Copyright  (C) 20112015 Edward Kmett 

License  BSDstyle (see the file LICENSE) 
Maintainer  libraries@haskell.org 
Stability  provisional 
Portability  portable 
Safe Haskell  Trustworthy 
Language  Haskell2010 
In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. A semigroup generalizes a monoid in that there might not exist an identity element. It also (originally) generalized a group (a monoid with all inverses) to a type where every element did not have to have an inverse, thus the name semigroup.
The use of (<>)
in this module conflicts with an operator with the same
name that is being exported by Data.Monoid. However, this package
reexports (most of) the contents of Data.Monoid, so to use semigroups
and monoids in the same package just
import Data.Semigroup
Since: 4.9.0.0
Synopsis
 class Semigroup a where
 stimesMonoid :: (Integral b, Monoid a) => b > a > a
 stimesIdempotent :: Integral b => b > a > a
 stimesIdempotentMonoid :: (Integral b, Monoid a) => b > a > a
 mtimesDefault :: (Integral b, Monoid a) => b > a > a
 newtype Min a = Min {
 getMin :: a
 newtype Max a = Max {
 getMax :: a
 newtype First a = First {
 getFirst :: a
 newtype Last a = Last {
 getLast :: a
 newtype WrappedMonoid m = WrapMonoid {
 unwrapMonoid :: m
 newtype Dual a = Dual {
 getDual :: a
 newtype Endo a = Endo {
 appEndo :: a > a
 newtype All = All {}
 newtype Any = Any {}
 newtype Sum a = Sum {
 getSum :: a
 newtype Product a = Product {
 getProduct :: a
 newtype Option a = Option {}
 option :: b > (a > b) > Option a > b
 diff :: Semigroup m => m > Endo m
 cycle1 :: Semigroup m => m > m
 data Arg a b = Arg a b
 type ArgMin a b = Min (Arg a b)
 type ArgMax a b = Max (Arg a b)
Documentation
class Semigroup a where Source #
The class of semigroups (types with an associative binary operation).
Instances should satisfy the associativity law:
Since: 4.9.0.0
(<>) :: 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 =
or stimesIdempotent
stimes =
respectively.stimesIdempotentMonoid
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: 4.9.0.0 
Functor Min Source #  Since: 4.9.0.0 
MonadFix Min Source #  Since: 4.9.0.0 
Applicative Min Source #  Since: 4.9.0.0 
Foldable Min Source #  Since: 4.9.0.0 
fold :: Monoid m => Min m > m Source # foldMap :: Monoid m => (a > m) > Min a > m Source # foldr :: (a > b > b) > b > Min a > b Source # foldr' :: (a > b > b) > b > Min a > b Source # foldl :: (b > a > b) > b > Min a > b Source # foldl' :: (b > a > b) > b > Min a > b Source # foldr1 :: (a > a > a) > Min a > a Source # foldl1 :: (a > a > a) > Min a > a Source # toList :: Min a > [a] Source # null :: Min a > Bool Source # length :: Min a > Int Source # elem :: Eq a => a > Min a > Bool Source # maximum :: Ord a => Min a > a Source # minimum :: Ord a => Min a > a Source #  
Traversable Min Source #  Since: 4.9.0.0 
Bounded a => Bounded (Min a) Source #  
Enum a => Enum (Min a) Source #  Since: 4.9.0.0 
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 #  
Data a => Data (Min a) Source #  
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Min a > c (Min a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Min a) Source # toConstr :: Min a > Constr Source # dataTypeOf :: Min a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Min a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Min a)) Source # gmapT :: (forall b. Data b => b > b) > Min a > Min a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Min a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Min a > r Source # gmapQ :: (forall d. Data d => d > u) > Min a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Min a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Min a > m (Min a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Min a > m (Min a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Min a > m (Min a) Source #  
Num a => Num (Min a) Source #  Since: 4.9.0.0 
Ord a => Ord (Min a) Source #  
Read a => Read (Min a) Source #  
Show a => Show (Min a) Source #  
Generic (Min a) Source #  
Ord a => Semigroup (Min a) Source #  Since: 4.9.0.0 
(Ord a, Bounded a) => Monoid (Min a) Source #  Since: 4.9.0.0 
Generic1 Min Source #  
type Rep (Min a) Source #  
type Rep1 Min Source #  
Instances
Monad Max Source #  Since: 4.9.0.0 
Functor Max Source #  Since: 4.9.0.0 
MonadFix Max Source #  Since: 4.9.0.0 
Applicative Max Source #  Since: 4.9.0.0 
Foldable Max Source #  Since: 4.9.0.0 
fold :: Monoid m => Max m > m Source # foldMap :: Monoid m => (a > m) > Max a > m Source # foldr :: (a > b > b) > b > Max a > b Source # foldr' :: (a > b > b) > b > Max a > b Source # foldl :: (b > a > b) > b > Max a > b Source # foldl' :: (b > a > b) > b > Max a > b Source # foldr1 :: (a > a > a) > Max a > a Source # foldl1 :: (a > a > a) > Max a > a Source # toList :: Max a > [a] Source # null :: Max a > Bool Source # length :: Max a > Int Source # elem :: Eq a => a > Max a > Bool Source # maximum :: Ord a => Max a > a Source # minimum :: Ord a => Max a > a Source #  
Traversable Max Source #  Since: 4.9.0.0 
Bounded a => Bounded (Max a) Source #  
Enum a => Enum (Max a) Source #  Since: 4.9.0.0 
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 #  
Data a => Data (Max a) Source #  
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Max a > c (Max a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Max a) Source # toConstr :: Max a > Constr Source # dataTypeOf :: Max a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Max a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Max a)) Source # gmapT :: (forall b. Data b => b > b) > Max a > Max a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Max a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Max a > r Source # gmapQ :: (forall d. Data d => d > u) > Max a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Max a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Max a > m (Max a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Max a > m (Max a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Max a > m (Max a) Source #  
Num a => Num (Max a) Source #  Since: 4.9.0.0 
Ord a => Ord (Max a) Source #  
Read a => Read (Max a) Source #  
Show a => Show (Max a) Source #  
Generic (Max a) Source #  
Ord a => Semigroup (Max a) Source #  Since: 4.9.0.0 
(Ord a, Bounded a) => Monoid (Max a) Source #  Since: 4.9.0.0 
Generic1 Max Source #  
type Rep (Max a) Source #  
type Rep1 Max Source #  
Use
to get the behavior of
Option
(First
a)First
from Data.Monoid.
Instances
Monad First Source #  Since: 4.9.0.0 
Functor First Source #  Since: 4.9.0.0 
MonadFix First Source #  Since: 4.9.0.0 
Applicative First Source #  Since: 4.9.0.0 
Foldable First Source #  Since: 4.9.0.0 
fold :: Monoid m => First m > m Source # foldMap :: Monoid m => (a > m) > First a > m Source # foldr :: (a > b > b) > b > First a > b Source # foldr' :: (a > b > b) > b > First a > b Source # foldl :: (b > a > b) > b > First a > b Source # foldl' :: (b > a > b) > b > First a > b Source # foldr1 :: (a > a > a) > First a > a Source # foldl1 :: (a > a > a) > First a > a Source # toList :: First a > [a] Source # null :: First a > Bool Source # length :: First a > Int Source # elem :: Eq a => a > First a > Bool Source # maximum :: Ord a => First a > a Source # minimum :: Ord a => First a > a Source #  
Traversable First Source #  Since: 4.9.0.0 
Bounded a => Bounded (First a) Source #  
Enum a => Enum (First a) Source #  Since: 4.9.0.0 
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 #  
Data a => Data (First a) Source #  
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > First a > c (First a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (First a) Source # toConstr :: First a > Constr Source # dataTypeOf :: First a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (First a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b > b) > First a > First a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > First a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > First a > r Source # gmapQ :: (forall d. Data d => d > u) > First a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > First a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > First a > m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source #  
Ord a => Ord (First a) Source #  
Read a => Read (First a) Source #  
Show a => Show (First a) Source #  
Generic (First a) Source #  
Semigroup (First a) Source #  Since: 4.9.0.0 
Generic1 First Source #  
type Rep (First a) Source #  
type Rep1 First Source #  
Use
to get the behavior of
Option
(Last
a)Last
from Data.Monoid
Instances
Monad Last Source #  Since: 4.9.0.0 
Functor Last Source #  Since: 4.9.0.0 
MonadFix Last Source #  Since: 4.9.0.0 
Applicative Last Source #  Since: 4.9.0.0 
Foldable Last Source #  Since: 4.9.0.0 
fold :: Monoid m => Last m > m Source # foldMap :: Monoid m => (a > m) > Last a > m Source # foldr :: (a > b > b) > b > Last a > b Source # foldr' :: (a > b > b) > b > Last a > b Source # foldl :: (b > a > b) > b > Last a > b Source # foldl' :: (b > a > b) > b > Last a > b Source # foldr1 :: (a > a > a) > Last a > a Source # foldl1 :: (a > a > a) > Last a > a Source # toList :: Last a > [a] Source # null :: Last a > Bool Source # length :: Last a > Int Source # elem :: Eq a => a > Last a > Bool Source # maximum :: Ord a => Last a > a Source # minimum :: Ord a => Last a > a Source #  
Traversable Last Source #  Since: 4.9.0.0 
Bounded a => Bounded (Last a) Source #  
Enum a => Enum (Last a) Source #  Since: 4.9.0.0 
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 #  
Data a => Data (Last a) Source #  
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Last a > c (Last a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Last a) Source # toConstr :: Last a > Constr Source # dataTypeOf :: Last a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Last a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b > b) > Last a > Last a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Last a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Last a > r Source # gmapQ :: (forall d. Data d => d > u) > Last a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Last a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Last a > m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source #  
Ord a => Ord (Last a) Source #  
Read a => Read (Last a) Source #  
Show a => Show (Last a) Source #  
Generic (Last a) Source #  
Semigroup (Last a) Source #  Since: 4.9.0.0 
Generic1 Last Source #  
type Rep (Last a) Source #  
type Rep1 Last Source #  
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: 4.8.0.0 
Functor Dual Source #  Since: 4.8.0.0 
MonadFix Dual Source #  Since: 4.8.0.0 
Applicative Dual Source #  Since: 4.8.0.0 
Foldable Dual Source #  Since: 4.8.0.0 
fold :: Monoid m => Dual m > m Source # foldMap :: Monoid m => (a > m) > Dual a > m Source # foldr :: (a > b > b) > b > Dual a > b Source # foldr' :: (a > b > b) > b > Dual a > b Source # foldl :: (b > a > b) > b > Dual a > b Source # foldl' :: (b > a > b) > b > Dual a > b Source # foldr1 :: (a > a > a) > Dual a > a Source # foldl1 :: (a > a > a) > Dual a > a Source # toList :: Dual a > [a] Source # null :: Dual a > Bool Source # length :: Dual a > Int Source # elem :: Eq a => a > Dual a > Bool Source # maximum :: Ord a => Dual a > a Source # minimum :: Ord a => Dual a > a Source #  
Traversable Dual Source #  Since: 4.8.0.0 
MonadZip Dual Source #  Since: 4.8.0.0 
Bounded a => Bounded (Dual a) Source #  
Eq a => Eq (Dual a) Source #  
Data a => Data (Dual a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Dual a > c (Dual a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Dual a) Source # toConstr :: Dual a > Constr Source # dataTypeOf :: Dual a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Dual a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b > b) > Dual a > Dual a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Dual a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Dual a > r Source # gmapQ :: (forall d. Data d => d > u) > Dual a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Dual a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source #  
Ord a => Ord (Dual a) Source #  
Read a => Read (Dual a) Source #  
Show a => Show (Dual a) Source #  
Generic (Dual a) Source #  
Semigroup a => Semigroup (Dual a) Source #  Since: 4.9.0.0 
Monoid a => Monoid (Dual a) Source #  Since: 2.1 
Generic1 Dual Source #  
type Rep (Dual a) Source #  
type Rep1 Dual Source #  
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 #  
Eq All Source #  
Data All Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > All > c All Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c All Source # toConstr :: All > Constr Source # dataTypeOf :: All > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c All) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c All) Source # gmapT :: (forall b. Data b => b > b) > All > All Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > All > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > All > r Source # gmapQ :: (forall d. Data d => d > u) > All > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > All > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > All > m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source #  
Ord All Source #  
Read All Source #  
Show All Source #  
Generic All Source #  
Semigroup All Source #  Since: 4.9.0.0 
Monoid All Source #  Since: 2.1 
type Rep All Source #  
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 #  
Eq Any Source #  
Data Any Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Any > c Any Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c Any Source # toConstr :: Any > Constr Source # dataTypeOf :: Any > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c Any) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c Any) Source # gmapT :: (forall b. Data b => b > b) > Any > Any Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Any > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Any > r Source # gmapQ :: (forall d. Data d => d > u) > Any > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Any > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Any > m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source #  
Ord Any Source #  
Read Any Source #  
Show Any Source #  
Generic Any Source #  
Semigroup Any Source #  Since: 4.9.0.0 
Monoid Any Source #  Since: 2.1 
type Rep Any Source #  
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Monad Sum Source #  Since: 4.8.0.0 
Functor Sum Source #  Since: 4.8.0.0 
MonadFix Sum Source #  Since: 4.8.0.0 
Applicative Sum Source #  Since: 4.8.0.0 
Foldable Sum Source #  Since: 4.8.0.0 
fold :: Monoid m => Sum m > m Source # foldMap :: Monoid m => (a > m) > Sum a > m Source # foldr :: (a > b > b) > b > Sum a > b Source # foldr' :: (a > b > b) > b > Sum a > b Source # foldl :: (b > a > b) > b > Sum a > b Source # foldl' :: (b > a > b) > b > Sum a > b Source # foldr1 :: (a > a > a) > Sum a > a Source # foldl1 :: (a > a > a) > Sum a > a Source # toList :: Sum a > [a] Source # null :: Sum a > Bool Source # length :: Sum a > Int Source # elem :: Eq a => a > Sum a > Bool Source # maximum :: Ord a => Sum a > a Source # minimum :: Ord a => Sum a > a Source #  
Traversable Sum Source #  Since: 4.8.0.0 
MonadZip Sum Source #  Since: 4.8.0.0 
Bounded a => Bounded (Sum a) Source #  
Eq a => Eq (Sum a) Source #  
Data a => Data (Sum a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Sum a > c (Sum a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Sum a) Source # toConstr :: Sum a > Constr Source # dataTypeOf :: Sum a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Sum a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b > b) > Sum a > Sum a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Sum a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Sum a > r Source # gmapQ :: (forall d. Data d => d > u) > Sum a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Sum a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source #  
Num a => Num (Sum a) Source #  
Ord a => Ord (Sum a) Source #  
Read a => Read (Sum a) Source #  
Show a => Show (Sum a) Source #  
Generic (Sum a) Source #  
Num a => Semigroup (Sum a) Source #  Since: 4.9.0.0 
Num a => Monoid (Sum a) Source #  Since: 2.1 
Generic1 Sum Source #  
type Rep (Sum a) Source #  
type Rep1 Sum Source #  
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product  

Instances
Monad Product Source #  Since: 4.8.0.0 
Functor Product Source #  Since: 4.8.0.0 
MonadFix Product Source #  Since: 4.8.0.0 
Applicative Product Source #  Since: 4.8.0.0 
Foldable Product Source #  Since: 4.8.0.0 
fold :: Monoid m => Product m > m Source # foldMap :: Monoid m => (a > m) > Product a > m Source # foldr :: (a > b > b) > b > Product a > b Source # foldr' :: (a > b > b) > b > Product a > b Source # foldl :: (b > a > b) > b > Product a > b Source # foldl' :: (b > a > b) > b > Product a > b Source # foldr1 :: (a > a > a) > Product a > a Source # foldl1 :: (a > a > a) > Product a > a Source # toList :: Product a > [a] Source # null :: Product a > Bool Source # length :: Product a > Int Source # elem :: Eq a => a > Product a > Bool Source # maximum :: Ord a => Product a > a Source # minimum :: Ord a => Product a > a Source #  
Traversable Product Source #  Since: 4.8.0.0 
MonadZip Product Source #  Since: 4.8.0.0 
Bounded a => Bounded (Product a) Source #  
Eq a => Eq (Product a) Source #  
Data a => Data (Product a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Product a > c (Product a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Product a) Source # toConstr :: Product a > Constr Source # dataTypeOf :: Product a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Product a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b > b) > Product a > Product a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Product a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Product a > r Source # gmapQ :: (forall d. Data d => d > u) > Product a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Product a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Product a > m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source #  
Num a => Num (Product a) Source #  
(+) :: 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 #  
Read a => Read (Product a) Source #  
Show a => Show (Product a) Source #  
Generic (Product a) Source #  
Num a => Semigroup (Product a) Source #  Since: 4.9.0.0 
Num a => Monoid (Product a) Source #  Since: 2.1 
Generic1 Product Source #  
type Rep (Product a) Source #  
type Rep1 Product Source #  
A better monoid for Maybe
Option
is effectively Maybe
with a better instance of
Monoid
, built off of an underlying Semigroup
instead of an
underlying Monoid
.
Ideally, this type would not exist at all and we would just fix the
Monoid
instance of Maybe
Instances
Monad Option Source #  Since: 4.9.0.0 
Functor Option Source #  Since: 4.9.0.0 
MonadFix Option Source #  Since: 4.9.0.0 
Applicative Option Source #  Since: 4.9.0.0 
Foldable Option Source #  Since: 4.9.0.0 
fold :: Monoid m => Option m > m Source # foldMap :: Monoid m => (a > m) > Option a > m Source # foldr :: (a > b > b) > b > Option a > b Source # foldr' :: (a > b > b) > b > Option a > b Source # foldl :: (b > a > b) > b > Option a > b Source # foldl' :: (b > a > b) > b > Option a > b Source # foldr1 :: (a > a > a) > Option a > a Source # foldl1 :: (a > a > a) > Option a > a Source # toList :: Option a > [a] Source # null :: Option a > Bool Source # length :: Option a > Int Source # elem :: Eq a => a > Option a > Bool Source # maximum :: Ord a => Option a > a Source # minimum :: Ord a => Option a > a Source #  
Traversable Option Source #  Since: 4.9.0.0 
MonadPlus Option Source #  Since: 4.9.0.0 
Alternative Option Source #  Since: 4.9.0.0 
Eq a => Eq (Option a) Source #  
Data a => Data (Option a) Source #  
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Option a > c (Option a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Option a) Source # toConstr :: Option a > Constr Source # dataTypeOf :: Option a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Option a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Option a)) Source # gmapT :: (forall b. Data b => b > b) > Option a > Option a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Option a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Option a > r Source # gmapQ :: (forall d. Data d => d > u) > Option a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Option a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Option a > m (Option a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Option a > m (Option a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Option a > m (Option a) Source #  
Ord a => Ord (Option a) Source #  
Read a => Read (Option a) Source #  
Show a => Show (Option a) Source #  
Generic (Option a) Source #  
Semigroup a => Semigroup (Option a) Source #  Since: 4.9.0.0 
Semigroup a => Monoid (Option a) Source #  Since: 4.9.0.0 
Generic1 Option Source #  
type Rep (Option a) Source #  
type Rep1 Option Source #  
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: 4.9.0.0 
Bifoldable Arg Source #  Since: 4.10.0.0 
Bitraversable Arg Source #  Since: 4.10.0.0 
bitraverse :: Applicative f => (a > f c) > (b > f d) > Arg a b > f (Arg c d) Source #  
Functor (Arg a) Source #  Since: 4.9.0.0 
Foldable (Arg a) Source #  Since: 4.9.0.0 
fold :: Monoid m => Arg a m > m Source # foldMap :: Monoid m => (a0 > m) > Arg a a0 > m Source # foldr :: (a0 > b > b) > b > Arg a a0 > b Source # foldr' :: (a0 > b > b) > b > Arg a a0 > b Source # foldl :: (b > a0 > b) > b > Arg a a0 > b Source # foldl' :: (b > a0 > b) > b > Arg a a0 > b Source # foldr1 :: (a0 > a0 > a0) > Arg a a0 > a0 Source # foldl1 :: (a0 > a0 > a0) > Arg a a0 > a0 Source # toList :: Arg a a0 > [a0] Source # null :: Arg a a0 > Bool Source # length :: Arg a a0 > Int Source # elem :: Eq a0 => a0 > Arg a a0 > Bool Source # maximum :: Ord a0 => Arg a a0 > a0 Source # minimum :: Ord a0 => Arg a a0 > a0 Source #  
Traversable (Arg a) Source #  Since: 4.9.0.0 
Generic1 (Arg a :: * > *) Source #  
Eq a => Eq (Arg a b) Source #  Since: 4.9.0.0 
(Data a, Data b) => Data (Arg a b) Source #  
gfoldl :: (forall d b0. Data d => c (d > b0) > d > c b0) > (forall g. g > c g) > Arg a b > c (Arg a b) Source # gunfold :: (forall b0 r. Data b0 => c (b0 > r) > c r) > (forall r. r > c r) > Constr > c (Arg a b) Source # toConstr :: Arg a b > Constr Source # dataTypeOf :: Arg a b > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Arg a b)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Arg a b)) Source # gmapT :: (forall b0. Data b0 => b0 > b0) > Arg a b > Arg a b Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Arg a b > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Arg a b > r Source # gmapQ :: (forall d. Data d => d > u) > Arg a b > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Arg a b > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Arg a b > m (Arg a b) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Arg a b > m (Arg a b) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Arg a b > m (Arg a b) Source #  
Ord a => Ord (Arg a b) Source #  Since: 4.9.0.0 
(Read a, Read b) => Read (Arg a b) Source #  
(Show a, Show b) => Show (Arg a b) Source #  
Generic (Arg a b) Source #  
type Rep1 (Arg a :: * > *) Source #  
type Rep1 (Arg a :: * > *) = D1 (MetaData "Arg" "Data.Semigroup" "base" False) (C1 (MetaCons "Arg" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) Par1))  
type Rep (Arg a b) Source #  
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))) 