined in GHC.Classes

Methods

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

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

(Eq1 f, Eq1 g, Eq a) => Eq (Compose f g a)

Since: base-4.9.0.0

Defined in Data.Functor.Compose

Methods

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

(/=) :: Compose f g a -> Compose f g a -> Bool

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

Orphan instances

(Finite a, Eq a) => Eq (Endo a)

Methods

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

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

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

Methods

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

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