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/Haskell 8

Data.Monoid

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

Description

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

Monoid typeclass

class 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

Since: 2.1

Monoid ()

Since: 2.1

Methods

mempty :: () Source

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

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

Monoid Any

Since: 2.1

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

Monoid All

Since: 2.1

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

Monoid Lifetime

mappend takes the longer of two lifetimes.

Since: 4.8.0.0

Monoid Event

Since: 4.3.1.0

Monoid [a]

Since: 2.1

Methods

mempty :: [a] Source

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

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

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 Source

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

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

Monoid a => Monoid (IO a)

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)

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)

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)

Since: 2.1

Num a => Monoid (Sum a)

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)

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)

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)
Semigroup a => Monoid (Option a)

Since: 4.9.0.0

Methods

mempty :: Option a Source

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

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

Monoid m => Monoid (WrappedMonoid m)

Since: 4.9.0.0

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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

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

Since: 4.8.0.0

Methods

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

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

MonadFix Dual

Since: 4.8.0.0

Methods

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

Applicative Dual

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

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

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

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)

Methods

minBound :: Dual a Source

maxBound :: Dual a Source

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) 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)

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 Source

show :: Dual a -> String Source

showList :: [Dual a] -> ShowS Source

Generic (Dual a)

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)

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)

Since: 2.1

Methods

mempty :: Dual a Source

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

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

Generic1 * Dual

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)
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 Source

The monoid of endomorphisms under composition.

Constructors

Endo

Fields

Instances

Generic (Endo a)

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)

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)

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)
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
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 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

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 Source

show :: All -> String Source

showList :: [All] -> ShowS Source

Generic All

Associated Types

type Rep All :: * -> * Source

Methods

from :: All -> Rep All x Source

to :: Rep All x -> All Source

Semigroup All

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty All -> All Source

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

Monoid All

Since: 2.1

Methods

mempty :: All Source

mappend :: All -> All -> All Source

mconcat :: [All] -> All Source

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 Source

Boolean monoid under disjunction (||).

Constructors

Any

Fields

Instances

Bounded 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 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

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 Source

show :: Any -> String Source

showList :: [Any] -> ShowS Source

Generic Any

Associated Types

type Rep Any :: * -> * Source

Methods

from :: Any -> Rep Any x Source

to :: Rep Any x -> Any Source

Semigroup Any

Since: 4.9.0.0

Methods

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

sconcat :: NonEmpty Any -> Any Source

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

Monoid Any

Since: 2.1

Methods

mempty :: Any Source

mappend :: Any -> Any -> Any Source

mconcat :: [Any] -> Any Source

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 Source

Monoid under addition.

Constructors

Sum

Fields

Instances

Monad Sum

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

Since: 4.8.0.0

Methods

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

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

MonadFix Sum

Since: 4.8.0.0

Methods

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

Applicative Sum

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

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

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

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)

Methods

minBound :: Sum a Source

maxBound :: Sum a Source

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) 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)

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)

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 Source

show :: Sum a -> String Source

showList :: [Sum a] -> ShowS Source

Generic (Sum a)

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)

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)

Since: 2.1

Methods

mempty :: Sum a Source

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

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

Generic1 * Sum

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)
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 Source

Monoid under multiplication.

Constructors

Product

Fields

Instances

Monad Product

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

Since: 4.8.0.0

Methods

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

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

MonadFix Product

Since: 4.8.0.0

Methods

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

Applicative Product

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

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

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

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)
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) 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)
Ord a => Ord (Product a)

Methods

compare :: Product a -> Product a -> Ordering Source

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

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

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

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

max :: Product a -> Product a -> Product a Source

min :: Product a -> Product a -> Product a Source

Read a => Read (Product a)
Show a => Show (Product a)
Generic (Product a)

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)

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)

Since: 2.1

Generic1 * Product

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)
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 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

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

Methods

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

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

MonadFix First

Since: 4.8.0.0

Methods

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

Applicative First

Methods

pure :: a -> First a Source

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

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

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

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

Foldable First

Since: 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

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

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)

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) 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)

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 Source

show :: First a -> String Source

showList :: [First a] -> ShowS Source

Generic (First a)

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)

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)

Since: 2.1

Methods

mempty :: First a Source

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

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

Generic1 * First

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)
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 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

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

Methods

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

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

MonadFix Last

Since: 4.8.0.0

Methods

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

Applicative Last

Methods

pure :: a -> Last a Source

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

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

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

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

Foldable Last

Since: 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

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

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)

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) 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)

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 Source

show :: Last a -> String Source

showList :: [Last a] -> ShowS Source

Generic (Last a)

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)

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)

Since: 2.1

Methods

mempty :: Last a Source

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

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

Generic1 * Last

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)
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 Source

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 -> * 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)

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)

Methods

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

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

MonadFix f => MonadFix (Alt * f)

Since: 4.8.0.0

Methods

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

Applicative f => Applicative (Alt * f)

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)

Methods

mzero :: Alt * f a Source

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

Alternative f => Alternative (Alt * f)

Methods

empty :: Alt * f a Source

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

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

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

MonadZip f => MonadZip (Alt * f)

Since: 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)

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)

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) 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)

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)

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) 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)

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)

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)

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)

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)
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))))

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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Monoid.html