| 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 |
A type a is a Semigroup if it provides an associative function (<>) that lets you combine any two values of type a into one. Where being associative means that the following must always hold:
>>> (a <> b) <> c == a <> (b <> c)
The Min Semigroup instance for Int is defined to always pick the smaller number: >>> Min 1 <> Min 2 <> Min 3 <> Min 4 :: Min Int Min {getMin = 1}
If we need to combine multiple values we can use the sconcat function to do so. We need to ensure however that we have at least one value to operate on, since otherwise our result would be undefined. It is for this reason that sconcat uses Data.List.NonEmpty.NonEmpty - a list that can never be empty:
>>> (1 :| []) 1 :| [] -- equivalent to [1] but guaranteed to be non-empty >>> (1 :| [2, 3, 4]) 1 :| [2,3,4] -- equivalent to [1,2,3,4] but guaranteed to be non-empty
Equipped with this guaranteed to be non-empty data structure, we can combine values using sconcat and a Semigroup of our choosing. We can try the Min and Max instances of Int which pick the smallest, or largest number respectively:
>>> sconcat (1 :| [2, 3, 4]) :: Min Int
Min {getMin = 1}
>>> sconcat (1 :| [2, 3, 4]) :: Max Int
Max {getMax = 4}
String concatenation is another example of a Semigroup instance:
>>> "foo" <> "bar" "foobar"
A Semigroup is a generalization of a Monoid. Yet unlike the Semigroup, the Monoid requires the presence of a neutral element (mempty) in addition to the associative operator. The requirement for a neutral element prevents many types from being a full Monoid, like Data.List.NonEmpty.NonEmpty.
Note that 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
class Semigroup a where Source
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base-4.9.0.0
(<>) :: 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 = stimesIdempotent or stimes =
stimesIdempotentMonoid respectively.
| 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 p => Semigroup (Par1 p) | Since: base-4.12.0.0 |
| 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) | Since: base-4.9.0.0 |
| 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 (Equivalence a) | |
Defined in Data.Functor.Contravariant Methods(<>) :: Equivalence a -> Equivalence a -> Equivalence a Source sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source stimes :: Integral b => b -> Equivalence a -> Equivalence a Source | |
| Semigroup (Comparison a) | |
Defined in Data.Functor.Contravariant Methods(<>) :: Comparison a -> Comparison a -> Comparison a Source sconcat :: NonEmpty (Comparison a) -> Comparison a Source stimes :: Integral b => b -> Comparison a -> Comparison a Source | |
| Semigroup (Predicate a) | |
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| Semigroup (U1 p) | Since: base-4.12.0.0 |
| (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 (Op a b) | |
| Semigroup (f p) => Semigroup (Rec1 f p) | Since: base-4.12.0.0 |
| (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 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| Semigroup c => Semigroup (K1 i c p) | Since: base-4.12.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | Since: base-4.12.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) | Since: base-4.12.0.0 |
| (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
This is a valid definition of stimes for a Monoid.
Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.
stimesIdempotent :: Integral b => b -> a -> a Source
This is a valid definition of stimes for an idempotent Semigroup.
When x <> x = x, this definition should be preferred, because it works in O(1) rather than O(log n).
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source
This is a valid definition of stimes for an idempotent Monoid.
When mappend x x = x, this definition should be preferred, because it works in O(1) rather than O(log n)
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source
Repeat a value n times.
mtimesDefault n a = a <> a <> ... <> a -- using <> (n-1) times
Implemented using stimes and mempty.
This is a suitable definition for an mtimes member of Monoid.
| Monad Min | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| MonadFix Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Applicative Min | Since: base-4.9.0.0 |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => Min m -> m Source foldMap :: Monoid m => (a -> m) -> Min a -> 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 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) | Since: base-4.9.0.0 |
| Enum a => Enum (Min a) | Since: base-4.9.0.0 |
| Eq a => Eq (Min a) | Since: base-4.9.0.0 |
| Data a => Data (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Read a => Read (Min a) | Since: base-4.9.0.0 |
| Show a => Show (Min a) | Since: base-4.9.0.0 |
| Generic (Min a) | Since: base-4.9.0.0 |
| 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 | Since: base-4.9.0.0 |
| type Rep (Min a) | |
Defined in Data.Semigroup | |
| type Rep1 Min | |
Defined in Data.Semigroup | |
| Monad Max | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| MonadFix Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Applicative Max | Since: base-4.9.0.0 |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => Max m -> m Source foldMap :: Monoid m => (a -> m) -> Max a -> 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 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) | Since: base-4.9.0.0 |
| Enum a => Enum (Max a) | Since: base-4.9.0.0 |
| Eq a => Eq (Max a) | Since: base-4.9.0.0 |
| Data a => Data (Max a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Read a => Read (Max a) | Since: base-4.9.0.0 |
| Show a => Show (Max a) | Since: base-4.9.0.0 |
| Generic (Max a) | Since: base-4.9.0.0 |
| 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 | Since: base-4.9.0.0 |
| type Rep (Max a) | |
Defined in Data.Semigroup | |
| type Rep1 Max | |
Defined in Data.Semigroup | |
Use Option (First a) to get the behavior of First from Data.Monoid.
| Monad First | Since: base-4.9.0.0 |
| Functor First | Since: base-4.9.0.0 |
| MonadFix First | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Applicative First | Since: base-4.9.0.0 |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => First m -> m Source foldMap :: Monoid m => (a -> m) -> First a -> 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) | Since: base-4.9.0.0 |
| Enum a => Enum (First a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodssucc :: 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) | Since: base-4.9.0.0 |
| Data a => Data (First a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Show a => Show (First a) | Since: base-4.9.0.0 |
| Generic (First a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Generic1 First | Since: base-4.9.0.0 |
| type Rep (First a) | |
Defined in Data.Semigroup | |
| type Rep1 First | |
Defined in Data.Semigroup | |
Use Option (Last a) to get the behavior of Last from Data.Monoid
| Monad Last | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| MonadFix Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Applicative Last | Since: base-4.9.0.0 |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => Last m -> m Source foldMap :: Monoid m => (a -> m) -> Last a -> 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 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) | Since: base-4.9.0.0 |
| Enum a => Enum (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodssucc :: 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) | Since: base-4.9.0.0 |
| Data a => Data (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Read a => Read (Last a) | Since: base-4.9.0.0 |
| Show a => Show (Last a) | Since: base-4.9.0.0 |
| Generic (Last a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Generic1 Last | Since: base-4.9.0.0 |
| 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.
| WrapMonoid | |
Fields
| |
The dual of a Monoid, obtained by swapping the arguments of mappend.
>>> getDual (mappend (Dual "Hello") (Dual "World")) "WorldHello"
| Monad Dual | Since: base-4.8.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| MonadFix Dual | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative Dual | Since: base-4.8.0.0 |
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => Dual m -> m Source foldMap :: Monoid m => (a -> m) -> Dual a -> 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 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) | Since: base-2.1 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Data a => Data (Dual a) | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Dual a) | Since: base-2.1 |
| Show a => Show (Dual a) | Since: base-2.1 |
| Generic (Dual a) | Since: base-4.7.0.0 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Generic1 Dual | Since: base-4.7.0.0 |
| 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
| Bounded All | Since: base-2.1 |
| Eq All | Since: base-2.1 |
| Data All | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 :: forall r r'. (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 | Since: base-2.1 |
| Read All | Since: base-2.1 |
| Show All | Since: base-2.1 |
| Generic All | Since: base-4.7.0.0 |
| 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
| Bounded Any | Since: base-2.1 |
| Eq Any | Since: base-2.1 |
| Data Any | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 :: forall r r'. (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 | Since: base-2.1 |
| Read Any | Since: base-2.1 |
| Show Any | Since: base-2.1 |
| Generic Any | Since: base-4.7.0.0 |
| 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
| Monad Sum | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| MonadFix Sum | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| Applicative Sum | Since: base-4.8.0.0 |
| Foldable Sum | Since: base-4.8.0.0 |
Defined in Data.Foldable Methodsfold :: Monoid m => Sum m -> m Source foldMap :: Monoid m => (a -> m) -> Sum a -> 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 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) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Data a => Data (Sum a) | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.7.0.0 |
| Ord a => Ord (Sum a) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Sum a) | Since: base-2.1 |
| Show a => Show (Sum a) | Since: base-2.1 |
| Generic (Sum a) | Since: base-4.7.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Generic1 Sum | Since: base-4.7.0.0 |
| 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
| Product | |
Fields
| |
| Monad Product | Since: base-4.8.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| MonadFix Product | Since: base-4.8.0.0 |
Defined in Control.Monad.Fix | |
| 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 Methodsfold :: Monoid m => Product m -> m Source foldMap :: Monoid m => (a -> m) -> Product a -> 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) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Data a => Data (Product a) | Since: base-4.8.0.0 |
Defined in Data.Data Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.7.0.0 |
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) | Since: base-2.1 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Product a) | Since: base-2.1 |
| Show a => Show (Product a) | Since: base-2.1 |
| Generic (Product a) | Since: base-4.7.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Generic1 Product | Since: base-4.7.0.0 |
| type Rep (Product a) | |
Defined in Data.Semigroup.Internal | |
| type Rep1 Product | |
Defined in Data.Semigroup.Internal | |
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.
In GHC 8.4 and higher, the Monoid instance for Maybe has been corrected to lift a Semigroup instance instead of a Monoid instance. Consequently, this type is no longer useful. It will be marked deprecated in GHC 8.8 and removed in GHC 8.10.
| Monad Option | Since: base-4.9.0.0 |
| Functor Option | Since: base-4.9.0.0 |
| MonadFix Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Applicative Option | Since: base-4.9.0.0 |
| Foldable Option | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsfold :: Monoid m => Option m -> m Source foldMap :: Monoid m => (a -> m) -> Option a -> 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 |
| MonadPlus Option | Since: base-4.9.0.0 |
| Alternative Option | Since: base-4.9.0.0 |
| Eq a => Eq (Option a) | Since: base-4.9.0.0 |
| Data a => Data (Option a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Read a => Read (Option a) | Since: base-4.9.0.0 |
| Show a => Show (Option a) | Since: base-4.9.0.0 |
| Generic (Option a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Option a) | Since: base-4.9.0.0 |
| Semigroup a => Monoid (Option a) | Since: base-4.9.0.0 |
| Generic1 Option | Since: base-4.9.0.0 |
| type Rep (Option a) | |
Defined in Data.Semigroup | |
| type Rep1 Option | |
Defined in Data.Semigroup | |
option :: b -> (a -> b) -> Option a -> b Source
Fold an Option case-wise, just like maybe.
diff :: Semigroup m => m -> Endo m Source
This lets you use a difference list of a Semigroup as a Monoid.
cycle1 :: Semigroup m => m -> m Source
A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.
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.
| Arg a b |
| 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 Methodsbitraverse :: 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 Methodsfold :: Monoid m => Arg a m -> m Source foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> 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 |
| Generic1 (Arg a :: Type -> Type) | Since: base-4.9.0.0 |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| (Data a, Data b) => Data (Arg a b) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methodsgfoldl :: (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 :: forall r r'. (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) | Since: base-4.9.0.0 |
| (Show a, Show b) => Show (Arg a b) | Since: base-4.9.0.0 |
| Generic (Arg a b) | Since: base-4.9.0.0 |
| type Rep1 (Arg a :: Type -> Type) | |
Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = 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))) | |
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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base-4.13.0.0/Data-Semigroup.html