| Copyright | (C) 2011-2015 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | [email protected] |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Data.Semigroup
Contents
Description
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.
The use of (<>) in this module conflicts with an operator with the same
name that is being exported by Data.Monoid. However, this package
re-exports (most of) the contents of Data.Monoid, so to use semigroups
and monoids in the same package just
import Data.Semigroup
Since: base-4.9.0.0
Synopsis
- class Semigroup a where
- stimesMonoid :: (Integral b, Monoid a) => b -> a -> a
- stimesIdempotent :: Integral b => b -> a -> a
- stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a
- mtimesDefault :: (Integral b, Monoid a) => b -> a -> a
- newtype Min a = Min {
- getMin :: a
- newtype Max a = Max {
- getMax :: a
- newtype First a = First {
- getFirst :: a
- newtype Last a = Last {
- getLast :: a
- newtype WrappedMonoid m = WrapMonoid {
- unwrapMonoid :: m
- newtype Dual a = Dual {
- getDual :: a
- newtype Endo a = Endo {
- appEndo :: a -> a
- newtype All = All {}
- newtype Any = Any {}
- newtype Sum a = Sum {
- getSum :: a
- newtype Product a = Product {
- getProduct :: a
- newtype Option a = Option {}
- option :: b -> (a -> b) -> Option a -> b
- diff :: Semigroup m => m -> Endo m
- cycle1 :: Semigroup m => m -> m
- data Arg a b = Arg a b
- type ArgMin a b = Min (Arg a b)
- type ArgMax a b = Max (Arg a b)
Documentation
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the associativity law:
Since: base-4.9.0.0
Minimal complete definition
Methods
(<>) :: a -> a -> a infixr 6 Source #
An associative operation.
sconcat :: NonEmpty a -> a Source #
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
stimes :: Integral b => b -> a -> a Source #
Repeat a value n times.
Given that this works on a Semigroup it is allowed to fail if
you request 0 or fewer repetitions, and the default definition
will do so.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in O(1) by
picking stimes = or stimesIdempotentstimes =
respectively.stimesIdempotentMonoid
Instances
| Semigroup Ordering # | Since: base-4.9.0.0 |
| Semigroup () # | Since: base-4.9.0.0 |
| Semigroup Any # | Since: base-4.9.0.0 |
| Semigroup All # | Since: base-4.9.0.0 |
| Semigroup Lifetime # | Since: base-4.10.0.0 |
| Semigroup Event # | Since: base-4.10.0.0 |
| Semigroup Void # | Since: base-4.9.0.0 |
| Semigroup [a] # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Maybe a) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (IO a) # | Since: base-4.10.0.0 |
| Semigroup (NonEmpty a) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) # | Since: base-4.11.0.0 |
| Num a => Semigroup (Product a) # | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) # | Since: base-4.9.0.0 |
| Semigroup (Endo a) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Dual a) # | Since: base-4.9.0.0 |
| Semigroup (Last a) # | Since: base-4.9.0.0 |
| Semigroup (First a) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Identity a) # | |
| Semigroup a => Semigroup (Option a) # | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # | |
| Semigroup (Last a) # | Since: base-4.9.0.0 |
| Semigroup (First a) # | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) # | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) # | Since: base-4.9.0.0 |
| Semigroup b => Semigroup (a -> b) # | Since: base-4.9.0.0 |
| Semigroup (Either a b) # | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (ST s a) # | Since: base-4.11.0.0 |
| Semigroup (Proxy s) # | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) # | Since: base-4.9.0.0 |
| Alternative f => Semigroup (Alt f a) # | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) # | |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) # | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) # | Since: base-4.9.0.0 |
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source #
stimesIdempotent :: Integral b => b -> a -> a Source #
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source #
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source #
Semigroups
Instances
| Monad Min # | Since: base-4.9.0.0 |
| Functor Min # | Since: base-4.9.0.0 |
| MonadFix Min # | Since: base-4.9.0.0 |
| Applicative Min # | Since: base-4.9.0.0 |
| Foldable Min # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m Source # foldMap :: Monoid m => (a -> m) -> Min a -> m Source # foldr :: (a -> b -> b) -> b -> Min a -> b Source # foldr' :: (a -> b -> b) -> b -> Min a -> b Source # foldl :: (b -> a -> b) -> b -> Min a -> b Source # foldl' :: (b -> a -> b) -> b -> Min a -> b Source # foldr1 :: (a -> a -> a) -> Min a -> a Source # foldl1 :: (a -> a -> a) -> Min a -> a Source # toList :: Min a -> [a] Source # null :: Min a -> Bool Source # length :: Min a -> Int Source # elem :: Eq a => a -> Min a -> Bool Source # maximum :: Ord a => Min a -> a Source # minimum :: Ord a => Min a -> a Source # | |
| Traversable Min # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Min a) # | |
| Enum a => Enum (Min a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Min a -> Min a Source # pred :: Min a -> Min a Source # toEnum :: Int -> Min a Source # fromEnum :: Min a -> Int Source # enumFrom :: Min a -> [Min a] Source # enumFromThen :: Min a -> Min a -> [Min a] Source # enumFromTo :: Min a -> Min a -> [Min a] Source # enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source # | |
| Eq a => Eq (Min a) # | |
| Data a => Data (Min a) # | |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source # toConstr :: Min a -> Constr Source # dataTypeOf :: Min a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source # gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source # | |
| Num a => Num (Min a) # | Since: base-4.9.0.0 |
| Ord a => Ord (Min a) # | |
Defined in Data.Semigroup | |
| Read a => Read (Min a) # | |
| Show a => Show (Min a) # | |
| Generic (Min a) # | |
| Ord a => Semigroup (Min a) # | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Min a) # | Since: base-4.9.0.0 |
| Generic1 Min # | |
| type Rep (Min a) # | |
Defined in Data.Semigroup | |
| type Rep1 Min # | |
Defined in Data.Semigroup | |
Instances
| Monad Max # | Since: base-4.9.0.0 |
| Functor Max # | Since: base-4.9.0.0 |
| MonadFix Max # | Since: base-4.9.0.0 |
| Applicative Max # | Since: base-4.9.0.0 |
| Foldable Max # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m Source # foldMap :: Monoid m => (a -> m) -> Max a -> m Source # foldr :: (a -> b -> b) -> b -> Max a -> b Source # foldr' :: (a -> b -> b) -> b -> Max a -> b Source # foldl :: (b -> a -> b) -> b -> Max a -> b Source # foldl' :: (b -> a -> b) -> b -> Max a -> b Source # foldr1 :: (a -> a -> a) -> Max a -> a Source # foldl1 :: (a -> a -> a) -> Max a -> a Source # toList :: Max a -> [a] Source # null :: Max a -> Bool Source # length :: Max a -> Int Source # elem :: Eq a => a -> Max a -> Bool Source # maximum :: Ord a => Max a -> a Source # minimum :: Ord a => Max a -> a Source # | |
| Traversable Max # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Max a) # | |
| Enum a => Enum (Max a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Max a -> Max a Source # pred :: Max a -> Max a Source # toEnum :: Int -> Max a Source # fromEnum :: Max a -> Int Source # enumFrom :: Max a -> [Max a] Source # enumFromThen :: Max a -> Max a -> [Max a] Source # enumFromTo :: Max a -> Max a -> [Max a] Source # enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source # | |
| Eq a => Eq (Max a) # | |
| Data a => Data (Max a) # | |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source # toConstr :: Max a -> Constr Source # dataTypeOf :: Max a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source # gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source # | |
| Num a => Num (Max a) # | Since: base-4.9.0.0 |
| Ord a => Ord (Max a) # | |
Defined in Data.Semigroup | |
| Read a => Read (Max a) # | |
| Show a => Show (Max a) # | |
| Generic (Max a) # | |
| Ord a => Semigroup (Max a) # | Since: base-4.9.0.0 |
| (Ord a, Bounded a) => Monoid (Max a) # | Since: base-4.9.0.0 |
| Generic1 Max # | |
| type Rep (Max a) # | |
Defined in Data.Semigroup | |
| type Rep1 Max # | |
Defined in Data.Semigroup | |
Use Option (First a)First from Data.Monoid.
Instances
| Monad First # | Since: base-4.9.0.0 |
| Functor First # | Since: base-4.9.0.0 |
| MonadFix First # | Since: base-4.9.0.0 |
| Applicative First # | Since: base-4.9.0.0 |
| Foldable First # | Since: base-4.9.0.0 |
Defined in Data.Semigroup 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 # | |
| Traversable First # | Since: base-4.9.0.0 |
| Bounded a => Bounded (First a) # | |
| Enum a => Enum (First a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: First a -> First a Source # pred :: First a -> First a Source # toEnum :: Int -> First a Source # fromEnum :: First a -> Int Source # enumFrom :: First a -> [First a] Source # enumFromThen :: First a -> First a -> [First a] Source # enumFromTo :: First a -> First a -> [First a] Source # enumFromThenTo :: First a -> First a -> First a -> [First a] Source # | |
| Eq a => Eq (First a) # | |
| Data a => Data (First a) # | |
Defined in Data.Semigroup 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) # | |
| Read a => Read (First a) # | |
| Show a => Show (First a) # | |
| Generic (First a) # | |
| Semigroup (First a) # | Since: base-4.9.0.0 |
| Generic1 First # | |
| type Rep (First a) # | |
Defined in Data.Semigroup | |
| type Rep1 First # | |
Defined in Data.Semigroup | |
Use Option (Last a)Last from Data.Monoid
Instances
| Monad Last # | Since: base-4.9.0.0 |
| Functor Last # | Since: base-4.9.0.0 |
| MonadFix Last # | Since: base-4.9.0.0 |
| Applicative Last # | Since: base-4.9.0.0 |
| Foldable Last # | Since: base-4.9.0.0 |
Defined in Data.Semigroup 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 # | |
| Traversable Last # | Since: base-4.9.0.0 |
| Bounded a => Bounded (Last a) # | |
| Enum a => Enum (Last a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods succ :: Last a -> Last a Source # pred :: Last a -> Last a Source # toEnum :: Int -> Last a Source # fromEnum :: Last a -> Int Source # enumFrom :: Last a -> [Last a] Source # enumFromThen :: Last a -> Last a -> [Last a] Source # enumFromTo :: Last a -> Last a -> [Last a] Source # enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source # | |
| Eq a => Eq (Last a) # | |
| Data a => Data (Last a) # | |
Defined in Data.Semigroup 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) # | |
| Read a => Read (Last a) # | |
| Show a => Show (Last a) # | |
| Generic (Last a) # | |
| Semigroup (Last a) # | Since: base-4.9.0.0 |
| Generic1 Last # | |
| type Rep (Last a) # | |
Defined in Data.Semigroup | |
| type Rep1 Last # | |
Defined in Data.Semigroup | |
newtype WrappedMonoid m Source #
Provide a Semigroup for an arbitrary Monoid.
NOTE: This is not needed anymore since Semigroup became a superclass of
Monoid in base-4.11 and this newtype be deprecated at some point in the future.
Constructors
| WrapMonoid | |
Fields
| |
Instances
Re-exported monoids from Data.Monoid
The dual of a Monoid, obtained by swapping the arguments of mappend.
>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"
Instances
| Monad Dual # | Since: base-4.8.0.0 |
| Functor Dual # | Since: base-4.8.0.0 |
| MonadFix Dual # | Since: base-4.8.0.0 |
| Applicative Dual # | Since: base-4.8.0.0 |
| Foldable Dual # | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 # | |
| Traversable Dual # | Since: base-4.8.0.0 |
| MonadZip Dual # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Dual a) # | |
| Eq a => Eq (Dual a) # | |
| Data a => Data (Dual a) # | Since: base-4.8.0.0 |
Defined in Data.Data 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) # | |
| Read a => Read (Dual a) # | |
| Show a => Show (Dual a) # | |
| Generic (Dual a) # | |
| Semigroup a => Semigroup (Dual a) # | Since: base-4.9.0.0 |
| Monoid a => Monoid (Dual a) # | Since: base-2.1 |
| Generic1 Dual # | |
| type Rep (Dual a) # | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Dual # | |
Defined in Data.Semigroup.Internal | |
The monoid of endomorphisms under composition.
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
Boolean monoid under conjunction (&&).
>>>getAll (All True <> mempty <> All False)False
>>>getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8]))False
Instances
| Bounded All # | |
| Eq All # | |
| Data All # | Since: base-4.8.0.0 |
Defined in Data.Data 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 # | |
| Read All # | |
| Show All # | |
| Generic All # | |
| Semigroup All # | Since: base-4.9.0.0 |
| Monoid All # | Since: base-2.1 |
| type Rep All # | |
Defined in Data.Semigroup.Internal | |
Boolean monoid under disjunction (||).
>>>getAny (Any True <> mempty <> Any False)True
>>>getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8]))True
Instances
| Bounded Any # | |
| Eq Any # | |
| Data Any # | Since: base-4.8.0.0 |
Defined in Data.Data 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 # | |
| Read Any # | |
| Show Any # | |
| Generic Any # | |
| Semigroup Any # | Since: base-4.9.0.0 |
| Monoid Any # | Since: base-2.1 |
| type Rep Any # | |
Defined in Data.Semigroup.Internal | |
Monoid under addition.
>>>getSum (Sum 1 <> Sum 2 <> mempty)3
Instances
| Monad Sum # | Since: base-4.8.0.0 |
| Functor Sum # | Since: base-4.8.0.0 |
| MonadFix Sum # | Since: base-4.8.0.0 |
| Applicative Sum # | Since: base-4.8.0.0 |
| Foldable Sum # | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 # | |
| Traversable Sum # | Since: base-4.8.0.0 |
| MonadZip Sum # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Sum a) # | |
| Eq a => Eq (Sum a) # | |
| Data a => Data (Sum a) # | Since: base-4.8.0.0 |
Defined in Data.Data 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) # | |
| Ord a => Ord (Sum a) # | |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Sum a) # | |
| Show a => Show (Sum a) # | |
| Generic (Sum a) # | |
| Num a => Semigroup (Sum a) # | Since: base-4.9.0.0 |
| Num a => Monoid (Sum a) # | Since: base-2.1 |
| Generic1 Sum # | |
| type Rep (Sum a) # | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Sum # | |
Defined in Data.Semigroup.Internal | |
Monoid under multiplication.
>>>getProduct (Product 3 <> Product 4 <> mempty)12
Constructors
| Product | |
Fields
| |
Instances
| Monad Product # | Since: base-4.8.0.0 |
| Functor Product # | Since: base-4.8.0.0 |
| MonadFix Product # | Since: base-4.8.0.0 |
| Applicative Product # | Since: base-4.8.0.0 |
Defined in Data.Semigroup.Internal | |
| Foldable Product # | Since: base-4.8.0.0 |
Defined in Data.Foldable 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 # | |
| Traversable Product # | Since: base-4.8.0.0 |
Defined in Data.Traversable | |
| MonadZip Product # | Since: base-4.8.0.0 |
| Bounded a => Bounded (Product a) # | |
| Eq a => Eq (Product a) # | |
| Data a => Data (Product a) # | Since: base-4.8.0.0 |
Defined in Data.Data 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) # | |
Defined in Data.Semigroup.Internal 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) # | |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Product a) # | |
| Show a => Show (Product a) # | |
| Generic (Product a) # | |
| Num a => Semigroup (Product a) # | Since: base-4.9.0.0 |
| Num a => Monoid (Product a) # | Since: base-2.1 |
| Generic1 Product # | |
| type Rep (Product a) # | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Product # | |
Defined in Data.Semigroup.Internal | |
A better monoid for Maybe
Option is effectively Maybe with a better instance of
Monoid, built off of an underlying Semigroup instead of an
underlying Monoid.
Ideally, this type would not exist at all and we would just fix the
Monoid instance of Maybe
Instances
| Monad Option # | Since: base-4.9.0.0 |
| Functor Option # | Since: base-4.9.0.0 |
| MonadFix Option # | Since: base-4.9.0.0 |
| Applicative Option # | Since: base-4.9.0.0 |
| Foldable Option # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Option m -> m Source # foldMap :: Monoid m => (a -> m) -> Option a -> m Source # foldr :: (a -> b -> b) -> b -> Option a -> b Source # foldr' :: (a -> b -> b) -> b -> Option a -> b Source # foldl :: (b -> a -> b) -> b -> Option a -> b Source # foldl' :: (b -> a -> b) -> b -> Option a -> b Source # foldr1 :: (a -> a -> a) -> Option a -> a Source # foldl1 :: (a -> a -> a) -> Option a -> a Source # toList :: Option a -> [a] Source # null :: Option a -> Bool Source # length :: Option a -> Int Source # elem :: Eq a => a -> Option a -> Bool Source # maximum :: Ord a => Option a -> a Source # minimum :: Ord a => Option a -> a Source # | |
| Traversable Option # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| MonadPlus Option # | Since: base-4.9.0.0 |
| Alternative Option # | Since: base-4.9.0.0 |
| Eq a => Eq (Option a) # | |
| Data a => Data (Option a) # | |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Option a -> c (Option a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) Source # toConstr :: Option a -> Constr Source # dataTypeOf :: Option a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) Source # gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) Source # | |
| Ord a => Ord (Option a) # | |
Defined in Data.Semigroup | |
| Read a => Read (Option a) # | |
| Show a => Show (Option a) # | |
| Generic (Option a) # | |
| Semigroup a => Semigroup (Option a) # | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Option a) # | Since: base-4.9.0.0 |
| Generic1 Option # | |
| type Rep (Option a) # | |
Defined in Data.Semigroup | |
| type Rep1 Option # | |
Defined in Data.Semigroup | |
Difference lists of a semigroup
ArgMin, ArgMax
Arg isn't itself a Semigroup in its own right, but it can be
placed inside Min and Max to compute an arg min or arg max.
Constructors
| Arg a b |
Instances
| Bifunctor Arg # | Since: base-4.9.0.0 |
| Bifoldable Arg # | Since: base-4.10.0.0 |
| Bitraversable Arg # | Since: base-4.10.0.0 |
Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source # | |
| Functor (Arg a) # | Since: base-4.9.0.0 |
| Foldable (Arg a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source # toList :: Arg a a0 -> [a0] Source # null :: Arg a a0 -> Bool Source # length :: Arg a a0 -> Int Source # elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source # maximum :: Ord a0 => Arg a a0 -> a0 Source # minimum :: Ord a0 => Arg a a0 -> a0 Source # | |
| Traversable (Arg a) # | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Generic1 (Arg a :: * -> *) # | |
| Eq a => Eq (Arg a b) # | Since: base-4.9.0.0 |
| (Data a, Data b) => Data (Arg a b) # | |
Defined in Data.Semigroup Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source # toConstr :: Arg a b -> Constr Source # dataTypeOf :: Arg a b -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source # | |
| Ord a => Ord (Arg a b) # | Since: base-4.9.0.0 |
| (Read a, Read b) => Read (Arg a b) # | |
| (Show a, Show b) => Show (Arg a b) # | |
| Generic (Arg a b) # | |
| type Rep1 (Arg a :: * -> *) # | |
Defined in Data.Semigroup type Rep1 (Arg a :: * -> *) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1)) | |
| type Rep (Arg a b) # | |
Defined in Data.Semigroup type Rep (Arg a b) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 b))) | |