base-4.10.1.0: 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 Monoid a where Source #

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

  • mappend mempty x = x
  • mappend x mempty = x
  • mappend x (mappend y z) = mappend (mappend x y) z
  • mconcat = foldr mappend mempty

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

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

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source #

Identity of mappend

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

An associative operation

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

Monoid () Source #

Since: 2.1

Methods

mempty :: () Source #

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

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

Monoid Any Source #

Since: 2.1

Monoid All Source #

Since: 2.1

Monoid Lifetime Source #

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Monoid Event Source #

Since: 4.3.1.0

Monoid [a] Source #

Since: 2.1

Methods

mempty :: [a] Source #

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

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

Monoid 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 there used to be no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Since: 2.1

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

Methods

mempty :: IO a Source #

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

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

Monoid (Last a) Source #

Since: 2.1

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

Methods

mempty :: First a Source #

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

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

Num a => Monoid (Product a) Source #

Since: 2.1

Num a => Monoid (Sum a) Source #

Since: 2.1

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

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

Methods

mempty :: Dual a Source #

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

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

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

Since: 4.9.0.0

Monoid m => Monoid (WrappedMonoid m) Source #

Since: 4.9.0.0

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

Since: 4.9.0.0

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

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

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

Methods

mempty :: (a, b) Source #

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

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

Monoid (Proxy k s) Source #

Since: 4.7.0.0

Methods

mempty :: Proxy k s Source #

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

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

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

Since: 2.1

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

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 k a b) Source # 

Methods

mempty :: Const k a b Source #

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

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

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

Since: 2.1

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

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 #

(<>) :: Monoid m => m -> m -> m infixr 6 Source #

An infix synonym for mappend.

Since: 4.5.0.0

newtype Dual a Source #

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

Constructors

Dual 

Fields

Instances

Monad Dual Source #

Since: 4.8.0.0

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

Methods

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

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

MonadFix Dual Source #

Since: 4.8.0.0

Methods

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

Applicative Dual Source #

Since: 4.8.0.0

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

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

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

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 # 
Eq a => Eq (Dual a) Source # 

Methods

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

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

Data a => Data (Dual a) Source #

Since: 4.8.0.0

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 # 

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 # 
Show a => Show (Dual a) Source # 

Methods

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

show :: Dual a -> String Source #

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

Generic (Dual a) Source # 

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

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

Methods

mempty :: Dual a Source #

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

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

Generic1 * Dual Source # 

Associated Types

type Rep1 Dual (f :: Dual -> *) :: k -> * Source #

Methods

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

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

type Rep (Dual a) Source # 
type Rep (Dual a) = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Dual Source # 
type Rep1 * Dual = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Constructors

Endo 

Fields

Instances

Generic (Endo a) Source # 

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

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

Methods

mempty :: Endo a Source #

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

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

type Rep (Endo a) Source # 
type Rep (Endo a) = D1 * (MetaData "Endo" "Data.Monoid" "base" True) (C1 * (MetaCons "Endo" PrefixI True) (S1 * (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a -> a))))

Bool wrappers

newtype All Source #

Boolean monoid under conjunction (&&).

Constructors

All 

Fields

Instances

Bounded All Source # 
Eq All Source # 

Methods

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

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

Data All Source #

Since: 4.8.0.0

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 # 

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 # 
Show All Source # 
Generic All Source # 

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

Methods

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

sconcat :: NonEmpty All -> All Source #

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

Monoid All Source #

Since: 2.1

type Rep All Source # 
type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

Constructors

Any 

Fields

Instances

Bounded Any Source # 
Eq Any Source # 

Methods

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

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

Data Any Source #

Since: 4.8.0.0

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 # 

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 # 
Show Any Source # 
Generic Any Source # 

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

Methods

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

sconcat :: NonEmpty Any -> Any Source #

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

Monoid Any Source #

Since: 2.1

type Rep Any Source # 
type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

Num wrappers

newtype Sum a Source #

Monoid under addition.

Constructors

Sum 

Fields

Instances

Monad Sum Source #

Since: 4.8.0.0

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

Methods

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

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

MonadFix Sum Source #

Since: 4.8.0.0

Methods

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

Applicative Sum Source #

Since: 4.8.0.0

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

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

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

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 # 
Eq a => Eq (Sum a) Source # 

Methods

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

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

Data a => Data (Sum a) Source #

Since: 4.8.0.0

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 # 

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 # 

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 # 
Show a => Show (Sum a) Source # 

Methods

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

show :: Sum a -> String Source #

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

Generic (Sum a) Source # 

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

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

Methods

mempty :: Sum a Source #

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

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

Generic1 * Sum Source # 

Associated Types

type Rep1 Sum (f :: Sum -> *) :: k -> * Source #

Methods

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

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

type Rep (Sum a) Source # 
type Rep (Sum a) = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Sum Source # 
type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

Constructors

Product 

Fields

Instances

Monad Product Source #

Since: 4.8.0.0

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

Methods

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

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

MonadFix Product Source #

Since: 4.8.0.0

Methods

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

Applicative Product Source #

Since: 4.8.0.0

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

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

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

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 # 
Eq a => Eq (Product a) Source # 

Methods

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

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

Data a => Data (Product a) Source #

Since: 4.8.0.0

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

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 # 
Show a => Show (Product a) Source # 
Generic (Product a) Source # 

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

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

Generic1 * Product Source # 

Associated Types

type Rep1 Product (f :: Product -> *) :: k -> * Source #

Methods

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

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

type Rep (Product a) Source # 
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Product Source # 
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "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.

Constructors

First 

Fields

Instances

Monad First Source # 

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 # 

Methods

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

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

MonadFix First Source #

Since: 4.8.0.0

Methods

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

Applicative First Source # 

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

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

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

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 # 

Methods

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

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

Data a => Data (First a) Source #

Since: 4.8.0.0

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 # 

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 # 
Show a => Show (First a) Source # 
Generic (First a) Source # 

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

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

Methods

mempty :: First a Source #

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

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

Generic1 * First Source # 

Associated Types

type Rep1 First (f :: First -> *) :: k -> * Source #

Methods

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

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

type Rep (First a) Source # 
type Rep (First a) = D1 * (MetaData "First" "Data.Monoid" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * First Source # 
type Rep1 * First = D1 * (MetaData "First" "Data.Monoid" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "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)

Constructors

Last 

Fields

Instances

Monad Last Source # 

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 # 

Methods

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

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

MonadFix Last Source #

Since: 4.8.0.0

Methods

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

Applicative Last Source # 

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

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

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

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 # 

Methods

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

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

Data a => Data (Last a) Source #

Since: 4.8.0.0

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 # 

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 # 
Show a => Show (Last a) Source # 

Methods

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

show :: Last a -> String Source #

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

Generic (Last a) Source # 

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

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

Methods

mempty :: Last a Source #

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

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

Generic1 * Last Source # 

Associated Types

type Rep1 Last (f :: Last -> *) :: k -> * Source #

Methods

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

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

type Rep (Last a) Source # 
type Rep (Last a) = D1 * (MetaData "Last" "Data.Monoid" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * Last Source # 
type Rep1 * Last = D1 * (MetaData "Last" "Data.Monoid" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "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 k (Alt k f) Source # 

Associated Types

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

Methods

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

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

Monad f => Monad (Alt * f) Source # 

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 # 

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

Methods

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

Applicative f => Applicative (Alt * f) Source # 

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 # 

Methods

mzero :: Alt * f a Source #

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

Alternative f => Alternative (Alt * f) Source # 

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

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 k f a) Source # 

Methods

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

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

toEnum :: Int -> Alt k f a Source #

fromEnum :: Alt k f a -> Int Source #

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

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

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

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

Eq (f a) => Eq (Alt k f a) Source # 

Methods

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

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

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

Since: 4.8.0.0

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 k f a) Source # 

Methods

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

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

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

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

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

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

fromInteger :: Integer -> Alt k f a Source #

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

Methods

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

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

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

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

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

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

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

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

Methods

readsPrec :: Int -> ReadS (Alt k f a) Source #

readList :: ReadS [Alt k f a] Source #

readPrec :: ReadPrec (Alt k f a) Source #

readListPrec :: ReadPrec [Alt k f a] Source #

Show (f a) => Show (Alt k f a) Source # 

Methods

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

show :: Alt k f a -> String Source #

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

Generic (Alt k f a) Source # 

Associated Types

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

Methods

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

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

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

Since: 4.9.0.0

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

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 k (Alt k f) Source # 
type Rep1 k (Alt k f) = D1 k (MetaData "Alt" "Data.Monoid" "base" True) (C1 k (MetaCons "Alt" PrefixI True) (S1 k (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 k f)))
type Rep (Alt k f a) Source # 
type Rep (Alt k f a) = D1 * (MetaData "Alt" "Data.Monoid" "base" True) (C1 * (MetaCons "Alt" PrefixI True) (S1 * (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (f a))))