Safe Haskell  SafeInferred 

Language  Haskell2010 
Synopsis
 newtype Any = Any {}
 newtype Sum a = Sum {
 getSum :: a
 newtype Product a = Product {
 getProduct :: a
 class Semigroup a => Monoid a where
 newtype Alt (f :: k > Type) (a :: k) = Alt {
 getAlt :: f a
 newtype All = All {}
 newtype Endo a = Endo {
 appEndo :: a > a
 newtype Dual a = Dual {
 getDual :: a
 newtype Ap (f :: k > Type) (a :: k) = Ap {
 getAp :: f a
 newtype Last a = Last {}
 newtype First a = First {}
 (<>) :: Semigroup a => a > a > a
Documentation
Boolean monoid under disjunction (
).
>>>
getAny (Any True <> mempty <> Any False)
True
>>>
getAny (mconcat (map (\x > Any (even x)) [2,4,6,7,8]))
True
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Foldable Sum  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  Since: base4.8.0.0 
Applicative Sum  Since: base4.8.0.0 
Functor Sum  Since: base4.8.0.0 
Monad Sum  Since: base4.8.0.0 
Generic1 Sum  
Num a => Monoid (Sum a)  Since: base2.1 
Num a => Semigroup (Sum a)  Since: base4.9.0.0 
Bounded a => Bounded (Sum a)  Since: base2.1 
Generic (Sum a)  
Num a => Num (Sum a)  Since: base4.7.0.0 
Read a => Read (Sum a)  Since: base2.1 
Show a => Show (Sum a)  Since: base2.1 
Eq a => Eq (Sum a)  Since: base2.1 
Ord a => Ord (Sum a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
type Rep1 Sum  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep (Sum a)  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product  

Instances
Foldable Product  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  Since: base4.8.0.0 
Defined in Data.Traversable  
Applicative Product  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Functor Product  Since: base4.8.0.0 
Monad Product  Since: base4.8.0.0 
Generic1 Product  
Num a => Monoid (Product a)  Since: base2.1 
Num a => Semigroup (Product a)  Since: base4.9.0.0 
Bounded a => Bounded (Product a)  Since: base2.1 
Generic (Product a)  
Num a => Num (Product a)  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal (+) :: Product a > Product a > Product a Source # () :: Product a > Product a > Product a Source # (*) :: Product a > Product a > Product a Source # negate :: Product a > Product a Source # abs :: Product a > Product a Source # signum :: Product a > Product a Source # fromInteger :: Integer > Product a Source #  
Read a => Read (Product a)  Since: base2.1 
Show a => Show (Product a)  Since: base2.1 
Eq a => Eq (Product a)  Since: base2.1 
Ord a => Ord (Product a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
type Rep1 Product  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep (Product a)  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
class Semigroup a => Monoid a where Source #
The class of monoids (types with an associative binary operation that has an identity). Instances should satisfy the following:
 Right identity
x
<>
mempty
= x Left identity
mempty
<>
x = x Associativity
x
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
law) Concatenation
mconcat
=foldr
(<>
)mempty
The method names refer to the monoid of lists under concatenation, but there are many other instances.
Some types can be viewed as a monoid in more than one way,
e.g. both addition and multiplication on numbers.
In such cases we often define newtype
s and make those instances
of Monoid
, e.g. Sum
and Product
.
NOTE: Semigroup
is a superclass of Monoid
since base4.11.0.0.
Identity of mappend
>>>
"Hello world" <> mempty
"Hello world"
mappend :: a > a > a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation
since base4.11.0.0.
Should it be implemented manually, since mappend
= (<>
)mappend
is a synonym for
(<>
), it is expected that the two functions are defined the same
way. In a future GHC release mappend
will be removed from Monoid
.
Fold a list using the monoid.
For most types, the default definition for mconcat
will be
used, but the function is included in the class definition so
that an optimized version can be provided for specific types.
>>>
mconcat ["Hello", " ", "Haskell", "!"]
"Hello Haskell!"
Instances
Monoid All  Since: base2.1 
Monoid Any  Since: base2.1 
Monoid Ordering  Since: base2.1 
Monoid ()  Since: base2.1 
FiniteBits a => Monoid (And a)  This constraint is arguably too strong. However,
as some types (such as Since: base4.16 
FiniteBits a => Monoid (Iff a)  This constraint is arguably
too strong. However, as some types (such as Since: base4.16 
Bits a => Monoid (Ior a)  Since: base4.16 
Bits a => Monoid (Xor a)  Since: base4.16 
Monoid (Comparison a) 
mempty :: Comparison a mempty = Comparison _ _ > EQ 
Defined in Data.Functor.Contravariant mempty :: Comparison a Source # mappend :: Comparison a > Comparison a > Comparison a Source # mconcat :: [Comparison a] > Comparison a Source #  
Monoid (Equivalence a) 
mempty :: Equivalence a mempty = Equivalence _ _ > True 
Defined in Data.Functor.Contravariant mempty :: Equivalence a Source # mappend :: Equivalence a > Equivalence a > Equivalence a Source # mconcat :: [Equivalence a] > Equivalence a Source #  
Monoid (Predicate a) 
mempty :: Predicate a mempty = _ > True 
Monoid a => Monoid (Identity a)  Since: base4.9.0.0 
Monoid (First a)  Since: base2.1 
Monoid (Last a)  Since: base2.1 
(Ord a, Bounded a) => Monoid (Max a)  Since: base4.9.0.0 
(Ord a, Bounded a) => Monoid (Min a)  Since: base4.9.0.0 
Monoid m => Monoid (WrappedMonoid m)  Since: base4.9.0.0 
Defined in Data.Semigroup mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m > WrappedMonoid m > WrappedMonoid m Source # mconcat :: [WrappedMonoid m] > WrappedMonoid m Source #  
Monoid a => Monoid (Dual a)  Since: base2.1 
Monoid (Endo a)  Since: base2.1 
Num a => Monoid (Product a)  Since: base2.1 
Num a => Monoid (Sum a)  Since: base2.1 
Monoid a => Monoid (STM a)  Since: base4.17.0.0 
Monoid a => Monoid (IO a)  Since: base4.9.0.0 
Semigroup a => Monoid (Maybe a)  Lift a semigroup into Since 4.11.0: constraint on inner Since: base2.1 
Monoid a => Monoid (a)  Since: base4.15 
Monoid [a]  Since: base2.1 
Monoid a => Monoid (Op a b) 
mempty :: Op a b mempty = Op _ > mempty 
Monoid (Proxy s)  Since: base4.7.0.0 
Monoid b => Monoid (a > b)  Since: base2.1 
(Monoid a, Monoid b) => Monoid (a, b)  Since: base2.1 
Monoid a => Monoid (Const a b)  Since: base4.9.0.0 
(Applicative f, Monoid a) => Monoid (Ap f a)  Since: base4.12.0.0 
Alternative f => Monoid (Alt f a)  Since: base4.8.0.0 
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)  Since: base2.1 
(Monoid (f a), Monoid (g a)) => Monoid (Product f g a)  Since: base4.16.0.0 
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)  Since: base2.1 
Monoid (f (g a)) => Monoid (Compose f g a)  Since: base4.16.0.0 
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)  Since: base2.1 
newtype Alt (f :: k > Type) (a :: k) Source #
Monoid under <>
.
>>>
getAlt (Alt (Just 12) <> Alt (Just 24))
Just 12
>>>
getAlt $ Alt Nothing <> Alt (Just 24)
Just 24
Since: base4.8.0.0
Instances
Generic1 (Alt f :: k > Type)  
Foldable f => Foldable (Alt f)  Since: base4.12.0.0 
Defined in Data.Foldable fold :: Monoid m => Alt f m > m Source # foldMap :: Monoid m => (a > m) > Alt f a > m Source # foldMap' :: Monoid m => (a > m) > Alt f a > m Source # foldr :: (a > b > b) > b > Alt f a > b Source # foldr' :: (a > b > b) > b > Alt f a > b Source # foldl :: (b > a > b) > b > Alt f a > b Source # foldl' :: (b > a > b) > b > Alt f a > b Source # foldr1 :: (a > a > a) > Alt f a > a Source # foldl1 :: (a > a > a) > Alt f a > a Source # toList :: Alt f a > [a] Source # null :: Alt f a > Bool Source # length :: Alt f a > Int Source # elem :: Eq a => a > Alt f a > Bool Source # maximum :: Ord a => Alt f a > a Source # minimum :: Ord a => Alt f a > a Source #  
Contravariant f => Contravariant (Alt f)  
Traversable f => Traversable (Alt f)  Since: base4.12.0.0 
Alternative f => Alternative (Alt f)  Since: base4.8.0.0 
Applicative f => Applicative (Alt f)  Since: base4.8.0.0 
Functor f => Functor (Alt f)  Since: base4.8.0.0 
Monad f => Monad (Alt f)  Since: base4.8.0.0 
MonadPlus f => MonadPlus (Alt f)  Since: base4.8.0.0 
Alternative f => Monoid (Alt f a)  Since: base4.8.0.0 
Alternative f => Semigroup (Alt f a)  Since: base4.9.0.0 
Enum (f a) => Enum (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal succ :: Alt f a > Alt f a Source # pred :: Alt f a > Alt f a Source # toEnum :: Int > Alt f a Source # fromEnum :: Alt f a > Int Source # enumFrom :: Alt f a > [Alt f a] Source # enumFromThen :: Alt f a > Alt f a > [Alt f a] Source # enumFromTo :: Alt f a > Alt f a > [Alt f a] Source # enumFromThenTo :: Alt f a > Alt f a > Alt f a > [Alt f a] Source #  
Generic (Alt f a)  
Num (f a) => Num (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Read (f a) => Read (Alt f a)  Since: base4.8.0.0 
Show (f a) => Show (Alt f a)  Since: base4.8.0.0 
Eq (f a) => Eq (Alt f a)  Since: base4.8.0.0 
Ord (f a) => Ord (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
type Rep1 (Alt f :: k > Type)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
type Rep (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal 
Boolean monoid under conjunction (&&
).
>>>
getAll (All True <> mempty <> All False)
False
>>>
getAll (mconcat (map (\x > All (even x)) [2,4,6,7,8]))
False
The monoid of endomorphisms under composition.
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>>
getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
Foldable Dual  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  Since: base4.8.0.0 
Applicative Dual  Since: base4.8.0.0 
Functor Dual  Since: base4.8.0.0 
Monad Dual  Since: base4.8.0.0 
Generic1 Dual  
Monoid a => Monoid (Dual a)  Since: base2.1 
Semigroup a => Semigroup (Dual a)  Since: base4.9.0.0 
Bounded a => Bounded (Dual a)  Since: base2.1 
Generic (Dual a)  
Read a => Read (Dual a)  Since: base2.1 
Show a => Show (Dual a)  Since: base2.1 
Eq a => Eq (Dual a)  Since: base2.1 
Ord a => Ord (Dual a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
type Rep1 Dual  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal  
type Rep (Dual a)  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal 
newtype Ap (f :: k > Type) (a :: k) Source #
This data type witnesses the lifting of a Monoid
into an
Applicative
pointwise.
Since: base4.12.0.0
Instances
Generic1 (Ap f :: k > Type)  
MonadFail f => MonadFail (Ap f)  Since: base4.12.0.0 
Foldable f => Foldable (Ap f)  Since: base4.12.0.0 
Defined in Data.Foldable fold :: Monoid m => Ap f m > m Source # foldMap :: Monoid m => (a > m) > Ap f a > m Source # foldMap' :: Monoid m => (a > m) > Ap f a > m Source # foldr :: (a > b > b) > b > Ap f a > b Source # foldr' :: (a > b > b) > b > Ap f a > b Source # foldl :: (b > a > b) > b > Ap f a > b Source # foldl' :: (b > a > b) > b > Ap f a > b Source # foldr1 :: (a > a > a) > Ap f a > a Source # foldl1 :: (a > a > a) > Ap f a > a Source # toList :: Ap f a > [a] Source # null :: Ap f a > Bool Source # length :: Ap f a > Int Source # elem :: Eq a => a > Ap f a > Bool Source # maximum :: Ord a => Ap f a > a Source # minimum :: Ord a => Ap f a > a Source #  
Traversable f => Traversable (Ap f)  Since: base4.12.0.0 
Alternative f => Alternative (Ap f)  Since: base4.12.0.0 
Applicative f => Applicative (Ap f)  Since: base4.12.0.0 
Functor f => Functor (Ap f)  Since: base4.12.0.0 
Monad f => Monad (Ap f)  Since: base4.12.0.0 
MonadPlus f => MonadPlus (Ap f)  Since: base4.12.0.0 
(Applicative f, Monoid a) => Monoid (Ap f a)  Since: base4.12.0.0 
(Applicative f, Semigroup a) => Semigroup (Ap f a)  Since: base4.12.0.0 
(Applicative f, Bounded a) => Bounded (Ap f a)  Since: base4.12.0.0 
Enum (f a) => Enum (Ap f a)  Since: base4.12.0.0 
Defined in Data.Monoid succ :: Ap f a > Ap f a Source # pred :: Ap f a > Ap f a Source # toEnum :: Int > Ap f a Source # fromEnum :: Ap f a > Int Source # enumFrom :: Ap f a > [Ap f a] Source # enumFromThen :: Ap f a > Ap f a > [Ap f a] Source # enumFromTo :: Ap f a > Ap f a > [Ap f a] Source # enumFromThenTo :: Ap f a > Ap f a > Ap f a > [Ap f a] Source #  
Generic (Ap f a)  
(Applicative f, Num a) => Num (Ap f a)  Note that even if the underlying Commutativity:
Additive inverse:
Distributivity:
Since: base4.12.0.0 
Read (f a) => Read (Ap f a)  Since: base4.12.0.0 
Show (f a) => Show (Ap f a)  Since: base4.12.0.0 
Eq (f a) => Eq (Ap f a)  Since: base4.12.0.0 
Ord (f a) => Ord (Ap f a)  Since: base4.12.0.0 
Defined in Data.Monoid  
type Rep1 (Ap f :: k > Type)  Since: base4.12.0.0 
Defined in Data.Monoid  
type Rep (Ap f a)  Since: base4.12.0.0 
Defined in Data.Monoid 
Maybe monoid returning the rightmost nonNothing value.
is isomorphic to Last
a
, and thus to
Dual
(First
a)Dual
(Alt
Maybe
a)
>>>
getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world"))
Just "world"
Instances
Foldable Last  Since: base4.8.0.0 
Defined in Data.Foldable 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  Since: base4.8.0.0 
Applicative Last  Since: base4.8.0.0 
Functor Last  Since: base4.8.0.0 
Monad Last  Since: base4.8.0.0 
Generic1 Last  
Monoid (Last a)  Since: base2.1 
Semigroup (Last a)  Since: base4.9.0.0 
Generic (Last a)  
Read a => Read (Last a)  Since: base2.1 
Show a => Show (Last a)  Since: base2.1 
Eq a => Eq (Last a)  Since: base2.1 
Ord a => Ord (Last a)  Since: base2.1 
Defined in Data.Monoid  
type Rep1 Last  Since: base4.7.0.0 
Defined in Data.Monoid  
type Rep (Last a)  Since: base4.7.0.0 
Defined in Data.Monoid 
Maybe monoid returning the leftmost nonNothing value.
is isomorphic to First
a
, but precedes it
historically.Alt
Maybe
a
>>>
getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"
Instances
Foldable First  Since: base4.8.0.0 
Defined in Data.Foldable 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  Since: base4.8.0.0 
Applicative First  Since: base4.8.0.0 
Functor First  Since: base4.8.0.0 
Monad First  Since: base4.8.0.0 
Generic1 First  
Monoid (First a)  Since: base2.1 
Semigroup (First a)  Since: base4.9.0.0 
Generic (First a)  
Read a => Read (First a)  Since: base2.1 
Show a => Show (First a)  Since: base2.1 
Eq a => Eq (First a)  Since: base2.1 
Ord a => Ord (First a)  Since: base2.1 
type Rep1 First  Since: base4.7.0.0 
Defined in Data.Monoid  
type Rep (First a)  Since: base4.7.0.0 
Defined in Data.Monoid 