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

Data.Monoid

Contents

Description

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

Synopsis

class Semigroup a => Monoid a where
(<>) :: Semigroup a => a -> a -> a
newtype Dual a = Dual {
- getDual :: a
}
newtype Endo a = Endo {
- appEndo :: a -> a
}
newtype All = All {
- getAll :: Bool
}
newtype Any = Any {
- getAny :: Bool
}
newtype Sum a = Sum {
- getSum :: a
}
newtype Product a = Product {
- getProduct :: a
}
newtype First a = First {
- getFirst :: Maybe a
}
newtype Last a = Last {
- getLast :: Maybe a
}
newtype Alt f a = Alt {
- getAlt :: f a
}

`Monoid` typeclass

class Semigroup a => Monoid a where Source #

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

```
x <> mempty = x
```
```
mempty <> x = x
```
x <> (y <> z) = (x <> y) <> z (Semigroup law)
```
mconcat = foldr '(<>)' 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.

NOTE: Semigroup is a superclass of Monoid since base-4.11.0.0.

Minimal complete definition

mempty

Methods

mempty :: a Source #

Identity of mappend

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

An associative operation

NOTE: This method is redundant and has the default implementation mappend = '(<>)' since base-4.11.0.0.

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
Instance details Methods mempty :: Ordering Source # mappend :: Ordering -> Ordering -> Ordering Source # mconcat :: [Ordering] -> Ordering Source #
Monoid () Source #	Since: 2.1
Instance details Methods mempty :: () Source # mappend :: () -> () -> () Source # mconcat :: [()] -> () Source #
Monoid Any Source #	Since: 2.1
Instance details Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
Monoid All Source #	Since: 2.1
Instance details 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
Instance details Methods mempty :: Lifetime Source # mappend :: Lifetime -> Lifetime -> Lifetime Source # mconcat :: [Lifetime] -> Lifetime Source #
Monoid Event Source #	Since: 4.3.1.0
Instance details Methods mempty :: Event Source # mappend :: Event -> Event -> Event Source # mconcat :: [Event] -> Event Source #
Monoid [a] Source #	Since: 2.1
Instance details Methods mempty :: [a] Source # mappend :: [a] -> [a] -> [a] Source # mconcat :: [[a]] -> [a] Source #
Semigroup 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 4.11.0: constraint on inner `a` value generalised from `Monoid` to `Semigroup`. Since: 2.1*
Instance details 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
Instance details Methods mempty :: IO a Source # mappend :: IO a -> IO a -> IO a Source # mconcat :: [IO a] -> IO a Source #
Monoid a => Monoid (Down a) Source #	Since: 4.11.0.0
Instance details Methods mempty :: Down a Source # mappend :: Down a -> Down a -> Down a Source # mconcat :: [Down a] -> Down a Source #
Num a => Monoid (Product a) Source #	Since: 2.1
Instance details 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
Instance details 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
Instance details 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
Instance details Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Monoid (Last a) Source #	Since: 2.1
Instance details 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
Instance details Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Monoid a => Monoid (Identity a) Source #
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details 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
Instance details Methods mempty :: (a, b) Source # mappend :: (a, b) -> (a, b) -> (a, b) Source # mconcat :: [(a, b)] -> (a, b) Source #
Monoid a => Monoid (ST s a) Source #	Since: 4.11.0.0
Instance details Methods mempty :: ST s a Source # mappend :: ST s a -> ST s a -> ST s a Source # mconcat :: [ST s a] -> ST s a Source #
Monoid (Proxy s) Source #	Since: 4.7.0.0
Instance details Methods mempty :: Proxy s Source # mappend :: Proxy s -> Proxy s -> Proxy s Source # mconcat :: [Proxy s] -> Proxy s Source #
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source #	Since: 2.1
Instance details 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
Instance details 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 a b) Source #
Instance details Methods mempty :: Const a b Source # mappend :: Const a b -> Const a b -> Const a b Source # mconcat :: [Const a b] -> Const a b Source #
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #	Since: 2.1
Instance details 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
Instance details 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 #

(<>) :: Semigroup a => a -> a -> a infixr 6 Source #

An associative operation.

newtype Dual a Source #

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

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"

Constructors

Dual
Fields getDual :: a

Instances

Monad Dual Source #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Dual a -> Dual b Source # (<$) :: a -> Dual b -> Dual a Source #
MonadFix Dual Source #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Dual a) -> Dual a Source #
Applicative Dual Source #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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 #
Instance details Methods minBound :: Dual a Source # maxBound :: Dual a Source #
Eq a => Eq (Dual a) Source #
Instance details Methods (==) :: Dual a -> Dual a -> Bool # (/=) :: Dual a -> Dual a -> Bool #
Data a => Data (Dual a) Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Methods showsPrec :: Int -> Dual a -> ShowS Source # show :: Dual a -> String Source # showList :: [Dual a] -> ShowS Source #
Generic (Dual a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: Dual a Source # mappend :: Dual a -> Dual a -> Dual a Source # mconcat :: [Dual a] -> Dual a Source #
Generic1 Dual Source #
Instance details Associated Types type Rep1 Dual :: k -> * Source # Methods from1 :: Dual a -> Rep1 Dual a Source # to1 :: Rep1 Dual a -> Dual a Source #
type Rep (Dual a) Source #
Instance details type Rep (Dual a) = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Dual Source #
Instance details type Rep1 Dual = D1 (MetaData "Dual" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Dual" PrefixI True) (S1 (MetaSel (Just "getDual") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Endo a Source #

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, "   ) <> Endo (   "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo
Fields appEndo :: a -> a

Instances

Generic (Endo a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: Endo a Source # mappend :: Endo a -> Endo a -> Endo a Source # mconcat :: [Endo a] -> Endo a Source #
type Rep (Endo a) Source #
Instance details type Rep (Endo a) = D1 (MetaData "Endo" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))

`Bool` wrappers

newtype All Source #

Boolean monoid under conjunction (&&).

>>> getAll (All True <> mempty <> All False)
False

>>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))
False

Constructors

All
Fields getAll :: Bool

Instances

Bounded All Source #
Instance details Methods minBound :: All Source # maxBound :: All Source #
Eq All Source #
Instance details Methods (==) :: All -> All -> Bool # (/=) :: All -> All -> Bool #
Data All Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details Methods readsPrec :: Int -> ReadS All Source # readList :: ReadS [All] Source # readPrec :: ReadPrec All Source # readListPrec :: ReadPrec [All] Source #
Show All Source #
Instance details Methods showsPrec :: Int -> All -> ShowS Source # show :: All -> String Source # showList :: [All] -> ShowS Source #
Generic All Source #
Instance details 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
Instance details Methods (<>) :: All -> All -> All Source # sconcat :: NonEmpty All -> All Source # stimes :: Integral b => b -> All -> All Source #
Monoid All Source #	Since: 2.1
Instance details Methods mempty :: All Source # mappend :: All -> All -> All Source # mconcat :: [All] -> All Source #
type Rep All Source #
Instance details type Rep All = D1 (MetaData "All" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "All" PrefixI True) (S1 (MetaSel (Just "getAll") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

>>> getAny (Any True <> mempty <> Any False)
True

>>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))
True

Constructors

Any
Fields getAny :: Bool

Instances

Bounded Any Source #
Instance details Methods minBound :: Any Source # maxBound :: Any Source #
Eq Any Source #
Instance details Methods (==) :: Any -> Any -> Bool # (/=) :: Any -> Any -> Bool #
Data Any Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details Methods readsPrec :: Int -> ReadS Any Source # readList :: ReadS [Any] Source # readPrec :: ReadPrec Any Source # readListPrec :: ReadPrec [Any] Source #
Show Any Source #
Instance details Methods showsPrec :: Int -> Any -> ShowS Source # show :: Any -> String Source # showList :: [Any] -> ShowS Source #
Generic Any Source #
Instance details 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
Instance details Methods (<>) :: Any -> Any -> Any Source # sconcat :: NonEmpty Any -> Any Source # stimes :: Integral b => b -> Any -> Any Source #
Monoid Any Source #	Since: 2.1
Instance details Methods mempty :: Any Source # mappend :: Any -> Any -> Any Source # mconcat :: [Any] -> Any Source #
type Rep Any Source #
Instance details type Rep Any = D1 (MetaData "Any" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Any" PrefixI True) (S1 (MetaSel (Just "getAny") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool)))

`Num` wrappers

newtype Sum a Source #

Monoid under addition.

>>> getSum (Sum 1 <> Sum 2 <> mempty)
3

Constructors

Sum
Fields getSum :: a

Instances

Monad Sum Source #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Sum a -> Sum b Source # (<$) :: a -> Sum b -> Sum a Source #
MonadFix Sum Source #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Sum a) -> Sum a Source #
Applicative Sum Source #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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 #
Instance details Methods minBound :: Sum a Source # maxBound :: Sum a Source #
Eq a => Eq (Sum a) Source #
Instance details Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Data a => Data (Sum a) Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Methods showsPrec :: Int -> Sum a -> ShowS Source # show :: Sum a -> String Source # showList :: [Sum a] -> ShowS Source #
Generic (Sum a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: Sum a Source # mappend :: Sum a -> Sum a -> Sum a Source # mconcat :: [Sum a] -> Sum a Source #
Generic1 Sum Source #
Instance details Associated Types type Rep1 Sum :: k -> * Source # Methods from1 :: Sum a -> Rep1 Sum a Source # to1 :: Rep1 Sum a -> Sum a Source #
type Rep (Sum a) Source #
Instance details type Rep (Sum a) = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Sum Source #
Instance details type Rep1 Sum = D1 (MetaData "Sum" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Sum" PrefixI True) (S1 (MetaSel (Just "getSum") NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))

newtype Product a Source #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12

Constructors

Product
Fields getProduct :: a

Instances

Monad Product Source #	Since: 4.8.0.0
Instance details 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
Instance details Methods fmap :: (a -> b) -> Product a -> Product b Source # (<$) :: a -> Product b -> Product a Source #
MonadFix Product Source #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Product a) -> Product a Source #
Applicative Product Source #	Since: 4.8.0.0
Instance details 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
Instance details 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
Instance details 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
Instance details 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 #
Instance details Methods minBound :: Product a Source # maxBound :: Product a Source #
Eq a => Eq (Product a) Source #
Instance details Methods (==) :: Product a -> Product a -> Bool # (/=) :: Product a -> Product a -> Bool #
Data a => Data (Product a) Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Methods showsPrec :: Int -> Product a -> ShowS Source # show :: Product a -> String Source # showList :: [Product a] -> ShowS Source #
Generic (Product a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: Product a Source # mappend :: Product a -> Product a -> Product a Source # mconcat :: [Product a] -> Product a Source #
Generic1 Product Source #
Instance details Associated Types type Rep1 Product :: k -> * Source # Methods from1 :: Product a -> Rep1 Product a Source # to1 :: Rep1 Product a -> Product a Source #
type Rep (Product a) Source #
Instance details type Rep (Product a) = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "getProduct") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))
type Rep1 Product Source #
Instance details type Rep1 Product = D1 (MetaData "Product" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Product" PrefixI True) (S1 (MetaSel (Just "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.

>>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"

Constructors

First
Fields getFirst :: Maybe a

Instances

Monad First Source #
Instance details 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 #
Instance details Methods fmap :: (a -> b) -> First a -> First b Source # (<$) :: a -> First b -> First a Source #
MonadFix First Source #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> First a) -> First a Source #
Applicative First Source #
Instance details 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
Instance details 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
Instance details 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
Instance details 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 #
Instance details Methods (==) :: First a -> First a -> Bool # (/=) :: First a -> First a -> Bool #
Data a => Data (First a) Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Methods showsPrec :: Int -> First a -> ShowS Source # show :: First a -> String Source # showList :: [First a] -> ShowS Source #
Generic (First a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: First a Source # mappend :: First a -> First a -> First a Source # mconcat :: [First a] -> First a Source #
Generic1 First Source #
Instance details Associated Types type Rep1 First :: k -> * Source # Methods from1 :: First a -> Rep1 First a Source # to1 :: Rep1 First a -> First a Source #
type Rep (First a) Source #
Instance details type Rep (First a) = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "getFirst") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type Rep1 First Source #
Instance details type Rep1 First = D1 (MetaData "First" "Data.Monoid" "base" True) (C1 (MetaCons "First" PrefixI True) (S1 (MetaSel (Just "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)

>>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
Just "world"

Constructors

Last
Fields getLast :: Maybe a

Instances

Monad Last Source #
Instance details 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 #
Instance details Methods fmap :: (a -> b) -> Last a -> Last b Source # (<$) :: a -> Last b -> Last a Source #
MonadFix Last Source #	Since: 4.8.0.0
Instance details Methods mfix :: (a -> Last a) -> Last a Source #
Applicative Last Source #
Instance details 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
Instance details 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
Instance details 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
Instance details 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 #
Instance details Methods (==) :: Last a -> Last a -> Bool # (/=) :: Last a -> Last a -> Bool #
Data a => Data (Last a) Source #	Since: 4.8.0.0
Instance details 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 #
Instance details 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 #
Instance details 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 #
Instance details Methods showsPrec :: Int -> Last a -> ShowS Source # show :: Last a -> String Source # showList :: [Last a] -> ShowS Source #
Generic (Last a) Source #
Instance details 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
Instance details 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
Instance details Methods mempty :: Last a Source # mappend :: Last a -> Last a -> Last a Source # mconcat :: [Last a] -> Last a Source #
Generic1 Last Source #
Instance details Associated Types type Rep1 Last :: k -> * Source # Methods from1 :: Last a -> Rep1 Last a Source # to1 :: Rep1 Last a -> Last a Source #
type Rep (Last a) Source #
Instance details type Rep (Last a) = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "getLast") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe a))))
type Rep1 Last Source #
Instance details type Rep1 Last = D1 (MetaData "Last" "Data.Monoid" "base" True) (C1 (MetaCons "Last" PrefixI True) (S1 (MetaSel (Just "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 (Alt f :: k -> *) Source #
Instance details Associated Types type Rep1 (Alt f) :: k -> * Source # Methods from1 :: Alt f a -> Rep1 (Alt f) a Source # to1 :: Rep1 (Alt f) a -> Alt f a Source #
Monad f => Monad (Alt f) Source #
Instance details 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 #
Instance details 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
Instance details Methods mfix :: (a -> Alt f a) -> Alt f a Source #
Applicative f => Applicative (Alt f) Source #
Instance details 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 #
Instance details Methods mzero :: Alt f a Source # mplus :: Alt f a -> Alt f a -> Alt f a Source #
Alternative f => Alternative (Alt f) Source #
Instance details 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
Instance details 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 f a) Source #
Instance details Methods succ :: Alt f a -> Alt f a Source # pred :: Alt f a -> Alt f a Source # toEnum :: Int -> Alt f a Source # fromEnum :: Alt f a -> Int Source # enumFrom :: Alt f a -> [Alt f a] Source # enumFromThen :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromTo :: Alt f a -> Alt f a -> [Alt f a] Source # enumFromThenTo :: Alt f a -> Alt f a -> Alt f a -> [Alt f a] Source #
Eq (f a) => Eq (Alt f a) Source #
Instance details Methods (==) :: Alt f a -> Alt f a -> Bool # (/=) :: Alt f a -> Alt f a -> Bool #
(Data (f a), Data a, Typeable f) => Data (Alt f a) Source #	Since: 4.8.0.0
Instance details 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 f a) Source #
Instance details Methods ( ) :: Alt f a -> Alt f a -> Alt f a Source # (-) :: Alt f a -> Alt f a -> Alt f a Source # (*) :: Alt f a -> Alt f a -> Alt f a Source # negate :: Alt f a -> Alt f a Source # abs :: Alt f a -> Alt f a Source # signum :: Alt f a -> Alt f a Source # fromInteger :: Integer -> Alt f a Source #
Ord (f a) => Ord (Alt f a) Source #
Instance details Methods compare :: Alt f a -> Alt f a -> Ordering # (<) :: Alt f a -> Alt f a -> Bool # (<=) :: Alt f a -> Alt f a -> Bool # (>) :: Alt f a -> Alt f a -> Bool # (>=) :: Alt f a -> Alt f a -> Bool # max :: Alt f a -> Alt f a -> Alt f a # min :: Alt f a -> Alt f a -> Alt f a #
Read (f a) => Read (Alt f a) Source #
Instance details Methods readsPrec :: Int -> ReadS (Alt f a) Source # readList :: ReadS [Alt f a] Source # readPrec :: ReadPrec (Alt f a) Source # readListPrec :: ReadPrec [Alt f a] Source #
Show (f a) => Show (Alt f a) Source #
Instance details Methods showsPrec :: Int -> Alt f a -> ShowS Source # show :: Alt f a -> String Source # showList :: [Alt f a] -> ShowS Source #
Generic (Alt f a) Source #
Instance details Associated Types type Rep (Alt f a) :: * -> * Source # Methods from :: Alt f a -> Rep (Alt f a) x Source # to :: Rep (Alt f a) x -> Alt f a Source #
Alternative f => Semigroup (Alt f a) Source #	Since: 4.9.0.0
Instance details 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
Instance details 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 :: k -> *) Source #
Instance details type Rep1 (Alt f :: k -> *) = D1 (MetaData "Alt" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just "getAlt") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)))
type Rep (Alt f a) Source #
Instance details type Rep (Alt f a) = D1 (MetaData "Alt" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Alt" PrefixI True) (S1 (MetaSel (Just "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