base-4.11.0.0: Basic libraries

Copyright(c) Andy Gill 2001
(c) Oregon Graduate Institute of Science and Technology 2001
LicenseBSD-style (see the file libraries/base/LICENSE)
Maintainerlibraries@haskell.org
Stabilityexperimental
Portabilityportable
Safe HaskellTrustworthy
LanguageHaskell2010

Data.Monoid

Contents

Description

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

Synopsis

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 Source #

Since: 2.1

Instance details
Monoid () Source #

Since: 2.1

Instance details

Methods

mempty :: () Source #

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

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

Monoid Any Source #

Since: 2.1

Instance details
Monoid All Source #

Since: 2.1

Instance details
Monoid Lifetime Source #

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Instance details
Monoid Event Source #

Since: 4.3.1.0

Instance details
Monoid [a] Source #

Since: 2.1

Instance details

Methods

mempty :: [a] Source #

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

mconcat :: [[a]] -> [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 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: 2.1

Instance details

Methods

mempty :: Maybe a Source #

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

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

Monoid a => Monoid (IO a) Source #

Since: 4.9.0.0

Instance details

Methods

mempty :: IO a Source #

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

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

Monoid a => Monoid (Down a) Source #

Since: 4.11.0.0

Instance details

Methods

mempty :: Down a Source #

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

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

Num a => Monoid (Product a) Source #

Since: 2.1

Instance details
Num a => Monoid (Sum a) Source #

Since: 2.1

Instance details

Methods

mempty :: Sum a Source #

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

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

Monoid (Endo a) Source #

Since: 2.1

Instance details

Methods

mempty :: Endo a Source #

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

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

Monoid a => Monoid (Dual a) Source #

Since: 2.1

Instance details

Methods

mempty :: Dual a Source #

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

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

Monoid (Last a) Source #

Since: 2.1

Instance details

Methods

mempty :: Last a Source #

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

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

Monoid (First a) Source #

Since: 2.1

Instance details

Methods

mempty :: First a Source #

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

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

Monoid a => Monoid (Identity a) Source # 
Instance details
Semigroup a => Monoid (Option a) Source #

Since: 4.9.0.0

Instance details
Monoid m => Monoid (WrappedMonoid m) Source #

Since: 4.9.0.0

Instance details
(Ord a, Bounded a) => Monoid (Max a) Source #

Since: 4.9.0.0

Instance details

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: 4.9.0.0

Instance details

Methods

mempty :: Min a Source #

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

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

Monoid b => Monoid (a -> b) Source #

Since: 2.1

Instance details

Methods

mempty :: a -> b Source #

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

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

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

Since: 2.1

Instance details

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) Source #

Since: 4.11.0.0

Instance details

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) Source #

Since: 4.7.0.0

Instance details

Methods

mempty :: Proxy s Source #

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

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

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

Since: 2.1

Instance details

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) Source #

Since: 4.8.0.0

Instance details

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 a => Monoid (Const a b) Source # 
Instance details

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

Since: 2.1

Instance details

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

Since: 2.1

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

Methods

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

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

MonadFix Dual Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative Dual Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details
Eq a => Eq (Dual a) Source # 
Instance details

Methods

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

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

Data a => Data (Dual a) Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

Methods

compare :: Dual a -> Dual a -> Ordering #

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

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

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

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

max :: Dual a -> Dual a -> Dual a #

min :: Dual a -> Dual a -> Dual a #

Read a => Read (Dual a) Source # 
Instance details
Show a => Show (Dual a) Source # 
Instance details

Methods

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

show :: Dual a -> String Source #

showList :: [Dual a] -> ShowS Source #

Generic (Dual a) Source # 
Instance details

Associated Types

type Rep (Dual a) :: * -> * Source #

Methods

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

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

Semigroup a => Semigroup (Dual a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details

Methods

mempty :: Dual a Source #

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

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

Generic1 Dual Source # 
Instance details

Associated Types

type Rep1 Dual :: k -> * Source #

Methods

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

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

type Rep (Dual a) Source # 
Instance details
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 Source # 
Instance details
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) Source # 
Instance details

Associated Types

type Rep (Endo a) :: * -> * Source #

Methods

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

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

Semigroup (Endo a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details

Methods

mempty :: Endo a Source #

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

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

type Rep (Endo a) Source # 
Instance details
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 Source # 
Instance details
Eq All Source # 
Instance details

Methods

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

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

Data All Source #

Since: 4.8.0.0

Instance details

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 Source # 
Instance details

Methods

compare :: All -> All -> Ordering #

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

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

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

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

max :: All -> All -> All #

min :: All -> All -> All #

Read All Source # 
Instance details
Show All Source # 
Instance details
Generic All Source # 
Instance details

Associated Types

type Rep All :: * -> * Source #

Methods

from :: All -> Rep All x Source #

to :: Rep All x -> All Source #

Semigroup All Source #

Since: 4.9.0.0

Instance details

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Monoid All Source #

Since: 2.1

Instance details
type Rep All Source # 
Instance details
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 Source # 
Instance details
Eq Any Source # 
Instance details

Methods

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

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

Data Any Source #

Since: 4.8.0.0

Instance details

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 Source # 
Instance details

Methods

compare :: Any -> Any -> Ordering #

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

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

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

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

max :: Any -> Any -> Any #

min :: Any -> Any -> Any #

Read Any Source # 
Instance details
Show Any Source # 
Instance details
Generic Any Source # 
Instance details

Associated Types

type Rep Any :: * -> * Source #

Methods

from :: Any -> Rep Any x Source #

to :: Rep Any x -> Any Source #

Semigroup Any Source #

Since: 4.9.0.0

Instance details

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Monoid Any Source #

Since: 2.1

Instance details
type Rep Any Source # 
Instance details
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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

Methods

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

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

MonadFix Sum Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative Sum Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details
Eq a => Eq (Sum a) Source # 
Instance details

Methods

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

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

Data a => Data (Sum a) Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

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) Source # 
Instance details

Methods

compare :: Sum a -> Sum a -> Ordering #

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

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

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

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

max :: Sum a -> Sum a -> Sum a #

min :: Sum a -> Sum a -> Sum a #

Read a => Read (Sum a) Source # 
Instance details
Show a => Show (Sum a) Source # 
Instance details

Methods

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

show :: Sum a -> String Source #

showList :: [Sum a] -> ShowS Source #

Generic (Sum a) Source # 
Instance details

Associated Types

type Rep (Sum a) :: * -> * Source #

Methods

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

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

Num a => Semigroup (Sum a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details

Methods

mempty :: Sum a Source #

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

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

Generic1 Sum Source # 
Instance details

Associated Types

type Rep1 Sum :: k -> * Source #

Methods

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

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

type Rep (Sum a) Source # 
Instance details
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 Source # 
Instance details
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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

Methods

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

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

MonadFix Product Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative Product Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details
Eq a => Eq (Product a) Source # 
Instance details

Methods

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

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

Data a => Data (Product a) Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details
Ord a => Ord (Product a) Source # 
Instance details

Methods

compare :: Product a -> Product a -> Ordering #

(<) :: Product a -> Product a -> Bool #

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

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

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

max :: Product a -> Product a -> Product a #

min :: Product a -> Product a -> Product a #

Read a => Read (Product a) Source # 
Instance details
Show a => Show (Product a) Source # 
Instance details
Generic (Product a) Source # 
Instance details

Associated Types

type Rep (Product a) :: * -> * Source #

Methods

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

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

Num a => Semigroup (Product a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details
Generic1 Product Source # 
Instance details

Associated Types

type Rep1 Product :: k -> * Source #

type Rep (Product a) Source # 
Instance details
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 Source # 
Instance details
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"

Constructors

First 

Fields

Instances
Monad First Source # 
Instance details

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 Source # 
Instance details

Methods

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

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

MonadFix First Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative First Source # 
Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

Methods

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

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

Data a => Data (First a) Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

Methods

compare :: First a -> First a -> Ordering #

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

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

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

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

max :: First a -> First a -> First a #

min :: First a -> First a -> First a #

Read a => Read (First a) Source # 
Instance details
Show a => Show (First a) Source # 
Instance details
Generic (First a) Source # 
Instance details

Associated Types

type Rep (First a) :: * -> * Source #

Methods

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

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

Semigroup (First a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details

Methods

mempty :: First a Source #

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

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

Generic1 First Source # 
Instance details

Associated Types

type Rep1 First :: k -> * Source #

Methods

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

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

type Rep (First a) Source # 
Instance details
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 Source # 
Instance details
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"

Constructors

Last 

Fields

Instances
Monad Last Source # 
Instance details

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 Source # 
Instance details

Methods

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

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

MonadFix Last Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative Last Source # 
Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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 Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

Methods

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

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

Data a => Data (Last a) Source #

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

Methods

compare :: Last a -> Last a -> Ordering #

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

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

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

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

max :: Last a -> Last a -> Last a #

min :: Last a -> Last a -> Last a #

Read a => Read (Last a) Source # 
Instance details
Show a => Show (Last a) Source # 
Instance details

Methods

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

show :: Last a -> String Source #

showList :: [Last a] -> ShowS Source #

Generic (Last a) Source # 
Instance details

Associated Types

type Rep (Last a) :: * -> * Source #

Methods

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

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

Semigroup (Last a) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 2.1

Instance details

Methods

mempty :: Last a Source #

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

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

Generic1 Last Source # 
Instance details

Associated Types

type Rep1 Last :: k -> * Source #

Methods

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

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

type Rep (Last a) Source # 
Instance details
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 Source # 
Instance details
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: 4.8.0.0

Constructors

Alt 

Fields

Instances
Generic1 (Alt f :: k -> *) Source # 
Instance details

Associated Types

type Rep1 (Alt f) :: k -> * 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) Source # 
Instance details

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) Source # 
Instance details

Methods

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

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

MonadFix f => MonadFix (Alt f) Source #

Since: 4.8.0.0

Instance details

Methods

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

Applicative f => Applicative (Alt f) Source # 
Instance details

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 #

MonadPlus f => MonadPlus (Alt f) Source # 
Instance details

Methods

mzero :: Alt f a Source #

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

Alternative f => Alternative (Alt f) Source # 
Instance details

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) Source #

Since: 4.8.0.0

Instance details

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 #

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

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) Source # 
Instance details

Methods

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

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

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

Since: 4.8.0.0

Instance details

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) Source # 
Instance details

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) Source # 
Instance details

Methods

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

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

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

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

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

max :: Alt f a -> Alt f a -> Alt f a #

min :: Alt f a -> Alt f a -> Alt f a #

Read (f a) => Read (Alt f a) Source # 
Instance details
Show (f a) => Show (Alt f a) Source # 
Instance details

Methods

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

show :: Alt f a -> String Source #

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

Generic (Alt f a) Source # 
Instance details

Associated Types

type Rep (Alt f a) :: * -> * 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) Source #

Since: 4.9.0.0

Instance details

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) Source #

Since: 4.8.0.0

Instance details

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 -> *) Source # 
Instance details
type Rep1 (Alt f :: k -> *) = 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 # 
Instance details
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))))