Control.Subcategory.RebindableSyntax

Documentation

ifThenElse :: Bool -> a -> a -> 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, instances are encouraged to follow these properties:

Reflexivity

x == x = True

Symmetry

x == y = y == x

Transitivity

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

Extensionality

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

Negation

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

Minimal complete definition: either == or /=.

Minimal complete definition

(==) | (/=)

Methods

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

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

Instances

Eq ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

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

(/=) :: ByteArray -> ByteArray -> 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 Version

Since: base-2.1

Defined in Data.Version

Methods

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

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

Eq IntPtr

Defined in Foreign.Ptr

Methods

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

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

Eq WordPtr

Defined in Foreign.Ptr

Methods

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

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

Eq Void

Since: base-4.8.0.0

Defined in GHC.Base

Methods

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

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

Eq BlockReason

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

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

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

Eq ThreadId

Since: base-4.2.0.0

Defined in GHC.Conc.Sync

Methods

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

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

Eq ThreadStatus

Since: base-4.3.0.0

Defined in GHC.Conc.Sync

Methods

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

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

Eq SpecConstrAnnotation

Since: base-4.3.0.0

Defined in GHC.Exts

Methods

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

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

Eq Associativity

Since: base-4.6.0.0

Defined in GHC.Generics

Methods

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

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

Eq DecidedStrictness

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Eq Fixity

Since: base-4.6.0.0

Defined in GHC.Generics

Methods

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

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

Eq SourceStrictness

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Eq SourceUnpackedness

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

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

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

Eq MaskingState

Since: base-4.3.0.0

Defined in GHC.IO

Methods

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

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

Eq ArrayException

Since: base-4.2.0.0

Defined in GHC.IO.Exception

Methods

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

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

Eq AsyncException

Since: base-4.2.0.0

Defined in GHC.IO.Exception

Methods

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

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

Since: base-4.1.0.0

Defined in GHC.IO.Exception

Methods

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

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

Since: base-2.1

Defined in GHC.Int

Methods

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

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

Eq IoSubSystem

Defined in GHC.RTS.Flags

Methods

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

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

Eq SrcLoc

Since: base-4.9.0.0

Defined in GHC.Stack.Types

Methods

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

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

Since: base-2.1

Defined in GHC.Word

Methods

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

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

Defined in Data.ByteString.Internal.Type

Methods

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

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

Eq ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

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

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

Eq ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

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

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

Eq IntSet

Defined in Data.IntSet.Internal

Methods

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

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

Eq BigNat

Defined in GHC.Num.BigNat

Methods

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

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

Eq ForeignSrcLang

Defined in GHC.ForeignSrcLang.Type

Methods

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

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

Eq Extension

Defined in GHC.LanguageExtensions.Type

Methods

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

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

Eq Module

Defined in GHC.Classes

Methods

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

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

Eq Ordering

Defined in GHC.Classes

Methods

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

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

Eq TrName

Defined in GHC.Classes

Methods

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

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

Eq TyCon

Defined in GHC.Classes

Methods

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

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

Eq OsChar

Byte equality of the internal representation.

Defined in System.OsString.Internal.Types

Methods

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

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

Eq OsString

Byte equality of the internal representation.

Defined in System.OsString.Internal.Types

Methods

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

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

Eq PosixChar

Defined in System.OsString.Internal.Types

Methods

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

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

Eq PosixString

Defined in System.OsString.Internal.Types

Methods

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

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

Eq WindowsChar

Defined in System.OsString.Internal.Types

Methods

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

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

Eq WindowsString

Defined in System.OsString.Internal.Types

Methods

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

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

Eq Mode

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq Style

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq TextDetails

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

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

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

Eq StdGen

Defined in System.Random.Internal

Methods

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

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

Eq AnnLookup

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq AnnTarget

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Bang

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Body

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Bytes

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Callconv

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Clause

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Con

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Dec

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq DecidedStrictness

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq DerivClause

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq DerivStrategy

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq DocLoc

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Exp

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FamilyResultSig

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Fixity

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FixityDirection

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Foreign

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FunDep

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Guard

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Info

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq InjectivityAnn

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Inline

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Lit

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Loc

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Match

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq ModName

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Module

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq ModuleInfo

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Name

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq NameFlavour

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq NameSpace

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq OccName

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Overlap

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Pat

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq PatSynArgs

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq PatSynDir

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Phases

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq PkgName

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Pragma

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Range

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Role

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq RuleBndr

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq RuleMatch

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Safety

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq SourceStrictness

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq SourceUnpackedness

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Specificity

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Stmt

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TyLit

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TySynEqn

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Type

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TypeFamilyHead

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Integer

Defined in GHC.Num.Integer

Methods

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

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

Eq ()

Defined in GHC.Classes

Methods

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

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

Eq Bool

Defined in GHC.Classes

Methods

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

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

Eq Char

Defined in GHC.Classes

Methods

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

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

Eq Double

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

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

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

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

Defined in GHC.Classes

Methods

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

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

Eq Float

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

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

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

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

Defined in GHC.Classes

Methods

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

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

Eq Int

Defined in GHC.Classes

Methods

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

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

Eq Word

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Defined in Control.Applicative

Methods

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

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

Eq (MutableByteArray s)

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

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

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

Eq a => Eq (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

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

(/=) :: Complex a -> Complex 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 (Down a)

Since: base-4.6.0.0

Defined in Data.Ord

Methods

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

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

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

Eq (TVar a)

Since: base-4.8.0.0

Defined in GHC.Conc.Sync

Methods

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

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

Eq (ForeignPtr a)

Since: base-2.1

Defined in GHC.ForeignPtr

Methods

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

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

Eq p => Eq (Par1 p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: Par1 p -> Par1 p -> Bool

(/=) :: Par1 p -> Par1 p -> Bool

Eq (FunPtr a)

Defined in GHC.Ptr

Methods

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

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

Eq (Ptr a)

Since: base-2.1

Defined in GHC.Ptr

Methods

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

(/=) :: Ptr a -> Ptr 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 (IntMap a)

Defined in Data.IntMap.Internal

Methods

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

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

Eq a => Eq (Seq a)

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (ViewL a)

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (ViewR a)

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (Intersection a)

Defined in Data.Set.Internal

Methods

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

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

Eq a => Eq (Set a)

Defined in Data.Set.Internal

Methods

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

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

Eq a => Eq (Tree a)

Defined in Data.Tree

Methods

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

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

Eq a => Eq (Hashed a)

Uses precomputed hash to detect inequality faster

Defined in Data.Hashable.Class

Methods

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

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

Eq a => Eq (AnnotDetails a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq (Doc a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq a => Eq (Span a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq a => Eq (Array a)

Defined in Data.Primitive.Array

Methods

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

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

(Eq a, Prim a) => Eq (PrimArray a)

Since: primitive-0.6.4.0

Defined in Data.Primitive.PrimArray

Methods

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

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

Eq a => Eq (SmallArray a)

Defined in Data.Primitive.SmallArray

Methods

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

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

Eq g => Eq (StateGen g)

Defined in System.Random.Internal

Methods

(==) :: StateGen g -> StateGen g -> Bool

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

Eq flag => Eq (TyVarBndr flag)

Defined in Language.Haskell.TH.Syntax

Methods

(==) :: TyVarBndr flag -> TyVarBndr flag -> Bool

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

Eq a => Eq (HashSet a)

Note that, in the presence of hash collisions, equal HashSets may behave differently, i.e. extensionality may be violated:

>>> data D = A | B deriving (Eq, Show)
>>> instance Hashable D where hashWithSalt salt _d = salt

>>> x = fromList [A, B]
>>> y = fromList [B, A]

>>> x == y
True
>>> toList x
[A,B]
>>> toList y
[B,A]

In general, the lack of extensionality can be observed with any function that depends on the key ordering, such as folds and traversals.

Defined in Data.HashSet.Internal

Methods

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

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

Eq a => Eq (Vector a)

Defined in Data.Vector

Methods

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

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

(Prim a, Eq a) => Eq (Vector a)

Defined in Data.Vector.Primitive

Methods

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

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

(Storable a, Eq a) => Eq (Vector a)

Defined in Data.Vector.Storable

Methods

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

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

Defined in GHC.Classes

Methods

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

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

Eq a => Eq [a]

Defined in GHC.Classes

Methods

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

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

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

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

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

(/=) :: Proxy s -> Proxy s -> 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 (U1 p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(==) :: U1 p -> U1 p -> Bool

(/=) :: U1 p -> U1 p -> Bool

Eq (V1 p)

Since: base-4.9.0.0

Defined in GHC.Generics

Methods

(==) :: V1 p -> V1 p -> Bool

(/=) :: V1 p -> V1 p -> 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

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

Defined in Control.Comonad.Cofree

Methods

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

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

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

Defined in Control.Monad.Free

Methods

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

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

Eq (MutableArray s a)

Defined in Data.Primitive.Array

Methods

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

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

Eq (MutablePrimArray s a)

Defined in Data.Primitive.PrimArray

Methods

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

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

Eq (SmallMutableArray s a)

Defined in Data.Primitive.SmallArray

Methods

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

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

Eq (f a) => Eq (Zippy f a)

Defined in Data.Zip

Methods

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

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

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

Defined in Data.These

Methods

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

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

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

Defined in Control.Applicative.Lift

Methods

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

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

(Eq1 m, Eq a) => Eq (MaybeT m a)

Defined in Control.Monad.Trans.Maybe

Methods

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

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

(Eq k, Eq v) => Eq (HashMap k v)

Note that, in the presence of hash collisions, equal HashMaps may behave differently, i.e. extensionality may be violated:

>>> data D = A | B deriving (Eq, Show)
>>> instance Hashable D where hashWithSalt salt _d = salt

>>> x = fromList [(A,1), (B,2)]
>>> y = fromList [(B,2), (A,1)]

>>> x == y
True
>>> toList x
[(A,1),(B,2)]
>>> toList y
[(B,2),(A,1)]

In general, the lack of extensionality can be observed with any function that depends on the key ordering, such as folds and traversals.

Defined in Data.HashMap.Internal

Methods

(==) :: HashMap k v -> HashMap k v -> Bool

(/=) :: HashMap k v -> HashMap k v -> Bool

(Eq k, Eq v) => Eq (Leaf k v)

Defined in Data.HashMap.Internal

Methods

(==) :: Leaf k v -> Leaf k v -> Bool

(/=) :: Leaf k v -> Leaf k v -> Bool

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

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (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 (OrderingI a b)

Defined in Data.Type.Ord

Methods

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

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

(Generic1 f, Eq (Rep1 f a)) => Eq (Generically1 f a)

Since: base-4.18.0.0

Defined in GHC.Generics

Methods

(==) :: Generically1 f a -> Generically1 f a -> Bool

(/=) :: Generically1 f a -> Generically1 f a -> Bool

Eq (f p) => Eq (Rec1 f p)

Since: base-4.7.0.0

Defined 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

Defined 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

Defined 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

Defined in GHC.Generics

Methods

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

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

Eq (URec Float p)

Defined 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

Defined 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

Defined in GHC.Generics

Methods

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

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

Eq (p a a) => Eq (Join p a)

Defined in Data.Bifunctor.Join

Methods

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

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

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

Defined in Control.Monad.Trans.Free

Methods

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

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

(Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a)

Defined in Control.Monad.Trans.Free

Methods

(==) :: FreeT f m a -> FreeT f m a -> Bool

(/=) :: FreeT f m a -> FreeT f m a -> Bool

Eq (f a) => Eq (CApp f a)

Defined in Control.Subcategory.Applicative

Methods

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

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

Eq (f a) => Eq (CZippy f a)

Defined in Control.Subcategory.Zip

Methods

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

(/=) :: CZippy f a -> CZippy 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 (Backwards f a)

Defined in Control.Applicative.Backwards

Methods

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

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

(Eq e, Eq1 m, Eq a) => Eq (ExceptT e m a)

Defined in Control.Monad.Trans.Except

Methods

(==) :: ExceptT e m a -> ExceptT e m a -> Bool

(/=) :: ExceptT e m a -> ExceptT e m a -> 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 w, Eq1 m, Eq a) => Eq (WriterT w m a)

Defined in Control.Monad.Trans.Writer.Lazy

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool

(/=) :: WriterT w m a -> WriterT w m a -> Bool

(Eq w, Eq1 m, Eq a) => Eq (WriterT w m a)

Defined in Control.Monad.Trans.Writer.Strict

Methods

(==) :: WriterT w m a -> WriterT w m a -> Bool

(/=) :: WriterT w m a -> WriterT w m a -> Bool

Eq a => Eq (Constant a b)

Defined in Data.Functor.Constant

Methods

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

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

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

Defined in Data.Functor.Reverse

Methods

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

(/=) :: Reverse f a -> Reverse f 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 (f a), Eq (g a)) => Eq (Product f g a)

Since: base-4.18.0.0

Defined in Data.Functor.Product

Methods

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

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

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

Since: base-4.18.0.0

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 (f p), Eq (g p)) => Eq ((f :*: g) p)

Since: base-4.7.0.0

Defined 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

Defined in GHC.Generics

Methods

(==) :: (f :+: g) p -> (f :+: g) p -> Bool

(/=) :: (f :+: g) p -> (f :+: g) p -> Bool

Eq c => Eq (K1 i c p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: K1 i c p -> K1 i c p -> Bool

(/=) :: K1 i c p -> K1 i c p -> Bool

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

Defined in GHC.Classes

Methods

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

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

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

Since: base-4.18.0.0

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 (f (g p)) => Eq ((f :.: g) p)

Since: base-4.7.0.0

Defined in GHC.Generics

Methods

(==) :: (f :.: g) p -> (f :.: g) p -> Bool

(/=) :: (f :.: g) p -> (f :.: g) p -> Bool

Eq (f p) => Eq (M1 i c f p)

Since: base-4.7.0.0

Defined 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 a) => Eq (Clown f a b)

Defined in Data.Bifunctor.Clown

Methods

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

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

Eq (p b a) => Eq (Flip p a b)

Defined in Data.Bifunctor.Flip

Methods

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

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

Eq (g b) => Eq (Joker g a b)

Defined in Data.Bifunctor.Joker

Methods

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

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

Eq (p a b) => Eq (WrappedBifunctor p a b)

Defined in Data.Bifunctor.Wrapped

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in Data.Bifunctor.Product

Methods

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

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

(Eq (p a b), Eq (q a b)) => Eq (Sum p q a b)

Defined in Data.Bifunctor.Sum

Methods

(==) :: Sum p q a b -> Sum p q a b -> Bool

(/=) :: Sum p q a b -> Sum p q a b -> 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 (f (p a b)) => Eq (Tannen f p a b)

Defined in Data.Bifunctor.Tannen

Methods

(==) :: Tannen f p a b -> Tannen f p a b -> Bool

(/=) :: Tannen f p a b -> Tannen f p a b -> 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 (p (f a) (g b)) => Eq (Biff p f g a b)

Defined in Data.Bifunctor.Biff

Methods

(==) :: Biff p f g a b -> Biff p f g a b -> Bool

(/=) :: Biff p f g a b -> Biff p f g a b -> Bool

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

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

Defined in GHC.Classes

Methods

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

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

class 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)

Coherence with toInteger

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

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

Minimal complete definition

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

Methods

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

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

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

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

Num IntPtr

Defined in Foreign.Ptr

Methods

(+) :: IntPtr -> IntPtr -> IntPtr

(-) :: IntPtr -> IntPtr -> IntPtr

(*) :: IntPtr -> IntPtr -> IntPtr

negate :: IntPtr -> IntPtr

abs :: IntPtr -> IntPtr

signum :: IntPtr -> IntPtr

fromInteger :: Integer -> IntPtr

Num WordPtr

Defined in Foreign.Ptr

Methods

(+) :: WordPtr -> WordPtr -> WordPtr

(-) :: WordPtr -> WordPtr -> WordPtr

(*) :: WordPtr -> WordPtr -> WordPtr

negate :: WordPtr -> WordPtr

abs :: WordPtr -> WordPtr

signum :: WordPtr -> WordPtr

fromInteger :: Integer -> WordPtr

Num Int16

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int16 -> Int16 -> Int16

(-) :: Int16 -> Int16 -> Int16

(*) :: Int16 -> Int16 -> Int16

negate :: Int16 -> Int16

abs :: Int16 -> Int16

signum :: Int16 -> Int16

fromInteger :: Integer -> Int16

Num Int32

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int32 -> Int32 -> Int32

(-) :: Int32 -> Int32 -> Int32

(*) :: Int32 -> Int32 -> Int32

negate :: Int32 -> Int32

abs :: Int32 -> Int32

signum :: Int32 -> Int32

fromInteger :: Integer -> Int32

Num Int64

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int64 -> Int64 -> Int64

(-) :: Int64 -> Int64 -> Int64

(*) :: Int64 -> Int64 -> Int64

negate :: Int64 -> Int64

abs :: Int64 -> Int64

signum :: Int64 -> Int64

fromInteger :: Integer -> Int64

Num Int8

Since: base-2.1

Defined in GHC.Int

Methods

(+) :: Int8 -> Int8 -> Int8

(-) :: Int8 -> Int8 -> Int8

(*) :: Int8 -> Int8 -> Int8

negate :: Int8 -> Int8

abs :: Int8 -> Int8

signum :: Int8 -> Int8

fromInteger :: Integer -> Int8

Num Word16

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word16 -> Word16 -> Word16

(-) :: Word16 -> Word16 -> Word16

(*) :: Word16 -> Word16 -> Word16

negate :: Word16 -> Word16

abs :: Word16 -> Word16

signum :: Word16 -> Word16

fromInteger :: Integer -> Word16

Num Word32

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word32 -> Word32 -> Word32

(-) :: Word32 -> Word32 -> Word32

(*) :: Word32 -> Word32 -> Word32

negate :: Word32 -> Word32

abs :: Word32 -> Word32

signum :: Word32 -> Word32

fromInteger :: Integer -> Word32

Num Word64

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word64 -> Word64 -> Word64

(-) :: Word64 -> Word64 -> Word64

(*) :: Word64 -> Word64 -> Word64

negate :: Word64 -> Word64

abs :: Word64 -> Word64

signum :: Word64 -> Word64

fromInteger :: Integer -> Word64

Num Word8

Since: base-2.1

Defined in GHC.Word

Methods

(+) :: Word8 -> Word8 -> Word8

(-) :: Word8 -> Word8 -> Word8

(*) :: Word8 -> Word8 -> Word8

negate :: Word8 -> Word8

abs :: Word8 -> Word8

signum :: Word8 -> Word8

fromInteger :: Integer -> Word8

Num Integer

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Integer -> Integer

abs :: Integer -> Integer

signum :: Integer -> Integer

fromInteger :: Integer -> Integer

Num Natural

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

Since: base-4.8.0.0

Defined in GHC.Num

Methods

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

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

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

negate :: Natural -> Natural

abs :: Natural -> Natural

signum :: Natural -> Natural

fromInteger :: Integer -> Natural

Num Int

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Int -> Int

abs :: Int -> Int

signum :: Int -> Int

fromInteger :: Integer -> Int

Num Word

Since: base-2.1

Defined in GHC.Num

Methods

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

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

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

negate :: Word -> Word

abs :: Word -> Word

signum :: Word -> Word

fromInteger :: Integer -> Word

RealFloat a => Num (Complex a)

Since: base-2.1

Defined in Data.Complex

Methods

(+) :: Complex a -> Complex a -> Complex a

(-) :: Complex a -> Complex a -> Complex a

(*) :: Complex a -> Complex a -> Complex a

negate :: Complex a -> Complex a

abs :: Complex a -> Complex a

signum :: Complex a -> Complex a

fromInteger :: Integer -> Complex a

Num a => Num (Identity a)

Since: base-4.9.0.0

Defined in Data.Functor.Identity

Methods

(+) :: Identity a -> Identity a -> Identity a

(-) :: Identity a -> Identity a -> Identity a

(*) :: Identity a -> Identity a -> Identity a

negate :: Identity a -> Identity a

abs :: Identity a -> Identity a

signum :: Identity a -> Identity a

fromInteger :: Integer -> Identity a

Num a => Num (Down a)

Since: base-4.11.0.0

Defined 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

fromInteger :: Integer -> Down a

Num a => Num (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(+) :: Max a -> Max a -> Max a

(-) :: Max a -> Max a -> Max a

(*) :: Max a -> Max a -> Max a

negate :: Max a -> Max a

abs :: Max a -> Max a

signum :: Max a -> Max a

fromInteger :: Integer -> Max a

Num a => Num (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(+) :: Min a -> Min a -> Min a

(-) :: Min a -> Min a -> Min a

(*) :: Min a -> Min a -> Min a

negate :: Min a -> Min a

abs :: Min a -> Min a

signum :: Min a -> Min a

fromInteger :: Integer -> Min a

Num a => Num (Product a)

Since: base-4.7.0.0

Defined 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

fromInteger :: Integer -> Product a

Num a => Num (Sum a)

Since: base-4.7.0.0

Defined 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

fromInteger :: Integer -> Sum a

Integral a => Num (Ratio a)

Since: base-2.0.1

Defined in GHC.Real

Methods

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

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

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

negate :: Ratio a -> Ratio a

abs :: Ratio a -> Ratio a

signum :: Ratio a -> Ratio a

fromInteger :: Integer -> Ratio a

Num a => Num (Op a b)

Defined in Data.Functor.Contravariant

Methods

(+) :: Op a b -> Op a b -> Op a b

(-) :: Op a b -> Op a b -> Op a b

(*) :: Op a b -> Op a b -> Op a b

negate :: Op a b -> Op a b

abs :: Op a b -> Op a b

signum :: Op a b -> Op a b

fromInteger :: Integer -> Op a b

Num b => Num (Fold a b)

Defined in Control.Foldl

Methods

(+) :: Fold a b -> Fold a b -> Fold a b

(-) :: Fold a b -> Fold a b -> Fold a b

(*) :: Fold a b -> Fold a b -> Fold a b

negate :: Fold a b -> Fold a b

abs :: Fold a b -> Fold a b

signum :: Fold a b -> Fold a b

fromInteger :: Integer -> Fold a b

Num a => Num (Const a b)

Since: base-4.9.0.0

Defined 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)

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

>>> Ap [10,20] + Ap [1,2]
Ap {getAp = [11,12,21,22]}
>>> Ap [1,2] + Ap [10,20]
Ap {getAp = [11,21,12,22]}

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

Defined 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

Defined 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

(Monad m, Num b) => Num (FoldM m a b)

Defined in Control.Foldl

Methods

(+) :: FoldM m a b -> FoldM m a b -> FoldM m a b

(-) :: FoldM m a b -> FoldM m a b -> FoldM m a b

(*) :: FoldM m a b -> FoldM m a b -> FoldM m a b

negate :: FoldM m a b -> FoldM m a b

abs :: FoldM m a b -> FoldM m a b

signum :: FoldM m a b -> FoldM m a b

fromInteger :: Integer -> FoldM m a b

Num a => Num (Tagged s a)

Defined in Data.Tagged

Methods

(+) :: Tagged s a -> Tagged s a -> Tagged s a

(-) :: Tagged s a -> Tagged s a -> Tagged s a

(*) :: Tagged s a -> Tagged s a -> Tagged s a

negate :: Tagged s a -> Tagged s a

abs :: Tagged s a -> Tagged s a

signum :: Tagged s a -> Tagged s a

fromInteger :: Integer -> Tagged s a

(>>=) :: (Dom m a, Dom m b, CBind m) => m a -> (a -> m b) -> m b

(>>) :: (Dom m a, Dom m b, CApplicative m) => m a -> m b -> m b

fromLabel :: IsLabel x a => a

return :: (Dom m a, CPointed m) => a -> m a

module Control.Arrow