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/Haskell 8

Data.Monoid

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

Description

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

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 laws:

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

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

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

Minimal complete definition

mempty

Methods

mempty :: a Source

Identity of mappend

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.

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.

Instances
Monoid Ordering

Since: base-2.1

Instance details

Defined in GHC.Base

Monoid ()

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: () Source

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

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

Monoid Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

Monoid All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: base-4.8.0.0

Instance details

Defined in GHC.Event.Internal

Monoid Event

Since: base-4.4.0.0

Instance details

Defined in GHC.Event.Internal

Monoid [a]

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: [a] Source

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

mconcat :: [[a]] -> [a] Source

Semigroup a => Monoid (Maybe a)

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining 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 Source

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

mconcat :: [Maybe a] -> Maybe a Source

Monoid a => Monoid (IO a)

Since: base-4.9.0.0

Instance details

Defined in GHC.Base

Methods

mempty :: IO a Source

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

mconcat :: [IO a] -> IO a Source

Monoid p => Monoid (Par1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Par1 p Source

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

mconcat :: [Par1 p] -> Par1 p Source

Monoid a => Monoid (Down a)

Since: base-4.11.0.0

Instance details

Defined in Data.Ord

Methods

mempty :: Down a Source

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

mconcat :: [Down a] -> Down a Source

Num a => Monoid (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Num a => Monoid (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source

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

mconcat :: [Sum a] -> Sum a Source

Monoid (Endo a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source

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

mconcat :: [Endo a] -> Endo a Source

Monoid a => Monoid (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source

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

mconcat :: [Dual a] -> Dual a Source

Monoid (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a Source

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

mconcat :: [Last a] -> Last a Source

Monoid (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a Source

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

mconcat :: [First a] -> First a Source

Monoid a => Monoid (Identity a)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Identity

Semigroup a => Monoid (Option a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Option a Source

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

mconcat :: [Option a] -> Option a Source

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

(Ord a, Bounded a) => Monoid (Max a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Max a Source

mappend :: Max a -> Max a -> Max a Source

mconcat :: [Max a] -> Max a Source

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup

Methods

mempty :: Min a Source

mappend :: Min a -> Min a -> Min a Source

mconcat :: [Min a] -> Min a Source

Monoid (Equivalence a)
Instance details

Defined in Data.Functor.Contravariant

Monoid (Comparison a)
Instance details

Defined in Data.Functor.Contravariant

Monoid (Predicate a)
Instance details

Defined in Data.Functor.Contravariant

Monoid b => Monoid (a -> b)

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: a -> b Source

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

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

Monoid (U1 p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: U1 p Source

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

mconcat :: [U1 p] -> U1 p Source

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b) Source

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

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

Monoid a => Monoid (ST s a)

Since: base-4.11.0.0

Instance details

Defined in GHC.ST

Methods

mempty :: ST s a Source

mappend :: ST s a -> ST s a -> ST s a Source

mconcat :: [ST s a] -> ST s a Source

Monoid (Proxy s)

Since: base-4.7.0.0

Instance details

Defined in Data.Proxy

Methods

mempty :: Proxy s Source

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

mconcat :: [Proxy s] -> Proxy s Source

Monoid a => Monoid (Op a b)
Instance details

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b Source

mappend :: Op a b -> Op a b -> Op a b Source

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

Monoid (f p) => Monoid (Rec1 f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: Rec1 f p Source

mappend :: Rec1 f p -> Rec1 f p -> Rec1 f p Source

mconcat :: [Rec1 f p] -> Rec1 f p Source

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c) Source

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

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

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a Source

mappend :: Alt f a -> Alt f a -> Alt f a Source

mconcat :: [Alt f a] -> Alt f a Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a Source

mappend :: Ap f a -> Ap f a -> Ap f a Source

mconcat :: [Ap f a] -> Ap f a Source

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Instance details

Defined in Data.Functor.Const

Methods

mempty :: Const a b Source

mappend :: Const a b -> Const a b -> Const a b Source

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

Monoid c => Monoid (K1 i c p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: K1 i c p Source

mappend :: K1 i c p -> K1 i c p -> K1 i c p Source

mconcat :: [K1 i c p] -> K1 i c p Source

(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :*: g) p Source

mappend :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source

mconcat :: [(f :*: g) p] -> (f :*: g) p Source

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c, d) Source

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

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

Monoid (f p) => Monoid (M1 i c f p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: M1 i c f p Source

mappend :: M1 i c f p -> M1 i c f p -> M1 i c f p Source

mconcat :: [M1 i c f p] -> M1 i c f p Source

Monoid (f (g p)) => Monoid ((f :.: g) p)

Since: base-4.12.0.0

Instance details

Defined in GHC.Generics

Methods

mempty :: (f :.: g) p Source

mappend :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source

mconcat :: [(f :.: g) p] -> (f :.: g) p Source

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

Since: base-2.1

Instance details

Defined in GHC.Base

Methods

mempty :: (a, b, c, d, e) Source

mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source

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

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

An associative operation.

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

Instances
Monad Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Dual a Source

fail :: String -> Dual a Source

Functor Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Dual

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source

(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source

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

(<*) :: Dual a -> Dual b -> Dual a Source

Foldable Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> Dual a -> m Source

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

foldr' :: (a -> b -> b) -> b -> Dual a -> b Source

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

foldl' :: (b -> a -> b) -> b -> Dual a -> b Source

foldr1 :: (a -> a -> a) -> Dual a -> a Source

foldl1 :: (a -> a -> a) -> Dual a -> a Source

toList :: Dual a -> [a] Source

null :: Dual a -> Bool Source

length :: Dual a -> Int Source

elem :: Eq a => a -> Dual a -> Bool Source

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

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

sum :: Num a => Dual a -> a Source

product :: Num a => Dual a -> a Source

Traversable Dual

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source

sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source

sequence :: Monad m => Dual (m a) -> m (Dual a) Source

MonadZip Dual

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Dual a -> Dual b -> Dual (a, b) Source

mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source

munzip :: Dual (a, b) -> (Dual a, Dual b) Source

Bounded a => Bounded (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a Source

maxBound :: Dual a Source

Eq a => Eq (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Dual a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Dual a -> Constr Source

dataTypeOf :: Dual a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering Source

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

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

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

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

max :: Dual a -> Dual a -> Dual a Source

min :: Dual a -> Dual a -> Dual a Source

Read a => Read (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS Source

show :: Dual a -> String Source

showList :: [Dual a] -> ShowS Source

Generic (Dual a)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid a => Monoid (Dual a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a Source

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

mconcat :: [Dual a] -> Dual a Source

Generic1 Dual
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type Source

Methods

from1 :: Dual a -> Rep1 Dual a Source

to1 :: Rep1 Dual a -> Dual a Source

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 Source

The monoid of endomorphisms under composition.

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

Constructors

Endo

Fields

Instances
Generic (Endo a)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Semigroup (Endo a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Monoid (Endo a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a Source

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

mconcat :: [Endo a] -> Endo a Source

type Rep (Endo a)

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

Instances
Bounded All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data All

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source

toConstr :: All -> Constr Source

dataTypeOf :: All -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) Source

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

gmapT :: (forall b. Data b => b -> b) -> All -> All Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source

gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source

Ord All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering Source

(<) :: All -> All -> Bool Source

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

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

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

max :: All -> All -> All Source

min :: All -> All -> All Source

Read All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS Source

show :: All -> String Source

showList :: [All] -> ShowS Source

Generic All
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type Source

Methods

from :: All -> Rep All x Source

to :: Rep All x -> All Source

Semigroup All

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty All -> All Source

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

Monoid All

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

type Rep All

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

Instances
Bounded Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data Any

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source

toConstr :: Any -> Constr Source

dataTypeOf :: Any -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source

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

gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source

Ord Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering Source

(<) :: Any -> Any -> Bool Source

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

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

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

max :: Any -> Any -> Any Source

min :: Any -> Any -> Any Source

Read Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS Source

show :: Any -> String Source

showList :: [Any] -> ShowS Source

Generic Any
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type Source

Methods

from :: Any -> Rep Any x Source

to :: Rep Any x -> Any Source

Semigroup Any

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty Any -> Any Source

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

Monoid Any

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

type Rep Any

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

Instances
Monad Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Sum a Source

fail :: String -> Sum a Source

Functor Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Sum

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source

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

(<*) :: Sum a -> Sum b -> Sum a Source

Foldable Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> Sum a -> m Source

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

foldr' :: (a -> b -> b) -> b -> Sum a -> b Source

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

foldl' :: (b -> a -> b) -> b -> Sum a -> b Source

foldr1 :: (a -> a -> a) -> Sum a -> a Source

foldl1 :: (a -> a -> a) -> Sum a -> a Source

toList :: Sum a -> [a] Source

null :: Sum a -> Bool Source

length :: Sum a -> Int Source

elem :: Eq a => a -> Sum a -> Bool Source

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

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

sum :: Num a => Sum a -> a Source

product :: Num a => Sum a -> a Source

Traversable Sum

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source

sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source

mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source

sequence :: Monad m => Sum (m a) -> m (Sum a) Source

MonadZip Sum

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Sum a -> Sum b -> Sum (a, b) Source

mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source

munzip :: Sum (a, b) -> (Sum a, Sum b) Source

Bounded a => Bounded (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a Source

maxBound :: Sum a Source

Eq a => Eq (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Sum a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Sum a -> Constr Source

dataTypeOf :: Sum a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Num a => Num (Sum a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

negate :: Sum a -> Sum a Source

abs :: Sum a -> Sum a Source

signum :: Sum a -> Sum a Source

fromInteger :: Integer -> Sum a Source

Ord a => Ord (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering Source

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

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

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

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

max :: Sum a -> Sum a -> Sum a Source

min :: Sum a -> Sum a -> Sum a Source

Read a => Read (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Show a => Show (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS Source

show :: Sum a -> String Source

showList :: [Sum a] -> ShowS Source

Generic (Sum a)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Sum a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a Source

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

mconcat :: [Sum a] -> Sum a Source

Generic1 Sum
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type Source

Methods

from1 :: Sum a -> Rep1 Sum a Source

to1 :: Rep1 Sum a -> Sum a Source

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 Source

Monoid under multiplication.

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

Constructors

Product

Fields

Instances
Monad Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Product a Source

fail :: String -> Product a Source

Functor Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix Product

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Product

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Product a Source

(<*>) :: Product (a -> b) -> Product a -> Product b Source

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source

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

(<*) :: Product a -> Product b -> Product a Source

Foldable Product

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> Product a -> m Source

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

foldr' :: (a -> b -> b) -> b -> Product a -> b Source

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

foldl' :: (b -> a -> b) -> b -> Product a -> b Source

foldr1 :: (a -> a -> a) -> Product a -> a Source

foldl1 :: (a -> a -> a) -> Product a -> a Source

toList :: Product a -> [a] Source

null :: Product a -> Bool Source

length :: Product a -> Int Source

elem :: Eq a => a -> Product a -> Bool Source

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

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

sum :: Num a => Product a -> a Source

product :: Num a => Product a -> a Source

Traversable Product

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source

sequenceA :: Applicative f => Product (f a) -> f (Product a) Source

mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source

sequence :: Monad m => Product (m a) -> m (Product a) Source

MonadZip Product

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Product a -> Product b -> Product (a, b) Source

mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source

munzip :: Product (a, b) -> (Product a, Product b) Source

Bounded a => Bounded (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Eq a => Eq (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

Data a => Data (Product a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Product a -> Constr Source

dataTypeOf :: Product a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Num a => Num (Product a)

Since: base-4.7.0.0

Instance details

Defined in Data.Semigroup.Internal

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

Show a => Show (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic (Product a)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Num a => Monoid (Product a)

Since: base-2.1

Instance details

Defined in Data.Semigroup.Internal

Generic1 Product
Instance details

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type Source

Methods

from1 :: Product a -> Rep1 Product a Source

to1 :: Rep1 Product a -> Product a Source

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 Source

Maybe monoid returning the leftmost non-Nothing value.

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

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

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

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

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

Constructors

First

Fields

Instances
Monad First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> First a Source

fail :: String -> First a Source

Functor First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

MonadFix First

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative First

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> First a Source

(<*>) :: First (a -> b) -> First a -> First b Source

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source

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

(<*) :: First a -> First b -> First a Source

Foldable First

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> First a -> m Source

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

foldr' :: (a -> b -> b) -> b -> First a -> b Source

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

foldl' :: (b -> a -> b) -> b -> First a -> b Source

foldr1 :: (a -> a -> a) -> First a -> a Source

foldl1 :: (a -> a -> a) -> First a -> a Source

toList :: First a -> [a] Source

null :: First a -> Bool Source

length :: First a -> Int Source

elem :: Eq a => a -> First a -> Bool Source

maximum :: Ord a => First a -> a Source

minimum :: Ord a => First a -> a Source

sum :: Num a => First a -> a Source

product :: Num a => First a -> a Source

Traversable First

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source

sequenceA :: Applicative f => First (f a) -> f (First a) Source

mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source

sequence :: Monad m => First (m a) -> m (First a) Source

MonadZip First

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: First a -> First b -> First (a, b) Source

mzipWith :: (a -> b -> c) -> First a -> First b -> First c Source

munzip :: First (a, b) -> (First a, First b) Source

Eq a => Eq (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Data a => Data (First a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: First a -> Constr Source

dataTypeOf :: First a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

compare :: First a -> First a -> Ordering Source

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

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

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

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

max :: First a -> First a -> First a Source

min :: First a -> First a -> First a Source

Read a => Read (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Show a => Show (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> First a -> ShowS Source

show :: First a -> String Source

showList :: [First a] -> ShowS Source

Generic (First a)
Instance details

Defined in Data.Monoid

Associated Types

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

Methods

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

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

Semigroup (First a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Monoid (First a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: First a Source

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

mconcat :: [First a] -> First a Source

Generic1 First
Instance details

Defined in Data.Monoid

Associated Types

type Rep1 First :: k -> Type Source

Methods

from1 :: First a -> Rep1 First a Source

to1 :: Rep1 First a -> First a Source

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 Source

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

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

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

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

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

Instances
Monad Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

return :: a -> Last a Source

fail :: String -> Last a Source

Functor Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

MonadFix Last

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative Last

Since: base-4.8.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Last a Source

(<*>) :: Last (a -> b) -> Last a -> Last b Source

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source

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

(<*) :: Last a -> Last b -> Last a Source

Foldable Last

Since: base-4.8.0.0

Instance details

Defined in Data.Foldable

Methods

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

foldMap :: Monoid m => (a -> m) -> Last a -> m Source

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

foldr' :: (a -> b -> b) -> b -> Last a -> b Source

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

foldl' :: (b -> a -> b) -> b -> Last a -> b Source

foldr1 :: (a -> a -> a) -> Last a -> a Source

foldl1 :: (a -> a -> a) -> Last a -> a Source

toList :: Last a -> [a] Source

null :: Last a -> Bool Source

length :: Last a -> Int Source

elem :: Eq a => a -> Last a -> Bool Source

maximum :: Ord a => Last a -> a Source

minimum :: Ord a => Last a -> a Source

sum :: Num a => Last a -> a Source

product :: Num a => Last a -> a Source

Traversable Last

Since: base-4.8.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source

sequenceA :: Applicative f => Last (f a) -> f (Last a) Source

mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source

sequence :: Monad m => Last (m a) -> m (Last a) Source

MonadZip Last

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Last a -> Last b -> Last (a, b) Source

mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c Source

munzip :: Last (a, b) -> (Last a, Last b) Source

Eq a => Eq (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

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

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

Data a => Data (Last a)

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

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

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

toConstr :: Last a -> Constr Source

dataTypeOf :: Last a -> DataType Source

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

compare :: Last a -> Last a -> Ordering Source

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

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

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

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

max :: Last a -> Last a -> Last a Source

min :: Last a -> Last a -> Last a Source

Read a => Read (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Show a => Show (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Last a -> ShowS Source

show :: Last a -> String Source

showList :: [Last a] -> ShowS Source

Generic (Last a)
Instance details

Defined in Data.Monoid

Associated Types

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

Methods

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

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

Semigroup (Last a)

Since: base-4.9.0.0

Instance details

Defined in Data.Monoid

Methods

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

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

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

Monoid (Last a)

Since: base-2.1

Instance details

Defined in Data.Monoid

Methods

mempty :: Last a Source

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

mconcat :: [Last a] -> Last a Source

Generic1 Last
Instance details

Defined in Data.Monoid

Associated Types

type Rep1 Last :: k -> Type Source

Methods

from1 :: Last a -> Rep1 Last a Source

to1 :: Rep1 Last a -> Last a Source

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 Source

Monoid under <|>.

Since: base-4.8.0.0

Constructors

Alt

Fields

Instances
Generic1 (Alt f :: k -> Type)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Monad f => Monad (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

return :: a -> Alt f a Source

fail :: String -> Alt f a Source

Functor f => Functor (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

MonadFix f => MonadFix (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

Applicative f => Applicative (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source

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

(<*) :: Alt f a -> Alt f b -> Alt f a Source

Foldable f => Foldable (Alt f)

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Alt f m -> m Source

foldMap :: Monoid m => (a -> m) -> Alt f a -> m Source

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

foldr' :: (a -> b -> b) -> b -> Alt f a -> b Source

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

foldl' :: (b -> a -> b) -> b -> Alt f a -> b Source

foldr1 :: (a -> a -> a) -> Alt f a -> a Source

foldl1 :: (a -> a -> a) -> Alt f a -> a Source

toList :: Alt f a -> [a] Source

null :: Alt f a -> Bool Source

length :: Alt f a -> Int Source

elem :: Eq a => a -> Alt f a -> Bool Source

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

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

sum :: Num a => Alt f a -> a Source

product :: Num a => Alt f a -> a Source

Traversable f => Traversable (Alt f)

Since: base-4.12.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Alt f a -> f0 (Alt f b) Source

sequenceA :: Applicative f0 => Alt f (f0 a) -> f0 (Alt f a) Source

mapM :: Monad m => (a -> m b) -> Alt f a -> m (Alt f b) Source

sequence :: Monad m => Alt f (m a) -> m (Alt f a) Source

MonadPlus f => MonadPlus (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mzero :: Alt f a Source

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

Alternative f => Alternative (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

empty :: Alt f a Source

(<|>) :: Alt f a -> Alt f a -> Alt f a Source

some :: Alt f a -> Alt f [a] Source

many :: Alt f a -> Alt f [a] Source

MonadZip f => MonadZip (Alt f)

Since: base-4.8.0.0

Instance details

Defined in Control.Monad.Zip

Methods

mzip :: Alt f a -> Alt f b -> Alt f (a, b) Source

mzipWith :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source

munzip :: Alt f (a, b) -> (Alt f a, Alt f b) Source

Contravariant f => Contravariant (Alt f)
Instance details

Defined in Data.Functor.Contravariant

Methods

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

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

succ :: Alt f a -> Alt f a Source

pred :: Alt f a -> Alt f a Source

toEnum :: Int -> Alt f a Source

fromEnum :: Alt f a -> Int Source

enumFrom :: Alt f a -> [Alt f a] Source

enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source

enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source

enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

Since: base-4.8.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt f a -> c (Alt f a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt f a) Source

toConstr :: Alt f a -> Constr Source

dataTypeOf :: Alt f a -> DataType Source

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

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

gmapT :: (forall b. Data b => b -> b) -> Alt f a -> Alt f a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt f a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Alt f a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt f a -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt f a -> m (Alt f a) Source

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

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

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

negate :: Alt f a -> Alt f a Source

abs :: Alt f a -> Alt f a Source

signum :: Alt f a -> Alt f a Source

fromInteger :: Integer -> Alt f a Source

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

compare :: Alt f a -> Alt f a -> Ordering Source

(<) :: Alt f a -> Alt f a -> Bool Source

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

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

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

max :: Alt f a -> Alt f a -> Alt f a Source

min :: Alt f a -> Alt f a -> Alt f a Source

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

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Show (f a) => Show (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

show :: Alt f a -> String Source

showList :: [Alt f a] -> ShowS Source

Generic (Alt f a)
Instance details

Defined in Data.Semigroup.Internal

Associated Types

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

Methods

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

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

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

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

sconcat :: NonEmpty (Alt f a) -> Alt f a Source

stimes :: Integral b => b -> Alt f a -> Alt f a Source

Alternative f => Monoid (Alt f a)

Since: base-4.8.0.0

Instance details

Defined in Data.Semigroup.Internal

Methods

mempty :: Alt f a Source

mappend :: Alt f a -> Alt f a -> Alt f a Source

mconcat :: [Alt f a] -> Alt f a Source

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

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 Source

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

Since: base-4.12.0.0

Constructors

Ap

Fields

Instances
Generic1 (Ap f :: k -> Type)
Instance details

Defined in Data.Monoid

Associated Types

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

Methods

from1 :: Ap f a -> Rep1 (Ap f) a Source

to1 :: Rep1 (Ap f) a -> Ap f a Source

Monad f => Monad (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(>>=) :: Ap f a -> (a -> Ap f b) -> Ap f b Source

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

return :: a -> Ap f a Source

fail :: String -> Ap f a Source

Functor f => Functor (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fmap :: (a -> b) -> Ap f a -> Ap f b Source

(<$) :: a -> Ap f b -> Ap f a Source

MonadFix f => MonadFix (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Control.Monad.Fix

Methods

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

MonadFail f => MonadFail (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

fail :: String -> Ap f a Source

Applicative f => Applicative (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

pure :: a -> Ap f a Source

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source

(*>) :: Ap f a -> Ap f b -> Ap f b Source

(<*) :: Ap f a -> Ap f b -> Ap f a Source

Foldable f => Foldable (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Foldable

Methods

fold :: Monoid m => Ap f m -> m Source

foldMap :: Monoid m => (a -> m) -> Ap f a -> m Source

foldr :: (a -> b -> b) -> b -> Ap f a -> b Source

foldr' :: (a -> b -> b) -> b -> Ap f a -> b Source

foldl :: (b -> a -> b) -> b -> Ap f a -> b Source

foldl' :: (b -> a -> b) -> b -> Ap f a -> b Source

foldr1 :: (a -> a -> a) -> Ap f a -> a Source

foldl1 :: (a -> a -> a) -> Ap f a -> a Source

toList :: Ap f a -> [a] Source

null :: Ap f a -> Bool Source

length :: Ap f a -> Int Source

elem :: Eq a => a -> Ap f a -> Bool Source

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

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

sum :: Num a => Ap f a -> a Source

product :: Num a => Ap f a -> a Source

Traversable f => Traversable (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Traversable

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Ap f a -> f0 (Ap f b) Source

sequenceA :: Applicative f0 => Ap f (f0 a) -> f0 (Ap f a) Source

mapM :: Monad m => (a -> m b) -> Ap f a -> m (Ap f b) Source

sequence :: Monad m => Ap f (m a) -> m (Ap f a) Source

MonadPlus f => MonadPlus (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mzero :: Ap f a Source

mplus :: Ap f a -> Ap f a -> Ap f a Source

Alternative f => Alternative (Ap f)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

empty :: Ap f a Source

(<|>) :: Ap f a -> Ap f a -> Ap f a Source

some :: Ap f a -> Ap f [a] Source

many :: Ap f a -> Ap f [a] Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

minBound :: Ap f a Source

maxBound :: Ap f a Source

Enum (f a) => Enum (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

succ :: Ap f a -> Ap f a Source

pred :: Ap f a -> Ap f a Source

toEnum :: Int -> Ap f a Source

fromEnum :: Ap f a -> Int Source

enumFrom :: Ap f a -> [Ap f a] Source

enumFromThen :: Ap f a -> Ap f a -> [Ap f a] Source

enumFromTo :: Ap f a -> Ap f a -> [Ap f a] Source

enumFromThenTo :: Ap f a -> Ap f a -> Ap f a -> [Ap f a] Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(==) :: Ap f a -> Ap f a -> Bool Source

(/=) :: Ap f a -> Ap f a -> Bool Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Data

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Ap f a -> c (Ap f a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Ap f a) Source

toConstr :: Ap f a -> Constr Source

dataTypeOf :: Ap f a -> DataType Source

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

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

gmapT :: (forall b. Data b => b -> b) -> Ap f a -> Ap f a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Ap f a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Ap f a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Ap f a -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Ap f a -> m (Ap f a) Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(+) :: Ap f a -> Ap f a -> Ap f a Source

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

(*) :: Ap f a -> Ap f a -> Ap f a Source

negate :: Ap f a -> Ap f a Source

abs :: Ap f a -> Ap f a Source

signum :: Ap f a -> Ap f a Source

fromInteger :: Integer -> Ap f a Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

compare :: Ap f a -> Ap f a -> Ordering Source

(<) :: Ap f a -> Ap f a -> Bool Source

(<=) :: Ap f a -> Ap f a -> Bool Source

(>) :: Ap f a -> Ap f a -> Bool Source

(>=) :: Ap f a -> Ap f a -> Bool Source

max :: Ap f a -> Ap f a -> Ap f a Source

min :: Ap f a -> Ap f a -> Ap f a Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Show (f a) => Show (Ap f a)

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

showsPrec :: Int -> Ap f a -> ShowS Source

show :: Ap f a -> String Source

showList :: [Ap f a] -> ShowS Source

Generic (Ap f a)
Instance details

Defined in Data.Monoid

Associated Types

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

Methods

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

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

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

(<>) :: Ap f a -> Ap f a -> Ap f a Source

sconcat :: NonEmpty (Ap f a) -> Ap f a Source

stimes :: Integral b => b -> Ap f a -> Ap f a Source

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

Since: base-4.12.0.0

Instance details

Defined in Data.Monoid

Methods

mempty :: Ap f a Source

mappend :: Ap f a -> Ap f a -> Ap f a Source

mconcat :: [Ap f a] -> Ap f a Source

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

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))))

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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.6.1/docs/html/libraries/base-4.12.0.0/Data-Monoid.html