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	stable
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Data.Monoid

Contents

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 {getSum = 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}

Synopsis

class Semigroup a => Monoid a where
- mempty :: a
- mappend :: a -> a -> a
- mconcat :: [a] -> a
(<>) :: Semigroup a => a -> a -> a
$dm<> :: 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 :: k -> Type) (a :: k) = Alt {
- getAlt :: f a
}
newtype Ap (f :: k -> Type) (a :: k) = Ap {
- getAp :: f a
}

`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

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

Unit: mconcat (pure x) = x
Multiplication: mconcat (join xss) = mconcat (fmap mconcat xss)
Subclass: mconcat (toList xs) = sconcat xs

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

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

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

Minimal complete definition

mempty | mconcat

Methods

mempty :: a 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 ByteArray Source #	Since: base-4.17.0.0
Instance details Defined in Data.Array.Byte Methods mempty :: ByteArray Source # mappend :: ByteArray -> ByteArray -> ByteArray Source # mconcat :: [ByteArray] -> ByteArray Source #
Monoid All Source #	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 Any Source #	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 Event Source #	Since: base-4.4.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid Lifetime Source #	`mappend` takes the longer of two lifetimes. Since: base-4.8.0.0
Instance details Defined in GHC.Event.Internal.Types Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Ordering Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
FiniteBits a => Monoid (And a) Source #	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: And a Source # mappend :: And a -> And a -> And a Source # mconcat :: [And a] -> And a Source #
FiniteBits a => Monoid (Iff a) Source #	This constraint is arguably too strong. However, as some types (such as `Natural`) have undefined `complement`, this is the only safe choice. Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Iff a Source # mappend :: Iff a -> Iff a -> Iff a Source # mconcat :: [Iff a] -> Iff a Source #
Bits a => Monoid (Ior a) Source #	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Ior a Source # mappend :: Ior a -> Ior a -> Ior a Source # mconcat :: [Ior a] -> Ior a Source #
Bits a => Monoid (Xor a) Source #	Since: base-4.16
Instance details Defined in Data.Bits Methods mempty :: Xor a Source # mappend :: Xor a -> Xor a -> Xor a Source # mconcat :: [Xor a] -> Xor a Source #
Monoid (Comparison a) Source #	`mempty` on comparisons always returns `EQ`. Without newtypes this equals `pure (pure EQ)`. mempty :: Comparison a mempty = Comparison _ _ -> EQ
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 (Equivalence a) Source #	`mempty` on equivalences always returns `True`. Without newtypes this equals `pure (pure True)`. mempty :: Equivalence a mempty = Equivalence _ _ -> True
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 (Predicate a) Source #	`mempty` on predicates always returns `True`. Without newtypes this equals `pure True`. mempty :: Predicate a mempty = _ -> True
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 a => Monoid (Identity a) Source #	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 #
Monoid (First a) Source #	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 (Last a) Source #	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 a => Monoid (Down a) Source #	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 #
(Ord a, Bounded a) => Monoid (Max a) Source #	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) Source #	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 m => Monoid (WrappedMonoid m) Source #	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 #
Monoid a => Monoid (Dual a) Source #	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 (Endo a) Source #	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 #
Num a => Monoid (Product a) Source #	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) Source #	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 a => Monoid (STM a) Source #	Since: base-4.17.0.0
Instance details Defined in GHC.Conc.Sync Methods mempty :: STM a Source # mappend :: STM a -> STM a -> STM a Source # mconcat :: [STM a] -> STM a Source #
(Generic a, Monoid (Rep a ())) => Monoid (Generically a) Source #	Since: base-4.17.0.0
Instance details Defined in GHC.Generics Methods mempty :: Generically a Source # mappend :: Generically a -> Generically a -> Generically a Source # mconcat :: [Generically a] -> Generically a Source #
Monoid p => Monoid (Par1 p) Source #	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 (IO a) Source #	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 #
Semigroup a => Monoid (Maybe a) Source #	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 = se` 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 (Solo a) Source #	Since: base-4.15
Instance details Defined in GHC.Base Methods mempty :: Solo a Source # mappend :: Solo a -> Solo a -> Solo a Source # mconcat :: [Solo a] -> Solo a Source #
Monoid [a] Source #	Since: base-2.1
Instance details Defined in GHC.Base Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Monoid a => Monoid (Op a b) Source #	`mempty @(Op a b)` without newtypes is `mempty @(b->a)` = `_ -> mempty`. mempty :: Op a b mempty = Op _ -> mempty
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 (Proxy s) Source #	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 (U1 p) Source #	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 (ST s a) Source #	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 a, Monoid b) => Monoid (a, b) Source #	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 b => Monoid (a -> b) Source #	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 (Const a b) Source #	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 #
(Applicative f, Monoid a) => Monoid (Ap f a) Source #	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 #
Alternative f => Monoid (Alt f a) Source #	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 #
Monoid (f p) => Monoid (Rec1 f p) Source #	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) Source #	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 #
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a) Source #	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Product Methods mempty :: Product f g a Source # mappend :: Product f g a -> Product f g a -> Product f g a Source # mconcat :: [Product f g a] -> Product f g a Source #
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) Source #	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 c => Monoid (K1 i c p) Source #	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 a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #	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 (g a)) => Monoid (Compose f g a) Source #	Since: base-4.16.0.0
Instance details Defined in Data.Functor.Compose Methods mempty :: Compose f g a Source # mappend :: Compose f g a -> Compose f g a -> Compose f g a Source # mconcat :: [Compose f g a] -> Compose f g a Source #
Monoid (f (g p)) => Monoid ((f :.: g) p) Source #	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 (f p) => Monoid (M1 i c f p) Source #	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 a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source #	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]

$dm<> :: Semigroup a => a -> a -> a Source #

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

MonadFix Dual Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Dual a) -> Dual a Source #

MonadZip Dual Source #

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 #

Foldable Dual Source #

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 #

Foldable1 Dual Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

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

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

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

toNonEmpty :: Dual a -> NonEmpty a Source #

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

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

head :: Dual a -> a Source #

last :: Dual a -> a Source #

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

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

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

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

Traversable Dual Source #

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 #

Applicative Dual Source #

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 #

Functor Dual Source #

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 #

Monad Dual Source #

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 #

Generic1 Dual Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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))

Methods

from1 :: Dual a -> Rep1 Dual a Source #

to1 :: Rep1 Dual a -> Dual a Source #

Data a => Data (Dual a) Source #

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 #

Monoid a => Monoid (Dual a) Source #

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 #

Semigroup a => Semigroup (Dual a) Source #

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 #

Bounded a => Bounded (Dual a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a Source #

maxBound :: Dual a Source #

Generic (Dual a) Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

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

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

Read a => Read (Dual a) Source #

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) Source #

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 #

Eq a => Eq (Dual a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Dual a) Source #

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 #

type Rep1 Dual Source #

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))

type Rep (Dual a) Source #

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)))

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

Monoid (Endo a) Source #

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 #

Semigroup (Endo a) Source #

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 #

Generic (Endo a) Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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))))

Methods

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

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

type Rep (Endo a) Source #

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 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

Data All Source #

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 #

Monoid All Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: All Source #

mappend :: All -> All -> All Source #

mconcat :: [All] -> All Source #

Semigroup All Source #

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 #

Bounded All Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: All Source #

maxBound :: All Source #

Generic All Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Read All Source #

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 Source #

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 #

Eq All Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Ord All Source #

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 #

type Rep All Source #

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 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

Data Any Source #

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 #

Monoid Any Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Any Source #

mappend :: Any -> Any -> Any Source #

mconcat :: [Any] -> Any Source #

Semigroup Any Source #

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 #

Bounded Any Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Any Source #

maxBound :: Any Source #

Generic Any Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Read Any Source #

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 Source #

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 #

Eq Any Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Ord Any Source #

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 #

type Rep Any Source #

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 Source #

Monoid under addition.

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

Constructors

Sum
Fields getSum :: a

Instances

Instances details

MonadFix Sum Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Sum a) -> Sum a Source #

MonadZip Sum Source #

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 #

Foldable Sum Source #

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 #

Foldable1 Sum Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

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

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

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

toNonEmpty :: Sum a -> NonEmpty a Source #

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

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

head :: Sum a -> a Source #

last :: Sum a -> a Source #

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

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

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

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

Traversable Sum Source #

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 #

Applicative Sum Source #

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 #

Functor Sum Source #

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 #

Monad Sum Source #

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 #

Generic1 Sum Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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))

Methods

from1 :: Sum a -> Rep1 Sum a Source #

to1 :: Rep1 Sum a -> Sum a Source #

Data a => Data (Sum a) Source #

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 => Monoid (Sum a) Source #

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 #

Num a => Semigroup (Sum a) Source #

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 #

Bounded a => Bounded (Sum a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a Source #

maxBound :: Sum a Source #

Generic (Sum a) Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

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

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

Num a => Num (Sum a) Source #

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 #

Read a => Read (Sum a) Source #

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) Source #

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 #

Eq a => Eq (Sum a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Sum a) Source #

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 #

type Rep1 Sum Source #

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))

type Rep (Sum a) Source #

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)))

newtype Product a Source #

Monoid under multiplication.

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

Constructors

Product
Fields getProduct :: a

Instances

Instances details

MonadFix Product Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Product a) -> Product a Source #

MonadZip Product Source #

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 #

Foldable Product Source #

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 #

Foldable1 Product Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

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

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

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

toNonEmpty :: Product a -> NonEmpty a Source #

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

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

head :: Product a -> a Source #

last :: Product a -> a Source #

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

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

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

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

Traversable Product Source #

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 #

Applicative Product Source #

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 #

Functor Product Source #

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 #

Monad Product Source #

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 #

Generic1 Product Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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))

Methods

from1 :: Product a -> Rep1 Product a Source #

to1 :: Rep1 Product a -> Product a Source #

Data a => Data (Product a) Source #

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 => Monoid (Product a) Source #

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 => Semigroup (Product a) Source #

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 #

Bounded a => Bounded (Product a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a Source #

maxBound :: Product a Source #

Generic (Product a) Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

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

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

Num a => Num (Product a) Source #

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 #

Read a => Read (Product a) Source #

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) Source #

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 #

Eq a => Eq (Product a) Source #

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Ord a => Ord (Product a) Source #

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 #

type Rep1 Product Source #

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))

type Rep (Product a) Source #

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)))

`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"

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

Constructors

First
Fields getFirst :: Maybe a

Instances

Instances details

MonadFix First Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> First a) -> First a Source #

MonadZip First Source #

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 #

Foldable First Source #

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 Source #

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 #

Applicative First Source #

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 #

Functor First Source #

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 #

Monad First Source #

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 #

Generic1 First Source #

Instance details

Defined in Data.Monoid

Associated Types

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)))

Methods

from1 :: First a -> Rep1 First a Source #

to1 :: Rep1 First a -> First a Source #

Data a => Data (First a) Source #

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 #

Monoid (First a) Source #

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 #

Semigroup (First a) Source #

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 #

Generic (First a) Source #

Instance details

Defined in Data.Monoid

Associated Types

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))))

Methods

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

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

Read a => Read (First a) Source #

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) Source #

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 #

Eq a => Eq (First a) Source #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Ord a => Ord (First a) Source #

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 #

type Rep1 First Source #

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)))

type Rep (First a) Source #

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))))

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"

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

Constructors

Last
Fields getLast :: Maybe a

Instances

Instances details

MonadFix Last Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Last a) -> Last a Source #

MonadZip Last Source #

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 #

Foldable Last Source #

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 Source #

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 #

Applicative Last Source #

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 #

Functor Last Source #

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 #

Monad Last Source #

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 #

Generic1 Last Source #

Instance details

Defined in Data.Monoid

Associated Types

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)))

Methods

from1 :: Last a -> Rep1 Last a Source #

to1 :: Rep1 Last a -> Last a Source #

Data a => Data (Last a) Source #

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 #

Monoid (Last a) Source #

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 #

Semigroup (Last a) Source #

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 #

Generic (Last a) Source #

Instance details

Defined in Data.Monoid

Associated Types

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))))

Methods

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

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

Read a => Read (Last a) Source #

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) Source #

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 #

Eq a => Eq (Last a) Source #

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Ord a => Ord (Last a) Source #

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 #

type Rep1 Last Source #

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)))

type Rep (Last a) Source #

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))))

`Alternative` wrapper

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

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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)))

Methods

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

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

MonadFix f => MonadFix (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Alt f a) -> Alt f a Source #

MonadZip f => MonadZip (Alt f) Source #

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 #

Foldable f => Foldable (Alt f) Source #

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 #

Foldable1 f => Foldable1 (Alt f) Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

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

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

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

toNonEmpty :: Alt f a -> NonEmpty a Source #

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

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

head :: Alt f a -> a Source #

last :: Alt f a -> a Source #

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

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

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

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

Contravariant f => Contravariant (Alt f) Source #

Instance details

Defined in Data.Functor.Contravariant

Methods

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

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

Traversable f => Traversable (Alt f) Source #

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 #

Alternative f => Alternative (Alt f) Source #

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 #

Applicative f => Applicative (Alt f) Source #

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 #

Functor f => Functor (Alt f) Source #

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 #

Monad f => Monad (Alt f) Source #

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 #

MonadPlus f => MonadPlus (Alt f) Source #

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 #

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

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 #

Alternative f => Monoid (Alt f a) Source #

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 #

Alternative f => Semigroup (Alt f a) Source #

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 #

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

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 #

Generic (Alt f a) Source #

Instance details

Defined in Data.Semigroup.Internal

Associated Types

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))))

Methods

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

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

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

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 #

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

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) Source #

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 #

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

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 #

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

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 #

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

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) Source #

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 :: k -> Type) (a :: k) 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) Source #

Instance details

Defined in Data.Monoid

Associated Types

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)))

Methods

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

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

MonadFail f => MonadFail (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fail :: String -> Ap f a Source #

MonadFix f => MonadFix (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Ap f a) -> Ap f a Source #

Foldable f => Foldable (Ap f) Source #

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 #

Foldable1 f => Foldable1 (Ap f) Source #

Since: base-4.18.0.0

Instance details

Defined in Data.Foldable1

Methods

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

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

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

toNonEmpty :: Ap f a -> NonEmpty a Source #

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

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

head :: Ap f a -> a Source #

last :: Ap f a -> a Source #

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

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

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

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

Traversable f => Traversable (Ap f) Source #

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 #

Alternative f => Alternative (Ap f) Source #

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 => Applicative (Ap f) Source #

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 #

Functor f => Functor (Ap f) Source #

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 #

Monad f => Monad (Ap f) Source #

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 #

MonadPlus f => MonadPlus (Ap f) Source #

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 #

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

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, Monoid a) => Monoid (Ap f a) Source #

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 #

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

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, Bounded a) => Bounded (Ap f a) Source #

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) Source #

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 #

Generic (Ap f a) Source #

Instance details

Defined in Data.Monoid

Associated Types

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))))

Methods

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

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

(Applicative f, Num a) => Num (Ap f a) Source #

Note that even if the underlying Num and Applicative instances are lawful, for most Applicatives, this instance will not be lawful. If you use this instance with the list Applicative, the following customary laws will not hold:

Commutativity:

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

Additive inverse:

>>> Ap [] + negate (Ap [])
Ap {getAp = []}
>>> fromInteger 0 :: Ap [] Int
Ap {getAp = [0]}

Distributivity:

>>> Ap [1,2] * (3 + 4)
Ap {getAp = [7,14]}
>>> (Ap [1,2] * 3) + (Ap [1,2] * 4)
Ap {getAp = [7,11,10,14]}

Since: base-4.12.0.0

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 #

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

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) Source #

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 #

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

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 #

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

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 #

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

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) Source #

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))))

Examples

Monoid typeclass

Instances

Instances

Instances

Bool wrappers

Instances

Instances

Num wrappers

Instances

Instances

Maybe wrappers

Instances

Instances

Alternative wrapper

Instances

Applicative wrapper

Instances

`Monoid` typeclass

`Bool` wrappers

`Num` wrappers

`Maybe` wrappers

`Alternative` wrapper

`Applicative` wrapper