Copyright  (C) 20112015 Edward Kmett 

License  BSDstyle (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 nonempty >>> (1 : [2, 3, 4]) 1 : [2,3,4]  equivalent to [1,2,3,4] but guaranteed to be nonempty
Equipped with this guaranteed to be nonempty 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 reexports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just
import Data.Semigroup
Since: base4.9.0.0
class Semigroup a where Source
The class of semigroups (types with an associative binary operation).
Instances should satisfy the following:
Since: base4.9.0.0
(<>) :: a > a > a infixr 6 Source
An associative operation.
sconcat :: NonEmpty a > a Source
Reduce a nonempty 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: base4.9.0.0 
Semigroup ()  Since: base4.9.0.0 
Semigroup Any  Since: base4.9.0.0 
Semigroup All  Since: base4.9.0.0 
Semigroup Lifetime  Since: base4.10.0.0 
Semigroup Event  Since: base4.10.0.0 
Semigroup Void  Since: base4.9.0.0 
Semigroup [a]  Since: base4.9.0.0 
Semigroup a => Semigroup (Maybe a)  Since: base4.9.0.0 
Semigroup a => Semigroup (IO a)  Since: base4.10.0.0 
Semigroup p => Semigroup (Par1 p)  Since: base4.12.0.0 
Semigroup (NonEmpty a)  Since: base4.9.0.0 
Semigroup a => Semigroup (Down a)  Since: base4.11.0.0 
Num a => Semigroup (Product a)  Since: base4.9.0.0 
Num a => Semigroup (Sum a)  Since: base4.9.0.0 
Semigroup (Endo a)  Since: base4.9.0.0 
Semigroup a => Semigroup (Dual a)  Since: base4.9.0.0 
Semigroup (Last a)  Since: base4.9.0.0 
Semigroup (First a)  Since: base4.9.0.0 
Semigroup a => Semigroup (Identity a)  Since: base4.9.0.0 
Semigroup a => Semigroup (Option a)  Since: base4.9.0.0 
Monoid m => Semigroup (WrappedMonoid m)  Since: base4.9.0.0 
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: base4.9.0.0 
Semigroup (First a)  Since: base4.9.0.0 
Ord a => Semigroup (Max a)  Since: base4.9.0.0 
Ord a => Semigroup (Min a)  Since: base4.9.0.0 
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: base4.9.0.0 
Semigroup (Either a b)  Since: base4.9.0.0 
Semigroup (V1 p)  Since: base4.12.0.0 
Semigroup (U1 p)  Since: base4.12.0.0 
(Semigroup a, Semigroup b) => Semigroup (a, b)  Since: base4.9.0.0 
Semigroup a => Semigroup (ST s a)  Since: base4.11.0.0 
Semigroup (Proxy s)  Since: base4.9.0.0 
Semigroup a => Semigroup (Op a b)  
Semigroup (f p) => Semigroup (Rec1 f p)  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)  Since: base4.9.0.0 
Alternative f => Semigroup (Alt f a)  Since: base4.9.0.0 
(Applicative f, Semigroup a) => Semigroup (Ap f a)  Since: base4.12.0.0 
Semigroup a => Semigroup (Const a b)  Since: base4.9.0.0 
Semigroup c => Semigroup (K1 i c p)  Since: base4.12.0.0 
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)  Since: base4.9.0.0 
Semigroup (f p) => Semigroup (M1 i c f p)  Since: base4.12.0.0 
Semigroup (f (g p)) => Semigroup ((f :.: g) p)  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)  Since: base4.9.0.0 
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 <> (n1) times
Implemented using stimes
and mempty
.
This is a suitable definition for an mtimes
member of Monoid
.
Monad Min  Since: base4.9.0.0 
Functor Min  Since: base4.9.0.0 
MonadFix Min  Since: base4.9.0.0 
Defined in Data.Semigroup  
Applicative Min  Since: base4.9.0.0 
Foldable Min  Since: base4.9.0.0 
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: base4.9.0.0 
Bounded a => Bounded (Min a)  Since: base4.9.0.0 
Enum a => Enum (Min a)  Since: base4.9.0.0 
Eq a => Eq (Min a)  Since: base4.9.0.0 
Data a => Data (Min a)  Since: base4.9.0.0 
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: base4.9.0.0 
Ord a => Ord (Min a)  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Min a)  Since: base4.9.0.0 
Show a => Show (Min a)  Since: base4.9.0.0 
Generic (Min a)  Since: base4.9.0.0 
Ord a => Semigroup (Min a)  Since: base4.9.0.0 
(Ord a, Bounded a) => Monoid (Min a)  Since: base4.9.0.0 
Generic1 Min  Since: base4.9.0.0 
type Rep (Min a)  
Defined in Data.Semigroup  
type Rep1 Min  
Defined in Data.Semigroup 
Monad Max  Since: base4.9.0.0 
Functor Max  Since: base4.9.0.0 
MonadFix Max  Since: base4.9.0.0 
Defined in Data.Semigroup  
Applicative Max  Since: base4.9.0.0 
Foldable Max  Since: base4.9.0.0 
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: base4.9.0.0 
Bounded a => Bounded (Max a)  Since: base4.9.0.0 
Enum a => Enum (Max a)  Since: base4.9.0.0 
Eq a => Eq (Max a)  Since: base4.9.0.0 
Data a => Data (Max a)  Since: base4.9.0.0 
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: base4.9.0.0 
Ord a => Ord (Max a)  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Max a)  Since: base4.9.0.0 
Show a => Show (Max a)  Since: base4.9.0.0 
Generic (Max a)  Since: base4.9.0.0 
Ord a => Semigroup (Max a)  Since: base4.9.0.0 
(Ord a, Bounded a) => Monoid (Max a)  Since: base4.9.0.0 
Generic1 Max  Since: base4.9.0.0 
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: base4.9.0.0 
Functor First  Since: base4.9.0.0 
MonadFix First  Since: base4.9.0.0 
Defined in Data.Semigroup  
Applicative First  Since: base4.9.0.0 
Foldable First  Since: base4.9.0.0 
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: base4.9.0.0 
Bounded a => Bounded (First a)  Since: base4.9.0.0 
Enum a => Enum (First a)  Since: base4.9.0.0 
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: base4.9.0.0 
Data a => Data (First a)  Since: base4.9.0.0 
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: base4.9.0.0 
Read a => Read (First a)  Since: base4.9.0.0 
Show a => Show (First a)  Since: base4.9.0.0 
Generic (First a)  Since: base4.9.0.0 
Semigroup (First a)  Since: base4.9.0.0 
Generic1 First  Since: base4.9.0.0 
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: base4.9.0.0 
Functor Last  Since: base4.9.0.0 
MonadFix Last  Since: base4.9.0.0 
Defined in Data.Semigroup  
Applicative Last  Since: base4.9.0.0 
Foldable Last  Since: base4.9.0.0 
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: base4.9.0.0 
Bounded a => Bounded (Last a)  Since: base4.9.0.0 
Enum a => Enum (Last a)  Since: base4.9.0.0 
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: base4.9.0.0 
Data a => Data (Last a)  Since: base4.9.0.0 
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: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Last a)  Since: base4.9.0.0 
Show a => Show (Last a)  Since: base4.9.0.0 
Generic (Last a)  Since: base4.9.0.0 
Semigroup (Last a)  Since: base4.9.0.0 
Generic1 Last  Since: base4.9.0.0 
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 base4.11 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: base4.8.0.0 
Functor Dual  Since: base4.8.0.0 
MonadFix Dual  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Dual  Since: base4.8.0.0 
Foldable Dual  Since: base4.8.0.0 
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: base4.8.0.0 
MonadZip Dual  Since: base4.8.0.0 
Bounded a => Bounded (Dual a)  Since: base2.1 
Eq a => Eq (Dual a)  Since: base2.1 
Data a => Data (Dual a)  Since: base4.8.0.0 
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: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Dual a)  Since: base2.1 
Show a => Show (Dual a)  Since: base2.1 
Generic (Dual a)  Since: base4.7.0.0 
Semigroup a => Semigroup (Dual a)  Since: base4.9.0.0 
Monoid a => Monoid (Dual a)  Since: base2.1 
Generic1 Dual  Since: base4.7.0.0 
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: base2.1 
Eq All  Since: base2.1 
Data All  Since: base4.8.0.0 
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: base2.1 
Read All  Since: base2.1 
Show All  Since: base2.1 
Generic All  Since: base4.7.0.0 
Semigroup All  Since: base4.9.0.0 
Monoid All  Since: base2.1 
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: base2.1 
Eq Any  Since: base2.1 
Data Any  Since: base4.8.0.0 
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: base2.1 
Read Any  Since: base2.1 
Show Any  Since: base2.1 
Generic Any  Since: base4.7.0.0 
Semigroup Any  Since: base4.9.0.0 
Monoid Any  Since: base2.1 
type Rep Any  
Defined in Data.Semigroup.Internal 
Monoid under addition.
>>> getSum (Sum 1 <> Sum 2 <> mempty) 3
Monad Sum  Since: base4.8.0.0 
Functor Sum  Since: base4.8.0.0 
MonadFix Sum  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Sum  Since: base4.8.0.0 
Foldable Sum  Since: base4.8.0.0 
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: base4.8.0.0 
MonadZip Sum  Since: base4.8.0.0 
Bounded a => Bounded (Sum a)  Since: base2.1 
Eq a => Eq (Sum a)  Since: base2.1 
Data a => Data (Sum a)  Since: base4.8.0.0 
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: base4.7.0.0 
Ord a => Ord (Sum a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Sum a)  Since: base2.1 
Show a => Show (Sum a)  Since: base2.1 
Generic (Sum a)  Since: base4.7.0.0 
Num a => Semigroup (Sum a)  Since: base4.9.0.0 
Num a => Monoid (Sum a)  Since: base2.1 
Generic1 Sum  Since: base4.7.0.0 
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: base4.8.0.0 
Functor Product  Since: base4.8.0.0 
MonadFix Product  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Product  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Foldable Product  Since: base4.8.0.0 
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: base4.8.0.0 
Defined in Data.Traversable  
MonadZip Product  Since: base4.8.0.0 
Bounded a => Bounded (Product a)  Since: base2.1 
Eq a => Eq (Product a)  Since: base2.1 
Data a => Data (Product a)  Since: base4.8.0.0 
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: base4.7.0.0 
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: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Product a)  Since: base2.1 
Show a => Show (Product a)  Since: base2.1 
Generic (Product a)  Since: base4.7.0.0 
Num a => Semigroup (Product a)  Since: base4.9.0.0 
Num a => Monoid (Product a)  Since: base2.1 
Generic1 Product  Since: base4.7.0.0 
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: base4.9.0.0 
Functor Option  Since: base4.9.0.0 
MonadFix Option  Since: base4.9.0.0 
Defined in Data.Semigroup  
Applicative Option  Since: base4.9.0.0 
Foldable Option  Since: base4.9.0.0 
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: base4.9.0.0 
MonadPlus Option  Since: base4.9.0.0 
Alternative Option  Since: base4.9.0.0 
Eq a => Eq (Option a)  Since: base4.9.0.0 
Data a => Data (Option a)  Since: base4.9.0.0 
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: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Option a)  Since: base4.9.0.0 
Show a => Show (Option a)  Since: base4.9.0.0 
Generic (Option a)  Since: base4.9.0.0 
Semigroup a => Semigroup (Option a)  Since: base4.9.0.0 
Semigroup a => Monoid (Option a)  Since: base4.9.0.0 
Generic1 Option  Since: base4.9.0.0 
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
casewise, 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: base4.9.0.0 
Bifoldable Arg  Since: base4.10.0.0 
Bitraversable Arg  Since: base4.10.0.0 
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: base4.9.0.0 
Foldable (Arg a)  Since: base4.9.0.0 
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: base4.9.0.0 
Generic1 (Arg a :: Type > Type)  Since: base4.9.0.0 
Eq a => Eq (Arg a b)  Since: base4.9.0.0 
(Data a, Data b) => Data (Arg a b)  Since: base4.9.0.0 
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: base4.9.0.0 
(Read a, Read b) => Read (Arg a b)  Since: base4.9.0.0 
(Show a, Show b) => Show (Arg a b)  Since: base4.9.0.0 
Generic (Arg a b)  Since: base4.9.0.0 
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))) 
© The University of Glasgow and others
Licensed under a BSDstyle license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base4.13.0.0/DataSemigroup.html