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:
You can alternatively define sconcat
instead of (<>
), in which case the
laws are:
@since base4.9.0.0
(<>) :: a > a > a infixr 6 Source #
An associative operation.
Examples
>>>
[1,2,3] <> [4,5,6]
[1,2,3,4,5,6]
>>>
Just [1, 2, 3] <> Just [4, 5, 6]
Just [1,2,3,4,5,6]
>>>
putStr "Hello, " <> putStrLn "World!"
Hello, World!
sconcat :: NonEmpty a > a Source #
Reduce a nonempty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
Examples
For the following examples, we will assume that we have:
>>>
import Data.List.NonEmpty (NonEmpty (..))
>>>
sconcat $ "Hello" : [" ", "Haskell", "!"]
"Hello Haskell!"
>>>
sconcat $ Just [1, 2, 3] : [Nothing, Just [4, 5, 6]]
Just [1,2,3,4,5,6]
>>>
sconcat $ Left 1 : [Right 2, Left 3, Right 4]
Right 2
stimes :: Integral b => b > a > a Source #
Repeat a value n
times.
The default definition will raise an exception for a multiplier that is <= 0
.
This may be overridden with an implementation that is total. For monoids
it is preferred to use stimesMonoid
.
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
Examples
>>>
stimes 4 [1]
[1,1,1,1]
>>>
stimes 5 (putStr "hi!")
hi!hi!hi!hi!hi!
>>>
stimes 3 (Right ":)")
Right ":)"
Instances
Semigroup ByteArray Source #  Since: base4.17.0.0 
Semigroup Void  @since base4.9.0.0 
Semigroup All  @since base4.9.0.0 
Semigroup Any  @since base4.9.0.0 
Semigroup Event  @since base4.10.0.0 
Semigroup EventLifetime  @since base4.11.0.0 
Semigroup Lifetime  @since base4.10.0.0 
Semigroup ExceptionContext  
Defined in GHC.Internal.Exception.Context (<>) :: ExceptionContext > ExceptionContext > ExceptionContext Source # sconcat :: NonEmpty ExceptionContext > ExceptionContext Source # stimes :: Integral b => b > ExceptionContext > ExceptionContext Source #  
Semigroup Ordering  @since base4.9.0.0 
Semigroup ()  @since base4.9.0.0 
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 (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 (NonEmpty a)  @since base4.9.0.0 
Semigroup a => Semigroup (STM a)  @since base4.17.0.0 
Bits a => Semigroup (And a)  @since base4.16 
FiniteBits a => Semigroup (Iff a)  This constraint is arguably
too strong. However, as some types (such as @since base4.16 
Bits a => Semigroup (Ior a)  @since base4.16 
Bits a => Semigroup (Xor a)  @since base4.16 
Semigroup a => Semigroup (Identity a)  @since base4.9.0.0 
Ord a => Semigroup (Max a)  @since base4.11.0.0 
Ord a => Semigroup (Min a)  @since base4.11.0.0 
Semigroup (First a)  @since base4.9.0.0 
Semigroup (Last a)  @since base4.9.0.0 
Semigroup a => Semigroup (Down a)  @since base4.11.0.0 
Semigroup a => Semigroup (Dual a)  @since base4.9.0.0 
Semigroup (Endo a)  @since base4.9.0.0 
Num a => Semigroup (Product a)  @since base4.9.0.0 
Num a => Semigroup (Sum a)  @since base4.9.0.0 
(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)  @since base4.17.0.0 
Defined in GHC.Internal.Generics (<>) :: Generically a > Generically a > Generically a Source # sconcat :: NonEmpty (Generically a) > Generically a Source # stimes :: Integral b => b > Generically a > Generically a Source #  
Semigroup p => Semigroup (Par1 p)  @since base4.12.0.0 
Semigroup a => Semigroup (IO a)  @since base4.10.0.0 
Semigroup a => Semigroup (Maybe a)  @since base4.9.0.0 
Semigroup a => Semigroup (Solo a)  @since base4.15 
Semigroup [a]  @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 (Either a b)  @since base4.9.0.0 
Semigroup (Proxy s)  @since base4.9.0.0 
Semigroup (U1 p)  @since base4.12.0.0 
Semigroup (V1 p)  @since base4.12.0.0 
Semigroup a => Semigroup (ST s a)  @since base4.11.0.0 
(Semigroup a, Semigroup b) => Semigroup (a, b)  @since base4.9.0.0 
Semigroup b => Semigroup (a > b)  @since base4.9.0.0 
Semigroup a => Semigroup (Const a b)  @since base4.9.0.0 
(Applicative f, Semigroup a) => Semigroup (Ap f a)  @since base4.12.0.0 
Alternative f => Semigroup (Alt f a)  @since base4.9.0.0 
Semigroup (f p) => Semigroup (Rec1 f p)  @since base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c)  @since base4.9.0.0 
(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)  @since base4.12.0.0 
Semigroup c => Semigroup (K1 i c p)  @since base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)  @since base4.9.0.0 
Semigroup (f (g a)) => Semigroup (Compose f g a) Source #  Since: base4.16.0.0 
Semigroup (f (g p)) => Semigroup ((f :.: g) p)  @since base4.12.0.0 
Semigroup (f p) => Semigroup (M1 i c f p)  @since base4.12.0.0 
(Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)  @since base4.9.0.0 
stimesMonoid :: (Integral b, Monoid a) => b > a > a Source #
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 #
Repeat a value n
times.
mtimesDefault n a = a <> a <> ... <> a  using <> (n1) times
In many cases,
for a stimes
0 aMonoid
will produce mempty
.
However, there are situations when it cannot do so. In particular,
the following situation is fairly common:
data T a = ... class Constraint1 a class Constraint1 a => Constraint2 a
instance Constraint1 a =>Semigroup
(T a) instance Constraint2 a =>Monoid
(T a)
Since Constraint1
is insufficient to implement mempty
,
stimes
for T a
cannot do so.
When working with such a type, or when working polymorphically with
Semigroup
instances, mtimesDefault
should be used when the
multiplier might be zero. It is implemented using stimes
when
the multiplier is nonzero and mempty
when it is zero.
Examples
>>>
mtimesDefault 0 "bark"
[]
>>>
mtimesDefault 3 "meow"
"meowmeowmeow"
Semigroups
The Min
Monoid
and Semigroup
always choose the smaller element as
by the Ord
instance and min
of the contained type.
Examples
>>>
Min 42 <> Min 3
Min 3
>>>
sconcat $ Min 1 : [ Min n  n < [2 .. 100]]
Min {getMin = 1}
Instances
Foldable1 Min Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Min m > m Source # foldMap1 :: Semigroup m => (a > m) > Min a > m Source # foldMap1' :: Semigroup m => (a > m) > Min a > m Source # toNonEmpty :: Min a > NonEmpty a Source # maximum :: Ord a => Min a > a Source # minimum :: Ord a => Min a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Min a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Min a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Min a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Min a > b Source #  
Applicative Min Source #  Since: base4.9.0.0  
Functor Min Source #  Since: base4.9.0.0  
Monad Min Source #  Since: base4.9.0.0  
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  
Generic1 Min Source #  
Defined in Data.Semigroup
 
(Ord a, Bounded a) => Monoid (Min a) Source #  Since: base4.9.0.0  
Ord a => Semigroup (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 #  
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 #  
Defined in Data.Semigroup
 
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  
type Rep1 Min Source #  Since: base4.9.0.0  
Defined in Data.Semigroup  
type Rep (Min a) Source #  Since: base4.9.0.0  
Defined in Data.Semigroup 
The Max
Monoid
and Semigroup
always choose the bigger element as
by the Ord
instance and max
of the contained type.
Examples
>>>
Max 42 <> Max 3
Max 42
>>>
sconcat $ Max 1 : [ Max n  n < [2 .. 100]]
Max {getMax = 100}
Instances
Foldable1 Max Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Max m > m Source # foldMap1 :: Semigroup m => (a > m) > Max a > m Source # foldMap1' :: Semigroup m => (a > m) > Max a > m Source # toNonEmpty :: Max a > NonEmpty a Source # maximum :: Ord a => Max a > a Source # minimum :: Ord a => Max a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Max a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Max a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Max a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Max a > b Source #  
Applicative Max Source #  Since: base4.9.0.0  
Functor Max Source #  Since: base4.9.0.0  
Monad Max Source #  Since: base4.9.0.0  
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  
Generic1 Max Source #  
Defined in Data.Semigroup
 
(Ord a, Bounded a) => Monoid (Max a) Source #  Since: base4.9.0.0  
Ord a => Semigroup (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 #  
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 #  
Defined in Data.Semigroup
 
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  
type Rep1 Max Source #  Since: base4.9.0.0  
Defined in Data.Semigroup  
type Rep (Max a) Source #  Since: base4.9.0.0  
Defined in Data.Semigroup 
Beware that Data.Semigroup.
First
is different from
Data.Monoid.
First
. The former simply returns the first value,
so Data.Semigroup.First Nothing <> x = Data.Semigroup.First Nothing
.
The latter returns the first nonNothing
,
thus Data.Monoid.First Nothing <> x = x
.
Examples
>>>
First 0 <> First 10
First 0
>>>
sconcat $ First 1 : [ First n  n < [2 ..] ]
First 1
Instances
Foldable1 First Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => First m > m Source # foldMap1 :: Semigroup m => (a > m) > First a > m Source # foldMap1' :: Semigroup m => (a > m) > First a > m Source # toNonEmpty :: First a > NonEmpty a Source # maximum :: Ord a => First a > a Source # minimum :: Ord a => First a > a Source # foldrMap1 :: (a > b) > (a > b > b) > First a > b Source # foldlMap1' :: (a > b) > (b > a > b) > First a > b Source # foldlMap1 :: (a > b) > (b > a > b) > First a > b Source # foldrMap1' :: (a > b) > (a > b > b) > First a > b Source #  
Applicative First Source #  Since: base4.9.0.0  
Functor First Source #  Since: base4.9.0.0  
Monad First Source #  Since: base4.9.0.0  
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  
Generic1 First Source #  
Defined in Data.Semigroup
 
Semigroup (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 #  
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 #  
Defined in Data.Semigroup
 
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  
type Rep1 First Source #  Since: base4.9.0.0  
Defined in Data.Semigroup  
type Rep (First a) Source #  Since: base4.9.0.0  
Defined in Data.Semigroup 
Beware that Data.Semigroup.
Last
is different from
Data.Monoid.
Last
. The former simply returns the last value,
so x <> Data.Semigroup.Last Nothing = Data.Semigroup.Last Nothing
.
The latter returns the last nonNothing
,
thus x <> Data.Monoid.Last Nothing = x
.
Examples
>>>
Last 0 <> Last 10
Last {getLast = 10}
>>>
sconcat $ Last 1 : [ Last n  n < [2..]]
Last {getLast = * hangs forever *
Instances
Foldable1 Last Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Last m > m Source # foldMap1 :: Semigroup m => (a > m) > Last a > m Source # foldMap1' :: Semigroup m => (a > m) > Last a > m Source # toNonEmpty :: Last a > NonEmpty a Source # maximum :: Ord a => Last a > a Source # minimum :: Ord a => Last a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Last a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Last a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Last a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Last a > b Source #  
Applicative Last Source #  Since: base4.9.0.0  
Functor Last Source #  Since: base4.9.0.0  
Monad Last Source #  Since: base4.9.0.0  
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  
Generic1 Last Source #  
Defined in Data.Semigroup
 
Semigroup (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 #  
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 #  
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  
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  
type Rep1 Last Source #  Since: base4.9.0.0  
Defined in Data.Semigroup  
type Rep (Last a) 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 GHC.Internal.Data.Monoid
The dual of a Monoid
, obtained by swapping the arguments of (<>)
.
Dual a <> Dual b == Dual (b <> a)
Examples
>>>
Dual "Hello" <> Dual "World"
Dual {getDual = "WorldHello"}
>>>
Dual (Dual "Hello") <> Dual (Dual "World")
Dual {getDual = Dual {getDual = "HelloWorld"}}
Instances
MonadZip Dual Source #  Since: base4.8.0.0  
Foldable1 Dual Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Dual m > m Source # foldMap1 :: Semigroup m => (a > m) > Dual a > m Source # foldMap1' :: Semigroup m => (a > m) > Dual a > m Source # toNonEmpty :: Dual a > NonEmpty a Source # maximum :: Ord a => Dual a > a Source # minimum :: Ord a => Dual a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Dual a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Dual a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Dual a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Dual a > b Source #  
Applicative Dual  @since base4.8.0.0  
Functor Dual  @since base4.8.0.0  
Monad Dual  @since base4.8.0.0  
MonadFix Dual  @since base4.8.0.0  
Foldable Dual  @since base4.8.0.0  
Defined in GHC.Internal.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  @since base4.8.0.0  
Generic1 Dual  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Monoid a => Monoid (Dual a)  @since base2.01  
Semigroup a => Semigroup (Dual a)  @since base4.9.0.0  
Data a => Data (Dual a)  @since base4.8.0.0  
Defined in GHC.Internal.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 #  
Bounded a => Bounded (Dual a)  @since base2.01  
Generic (Dual a)  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Read a => Read (Dual a)  @since base2.01  
Show a => Show (Dual a)  @since base2.01  
Eq a => Eq (Dual a)  @since base2.01  
Ord a => Ord (Dual a)  @since base2.01  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep1 Dual  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep (Dual a)  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal 
The monoid of endomorphisms under composition.
Endo f <> Endo g == Endo (f . g)
Examples
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
>>>
let computation = Endo (*3) <> Endo (+1)
>>>
appEndo computation 1
6
Instances
Monoid (Endo a)  @since base2.01  
Semigroup (Endo a)  @since base4.9.0.0  
Generic (Endo a)  
Defined in GHC.Internal.Data.Semigroup.Internal
 
type Rep (Endo a)  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal 
Boolean monoid under conjunction (&&)
.
All x <> All y = All (x && y)
Examples
>>>
All True <> mempty <> All False)
All {getAll = False}
>>>
mconcat (map (\x > All (even x)) [2,4,6,7,8])
All {getAll = False}
>>>
All True <> mempty
All {getAll = True}
Instances
Monoid All  @since base2.01  
Semigroup All  @since base4.9.0.0  
Data All  @since base4.8.0.0  
Defined in GHC.Internal.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 #  
Bounded All  @since base2.01  
Generic All  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Read All  @since base2.01  
Show All  @since base2.01  
Eq All  @since base2.01  
Ord All  @since base2.01  
type Rep All  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal 
Boolean monoid under disjunction ()
.
Any x <> Any y = Any (x  y)
Examples
>>>
Any True <> mempty <> Any False
Any {getAny = True}
>>>
mconcat (map (\x > Any (even x)) [2,4,6,7,8])
Any {getAny = True}
>>>
Any False <> mempty
Any {getAny = False}
Instances
Monoid Any  @since base2.01  
Semigroup Any  @since base4.9.0.0  
Data Any  @since base4.8.0.0  
Defined in GHC.Internal.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 #  
Bounded Any  @since base2.01  
Generic Any  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Read Any  @since base2.01  
Show Any  @since base2.01  
Eq Any  @since base2.01  
Ord Any  @since base2.01  
type Rep Any  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal 
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>
Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}
>>>
mconcat [ Sum n  n < [3 .. 9]]
Sum {getSum = 42}
Instances
MonadZip Sum Source #  Since: base4.8.0.0  
Foldable1 Sum Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Sum m > m Source # foldMap1 :: Semigroup m => (a > m) > Sum a > m Source # foldMap1' :: Semigroup m => (a > m) > Sum a > m Source # toNonEmpty :: Sum a > NonEmpty a Source # maximum :: Ord a => Sum a > a Source # minimum :: Ord a => Sum a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Sum a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Sum a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Sum a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Sum a > b Source #  
Applicative Sum  @since base4.8.0.0  
Functor Sum  @since base4.8.0.0  
Monad Sum  @since base4.8.0.0  
MonadFix Sum  @since base4.8.0.0  
Foldable Sum  @since base4.8.0.0  
Defined in GHC.Internal.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  @since base4.8.0.0  
Generic1 Sum  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Num a => Monoid (Sum a)  @since base2.01  
Num a => Semigroup (Sum a)  @since base4.9.0.0  
Data a => Data (Sum a)  @since base4.8.0.0  
Defined in GHC.Internal.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 #  
Bounded a => Bounded (Sum a)  @since base2.01  
Generic (Sum a)  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Num a => Num (Sum a)  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal  
Read a => Read (Sum a)  @since base2.01  
Show a => Show (Sum a)  @since base2.01  
Eq a => Eq (Sum a)  @since base2.01  
Ord a => Ord (Sum a)  @since base2.01  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep1 Sum  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep (Sum a)  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal 
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>
Product 3 <> Product 4 <> mempty
Product {getProduct = 12}
>>>
mconcat [ Product n  n < [2 .. 10]]
Product {getProduct = 3628800}
Product  

Instances
MonadZip Product Source #  Since: base4.8.0.0  
Foldable1 Product Source #  Since: base4.18.0.0  
Defined in Data.Foldable1 fold1 :: Semigroup m => Product m > m Source # foldMap1 :: Semigroup m => (a > m) > Product a > m Source # foldMap1' :: Semigroup m => (a > m) > Product a > m Source # toNonEmpty :: Product a > NonEmpty a Source # maximum :: Ord a => Product a > a Source # minimum :: Ord a => Product a > a Source # head :: Product a > a Source # last :: Product a > a Source # foldrMap1 :: (a > b) > (a > b > b) > Product a > b Source # foldlMap1' :: (a > b) > (b > a > b) > Product a > b Source # foldlMap1 :: (a > b) > (b > a > b) > Product a > b Source # foldrMap1' :: (a > b) > (a > b > b) > Product a > b Source #  
Applicative Product  @since base4.8.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal  
Functor Product  @since base4.8.0.0  
Monad Product  @since base4.8.0.0  
MonadFix Product  @since base4.8.0.0  
Foldable Product  @since base4.8.0.0  
Defined in GHC.Internal.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  @since base4.8.0.0  
Defined in GHC.Internal.Data.Traversable  
Generic1 Product  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Num a => Monoid (Product a)  @since base2.01  
Num a => Semigroup (Product a)  @since base4.9.0.0  
Data a => Data (Product a)  @since base4.8.0.0  
Defined in GHC.Internal.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 #  
Bounded a => Bounded (Product a)  @since base2.01  
Generic (Product a)  
Defined in GHC.Internal.Data.Semigroup.Internal
 
Num a => Num (Product a)  @since base4.7.0.0  
Defined in GHC.Internal.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)  @since base2.01  
Show a => Show (Product a)  @since base2.01  
Eq a => Eq (Product a)  @since base2.01  
Ord a => Ord (Product a)  @since base2.01  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep1 Product  @since base4.7.0.0  
Defined in GHC.Internal.Data.Semigroup.Internal  
type Rep (Product a)  @since base4.7.0.0  
Defined in GHC.Internal.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
.
Examples
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.
Examples
>>>
minimum [ Arg (x * x) x  x < [10 .. 10] ]
Arg 0 0
>>>
maximum [ Arg (0.2*x^2 + 1.5*x + 1) x  x < [10 .. 10] ]
Arg 3.8 4.0
>>>
minimum [ Arg (0.2*x^2 + 1.5*x + 1) x  x < [10 .. 10] ]
Arg (34.0) (10.0)
Instances
Bifoldable Arg Source #  Since: base4.10.0.0  
Bifoldable1 Arg Source #  
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 #  
Generic1 (Arg a :: Type > Type) Source #  
Defined in Data.Semigroup
 
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  
(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 #  
Defined in Data.Semigroup
 
(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))) 