Data.Monoid

Copyright	(c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001
License	BSD-style (see the file libraries/base/LICENSE)
Maintainer	[email protected]
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Monoid typeclass
Bool wrappers
Num wrappers
Maybe wrappers
Alternative wrapper
Applicative wrapper

Description

A type a is a Monoid if it provides an associative function (<>) that lets you combine any two values of type a into one, and a neutral element (mempty) such that

a <> mempty == mempty <> a == a

A Monoid is a Semigroup with the added requirement of a neutral element. Thus any Monoid is a Semigroup, but not the other way around.

Examples

Expand

The Sum monoid is defined by the numerical addition operator and `0` as neutral element:

>>> mempty :: Sum Int
Sum 0
>>> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum Int
Sum {getSum = 10}

We can combine multiple values in a list into a single value using the mconcat function. Note that we have to specify the type here since Int is a monoid under several different operations:

>>> mconcat [1,2,3,4] :: Sum Int
Sum {getSum = 10}
>>> mconcat [] :: Sum Int
Sum {getSum = 0}

Another valid monoid instance of Int is Product It is defined by multiplication and `1` as neutral element:

>>> Product 1 <> Product 2 <> Product 3 <> Product 4 :: Product Int
Product {getProduct = 24}
>>> mconcat [1,2,3,4] :: Product Int
Product {getProduct = 24}
>>> mconcat [] :: Product Int
Product {getProduct = 1}

Monoid typeclass

class Semigroup a => Monoid a where Source

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 Source

Identity of mappend

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

mappend :: a -> a -> a Source

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 Source

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

Instances details

Monoid Ordering	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source mappend :: Ordering -> Ordering -> Ordering Source mconcat :: [Ordering] -> Ordering Source
Monoid ()	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source mappend :: () -> () -> () Source mconcat :: [()] -> () Source
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Monoid Lifetime	`mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal Methods mempty :: Lifetime Source mappend :: Lifetime -> Lifetime -> Lifetime Source mconcat :: [Lifetime] -> Lifetime Source
Monoid Event	Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal Methods mempty :: Event Source mappend :: Event -> Event -> Event Source mconcat :: [Event] -> Event Source
Monoid [a]	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source mappend :: [a] -> [a] -> [a] Source mconcat :: [[a]] -> [a] Source
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 `ee = e` and `es = 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
Instance details Defined in GHC.Base Methods mempty :: Maybe a Source mappend :: Maybe a -> Maybe a -> Maybe a Source mconcat :: [Maybe a] -> Maybe a Source
Monoid a => Monoid (IO a)	Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a Source mappend :: IO a -> IO a -> IO a Source mconcat :: [IO a] -> IO a Source
Monoid p => Monoid (Par1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p Source mappend :: Par1 p -> Par1 p -> Par1 p Source mconcat :: [Par1 p] -> Par1 p Source
Monoid a => Monoid (Down a)	Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a Source mappend :: Down a -> Down a -> Down a Source mconcat :: [Down a] -> Down a Source
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Monoid a => Monoid (Identity a)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a Source mappend :: Identity a -> Identity a -> Identity a Source mconcat :: [Identity a] -> Identity a Source
Semigroup a => Monoid (Option a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a Source mappend :: Option a -> Option a -> Option a Source mconcat :: [Option a] -> Option a Source
Monoid m => Monoid (WrappedMonoid m)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
(Ord a, Bounded a) => Monoid (Max a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Max a Source mappend :: Max a -> Max a -> Max a Source mconcat :: [Max a] -> Max a Source
(Ord a, Bounded a) => Monoid (Min a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Monoid (Equivalence a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a Source mappend :: Equivalence a -> Equivalence a -> Equivalence a Source mconcat :: [Equivalence a] -> Equivalence a Source
Monoid (Comparison a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a Source mappend :: Comparison a -> Comparison a -> Comparison a Source mconcat :: [Comparison a] -> Comparison a Source
Monoid (Predicate a)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a Source mappend :: Predicate a -> Predicate a -> Predicate a Source mconcat :: [Predicate a] -> Predicate a Source
Monoid b => Monoid (a -> b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b Source mappend :: (a -> b) -> (a -> b) -> a -> b Source mconcat :: [a -> b] -> a -> b Source
Monoid (U1 p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p Source mappend :: U1 p -> U1 p -> U1 p Source mconcat :: [U1 p] -> U1 p Source
(Monoid a, Monoid b) => Monoid (a, b)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) Source mappend :: (a, b) -> (a, b) -> (a, b) Source mconcat :: [(a, b)] -> (a, b) Source
Monoid a => Monoid (ST s a)	Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a Source mappend :: ST s a -> ST s a -> ST s a Source mconcat :: [ST s a] -> ST s a Source
Monoid (Proxy s)	Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s Source mappend :: Proxy s -> Proxy s -> Proxy s Source mconcat :: [Proxy s] -> Proxy s Source
Monoid a => Monoid (Op a b)
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Op a b Source mappend :: Op a b -> Op a b -> Op a b Source mconcat :: [Op a b] -> Op a b Source
Monoid (f p) => Monoid (Rec1 f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Rec1 f p Source mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source mconcat :: [Rec1 f p] -> Rec1 f p Source
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c) Source mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source mconcat :: [(a, b, c)] -> (a, b, c) Source
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source mappend :: Alt f a -> Alt f a -> Alt f a Source mconcat :: [Alt f a] -> Alt f a Source
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source mappend :: Ap f a -> Ap f a -> Ap f a Source mconcat :: [Ap f a] -> Ap f a Source
Monoid a => Monoid (Const a b)	Since: base-4.9.0.0
Instance details Defined in Data.Functor.Const Methods mempty :: Const a b Source mappend :: Const a b -> Const a b -> Const a b Source mconcat :: [Const a b] -> Const a b Source
Monoid c => Monoid (K1 i c p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: K1 i c p Source mappend :: K1 i c p -> K1 i c p -> K1 i c p Source mconcat :: [K1 i c p] -> K1 i c p Source
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :: g) p Source mappend :: (f :: g) p -> (f :: g) p -> (f :: g) p Source mconcat :: [(f :: g) p] -> (f :: g) p Source
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d) Source mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source
Monoid (f p) => Monoid (M1 i c f p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: M1 i c f p Source mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source mconcat :: [M1 i c f p] -> M1 i c f p Source
Monoid (f (g p)) => Monoid ((f :.: g) p)	Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: (f :.: g) p Source mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source mconcat :: [(f :.: g) p] -> (f :.: g) p Source
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b, c, d, e) Source mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source

(<>) :: Semigroup a => a -> a -> a infixr 6 Source

An associative operation.

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

newtype Dual a Source

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

Instances details

Monad Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source (>>) :: Dual a -> Dual b -> Dual b Source return :: a -> Dual a Source
Functor Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
MonadFix Dual	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Dual a) -> Dual a Source
Applicative Dual	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Dual a Source (<>) :: Dual (a -> b) -> Dual a -> Dual b Source liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source (>) :: Dual a -> Dual b -> Dual b Source (<*) :: Dual a -> Dual b -> Dual a Source
Foldable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m Source foldMap :: Monoid m => (a -> m) -> Dual a -> m Source foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source foldr :: (a -> b -> b) -> b -> Dual a -> b Source foldr' :: (a -> b -> b) -> b -> Dual a -> b Source foldl :: (b -> a -> b) -> b -> Dual a -> b Source foldl' :: (b -> a -> b) -> b -> Dual a -> b Source foldr1 :: (a -> a -> a) -> Dual a -> a Source foldl1 :: (a -> a -> a) -> Dual a -> a Source toList :: Dual a -> [a] Source null :: Dual a -> Bool Source length :: Dual a -> Int Source elem :: Eq a => a -> Dual a -> Bool Source maximum :: Ord a => Dual a -> a Source minimum :: Ord a => Dual a -> a Source sum :: Num a => Dual a -> a Source product :: Num a => Dual a -> a Source
Traversable Dual	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source sequence :: Monad m => Dual (m a) -> m (Dual a) Source
MonadZip Dual	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Dual a -> Dual b -> Dual (a, b) Source mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source munzip :: Dual (a, b) -> (Dual a, Dual b) Source
Bounded a => Bounded (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Dual a Source maxBound :: Dual a Source
Eq a => Eq (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Dual a -> Dual a -> Bool Source (/=) :: Dual a -> Dual a -> Bool Source
Data a => Data (Dual a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source toConstr :: Dual a -> Constr Source dataTypeOf :: Dual a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source
Ord a => Ord (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Dual a -> Dual a -> Ordering Source (<) :: Dual a -> Dual a -> Bool Source (<=) :: Dual a -> Dual a -> Bool Source (>) :: Dual a -> Dual a -> Bool Source (>=) :: Dual a -> Dual a -> Bool Source max :: Dual a -> Dual a -> Dual a Source min :: Dual a -> Dual a -> Dual a Source
Read a => Read (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Dual a) Source readList :: ReadS [Dual a] Source readPrec :: ReadPrec (Dual a) Source readListPrec :: ReadPrec [Dual a] Source
Show a => Show (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Dual a -> ShowS Source show :: Dual a -> String Source showList :: [Dual a] -> ShowS Source
Generic (Dual a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Dual a) :: Type -> Type Source Methods from :: Dual a -> Rep (Dual a) x Source to :: Rep (Dual a) x -> Dual a Source
Semigroup a => Semigroup (Dual a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Dual a -> Dual a -> Dual a Source sconcat :: NonEmpty (Dual a) -> Dual a Source stimes :: Integral b => b -> Dual a -> Dual a Source
Monoid a => Monoid (Dual a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Generic1 Dual	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Dual :: k -> Type Source Methods from1 :: forall (a :: k). Dual a -> Rep1 Dual a Source to1 :: forall (a :: k). Rep1 Dual a -> Dual a Source
type Rep (Dual a)
Instance details 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
Instance details Defined in Data.Semigroup.Internal type Rep1 Dual = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype Endo a Source

The monoid of endomorphisms under composition.

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

Constructors

Endo
Fields appEndo :: a -> a

Instances

Instances details

Generic (Endo a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Endo a) :: Type -> Type Source Methods from :: Endo a -> Rep (Endo a) x Source to :: Rep (Endo a) x -> Endo a Source
Semigroup (Endo a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Endo a -> Endo a -> Endo a Source sconcat :: NonEmpty (Endo a) -> Endo a Source stimes :: Integral b => b -> Endo a -> Endo a Source
Monoid (Endo a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
type Rep (Endo a)
Instance details 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))))

Bool wrappers

newtype All Source

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

Instances details

Bounded All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: All Source maxBound :: All Source
Eq All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: All -> All -> Bool Source (/=) :: All -> All -> Bool Source
Data All	Since: base-4.8.0.0
Instance details 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 Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source toConstr :: All -> Constr Source dataTypeOf :: All -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source gmapT :: (forall b. Data b => b -> b) -> All -> All Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source
Ord All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: All -> All -> Ordering Source (<) :: All -> All -> Bool Source (<=) :: All -> All -> Bool Source (>) :: All -> All -> Bool Source (>=) :: All -> All -> Bool Source max :: All -> All -> All Source min :: All -> All -> All Source
Read All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS All Source readList :: ReadS [All] Source readPrec :: ReadPrec All Source readListPrec :: ReadPrec [All] Source
Show All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> All -> ShowS Source show :: All -> String Source showList :: [All] -> ShowS Source
Generic All	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep All :: Type -> Type Source Methods from :: All -> Rep All x Source to :: Rep All x -> All Source
Semigroup All	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Monoid All	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
type Rep All
Instance details Defined in Data.Semigroup.Internal type Rep All = D1 ('MetaData "All" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Any Source

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

Instances details

Bounded Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Any Source maxBound :: Any Source
Eq Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Any -> Any -> Bool Source (/=) :: Any -> Any -> Bool Source
Data Any	Since: base-4.8.0.0
Instance details 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 Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source toConstr :: Any -> Constr Source dataTypeOf :: Any -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source
Ord Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Any -> Any -> Ordering Source (<) :: Any -> Any -> Bool Source (<=) :: Any -> Any -> Bool Source (>) :: Any -> Any -> Bool Source (>=) :: Any -> Any -> Bool Source max :: Any -> Any -> Any Source min :: Any -> Any -> Any Source
Read Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS Any Source readList :: ReadS [Any] Source readPrec :: ReadPrec Any Source readListPrec :: ReadPrec [Any] Source
Show Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Any -> ShowS Source show :: Any -> String Source showList :: [Any] -> ShowS Source
Generic Any	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep Any :: Type -> Type Source Methods from :: Any -> Rep Any x Source to :: Rep Any x -> Any Source
Semigroup Any	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Monoid Any	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
type Rep Any
Instance details 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)))

Num wrappers

newtype Sum a Source

Monoid under addition.

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

Constructors

Sum
Fields getSum :: a

Instances

Instances details

Monad Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source (>>) :: Sum a -> Sum b -> Sum b Source return :: a -> Sum a Source
Functor Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
MonadFix Sum	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Sum a) -> Sum a Source
Applicative Sum	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Sum a Source (<>) :: Sum (a -> b) -> Sum a -> Sum b Source liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source (>) :: Sum a -> Sum b -> Sum b Source (<*) :: Sum a -> Sum b -> Sum a Source
Foldable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m Source foldMap :: Monoid m => (a -> m) -> Sum a -> m Source foldMap' :: Monoid m => (a -> m) -> Sum a -> m Source foldr :: (a -> b -> b) -> b -> Sum a -> b Source foldr' :: (a -> b -> b) -> b -> Sum a -> b Source foldl :: (b -> a -> b) -> b -> Sum a -> b Source foldl' :: (b -> a -> b) -> b -> Sum a -> b Source foldr1 :: (a -> a -> a) -> Sum a -> a Source foldl1 :: (a -> a -> a) -> Sum a -> a Source toList :: Sum a -> [a] Source null :: Sum a -> Bool Source length :: Sum a -> Int Source elem :: Eq a => a -> Sum a -> Bool Source maximum :: Ord a => Sum a -> a Source minimum :: Ord a => Sum a -> a Source sum :: Num a => Sum a -> a Source product :: Num a => Sum a -> a Source
Traversable Sum	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source sequence :: Monad m => Sum (m a) -> m (Sum a) Source
MonadZip Sum	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Sum a -> Sum b -> Sum (a, b) Source mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source munzip :: Sum (a, b) -> (Sum a, Sum b) Source
Bounded a => Bounded (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Sum a Source maxBound :: Sum a Source
Eq a => Eq (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Sum a -> Sum a -> Bool Source (/=) :: Sum a -> Sum a -> Bool Source
Data a => Data (Sum a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source toConstr :: Sum a -> Constr Source dataTypeOf :: Sum a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source
Num a => Num (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Sum a -> Sum a -> Sum a Source (-) :: Sum a -> Sum a -> Sum a Source (*) :: Sum a -> Sum a -> Sum a Source negate :: Sum a -> Sum a Source abs :: Sum a -> Sum a Source signum :: Sum a -> Sum a Source fromInteger :: Integer -> Sum a Source
Ord a => Ord (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Sum a -> Sum a -> Ordering Source (<) :: Sum a -> Sum a -> Bool Source (<=) :: Sum a -> Sum a -> Bool Source (>) :: Sum a -> Sum a -> Bool Source (>=) :: Sum a -> Sum a -> Bool Source max :: Sum a -> Sum a -> Sum a Source min :: Sum a -> Sum a -> Sum a Source
Read a => Read (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Sum a) Source readList :: ReadS [Sum a] Source readPrec :: ReadPrec (Sum a) Source readListPrec :: ReadPrec [Sum a] Source
Show a => Show (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Sum a -> ShowS Source show :: Sum a -> String Source showList :: [Sum a] -> ShowS Source
Generic (Sum a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Sum a) :: Type -> Type Source Methods from :: Sum a -> Rep (Sum a) x Source to :: Rep (Sum a) x -> Sum a Source
Num a => Semigroup (Sum a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Sum a -> Sum a -> Sum a Source sconcat :: NonEmpty (Sum a) -> Sum a Source stimes :: Integral b => b -> Sum a -> Sum a Source
Num a => Monoid (Sum a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Generic1 Sum	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Sum :: k -> Type Source Methods from1 :: forall (a :: k). Sum a -> Rep1 Sum a Source to1 :: forall (a :: k). Rep1 Sum a -> Sum a Source
type Rep (Sum a)
Instance details 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
Instance details 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 Source

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Instances details

Monad Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source (>>) :: Product a -> Product b -> Product b Source return :: a -> Product a Source
Functor Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
MonadFix Product	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a Source
Applicative Product	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a Source (<>) :: Product (a -> b) -> Product a -> Product b Source liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source (>) :: Product a -> Product b -> Product b Source (<*) :: Product a -> Product b -> Product a Source
Foldable Product	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m Source foldMap :: Monoid m => (a -> m) -> Product a -> m Source foldMap' :: Monoid m => (a -> m) -> Product a -> m Source foldr :: (a -> b -> b) -> b -> Product a -> b Source foldr' :: (a -> b -> b) -> b -> Product a -> b Source foldl :: (b -> a -> b) -> b -> Product a -> b Source foldl' :: (b -> a -> b) -> b -> Product a -> b Source foldr1 :: (a -> a -> a) -> Product a -> a Source foldl1 :: (a -> a -> a) -> Product a -> a Source toList :: Product a -> [a] Source null :: Product a -> Bool Source length :: Product a -> Int Source elem :: Eq a => a -> Product a -> Bool Source maximum :: Ord a => Product a -> a Source minimum :: Ord a => Product a -> a Source sum :: Num a => Product a -> a Source product :: Num a => Product a -> a Source
Traversable Product	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source sequenceA :: Applicative f => Product (f a) -> f (Product a) Source mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source sequence :: Monad m => Product (m a) -> m (Product a) Source
MonadZip Product	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Product a -> Product b -> Product (a, b) Source mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source munzip :: Product (a, b) -> (Product a, Product b) Source
Bounded a => Bounded (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a Source maxBound :: Product a Source
Eq a => Eq (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Product a -> Product a -> Bool Source (/=) :: Product a -> Product a -> Bool Source
Data a => Data (Product a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source toConstr :: Product a -> Constr Source dataTypeOf :: Product a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source
Num a => Num (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a Source (-) :: Product a -> Product a -> Product a Source (*) :: Product a -> Product a -> Product a Source negate :: Product a -> Product a Source abs :: Product a -> Product a Source signum :: Product a -> Product a Source fromInteger :: Integer -> Product a Source
Ord a => Ord (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods compare :: Product a -> Product a -> Ordering Source (<) :: Product a -> Product a -> Bool Source (<=) :: Product a -> Product a -> Bool Source (>) :: Product a -> Product a -> Bool Source (>=) :: Product a -> Product a -> Bool Source max :: Product a -> Product a -> Product a Source min :: Product a -> Product a -> Product a Source
Read a => Read (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Product a) Source readList :: ReadS [Product a] Source readPrec :: ReadPrec (Product a) Source readListPrec :: ReadPrec [Product a] Source
Show a => Show (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS Source show :: Product a -> String Source showList :: [Product a] -> ShowS Source
Generic (Product a)	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Product a) :: Type -> Type Source Methods from :: Product a -> Rep (Product a) x Source to :: Rep (Product a) x -> Product a Source
Num a => Semigroup (Product a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a Source sconcat :: NonEmpty (Product a) -> Product a Source stimes :: Integral b => b -> Product a -> Product a Source
Num a => Monoid (Product a)	Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Generic1 Product	Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type Source Methods from1 :: forall (a :: k). Product a -> Rep1 Product a Source to1 :: forall (a :: k). Rep1 Product a -> Product a Source
type Rep (Product a)
Instance details 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
Instance details 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))

Maybe wrappers

To implement find or findLast on any Foldable:

findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a
findLast pred = getLast . foldMap (x -> if pred x
                                           then Last (Just x)
                                           else Last Nothing)

Much of Maps interface can be implemented with alter. Some of the rest can be implemented with a new alterF function and either First or Last:

alterF :: (Functor f, Ord k) =>
          (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

instance Monoid a => Functor ((,) a)  -- from Data.Functor

insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
                    -> Map k v -> (Maybe v, Map k v)
insertLookupWithKey combine key value =
  Arrow.first getFirst . alterF doChange key
  where
  doChange Nothing = (First Nothing, Just value)
  doChange (Just oldValue) =
    (First (Just oldValue),
     Just (combine key value oldValue))

newtype First a Source

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"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.First x === Maybe (Data.Semigroup.First x)

In addition to being equivalent in the structural sense, the two also have Monoid instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in Maybe.

Constructors

First
Fields getFirst :: Maybe a

Instances

Instances details

Monad First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: First a -> (a -> First b) -> First b Source (>>) :: First a -> First b -> First b Source return :: a -> First a Source
Functor First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> First a -> First b Source (<$) :: a -> First b -> First a Source
MonadFix First	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> First a) -> First a Source
Applicative First	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> First a Source (<>) :: First (a -> b) -> First a -> First b Source liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source (>) :: First a -> First b -> First b Source (<*) :: First a -> First b -> First a Source
Foldable First	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => First m -> m Source foldMap :: Monoid m => (a -> m) -> First a -> m Source foldMap' :: Monoid m => (a -> m) -> First a -> m Source foldr :: (a -> b -> b) -> b -> First a -> b Source foldr' :: (a -> b -> b) -> b -> First a -> b Source foldl :: (b -> a -> b) -> b -> First a -> b Source foldl' :: (b -> a -> b) -> b -> First a -> b Source foldr1 :: (a -> a -> a) -> First a -> a Source foldl1 :: (a -> a -> a) -> First a -> a Source toList :: First a -> [a] Source null :: First a -> Bool Source length :: First a -> Int Source elem :: Eq a => a -> First a -> Bool Source maximum :: Ord a => First a -> a Source minimum :: Ord a => First a -> a Source sum :: Num a => First a -> a Source product :: Num a => First a -> a Source
Traversable First	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source sequenceA :: Applicative f => First (f a) -> f (First a) Source mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source sequence :: Monad m => First (m a) -> m (First a) Source
MonadZip First	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: First a -> First b -> First (a, b) Source mzipWith :: (a -> b -> c) -> First a -> First b -> First c Source munzip :: First (a, b) -> (First a, First b) Source
Eq a => Eq (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: First a -> First a -> Bool Source (/=) :: First a -> First a -> Bool Source
Data a => Data (First a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source toConstr :: First a -> Constr Source dataTypeOf :: First a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source
Ord a => Ord (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: First a -> First a -> Ordering Source (<) :: First a -> First a -> Bool Source (<=) :: First a -> First a -> Bool Source (>) :: First a -> First a -> Bool Source (>=) :: First a -> First a -> Bool Source max :: First a -> First a -> First a Source min :: First a -> First a -> First a Source
Read a => Read (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (First a) Source readList :: ReadS [First a] Source readPrec :: ReadPrec (First a) Source readListPrec :: ReadPrec [First a] Source
Show a => Show (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> First a -> ShowS Source show :: First a -> String Source showList :: [First a] -> ShowS Source
Generic (First a)	Since: base-4.7.0.0
Instance details Defined in Data.Monoid Associated Types type Rep (First a) :: Type -> Type Source Methods from :: First a -> Rep (First a) x Source to :: Rep (First a) x -> First a Source
Semigroup (First a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: First a -> First a -> First a Source sconcat :: NonEmpty (First a) -> First a Source stimes :: Integral b => b -> First a -> First a Source
Monoid (First a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Generic1 First	Since: base-4.7.0.0
Instance details Defined in Data.Monoid Associated Types type Rep1 First :: k -> Type Source Methods from1 :: forall (a :: k). First a -> Rep1 First a Source to1 :: forall (a :: k). Rep1 First a -> First a Source
type Rep (First a)
Instance details 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
Instance details Defined in Data.Monoid type Rep1 First = D1 ('MetaData "First" "Data.Monoid" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

newtype Last a Source

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"

Use of this type is discouraged. Note the following equivalence:

Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)

Constructors

Last
Fields getLast :: Maybe a

Instances

Instances details

Monad Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source (>>) :: Last a -> Last b -> Last b Source return :: a -> Last a Source
Functor Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Last a -> Last b Source (<$) :: a -> Last b -> Last a Source
MonadFix Last	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Last a) -> Last a Source
Applicative Last	Since: base-4.8.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Last a Source (<>) :: Last (a -> b) -> Last a -> Last b Source liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source (>) :: Last a -> Last b -> Last b Source (<*) :: Last a -> Last b -> Last a Source
Foldable Last	Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Last m -> m Source foldMap :: Monoid m => (a -> m) -> Last a -> m Source foldMap' :: Monoid m => (a -> m) -> Last a -> m Source foldr :: (a -> b -> b) -> b -> Last a -> b Source foldr' :: (a -> b -> b) -> b -> Last a -> b Source foldl :: (b -> a -> b) -> b -> Last a -> b Source foldl' :: (b -> a -> b) -> b -> Last a -> b Source foldr1 :: (a -> a -> a) -> Last a -> a Source foldl1 :: (a -> a -> a) -> Last a -> a Source toList :: Last a -> [a] Source null :: Last a -> Bool Source length :: Last a -> Int Source elem :: Eq a => a -> Last a -> Bool Source maximum :: Ord a => Last a -> a Source minimum :: Ord a => Last a -> a Source sum :: Num a => Last a -> a Source product :: Num a => Last a -> a Source
Traversable Last	Since: base-4.8.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source sequenceA :: Applicative f => Last (f a) -> f (Last a) Source mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source sequence :: Monad m => Last (m a) -> m (Last a) Source
MonadZip Last	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Last a -> Last b -> Last (a, b) Source mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c Source munzip :: Last (a, b) -> (Last a, Last b) Source
Eq a => Eq (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods (==) :: Last a -> Last a -> Bool Source (/=) :: Last a -> Last a -> Bool Source
Data a => Data (Last a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source toConstr :: Last a -> Constr Source dataTypeOf :: Last a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source
Ord a => Ord (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods compare :: Last a -> Last a -> Ordering Source (<) :: Last a -> Last a -> Bool Source (<=) :: Last a -> Last a -> Bool Source (>) :: Last a -> Last a -> Bool Source (>=) :: Last a -> Last a -> Bool Source max :: Last a -> Last a -> Last a Source min :: Last a -> Last a -> Last a Source
Read a => Read (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Last a) Source readList :: ReadS [Last a] Source readPrec :: ReadPrec (Last a) Source readListPrec :: ReadPrec [Last a] Source
Show a => Show (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Last a -> ShowS Source show :: Last a -> String Source showList :: [Last a] -> ShowS Source
Generic (Last a)	Since: base-4.7.0.0
Instance details Defined in Data.Monoid Associated Types type Rep (Last a) :: Type -> Type Source Methods from :: Last a -> Rep (Last a) x Source to :: Rep (Last a) x -> Last a Source
Semigroup (Last a)	Since: base-4.9.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Last a -> Last a -> Last a Source sconcat :: NonEmpty (Last a) -> Last a Source stimes :: Integral b => b -> Last a -> Last a Source
Monoid (Last a)	Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Generic1 Last	Since: base-4.7.0.0
Instance details Defined in Data.Monoid Associated Types type Rep1 Last :: k -> Type Source Methods from1 :: forall (a :: k). Last a -> Rep1 Last a Source to1 :: forall (a :: k). Rep1 Last a -> Last a Source
type Rep (Last a)
Instance details 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
Instance details 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)))

Alternative wrapper

newtype Alt f a Source

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

Instances details

Generic1 (Alt f :: k -> Type)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 (Alt f) :: k -> Type Source Methods from1 :: forall (a :: k0). Alt f a -> Rep1 (Alt f) a Source to1 :: forall (a :: k0). Rep1 (Alt f) a -> Alt f a Source
Monad f => Monad (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Alt f a -> (a -> Alt f b) -> Alt f b Source (>>) :: Alt f a -> Alt f b -> Alt f b Source return :: a -> Alt f a Source
Functor f => Functor (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Alt f a -> Alt f b Source (<$) :: a -> Alt f b -> Alt f a Source
MonadFix f => MonadFix (Alt f)	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Alt f a) -> Alt f a Source
Applicative f => Applicative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Alt f a Source (<>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source (>) :: Alt f a -> Alt f b -> Alt f b Source (<*) :: Alt f a -> Alt f b -> Alt f a Source
Foldable f => Foldable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Alt f m -> m Source foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source foldMap' :: Monoid m => (a -> m) -> Alt f a -> m Source foldr :: (a -> b -> b) -> b -> Alt f a -> b Source foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source foldl :: (b -> a -> b) -> b -> Alt f a -> b Source foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source foldr1 :: (a -> a -> a) -> Alt f a -> a Source foldl1 :: (a -> a -> a) -> Alt f a -> a Source toList :: Alt f a -> [a] Source null :: Alt f a -> Bool Source length :: Alt f a -> Int Source elem :: Eq a => a -> Alt f a -> Bool Source maximum :: Ord a => Alt f a -> a Source minimum :: Ord a => Alt f a -> a Source sum :: Num a => Alt f a -> a Source product :: Num a => Alt f a -> a Source
Traversable f => Traversable (Alt f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source
MonadPlus f => MonadPlus (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a Source mplus :: Alt f a -> Alt f a -> Alt f a Source
Alternative f => Alternative (Alt f)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods empty :: Alt f a Source (<\|>) :: Alt f a -> Alt f a -> Alt f a Source some :: Alt f a -> Alt f [a] Source many :: Alt f a -> Alt f [a] Source
MonadZip f => MonadZip (Alt f)	Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Alt f a -> Alt f b -> Alt f (a, b) Source mzipWith :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source munzip :: Alt f (a, b) -> (Alt f a, Alt f b) Source
Contravariant f => Contravariant (Alt f)
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a Source (>$) :: b -> Alt f b -> Alt f a Source
Enum (f a) => Enum (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods succ :: Alt f a -> Alt f a Source pred :: Alt f a -> Alt f a Source toEnum :: Int -> Alt f a Source fromEnum :: Alt f a -> Int Source enumFrom :: Alt f a -> [Alt f a] Source enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source
Eq (f a) => Eq (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (==) :: Alt f a -> Alt f a -> Bool Source (/=) :: Alt f a -> Alt f a -> Bool Source
(Data (f a), Data a, Typeable f) => Data (Alt f a)	Since: base-4.8.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) Source toConstr :: Alt f a -> Constr Source dataTypeOf :: Alt f a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) Source gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source
Num (f a) => Num (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a Source (-) :: Alt f a -> Alt f a -> Alt f a Source (*) :: Alt f a -> Alt f a -> Alt f a Source negate :: Alt f a -> Alt f a Source abs :: Alt f a -> Alt f a Source signum :: Alt f a -> Alt f a Source fromInteger :: Integer -> Alt f a Source
Ord (f a) => Ord (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods compare :: Alt f a -> Alt f a -> Ordering Source (<) :: Alt f a -> Alt f a -> Bool Source (<=) :: Alt f a -> Alt f a -> Bool Source (>) :: Alt f a -> Alt f a -> Bool Source (>=) :: Alt f a -> Alt f a -> Bool Source max :: Alt f a -> Alt f a -> Alt f a Source min :: Alt f a -> Alt f a -> Alt f a Source
Read (f a) => Read (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods readsPrec :: Int -> ReadS (Alt f a) Source readList :: ReadS [Alt f a] Source readPrec :: ReadPrec (Alt f a) Source readListPrec :: ReadPrec [Alt f a] Source
Show (f a) => Show (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS Source show :: Alt f a -> String Source showList :: [Alt f a] -> ShowS Source
Generic (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep (Alt f a) :: Type -> Type Source Methods from :: Alt f a -> Rep (Alt f a) x Source to :: Rep (Alt f a) x -> Alt f a Source
Alternative f => Semigroup (Alt f a)	Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Alt f a -> Alt f a -> Alt f a Source sconcat :: NonEmpty (Alt f a) -> Alt f a Source stimes :: Integral b => b -> Alt f a -> Alt f a Source
Alternative f => Monoid (Alt f a)	Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a Source mappend :: Alt f a -> Alt f a -> Alt f a Source mconcat :: [Alt f a] -> Alt f a Source
type Rep1 (Alt f :: k -> Type)
Instance details 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)
Instance details 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))))

Applicative wrapper

newtype Ap f a Source

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

Instances details

Generic1 (Ap f :: k -> Type)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Associated Types type Rep1 (Ap f) :: k -> Type Source Methods from1 :: forall (a :: k0). Ap f a -> Rep1 (Ap f) a Source to1 :: forall (a :: k0). Rep1 (Ap f) a -> Ap f a Source
Monad f => Monad (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source (>>) :: Ap f a -> Ap f b -> Ap f b Source return :: a -> Ap f a Source
Functor f => Functor (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fmap :: (a -> b) -> Ap f a -> Ap f b Source (<$) :: a -> Ap f b -> Ap f a Source
MonadFix f => MonadFix (Ap f)	Since: base-4.12.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Ap f a) -> Ap f a Source
MonadFail f => MonadFail (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fail :: String -> Ap f a Source
Applicative f => Applicative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods pure :: a -> Ap f a Source (<>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source (>) :: Ap f a -> Ap f b -> Ap f b Source (<*) :: Ap f a -> Ap f b -> Ap f a Source
Foldable f => Foldable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Ap f m -> m Source foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source foldMap' :: Monoid m => (a -> m) -> Ap f a -> m Source foldr :: (a -> b -> b) -> b -> Ap f a -> b Source foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source foldl :: (b -> a -> b) -> b -> Ap f a -> b Source foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source foldr1 :: (a -> a -> a) -> Ap f a -> a Source foldl1 :: (a -> a -> a) -> Ap f a -> a Source toList :: Ap f a -> [a] Source null :: Ap f a -> Bool Source length :: Ap f a -> Int Source elem :: Eq a => a -> Ap f a -> Bool Source maximum :: Ord a => Ap f a -> a Source minimum :: Ord a => Ap f a -> a Source sum :: Num a => Ap f a -> a Source product :: Num a => Ap f a -> a Source
Traversable f => Traversable (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Traversable Methods traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source
MonadPlus f => MonadPlus (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a Source mplus :: Ap f a -> Ap f a -> Ap f a Source
Alternative f => Alternative (Ap f)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods empty :: Ap f a Source (<\|>) :: Ap f a -> Ap f a -> Ap f a Source some :: Ap f a -> Ap f [a] Source many :: Ap f a -> Ap f [a] Source
(Applicative f, Bounded a) => Bounded (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods minBound :: Ap f a Source maxBound :: Ap f a Source
Enum (f a) => Enum (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods succ :: Ap f a -> Ap f a Source pred :: Ap f a -> Ap f a Source toEnum :: Int -> Ap f a Source fromEnum :: Ap f a -> Int Source enumFrom :: Ap f a -> [Ap f a] Source enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source
Eq (f a) => Eq (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (==) :: Ap f a -> Ap f a -> Bool Source (/=) :: Ap f a -> Ap f a -> Bool Source
(Data (f a), Data a, Typeable f) => Data (Ap f a)	Since: base-4.12.0.0
Instance details 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) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) Source toConstr :: Ap f a -> Constr Source dataTypeOf :: Ap f a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Ap f a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Ap f a)) Source gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source
(Applicative f, Num a) => Num (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (+) :: Ap f a -> Ap f a -> Ap f a Source (-) :: Ap f a -> Ap f a -> Ap f a Source (*) :: Ap f a -> Ap f a -> Ap f a Source negate :: Ap f a -> Ap f a Source abs :: Ap f a -> Ap f a Source signum :: Ap f a -> Ap f a Source fromInteger :: Integer -> Ap f a Source
Ord (f a) => Ord (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods compare :: Ap f a -> Ap f a -> Ordering Source (<) :: Ap f a -> Ap f a -> Bool Source (<=) :: Ap f a -> Ap f a -> Bool Source (>) :: Ap f a -> Ap f a -> Bool Source (>=) :: Ap f a -> Ap f a -> Bool Source max :: Ap f a -> Ap f a -> Ap f a Source min :: Ap f a -> Ap f a -> Ap f a Source
Read (f a) => Read (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods readsPrec :: Int -> ReadS (Ap f a) Source readList :: ReadS [Ap f a] Source readPrec :: ReadPrec (Ap f a) Source readListPrec :: ReadPrec [Ap f a] Source
Show (f a) => Show (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS Source show :: Ap f a -> String Source showList :: [Ap f a] -> ShowS Source
Generic (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Associated Types type Rep (Ap f a) :: Type -> Type Source Methods from :: Ap f a -> Rep (Ap f a) x Source to :: Rep (Ap f a) x -> Ap f a Source
(Applicative f, Semigroup a) => Semigroup (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods (<>) :: Ap f a -> Ap f a -> Ap f a Source sconcat :: NonEmpty (Ap f a) -> Ap f a Source stimes :: Integral b => b -> Ap f a -> Ap f a Source
(Applicative f, Monoid a) => Monoid (Ap f a)	Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mempty :: Ap f a Source mappend :: Ap f a -> Ap f a -> Ap f a Source mconcat :: [Ap f a] -> Ap f a Source
type Rep1 (Ap f :: k -> Type)
Instance details 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)
Instance details 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))))

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.10.2/docs/html/libraries/base-4.14.1.0/Data-Monoid.html

Data.Monoid

Contents

Description

Examples

Monoid typeclass

Minimal complete definition

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Bool wrappers