Relude.Monoid

This module reexports functions to work with monoids plus adds extra useful functions.

Documentation

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 laws:

• x <> mempty = x

• mempty <> x = x

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

• mconcat = foldr '(<>)' mempty

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

Methods

mempty :: a

Identity of mappend

mappend :: a -> a -> a

An associative operation

NOTE: This method is redundant and has the default implementation mappend = '(<>)' since base-4.11.0.0.

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.

Instances

Monoid Ordering

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

Monoid ()

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: ()

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

mconcat :: [()] -> ()

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Monoid ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

mempty :: ShortByteString

mappend :: ShortByteString -> ShortByteString -> ShortByteString

mconcat :: [ShortByteString] -> ShortByteString

Monoid ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid ByteString

Defined in Data.ByteString.Internal

Methods

mempty :: ByteString

mappend :: ByteString -> ByteString -> ByteString

mconcat :: [ByteString] -> ByteString

Monoid Builder

Defined in Data.ByteString.Builder.Internal

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid IntSet

Defined in Data.IntSet.Internal

Methods

mempty :: IntSet

mappend :: IntSet -> IntSet -> IntSet

mconcat :: [IntSet] -> IntSet

Monoid [a]

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: [a]

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

mconcat :: [[a]] -> [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-2.1

Defined in GHC.Base

Methods

mempty :: Maybe a

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

mconcat :: [Maybe a] -> Maybe a

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

mempty :: IO a

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

mconcat :: [IO a] -> IO 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

(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

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

Semigroup a => Monoid (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Option a

mappend :: Option a -> Option a -> Option a

mconcat :: [Option a] -> Option a

Monoid a => Monoid (Identity a)

Defined in Data.Functor.Identity

Methods

mempty :: Identity a

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

mconcat :: [Identity a] -> Identity a

Monoid (First a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: First a

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

mconcat :: [First a] -> First a

Monoid (Last a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: Last a

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

mconcat :: [Last a] -> Last a

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a

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

mconcat :: [Dual a] -> Dual a

Monoid (Endo a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a

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

mconcat :: [Endo a] -> Endo a

Num a => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

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

mconcat :: [Sum a] -> Sum a

Num a => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

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

mconcat :: [Product a] -> Product a

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

mempty :: Down a

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

mconcat :: [Down a] -> Down a

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

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

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

Defined in Data.HashSet

Methods

mempty :: HashSet a

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

mconcat :: [HashSet a] -> HashSet 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

Monoid b => Monoid (a -> b)

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: a -> b

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

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

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

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b)

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

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

Monoid (Proxy s)

Since: base-4.7.0.0

Defined in Data.Proxy

Methods

mempty :: Proxy s

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

mconcat :: [Proxy s] -> Proxy s

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

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

Defined in Data.HashMap.Base

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

Since: base-2.1

Defined in GHC.Base

Methods

mempty :: (a, b, c)

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

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

Monoid a => Monoid (Const a b)

Defined in 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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

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

Since: base-2.1

Defined in GHC.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 a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)

Since: base-2.1

Defined in GHC.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 First a

Maybe monoid returning the leftmost non-Nothing value.

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

>>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"

Constructors

First

Fields

• getFirst :: Maybe a

Instances

Monad First

Defined in Data.Monoid

Methods

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

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

return :: a -> First a

fail :: String -> First a

Functor First

Defined in Data.Monoid

Methods

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

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

Applicative First

Defined in 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

Foldable First

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

NFData1 First

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

Eq a => Eq (First a)

Defined in Data.Monoid

Methods

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

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

Data a => Data (First a)

Since: base-4.8.0.0

Defined in 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 :: (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)

Ord a => Ord (First a)

Defined in 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

Read a => Read (First a)

Defined in 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)

Defined in Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Generic (First a)

Defined in Data.Monoid

Associated Types

type Rep (First a) :: * -> *

Methods

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

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

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

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

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

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

Monoid (First a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: First a

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

mconcat :: [First a] -> First a

NFData a => NFData (First a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: First a -> ()

Generic1 First

Defined in Data.Monoid

Associated Types

type Rep1 First :: k -> *

Methods

from1 :: First a -> Rep1 First a

to1 :: Rep1 First a -> First a

type Rep (First a)

Defined in Data.Monoid

type Rep (First a) = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

type Rep1 First

Defined in Data.Monoid

type Rep1 First = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

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)

>>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
Just "world"

Constructors

Last

Fields

• getLast :: Maybe a

Instances

Monad Last

Defined in Data.Monoid

Methods

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

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

return :: a -> Last a

fail :: String -> Last a

Functor Last

Defined in Data.Monoid

Methods

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

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

Applicative Last

Defined in 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

Foldable Last

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

NFData1 Last

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

Eq a => Eq (Last a)

Defined in Data.Monoid

Methods

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

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

Data a => Data (Last a)

Since: base-4.8.0.0

Defined in 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 :: (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)

Ord a => Ord (Last a)

Defined in 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

Read a => Read (Last a)

Defined in 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)

Defined in Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Generic (Last a)

Defined in Data.Monoid

Associated Types

type Rep (Last a) :: * -> *

Methods

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

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

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

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

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

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

Monoid (Last a)

Since: base-2.1

Defined in Data.Monoid

Methods

mempty :: Last a

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

mconcat :: [Last a] -> Last a

NFData a => NFData (Last a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Last a -> ()

Generic1 Last

Defined in Data.Monoid

Associated Types

type Rep1 Last :: k -> *

Methods

from1 :: Last a -> Rep1 Last a

to1 :: Rep1 Last a -> Last a

type Rep (Last a)

Defined in Data.Monoid

type Rep (Last a) = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

type Rep1 Last

Defined in Data.Monoid

type Rep1 Last = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

newtype Dual a

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual

Fields

• getDual :: a

Instances

Monad Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a

fail :: String -> Dual a

Functor Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

Applicative Dual

Since: base-4.8.0.0

Defined in 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

Foldable Dual

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

NFData1 Dual

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

Bounded a => Bounded (Dual a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a

maxBound :: Dual a

Eq a => Eq (Dual a)

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Dual a)

Since: base-4.8.0.0

Defined in 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 :: (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)

Ord a => Ord (Dual a)

Defined in 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

Read a => Read (Dual a)

Defined in 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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

Generic (Dual a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Dual a) :: * -> *

Methods

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

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

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a

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

mconcat :: [Dual a] -> Dual a

NFData a => NFData (Dual a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Dual a -> ()

Generic1 Dual

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> *

Methods

from1 :: Dual a -> Rep1 Dual a

to1 :: Rep1 Dual a -> Dual a

type Rep (Dual a)

Defined in Data.Semigroup.Internal

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

type Rep1 Dual

Defined in Data.Semigroup.Internal

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

newtype Endo a

The monoid of endomorphisms under composition.

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

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Generic (Endo a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: * -> *

Methods

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

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

Semigroup (Endo a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid (Endo a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a

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

mconcat :: [Endo a] -> Endo a

type Rep (Endo a)

Defined in Data.Semigroup.Internal

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

newtype All

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False

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

Constructors

All

Fields

• getAll :: Bool

Instances

Bounded All

Defined in Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Eq All

Defined in Data.Semigroup.Internal

Methods

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

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

Data All

Since: base-4.8.0.0

Defined in 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 :: (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

Ord All

Defined in 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

Read All

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Generic All

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: * -> *

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All

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

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

NFData All

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: All -> ()

type Rep All

Defined in Data.Semigroup.Internal

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

newtype Any

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True

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

Constructors

Any

Fields

• getAny :: Bool

Instances

Bounded Any

Defined in Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Eq Any

Defined in Data.Semigroup.Internal

Methods

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

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

Data Any

Since: base-4.8.0.0

Defined in 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 :: (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

Ord Any

Defined in 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

Read Any

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Generic Any

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: * -> *

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any

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

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

NFData Any

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Any -> ()

type Rep Any

Defined in Data.Semigroup.Internal

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

newtype Sum a

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum

Fields

• getSum :: a

Instances

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a

fail :: String -> Sum a

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

Applicative Sum

Since: base-4.8.0.0

Defined in 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

Foldable Sum

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

NFData1 Sum

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

Bounded a => Bounded (Sum a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Eq a => Eq (Sum a)

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Sum a)

Since: base-4.8.0.0

Defined in 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 :: (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)

Num a => Num (Sum a)

Defined in Data.Semigroup.Internal

Methods

(+) :: Sum a -> Sum a -> Sum a

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

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

negate :: Sum a -> Sum a

abs :: Sum a -> Sum a

signum :: Sum a -> Sum a

fromInteger :: Integer -> Sum a

Ord a => Ord (Sum a)

Defined in 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

Read a => Read (Sum a)

Defined in 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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: * -> *

Methods

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

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

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

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

mconcat :: [Sum a] -> Sum a

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> *

Methods

from1 :: Sum a -> Rep1 Sum a

to1 :: Rep1 Sum a -> Sum a

type Rep (Sum a)

Defined in Data.Semigroup.Internal

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

type Rep1 Sum

Defined in Data.Semigroup.Internal

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

newtype Product a

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product

Fields

• getProduct :: a

Instances

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a

fail :: String -> Product a

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

Applicative Product

Since: base-4.8.0.0

Defined in 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

Foldable Product

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

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

NFData1 Product

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

Bounded a => Bounded (Product a)

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Eq a => Eq (Product a)

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Product a)

Since: base-4.8.0.0

Defined in 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 :: (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)

Num a => Num (Product a)

Defined in Data.Semigroup.Internal

Methods

(+) :: Product a -> Product a -> Product a

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

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

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Ord a => Ord (Product a)

Defined in 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

Read a => Read (Product a)

Defined in 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)

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: * -> *

Methods

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

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

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in 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 => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

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

mconcat :: [Product a] -> Product a

NFData a => NFData (Product a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> *

Methods

from1 :: Product a -> Rep1 Product a

to1 :: Rep1 Product a -> Product a

type Rep (Product a)

Defined in Data.Semigroup.Internal

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

type Rep1 Product

Defined in Data.Semigroup.Internal

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

newtype Alt (f :: k -> *) (a :: k) :: forall k. (k -> *) -> k -> *

Monoid under <|>.

Since: base-4.8.0.0

Constructors

Alt

Fields

• getAlt :: f a

Instances

Generic1 (Alt f :: k -> *)

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

from1 :: Alt f a -> Rep1 (Alt f) a

to1 :: Rep1 (Alt f) a -> Alt f a

Monad f => Monad (Alt f)

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Alt f a

fail :: String -> Alt f a

Functor f => Functor (Alt f)

Defined in Data.Semigroup.Internal

Methods

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

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

Applicative f => Applicative (Alt f)

Defined in 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

Alternative f => Alternative (Alt f)

Defined in 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]

MonadPlus f => MonadPlus (Alt f)

Defined in Data.Semigroup.Internal

Methods

mzero :: Alt f a

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

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

Defined in 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]

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

Defined in Data.Semigroup.Internal

Methods

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

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

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

Since: base-4.8.0.0

Defined in 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 :: (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)

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

Defined in Data.Semigroup.Internal

Methods

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

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

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

negate :: Alt f a -> Alt f a

abs :: Alt f a -> Alt f a

signum :: Alt f a -> Alt f a

fromInteger :: Integer -> Alt f a

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

Defined in 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

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

Defined in 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)

Defined in Data.Semigroup.Internal

Methods

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

show :: Alt f a -> String

showList :: [Alt f a] -> ShowS

Generic (Alt f a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Alt f a) :: * -> *

Methods

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

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

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined in 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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Defined in 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

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

Defined in Data.Semigroup.Internal

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

type Rep (Alt f a)

Defined in Data.Semigroup.Internal

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

class Semigroup a where

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

Instances should satisfy the associativity law:

• x <> (y <> z) = (x <> y) <> z

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

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

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

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

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

Instances

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty Ordering -> Ordering

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

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty () -> ()

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

Semigroup Void

Since: base-4.9.0.0

Defined in Data.Void

Methods

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

sconcat :: NonEmpty Void -> Void

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

Semigroup All

Since: base-4.9.0.0

Defined in 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 Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any

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

Semigroup ShortByteString

Defined in Data.ByteString.Short.Internal

Methods

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

sconcat :: NonEmpty ShortByteString -> ShortByteString

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

Semigroup ByteString

Defined in Data.ByteString.Lazy.Internal

Methods

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

sconcat :: NonEmpty ByteString -> ByteString

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

Semigroup ByteString

Defined in Data.ByteString.Internal

Methods

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

sconcat :: NonEmpty ByteString -> ByteString

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

Semigroup Builder

Defined in Data.ByteString.Builder.Internal

Methods

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

sconcat :: NonEmpty Builder -> Builder

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

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 [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

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

Semigroup a => Semigroup (Maybe a)

Since: base-4.9.0.0

Defined in GHC.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 (IO a)

Since: base-4.10.0.0

Defined in GHC.Base

Methods

(<>) :: IO a -> IO a -> IO a

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

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

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

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

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 a => Semigroup (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Option a -> Option a -> Option a

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

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

Semigroup a => Semigroup (Identity a)

Defined in 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 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 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 (Dual a)

Since: base-4.9.0.0

Defined in 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 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 (Sum a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

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

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

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

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a

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

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

Semigroup (NonEmpty a)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a

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

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

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 (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

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

Defined in Data.HashSet

Methods

(<>) :: HashSet a -> HashSet a -> HashSet a

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

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

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

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

stimes :: Integral b0 => b0 -> (a -> b) -> a -> b

Semigroup (Either a b)

Since: base-4.9.0.0

Defined in 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 a, Semigroup b) => Semigroup (a, b)

Since: base-4.9.0.0

Defined in GHC.Base

Methods

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

sconcat :: NonEmpty (a, b) -> (a, b)

stimes :: Integral b0 => b0 -> (a, b) -> (a, b)

Semigroup (Proxy s)

Since: base-4.9.0.0

Defined in Data.Proxy

Methods

(<>) :: Proxy s -> Proxy s -> Proxy s

sconcat :: NonEmpty (Proxy s) -> Proxy s

stimes :: Integral b => b -> Proxy s -> Proxy s

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

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

Defined in Data.HashMap.Base

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

Since: base-4.9.0.0

Defined in GHC.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 a => Semigroup (Const a b)

Defined in 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

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined in 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 a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Defined in GHC.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 a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined in GHC.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)

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using stimes and mempty.

This is a suitable definition for an mtimes member of Monoid.

cycle1 :: Semigroup m => m -> m

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

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 -> ()

Bounded m => Bounded (WrappedMonoid m)

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]

Eq m => Eq (WrappedMonoid m)

Defined in Data.Semigroup

Methods

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

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

Data m => Data (WrappedMonoid m)

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 :: (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)

Ord m => Ord (WrappedMonoid m)

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

Read m => Read (WrappedMonoid m)

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)

Defined in Data.Semigroup

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

Generic (WrappedMonoid m)

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m) :: * -> *

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x

to :: Rep (WrappedMonoid m) x -> 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

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

NFData m => NFData (WrappedMonoid m)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: WrappedMonoid m -> ()

Hashable a => Hashable (WrappedMonoid a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> WrappedMonoid a -> Int

hash :: WrappedMonoid a -> Int

Generic1 WrappedMonoid

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid :: k -> *

Methods

from1 :: WrappedMonoid a -> Rep1 WrappedMonoid a

to1 :: Rep1 WrappedMonoid a -> WrappedMonoid a

type Rep (WrappedMonoid m)

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)))

type Rep1 WrappedMonoid

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))

newtype Option a

Option is effectively Maybe with a better instance of Monoid, built off of an underlying Semigroup instead of an underlying Monoid.

Ideally, this type would not exist at all and we would just fix the Monoid instance of Maybe

Constructors

Option

Fields

• getOption :: Maybe a

Instances

Monad Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

(>>) :: Option a -> Option b -> Option b

return :: a -> Option a

fail :: String -> Option a

Functor Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

MonadFix Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mfix :: (a -> Option a) -> Option a

Applicative Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: a -> Option a

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

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

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

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

Foldable Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Option m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Option a -> a

foldl1 :: (a -> a -> a) -> Option a -> a

toList :: Option a -> [a]

null :: Option a -> Bool

length :: Option a -> Int

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

maximum :: Ord a => Option a -> a

minimum :: Ord a => Option a -> a

sum :: Num a => Option a -> a

product :: Num a => Option a -> a

Traversable Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

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

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

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

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

Alternative Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

empty :: Option a

(<|>) :: Option a -> Option a -> Option a

some :: Option a -> Option [a]

many :: Option a -> Option [a]

MonadPlus Option

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mzero :: Option a

mplus :: Option a -> Option a -> Option a

NFData1 Option

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a -> ()) -> Option a -> ()

Eq a => Eq (Option a)

Defined in Data.Semigroup

Methods

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

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

Data a => Data (Option a)

Defined in Data.Semigroup

Methods

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

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

toConstr :: Option a -> Constr

dataTypeOf :: Option a -> DataType

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Option a)

Defined in Data.Semigroup

Methods

compare :: Option a -> Option a -> Ordering

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

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

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

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

max :: Option a -> Option a -> Option a

min :: Option a -> Option a -> Option a

Read a => Read (Option a)

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Option a)

readList :: ReadS [Option a]

readPrec :: ReadPrec (Option a)

readListPrec :: ReadPrec [Option a]

Show a => Show (Option a)

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Option a -> ShowS

show :: Option a -> String

showList :: [Option a] -> ShowS

Generic (Option a)

Defined in Data.Semigroup

Associated Types

type Rep (Option a) :: * -> *

Methods

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

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

Semigroup a => Semigroup (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Option a -> Option a -> Option a

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

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

Semigroup a => Monoid (Option a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Option a

mappend :: Option a -> Option a -> Option a

mconcat :: [Option a] -> Option a

NFData a => NFData (Option a)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: Option a -> ()

Hashable a => Hashable (Option a)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Option a -> Int

hash :: Option a -> Int

Generic1 Option

Defined in Data.Semigroup

Associated Types

type Rep1 Option :: k -> *

Methods

from1 :: Option a -> Rep1 Option a

to1 :: Rep1 Option a -> Option a

type Rep (Option a)

Defined in Data.Semigroup

type Rep (Option a) = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))

type Rep1 Option

Defined in Data.Semigroup

type Rep1 Option = D1 (MetaData "Option" "Data.Semigroup" "base" True) (C1 (MetaCons "Option" PrefixI True) (S1 (MetaSel (Just "getOption") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 Maybe)))

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.

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 O(1) rather than O(log n).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in O(1) rather than O(log n)

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])
[]