subcategories-0.2.0.1: Subcategories induced by class constraints
Safe HaskellSafe-Inferred
LanguageHaskell2010

Control.Subcategory.RebindableSyntax

Synopsis

Documentation

ifThenElse :: Bool -> a -> a -> a Source #

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

Instances details
Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq Version

Since: base-2.1

Instance details

Defined in Data.Version

Methods

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

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

Eq Void

Since: base-4.8.0.0

Instance details

Defined in Data.Void

Methods

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

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

Eq IntPtr 
Instance details

Defined in Foreign.Ptr

Methods

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

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

Eq WordPtr 
Instance details

Defined in Foreign.Ptr

Methods

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

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

Eq BlockReason

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq ThreadId

Since: base-4.2.0.0

Instance details

Defined in GHC.Conc.Sync

Eq ThreadStatus

Since: base-4.3.0.0

Instance details

Defined in GHC.Conc.Sync

Eq SpecConstrAnnotation

Since: base-4.3.0.0

Instance details

Defined in GHC.Exts

Eq Associativity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Eq DecidedStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq Fixity

Since: base-4.6.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Eq SourceStrictness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq SourceUnpackedness

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Eq MaskingState

Since: base-4.3.0.0

Instance details

Defined in GHC.IO

Eq ArrayException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq AsyncException

Since: base-4.2.0.0

Instance details

Defined in GHC.IO.Exception

Eq ExitCode 
Instance details

Defined in GHC.IO.Exception

Eq IOErrorType

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq IOException

Since: base-4.1.0.0

Instance details

Defined in GHC.IO.Exception

Eq Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

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

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

Eq Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

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

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

Eq Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

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

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

Eq Int8

Since: base-2.1

Instance details

Defined in GHC.Int

Methods

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

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

Eq IoSubSystem 
Instance details

Defined in GHC.RTS.Flags

Eq SrcLoc

Since: base-4.9.0.0

Instance details

Defined in GHC.Stack.Types

Methods

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

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

Eq GeneralCategory

Since: base-2.1

Instance details

Defined in GHC.Unicode

Eq Word16

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Methods

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

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

Eq Lexeme

Since: base-2.1

Instance details

Defined in Text.Read.Lex

Methods

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

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

Eq Number

Since: base-4.6.0.0

Instance details

Defined in Text.Read.Lex

Methods

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

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

Eq ByteString 
Instance details

Defined in Data.ByteString.Internal

Eq ByteString 
Instance details

Defined in Data.ByteString.Lazy.Internal

Eq ShortByteString 
Instance details

Defined in Data.ByteString.Short.Internal

Eq IntSet 
Instance details

Defined in Data.IntSet.Internal

Methods

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

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

Eq ByteArray 
Instance details

Defined in Data.Array.Byte

Eq BigNat 
Instance details

Defined in GHC.Num.BigNat

Methods

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

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

Eq ForeignSrcLang 
Instance details

Defined in GHC.ForeignSrcLang.Type

Eq Extension 
Instance details

Defined in GHC.LanguageExtensions.Type

Eq Module 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Ordering 
Instance details

Defined in GHC.Classes

Eq TrName 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq TyCon 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Mode 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq Style 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq TextDetails 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Eq Doc 
Instance details

Defined in Text.PrettyPrint.HughesPJ

Methods

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

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

Eq StdGen 
Instance details

Defined in System.Random.Internal

Methods

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

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

Eq AnnLookup 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq AnnTarget 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Bang 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Body 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Bytes 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Callconv 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Clause 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Con 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Dec 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq DecidedStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq DerivClause 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq DerivStrategy 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq DocLoc 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Exp 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FamilyResultSig 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Fixity 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FixityDirection 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Foreign 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq FunDep 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Guard 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Info 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq InjectivityAnn 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Inline 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Lit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Loc 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Match 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq ModName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Module 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq ModuleInfo 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Name 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq NameFlavour 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq NameSpace 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq OccName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Overlap 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Pat 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq PatSynArgs 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq PatSynDir 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Phases 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq PkgName 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Pragma 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Range 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq Role 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq RuleBndr 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq RuleMatch 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Safety 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq SourceStrictness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq SourceUnpackedness 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Specificity 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Stmt 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TyLit 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TySynEqn 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Type 
Instance details

Defined in Language.Haskell.TH.Syntax

Methods

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

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

Eq TypeFamilyHead 
Instance details

Defined in Language.Haskell.TH.Syntax

Eq Integer 
Instance details

Defined in GHC.Num.Integer

Methods

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

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

Eq Natural 
Instance details

Defined in GHC.Num.Natural

Methods

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

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

Eq () 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Bool 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Char 
Instance details

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
Instance details

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
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Int 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq Word 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq a => Eq (ZipList a)

Since: base-4.7.0.0

Instance details

Defined in Control.Applicative

Methods

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

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

Eq a => Eq (Complex a)

Since: base-2.1

Instance details

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

Instance details

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

Instance details

Defined in Data.Monoid

Methods

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

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

Eq a => Eq (Last a)

Since: base-2.1

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

Defined in Data.Semigroup

Eq a => Eq (Dual a)

Since: base-2.1

Instance details

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

Instance details

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

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq (TVar a)

Since: base-4.8.0.0

Instance details

Defined in GHC.Conc.Sync

Methods

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

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

Eq (ForeignPtr a)

Since: base-2.1

Instance details

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

Instance details

Defined in GHC.Generics

Methods

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

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

Eq (FunPtr a) 
Instance details

Defined in GHC.Ptr

Methods

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

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

Eq (Ptr a)

Since: base-2.1

Instance details

Defined in GHC.Ptr

Methods

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

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

Eq a => Eq (Ratio a)

Since: base-2.1

Instance details

Defined in GHC.Real

Methods

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

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

Eq a => Eq (IntMap a) 
Instance details

Defined in Data.IntMap.Internal

Methods

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

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

Eq a => Eq (Seq a) 
Instance details

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (ViewL a) 
Instance details

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (ViewR a) 
Instance details

Defined in Data.Sequence.Internal

Methods

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

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

Eq a => Eq (Set a) 
Instance details

Defined in Data.Set.Internal

Methods

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

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

Eq a => Eq (Tree a) 
Instance details

Defined in Data.Tree

Methods

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

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

Eq (MutableByteArray s) 
Instance details

Defined in Data.Array.Byte

Eq a => Eq (Hashed a)

Uses precomputed hash to detect inequality faster

Instance details

Defined in Data.Hashable.Class

Methods

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

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

Eq a => Eq (AnnotDetails a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Eq (Doc a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq a => Eq (Span a) 
Instance details

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

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

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

Eq a => Eq (Array a) 
Instance details

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

Instance details

Defined in Data.Primitive.PrimArray

Methods

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

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

Eq a => Eq (SmallArray a) 
Instance details

Defined in Data.Primitive.SmallArray

Methods

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

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

Eq g => Eq (StateGen g) 
Instance details

Defined in System.Random.Internal

Methods

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

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

Eq flag => Eq (TyVarBndr flag) 
Instance details

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. substitutivity 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 substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals.

Instance details

Defined in Data.HashSet.Internal

Methods

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

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

Eq a => Eq (Vector a) 
Instance details

Defined in Data.Vector

Methods

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

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

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

Defined in Data.Vector.Primitive

Methods

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

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

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

Defined in Data.Vector.Storable

Methods

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

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

Eq a => Eq (NonEmpty a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

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

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

Eq a => Eq (Maybe a)

Since: base-2.1

Instance details

Defined in GHC.Maybe

Methods

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

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

Eq a => Eq (a) 
Instance details

Defined in GHC.Classes

Methods

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

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

Eq a => Eq [a] 
Instance details

Defined in GHC.Classes

Methods

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

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

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

Since: base-2.1

Instance details

Defined in Data.Either

Methods

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

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

Eq (Proxy s)

Since: base-4.7.0.0

Instance details

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

Instance details

Defined in Data.Semigroup

Methods

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

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

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

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

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

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

Eq (U1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

Eq (V1 p)

Since: base-4.9.0.0

Instance details

Defined in GHC.Generics

Methods

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

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

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

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) 
Instance details

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) 
Instance details

Defined in Control.Monad.Free

Methods

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

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

Eq (MutableArray s a) 
Instance details

Defined in Data.Primitive.Array

Methods

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

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

Eq (MutablePrimArray s a) 
Instance details

Defined in Data.Primitive.PrimArray

Eq (SmallMutableArray s a) 
Instance details

Defined in Data.Primitive.SmallArray

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

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) 
Instance details

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) 
Instance details

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 (ListT m a) 
Instance details

Defined in Control.Monad.Trans.List

Methods

(==) :: ListT m a -> ListT m a -> Bool #

(/=) :: ListT m a -> ListT m a -> Bool #

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

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. substitutivity 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 substitutivity can be observed with any function that depends on the key ordering, such as folds and traversals.

Instance details

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) 
Instance details

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) 
Instance details

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

Instance details

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

Instance details

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

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Eq (OrderingI a b) 
Instance details

Defined in Data.Type.Ord

Methods

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

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

Eq (STArray s i e)

Since: base-2.1

Instance details

Defined in GHC.Arr

Methods

(==) :: STArray s i e -> STArray s i e -> Bool #

(/=) :: STArray s i e -> STArray s i e -> Bool #

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

Since: base-4.7.0.0

Instance details

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

Instance details

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

Instance details

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

Instance details

Defined in GHC.Generics

Methods

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

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

Eq (URec Float p) 
Instance details

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

Instance details

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

Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) 
Instance details

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) 
Instance details

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 (ErrorT e m a) 
Instance details

Defined in Control.Monad.Trans.Error

Methods

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

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

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

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

Defined in GHC.Classes

Methods

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

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

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

Since: base-4.9.0.0

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

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) 
Instance details

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 (Compose f g a)

Since: base-4.9.0.0

Instance details

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

Instance details

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

Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

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) 
Instance details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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 details

Defined in GHC.Classes

Methods

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

(/=) :: (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)

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

Instances details
Num IntPtr 
Instance details

Defined in Foreign.Ptr

Num WordPtr 
Instance details

Defined in Foreign.Ptr

Num Int16

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int32

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int64

Since: base-2.1

Instance details

Defined in GHC.Int

Num Int8

Since: base-2.1

Instance details

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

Instance details

Defined in GHC.Word

Num Word32

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word64

Since: base-2.1

Instance details

Defined in GHC.Word

Num Word8

Since: base-2.1

Instance details

Defined in GHC.Word

Num Integer

Since: base-2.1

Instance details

Defined in GHC.Num

Num Natural

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

Since: base-4.8.0.0

Instance details

Defined in GHC.Num

Num Int

Since: base-2.1

Instance details

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

Instance details

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

Instance details

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

Instance details

Defined in Data.Functor.Identity

Num a => Num (Down a)

Since: base-4.11.0.0

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

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

Instance details

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) 
Instance details

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) 
Instance details

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

Instance details

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

Instance details

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

Instance details

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) 
Instance details

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) 
Instance details

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 Source #

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

fromLabel :: IsLabel x a => a #

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