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 #

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 #

Identity of mappend

mappend :: a -> a -> a #

An associative operation

mconcat :: [a] -> a #

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

Instances

Monoid Ordering #

Since: 2.1

Monoid () #

Since: 2.1

Methods

mempty :: () #

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

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

Monoid Any #

Since: 2.1

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

Monoid All #

Since: 2.1

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

Monoid Lifetime #

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Monoid Event #

Since: 4.3.1.0

Methods

mempty :: Event #

mappend :: Event -> Event -> Event #

mconcat :: [Event] -> Event #

Monoid [a] #

Since: 2.1

Methods

mempty :: [a] #

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

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

Monoid a => Monoid (Maybe a) #

Lift a semigroup into Maybe forming a Monoid according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup S may be turned into a monoid simply by adjoining an element e not in S and defining e*e = e and e*s = s = s*e for all s ∈ S." Since there used to be no "Semigroup" typeclass providing just mappend, we use Monoid instead.

Since: 2.1

Methods

mempty :: Maybe a #

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

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

Monoid a => Monoid (IO a) #

Since: 4.9.0.0

Methods

mempty :: IO a #

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

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

Monoid (Last a) #

Since: 2.1

Methods

mempty :: Last a #

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

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

Monoid (First a) #

Since: 2.1

Methods

mempty :: First a #

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

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

Num a => Monoid (Product a) #

Since: 2.1

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

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

Num a => Monoid (Sum a) #

Since: 2.1

Methods

mempty :: Sum a #

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

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

Monoid (Endo a) #

Since: 2.1

Methods

mempty :: Endo a #

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

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

Monoid a => Monoid (Dual a) #

Since: 2.1

Methods

mempty :: Dual a #

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

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

Monoid a => Monoid (Identity a) # 

Methods

mempty :: Identity a #

mappend :: Identity a -> Identity a -> Identity a #

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

Semigroup a => Monoid (Option a) #

Since: 4.9.0.0

Methods

mempty :: Option a #

mappend :: Option a -> Option a -> Option a #

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

Monoid m => Monoid (WrappedMonoid m) #

Since: 4.9.0.0

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

Since: 4.9.0.0

Methods

mempty :: Max a #

mappend :: Max a -> Max a -> Max a #

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

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

Since: 4.9.0.0

Methods

mempty :: Min a #

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

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

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

Since: 2.1

Methods

mempty :: a -> b #

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

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

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

Since: 2.1

Methods

mempty :: (a, b) #

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

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

Monoid (Proxy k s) #

Since: 4.7.0.0

Methods

mempty :: Proxy k s #

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

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

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

Since: 2.1

Methods

mempty :: (a, b, c) #

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

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

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

Since: 4.8.0.0

Methods

mempty :: Alt * f a #

mappend :: Alt * f a -> Alt * f a -> Alt * f a #

mconcat :: [Alt * f a] -> Alt * f a #

Monoid a => Monoid (Const k a b) # 

Methods

mempty :: Const k a b #

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

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

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

Since: 2.1

Methods

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

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

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

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

Since: 2.1

Methods

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

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

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

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

An infix synonym for mappend.

Since: 4.5.0.0

newtype Dual a #

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

Constructors

Dual 

Fields

Instances

Monad Dual #

Since: 4.8.0.0

Methods

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

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

return :: a -> Dual a #

fail :: String -> Dual a #

Functor Dual #

Since: 4.8.0.0

Methods

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

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

MonadFix Dual #

Since: 4.8.0.0

Methods

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

Applicative Dual #

Since: 4.8.0.0

Methods

pure :: a -> Dual a #

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

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

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

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

Foldable Dual #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Dual a -> [a] #

null :: Dual a -> Bool #

length :: Dual a -> Int #

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

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

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

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

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

Traversable Dual #

Since: 4.8.0.0

Methods

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

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

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

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

MonadZip Dual #

Since: 4.8.0.0

Methods

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

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

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

Bounded a => Bounded (Dual a) # 

Methods

minBound :: Dual a #

maxBound :: Dual a #

Eq a => Eq (Dual a) # 

Methods

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

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

Data a => Data (Dual a) #

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) #

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

toConstr :: Dual a -> Constr #

dataTypeOf :: Dual a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Dual a) # 

Methods

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

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

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

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

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

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

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

Read a => Read (Dual a) # 
Show a => Show (Dual a) # 

Methods

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

show :: Dual a -> String #

showList :: [Dual a] -> ShowS #

Generic (Dual a) # 

Associated Types

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

Methods

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

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

Semigroup a => Semigroup (Dual a) #

Since: 4.9.0.0

Methods

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

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

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

Monoid a => Monoid (Dual a) #

Since: 2.1

Methods

mempty :: Dual a #

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

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

Generic1 * Dual # 

Associated Types

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

Methods

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

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

type Rep (Dual a) # 
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 # 
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 #

The monoid of endomorphisms under composition.

Constructors

Endo 

Fields

Instances

Generic (Endo a) # 

Associated Types

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

Methods

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

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

Semigroup (Endo a) #

Since: 4.9.0.0

Methods

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

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

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

Monoid (Endo a) #

Since: 2.1

Methods

mempty :: Endo a #

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

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

type Rep (Endo a) # 
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 #

Boolean monoid under conjunction (&&).

Constructors

All 

Fields

Instances

Bounded All # 

Methods

minBound :: All #

maxBound :: All #

Eq All # 

Methods

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

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

Data All #

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 #

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

toConstr :: All -> Constr #

dataTypeOf :: All -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord All # 

Methods

compare :: All -> All -> Ordering Source #

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

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

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

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

max :: All -> All -> All Source #

min :: All -> All -> All Source #

Read All # 
Show All # 

Methods

showsPrec :: Int -> All -> ShowS #

show :: All -> String #

showList :: [All] -> ShowS #

Generic All # 

Associated Types

type Rep All :: * -> * #

Methods

from :: All -> Rep All x #

to :: Rep All x -> All #

Semigroup All #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty All -> All #

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

Monoid All #

Since: 2.1

Methods

mempty :: All #

mappend :: All -> All -> All #

mconcat :: [All] -> All #

type Rep All # 
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 #

Boolean monoid under disjunction (||).

Constructors

Any 

Fields

Instances

Bounded Any # 

Methods

minBound :: Any #

maxBound :: Any #

Eq Any # 

Methods

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

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

Data Any #

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 #

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

toConstr :: Any -> Constr #

dataTypeOf :: Any -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord Any # 

Methods

compare :: Any -> Any -> Ordering Source #

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

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

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

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

max :: Any -> Any -> Any Source #

min :: Any -> Any -> Any Source #

Read Any # 
Show Any # 

Methods

showsPrec :: Int -> Any -> ShowS #

show :: Any -> String #

showList :: [Any] -> ShowS #

Generic Any # 

Associated Types

type Rep Any :: * -> * #

Methods

from :: Any -> Rep Any x #

to :: Rep Any x -> Any #

Semigroup Any #

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Any -> Any #

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

Monoid Any #

Since: 2.1

Methods

mempty :: Any #

mappend :: Any -> Any -> Any #

mconcat :: [Any] -> Any #

type Rep Any # 
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 #

Monoid under addition.

Constructors

Sum 

Fields

Instances

Monad Sum #

Since: 4.8.0.0

Methods

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

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

return :: a -> Sum a #

fail :: String -> Sum a #

Functor Sum #

Since: 4.8.0.0

Methods

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

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

MonadFix Sum #

Since: 4.8.0.0

Methods

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

Applicative Sum #

Since: 4.8.0.0

Methods

pure :: a -> Sum a #

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

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

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

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

Foldable Sum #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Sum a -> [a] #

null :: Sum a -> Bool #

length :: Sum a -> Int #

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

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

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

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

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

Traversable Sum #

Since: 4.8.0.0

Methods

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

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

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

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

MonadZip Sum #

Since: 4.8.0.0

Methods

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

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

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

Bounded a => Bounded (Sum a) # 

Methods

minBound :: Sum a #

maxBound :: Sum a #

Eq a => Eq (Sum a) # 

Methods

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

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

Data a => Data (Sum a) #

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) #

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

toConstr :: Sum a -> Constr #

dataTypeOf :: Sum a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Sum a) # 

Methods

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

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

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

negate :: Sum a -> Sum a #

abs :: Sum a -> Sum a #

signum :: Sum a -> Sum a #

fromInteger :: Integer -> Sum a #

Ord a => Ord (Sum a) # 

Methods

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

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

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

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

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

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

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

Read a => Read (Sum a) # 
Show a => Show (Sum a) # 

Methods

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

show :: Sum a -> String #

showList :: [Sum a] -> ShowS #

Generic (Sum a) # 

Associated Types

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

Methods

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

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

Num a => Semigroup (Sum a) #

Since: 4.9.0.0

Methods

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

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

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

Num a => Monoid (Sum a) #

Since: 2.1

Methods

mempty :: Sum a #

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

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

Generic1 * Sum # 

Associated Types

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

Methods

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

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

type Rep (Sum a) # 
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 # 
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 #

Monoid under multiplication.

Constructors

Product 

Fields

Instances

Monad Product #

Since: 4.8.0.0

Methods

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

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

return :: a -> Product a #

fail :: String -> Product a #

Functor Product #

Since: 4.8.0.0

Methods

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

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

MonadFix Product #

Since: 4.8.0.0

Methods

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

Applicative Product #

Since: 4.8.0.0

Methods

pure :: a -> Product a #

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

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

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

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

Foldable Product #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Product a -> [a] #

null :: Product a -> Bool #

length :: Product a -> Int #

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

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

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

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

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

Traversable Product #

Since: 4.8.0.0

Methods

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

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

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

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

MonadZip Product #

Since: 4.8.0.0

Methods

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

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

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

Bounded a => Bounded (Product a) # 
Eq a => Eq (Product a) # 

Methods

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

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

Data a => Data (Product a) #

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) #

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

toConstr :: Product a -> Constr #

dataTypeOf :: Product a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num a => Num (Product a) # 

Methods

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

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

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

negate :: Product a -> Product a #

abs :: Product a -> Product a #

signum :: Product a -> Product a #

fromInteger :: Integer -> Product a #

Ord a => Ord (Product a) # 
Read a => Read (Product a) # 
Show a => Show (Product a) # 

Methods

showsPrec :: Int -> Product a -> ShowS #

show :: Product a -> String #

showList :: [Product a] -> ShowS #

Generic (Product a) # 

Associated Types

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

Methods

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

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

Num a => Semigroup (Product a) #

Since: 4.9.0.0

Methods

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

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

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

Num a => Monoid (Product a) #

Since: 2.1

Methods

mempty :: Product a #

mappend :: Product a -> Product a -> Product a #

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

Generic1 * Product # 

Associated Types

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

Methods

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

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

type Rep (Product a) # 
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 # 
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 #

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 # 

Methods

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

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

return :: a -> First a #

fail :: String -> First a #

Functor First # 

Methods

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

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

MonadFix First #

Since: 4.8.0.0

Methods

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

Applicative First # 

Methods

pure :: a -> First a #

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

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

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

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

Foldable First #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: First a -> [a] #

null :: First a -> Bool #

length :: First a -> Int #

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

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

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

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

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

Traversable First #

Since: 4.8.0.0

Methods

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

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

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

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

MonadZip First #

Since: 4.8.0.0

Methods

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

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

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

Eq a => Eq (First a) # 

Methods

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

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

Data a => Data (First a) #

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) #

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

toConstr :: First a -> Constr #

dataTypeOf :: First a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (First a) # 

Methods

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

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

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

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

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

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

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

Read a => Read (First a) # 
Show a => Show (First a) # 

Methods

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

show :: First a -> String #

showList :: [First a] -> ShowS #

Generic (First a) # 

Associated Types

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

Methods

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

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

Semigroup (First a) #

Since: 4.9.0.0

Methods

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

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

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

Monoid (First a) #

Since: 2.1

Methods

mempty :: First a #

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

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

Generic1 * First # 

Associated Types

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

Methods

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

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

type Rep (First a) # 
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 # 
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 #

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 # 

Methods

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

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

return :: a -> Last a #

fail :: String -> Last a #

Functor Last # 

Methods

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

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

MonadFix Last #

Since: 4.8.0.0

Methods

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

Applicative Last # 

Methods

pure :: a -> Last a #

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

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

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

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

Foldable Last #

Since: 4.8.0.0

Methods

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

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

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

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

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

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

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

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

toList :: Last a -> [a] #

null :: Last a -> Bool #

length :: Last a -> Int #

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

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

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

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

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

Traversable Last #

Since: 4.8.0.0

Methods

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

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

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

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

MonadZip Last #

Since: 4.8.0.0

Methods

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

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

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

Eq a => Eq (Last a) # 

Methods

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

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

Data a => Data (Last a) #

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) #

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

toConstr :: Last a -> Constr #

dataTypeOf :: Last a -> DataType #

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

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

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

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

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

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

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

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

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

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

Ord a => Ord (Last a) # 

Methods

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

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

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

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

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

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

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

Read a => Read (Last a) # 
Show a => Show (Last a) # 

Methods

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

show :: Last a -> String #

showList :: [Last a] -> ShowS #

Generic (Last a) # 

Associated Types

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

Methods

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

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

Semigroup (Last a) #

Since: 4.9.0.0

Methods

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

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

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

Monoid (Last a) #

Since: 2.1

Methods

mempty :: Last a #

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

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

Generic1 * Last # 

Associated Types

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

Methods

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

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

type Rep (Last a) # 
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 # 
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 #

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt 

Fields

Instances

Generic1 k (Alt k f) # 

Associated Types

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

Methods

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

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

Monad f => Monad (Alt * f) # 

Methods

(>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b #

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

return :: a -> Alt * f a #

fail :: String -> Alt * f a #

Functor f => Functor (Alt * f) # 

Methods

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

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

MonadFix f => MonadFix (Alt * f) #

Since: 4.8.0.0

Methods

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

Applicative f => Applicative (Alt * f) # 

Methods

pure :: a -> Alt * f a #

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

liftA2 :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c #

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

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

MonadPlus f => MonadPlus (Alt * f) # 

Methods

mzero :: Alt * f a #

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

Alternative f => Alternative (Alt * f) # 

Methods

empty :: Alt * f a #

(<|>) :: Alt * f a -> Alt * f a -> Alt * f a #

some :: Alt * f a -> Alt * f [a] #

many :: Alt * f a -> Alt * f [a] #

MonadZip f => MonadZip (Alt * f) #

Since: 4.8.0.0

Methods

mzip :: Alt * f a -> Alt * f b -> Alt * f (a, b) #

mzipWith :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c #

munzip :: Alt * f (a, b) -> (Alt * f a, Alt * f b) #

Enum (f a) => Enum (Alt k f a) # 

Methods

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

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

toEnum :: Int -> Alt k f a #

fromEnum :: Alt k f a -> Int #

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

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

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

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

Eq (f a) => Eq (Alt k f a) # 

Methods

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

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

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

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) #

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

toConstr :: Alt * f a -> Constr #

dataTypeOf :: Alt * f a -> DataType #

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

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

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

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

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

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

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

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

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

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

Num (f a) => Num (Alt k f a) # 

Methods

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

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

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

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

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

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

fromInteger :: Integer -> Alt k f a #

Ord (f a) => Ord (Alt k f a) # 

Methods

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

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

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

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

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

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

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

Read (f a) => Read (Alt k f a) # 

Methods

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

readList :: ReadS [Alt k f a] #

readPrec :: ReadPrec (Alt k f a) #

readListPrec :: ReadPrec [Alt k f a] #

Show (f a) => Show (Alt k f a) # 

Methods

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

show :: Alt k f a -> String #

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

Generic (Alt k f a) # 

Associated Types

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

Methods

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

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

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

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty (Alt * f a) -> Alt * f a #

stimes :: Integral b => b -> Alt * f a -> Alt * f a #

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

Since: 4.8.0.0

Methods

mempty :: Alt * f a #

mappend :: Alt * f a -> Alt * f a -> Alt * f a #

mconcat :: [Alt * f a] -> Alt * f a #

type Rep1 k (Alt k f) # 
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) # 
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))))