Data.Monoid

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

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

Methods

mempty :: Ordering

mappend :: Ordering -> Ordering -> Ordering

mconcat :: [Ordering] -> Ordering

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

Methods

mempty :: Lifetime

mappend :: Lifetime -> Lifetime -> Lifetime

mconcat :: [Lifetime] -> Lifetime

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

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

(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

• getDual :: a

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

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

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

(<) :: 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)

Methods

readsPrec :: Int -> ReadS (Dual a)

readList :: ReadS [Dual a]

readPrec :: ReadPrec (Dual a)

readListPrec :: ReadPrec [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

• appEndo :: a -> a

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

• getAll :: Bool

Instances

Bounded All

Methods

minBound :: All

maxBound :: All

Eq All

Methods

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

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

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

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

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

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

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

max :: All -> All -> All

min :: All -> All -> All

Read All

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [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

• getAny :: Bool

Instances

Bounded Any

Methods

minBound :: Any

maxBound :: Any

Eq Any

Methods

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

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

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

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

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

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

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

max :: Any -> Any -> Any

min :: Any -> Any -> Any

Read Any

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [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

• getSum :: a

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

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

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

(<) :: 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)

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [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

• getProduct :: a

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)

Methods

minBound :: Product a

maxBound :: Product a

Eq a => Eq (Product a)

Methods

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

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

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)

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)

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [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

• getFirst :: Maybe a

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

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

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

(<) :: 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)

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [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

• getLast :: Maybe a

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

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

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

(<) :: 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)

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [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

• getAlt :: f a

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

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

(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

(<) :: 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)

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))))