Data.Monoid

base-4.12.0.0: Basic libraries

Copyright | (c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001
License | BSD-style (see the file libraries/base/LICENSE)
Maintainer | libraries@haskell.org
Stability | experimental
Portability | portable
Safe Haskell | Trustworthy
Language | Haskell2010

Data.Monoid

Contents

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

Description

A class for monoids (types with an associative binary operation that has an identity) with various general-purpose instances.

Synopsis

- class Semigroup a => Monoid a where
  - mempty :: a
  - mappend :: a -> a -> a
  - mconcat :: [a] -> a
- (<>) :: Semigroup a => a -> a -> a
- newtype Dual a = Dual {
  - getDual :: a
  }
- newtype Endo a = Endo {
  - appEndo :: a -> a
  }
- newtype All = All {
  - getAll :: Bool
  }
- newtype Any = Any {
  - getAny :: Bool
  }
- newtype Sum a = Sum {
  - getSum :: a
  }
- newtype Product a = Product {
  - getProduct :: a
  }
- newtype First a = First {
  - getFirst :: Maybe a
  }
- newtype Last a = Last {
  - getLast :: Maybe a
  }
- newtype Alt f a = Alt {
  - getAlt :: f a
  }
- newtype Ap f a = Ap {
  - getAp :: f a
  }

# `Monoid` typeclass

class Semigroup a => Monoid a where #

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

-     x <> mempty = x

-     mempty <> x = x

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

-     mconcat = foldr '(<>)' mempty

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a #

Identity of `mappend`

mappend :: a -> a -> a #

An associative operation

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

mconcat :: [a] -> a #

Fold a list using the monoid.

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

Instances

Monoid Ordering # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering # mappend :: Ordering -> Ordering -> Ordering # mconcat :: [Ordering] -> Ordering #
Monoid () # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () # mappend :: () -> () -> () # mconcat :: [()] -> () #
Monoid Any # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Any # mappend :: Any -> Any -> Any # mconcat :: [Any] -> Any #
Monoid All # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: All # mappend :: All -> All -> All # mconcat :: [All] -> All #
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 # mappend :: Lifetime -> Lifetime -> Lifetime # mconcat :: [Lifetime] -> Lifetime #
Monoid Event # | Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal Methods mempty :: Event # mappend :: Event -> Event -> Event # mconcat :: [Event] -> Event #
Monoid [a] # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] # mappend :: [a] -> [a] -> [a] # mconcat :: [[a]] -> [a] #
Semigroup a => Monoid (Maybe a) # | Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `e*e = e` and `e*s = s = s*e` for all `s ∈ S`." Since 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Maybe a # mappend :: Maybe a -> Maybe a -> Maybe a # mconcat :: [Maybe a] -> Maybe a #
Monoid a => Monoid (IO a) # | Since: base-4.9.0.0
Instance details Defined in GHC.Base Methods mempty :: IO a # mappend :: IO a -> IO a -> IO a # mconcat :: [IO a] -> IO a #
Monoid p => Monoid (Par1 p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: Par1 p # mappend :: Par1 p -> Par1 p -> Par1 p # mconcat :: [Par1 p] -> Par1 p #
Monoid a => Monoid (Down a) # | Since: base-4.11.0.0
Instance details Defined in Data.Ord Methods mempty :: Down a # mappend :: Down a -> Down a -> Down a # mconcat :: [Down a] -> Down a #
Num a => Monoid (Product a) # | Since: base-2.1
Instance details 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
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
Monoid (Endo a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Endo a # mappend :: Endo a -> Endo a -> Endo a # mconcat :: [Endo a] -> Endo a #
Monoid a => Monoid (Dual a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Dual a # mappend :: Dual a -> Dual a -> Dual a # mconcat :: [Dual a] -> Dual a #
Monoid (Last a) # | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: Last a # mappend :: Last a -> Last a -> Last a # mconcat :: [Last a] -> Last a #
Monoid (First a) # | Since: base-2.1
Instance details Defined in Data.Monoid Methods mempty :: First a # mappend :: First a -> First a -> First a # mconcat :: [First a] -> First a #
Monoid a => Monoid (Identity a) # | Since: base-4.9.0.0
Instance details Defined in Data.Functor.Identity Methods mempty :: Identity a # mappend :: Identity a -> Identity a -> Identity a # mconcat :: [Identity a] -> Identity a #
Semigroup a => Monoid (Option a) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: Option a # mappend :: Option a -> Option a -> Option a # mconcat :: [Option a] -> Option a #
Monoid m => Monoid (WrappedMonoid m) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup Methods mempty :: WrappedMonoid m # mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # mconcat :: [WrappedMonoid m] -> WrappedMonoid m #
(Ord a, Bounded a) => Monoid (Max a) # | Since: base-4.9.0.0
Instance details 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
Instance details Defined in Data.Semigroup Methods mempty :: Min a # mappend :: Min a -> Min a -> Min a # mconcat :: [Min a] -> Min a #
Monoid (Equivalence a) # |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Equivalence a # mappend :: Equivalence a -> Equivalence a -> Equivalence a # mconcat :: [Equivalence a] -> Equivalence a #
Monoid (Comparison a) # |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Comparison a # mappend :: Comparison a -> Comparison a -> Comparison a # mconcat :: [Comparison a] -> Comparison a #
Monoid (Predicate a) # |
Instance details Defined in Data.Functor.Contravariant Methods mempty :: Predicate a # mappend :: Predicate a -> Predicate a -> Predicate a # mconcat :: [Predicate a] -> Predicate a #
Monoid b => Monoid (a -> b) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: a -> b # mappend :: (a -> b) -> (a -> b) -> a -> b # mconcat :: [a -> b] -> a -> b #
Monoid (U1 p) # | Since: base-4.12.0.0
Instance details Defined in GHC.Generics Methods mempty :: U1 p # mappend :: U1 p -> U1 p -> U1 p # mconcat :: [U1 p] -> U1 p #
(Monoid a, Monoid b) => Monoid (a, b) # | Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: (a, b) # mappend :: (a, b) -> (a, b) -> (a, b) # mconcat :: [(a, b)] -> (a, b) #
Monoid a => Monoid (ST s a) # | Since: base-4.11.0.0
Instance details Defined in GHC.ST Methods mempty :: ST s a # mappend :: ST s a -> ST s a -> ST s a # mconcat :: [ST s a] -> ST s a #
Monoid (Proxy s) # | Since: base-4.7.0.0
Instance details Defined in Data.Proxy Methods mempty :: Proxy s # mappend :: Proxy s -> Proxy s -> Proxy s # mconcat :: [Proxy s] -> Proxy s #
Monoid a => Monoid (Op a b) # |
Instance details 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 (f p) => Monoid (Rec1 f p) # | Since: base-4.12.0.0
Instance details 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
Instance details 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) #
Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0
Instance details 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 #
(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 # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
Monoid a => Monoid (Const a b) # | Since: base-4.9.0.0
Instance details 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 #
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 # mappend :: K1 i c p -> K1 i c p -> K1 i c p # mconcat :: [K1 i c p] -> K1 i c p #
(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 # mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p # mconcat :: [(f :*: g) p] -> (f :*: g) p #
(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) # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) # mconcat :: [(a, b, c, d)] -> (a, b, c, d) #
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 # 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 (f (g p)) => Monoid ((f :.: g) p) # | Since: base-4.12.0.0
Instance details 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 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) # 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) #

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

An associative operation.

newtype Dual a #

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

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

Constructors

Dual |
Fields getDual :: a

Instances

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

The monoid of endomorphisms under composition.

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

Constructors

Endo |
Fields appEndo :: a -> a

Instances

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

Boolean monoid under conjunction (`&&`).

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

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

Constructors

All |
Fields getAll :: Bool

Instances

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

Boolean monoid under disjunction (`||`).

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

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

Constructors

Any |
Fields getAny :: Bool

Instances

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

Monoid under addition.

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

Constructors

Sum |
Fields getSum :: a

Instances

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

Monoid under multiplication.

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

Constructors

Product |
Fields getProduct :: a

Instances

Monad Product # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (>>=) :: Product a -> (a -> Product b) -> Product b # (>>) :: Product a -> Product b -> Product b # return :: a -> Product a # fail :: String -> Product a #
Functor Product # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods fmap :: (a -> b) -> Product a -> Product b # (<$) :: a -> Product b -> Product a #
MonadFix Product # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Fix Methods mfix :: (a -> Product a) -> Product a #
Applicative Product # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods pure :: a -> Product a # (<*>) :: Product (a -> b) -> Product a -> Product b # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c # (*>) :: Product a -> Product b -> Product b # (<*) :: Product a -> Product b -> Product a #
Foldable Product # | Since: base-4.8.0.0
Instance details Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # toList :: Product a -> [a] # null :: Product a -> Bool # length :: Product a -> Int # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # sum :: Num a => Product a -> a # product :: Num a => Product a -> a #
Traversable Product # | Since: base-4.8.0.0
Instance details 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) #
MonadZip Product # | Since: base-4.8.0.0
Instance details Defined in Control.Monad.Zip Methods mzip :: Product a -> Product b -> Product (a, b) # mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c # munzip :: Product (a, b) -> (Product a, Product b) #
Bounded a => Bounded (Product a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods minBound :: Product a # maxBound :: Product a #
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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) # toConstr :: Product a -> Constr # dataTypeOf :: Product a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #
Num a => Num (Product a) # | Since: base-4.7.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Product a -> Product a -> Product a # (-) :: Product a -> Product a -> Product a # (*) :: Product a -> Product a -> Product a # negate :: Product a -> Product a # abs :: Product a -> Product a # signum :: Product a -> Product a # fromInteger :: Integer -> Product a #
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) # readList :: ReadS [Product a] # readPrec :: ReadPrec (Product a) # readListPrec :: ReadPrec [Product a] #
Show a => Show (Product a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Product a -> ShowS # show :: Product a -> String # showList :: [Product a] -> ShowS #
Generic (Product a) # |
Instance details 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 => Semigroup (Product a) # | Since: base-4.9.0.0
Instance details Defined in Data.Semigroup.Internal Methods (<>) :: Product a -> Product a -> Product a # sconcat :: NonEmpty (Product a) -> Product a # stimes :: Integral b => b -> Product a -> Product a #
Num a => Monoid (Product a) # | Since: base-2.1
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Product a # mappend :: Product a -> Product a -> Product a # mconcat :: [Product a] -> Product a #
Generic1 Product # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 Product :: k -> Type # Methods from1 :: Product a -> Rep1 Product a # to1 :: Rep1 Product a -> Product a #
type Rep (Product a) # | Since: base-4.7.0.0
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 # | Since: base-4.7.0.0
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 Data.Map's interface can be implemented with Data.Map.alter. Some of the rest can be implemented with a new `alterA` function and either `First` or `Last`:

    alterA :: (Applicative f, Ord k) =>
              (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

    instance Monoid a => Applicative ((,) a)  -- from Control.Applicative

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

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"

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

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

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)

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

Last |
Fields getLast :: Maybe a

Instances

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

Monoid under `<|>`.

Since: base-4.8.0.0

Constructors

Alt |
Fields getAlt :: f a

Instances

Generic1 (Alt f :: k -> Type) # |
Instance details Defined in Data.Semigroup.Internal Associated Types type Rep1 (Alt f) :: k -> Type # Methods from1 :: Alt f a -> Rep1 (Alt f) a # to1 :: Rep1 (Alt f) a -> Alt f a #
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 # (>>) :: Alt f a -> Alt f b -> Alt f b # return :: a -> Alt f a # fail :: String -> Alt f a #
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 # (<$) :: a -> Alt f b -> Alt f a #
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 #
Applicative f => Applicative (Alt f) # | Since: base-4.8.0.0
Instance details 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 #
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 # foldMap :: Monoid m => (a -> m) -> Alt f a -> m # foldr :: (a -> b -> b) -> b -> Alt f a -> b # foldr' :: (a -> b -> b) -> b -> Alt f a -> b # foldl :: (b -> a -> b) -> b -> Alt f a -> b # foldl' :: (b -> a -> b) -> b -> Alt f a -> b # foldr1 :: (a -> a -> a) -> Alt f a -> a # foldl1 :: (a -> a -> a) -> Alt f a -> a # toList :: Alt f a -> [a] # null :: Alt f a -> Bool # length :: Alt f a -> Int # elem :: Eq a => a -> Alt f a -> Bool # maximum :: Ord a => Alt f a -> a # minimum :: Ord a => Alt f a -> a # sum :: Num a => Alt f a -> a # product :: Num a => Alt f a -> a #
Traversable f => Traversable (Alt f) # | Since: base-4.12.0.0
Instance details 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) #
MonadPlus f => MonadPlus (Alt f) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mzero :: Alt f a # mplus :: Alt f a -> Alt f a -> Alt f a #
Alternative f => Alternative (Alt f) # | Since: base-4.8.0.0
Instance details 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] #
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) # mzipWith :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c # munzip :: Alt f (a, b) -> (Alt f a, Alt f b) #
Contravariant f => Contravariant (Alt f) # |
Instance details Defined in Data.Functor.Contravariant Methods contramap :: (a -> b) -> Alt f b -> Alt f a # (>$) :: b -> Alt f b -> Alt f a #
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 # pred :: Alt f a -> Alt f a # toEnum :: Int -> Alt f a # fromEnum :: Alt f a -> Int # enumFrom :: Alt f a -> [Alt f a] # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] #
Eq (f a) => Eq (Alt f a) # | 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) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) # toConstr :: Alt f a -> Constr # dataTypeOf :: Alt f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) # gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) #
Num (f a) => Num (Alt f a) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods (+) :: Alt f a -> Alt f a -> Alt f a # (-) :: Alt f a -> Alt f a -> Alt f a # (*) :: Alt f a -> Alt f a -> Alt f a # negate :: Alt f a -> Alt f a # abs :: Alt f a -> Alt f a # signum :: Alt f a -> Alt f a # fromInteger :: Integer -> Alt f a #
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) # 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
Instance details Defined in Data.Semigroup.Internal Methods showsPrec :: Int -> Alt f a -> ShowS # show :: Alt f a -> String # showList :: [Alt f a] -> ShowS #
Generic (Alt f a) # |
Instance details 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 #
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 # sconcat :: NonEmpty (Alt f a) -> Alt f a # stimes :: Integral b => b -> Alt f a -> Alt f a #
Alternative f => Monoid (Alt f a) # | Since: base-4.8.0.0
Instance details Defined in Data.Semigroup.Internal Methods mempty :: Alt f a # mappend :: Alt f a -> Alt f a -> Alt f a # mconcat :: [Alt f a] -> Alt f a #
type Rep1 (Alt f :: k -> Type) # | Since: base-4.8.0.0
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) # | Since: base-4.8.0.0
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 #

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) # |
Instance details Defined in Data.Monoid Associated Types type Rep1 (Ap f) :: k -> Type # Methods from1 :: Ap f a -> Rep1 (Ap f) a # to1 :: Rep1 (Ap f) a -> Ap f a #
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 # (>>) :: Ap f a -> Ap f b -> Ap f b # return :: a -> Ap f a # fail :: String -> Ap f a #
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 # (<$) :: a -> Ap f b -> Ap f a #
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 #
MonadFail f => MonadFail (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods fail :: String -> Ap f a #
Applicative f => Applicative (Ap f) # | Since: base-4.12.0.0
Instance details 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 #
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 # 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
Instance details 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) #
MonadPlus f => MonadPlus (Ap f) # | Since: base-4.12.0.0
Instance details Defined in Data.Monoid Methods mzero :: Ap f a # mplus :: Ap f a -> Ap f a -> Ap f a #
Alternative f => Alternative (Ap f) # | Since: base-4.12.0.0
Instance details 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, Bounded a) => Bounded (Ap f a) # | Since: base-4.12.0.0
Instance details 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
Instance details 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] #
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) # 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 :: (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, 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 # (-) :: 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 #
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) # 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
Instance details Defined in Data.Monoid Methods showsPrec :: Int -> Ap f a -> ShowS # show :: Ap f a -> String # showList :: [Ap f a] -> ShowS #
Generic (Ap f a) # |
Instance details 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, 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 # sconcat :: NonEmpty (Ap f a) -> Ap f a # stimes :: Integral b => b -> Ap f a -> Ap f a #
(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 # mappend :: Ap f a -> Ap f a -> Ap f a # mconcat :: [Ap f a] -> Ap f a #
type Rep1 (Ap f :: k -> Type) # | Since: base-4.12.0.0
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) # | Since: base-4.12.0.0
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))))