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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	libraries@haskell.org
Stability	experimental
Portability	portable
Safe Haskell	Trustworthy
Language	Haskell2010

Monoid typeclass
Bool wrappers
Num wrappers
Maybe wrappers
Alternative wrapper

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
Methods mempty :: Ordering Source mappend :: Ordering -> Ordering -> Ordering Source mconcat :: [Ordering] -> Ordering Source
Monoid ()
Methods mempty :: () Source mappend :: () -> () -> () Source mconcat :: [()] -> () Source
Monoid Any
Methods mempty :: Any Source mappend :: Any -> Any -> Any Source mconcat :: [Any] -> Any Source
Monoid All
Methods mempty :: All Source mappend :: All -> All -> All Source mconcat :: [All] -> All Source
Monoid Lifetime	`mappend` == `elSupremum`
Methods mempty :: Lifetime Source mappend :: Lifetime -> Lifetime -> Lifetime Source mconcat :: [Lifetime] -> Lifetime Source
Monoid Event
Methods mempty :: Event Source mappend :: Event -> Event -> Event Source mconcat :: [Event] -> Event Source
Monoid [a]
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 `ee = e` and `es = s = s*e` for all `s ∈ S`." Since there is no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead.
Methods mempty :: Maybe a Source mappend :: Maybe a -> Maybe a -> Maybe a Source mconcat :: [Maybe a] -> Maybe a Source
Monoid a => Monoid (IO a)
Methods mempty :: IO a Source mappend :: IO a -> IO a -> IO a Source mconcat :: [IO a] -> IO a Source
Monoid (Last a)
Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
Monoid (First a)
Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
Num a => Monoid (Product a)
Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
Num a => Monoid (Sum a)
Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
Monoid (Endo a)
Methods mempty :: Endo a Source mappend :: Endo a -> Endo a -> Endo a Source mconcat :: [Endo a] -> Endo a Source
Monoid a => Monoid (Dual a)
Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
Semigroup a => Monoid (Option a)
Methods mempty :: Option a Source mappend :: Option a -> Option a -> Option a Source mconcat :: [Option a] -> Option a Source
Monoid m => Monoid (WrappedMonoid m)
Methods mempty :: WrappedMonoid m Source mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source mconcat :: [WrappedMonoid m] -> WrappedMonoid m Source
(Ord a, Bounded a) => Monoid (Max a)
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)
Methods mempty :: Min a Source mappend :: Min a -> Min a -> Min a Source mconcat :: [Min a] -> Min a Source
Monoid a => Monoid (Identity a)
Methods mempty :: Identity a Source mappend :: Identity a -> Identity a -> Identity a Source mconcat :: [Identity a] -> Identity a Source
Monoid b => Monoid (a -> b)
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)
Methods mempty :: (a, b) Source mappend :: (a, b) -> (a, b) -> (a, b) Source mconcat :: [(a, b)] -> (a, b) Source
Monoid (Proxy k s)
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)
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)
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)
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)
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 getDual :: a

Instances

Monad Dual
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
Methods fmap :: (a -> b) -> Dual a -> Dual b Source (<$) :: a -> Dual b -> Dual a Source
MonadFix Dual
Methods mfix :: (a -> Dual a) -> Dual a Source
Applicative Dual
Methods pure :: a -> Dual a Source (<>) :: Dual (a -> b) -> Dual a -> Dual b Source (>) :: Dual a -> Dual b -> Dual b Source (<*) :: Dual a -> Dual b -> Dual a Source
Foldable Dual
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
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
Generic1 Dual
Associated Types type Rep1 (Dual :: * -> ) :: -> * Source Methods from1 :: Dual a -> Rep1 Dual a Source to1 :: Rep1 Dual a -> Dual a Source
MonadZip Dual
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)
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)
Methods readsPrec :: Int -> ReadS (Dual a) Source readList :: ReadS [Dual a] Source readPrec :: ReadPrec (Dual a) Source readListPrec :: ReadPrec [Dual a] Source
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)
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)
Methods mempty :: Dual a Source mappend :: Dual a -> Dual a -> Dual a Source mconcat :: [Dual a] -> Dual a Source
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))
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)))

newtype Endo a Source

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

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)
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)
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 getAll :: Bool

Instances

Bounded All
Methods minBound :: All Source maxBound :: All Source
Eq All
Methods (==) :: All -> All -> Bool Source (/=) :: All -> All -> Bool Source
Data All
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
Methods readsPrec :: Int -> ReadS All Source readList :: ReadS [All] Source readPrec :: ReadPrec All Source readListPrec :: ReadPrec [All] Source
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
Methods (<>) :: All -> All -> All Source sconcat :: NonEmpty All -> All Source stimes :: Integral b => b -> All -> All Source
Monoid All
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 getAny :: Bool

Instances

Bounded Any
Methods minBound :: Any Source maxBound :: Any Source
Eq Any
Methods (==) :: Any -> Any -> Bool Source (/=) :: Any -> Any -> Bool Source
Data Any
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
Methods readsPrec :: Int -> ReadS Any Source readList :: ReadS [Any] Source readPrec :: ReadPrec Any Source readListPrec :: ReadPrec [Any] Source
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
Methods (<>) :: Any -> Any -> Any Source sconcat :: NonEmpty Any -> Any Source stimes :: Integral b => b -> Any -> Any Source
Monoid Any
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 getSum :: a

Instances

Monad Sum
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
Methods fmap :: (a -> b) -> Sum a -> Sum b Source (<$) :: a -> Sum b -> Sum a Source
MonadFix Sum
Methods mfix :: (a -> Sum a) -> Sum a Source
Applicative Sum
Methods pure :: a -> Sum a Source (<>) :: Sum (a -> b) -> Sum a -> Sum b Source (>) :: Sum a -> Sum b -> Sum b Source (<*) :: Sum a -> Sum b -> Sum a Source
Foldable Sum
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
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
Generic1 Sum
Associated Types type Rep1 (Sum :: * -> ) :: -> * Source Methods from1 :: Sum a -> Rep1 Sum a Source to1 :: Rep1 Sum a -> Sum a Source
MonadZip Sum
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)
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)
Methods readsPrec :: Int -> ReadS (Sum a) Source readList :: ReadS [Sum a] Source readPrec :: ReadPrec (Sum a) Source readListPrec :: ReadPrec [Sum a] Source
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)
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)
Methods mempty :: Sum a Source mappend :: Sum a -> Sum a -> Sum a Source mconcat :: [Sum a] -> Sum a Source
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))
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)))

newtype Product a Source

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Monad Product
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
Methods fmap :: (a -> b) -> Product a -> Product b Source (<$) :: a -> Product b -> Product a Source
MonadFix Product
Methods mfix :: (a -> Product a) -> Product a Source
Applicative Product
Methods pure :: a -> Product a Source (<>) :: Product (a -> b) -> Product a -> Product b Source (>) :: Product a -> Product b -> Product b Source (<*) :: Product a -> Product b -> Product a Source
Foldable Product
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
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
Generic1 Product
Associated Types type Rep1 (Product :: * -> ) :: -> * Source Methods from1 :: Product a -> Rep1 Product a Source to1 :: Rep1 Product a -> Product a Source
MonadZip Product
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)
Methods minBound :: Product a Source maxBound :: Product a Source
Eq a => Eq (Product a)
Methods (==) :: Product a -> Product a -> Bool Source (/=) :: Product a -> Product a -> Bool Source
Data a => Data (Product a)
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)
Methods (+) :: Product a -> Product a -> Product a Source (-) :: Product a -> Product a -> Product a Source (*) :: Product a -> Product a -> Product a Source negate :: Product a -> Product a Source abs :: Product a -> Product a Source signum :: Product a -> Product a Source fromInteger :: Integer -> Product a Source
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)
Methods readsPrec :: Int -> ReadS (Product a) Source readList :: ReadS [Product a] Source readPrec :: ReadPrec (Product a) Source readListPrec :: ReadPrec [Product a] Source
Show a => Show (Product a)
Methods showsPrec :: Int -> Product a -> ShowS Source show :: Product a -> String Source showList :: [Product a] -> ShowS Source
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)
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)
Methods mempty :: Product a Source mappend :: Product a -> Product a -> Product a Source mconcat :: [Product a] -> Product a Source
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))
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)))

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 getFirst :: Maybe a

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
Methods mfix :: (a -> First a) -> First a Source
Applicative First
Methods pure :: a -> First a Source (<>) :: First (a -> b) -> First a -> First b Source (>) :: First a -> First b -> First b Source (<*) :: First a -> First b -> First a Source
Foldable First
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
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
Generic1 First
Associated Types type Rep1 (First :: * -> ) :: -> * Source Methods from1 :: First a -> Rep1 First a Source to1 :: Rep1 First a -> First a Source
MonadZip First
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)
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)
Methods readsPrec :: Int -> ReadS (First a) Source readList :: ReadS [First a] Source readPrec :: ReadPrec (First a) Source readListPrec :: ReadPrec [First a] Source
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)
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)
Methods mempty :: First a Source mappend :: First a -> First a -> First a Source mconcat :: [First a] -> First a Source
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)))
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))))

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 getLast :: Maybe a

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
Methods mfix :: (a -> Last a) -> Last a Source
Applicative Last
Methods pure :: a -> Last a Source (<>) :: Last (a -> b) -> Last a -> Last b Source (>) :: Last a -> Last b -> Last b Source (<*) :: Last a -> Last b -> Last a Source
Foldable Last
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
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
Generic1 Last
Associated Types type Rep1 (Last :: * -> ) :: -> * Source Methods from1 :: Last a -> Rep1 Last a Source to1 :: Rep1 Last a -> Last a Source
MonadZip Last
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)
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)
Methods readsPrec :: Int -> ReadS (Last a) Source readList :: ReadS [Last a] Source readPrec :: ReadPrec (Last a) Source readListPrec :: ReadPrec [Last a] Source
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)
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)
Methods mempty :: Last a Source mappend :: Last a -> Last a -> Last a Source mconcat :: [Last a] -> Last a Source
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)))
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))))

Alternative wrapper

newtype Alt f a Source

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt
Fields getAlt :: f a

Instances

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)
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 (>) :: Alt f a -> Alt * f b -> Alt * f b Source (<) :: Alt f a -> Alt * f b -> Alt * f a Source
Generic1 (Alt * f)
Associated Types type Rep1 (Alt * f :: * -> ) :: -> * Source Methods from1 :: Alt * f a -> Rep1 (Alt * f) a Source to1 :: Rep1 (Alt * f) a -> 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)
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)
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)
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)
Methods mempty :: Alt * f a Source mappend :: Alt * f a -> Alt * f a -> Alt * f a Source mconcat :: [Alt * f a] -> Alt * f a Source
type Rep1 (Alt * f)
type Rep1 (Alt * f) = D1 (MetaData "Alt" "Data.Monoid" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 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))))

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.0.1/docs/html/libraries/base-4.9.0.0/Data-Monoid.html

Data.Monoid

Data.Monoid

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Description

Monoid typeclass

Minimal complete definition

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