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

Data.Monoid

Contents

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.

Synopsis

`Monoid` typeclass

class Monoid a where Source #

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

```
mappend mempty x = x
```
```
mappend x mempty = x
```

mappend x (mappend y z) = mappend (mappend x y) z

```
mconcat = foldr mappend mempty
```

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

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

Minimal complete definition

mempty, mappend

Methods

mempty :: a Source #

Identity of mappend

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

An associative operation

mconcat :: [a] -> a Source #

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

Instances

Monoid Ordering Source #	Since: 2.1
Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () Source #	Since: 2.1
Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid Any Source #	Since: 2.1
Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid All Source #	Since: 2.1
Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
Monoid Lifetime Source #	`mappend` takes the longer of two lifetimes. Since: 4.8.0.0
Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Event Source #	Since: 4.3.1.0
Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid [a] Source #	Since: 2.1
Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Monoid a => Monoid (Maybe a) Source #	Lift a semigroup into `Maybe` forming a `Monoid` according to http://en.wikipedia.org/wiki/Monoid: "Any semigroup `S` may be turned into a monoid simply by adjoining an element `e` not in `S` and defining `ee = e` and `es = s = se` for all `s ∈ S`." Since there used to be no "Semigroup" typeclass providing just `mappend`, we use `Monoid` instead. Since: 2.1*
Methods mempty :: Maybe a Source # mappend :: Maybe a -> Maybe a -> Maybe a Source # mconcat :: [Maybe a] -> Maybe a Source #
Monoid a => Monoid (IO a) Source #	Since: 4.9.0.0
Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid (Last a) Source #	Since: 2.1
Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Monoid (First a) Source #	Since: 2.1
Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Num a => Monoid (Product a) Source #	Since: 2.1
Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Num a => Monoid (Sum a) Source #	Since: 2.1
Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Monoid (Endo a) Source #	Since: 2.1
Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
Monoid a => Monoid (Dual a) Source #	Since: 2.1
Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid a => Monoid (Identity a) Source #
Methods mempty :: Identity a Source # mappend :: Identity a -> Identity a -> Identity a Source # mconcat :: [Identity a] -> Identity a Source #
Semigroup a => Monoid (Option a) Source #	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) Source #	Since: 4.9.0.0
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) Source #	Since: 4.9.0.0
Methods mempty :: Max a Source # mappend :: Max a -> Max a -> Max a Source # mconcat :: [Max a] -> Max a Source #
(Ord a, Bounded a) => Monoid (Min a) Source #	Since: 4.9.0.0
Methods mempty :: Min a Source # mappend :: Min a -> Min a -> Min a Source # mconcat :: [Min a] -> Min a Source #
Monoid b => Monoid (a -> b) Source #	Since: 2.1
Methods mempty :: a -> b Source # mappend :: (a -> b) -> (a -> b) -> a -> b Source # mconcat :: [a -> b] -> a -> b Source #
(Monoid a, Monoid b) => Monoid (a, b) Source #	Since: 2.1
Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid (Proxy k s) Source #	Since: 4.7.0.0
Methods mempty :: Proxy k s Source # mappend :: Proxy k s -> Proxy k s -> Proxy k s Source # mconcat :: [Proxy k s] -> Proxy k s Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source #	Since: 2.1
Methods mempty :: (a, b, c) Source # mappend :: (a, b, c) -> (a, b, c) -> (a, b, c) Source # mconcat :: [(a, b, c)] -> (a, b, c) Source #
Alternative f => Monoid (Alt * f a) Source #	Since: 4.8.0.0
Methods mempty :: Alt * f a Source # mappend :: Alt * f a -> Alt * f a -> Alt * f a Source # mconcat :: [Alt * f a] -> Alt * f a Source #
Monoid a => Monoid (Const k a b) Source #
Methods mempty :: Const k a b Source # mappend :: Const k a b -> Const k a b -> Const k a b Source # mconcat :: [Const k a b] -> Const k a b Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #	Since: 2.1
Methods mempty :: (a, b, c, d) Source # mappend :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source # mconcat :: [(a, b, c, d)] -> (a, b, c, d) Source #
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source #	Since: 2.1
Methods mempty :: (a, b, c, d, e) Source # mappend :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source # mconcat :: [(a, b, c, d, e)] -> (a, b, c, d, e) Source #

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

An infix synonym for mappend.

Since: 4.5.0.0

newtype Dual a Source #

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

Constructors

Dual
Fields getDual :: a

Instances

Monad Dual Source #	Since: 4.8.0.0
Methods (>>=) :: Dual a -> (a -> Dual b) -> Dual b Source # (>>) :: Dual a -> Dual b -> Dual b Source # return :: a -> Dual a Source # fail :: String -> Dual a Source #
Functor Dual Source #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
MonadFix Dual Source #	Since: 4.8.0.0
Methods mfix :: (a -> Dual a) -> Dual a Source #
Applicative Dual Source #	Since: 4.8.0.0
Methods pure :: a -> Dual a Source # (<>) :: Dual (a -> b) -> Dual a -> Dual b Source # liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # (>) :: Dual a -> Dual b -> Dual b Source # (<*) :: Dual a -> Dual b -> Dual a Source #
Foldable Dual Source #	Since: 4.8.0.0
Methods fold :: Monoid m => Dual m -> m Source # foldMap :: Monoid m => (a -> m) -> Dual a -> m Source # foldr :: (a -> b -> b) -> b -> Dual a -> b Source # foldr' :: (a -> b -> b) -> b -> Dual a -> b Source # foldl :: (b -> a -> b) -> b -> Dual a -> b Source # foldl' :: (b -> a -> b) -> b -> Dual a -> b Source # foldr1 :: (a -> a -> a) -> Dual a -> a Source # foldl1 :: (a -> a -> a) -> Dual a -> a Source # toList :: Dual a -> [a] Source # null :: Dual a -> Bool Source # length :: Dual a -> Int Source # elem :: Eq a => a -> Dual a -> Bool Source # maximum :: Ord a => Dual a -> a Source # minimum :: Ord a => Dual a -> a Source # sum :: Num a => Dual a -> a Source # product :: Num a => Dual a -> a Source #
Traversable Dual Source #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source # sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source # mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source # sequence :: Monad m => Dual (m a) -> m (Dual a) Source #
MonadZip Dual Source #	Since: 4.8.0.0
Methods mzip :: Dual a -> Dual b -> Dual (a, b) Source # mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source # munzip :: Dual (a, b) -> (Dual a, Dual b) Source #
Bounded a => Bounded (Dual a) Source #
Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Eq a => Eq (Dual a) Source #
Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Data a => Data (Dual a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source # toConstr :: Dual a -> Constr Source # dataTypeOf :: Dual a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) Source #
Ord a => Ord (Dual a) Source #
Methods compare :: Dual a -> Dual a -> Ordering # (<) :: Dual a -> Dual a -> Bool # (<=) :: Dual a -> Dual a -> Bool # (>) :: Dual a -> Dual a -> Bool # (>=) :: Dual a -> Dual a -> Bool # max :: Dual a -> Dual a -> Dual a # min :: Dual a -> Dual a -> Dual a #
Read a => Read (Dual a) Source #
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) Source #
Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Generic (Dual a) Source #
Associated Types type Rep (Dual a) :: * -> * Source # Methods from :: Dual a -> Rep (Dual a) x Source # to :: Rep (Dual a) x -> Dual a Source #
Semigroup a => Semigroup (Dual a) Source #	Since: 4.9.0.0
Methods (<>) :: Dual a -> Dual a -> Dual a Source # sconcat :: NonEmpty (Dual a) -> Dual a Source # stimes :: Integral b => b -> Dual a -> Dual a Source #
Monoid a => Monoid (Dual a) Source #	Since: 2.1
Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Generic1 * Dual Source #
Associated Types type Rep1 Dual (f :: Dual -> ) :: k -> Source # Methods from1 :: f a -> Rep1 Dual f a Source # to1 :: Rep1 Dual f a -> f a Source #
type Rep (Dual a) Source #
type Rep (Dual a) = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Dual Source #
type Rep1 * Dual = D1 * (MetaData "Dual" "Data.Monoid" "base" True) (C1 * (MetaCons "Dual" PrefixI True) (S1 * (MetaSel (Just Symbol "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a) Source #
Associated Types type Rep (Endo a) :: * -> * Source # Methods from :: Endo a -> Rep (Endo a) x Source # to :: Rep (Endo a) x -> Endo a Source #
Semigroup (Endo a) Source #	Since: 4.9.0.0
Methods (<>) :: Endo a -> Endo a -> Endo a Source # sconcat :: NonEmpty (Endo a) -> Endo a Source # stimes :: Integral b => b -> Endo a -> Endo a Source #
Monoid (Endo a) Source #	Since: 2.1
Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
type Rep (Endo a) Source #
type Rep (Endo a) = D1 * (MetaData "Endo" "Data.Monoid" "base" True) (C1 * (MetaCons "Endo" PrefixI True) (S1 * (MetaSel (Just Symbol "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (a -> a))))

`Bool` wrappers

newtype All Source #

Boolean monoid under conjunction (&&).

Constructors

All
Fields getAll :: Bool

Instances

Bounded All Source #
Methods minBound :: All Source # maxBound :: All Source #
Eq All Source #
Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Data All Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source # toConstr :: All -> Constr Source # dataTypeOf :: All -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c All) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) Source # gmapT :: (forall b. Data b => b -> b) -> All -> All Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r Source # gmapQ :: (forall d. Data d => d -> u) -> All -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All Source #
Ord All Source #
Methods compare :: All -> All -> Ordering # (<) :: All -> All -> Bool # (<=) :: All -> All -> Bool # (>) :: All -> All -> Bool # (>=) :: All -> All -> Bool # max :: All -> All -> All # min :: All -> All -> All #
Read All Source #
Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All Source #
Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Generic All Source #
Associated Types type Rep All :: * -> * Source # Methods from :: All -> Rep All x Source # to :: Rep All x -> All Source #
Semigroup All Source #	Since: 4.9.0.0
Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Monoid All Source #	Since: 2.1
Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
type Rep All Source #
type Rep All = D1 * (MetaData "All" "Data.Monoid" "base" True) (C1 * (MetaCons "All" PrefixI True) (S1 * (MetaSel (Just Symbol "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any Source #
Methods minBound :: Any Source # maxBound :: Any Source #
Eq Any Source #
Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Data Any Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source # toConstr :: Any -> Constr Source # dataTypeOf :: Any -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c Any) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) Source # gmapT :: (forall b. Data b => b -> b) -> Any -> Any Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any Source #
Ord Any Source #
Methods compare :: Any -> Any -> Ordering # (<) :: Any -> Any -> Bool # (<=) :: Any -> Any -> Bool # (>) :: Any -> Any -> Bool # (>=) :: Any -> Any -> Bool # max :: Any -> Any -> Any # min :: Any -> Any -> Any #
Read Any Source #
Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any Source #
Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Generic Any Source #
Associated Types type Rep Any :: * -> * Source # Methods from :: Any -> Rep Any x Source # to :: Rep Any x -> Any Source #
Semigroup Any Source #	Since: 4.9.0.0
Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Monoid Any Source #	Since: 2.1
Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
type Rep Any Source #
type Rep Any = D1 * (MetaData "Any" "Data.Monoid" "base" True) (C1 * (MetaCons "Any" PrefixI True) (S1 * (MetaSel (Just Symbol "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * Bool)))

`Num` wrappers

newtype Sum a Source #

Monoid under addition.

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum Source #	Since: 4.8.0.0
Methods (>>=) :: Sum a -> (a -> Sum b) -> Sum b Source # (>>) :: Sum a -> Sum b -> Sum b Source # return :: a -> Sum a Source # fail :: String -> Sum a Source #
Functor Sum Source #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
MonadFix Sum Source #	Since: 4.8.0.0
Methods mfix :: (a -> Sum a) -> Sum a Source #
Applicative Sum Source #	Since: 4.8.0.0
Methods pure :: a -> Sum a Source # (<>) :: Sum (a -> b) -> Sum a -> Sum b Source # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # (>) :: Sum a -> Sum b -> Sum b Source # (<*) :: Sum a -> Sum b -> Sum a Source #
Foldable Sum Source #	Since: 4.8.0.0
Methods fold :: Monoid m => Sum m -> m Source # foldMap :: Monoid m => (a -> m) -> Sum a -> m Source # foldr :: (a -> b -> b) -> b -> Sum a -> b Source # foldr' :: (a -> b -> b) -> b -> Sum a -> b Source # foldl :: (b -> a -> b) -> b -> Sum a -> b Source # foldl' :: (b -> a -> b) -> b -> Sum a -> b Source # foldr1 :: (a -> a -> a) -> Sum a -> a Source # foldl1 :: (a -> a -> a) -> Sum a -> a Source # toList :: Sum a -> [a] Source # null :: Sum a -> Bool Source # length :: Sum a -> Int Source # elem :: Eq a => a -> Sum a -> Bool Source # maximum :: Ord a => Sum a -> a Source # minimum :: Ord a => Sum a -> a Source # sum :: Num a => Sum a -> a Source # product :: Num a => Sum a -> a Source #
Traversable Sum Source #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) Source # sequenceA :: Applicative f => Sum (f a) -> f (Sum a) Source # mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) Source # sequence :: Monad m => Sum (m a) -> m (Sum a) Source #
MonadZip Sum Source #	Since: 4.8.0.0
Methods mzip :: Sum a -> Sum b -> Sum (a, b) Source # mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source # munzip :: Sum (a, b) -> (Sum a, Sum b) Source #
Bounded a => Bounded (Sum a) Source #
Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Eq a => Eq (Sum a) Source #
Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Data a => Data (Sum a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Sum a -> c (Sum a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) Source # toConstr :: Sum a -> Constr Source # dataTypeOf :: Sum a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) Source #
Num a => Num (Sum a) Source #
Methods (+) :: Sum a -> Sum a -> Sum a Source # (-) :: Sum a -> Sum a -> Sum a Source # (*) :: Sum a -> Sum a -> Sum a Source # negate :: Sum a -> Sum a Source # abs :: Sum a -> Sum a Source # signum :: Sum a -> Sum a Source # fromInteger :: Integer -> Sum a Source #
Ord a => Ord (Sum a) Source #
Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Read a => Read (Sum a) Source #
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) Source #
Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Generic (Sum a) Source #
Associated Types type Rep (Sum a) :: * -> * Source # Methods from :: Sum a -> Rep (Sum a) x Source # to :: Rep (Sum a) x -> Sum a Source #
Num a => Semigroup (Sum a) Source #	Since: 4.9.0.0
Methods (<>) :: Sum a -> Sum a -> Sum a Source # sconcat :: NonEmpty (Sum a) -> Sum a Source # stimes :: Integral b => b -> Sum a -> Sum a Source #
Num a => Monoid (Sum a) Source #	Since: 2.1
Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Generic1 * Sum Source #
Associated Types type Rep1 Sum (f :: Sum -> ) :: k -> Source # Methods from1 :: f a -> Rep1 Sum f a Source # to1 :: Rep1 Sum f a -> f a Source #
type Rep (Sum a) Source #
type Rep (Sum a) = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Sum Source #
type Rep1 * Sum = D1 * (MetaData "Sum" "Data.Monoid" "base" True) (C1 * (MetaCons "Sum" PrefixI True) (S1 * (MetaSel (Just Symbol "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

Constructors

Product
Fields getProduct :: a

Instances

Monad Product Source #	Since: 4.8.0.0
Methods (>>=) :: Product a -> (a -> Product b) -> Product b Source # (>>) :: Product a -> Product b -> Product b Source # return :: a -> Product a Source # fail :: String -> Product a Source #
Functor Product Source #	Since: 4.8.0.0
Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
MonadFix Product Source #	Since: 4.8.0.0
Methods mfix :: (a -> Product a) -> Product a Source #
Applicative Product Source #	Since: 4.8.0.0
Methods pure :: a -> Product a Source # (<>) :: Product (a -> b) -> Product a -> Product b Source # liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source # (>) :: Product a -> Product b -> Product b Source # (<*) :: Product a -> Product b -> Product a Source #
Foldable Product Source #	Since: 4.8.0.0
Methods fold :: Monoid m => Product m -> m Source # foldMap :: Monoid m => (a -> m) -> Product a -> m Source # foldr :: (a -> b -> b) -> b -> Product a -> b Source # foldr' :: (a -> b -> b) -> b -> Product a -> b Source # foldl :: (b -> a -> b) -> b -> Product a -> b Source # foldl' :: (b -> a -> b) -> b -> Product a -> b Source # foldr1 :: (a -> a -> a) -> Product a -> a Source # foldl1 :: (a -> a -> a) -> Product a -> a Source # toList :: Product a -> [a] Source # null :: Product a -> Bool Source # length :: Product a -> Int Source # elem :: Eq a => a -> Product a -> Bool Source # maximum :: Ord a => Product a -> a Source # minimum :: Ord a => Product a -> a Source # sum :: Num a => Product a -> a Source # product :: Num a => Product a -> a Source #
Traversable Product Source #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) Source # sequenceA :: Applicative f => Product (f a) -> f (Product a) Source # mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) Source # sequence :: Monad m => Product (m a) -> m (Product a) Source #
MonadZip Product Source #	Since: 4.8.0.0
Methods mzip :: Product a -> Product b -> Product (a, b) Source # mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c Source # munzip :: Product (a, b) -> (Product a, Product b) Source #
Bounded a => Bounded (Product a) Source #
Methods minBound :: Product a Source # maxBound :: Product a Source #
Eq a => Eq (Product a) Source #
Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Data a => Data (Product a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Product a -> c (Product a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) Source # toConstr :: Product a -> Constr Source # dataTypeOf :: Product a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) Source #
Num a => Num (Product a) Source #
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) Source #
Methods compare :: Product a -> Product a -> Ordering # (<) :: Product a -> Product a -> Bool # (<=) :: Product a -> Product a -> Bool # (>) :: Product a -> Product a -> Bool # (>=) :: Product a -> Product a -> Bool # max :: Product a -> Product a -> Product a # min :: Product a -> Product a -> Product a #
Read a => Read (Product a) Source #
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) Source #
Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Generic (Product a) Source #
Associated Types type Rep (Product a) :: * -> * Source # Methods from :: Product a -> Rep (Product a) x Source # to :: Rep (Product a) x -> Product a Source #
Num a => Semigroup (Product a) Source #	Since: 4.9.0.0
Methods (<>) :: Product a -> Product a -> Product a Source # sconcat :: NonEmpty (Product a) -> Product a Source # stimes :: Integral b => b -> Product a -> Product a Source #
Num a => Monoid (Product a) Source #	Since: 2.1
Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Generic1 * Product Source #
Associated Types type Rep1 Product (f :: Product -> ) :: k -> Source # Methods from1 :: f a -> Rep1 Product f a Source # to1 :: Rep1 Product f a -> f a Source #
type Rep (Product a) Source #
type Rep (Product a) = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * a)))
type Rep1 * Product Source #
type Rep1 * Product = D1 * (MetaData "Product" "Data.Monoid" "base" True) (C1 * (MetaCons "Product" PrefixI True) (S1 * (MetaSel (Just Symbol "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

`Maybe` wrappers

To implement find or findLast on any Foldable:

findLast :: Foldable t => (a -> Bool) -> t a -> Maybe a
findLast pred = getLast . foldMap (x -> if pred x
                                           then Last (Just x)
                                           else Last Nothing)

Much of Data.Map's interface can be implemented with Data.Map.alter. Some of the rest can be implemented with a new alterA function and either First or Last:

alterA :: (Applicative f, Ord k) =>
          (Maybe a -> f (Maybe a)) -> k -> Map k a -> f (Map k a)

instance Monoid a => Applicative ((,) a)  -- from Control.Applicative

insertLookupWithKey :: Ord k => (k -> v -> v -> v) -> k -> v
                    -> Map k v -> (Maybe v, Map k v)
insertLookupWithKey combine key value =
  Arrow.first getFirst . alterA doChange key
  where
  doChange Nothing = (First Nothing, Just value)
  doChange (Just oldValue) =
    (First (Just oldValue),
     Just (combine key value oldValue))

newtype First a Source #

Maybe monoid returning the leftmost non-Nothing value.

First a is isomorphic to Alt Maybe a, but precedes it historically.

Constructors

First
Fields getFirst :: Maybe a

Instances

Monad First Source #
Methods (>>=) :: First a -> (a -> First b) -> First b Source # (>>) :: First a -> First b -> First b Source # return :: a -> First a Source # fail :: String -> First a Source #
Functor First Source #
Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
MonadFix First Source #	Since: 4.8.0.0
Methods mfix :: (a -> First a) -> First a Source #
Applicative First Source #
Methods pure :: a -> First a Source # (<>) :: First (a -> b) -> First a -> First b Source # liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source # (>) :: First a -> First b -> First b Source # (<*) :: First a -> First b -> First a Source #
Foldable First Source #	Since: 4.8.0.0
Methods fold :: Monoid m => First m -> m Source # foldMap :: Monoid m => (a -> m) -> First a -> m Source # foldr :: (a -> b -> b) -> b -> First a -> b Source # foldr' :: (a -> b -> b) -> b -> First a -> b Source # foldl :: (b -> a -> b) -> b -> First a -> b Source # foldl' :: (b -> a -> b) -> b -> First a -> b Source # foldr1 :: (a -> a -> a) -> First a -> a Source # foldl1 :: (a -> a -> a) -> First a -> a Source # toList :: First a -> [a] Source # null :: First a -> Bool Source # length :: First a -> Int Source # elem :: Eq a => a -> First a -> Bool Source # maximum :: Ord a => First a -> a Source # minimum :: Ord a => First a -> a Source # sum :: Num a => First a -> a Source # product :: Num a => First a -> a Source #
Traversable First Source #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source # sequenceA :: Applicative f => First (f a) -> f (First a) Source # mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source # sequence :: Monad m => First (m a) -> m (First a) Source #
MonadZip First Source #	Since: 4.8.0.0
Methods mzip :: First a -> First b -> First (a, b) Source # mzipWith :: (a -> b -> c) -> First a -> First b -> First c Source # munzip :: First (a, b) -> (First a, First b) Source #
Eq a => Eq (First a) Source #
Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Data a => Data (First a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) Source # toConstr :: First a -> Constr Source # dataTypeOf :: First a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b -> b) -> First a -> First a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) Source #
Ord a => Ord (First a) Source #
Methods compare :: First a -> First a -> Ordering # (<) :: First a -> First a -> Bool # (<=) :: First a -> First a -> Bool # (>) :: First a -> First a -> Bool # (>=) :: First a -> First a -> Bool # max :: First a -> First a -> First a # min :: First a -> First a -> First a #
Read a => Read (First a) Source #
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) Source #
Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Generic (First a) Source #
Associated Types type Rep (First a) :: * -> * Source # Methods from :: First a -> Rep (First a) x Source # to :: Rep (First a) x -> First a Source #
Semigroup (First a) Source #	Since: 4.9.0.0
Methods (<>) :: First a -> First a -> First a Source # sconcat :: NonEmpty (First a) -> First a Source # stimes :: Integral b => b -> First a -> First a Source #
Monoid (First a) Source #	Since: 2.1
Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Generic1 * First Source #
Associated Types type Rep1 First (f :: First -> ) :: k -> Source # Methods from1 :: f a -> Rep1 First f a Source # to1 :: Rep1 First f a -> f a Source #
type Rep (First a) Source #
type Rep (First a) = D1 * (MetaData "First" "Data.Monoid" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * First Source #
type Rep1 * First = D1 * (MetaData "First" "Data.Monoid" "base" True) (C1 * (MetaCons "First" PrefixI True) (S1 * (MetaSel (Just Symbol "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))

newtype Last a Source #

Maybe monoid returning the rightmost non-Nothing value.

Last a is isomorphic to Dual (First a), and thus to Dual (Alt Maybe a)

Constructors

Last
Fields getLast :: Maybe a

Instances

Monad Last Source #
Methods (>>=) :: Last a -> (a -> Last b) -> Last b Source # (>>) :: Last a -> Last b -> Last b Source # return :: a -> Last a Source # fail :: String -> Last a Source #
Functor Last Source #
Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
MonadFix Last Source #	Since: 4.8.0.0
Methods mfix :: (a -> Last a) -> Last a Source #
Applicative Last Source #
Methods pure :: a -> Last a Source # (<>) :: Last (a -> b) -> Last a -> Last b Source # liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source # (>) :: Last a -> Last b -> Last b Source # (<*) :: Last a -> Last b -> Last a Source #
Foldable Last Source #	Since: 4.8.0.0
Methods fold :: Monoid m => Last m -> m Source # foldMap :: Monoid m => (a -> m) -> Last a -> m Source # foldr :: (a -> b -> b) -> b -> Last a -> b Source # foldr' :: (a -> b -> b) -> b -> Last a -> b Source # foldl :: (b -> a -> b) -> b -> Last a -> b Source # foldl' :: (b -> a -> b) -> b -> Last a -> b Source # foldr1 :: (a -> a -> a) -> Last a -> a Source # foldl1 :: (a -> a -> a) -> Last a -> a Source # toList :: Last a -> [a] Source # null :: Last a -> Bool Source # length :: Last a -> Int Source # elem :: Eq a => a -> Last a -> Bool Source # maximum :: Ord a => Last a -> a Source # minimum :: Ord a => Last a -> a Source # sum :: Num a => Last a -> a Source # product :: Num a => Last a -> a Source #
Traversable Last Source #	Since: 4.8.0.0
Methods traverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source # sequenceA :: Applicative f => Last (f a) -> f (Last a) Source # mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source # sequence :: Monad m => Last (m a) -> m (Last a) Source #
MonadZip Last Source #	Since: 4.8.0.0
Methods mzip :: Last a -> Last b -> Last (a, b) Source # mzipWith :: (a -> b -> c) -> Last a -> Last b -> Last c Source # munzip :: Last (a, b) -> (Last a, Last b) Source #
Eq a => Eq (Last a) Source #
Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Data a => Data (Last a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) Source # toConstr :: Last a -> Constr Source # dataTypeOf :: Last a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) Source # dataCast2 :: Typeable ( -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) Source #
Ord a => Ord (Last a) Source #
Methods compare :: Last a -> Last a -> Ordering # (<) :: Last a -> Last a -> Bool # (<=) :: Last a -> Last a -> Bool # (>) :: Last a -> Last a -> Bool # (>=) :: Last a -> Last a -> Bool # max :: Last a -> Last a -> Last a # min :: Last a -> Last a -> Last a #
Read a => Read (Last a) Source #
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) Source #
Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Generic (Last a) Source #
Associated Types type Rep (Last a) :: * -> * Source # Methods from :: Last a -> Rep (Last a) x Source # to :: Rep (Last a) x -> Last a Source #
Semigroup (Last a) Source #	Since: 4.9.0.0
Methods (<>) :: Last a -> Last a -> Last a Source # sconcat :: NonEmpty (Last a) -> Last a Source # stimes :: Integral b => b -> Last a -> Last a Source #
Monoid (Last a) Source #	Since: 2.1
Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Generic1 * Last Source #
Associated Types type Rep1 Last (f :: Last -> ) :: k -> Source # Methods from1 :: f a -> Rep1 Last f a Source # to1 :: Rep1 Last f a -> f a Source #
type Rep (Last a) Source #
type Rep (Last a) = D1 * (MetaData "Last" "Data.Monoid" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (Maybe a))))
type Rep1 * Last Source #
type Rep1 * Last = D1 * (MetaData "Last" "Data.Monoid" "base" True) (C1 * (MetaCons "Last" PrefixI True) (S1 * (MetaSel (Just Symbol "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 * Maybe)))

`Alternative` wrapper

newtype Alt f a Source #

Monoid under <|>.

Since: 4.8.0.0

Constructors

Alt
Fields getAlt :: f a

Instances

Generic1 k (Alt k f) Source #
Associated Types type Rep1 (Alt k f) (f :: Alt k f -> ) :: k -> Source # Methods from1 :: f a -> Rep1 (Alt k f) f a Source # to1 :: Rep1 (Alt k f) f a -> f a Source #
Monad f => Monad (Alt * f) Source #
Methods (>>=) :: Alt * f a -> (a -> Alt * f b) -> Alt * f b Source # (>>) :: Alt * f a -> Alt * f b -> Alt * f b Source # return :: a -> Alt * f a Source # fail :: String -> Alt * f a Source #
Functor f => Functor (Alt * f) Source #
Methods fmap :: (a -> b) -> Alt * f a -> Alt * f b Source # (<$) :: a -> Alt * f b -> Alt * f a Source #
MonadFix f => MonadFix (Alt * f) Source #	Since: 4.8.0.0
Methods mfix :: (a -> Alt * f a) -> Alt * f a Source #
Applicative f => Applicative (Alt * f) Source #
Methods pure :: a -> Alt * f a Source # (<>) :: Alt f (a -> b) -> Alt * f a -> Alt * f b Source # liftA2 :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c Source # (>) :: Alt f a -> Alt * f b -> Alt * f b Source # (<) :: Alt f a -> Alt * f b -> Alt * f a Source #
MonadPlus f => MonadPlus (Alt * f) Source #
Methods mzero :: Alt * f a Source # mplus :: Alt * f a -> Alt * f a -> Alt * f a Source #
Alternative f => Alternative (Alt * f) Source #
Methods empty :: Alt * f a Source # (<\|>) :: Alt * f a -> Alt * f a -> Alt * f a Source # some :: Alt * f a -> Alt * f [a] Source # many :: Alt * f a -> Alt * f [a] Source #
MonadZip f => MonadZip (Alt * f) Source #	Since: 4.8.0.0
Methods mzip :: Alt * f a -> Alt * f b -> Alt * f (a, b) Source # mzipWith :: (a -> b -> c) -> Alt * f a -> Alt * f b -> Alt * f c Source # munzip :: Alt * f (a, b) -> (Alt * f a, Alt * f b) Source #
Enum (f a) => Enum (Alt k f a) Source #
Methods succ :: Alt k f a -> Alt k f a Source # pred :: Alt k f a -> Alt k f a Source # toEnum :: Int -> Alt k f a Source # fromEnum :: Alt k f a -> Int Source # enumFrom :: Alt k f a -> [Alt k f a] Source # enumFromThen :: Alt k f a -> Alt k f a -> [Alt k f a] Source # enumFromTo :: Alt k f a -> Alt k f a -> [Alt k f a] Source # enumFromThenTo :: Alt k f a -> Alt k f a -> Alt k f a -> [Alt k f a] Source #
Eq (f a) => Eq (Alt k f a) Source #
Methods (==) :: Alt k f a -> Alt k f a -> Bool # (/=) :: Alt k f a -> Alt k f a -> Bool #
(Data (f a), Data a, Typeable (* -> ) f) => Data (Alt f a) Source #	Since: 4.8.0.0
Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Alt * f a -> c (Alt * f a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Alt * f a) Source # toConstr :: Alt * f a -> Constr Source # dataTypeOf :: Alt * f a -> DataType Source # dataCast1 :: Typeable (* -> ) t => (forall d. Data d => c (t d)) -> Maybe (c (Alt f a)) Source # dataCast2 :: Typeable (* -> * -> ) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Alt f a)) Source # gmapT :: (forall b. Data b => b -> b) -> Alt * f a -> Alt * f a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Alt * f a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Alt * f a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Alt * f a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Alt * f a -> m (Alt * f a) Source #
Num (f a) => Num (Alt k f a) Source #
Methods (+) :: Alt k f a -> Alt k f a -> Alt k f a Source # (-) :: Alt k f a -> Alt k f a -> Alt k f a Source # (*) :: Alt k f a -> Alt k f a -> Alt k f a Source # negate :: Alt k f a -> Alt k f a Source # abs :: Alt k f a -> Alt k f a Source # signum :: Alt k f a -> Alt k f a Source # fromInteger :: Integer -> Alt k f a Source #
Ord (f a) => Ord (Alt k f a) Source #
Methods compare :: Alt k f a -> Alt k f a -> Ordering # (<) :: Alt k f a -> Alt k f a -> Bool # (<=) :: Alt k f a -> Alt k f a -> Bool # (>) :: Alt k f a -> Alt k f a -> Bool # (>=) :: Alt k f a -> Alt k f a -> Bool # max :: Alt k f a -> Alt k f a -> Alt k f a # min :: Alt k f a -> Alt k f a -> Alt k f a #
Read (f a) => Read (Alt k f a) Source #
Methods readsPrec :: Int -> ReadS (Alt k f a) Source # readList :: ReadS [Alt k f a] Source # readPrec :: ReadPrec (Alt k f a) Source # readListPrec :: ReadPrec [Alt k f a] Source #
Show (f a) => Show (Alt k f a) Source #
Methods showsPrec :: Int -> Alt k f a -> ShowS Source # show :: Alt k f a -> String Source # showList :: [Alt k f a] -> ShowS Source #
Generic (Alt k f a) Source #
Associated Types type Rep (Alt k f a) :: * -> * Source # Methods from :: Alt k f a -> Rep (Alt k f a) x Source # to :: Rep (Alt k f a) x -> Alt k f a Source #
Alternative f => Semigroup (Alt * f a) Source #	Since: 4.9.0.0
Methods (<>) :: Alt * f a -> Alt * f a -> Alt * f a Source # sconcat :: NonEmpty (Alt * f a) -> Alt * f a Source # stimes :: Integral b => b -> Alt * f a -> Alt * f a Source #
Alternative f => Monoid (Alt * f a) Source #	Since: 4.8.0.0
Methods mempty :: Alt * f a Source # mappend :: Alt * f a -> Alt * f a -> Alt * f a Source # mconcat :: [Alt * f a] -> Alt * f a Source #
type Rep1 k (Alt k f) Source #
type Rep1 k (Alt k f) = D1 k (MetaData "Alt" "Data.Monoid" "base" True) (C1 k (MetaCons "Alt" PrefixI True) (S1 k (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 k f)))
type Rep (Alt k f a) Source #
type Rep (Alt k f a) = D1 * (MetaData "Alt" "Data.Monoid" "base" True) (C1 * (MetaCons "Alt" PrefixI True) (S1 * (MetaSel (Just Symbol "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 * (f a))))

Monoid typeclass

Bool wrappers

Num wrappers

Maybe wrappers

Alternative wrapper

`Monoid` typeclass

`Bool` wrappers

`Num` wrappers

`Maybe` wrappers

`Alternative` wrapper