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
 newtype Option a = Option {}
 option :: b > (a > b) > Option a > b
 diff :: Semigroup m => m > Endo m
 cycle1 :: Semigroup m => m > m
 data Arg a b = Arg a b
 type ArgMin a b = Min (Arg a b)
 type ArgMax a b = Max (Arg a b)
Documentation
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the 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
>>>
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
stimesMonoid :: (Integral b, Monoid a) => b > a > a Source #
stimesIdempotent :: Integral b => b > a > a Source #
stimesIdempotentMonoid :: (Integral b, Monoid a) => b > a > a Source #
mtimesDefault :: (Integral b, Monoid a) => b > a > a Source #
Semigroups
Instances
Monad Min Source #  Since: base4.9.0.0 
Functor Min Source #  Since: base4.9.0.0 
MonadFix Min Source #  Since: base4.9.0.0 
Applicative 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 
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 #  
Eq a => Eq (Min a) 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 #  
Num a => Num (Min a) Source #  Since: base4.9.0.0 
Ord a => Ord (Min a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Min a) Source #  Since: base4.9.0.0 
Show a => Show (Min a) Source #  Since: base4.9.0.0 
Generic (Min a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Min a) Source #  Since: base4.9.0.0 
(Ord a, Bounded a) => Monoid (Min a) Source #  Since: base4.9.0.0 
Generic1 Min Source #  Since: base4.9.0.0 
type Rep (Min a) Source #  
Defined in Data.Semigroup  
type Rep1 Min Source #  
Defined in Data.Semigroup 
Instances
Monad Max Source #  Since: base4.9.0.0 
Functor Max Source #  Since: base4.9.0.0 
MonadFix Max Source #  Since: base4.9.0.0 
Applicative 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 
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 #  
Eq a => Eq (Max a) 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 #  
Num a => Num (Max a) Source #  Since: base4.9.0.0 
Ord a => Ord (Max a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Max a) Source #  Since: base4.9.0.0 
Show a => Show (Max a) Source #  Since: base4.9.0.0 
Generic (Max a) Source #  Since: base4.9.0.0 
Ord a => Semigroup (Max a) Source #  Since: base4.9.0.0 
(Ord a, Bounded a) => Monoid (Max a) Source #  Since: base4.9.0.0 
Generic1 Max Source #  Since: base4.9.0.0 
type Rep (Max a) Source #  
Defined in Data.Semigroup  
type Rep1 Max Source #  
Defined in Data.Semigroup 
Use
to get the behavior of
Option
(First
a)First
from Data.Monoid.
Instances
Monad First Source #  Since: base4.9.0.0 
Functor First Source #  Since: base4.9.0.0 
MonadFix First Source #  Since: base4.9.0.0 
Applicative 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 
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 #  
Eq a => Eq (First a) 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 #  
Ord a => Ord (First a) Source #  Since: base4.9.0.0 
Read a => Read (First a) Source #  Since: base4.9.0.0 
Show a => Show (First a) Source #  Since: base4.9.0.0 
Generic (First a) Source #  Since: base4.9.0.0 
Semigroup (First a) Source #  Since: base4.9.0.0 
Generic1 First Source #  Since: base4.9.0.0 
type Rep (First a) Source #  
Defined in Data.Semigroup  
type Rep1 First Source #  
Defined in Data.Semigroup 
Use
to get the behavior of
Option
(Last
a)Last
from Data.Monoid
Instances
Monad Last Source #  Since: base4.9.0.0 
Functor Last Source #  Since: base4.9.0.0 
MonadFix Last Source #  Since: base4.9.0.0 
Applicative 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 
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 #  
Eq a => Eq (Last a) 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 #  
Ord a => Ord (Last a) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Last a) Source #  Since: base4.9.0.0 
Show a => Show (Last a) Source #  Since: base4.9.0.0 
Generic (Last a) Source #  Since: base4.9.0.0 
Semigroup (Last a) Source #  Since: base4.9.0.0 
Generic1 Last Source #  Since: base4.9.0.0 
type Rep (Last a) Source #  
Defined in Data.Semigroup  
type Rep1 Last Source #  
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
Monad Dual Source #  Since: base4.8.0.0 
Functor Dual Source #  Since: base4.8.0.0 
MonadFix Dual Source #  Since: base4.8.0.0 
Applicative 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 
MonadZip Dual Source #  Since: base4.8.0.0 
Bounded a => Bounded (Dual a) Source #  Since: base2.1 
Eq a => Eq (Dual a) Source #  Since: base2.1 
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 #  
Ord a => Ord (Dual a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Dual a) Source #  Since: base2.1 
Show a => Show (Dual a) Source #  Since: base2.1 
Generic (Dual a) Source #  Since: base4.7.0.0 
Semigroup a => Semigroup (Dual a) Source #  Since: base4.9.0.0 
Monoid a => Monoid (Dual a) Source #  Since: base2.1 
Generic1 Dual Source #  Since: base4.7.0.0 
type Rep (Dual a) Source #  
Defined in Data.Semigroup.Internal  
type Rep1 Dual Source #  
Defined in Data.Semigroup.Internal 
The monoid of endomorphisms under composition.
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
Boolean monoid under conjunction (&&
).
>>>
getAll (All True <> mempty <> All False)
False
>>>
getAll (mconcat (map (\x > All (even x)) [2,4,6,7,8]))
False
Instances
Bounded All Source #  Since: base2.1 
Eq All Source #  Since: base2.1 
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 #  
Ord All Source #  Since: base2.1 
Read All Source #  Since: base2.1 
Show All Source #  Since: base2.1 
Generic All Source #  Since: base4.7.0.0 
Semigroup All Source #  Since: base4.9.0.0 
Monoid All Source #  Since: base2.1 
type Rep All Source #  
Defined in Data.Semigroup.Internal 
Boolean monoid under disjunction (
).
>>>
getAny (Any True <> mempty <> Any False)
True
>>>
getAny (mconcat (map (\x > Any (even x)) [2,4,6,7,8]))
True
Instances
Bounded Any Source #  Since: base2.1 
Eq Any Source #  Since: base2.1 
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 #  
Ord Any Source #  Since: base2.1 
Read Any Source #  Since: base2.1 
Show Any Source #  Since: base2.1 
Generic Any Source #  Since: base4.7.0.0 
Semigroup Any Source #  Since: base4.9.0.0 
Monoid Any Source #  Since: base2.1 
type Rep Any Source #  
Defined in Data.Semigroup.Internal 
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Monad Sum Source #  Since: base4.8.0.0 
Functor Sum Source #  Since: base4.8.0.0 
MonadFix Sum Source #  Since: base4.8.0.0 
Applicative 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 
MonadZip Sum Source #  Since: base4.8.0.0 
Bounded a => Bounded (Sum a) Source #  Since: base2.1 
Eq a => Eq (Sum a) Source #  Since: base2.1 
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 => Num (Sum a) Source #  Since: base4.7.0.0 
Ord a => Ord (Sum a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Sum a) Source #  Since: base2.1 
Show a => Show (Sum a) Source #  Since: base2.1 
Generic (Sum a) Source #  Since: base4.7.0.0 
Num a => Semigroup (Sum a) Source #  Since: base4.9.0.0 
Num a => Monoid (Sum a) Source #  Since: base2.1 
Generic1 Sum Source #  Since: base4.7.0.0 
type Rep (Sum a) Source #  
Defined in Data.Semigroup.Internal  
type Rep1 Sum Source #  
Defined in Data.Semigroup.Internal 
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product  

Instances
Monad Product Source #  Since: base4.8.0.0 
Functor Product Source #  Since: base4.8.0.0 
MonadFix Product Source #  Since: base4.8.0.0 
Applicative Product Source #  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
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  
MonadZip Product Source #  Since: base4.8.0.0 
Bounded a => Bounded (Product a) Source #  Since: base2.1 
Eq a => Eq (Product a) Source #  Since: base2.1 
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 => 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 #  
Ord a => Ord (Product a) Source #  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Product a) Source #  Since: base2.1 
Show a => Show (Product a) Source #  Since: base2.1 
Generic (Product a) Source #  Since: base4.7.0.0 
Num a => Semigroup (Product a) Source #  Since: base4.9.0.0 
Num a => Monoid (Product a) Source #  Since: base2.1 
Generic1 Product Source #  Since: base4.7.0.0 
type Rep (Product a) Source #  
Defined in Data.Semigroup.Internal  
type Rep1 Product Source #  
Defined in Data.Semigroup.Internal 
A better monoid for Maybe
Option
is effectively Maybe
with a better instance of
Monoid
, built off of an underlying Semigroup
instead of an
underlying Monoid
.
Ideally, this type would not exist at all and we would just fix the
Monoid
instance of Maybe
.
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.
Instances
Monad Option Source #  Since: base4.9.0.0 
Functor Option Source #  Since: base4.9.0.0 
MonadFix Option Source #  Since: base4.9.0.0 
Applicative Option Source #  Since: base4.9.0.0 
Foldable Option Source #  Since: base4.9.0.0 
Defined in Data.Semigroup fold :: 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 Source #  Since: base4.9.0.0 
MonadPlus Option Source #  Since: base4.9.0.0 
Alternative Option Source #  Since: base4.9.0.0 
Eq a => Eq (Option a) Source #  Since: base4.9.0.0 
Data a => Data (Option 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) > 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) Source #  Since: base4.9.0.0 
Defined in Data.Semigroup  
Read a => Read (Option a) Source #  Since: base4.9.0.0 
Show a => Show (Option a) Source #  Since: base4.9.0.0 
Generic (Option a) Source #  Since: base4.9.0.0 
Semigroup a => Semigroup (Option a) Source #  Since: base4.9.0.0 
Semigroup a => Monoid (Option a) Source #  Since: base4.9.0.0 
Generic1 Option Source #  Since: base4.9.0.0 
type Rep (Option a) Source #  
Defined in Data.Semigroup  
type Rep1 Option Source #  
Defined in Data.Semigroup 
Difference lists of a semigroup
ArgMin, ArgMax
Arg
isn't itself a Semigroup
in its own right, but it can be
placed inside Min
and Max
to compute an arg min or arg max.
Arg a b 
Instances
Bifunctor Arg Source #  Since: base4.9.0.0 
Bifoldable Arg Source #  Since: base4.10.0.0 
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 #  
Functor (Arg a) Source #  Since: base4.9.0.0 
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 
Generic1 (Arg a :: Type > Type) Source #  Since: base4.9.0.0 
Eq a => Eq (Arg a b) Source #  Since: base4.9.0.0 
(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 #  
Ord a => Ord (Arg a b) Source #  Since: base4.9.0.0 
(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 
Generic (Arg a b) Source #  Since: base4.9.0.0 
type Rep1 (Arg a :: Type > Type) Source #  
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 #  
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))) 