Relude.Monoid

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

Reexports

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

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

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

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 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 Builder

Defined in Data.ByteString.Builder.Internal

Methods

mempty :: Builder

mappend :: Builder -> Builder -> Builder

mconcat :: [Builder] -> Builder

Monoid ByteString

Defined in Data.ByteString.Internal

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 ByteArray

Defined in Data.Array.Byte

Methods

mempty :: ByteArray

mappend :: ByteArray -> ByteArray -> ByteArray

mconcat :: [ByteArray] -> ByteArray

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 :: [()] -> ()

FiniteBits a => Monoid (And a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: And a

mappend :: And a -> And a -> And a

mconcat :: [And a] -> And a

FiniteBits a => Monoid (Iff a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: Iff a

mappend :: Iff a -> Iff a -> Iff a

mconcat :: [Iff a] -> Iff a

Bits a => Monoid (Ior a)

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: Ior a

mappend :: Ior a -> Ior a -> Ior a

mconcat :: [Ior a] -> Ior a

Bits a => Monoid (Xor a)

Since: base-4.16

Defined in Data.Bits

Methods

mempty :: Xor a

mappend :: Xor a -> Xor a -> Xor a

mconcat :: [Xor a] -> Xor a

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

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

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 (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

(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 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 (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

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

Monoid p => Monoid (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: Par1 p

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

mconcat :: [Par1 p] -> Par1 p

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 (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

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

(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

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 (a)

Since: base-4.15

Defined in GHC.Base

Methods

mempty :: (a)

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

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

Monoid [a]

Since: base-2.1

Defined in GHC.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

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

Monoid (U1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

mempty :: U1 p

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

mconcat :: [U1 p] -> U1 p

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)

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 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 a => Monoid (Const a b)

Since: base-4.9.0.0

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

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

Since: base-4.12.0.0

Defined in 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 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.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 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 (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.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.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-2.1

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 (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.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.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-2.1

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 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

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

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)

Applicative Last

Since: base-4.8.0.0

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

Functor Last

Since: base-4.8.0.0

Defined in 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 Data.Monoid

Methods

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

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

return :: a -> Last a

NFData1 Last

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

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 :: 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)

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

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

Generic (Last a)

Defined in Data.Monoid

Associated Types

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

Methods

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

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

Read a => Read (Last a)

Since: base-2.1

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)

Since: base-2.1

Defined in Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

NFData a => NFData (Last a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Last a -> ()

Eq a => Eq (Last a)

Since: base-2.1

Defined in Data.Monoid

Methods

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

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

Ord a => Ord (Last a)

Since: base-2.1

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

Generic1 Last

Defined in Data.Monoid

Associated Types

type Rep1 Last :: k -> Type

Methods

from1 :: forall (a :: k). Last a -> Rep1 Last a

to1 :: forall (a :: k). Rep1 Last a -> Last a

type Rep (Last a)

Since: base-4.7.0.0

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

Since: base-4.7.0.0

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 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

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

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)

Applicative First

Since: base-4.8.0.0

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

Functor First

Since: base-4.8.0.0

Defined in 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 Data.Monoid

Methods

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

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

return :: a -> First a

NFData1 First

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

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 :: 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)

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

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

Generic (First a)

Defined in Data.Monoid

Associated Types

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

Methods

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

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

Read a => Read (First a)

Since: base-2.1

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)

Since: base-2.1

Defined in Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

NFData a => NFData (First a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: First a -> ()

Eq a => Eq (First a)

Since: base-2.1

Defined in Data.Monoid

Methods

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

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

Ord a => Ord (First a)

Since: base-2.1

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

Generic1 First

Defined in Data.Monoid

Associated Types

type Rep1 First :: k -> Type

Methods

from1 :: forall (a :: k). First a -> Rep1 First a

to1 :: forall (a :: k). Rep1 First a -> First a

type Rep (First a)

Since: base-4.7.0.0

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

Since: base-4.7.0.0

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

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

Since: base-4.12.0.0

Constructors

Ap

Fields

• getAp :: f a

Instances

Generic1 (Ap f :: k -> Type)

Defined in Data.Monoid

Associated Types

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

Methods

from1 :: forall (a :: k0). Ap f a -> Rep1 (Ap f) a

to1 :: forall (a :: k0). Rep1 (Ap f) a -> Ap f a

MonadFail f => MonadFail (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

fail :: String -> Ap f a

Foldable f => Foldable (Ap f)

Since: base-4.12.0.0

Defined in 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 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)

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Defined in 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 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 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 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 Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> 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 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, Monoid a) => Monoid (Ap f a)

Since: base-4.12.0.0

Defined in 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 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

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

Since: base-4.12.0.0

Defined in 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 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 Data.Monoid

Associated Types

type Rep (Ap f a) :: Type -> Type

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 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 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 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 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 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 Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "Data.Monoid" "base" '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 Data.Monoid

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

newtype Sum a

Monoid under addition.

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

Constructors

Sum

Fields

• getSum :: a

Instances

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

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)

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

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

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

NFData1 Sum

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

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 :: 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)

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 => 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

Bounded a => Bounded (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

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

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 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-2.1

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)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

NFData a => NFData (Sum a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Sum a -> ()

Eq a => Eq (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a)

Since: base-2.1

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

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type

Methods

from1 :: forall (a :: k). Sum a -> Rep1 Sum a

to1 :: forall (a :: k). Rep1 Sum a -> Sum a

type Rep (Sum a)

Since: base-4.7.0.0

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

Since: base-4.7.0.0

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

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

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)

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

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

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

NFData1 Product

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

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 :: 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)

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

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

Bounded a => Bounded (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

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

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 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-2.1

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)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

NFData a => NFData (Product a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Product a -> ()

Eq a => Eq (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a)

Since: base-2.1

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

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type

Methods

from1 :: forall (a :: k). Product a -> Rep1 Product a

to1 :: forall (a :: k). Rep1 Product a -> Product a

type Rep (Product a)

Since: base-4.7.0.0

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

Since: base-4.7.0.0

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 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

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

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

Generic (Endo a)

Defined in Data.Semigroup.Internal

Associated Types

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

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 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 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

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

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)

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

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

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

NFData1 Dual

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

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

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 :: 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)

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

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

Bounded a => Bounded (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a

maxBound :: Dual a

Generic (Dual a)

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Read a => Read (Dual a)

Since: base-2.1

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)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

NFData a => NFData (Dual a)

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Dual a -> ()

Eq a => Eq (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Dual a)

Since: base-2.1

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

Generic1 Dual

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type

Methods

from1 :: forall (a :: k). Dual a -> Rep1 Dual a

to1 :: forall (a :: k). Rep1 Dual a -> Dual a

type Rep (Dual a)

Since: base-4.7.0.0

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

Since: base-4.7.0.0

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 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

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 :: 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

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> 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

Bounded Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Generic Any

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Read Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

NFData Any

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: Any -> ()

Eq Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord Any

Since: base-2.1

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

type Rep Any

Since: base-4.7.0.0

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

Monoid under <|>.

>>> getAlt (Alt (Just 12) <> Alt (Just 24))
Just 12

>>> getAlt $ Alt Nothing <> Alt (Just 24)
Just 24

Since: base-4.8.0.0

Constructors

Alt

Fields

• getAlt :: f a

Instances

Generic1 (Alt f :: k -> Type)

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

from1 :: forall (a :: k0). Alt f a -> Rep1 (Alt f) a

to1 :: forall (a :: k0). Rep1 (Alt f) a -> Alt f a

Foldable f => Foldable (Alt f)

Since: base-4.12.0.0

Defined in 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

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

Traversable f => Traversable (Alt f)

Since: base-4.12.0.0

Defined in 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 => Alternative (Alt f)

Since: base-4.8.0.0

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]

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

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

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Defined in 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 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 Data.Semigroup.Internal

Methods

mzero :: Alt f a

mplus :: Alt f a -> 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 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)

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

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

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

Since: base-4.8.0.0

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]

Generic (Alt f a)

Defined in Data.Semigroup.Internal

Associated Types

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

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 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 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 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 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 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 Data.Semigroup.Internal

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

Since: base-4.8.0.0

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))))

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

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 :: 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

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> 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

Bounded All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Generic All

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Read All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

NFData All

Since: deepseq-1.4.0.0

Defined in Control.DeepSeq

Methods

rnf :: All -> ()

Eq All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

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

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

Ord All

Since: base-2.1

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

type Rep All

Since: base-4.7.0.0

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)))

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

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

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

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

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

>>> import Data.List.NonEmpty (NonEmpty (..))
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

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 \(\mathcal{O}(1)\) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

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

Instances

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 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 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

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 ByteArray

Defined in Data.Array.Byte

Methods

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

sconcat :: NonEmpty ByteArray -> ByteArray

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

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 -> () -> ()

Bits a => Semigroup (And a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: And a -> And a -> And a

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

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

FiniteBits a => Semigroup (Iff a)

This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a

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

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

Bits a => Semigroup (Ior a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a

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

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

Bits a => Semigroup (Xor a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a

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

stimes :: Integral b => b -> Xor a -> Xor 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 a => Semigroup (Identity a)

Since: base-4.9.0.0

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 (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 (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 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 (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 => 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

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p

sconcat :: NonEmpty (Par1 p) -> Par1 p

stimes :: Integral b => b -> Par1 p -> Par1 p

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

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 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

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

(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 (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 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 (a)

Since: base-4.15

Defined in GHC.Base

Methods

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

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

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

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 (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 (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

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

Semigroup (U1 p)

Since: base-4.12.0.0

Defined in GHC.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.Generics

Methods

(<>) :: V1 p -> V1 p -> V1 p

sconcat :: NonEmpty (V1 p) -> V1 p

stimes :: Integral b => b -> V1 p -> V1 p

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)

<> = 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 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 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 a => Semigroup (Const a b)

Since: base-4.9.0.0

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

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

Since: base-4.12.0.0

Defined in 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 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.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 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 (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.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.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.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.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.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.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)

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 -> ()

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)

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

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) :: Type -> Type

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

NFData m => NFData (WrappedMonoid m)

Since: deepseq-1.4.2.0

Defined in Control.DeepSeq

Methods

rnf :: WrappedMonoid m -> ()

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

Generic1 WrappedMonoid

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid :: k -> Type

Methods

from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a

to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a

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)))

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))

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.

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

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

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

Since: base-4.12.0.0

Constructors

Ap

Fields

• getAp :: f a

Instances

Generic1 (Ap f :: k -> Type)

Defined in Data.Monoid

Associated Types

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

Methods

from1 :: forall (a :: k0). Ap f a -> Rep1 (Ap f) a

to1 :: forall (a :: k0). Rep1 (Ap f) a -> Ap f a

MonadFail f => MonadFail (Ap f)

Since: base-4.12.0.0

Defined in Data.Monoid

Methods

fail :: String -> Ap f a

Foldable f => Foldable (Ap f)

Since: base-4.12.0.0

Defined in 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 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)

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Defined in 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 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 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 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 Data.Monoid

Methods

mzero :: Ap f a

mplus :: Ap f a -> 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 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, Monoid a) => Monoid (Ap f a)

Since: base-4.12.0.0

Defined in 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 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

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

Since: base-4.12.0.0

Defined in 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 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 Data.Monoid

Associated Types

type Rep (Ap f a) :: Type -> Type

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 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 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 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 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 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 Data.Monoid

type Rep1 (Ap f :: k -> Type) = D1 ('MetaData "Ap" "Data.Monoid" "base" '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 Data.Monoid

type Rep (Ap f a) = D1 ('MetaData "Ap" "Data.Monoid" "base" '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