Relude.Monoid

Reexports functions to work with monoids plus adds extra useful functions.

Reexports

newtype Any

Boolean monoid under disjunction (||).

Any x <> Any y = Any (x || y)

Examples

>>> Any True <> mempty <> Any False
Any {getAny = True}

>>> mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
Any {getAny = True}

>>> Any False <> mempty
Any {getAny = False}

Constructors

Any

Fields

• getAny :: Bool

Instances

NFData Any

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Any -> ()

Monoid Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Semigroup Any

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Data Any

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any

toConstr :: Any -> Constr

dataTypeOf :: Any -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any)

gmapT :: (forall b. Data b => b -> b) -> Any -> Any

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any

Bounded Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Generic Any

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep Any

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Read Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Eq Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering

(<) :: Any -> Any -> Bool

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

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

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

max :: Any -> Any -> Any

min :: Any -> Any -> Any

type Rep Any

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep Any = D1 ('MetaData "Any" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Last a

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

Data.Semigroup.Last. The former returns the last non-Nothing, so x <> Data.Monoid.Last Nothing = x. The latter simply returns the last value, thus x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing.

Examples

>>> Last (Just "hello") <> Last Nothing <> Last (Just "world")
Last {getLast = Just "world"}

>>> Last Nothing <> mempty
Last {getLast = Nothing}

Constructors

Last

Fields

• getLast :: Maybe a

Instances

MonadZip Last

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Last a -> Last b -> Last (a, b)

mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c

munzip :: Last (a, b) -> (Last a, Last b)

NFData1 Last

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Last a -> ()

Applicative Last

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Last a

(<*>) :: Last (a -> b) -> Last a -> Last b

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c

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

(<*) :: Last a -> Last b -> Last a

Functor Last

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Monad Last

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

Foldable Last

@since base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Last a -> m

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

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

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

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

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

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

toList :: Last a -> [a]

null :: Last a -> Bool

length :: Last a -> Int

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

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

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

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

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

Traversable Last

@since base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b)

sequenceA :: Applicative f => Last (f a) -> f (Last a)

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b)

sequence :: Monad m => Last (m a) -> m (Last a)

Generic1 Last

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 Last

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 Last = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

Methods

from1 :: Last a -> Rep1 Last a

to1 :: Rep1 Last a -> Last a

NFData a => NFData (Last a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Last a -> ()

Monoid (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Semigroup (Last a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Data a => Data (Last a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a)

toConstr :: Last a -> Constr

dataTypeOf :: Last a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a))

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

Generic (Last a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Last a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Last a) = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

Methods

from :: Last a -> Rep (Last a) x

to :: Rep (Last a) x -> Last a

Read a => Read (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [Last a]

Show a => Show (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Eq a => Eq (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord a => Ord (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering

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

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

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

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

max :: Last a -> Last a -> Last a

min :: Last a -> Last a -> Last a

type Rep1 Last

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 Last = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

type Rep (Last a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Last a) = D1 ('MetaData "Last" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

newtype First a

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic to Alt Maybe a, but precedes it historically.

Beware that Data.Monoid.First is different from Data.Semigroup.First. The former returns the first non-Nothing, so Data.Monoid.First Nothing <> x = x. The latter simply returns the first value, thus Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing.

Examples

>>> First (Just "hello") <> First Nothing <> First (Just "world")
First {getFirst = Just "hello"}

>>> First Nothing <> mempty
First {getFirst = Nothing}

Constructors

First

Fields

• getFirst :: Maybe a

Instances

MonadZip First

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: First a -> First b -> First (a, b)

mzipWith :: (a -> b -> c) -> First a -> First b -> First c

munzip :: First (a, b) -> (First a, First b)

NFData1 First

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> First a -> ()

Applicative First

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> First a

(<*>) :: First (a -> b) -> First a -> First b

liftA2 :: (a -> b -> c) -> First a -> First b -> First c

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

(<*) :: First a -> First b -> First a

Functor First

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Monad First

@since base-4.8.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

(>>) :: First a -> First b -> First b

return :: a -> First a

Foldable First

@since base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> First a -> m

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

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

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

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

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

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

toList :: First a -> [a]

null :: First a -> Bool

length :: First a -> Int

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

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

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

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

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

Traversable First

@since base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b)

sequenceA :: Applicative f => First (f a) -> f (First a)

mapM :: Monad m => (a -> m b) -> First a -> m (First b)

sequence :: Monad m => First (m a) -> m (First a)

Generic1 First

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 First

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 First = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

Methods

from1 :: First a -> Rep1 First a

to1 :: Rep1 First a -> First a

NFData a => NFData (First a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: First a -> ()

Monoid (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Semigroup (First a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Data a => Data (First a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a)

toConstr :: First a -> Constr

dataTypeOf :: First a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a))

gmapT :: (forall b. Data b => b -> b) -> First a -> First a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

Generic (First a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (First a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (First a) = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

Methods

from :: First a -> Rep (First a) x

to :: Rep (First a) x -> First a

Read a => Read (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [First a]

Show a => Show (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Eq a => Eq (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord a => Ord (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

compare :: First a -> First a -> Ordering

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

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

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

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

max :: First a -> First a -> First a

min :: First a -> First a -> First a

type Rep1 First

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 First = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

type Rep (First a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (First a) = D1 ('MetaData "First" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a))))

class Semigroup a => Monoid a where

The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:

Right identity

x <> mempty = x

Left identity

mempty <> x = x

Associativity

x <> (y <> z) = (x <> y) <> z (Semigroup law)

Concatenation

mconcat = foldr (<>) mempty

You can alternatively define mconcat instead of mempty, in which case the laws are:

Unit

mconcat (pure x) = x

Multiplication

mconcat (join xss) = mconcat (fmap mconcat xss)

Subclass

mconcat (toList xs) = sconcat xs

The method names refer to the monoid of lists under concatenation, but there are many other instances.

Some types can be viewed as a monoid in more than one way, e.g. both addition and multiplication on numbers. In such cases we often define newtypes and make those instances of Monoid, e.g. Sum and Product.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty | mconcat

Methods

mempty :: a

Identity of mappend

Examples

>>> "Hello world" <> mempty
"Hello world"

>>> mempty <> [1, 2, 3]
[1,2,3]

mappend :: a -> a -> a

An associative operation

NOTE: This method is redundant and has the default implementation mappend = (<>) since base-4.11.0.0. Should it be implemented manually, since mappend is a synonym for (<>), it is expected that the two functions are defined the same way. In a future GHC release mappend will be removed from Monoid.

mconcat :: [a] -> a

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

>>> mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"

Instances

Monoid ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

mempty :: ByteArray

mappend :: ByteArray -> ByteArray -> ByteArray

mconcat :: [ByteArray] -> ByteArray

Monoid Builder

Defined in Data.ByteString.Builder.Internal

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid ByteString

Defined in Data.ByteString.Internal.Type

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

mempty :: ShortByteString

mappend :: ShortByteString -> ShortByteString -> ShortByteString

mconcat :: [ShortByteString] -> ShortByteString

Monoid IntSet

Defined in Data.IntSet.Internal

Methods

mempty :: IntSet

mappend :: IntSet -> IntSet -> IntSet

mconcat :: [IntSet] -> IntSet

Monoid All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid Ordering

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid OsString

"String-Concatenation" for OsString. This is not the same as (</>).

Defined in System.OsString.Internal.Types

Methods

mempty :: OsString

mappend :: OsString -> OsString -> OsString

mconcat :: [OsString] -> OsString

Monoid PosixString

Defined in System.OsString.Internal.Types

Methods

mempty :: PosixString

mappend :: PosixString -> PosixString -> PosixString

mconcat :: [PosixString] -> PosixString

Monoid WindowsString

Defined in System.OsString.Internal.Types

Methods

mempty :: WindowsString

mappend :: WindowsString -> WindowsString -> WindowsString

mconcat :: [WindowsString] -> WindowsString

Monoid Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

mempty :: Doc

mappend :: Doc -> Doc -> Doc

mconcat :: [Doc] -> Doc

Monoid Builder

Defined in Data.Text.Internal.Builder

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid StrictBuilder

Defined in Data.Text.Internal.StrictBuilder

Methods

mempty :: StrictBuilder

mappend :: StrictBuilder -> StrictBuilder -> StrictBuilder

mconcat :: [StrictBuilder] -> StrictBuilder

Monoid ()

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: ()

mappend :: () -> () -> ()

mconcat :: [()] -> ()

Monoid (Comparison a)

mempty on comparisons always returns EQ. Without newtypes this equals pure (pure EQ).

mempty :: Comparison a
mempty = Comparison _ _ -> EQ

Defined in Data.Functor.Contravariant

Methods

mempty :: Comparison a

mappend :: Comparison a -> Comparison a -> Comparison a

mconcat :: [Comparison a] -> Comparison a

Monoid (Equivalence a)

mempty on equivalences always returns True. Without newtypes this equals pure (pure True).

mempty :: Equivalence a
mempty = Equivalence _ _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Equivalence a

mappend :: Equivalence a -> Equivalence a -> Equivalence a

mconcat :: [Equivalence a] -> Equivalence a

Monoid (Predicate a)

mempty on predicates always returns True. Without newtypes this equals pure True.

mempty :: Predicate a
mempty = _ -> True

Defined in Data.Functor.Contravariant

Methods

mempty :: Predicate a

mappend :: Predicate a -> Predicate a -> Predicate a

mconcat :: [Predicate a] -> Predicate a

(Ord a, Bounded a) => Monoid (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Monoid (IntMap a)

Defined in Data.IntMap.Internal

Methods

mempty :: IntMap a

mappend :: IntMap a -> IntMap a -> IntMap a

mconcat :: [IntMap a] -> IntMap a

Monoid (Seq a)

Defined in Data.Sequence.Internal

Methods

mempty :: Seq a

mappend :: Seq a -> Seq a -> Seq a

mconcat :: [Seq a] -> Seq a

Monoid (MergeSet a)

Defined in Data.Set.Internal

Methods

mempty :: MergeSet a

mappend :: MergeSet a -> MergeSet a -> MergeSet a

mconcat :: [MergeSet a] -> MergeSet a

Ord a => Monoid (Set a)

Defined in Data.Set.Internal

Methods

mempty :: Set a

mappend :: Set a -> Set a -> Set a

mconcat :: [Set a] -> Set a

Monoid a => Monoid (STM a)

@since base-4.17.0.0

Defined in GHC.Internal.Conc.Sync

Methods

mempty :: STM a

mappend :: STM a -> STM a -> STM a

mconcat :: [STM a] -> STM a

Monoid a => Monoid (Identity a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Identity

Methods

mempty :: Identity a

mappend :: Identity a -> Identity a -> Identity a

mconcat :: [Identity a] -> Identity a

Monoid (First a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: First a

mappend :: First a -> First a -> First a

mconcat :: [First a] -> First a

Monoid (Last a)

@since base-2.01

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Last a

mappend :: Last a -> Last a -> Last a

mconcat :: [Last a] -> Last a

Monoid a => Monoid (Down a)

@since base-4.11.0.0

Defined in GHC.Internal.Data.Ord

Methods

mempty :: Down a

mappend :: Down a -> Down a -> Down a

mconcat :: [Down a] -> Down a

Monoid a => Monoid (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Monoid (Endo a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Num a => Monoid (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Monoid (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

(Generic a, Monoid (Rep a ())) => Monoid (Generically a)

@since base-4.17.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Generically a

mappend :: Generically a -> Generically a -> Generically a

mconcat :: [Generically a] -> Generically a

Monoid p => Monoid (Par1 p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Par1 p

mappend :: Par1 p -> Par1 p -> Par1 p

mconcat :: [Par1 p] -> Par1 p

Monoid a => Monoid (IO a)

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

mempty :: IO a

mappend :: IO a -> IO a -> IO a

mconcat :: [IO a] -> IO a

Monoid (Validity k)

Defined in Data.HashMap.Internal.Debug

Methods

mempty :: Validity k

mappend :: Validity k -> Validity k -> Validity k

mconcat :: [Validity k] -> Validity k

(Hashable a, Eq a) => Monoid (HashSet a)

mempty = empty

mappend = union

\(O(n+m)\)

To obtain good performance, the smaller set must be presented as the first argument.

Examples

>>> mappend (fromList [1,2]) (fromList [2,3])
fromList [1,2,3]

Defined in Data.HashSet.Internal

Methods

mempty :: HashSet a

mappend :: HashSet a -> HashSet a -> HashSet a

mconcat :: [HashSet a] -> HashSet a

Monoid (Doc a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

mempty :: Doc a

mappend :: Doc a -> Doc a -> Doc a

mconcat :: [Doc a] -> Doc a

Monoid a => Monoid (Q a)

Since: template-haskell-2.17.0.0

Defined in Language.Haskell.TH.Syntax

Methods

mempty :: Q a

mappend :: Q a -> Q a -> Q a

mconcat :: [Q a] -> Q a

Semigroup a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S."

Since 4.11.0: constraint on inner a value generalised from Monoid to Semigroup.

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: Maybe a

mappend :: Maybe a -> Maybe a -> Maybe a

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (Solo a)

@since base-4.15

Defined in GHC.Internal.Base

Methods

mempty :: Solo a

mappend :: Solo a -> Solo a -> Solo a

mconcat :: [Solo a] -> Solo a

Monoid [a]

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: [a]

mappend :: [a] -> [a] -> [a]

mconcat :: [[a]] -> [a]

Monoid a => Monoid (Op a b)

mempty @(Op a b) without newtypes is mempty @(b->a) = _ -> mempty.

mempty :: Op a b
mempty = Op _ -> mempty

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b

mappend :: Op a b -> Op a b -> Op a b

mconcat :: [Op a b] -> Op a b

Ord k => Monoid (Map k v)

Defined in Data.Map.Internal

Methods

mempty :: Map k v

mappend :: Map k v -> Map k v -> Map k v

mconcat :: [Map k v] -> Map k v

Monoid (Proxy s)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Proxy

Methods

mempty :: Proxy s

mappend :: Proxy s -> Proxy s -> Proxy s

mconcat :: [Proxy s] -> Proxy s

Monoid (U1 p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: U1 p

mappend :: U1 p -> U1 p -> U1 p

mconcat :: [U1 p] -> U1 p

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

mempty = empty

mappend = union

If a key occurs in both maps, the mapping from the first will be the mapping in the result.

Examples

>>> mappend (fromList [(1,'a'),(2,'b')]) (fromList [(2,'c'),(3,'d')])
fromList [(1,'a'),(2,'b'),(3,'d')]

Defined in Data.HashMap.Internal

Methods

mempty :: HashMap k v

mappend :: HashMap k v -> HashMap k v -> HashMap k v

mconcat :: [HashMap k v] -> HashMap k v

(Monoid a, Monoid b) => Monoid (a, b)

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: (a, b)

mappend :: (a, b) -> (a, b) -> (a, b)

mconcat :: [(a, b)] -> (a, b)

Monoid b => Monoid (a -> b)

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: a -> b

mappend :: (a -> b) -> (a -> b) -> a -> b

mconcat :: [a -> b] -> a -> b

Monoid a => Monoid (Const a b)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Const

Methods

mempty :: Const a b

mappend :: Const a b -> Const a b -> Const a b

mconcat :: [Const a b] -> Const a b

(Applicative f, Monoid a) => Monoid (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

mconcat :: [Ap f a] -> Ap f a

Alternative f => Monoid (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a

mappend :: Alt f a -> Alt f a -> Alt f a

mconcat :: [Alt f a] -> Alt f a

Monoid (f p) => Monoid (Rec1 f p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: Rec1 f p

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p

mconcat :: [Rec1 f p] -> Rec1 f p

Monoid a => Monoid (Constant a b)

Defined in Data.Functor.Constant

Methods

mempty :: Constant a b

mappend :: Constant a b -> Constant a b -> Constant a b

mconcat :: [Constant a b] -> Constant a b

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

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c)

mappend :: (a, b, c) -> (a, b, c) -> (a, b, c)

mconcat :: [(a, b, c)] -> (a, b, c)

(Monoid (f a), Monoid (g a)) => Monoid (Product f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Product

Methods

mempty :: Product f g a

mappend :: Product f g a -> Product f g a -> Product f g a

mconcat :: [Product f g a] -> Product f g a

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: (f :*: g) p

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

mconcat :: [(f :*: g) p] -> (f :*: g) p

Monoid c => Monoid (K1 i c p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: K1 i c p

mappend :: K1 i c p -> K1 i c p -> K1 i c p

mconcat :: [K1 i c p] -> K1 i c p

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

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d)

mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

mconcat :: [(a, b, c, d)] -> (a, b, c, d)

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

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a

mappend :: Compose f g a -> Compose f g a -> Compose f g a

mconcat :: [Compose f g a] -> Compose f g a

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: (f :.: g) p

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

mconcat :: [(f :.: g) p] -> (f :.: g) p

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

mempty :: M1 i c f p

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p

mconcat :: [M1 i c f p] -> M1 i c f p

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

@since base-2.01

Defined in GHC.Internal.Base

Methods

mempty :: (a, b, c, d, e)

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e)

mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e)

newtype Alt (f :: k -> Type) (a :: k)

Monoid under <|>.

Alt l <> Alt r == Alt (l <|> r)

Examples

>>> Alt (Just 12) <> Alt (Just 24)
Alt {getAlt = Just 12}

>>> Alt Nothing <> Alt (Just 24)
Alt {getAlt = Just 24}

@since base-4.8.0.0

Constructors

Alt

Fields

• getAlt :: f a

Instances

Generic1 (Alt f :: k -> Type)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 (Alt f :: k -> Type)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: forall (a :: k). Alt f a -> Rep1 (Alt f) a

to1 :: forall (a :: k). Rep1 (Alt f) a -> Alt f a

MonadZip f => MonadZip (Alt f)

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Alt f a -> Alt f b -> Alt f (a, b)

mzipWith :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c

munzip :: Alt f (a, b) -> (Alt f a, Alt f b)

Foldable1 f => Foldable1 (Alt f)

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Alt f m -> m

foldMap1 :: Semigroup m => (a -> m) -> Alt f a -> m

foldMap1' :: Semigroup m => (a -> m) -> Alt f a -> m

toNonEmpty :: Alt f a -> NonEmpty a

maximum :: Ord a => Alt f a -> a

minimum :: Ord a => Alt f a -> a

head :: Alt f a -> a

last :: Alt f a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Alt f a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Alt f a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Alt f a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Alt f a -> b

Contravariant f => Contravariant (Alt f)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Alt f a -> Alt f a'

(>$) :: b -> Alt f b -> Alt f a

Alternative f => Alternative (Alt f)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

empty :: Alt f a

(<|>) :: Alt f a -> Alt f a -> Alt f a

some :: Alt f a -> Alt f [a]

many :: Alt f a -> Alt f [a]

Applicative f => Applicative (Alt f)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Alt f a

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c

(*>) :: Alt f a -> Alt f b -> Alt f b

(<*) :: Alt f a -> Alt f b -> Alt f a

Functor f => Functor (Alt f)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Alt f a -> Alt f b

(<$) :: a -> Alt f b -> Alt f a

Monad f => Monad (Alt f)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(>>) :: Alt f a -> Alt f b -> Alt f b

return :: a -> Alt f a

MonadPlus f => MonadPlus (Alt f)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mzero :: Alt f a

mplus :: Alt f a -> Alt f a -> Alt f a

Foldable f => Foldable (Alt f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m

foldMap :: Monoid m => (a -> m) -> Alt f a -> m

foldMap' :: Monoid m => (a -> m) -> Alt f a -> m

foldr :: (a -> b -> b) -> b -> Alt f a -> b

foldr' :: (a -> b -> b) -> b -> Alt f a -> b

foldl :: (b -> a -> b) -> b -> Alt f a -> b

foldl' :: (b -> a -> b) -> b -> Alt f a -> b

foldr1 :: (a -> a -> a) -> Alt f a -> a

foldl1 :: (a -> a -> a) -> Alt f a -> a

toList :: Alt f a -> [a]

null :: Alt f a -> Bool

length :: Alt f a -> Int

elem :: Eq a => a -> Alt f a -> Bool

maximum :: Ord a => Alt f a -> a

minimum :: Ord a => Alt f a -> a

sum :: Num a => Alt f a -> a

product :: Num a => Alt f a -> a

Traversable f => Traversable (Alt f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b)

sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a)

mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b)

sequence :: Monad m => Alt f (m a) -> m (Alt f a)

Alternative f => Monoid (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Alt f a

mappend :: Alt f a -> Alt f a -> Alt f a

mconcat :: [Alt f a] -> Alt f a

Alternative f => Semigroup (Alt f a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a

sconcat :: NonEmpty (Alt f a) -> Alt f a

stimes :: Integral b => b -> Alt f a -> Alt f a

(Data (f a), Data a, Typeable f) => Data (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a)

toConstr :: Alt f a -> Constr

dataTypeOf :: Alt f a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a))

gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r

gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a)

Enum (f a) => Enum (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a

pred :: Alt f a -> Alt f a

toEnum :: Int -> Alt f a

fromEnum :: Alt f a -> Int

enumFrom :: Alt f a -> [Alt f a]

enumFromThen :: Alt f a -> Alt f a -> [Alt f a]

enumFromTo :: Alt f a -> Alt f a -> [Alt f a]

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a]

Generic (Alt f a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Alt f a) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Alt f a -> Rep (Alt f a) x

to :: Rep (Alt f a) x -> Alt f a

Num (f a) => Num (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.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

Read (f a) => Read (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Alt f a)

readList :: ReadS [Alt f a]

readPrec :: ReadPrec (Alt f a)

readListPrec :: ReadPrec [Alt f a]

Show (f a) => Show (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Alt f a -> ShowS

show :: Alt f a -> String

showList :: [Alt f a] -> ShowS

Eq (f a) => Eq (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord (f a) => Ord (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Alt f a -> Alt f a -> Ordering

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

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

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

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

max :: Alt f a -> Alt f a -> Alt f a

min :: Alt f a -> Alt f a -> Alt f a

type Rep1 (Alt f :: k -> Type)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 (Alt f :: k -> Type) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

type Rep (Alt f a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Alt f a) = D1 ('MetaData "Alt" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Alt" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAlt") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

newtype Product a

Monoid under multiplication.

Product x <> Product y == Product (x * y)

Examples

>>> Product 3 <> Product 4 <> mempty
Product {getProduct = 12}

>>> mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}

Constructors

Product

Fields

• getProduct :: a

Instances

MonadZip Product

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Product a -> Product b -> Product (a, b)

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c

munzip :: Product (a, b) -> (Product a, Product b)

Foldable1 Product

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Product m -> m

foldMap1 :: Semigroup m => (a -> m) -> Product a -> m

foldMap1' :: Semigroup m => (a -> m) -> Product a -> m

toNonEmpty :: Product a -> NonEmpty a

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

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

head :: Product a -> a

last :: Product a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b

NFData1 Product

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Product a -> ()

Applicative Product

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Product a

(<*>) :: Product (a -> b) -> Product a -> Product b

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c

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

(<*) :: Product a -> Product b -> Product a

Functor Product

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Monad Product

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

Foldable Product

@since base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Product a -> m

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

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

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

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

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

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

toList :: Product a -> [a]

null :: Product a -> Bool

length :: Product a -> Int

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

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

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

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

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

Traversable Product

@since base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b)

sequenceA :: Applicative f => Product (f a) -> f (Product a)

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b)

sequence :: Monad m => Product (m a) -> m (Product a)

Generic1 Product

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Product

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Product a -> Rep1 Product a

to1 :: Rep1 Product a -> Product a

NFData a => NFData (Product a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

Num a => Monoid (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Semigroup (Product a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Data a => Data (Product a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a)

toConstr :: Product a -> Constr

dataTypeOf :: Product a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a))

gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r

gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a)

Bounded a => Bounded (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Generic (Product a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Product a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Num (Product a)

@since base-4.7.0.0

Defined in GHC.Internal.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

Read a => Read (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Eq a => Eq (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering

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

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

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

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

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

type Rep1 Product

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Product = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Product a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Product a) = D1 ('MetaData "Product" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Sum a

Monoid under addition.

Sum a <> Sum b = Sum (a + b)

Examples

>>> Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}

>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}

Constructors

Sum

Fields

• getSum :: a

Instances

MonadZip Sum

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Sum a -> Sum b -> Sum (a, b)

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

munzip :: Sum (a, b) -> (Sum a, Sum b)

Foldable1 Sum

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Sum m -> m

foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m

foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m

toNonEmpty :: Sum a -> NonEmpty a

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

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

head :: Sum a -> a

last :: Sum a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b

NFData1 Sum

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Sum a -> ()

Applicative Sum

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Sum a

(<*>) :: Sum (a -> b) -> Sum a -> Sum b

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

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

(<*) :: Sum a -> Sum b -> Sum a

Functor Sum

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Monad Sum

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

Foldable Sum

@since base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Sum a -> m

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

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

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

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

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

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

toList :: Sum a -> [a]

null :: Sum a -> Bool

length :: Sum a -> Int

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

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

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

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

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

Traversable Sum

@since base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b)

sequenceA :: Applicative f => Sum (f a) -> f (Sum a)

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b)

sequence :: Monad m => Sum (m a) -> m (Sum a)

Generic1 Sum

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Sum

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Sum a -> Rep1 Sum a

to1 :: Rep1 Sum a -> Sum a

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Num a => Monoid (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Num a => Semigroup (Sum a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Data a => Data (Sum a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a)

toConstr :: Sum a -> Constr

dataTypeOf :: Sum a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a))

gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r

gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a)

Bounded a => Bounded (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Generic (Sum a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Sum a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Num a => Num (Sum a)

@since base-4.7.0.0

Defined in GHC.Internal.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

Read a => Read (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Eq a => Eq (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering

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

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

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

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

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

type Rep1 Sum

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Sum = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Sum a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Sum a) = D1 ('MetaData "Sum" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype All

Boolean monoid under conjunction (&&).

All x <> All y = All (x && y)

Examples

>>> All True <> mempty <> All False)
All {getAll = False}

>>> mconcat (map (\x -> All (even x)) [2,4,6,7,8])
All {getAll = False}

>>> All True <> mempty
All {getAll = True}

Constructors

All

Fields

• getAll :: Bool

Instances

NFData All

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: All -> ()

Monoid All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Semigroup All

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Data All

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All

toConstr :: All -> Constr

dataTypeOf :: All -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All)

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All)

gmapT :: (forall b. Data b => b -> b) -> All -> All

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r

gmapQ :: (forall d. Data d => d -> u) -> All -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All

Bounded All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Generic All

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep All

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Read All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Eq All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord All

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering

(<) :: All -> All -> Bool

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

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

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

max :: All -> All -> All

min :: All -> All -> All

type Rep All

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep All = D1 ('MetaData "All" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Endo a

The monoid of endomorphisms under composition.

Endo f <> Endo g == Endo (f . g)

Examples

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

>>> let computation = Endo (*3) <> Endo (+1)
>>> appEndo computation 1
6

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Monoid (Endo a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Semigroup (Endo a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Generic (Endo a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Endo a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

Methods

from :: Endo a -> Rep (Endo a) x

to :: Rep (Endo a) x -> Endo a

type Rep (Endo a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Endo a) = D1 ('MetaData "Endo" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype Dual a

The dual of a Monoid, obtained by swapping the arguments of (<>).

Dual a <> Dual b == Dual (b <> a)

Examples

>>> Dual "Hello" <> Dual "World"
Dual {getDual = "WorldHello"}

>>> Dual (Dual "Hello") <> Dual (Dual "World")
Dual {getDual = Dual {getDual = "HelloWorld"}}

Constructors

Dual

Fields

• getDual :: a

Instances

MonadZip Dual

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: Dual a -> Dual b -> Dual (a, b)

mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

munzip :: Dual (a, b) -> (Dual a, Dual b)

Foldable1 Dual

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Dual m -> m

foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m

foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m

toNonEmpty :: Dual a -> NonEmpty a

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

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

head :: Dual a -> a

last :: Dual a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b

NFData1 Dual

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Dual a -> ()

Applicative Dual

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Dual a

(<*>) :: Dual (a -> b) -> Dual a -> Dual b

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

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

(<*) :: Dual a -> Dual b -> Dual a

Functor Dual

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Monad Dual

@since base-4.8.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

(>>) :: Dual a -> Dual b -> Dual b

return :: a -> Dual a

Foldable Dual

@since base-4.8.0.0

Defined in GHC.Internal.Data.Foldable

Methods

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

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

foldMap' :: Monoid m => (a -> m) -> Dual a -> m

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

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

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

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

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

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

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

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

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

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

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

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

Traversable Dual

@since base-4.8.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b)

sequenceA :: Applicative f => Dual (f a) -> f (Dual a)

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b)

sequence :: Monad m => Dual (m a) -> m (Dual a)

Generic1 Dual

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep1 Dual

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: Dual a -> Rep1 Dual a

to1 :: Rep1 Dual a -> Dual a

NFData a => NFData (Dual a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Dual a -> ()

Monoid a => Monoid (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Semigroup a => Semigroup (Dual a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Data a => Data (Dual a)

@since base-4.8.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a)

toConstr :: Dual a -> Constr

dataTypeOf :: Dual a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a))

gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r

gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a)

Bounded a => Bounded (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

minBound :: Dual a

maxBound :: Dual a

Generic (Dual a)

Defined in GHC.Internal.Data.Semigroup.Internal

Associated Types

type Rep (Dual a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Dual a -> Rep (Dual a) x

to :: Rep (Dual a) x -> Dual a

Read a => Read (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Dual a)

readList :: ReadS [Dual a]

readPrec :: ReadPrec (Dual a)

readListPrec :: ReadPrec [Dual a]

Show a => Show (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

Eq a => Eq (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Dual a)

@since base-2.01

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering

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

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

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

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

max :: Dual a -> Dual a -> Dual a

min :: Dual a -> Dual a -> Dual a

type Rep1 Dual

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep1 Dual = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Dual a)

@since base-4.7.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

type Rep (Dual a) = D1 ('MetaData "Dual" "GHC.Internal.Data.Semigroup.Internal" "ghc-internal" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Ap (f :: k -> Type) (a :: k)

This data type witnesses the lifting of a Monoid into an Applicative pointwise.

Examples

>>> Ap (Just [1, 2, 3]) <> Ap Nothing
Ap {getAp = Nothing}

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

@since base-4.12.0.0

Constructors

Ap

Fields

• getAp :: f a

Instances

Generic1 (Ap f :: k -> Type)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 (Ap f :: k -> Type)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: forall (a :: k). Ap f a -> Rep1 (Ap f) a

to1 :: forall (a :: k). Rep1 (Ap f) a -> Ap f a

Foldable1 f => Foldable1 (Ap f)

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Ap f m -> m

foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m

foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m

toNonEmpty :: Ap f a -> NonEmpty a

maximum :: Ord a => Ap f a -> a

minimum :: Ord a => Ap f a -> a

head :: Ap f a -> a

last :: Ap f a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b

Alternative f => Alternative (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

empty :: Ap f a

(<|>) :: Ap f a -> Ap f a -> Ap f a

some :: Ap f a -> Ap f [a]

many :: Ap f a -> Ap f [a]

Applicative f => Applicative (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Ap f a

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c

(*>) :: Ap f a -> Ap f b -> Ap f b

(<*) :: Ap f a -> Ap f b -> Ap f a

Functor f => Functor (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b

(<$) :: a -> Ap f b -> Ap f a

Monad f => Monad (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b

(>>) :: Ap f a -> Ap f b -> Ap f b

return :: a -> Ap f a

MonadPlus f => MonadPlus (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> Ap f a -> Ap f a

MonadFail f => MonadFail (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fail :: String -> Ap f a

Foldable f => Foldable (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m

foldMap :: Monoid m => (a -> m) -> Ap f a -> m

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m

foldr :: (a -> b -> b) -> b -> Ap f a -> b

foldr' :: (a -> b -> b) -> b -> Ap f a -> b

foldl :: (b -> a -> b) -> b -> Ap f a -> b

foldl' :: (b -> a -> b) -> b -> Ap f a -> b

foldr1 :: (a -> a -> a) -> Ap f a -> a

foldl1 :: (a -> a -> a) -> Ap f a -> a

toList :: Ap f a -> [a]

null :: Ap f a -> Bool

length :: Ap f a -> Int

elem :: Eq a => a -> Ap f a -> Bool

maximum :: Ord a => Ap f a -> a

minimum :: Ord a => Ap f a -> a

sum :: Num a => Ap f a -> a

product :: Num a => Ap f a -> a

Traversable f => Traversable (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b)

sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a)

mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b)

sequence :: Monad m => Ap f (m a) -> m (Ap f a)

(Applicative f, Monoid a) => Monoid (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

mconcat :: [Ap f a] -> Ap f a

(Applicative f, Semigroup a) => Semigroup (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

(Data (f a), Data a, Typeable f) => Data (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a)

toConstr :: Ap f a -> Constr

dataTypeOf :: Ap f a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a))

gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r

gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

(Applicative f, Bounded a) => Bounded (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

minBound :: Ap f a

maxBound :: Ap f a

Enum (f a) => Enum (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

succ :: Ap f a -> Ap f a

pred :: Ap f a -> Ap f a

toEnum :: Int -> Ap f a

fromEnum :: Ap f a -> Int

enumFrom :: Ap f a -> [Ap f a]

enumFromThen :: Ap f a -> Ap f a -> [Ap f a]

enumFromTo :: Ap f a -> Ap f a -> [Ap f a]

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a]

Generic (Ap f a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Ap f a -> Rep (Ap f a) x

to :: Rep (Ap f a) x -> Ap f a

(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 GHC.Internal.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

Read (f a) => Read (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Ap f a)

readList :: ReadS [Ap f a]

readPrec :: ReadPrec (Ap f a)

readListPrec :: ReadPrec [Ap f a]

Show (f a) => Show (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS

show :: Ap f a -> String

showList :: [Ap f a] -> ShowS

Eq (f a) => Eq (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord (f a) => Ord (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering

(<) :: Ap f a -> Ap f a -> Bool

(<=) :: Ap f a -> Ap f a -> Bool

(>) :: Ap f a -> Ap f a -> Bool

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

max :: Ap f a -> Ap f a -> Ap f a

min :: Ap f a -> Ap f a -> Ap f a

type Rep1 (Ap f :: k -> Type)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

type Rep (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

class Semigroup a where

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity

x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit

sconcat (pure x) = x

Multiplication

sconcat (join xss) = sconcat (fmap sconcat xss)

@since base-4.9.0.0

Minimal complete definition

(<>) | sconcat

Methods

(<>) :: a -> a -> a infixr 6

An associative operation.

Examples

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

>>> Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]

>>> putStr "Hello, " <> putStrLn "World!"
Hello, World!

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

Examples

For the following examples, we will assume that we have:

>>> import Data.List.NonEmpty (NonEmpty (..))

>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

>>> sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]

>>> sconcat $ Left 1 :| [Right 2, Left 3, Right 4]
Right 2

stimes :: Integral b => b -> a -> a

Repeat a value n times.

The default definition will raise an exception for a multiplier that is <= 0. This may be overridden with an implementation that is total. For monoids it is preferred to use stimesMonoid.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

Examples

>>> stimes 4 [1]
[1,1,1,1]

>>> stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!

>>> stimes 3 (Right ":)")
Right ":)"

Instances

Semigroup ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

(<>) :: ByteArray -> ByteArray -> ByteArray

sconcat :: NonEmpty ByteArray -> ByteArray

stimes :: Integral b => b -> ByteArray -> ByteArray

Semigroup Builder

Defined in Data.ByteString.Builder.Internal

Methods

(<>) :: Builder -> Builder -> Builder

sconcat :: NonEmpty Builder -> Builder

stimes :: Integral b => b -> Builder -> Builder

Semigroup ByteString

Defined in Data.ByteString.Internal.Type

Methods

(<>) :: ByteString -> ByteString -> ByteString

sconcat :: NonEmpty ByteString -> ByteString

stimes :: Integral b => b -> ByteString -> ByteString

Semigroup ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

(<>) :: ByteString -> ByteString -> ByteString

sconcat :: NonEmpty ByteString -> ByteString

stimes :: Integral b => b -> ByteString -> ByteString

Semigroup ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

(<>) :: ShortByteString -> ShortByteString -> ShortByteString

sconcat :: NonEmpty ShortByteString -> ShortByteString

stimes :: Integral b => b -> ShortByteString -> ShortByteString

Semigroup IntSet

Since: containers-0.5.7

Defined in Data.IntSet.Internal

Methods

(<>) :: IntSet -> IntSet -> IntSet

sconcat :: NonEmpty IntSet -> IntSet

stimes :: Integral b => b -> IntSet -> IntSet

Semigroup Void

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Semigroup All

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Any

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup Ordering

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup OsString

Defined in System.OsString.Internal.Types

Methods

(<>) :: OsString -> OsString -> OsString

sconcat :: NonEmpty OsString -> OsString

stimes :: Integral b => b -> OsString -> OsString

Semigroup PosixString

Defined in System.OsString.Internal.Types

Methods

(<>) :: PosixString -> PosixString -> PosixString

sconcat :: NonEmpty PosixString -> PosixString

stimes :: Integral b => b -> PosixString -> PosixString

Semigroup WindowsString

Defined in System.OsString.Internal.Types

Methods

(<>) :: WindowsString -> WindowsString -> WindowsString

sconcat :: NonEmpty WindowsString -> WindowsString

stimes :: Integral b => b -> WindowsString -> WindowsString

Semigroup Doc

Defined in Text.PrettyPrint.HughesPJ

Methods

(<>) :: Doc -> Doc -> Doc

sconcat :: NonEmpty Doc -> Doc

stimes :: Integral b => b -> Doc -> Doc

Semigroup Builder

Defined in Data.Text.Internal.Builder

Methods

(<>) :: Builder -> Builder -> Builder

sconcat :: NonEmpty Builder -> Builder

stimes :: Integral b => b -> Builder -> Builder

Semigroup StrictBuilder

Concatenation of StrictBuilder is right-biased: the right builder will be run first. This allows a builder to run tail-recursively when it was accumulated left-to-right.

Defined in Data.Text.Internal.StrictBuilder

Methods

(<>) :: StrictBuilder -> StrictBuilder -> StrictBuilder

sconcat :: NonEmpty StrictBuilder -> StrictBuilder

stimes :: Integral b => b -> StrictBuilder -> StrictBuilder

Semigroup ()

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: () -> () -> ()

sconcat :: NonEmpty () -> ()

stimes :: Integral b => b -> () -> ()

Semigroup (FromMaybe b)

Defined in Data.Foldable1

Methods

(<>) :: FromMaybe b -> FromMaybe b -> FromMaybe b

sconcat :: NonEmpty (FromMaybe b) -> FromMaybe b

stimes :: Integral b0 => b0 -> FromMaybe b -> FromMaybe b

Semigroup a => Semigroup (JoinWith a)

Defined in Data.Foldable1

Methods

(<>) :: JoinWith a -> JoinWith a -> JoinWith a

sconcat :: NonEmpty (JoinWith a) -> JoinWith a

stimes :: Integral b => b -> JoinWith a -> JoinWith a

Semigroup (NonEmptyDList a)

Defined in Data.Foldable1

Methods

(<>) :: NonEmptyDList a -> NonEmptyDList a -> NonEmptyDList a

sconcat :: NonEmpty (NonEmptyDList a) -> NonEmptyDList a

stimes :: Integral b => b -> NonEmptyDList a -> NonEmptyDList a

Semigroup (Comparison a)

(<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).

(<>) :: Comparison a -> Comparison a -> Comparison a
Comparison cmp <> Comparison cmp' = Comparison a a' ->
  cmp a a' <> cmp a a'

Defined in Data.Functor.Contravariant

Methods

(<>) :: Comparison a -> Comparison a -> Comparison a

sconcat :: NonEmpty (Comparison a) -> Comparison a

stimes :: Integral b => b -> Comparison a -> Comparison a

Semigroup (Equivalence a)

(<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).

(<>) :: Equivalence a -> Equivalence a -> Equivalence a
Equivalence equiv <> Equivalence equiv' = Equivalence a b ->
  equiv a b && equiv' a b

Defined in Data.Functor.Contravariant

Methods

(<>) :: Equivalence a -> Equivalence a -> Equivalence a

sconcat :: NonEmpty (Equivalence a) -> Equivalence a

stimes :: Integral b => b -> Equivalence a -> Equivalence a

Semigroup (Predicate a)

(<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).

(<>) :: Predicate a -> Predicate a -> Predicate a
Predicate pred <> Predicate pred' = Predicate a ->
  pred a && pred' a

Defined in Data.Functor.Contravariant

Methods

(<>) :: Predicate a -> Predicate a -> Predicate a

sconcat :: NonEmpty (Predicate a) -> Predicate a

stimes :: Integral b => b -> Predicate a -> Predicate a

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

sconcat :: NonEmpty (Max a) -> Max a

stimes :: Integral b => b -> Max a -> Max a

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

sconcat :: NonEmpty (Min a) -> Min a

stimes :: Integral b => b -> Min a -> Min a

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup (IntMap a)

Since: containers-0.5.7

Defined in Data.IntMap.Internal

Methods

(<>) :: IntMap a -> IntMap a -> IntMap a

sconcat :: NonEmpty (IntMap a) -> IntMap a

stimes :: Integral b => b -> IntMap a -> IntMap a

Semigroup (Seq a)

Since: containers-0.5.7

Defined in Data.Sequence.Internal

Methods

(<>) :: Seq a -> Seq a -> Seq a

sconcat :: NonEmpty (Seq a) -> Seq a

stimes :: Integral b => b -> Seq a -> Seq a

Ord a => Semigroup (Intersection a)

Defined in Data.Set.Internal

Methods

(<>) :: Intersection a -> Intersection a -> Intersection a

sconcat :: NonEmpty (Intersection a) -> Intersection a

stimes :: Integral b => b -> Intersection a -> Intersection a

Semigroup (MergeSet a)

Defined in Data.Set.Internal

Methods

(<>) :: MergeSet a -> MergeSet a -> MergeSet a

sconcat :: NonEmpty (MergeSet a) -> MergeSet a

stimes :: Integral b => b -> MergeSet a -> MergeSet a

Ord a => Semigroup (Set a)

Since: containers-0.5.7

Defined in Data.Set.Internal

Methods

(<>) :: Set a -> Set a -> Set a

sconcat :: NonEmpty (Set a) -> Set a

stimes :: Integral b => b -> Set a -> Set a

Semigroup (NonEmpty a)

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a

stimes :: Integral b => b -> NonEmpty a -> NonEmpty a

Semigroup a => Semigroup (STM a)

@since base-4.17.0.0

Defined in GHC.Internal.Conc.Sync

Methods

(<>) :: STM a -> STM a -> STM a

sconcat :: NonEmpty (STM a) -> STM a

stimes :: Integral b => b -> STM a -> STM a

Semigroup a => Semigroup (Identity a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Identity

Methods

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

sconcat :: NonEmpty (Identity a) -> Identity a

stimes :: Integral b => b -> Identity a -> Identity a

Semigroup (First a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

stimes :: Integral b => b -> First a -> First a

Semigroup (Last a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

stimes :: Integral b => b -> Last a -> Last a

Semigroup a => Semigroup (Down a)

@since base-4.11.0.0

Defined in GHC.Internal.Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a

sconcat :: NonEmpty (Down a) -> Down a

stimes :: Integral b => b -> Down a -> Down a

Semigroup a => Semigroup (Dual a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Dual a -> Dual a -> Dual a

sconcat :: NonEmpty (Dual a) -> Dual a

stimes :: Integral b => b -> Dual a -> Dual a

Semigroup (Endo a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Num a => Semigroup (Product a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Semigroup (Sum a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)

@since base-4.17.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: Generically a -> Generically a -> Generically a

sconcat :: NonEmpty (Generically a) -> Generically a

stimes :: Integral b => b -> Generically a -> Generically a

Semigroup p => Semigroup (Par1 p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p

sconcat :: NonEmpty (Par1 p) -> Par1 p

stimes :: Integral b => b -> Par1 p -> Par1 p

Semigroup a => Semigroup (IO a)

@since base-4.10.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: IO a -> IO a -> IO a

sconcat :: NonEmpty (IO a) -> IO a

stimes :: Integral b => b -> IO a -> IO a

Semigroup (Validity k)

Defined in Data.HashMap.Internal.Debug

Methods

(<>) :: Validity k -> Validity k -> Validity k

sconcat :: NonEmpty (Validity k) -> Validity k

stimes :: Integral b => b -> Validity k -> Validity k

(Hashable a, Eq a) => Semigroup (HashSet a)

<> = union

\(O(n+m)\)

To obtain good performance, the smaller set must be presented as the first argument.

Examples

>>> fromList [1,2] <> fromList [2,3]
fromList [1,2,3]

Defined in Data.HashSet.Internal

Methods

(<>) :: HashSet a -> HashSet a -> HashSet a

sconcat :: NonEmpty (HashSet a) -> HashSet a

stimes :: Integral b => b -> HashSet a -> HashSet a

Semigroup (Doc a)

Defined in Text.PrettyPrint.Annotated.HughesPJ

Methods

(<>) :: Doc a -> Doc a -> Doc a

sconcat :: NonEmpty (Doc a) -> Doc a

stimes :: Integral b => b -> Doc a -> Doc a

Semigroup a => Semigroup (Q a)

Since: template-haskell-2.17.0.0

Defined in Language.Haskell.TH.Syntax

Methods

(<>) :: Q a -> Q a -> Q a

sconcat :: NonEmpty (Q a) -> Q a

stimes :: Integral b => b -> Q a -> Q a

Semigroup a => Semigroup (Maybe a)

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: Maybe a -> Maybe a -> Maybe a

sconcat :: NonEmpty (Maybe a) -> Maybe a

stimes :: Integral b => b -> Maybe a -> Maybe a

Semigroup a => Semigroup (Solo a)

@since base-4.15

Defined in GHC.Internal.Base

Methods

(<>) :: Solo a -> Solo a -> Solo a

sconcat :: NonEmpty (Solo a) -> Solo a

stimes :: Integral b => b -> Solo a -> Solo a

Semigroup [a]

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup a => Semigroup (Op a b)

(<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.

(<>) :: Op a b -> Op a b -> Op a b
Op f <> Op g = Op a -> f a <> g a

Defined in Data.Functor.Contravariant

Methods

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

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

stimes :: Integral b0 => b0 -> Op a b -> Op a b

Ord k => Semigroup (Map k v)

Defined in Data.Map.Internal

Methods

(<>) :: Map k v -> Map k v -> Map k v

sconcat :: NonEmpty (Map k v) -> Map k v

stimes :: Integral b => b -> Map k v -> Map k v

Semigroup (Either a b)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Either

Methods

(<>) :: Either a b -> Either a b -> Either a b

sconcat :: NonEmpty (Either a b) -> Either a b

stimes :: Integral b0 => b0 -> Either a b -> Either a b

Semigroup (Proxy s)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

Semigroup (U1 p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: U1 p -> U1 p -> U1 p

sconcat :: NonEmpty (U1 p) -> U1 p

stimes :: Integral b => b -> U1 p -> U1 p

Semigroup (V1 p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p

sconcat :: NonEmpty (V1 p) -> V1 p

stimes :: Integral b => b -> V1 p -> V1 p

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

<> = union

If a key occurs in both maps, the mapping from the first will be the mapping in the result.

Examples

>>> fromList [(1,'a'),(2,'b')] <> fromList [(2,'c'),(3,'d')]
fromList [(1,'a'),(2,'b'),(3,'d')]

Defined in Data.HashMap.Internal

Methods

(<>) :: HashMap k v -> HashMap k v -> HashMap k v

sconcat :: NonEmpty (HashMap k v) -> HashMap k v

stimes :: Integral b => b -> HashMap k v -> HashMap k v

(Semigroup a, Semigroup b) => Semigroup (a, b)

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b) -> (a, b) -> (a, b)

sconcat :: NonEmpty (a, b) -> (a, b)

stimes :: Integral b0 => b0 -> (a, b) -> (a, b)

Semigroup b => Semigroup (a -> b)

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: (a -> b) -> (a -> b) -> a -> b

sconcat :: NonEmpty (a -> b) -> a -> b

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b

Semigroup a => Semigroup (Const a b)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b

sconcat :: NonEmpty (Const a b) -> Const a b

stimes :: Integral b0 => b0 -> Const a b -> Const a b

(Applicative f, Semigroup a) => Semigroup (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

Alternative f => Semigroup (Alt f a)

@since base-4.9.0.0

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

(<>) :: Alt f a -> Alt f a -> Alt f a

sconcat :: NonEmpty (Alt f a) -> Alt f a

stimes :: Integral b => b -> Alt f a -> Alt f a

Semigroup (f p) => Semigroup (Rec1 f p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p

sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p

stimes :: Integral b => b -> Rec1 f p -> Rec1 f p

Semigroup a => Semigroup (Constant a b)

Defined in Data.Functor.Constant

Methods

(<>) :: Constant a b -> Constant a b -> Constant a b

sconcat :: NonEmpty (Constant a b) -> Constant a b

stimes :: Integral b0 => b0 -> Constant a b -> Constant a b

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

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c)

sconcat :: NonEmpty (a, b, c) -> (a, b, c)

stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c)

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a

sconcat :: NonEmpty (Product f g a) -> Product f g a

stimes :: Integral b => b -> Product f g a -> Product f g a

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p

stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p

Semigroup c => Semigroup (K1 i c p)

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: K1 i c p -> K1 i c p -> K1 i c p

sconcat :: NonEmpty (K1 i c p) -> K1 i c p

stimes :: Integral b => b -> K1 i c p -> K1 i c p

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

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d)

sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d)

stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d)

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

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a

sconcat :: NonEmpty (Compose f g a) -> Compose f g a

stimes :: Integral b => b -> Compose f g a -> Compose f g a

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p

sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p

stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p

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

@since base-4.12.0.0

Defined in GHC.Internal.Generics

Methods

(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p

sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p

stimes :: Integral b => b -> M1 i c f p -> M1 i c f p

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

@since base-4.9.0.0

Defined in GHC.Internal.Base

Methods

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

sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e)

stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e)

stimesIdempotent :: Integral b => b -> a -> a

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a

This is a valid definition of stimes for an idempotent Monoid.

When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

data WrappedMonoid m

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Instances

NFData1 WrappedMonoid

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> WrappedMonoid a -> ()

Generic1 WrappedMonoid

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

Methods

from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a

to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a

NFData m => NFData (WrappedMonoid m)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: WrappedMonoid m -> ()

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Data m => Data (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m)

toConstr :: WrappedMonoid m -> Constr

dataTypeOf :: WrappedMonoid m -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m))

gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r

gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u

gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m)

gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m)

gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m)

Bounded m => Bounded (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: WrappedMonoid m

maxBound :: WrappedMonoid m

Enum a => Enum (WrappedMonoid a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: WrappedMonoid a -> WrappedMonoid a

pred :: WrappedMonoid a -> WrappedMonoid a

toEnum :: Int -> WrappedMonoid a

fromEnum :: WrappedMonoid a -> Int

enumFrom :: WrappedMonoid a -> [WrappedMonoid a]

enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a]

Generic (WrappedMonoid m)

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x

to :: Rep (WrappedMonoid m) x -> WrappedMonoid m

Read m => Read (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m)

readList :: ReadS [WrappedMonoid m]

readPrec :: ReadPrec (WrappedMonoid m)

readListPrec :: ReadPrec [WrappedMonoid m]

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

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

Ord m => Ord (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering

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

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

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

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

max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

Hashable a => Hashable (WrappedMonoid a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> WrappedMonoid a -> Int

hash :: WrappedMonoid a -> Int

type Rep1 WrappedMonoid

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m)))

cycle1 :: Semigroup m => m -> m

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

Examples

>>> take 10 $ cycle1 [1, 2, 3]
[1,2,3,1,2,3,1,2,3,1]

>>> cycle1 (Right 1)
Right 1

>>> cycle1 (Left 1)
* hangs forever *

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

In many cases, stimes 0 a for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a)
instance Constraint2 a => Monoid (T a)

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

Examples

>>> mtimesDefault 0 "bark"
[]

>>> mtimesDefault 3 "meow"
"meowmeowmeow"

newtype Ap (f :: k -> Type) (a :: k)

This data type witnesses the lifting of a Monoid into an Applicative pointwise.

Examples

>>> Ap (Just [1, 2, 3]) <> Ap Nothing
Ap {getAp = Nothing}

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

@since base-4.12.0.0

Constructors

Ap

Fields

• getAp :: f a

Instances

Generic1 (Ap f :: k -> Type)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep1 (Ap f :: k -> Type)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

Methods

from1 :: forall (a :: k). Ap f a -> Rep1 (Ap f) a

to1 :: forall (a :: k). Rep1 (Ap f) a -> Ap f a

Foldable1 f => Foldable1 (Ap f)

Since: base-4.18.0.0

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Ap f m -> m

foldMap1 :: Semigroup m => (a -> m) -> Ap f a -> m

foldMap1' :: Semigroup m => (a -> m) -> Ap f a -> m

toNonEmpty :: Ap f a -> NonEmpty a

maximum :: Ord a => Ap f a -> a

minimum :: Ord a => Ap f a -> a

head :: Ap f a -> a

last :: Ap f a -> a

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Ap f a -> b

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Ap f a -> b

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Ap f a -> b

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Ap f a -> b

Alternative f => Alternative (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

empty :: Ap f a

(<|>) :: Ap f a -> Ap f a -> Ap f a

some :: Ap f a -> Ap f [a]

many :: Ap f a -> Ap f [a]

Applicative f => Applicative (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Ap f a

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c

(*>) :: Ap f a -> Ap f b -> Ap f b

(<*) :: Ap f a -> Ap f b -> Ap f a

Functor f => Functor (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b

(<$) :: a -> Ap f b -> Ap f a

Monad f => Monad (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b

(>>) :: Ap f a -> Ap f b -> Ap f b

return :: a -> Ap f a

MonadPlus f => MonadPlus (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> Ap f a -> Ap f a

MonadFail f => MonadFail (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

fail :: String -> Ap f a

Foldable f => Foldable (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m

foldMap :: Monoid m => (a -> m) -> Ap f a -> m

foldMap' :: Monoid m => (a -> m) -> Ap f a -> m

foldr :: (a -> b -> b) -> b -> Ap f a -> b

foldr' :: (a -> b -> b) -> b -> Ap f a -> b

foldl :: (b -> a -> b) -> b -> Ap f a -> b

foldl' :: (b -> a -> b) -> b -> Ap f a -> b

foldr1 :: (a -> a -> a) -> Ap f a -> a

foldl1 :: (a -> a -> a) -> Ap f a -> a

toList :: Ap f a -> [a]

null :: Ap f a -> Bool

length :: Ap f a -> Int

elem :: Eq a => a -> Ap f a -> Bool

maximum :: Ord a => Ap f a -> a

minimum :: Ord a => Ap f a -> a

sum :: Num a => Ap f a -> a

product :: Num a => Ap f a -> a

Traversable f => Traversable (Ap f)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b)

sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a)

mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b)

sequence :: Monad m => Ap f (m a) -> m (Ap f a)

(Applicative f, Monoid a) => Monoid (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

mempty :: Ap f a

mappend :: Ap f a -> Ap f a -> Ap f a

mconcat :: [Ap f a] -> Ap f a

(Applicative f, Semigroup a) => Semigroup (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a

sconcat :: NonEmpty (Ap f a) -> Ap f a

stimes :: Integral b => b -> Ap f a -> Ap f a

(Data (f a), Data a, Typeable f) => Data (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a)

toConstr :: Ap f a -> Constr

dataTypeOf :: Ap f a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a))

gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r

gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a)

(Applicative f, Bounded a) => Bounded (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

minBound :: Ap f a

maxBound :: Ap f a

Enum (f a) => Enum (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

succ :: Ap f a -> Ap f a

pred :: Ap f a -> Ap f a

toEnum :: Int -> Ap f a

fromEnum :: Ap f a -> Int

enumFrom :: Ap f a -> [Ap f a]

enumFromThen :: Ap f a -> Ap f a -> [Ap f a]

enumFromTo :: Ap f a -> Ap f a -> [Ap f a]

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a]

Generic (Ap f a)

Defined in GHC.Internal.Data.Monoid

Associated Types

type Rep (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Methods

from :: Ap f a -> Rep (Ap f a) x

to :: Rep (Ap f a) x -> Ap f a

(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 GHC.Internal.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

Read (f a) => Read (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

readsPrec :: Int -> ReadS (Ap f a)

readList :: ReadS [Ap f a]

readPrec :: ReadPrec (Ap f a)

readListPrec :: ReadPrec [Ap f a]

Show (f a) => Show (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS

show :: Ap f a -> String

showList :: [Ap f a] -> ShowS

Eq (f a) => Eq (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

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

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

Ord (f a) => Ord (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering

(<) :: Ap f a -> Ap f a -> Bool

(<=) :: Ap f a -> Ap f a -> Bool

(>) :: Ap f a -> Ap f a -> Bool

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

max :: Ap f a -> Ap f a -> Ap f a

min :: Ap f a -> Ap f a -> Ap f a

type Rep1 (Ap f :: k -> Type)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 f)))

type Rep (Ap f a)

@since base-4.12.0.0

Defined in GHC.Internal.Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "GHC.Internal.Data.Monoid" "ghc-internal" 'True) (C1 ('MetaCons "Ap" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAp") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f a))))

Combinators

maybeToMonoid :: Monoid m => Maybe m -> m

Extracts Monoid value from Maybe returning mempty if Nothing.

>>> maybeToMonoid (Just [1,2,3] :: Maybe [Int])
[1,2,3]
>>> maybeToMonoid (Nothing :: Maybe [Int])
[]

memptyIfFalse :: Monoid m => Bool -> m -> m

Returns the given value in case of the given predicate is satisfied (is True). Otherwise, it returns mempty.

>>> memptyIfFalse True (Just "Hello")
Just "Hello"
>>> memptyIfFalse False "Doesn't matter"
""

Since: 0.7.0.0

memptyIfTrue :: Monoid m => Bool -> m -> m

Returns the given value in case of the given predicate is unsatisfied (is False). Otherwise, it returns mempty.

>>> memptyIfTrue True (Just "Hello")
Nothing
>>> memptyIfTrue False "Does matter"
"Does matter"

Since: 0.7.0.0