Copyright  (C) 20112015 Edward Kmett 

License  BSDstyle (see the file LICENSE) 
Maintainer  libraries@haskell.org 
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)
Examples
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
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
 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 following:
Since: base4.9.0.0
(<>) :: a > a > a infixr 6 Source #
An associative operation.
>>>
[1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
sconcat :: NonEmpty a > a Source #
Reduce a nonempty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
>>>
import Data.List.NonEmpty (NonEmpty (..))
>>>
sconcat $ "Hello" : [" ", "Haskell", "!"]
"Hello Haskell!"
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 \(\mathcal{O}(1)\) by
picking stimes =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
>>>
stimes 4 [1]
[1,1,1,1]
Instances
Semigroup All Source #  Since: base4.9.0.0 
Semigroup Any Source #  Since: base4.9.0.0 
Semigroup Void Source #  Since: base4.9.0.0 
Semigroup Event Source #  Since: base4.10.0.0 
Semigroup Lifetime Source #  Since: base4.10.0.0 
Semigroup Ordering Source #  Since: base4.9.0.0 
Semigroup () Source #  Since: base4.9.0.0 
Bits a => Semigroup (And a) Source #  Since: base4.16 
FiniteBits a => Semigroup (Iff a) Source #  This constraint is arguably
too strong. However, as some types (such as Since: base4.16 
Bits a => Semigroup (Ior a) Source #  Since: base4.16 
Bits a => Semigroup (Xor a) Source #  Since: base4.16 
Semigroup (Comparison a) Source # 
(<>) :: Comparison a > Comparison a > Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' > cmp a a' <> cmp a a' 
Defined in Data.Functor.Contravariant (<>) :: Comparison a > Comparison a > Comparison a Source # sconcat :: NonEmpty (Comparison a) > Comparison a Source # stimes :: Integral b => b > Comparison a > Comparison a Source #  
Semigroup (Equivalence a) Source # 
(<>) :: Equivalence a > Equivalence a > Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b > equiv a b && equiv a b 
Defined in Data.Functor.Contravariant (<>) :: Equivalence a > Equivalence a > Equivalence a Source # sconcat :: NonEmpty (Equivalence a) > Equivalence a Source # stimes :: Integral b => b > Equivalence a > Equivalence a Source #  
Semigroup (Predicate a) Source # 
(<>) :: Predicate a > Predicate a > Predicate a Predicate pred <> Predicate pred' = Predicate a > pred a && pred' a 
Semigroup a => Semigroup (Identity a) Source #  Since: base4.9.0.0 
Semigroup (First a) Source #  Since: base4.9.0.0 
Semigroup (Last a) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (Down a) Source #  Since: base4.11.0.0 
Semigroup (First a) Source #  Since: base4.9.0.0 
Semigroup (Last a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Max a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Min a) Source #  Since: base4.9.0.0 
Monoid m => Semigroup (WrappedMonoid m) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup (<>) :: WrappedMonoid m > WrappedMonoid m > WrappedMonoid m Source # sconcat :: NonEmpty (WrappedMonoid m) > WrappedMonoid m Source # stimes :: Integral b => b > WrappedMonoid m > WrappedMonoid m Source #  
Semigroup a => Semigroup (Dual a) Source #  Since: base4.9.0.0 
Semigroup (Endo a) Source #  Since: base4.9.0.0 
Num a => Semigroup (Product a) Source #  Since: base4.9.0.0 
Num a => Semigroup (Sum a) Source #  Since: base4.9.0.0 
Semigroup p => Semigroup (Par1 p) Source #  Since: base4.12.0.0 
Semigroup a => Semigroup (IO a) Source #  Since: base4.10.0.0 
Semigroup (NonEmpty a) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (Maybe a) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (a) Source #  Since: base4.15 
Semigroup [a] Source #  Since: base4.9.0.0 
Semigroup (Either a b) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (Op a b) Source # 
(<>) :: Op a b > Op a b > Op a b Op f <> Op g = Op a > f a <> g a 
Semigroup (Proxy s) Source #  Since: base4.9.0.0 
Semigroup (U1 p) Source #  Since: base4.12.0.0 
Semigroup (V1 p) Source #  Since: base4.12.0.0 
Semigroup a => Semigroup (ST s a) Source #  Since: base4.11.0.0 
Semigroup b => Semigroup (a > b) Source #  Since: base4.9.0.0 
(Semigroup a, Semigroup b) => Semigroup (a, b) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (Const a b) Source #  Since: base4.9.0.0 
(Applicative f, Semigroup a) => Semigroup (Ap f a) Source #  Since: base4.12.0.0 
Alternative f => Semigroup (Alt f a) Source #  Since: base4.9.0.0 
Semigroup (f p) => Semigroup (Rec1 f p) Source #  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source #  Since: base4.9.0.0 
(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source #  Since: base4.16.0.0 
(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source #  Since: base4.12.0.0 
Semigroup c => Semigroup (K1 i c p) Source #  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source #  Since: base4.9.0.0 
Semigroup (f (g a)) => Semigroup (Compose f g a) Source #  Since: base4.16.0.0 
Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source #  Since: base4.12.0.0 
Semigroup (f p) => Semigroup (M1 i c f p) Source #  Since: base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source #  Since: base4.9.0.0 
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
MonadFix Min Source #  Since: base4.9.0.0 
Foldable Min Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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 # 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 Source #  Since: base4.9.0.0 
Applicative Min Source #  Since: base4.9.0.0 
Functor Min Source #  Since: base4.9.0.0 
Monad Min Source #  Since: base4.9.0.0 
Data a => Data (Min a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 :: 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 #  
(Ord a, Bounded a) => Monoid (Min a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Min a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Min a) Source #  Since: base4.9.0.0 
Enum a => Enum (Min a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 #  
Generic (Min a) Source #  
Num a => Num (Min a) Source #  Since: base4.9.0.0 
Read a => Read (Min a) Source #  Since: base4.9.0.0 
Show a => Show (Min a) Source #  Since: base4.9.0.0 
Eq a => Eq (Min a) Source #  Since: base4.9.0.0 
Ord a => Ord (Min a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Generic1 Min Source #  
type Rep (Min a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
type Rep1 Min Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 
Instances
MonadFix Max Source #  Since: base4.9.0.0 
Foldable Max Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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 # 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 Source #  Since: base4.9.0.0 
Applicative Max Source #  Since: base4.9.0.0 
Functor Max Source #  Since: base4.9.0.0 
Monad Max Source #  Since: base4.9.0.0 
Data a => Data (Max a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 :: 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 #  
(Ord a, Bounded a) => Monoid (Max a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Max a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Max a) Source #  Since: base4.9.0.0 
Enum a => Enum (Max a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 #  
Generic (Max a) Source #  
Num a => Num (Max a) Source #  Since: base4.9.0.0 
Read a => Read (Max a) Source #  Since: base4.9.0.0 
Show a => Show (Max a) Source #  Since: base4.9.0.0 
Eq a => Eq (Max a) Source #  Since: base4.9.0.0 
Ord a => Ord (Max a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Generic1 Max Source #  
type Rep (Max a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
type Rep1 Max Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 
Instances
MonadFix First Source #  Since: base4.9.0.0 
Foldable First Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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 Source #  Since: base4.9.0.0 
Applicative First Source #  Since: base4.9.0.0 
Functor First Source #  Since: base4.9.0.0 
Monad First Source #  Since: base4.9.0.0 
Data a => Data (First a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 :: 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 #  
Semigroup (First a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (First a) Source #  Since: base4.9.0.0 
Enum a => Enum (First a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 #  
Generic (First a) Source #  
Read a => Read (First a) Source #  Since: base4.9.0.0 
Show a => Show (First a) Source #  Since: base4.9.0.0 
Eq a => Eq (First a) Source #  Since: base4.9.0.0 
Ord a => Ord (First a) Source #  Since: base4.9.0.0 
Generic1 First Source #  
type Rep (First a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
type Rep1 First Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 
Instances
MonadFix Last Source #  Since: base4.9.0.0 
Foldable Last Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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 # 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 Source #  Since: base4.9.0.0 
Applicative Last Source #  Since: base4.9.0.0 
Functor Last Source #  Since: base4.9.0.0 
Monad Last Source #  Since: base4.9.0.0 
Data a => Data (Last a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 :: 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 #  
Semigroup (Last a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Last a) Source #  Since: base4.9.0.0 
Enum a => Enum (Last a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 #  
Generic (Last a) Source #  
Read a => Read (Last a) Source #  Since: base4.9.0.0 
Show a => Show (Last a) Source #  Since: base4.9.0.0 
Eq a => Eq (Last a) Source #  Since: base4.9.0.0 
Ord a => Ord (Last a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Generic1 Last Source #  
type Rep (Last a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
type Rep1 Last Source #  Since: base4.9.0.0 
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  

Instances
Reexported monoids from Data.Monoid
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>>
getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
MonadFix Dual Source #  Since: base4.8.0.0 
MonadZip Dual Source #  Since: base4.8.0.0 
Foldable Dual Source #  Since: base4.8.0.0 
Defined in Data.Foldable fold :: 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 # 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 Source #  Since: base4.8.0.0 
Applicative Dual Source #  Since: base4.8.0.0 
Functor Dual Source #  Since: base4.8.0.0 
Monad Dual Source #  Since: base4.8.0.0 
Data a => Data (Dual a) Source #  Since: base4.8.0.0 
Defined in Data.Data 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 :: 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 #  
Monoid a => Monoid (Dual a) Source #  Since: base2.1 
Semigroup a => Semigroup (Dual a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Dual a) Source #  Since: base2.1 
Generic (Dual a) Source #  
Read a => Read (Dual a) Source #  Since: base2.1 
Show a => Show (Dual a) Source #  Since: base2.1 
Eq a => Eq (Dual a) Source #  Since: base2.1 
Ord a => Ord (Dual a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Generic1 Dual Source #  
type Rep (Dual a) Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep1 Dual Source #  Since: base4.7.0.0 
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
Data All Source #  Since: base4.8.0.0 
Defined in Data.Data 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 :: 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 #  
Monoid All Source #  Since: base2.1 
Semigroup All Source #  Since: base4.9.0.0 
Bounded All Source #  Since: base2.1 
Generic All Source #  
Read All Source #  Since: base2.1 
Show All Source #  Since: base2.1 
Eq All Source #  Since: base2.1 
Ord All Source #  Since: base2.1 
type Rep All Source #  Since: base4.7.0.0 
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
Data Any Source #  Since: base4.8.0.0 
Defined in Data.Data 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 :: 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 #  
Monoid Any Source #  Since: base2.1 
Semigroup Any Source #  Since: base4.9.0.0 
Bounded Any Source #  Since: base2.1 
Generic Any Source #  
Read Any Source #  Since: base2.1 
Show Any Source #  Since: base2.1 
Eq Any Source #  Since: base2.1 
Ord Any Source #  Since: base2.1 
type Rep Any Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
MonadFix Sum Source #  Since: base4.8.0.0 
MonadZip Sum Source #  Since: base4.8.0.0 
Foldable Sum Source #  Since: base4.8.0.0 
Defined in Data.Foldable fold :: 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 # 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 Source #  Since: base4.8.0.0 
Applicative Sum Source #  Since: base4.8.0.0 
Functor Sum Source #  Since: base4.8.0.0 
Monad Sum Source #  Since: base4.8.0.0 
Data a => Data (Sum a) Source #  Since: base4.8.0.0 
Defined in Data.Data 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 :: 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 => Monoid (Sum a) Source #  Since: base2.1 
Num a => Semigroup (Sum a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Sum a) Source #  Since: base2.1 
Generic (Sum a) Source #  
Num a => Num (Sum a) Source #  Since: base4.7.0.0 
Read a => Read (Sum a) Source #  Since: base2.1 
Show a => Show (Sum a) Source #  Since: base2.1 
Eq a => Eq (Sum a) Source #  Since: base2.1 
Ord a => Ord (Sum a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Generic1 Sum Source #  
type Rep (Sum a) Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep1 Sum Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product  

Instances
MonadFix Product Source #  Since: base4.8.0.0 
MonadZip Product Source #  Since: base4.8.0.0 
Foldable Product Source #  Since: base4.8.0.0 
Defined in Data.Foldable fold :: 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 Source #  Since: base4.8.0.0 
Defined in Data.Traversable  
Applicative Product Source #  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Functor Product Source #  Since: base4.8.0.0 
Monad Product Source #  Since: base4.8.0.0 
Data a => Data (Product a) Source #  Since: base4.8.0.0 
Defined in Data.Data 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 :: 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 => Monoid (Product a) Source #  Since: base2.1 
Num a => Semigroup (Product a) Source #  Since: base4.9.0.0 
Bounded a => Bounded (Product a) Source #  Since: base2.1 
Generic (Product a) Source #  
Num a => Num (Product a) Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal (+) :: 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 #  
Read a => Read (Product a) Source #  Since: base2.1 
Show a => Show (Product a) Source #  Since: base2.1 
Eq a => Eq (Product a) Source #  Since: base2.1 
Ord a => Ord (Product a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Generic1 Product Source #  
type Rep (Product a) Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep1 Product Source #  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
Difference lists of a semigroup
diff :: Semigroup m => m > Endo m Source #
This lets you use a difference list of a Semigroup
as a Monoid
.
Example:
>>>
let hello = diff "Hello, "
>>>
appEndo hello "World!"
"Hello, World!">>>
appEndo (hello <> mempty) "World!"
"Hello, World!">>>
appEndo (mempty <> hello) "World!"
"Hello, World!">>>
let world = diff "World"
>>>
let excl = diff "!"
>>>
appEndo (hello <> (world <> excl)) mempty
"Hello, World!">>>
appEndo ((hello <> world) <> excl) mempty
"Hello, World!"
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.
>>>
minimum [ Arg (x * x) x  x < [10 .. 10] ]
Arg 0 0
Instances
Bifoldable Arg Source #  Since: base4.10.0.0 
Bifunctor Arg Source #  Since: base4.9.0.0 
Bitraversable Arg Source #  Since: base4.10.0.0 
Defined in Data.Semigroup bitraverse :: Applicative f => (a > f c) > (b > f d) > Arg a b > f (Arg c d) Source #  
Foldable (Arg a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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) Source #  Since: base4.9.0.0 
Functor (Arg a) Source #  Since: base4.9.0.0 
Generic1 (Arg a :: Type > Type) Source #  
(Data a, Data b) => Data (Arg a b) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup 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 :: 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 #  
Generic (Arg a b) Source #  
(Read a, Read b) => Read (Arg a b) Source #  Since: base4.9.0.0 
(Show a, Show b) => Show (Arg a b) Source #  Since: base4.9.0.0 
Eq a => Eq (Arg a b) Source #  Since: base4.9.0.0 
Ord a => Ord (Arg a b) Source #  Since: base4.9.0.0 
type Rep1 (Arg a :: Type > Type) Source #  Since: base4.9.0.0 
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) Source #  Since: base4.9.0.0 
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))) 