Copyright  (c) Andy Gill 2001 (c) Oregon Graduate Institute of Science and Technology 2001 

License  BSDstyle (see the file libraries/base/LICENSE) 
Maintainer  [email protected] 
Stability  experimental 
Portability  portable 
Safe Haskell  Trustworthy 
Language  Haskell2010 
A type a
is a Monoid
if it provides an associative function (<>
) that lets you combine any two values of type a
into one, and a neutral element (mempty
) such that
a <> mempty == mempty <> a == a
A Monoid
is a Semigroup
with the added requirement of a neutral element. Thus any Monoid
is a Semigroup
, but not the other way around.
The Sum
monoid is defined by the numerical addition operator and `0` as neutral element:
>>> mempty :: Sum Int Sum 0 >>> Sum 1 <> Sum 2 <> Sum 3 <> Sum 4 :: Sum Int Sum {getSum = 10}
We can combine multiple values in a list into a single value using the mconcat
function. Note that we have to specify the type here since Int
is a monoid under several different operations:
>>> mconcat [1,2,3,4] :: Sum Int Sum {getSum = 10} >>> mconcat [] :: Sum Int Sum {getSum = 0}
Another valid monoid instance of Int
is Product
It is defined by multiplication and `1` as neutral element:
>>> Product 1 <> Product 2 <> Product 3 <> Product 4 :: Product Int Product {getProduct = 24} >>> mconcat [1,2,3,4] :: Product Int Product {getProduct = 24} >>> mconcat [] :: Product Int Product {getProduct = 1}
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:
x <> mempty = x
mempty <> x = x
x <> (y <> z) = (x <> y) <> z
(Semigroup
law)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
An associative operation
NOTE: This method is redundant and has the default implementation mappend = (<>)
since base4.11.0.0.
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.
Monoid Ordering  Since: base2.1 
Monoid ()  Since: base2.1 
Monoid Any  Since: base2.1 
Monoid All  Since: base2.1 
Monoid Lifetime 
Since: base4.8.0.0 
Monoid Event  Since: base4.4.0.0 
Monoid [a]  Since: base2.1 
Semigroup a => Monoid (Maybe a) 
Lift a semigroup into Since 4.11.0: constraint on inner Since: base2.1 
Monoid a => Monoid (IO a)  Since: base4.9.0.0 
Monoid p => Monoid (Par1 p)  Since: base4.12.0.0 
Monoid a => Monoid (Down a)  Since: base4.11.0.0 
Num a => Monoid (Product a)  Since: base2.1 
Num a => Monoid (Sum a)  Since: base2.1 
Monoid (Endo a)  Since: base2.1 
Monoid a => Monoid (Dual a)  Since: base2.1 
Monoid (Last a)  Since: base2.1 
Monoid (First a)  Since: base2.1 
Monoid a => Monoid (Identity a)  Since: base4.9.0.0 
Semigroup a => Monoid (Option a)  Since: base4.9.0.0 
Monoid m => Monoid (WrappedMonoid m)  Since: base4.9.0.0 
Defined in Data.Semigroup Methodsmempty :: WrappedMonoid m Source mappend :: WrappedMonoid m > WrappedMonoid m > WrappedMonoid m Source mconcat :: [WrappedMonoid m] > WrappedMonoid m Source  
(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 (Equivalence a)  
Defined in Data.Functor.Contravariant Methodsmempty :: Equivalence a Source mappend :: Equivalence a > Equivalence a > Equivalence a Source mconcat :: [Equivalence a] > Equivalence a Source  
Monoid (Comparison a)  
Defined in Data.Functor.Contravariant Methodsmempty :: Comparison a Source mappend :: Comparison a > Comparison a > Comparison a Source mconcat :: [Comparison a] > Comparison a Source  
Monoid (Predicate a)  
Monoid b => Monoid (a > b)  Since: base2.1 
Monoid (U1 p)  Since: base4.12.0.0 
(Monoid a, Monoid b) => Monoid (a, b)  Since: base2.1 
Monoid a => Monoid (ST s a)  Since: base4.11.0.0 
Monoid (Proxy s)  Since: base4.7.0.0 
Monoid a => Monoid (Op a b)  
Monoid (f p) => Monoid (Rec1 f p)  Since: base4.12.0.0 
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c)  Since: base2.1 
Alternative f => Monoid (Alt f a)  Since: base4.8.0.0 
(Applicative f, Monoid a) => Monoid (Ap f a)  Since: base4.12.0.0 
Monoid a => Monoid (Const a b)  Since: base4.9.0.0 
Monoid c => Monoid (K1 i c p)  Since: base4.12.0.0 
(Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p)  Since: base4.12.0.0 
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d)  Since: base2.1 
Monoid (f p) => Monoid (M1 i c f p)  Since: base4.12.0.0 
Monoid (f (g p)) => Monoid ((f :.: g) p)  Since: base4.12.0.0 
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e)  Since: base2.1 
(<>) :: Semigroup a => a > a > a infixr 6 Source
An associative operation.
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>> getDual (mappend (Dual "Hello") (Dual "World")) "WorldHello"
Monad Dual  Since: base4.8.0.0 
Functor Dual  Since: base4.8.0.0 
MonadFix Dual  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Dual  Since: base4.8.0.0 
Foldable Dual  Since: base4.8.0.0 
Defined in Data.Foldable Methodsfold :: 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 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 
MonadZip Dual  Since: base4.8.0.0 
Bounded a => Bounded (Dual a)  Since: base2.1 
Eq a => Eq (Dual a)  Since: base2.1 
Data a => Data (Dual a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Dual a > c (Dual a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Dual a) Source toConstr :: Dual a > Constr Source dataTypeOf :: Dual a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Dual a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Dual a)) Source gmapT :: (forall b. Data b => b > b) > Dual a > Dual a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Dual a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Dual a > r Source gmapQ :: (forall d. Data d => d > u) > Dual a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Dual a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source  
Ord a => Ord (Dual a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Dual a)  Since: base2.1 
Show a => Show (Dual a)  Since: base2.1 
Generic (Dual a)  Since: base4.7.0.0 
Semigroup a => Semigroup (Dual a)  Since: base4.9.0.0 
Monoid a => Monoid (Dual a)  Since: base2.1 
Generic1 Dual  Since: base4.7.0.0 
type Rep (Dual a)  
Defined in Data.Semigroup.Internal  
type Rep1 Dual  
Defined in Data.Semigroup.Internal 
The monoid of endomorphisms under composition.
>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!") >>> appEndo computation "Haskell" "Hello, Haskell!"
Boolean monoid under conjunction (&&
).
>>> getAll (All True <> mempty <> All False) False
>>> getAll (mconcat (map (\x > All (even x)) [2,4,6,7,8])) False
Bounded All  Since: base2.1 
Eq All  Since: base2.1 
Data All  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > All > c All Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c All Source toConstr :: All > Constr Source dataTypeOf :: All > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c All) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c All) Source gmapT :: (forall b. Data b => b > b) > All > All Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > All > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > All > r Source gmapQ :: (forall d. Data d => d > u) > All > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > All > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > All > m All Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source  
Ord All  Since: base2.1 
Read All  Since: base2.1 
Show All  Since: base2.1 
Generic All  Since: base4.7.0.0 
Semigroup All  Since: base4.9.0.0 
Monoid All  Since: base2.1 
type Rep All  
Defined in Data.Semigroup.Internal 
Boolean monoid under disjunction (
).
>>> getAny (Any True <> mempty <> Any False) True
>>> getAny (mconcat (map (\x > Any (even x)) [2,4,6,7,8])) True
Bounded Any  Since: base2.1 
Eq Any  Since: base2.1 
Data Any  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Any > c Any Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c Any Source toConstr :: Any > Constr Source dataTypeOf :: Any > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c Any) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c Any) Source gmapT :: (forall b. Data b => b > b) > Any > Any Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Any > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Any > r Source gmapQ :: (forall d. Data d => d > u) > Any > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Any > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Any > m Any Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source  
Ord Any  Since: base2.1 
Read Any  Since: base2.1 
Show Any  Since: base2.1 
Generic Any  Since: base4.7.0.0 
Semigroup Any  Since: base4.9.0.0 
Monoid Any  Since: base2.1 
type Rep Any  
Defined in Data.Semigroup.Internal 
Monoid under addition.
>>> getSum (Sum 1 <> Sum 2 <> mempty) 3
Monad Sum  Since: base4.8.0.0 
Functor Sum  Since: base4.8.0.0 
MonadFix Sum  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Sum  Since: base4.8.0.0 
Foldable Sum  Since: base4.8.0.0 
Defined in Data.Foldable Methodsfold :: 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 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 
MonadZip Sum  Since: base4.8.0.0 
Bounded a => Bounded (Sum a)  Since: base2.1 
Eq a => Eq (Sum a)  Since: base2.1 
Data a => Data (Sum a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Sum a > c (Sum a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Sum a) Source toConstr :: Sum a > Constr Source dataTypeOf :: Sum a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Sum a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Sum a)) Source gmapT :: (forall b. Data b => b > b) > Sum a > Sum a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Sum a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Sum a > r Source gmapQ :: (forall d. Data d => d > u) > Sum a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Sum a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source  
Num a => Num (Sum a)  Since: base4.7.0.0 
Ord a => Ord (Sum a)  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Sum a)  Since: base2.1 
Show a => Show (Sum a)  Since: base2.1 
Generic (Sum a)  Since: base4.7.0.0 
Num a => Semigroup (Sum a)  Since: base4.9.0.0 
Num a => Monoid (Sum a)  Since: base2.1 
Generic1 Sum  Since: base4.7.0.0 
type Rep (Sum a)  
Defined in Data.Semigroup.Internal  
type Rep1 Sum  
Defined in Data.Semigroup.Internal 
Monoid under multiplication.
>>> getProduct (Product 3 <> Product 4 <> mempty) 12
Product  
Fields

Monad Product  Since: base4.8.0.0 
Functor Product  Since: base4.8.0.0 
MonadFix Product  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Product  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Foldable Product  Since: base4.8.0.0 
Defined in Data.Foldable Methodsfold :: 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  
MonadZip Product  Since: base4.8.0.0 
Bounded a => Bounded (Product a)  Since: base2.1 
Eq a => Eq (Product a)  Since: base2.1 
Data a => Data (Product a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Product a > c (Product a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Product a) Source toConstr :: Product a > Constr Source dataTypeOf :: Product a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Product a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Product a)) Source gmapT :: (forall b. Data b => b > b) > Product a > Product a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Product a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Product a > r Source gmapQ :: (forall d. Data d => d > u) > Product a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Product a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Product a > m (Product a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source  
Num a => Num (Product a)  Since: base4.7.0.0 
Defined in Data.Semigroup.Internal Methods(+) :: 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)  Since: base2.1 
Defined in Data.Semigroup.Internal  
Read a => Read (Product a)  Since: base2.1 
Show a => Show (Product a)  Since: base2.1 
Generic (Product a)  Since: base4.7.0.0 
Num a => Semigroup (Product a)  Since: base4.9.0.0 
Num a => Monoid (Product a)  Since: base2.1 
Generic1 Product  Since: base4.7.0.0 
type Rep (Product a)  
Defined in Data.Semigroup.Internal  
type Rep1 Product  
Defined in Data.Semigroup.Internal 
To implement find
or findLast
on any Foldable
:
findLast :: Foldable t => (a > Bool) > t a > Maybe a findLast pred = getLast . foldMap (x > if pred x then Last (Just x) else Last Nothing)
Much of Map
s interface can be implemented with alter
. Some of the rest can be implemented with a new alterF
function and either First
or Last
:
alterF :: (Functor f, Ord k) => (Maybe a > f (Maybe a)) > k > Map k a > f (Map k a) instance Monoid a => Functor ((,) a)  from Data.Functor
insertLookupWithKey :: Ord k => (k > v > v > v) > k > v > Map k v > (Maybe v, Map k v) insertLookupWithKey combine key value = Arrow.first getFirst . alterF doChange key where doChange Nothing = (First Nothing, Just value) doChange (Just oldValue) = (First (Just oldValue), Just (combine key value oldValue))
Maybe monoid returning the leftmost nonNothing value.
First a
is isomorphic to Alt Maybe a
, but precedes it historically.
>>> getFirst (First (Just "hello") <> First Nothing <> First (Just "world")) Just "hello"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.First x === Maybe (Data.Semigroup.First x)
In addition to being equivalent in the structural sense, the two also have Monoid
instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in Maybe
.
Monad First  Since: base4.8.0.0 
Functor First  Since: base4.8.0.0 
MonadFix First  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative First  Since: base4.8.0.0 
Foldable First  Since: base4.8.0.0 
Defined in Data.Foldable Methodsfold :: 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 
MonadZip First  Since: base4.8.0.0 
Eq a => Eq (First a)  Since: base2.1 
Data a => Data (First a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > First a > c (First a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (First a) Source toConstr :: First a > Constr Source dataTypeOf :: First a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (First a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (First a)) Source gmapT :: (forall b. Data b => b > b) > First a > First a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > First a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > First a > r Source gmapQ :: (forall d. Data d => d > u) > First a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > First a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > First a > m (First a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source  
Ord a => Ord (First a)  Since: base2.1 
Read a => Read (First a)  Since: base2.1 
Show a => Show (First a)  Since: base2.1 
Generic (First a)  Since: base4.7.0.0 
Semigroup (First a)  Since: base4.9.0.0 
Monoid (First a)  Since: base2.1 
Generic1 First  Since: base4.7.0.0 
type Rep (First a)  
Defined in Data.Monoid  
type Rep1 First  
Defined in Data.Monoid 
Maybe monoid returning the rightmost nonNothing value.
Last a
is isomorphic to Dual (First a)
, and thus to Dual (Alt Maybe a)
>>> getLast (Last (Just "hello") <> Last Nothing <> Last (Just "world")) Just "world"
Use of this type is discouraged. Note the following equivalence:
Data.Monoid.Last x === Maybe (Data.Semigroup.Last x)
In addition to being equivalent in the structural sense, the two also have Monoid
instances that behave the same. This type will be marked deprecated in GHC 8.8, and removed in GHC 8.10. Users are advised to use the variant from Data.Semigroup and wrap it in Maybe
.
Monad Last  Since: base4.8.0.0 
Functor Last  Since: base4.8.0.0 
MonadFix Last  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative Last  Since: base4.8.0.0 
Foldable Last  Since: base4.8.0.0 
Defined in Data.Foldable Methodsfold :: 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 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 
MonadZip Last  Since: base4.8.0.0 
Eq a => Eq (Last a)  Since: base2.1 
Data a => Data (Last a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Last a > c (Last a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Last a) Source toConstr :: Last a > Constr Source dataTypeOf :: Last a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Last a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Last a)) Source gmapT :: (forall b. Data b => b > b) > Last a > Last a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Last a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Last a > r Source gmapQ :: (forall d. Data d => d > u) > Last a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Last a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Last a > m (Last a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source  
Ord a => Ord (Last a)  Since: base2.1 
Defined in Data.Monoid  
Read a => Read (Last a)  Since: base2.1 
Show a => Show (Last a)  Since: base2.1 
Generic (Last a)  Since: base4.7.0.0 
Semigroup (Last a)  Since: base4.9.0.0 
Monoid (Last a)  Since: base2.1 
Generic1 Last  Since: base4.7.0.0 
type Rep (Last a)  
Defined in Data.Monoid  
type Rep1 Last  
Defined in Data.Monoid 
Monoid under <>
.
Since: base4.8.0.0
Generic1 (Alt f :: k > Type)  Since: base4.8.0.0 
Monad f => Monad (Alt f)  Since: base4.8.0.0 
Functor f => Functor (Alt f)  Since: base4.8.0.0 
MonadFix f => MonadFix (Alt f)  Since: base4.8.0.0 
Defined in Control.Monad.Fix  
Applicative f => Applicative (Alt f)  Since: base4.8.0.0 
Foldable f => Foldable (Alt f)  Since: base4.12.0.0 
Defined in Data.Foldable Methodsfold :: 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  
Traversable f => Traversable (Alt f)  Since: base4.12.0.0 
MonadPlus f => MonadPlus (Alt f)  Since: base4.8.0.0 
Alternative f => Alternative (Alt f)  Since: base4.8.0.0 
MonadZip f => MonadZip (Alt f)  Since: base4.8.0.0 
Contravariant f => Contravariant (Alt f)  
Enum (f a) => Enum (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal Methodssucc :: 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  
Eq (f a) => Eq (Alt f a)  Since: base4.8.0.0 
(Data (f a), Data a, Typeable f) => Data (Alt f a)  Since: base4.8.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Alt f a > c (Alt f a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Alt f a) Source toConstr :: Alt f a > Constr Source dataTypeOf :: Alt f a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Alt f a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Alt f a)) Source gmapT :: (forall b. Data b => b > b) > Alt f a > Alt f a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Alt f a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Alt f a > r Source gmapQ :: (forall d. Data d => d > u) > Alt f a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Alt f a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Alt f a > m (Alt f a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Alt f a > m (Alt f a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Alt f a > m (Alt f a) Source  
Num (f a) => Num (Alt f a)  Since: base4.8.0.0 
Defined in Data.Semigroup.Internal  
Ord (f a) => Ord (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 
Generic (Alt f a)  Since: base4.8.0.0 
Alternative f => Semigroup (Alt f a)  Since: base4.9.0.0 
Alternative f => Monoid (Alt f a)  Since: base4.8.0.0 
type Rep1 (Alt f :: k > Type)  
Defined in Data.Semigroup.Internal  
type Rep (Alt f a)  
Defined in Data.Semigroup.Internal 
This data type witnesses the lifting of a Monoid
into an Applicative
pointwise.
Since: base4.12.0.0
Generic1 (Ap f :: k > Type)  Since: base4.12.0.0 
Monad f => Monad (Ap f)  Since: base4.12.0.0 
Functor f => Functor (Ap f)  Since: base4.12.0.0 
MonadFix f => MonadFix (Ap f)  Since: base4.12.0.0 
Defined in Control.Monad.Fix  
MonadFail f => MonadFail (Ap f)  Since: base4.12.0.0 
Defined in Data.Monoid  
Applicative f => Applicative (Ap f)  Since: base4.12.0.0 
Foldable f => Foldable (Ap f)  Since: base4.12.0.0 
Defined in Data.Foldable Methodsfold :: 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 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 
MonadPlus f => MonadPlus (Ap f)  Since: base4.12.0.0 
Alternative f => Alternative (Ap f)  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 Methodssucc :: 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  
Eq (f a) => Eq (Ap f a)  Since: base4.12.0.0 
(Data (f a), Data a, Typeable f) => Data (Ap f a)  Since: base4.12.0.0 
Defined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Ap f a > c (Ap f a) Source gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Ap f a) Source toConstr :: Ap f a > Constr Source dataTypeOf :: Ap f a > DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Ap f a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Ap f a)) Source gmapT :: (forall b. Data b => b > b) > Ap f a > Ap f a Source gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Ap f a > r Source gmapQr :: forall r r'. (r' > r > r) > r > (forall d. Data d => d > r') > Ap f a > r Source gmapQ :: (forall d. Data d => d > u) > Ap f a > [u] Source gmapQi :: Int > (forall d. Data d => d > u) > Ap f a > u Source gmapM :: Monad m => (forall d. Data d => d > m d) > Ap f a > m (Ap f a) Source gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Ap f a > m (Ap f a) Source gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Ap f a > m (Ap f a) Source  
(Applicative f, Num a) => Num (Ap f a)  Since: base4.12.0.0 
Ord (f a) => Ord (Ap f a)  Since: base4.12.0.0 
Defined in Data.Monoid  
Read (f a) => Read (Ap f a)  Since: base4.12.0.0 
Show (f a) => Show (Ap f a)  Since: base4.12.0.0 
Generic (Ap f a)  Since: base4.12.0.0 
(Applicative f, Semigroup a) => Semigroup (Ap f a)  Since: base4.12.0.0 
(Applicative f, Monoid a) => Monoid (Ap f a)  Since: base4.12.0.0 
type Rep1 (Ap f :: k > Type)  
Defined in Data.Monoid  
type Rep (Ap f a)  
Defined in Data.Monoid 
© The University of Glasgow and others
Licensed under a BSDstyle license (see top of the page).
https://downloads.haskell.org/~ghc/8.8.3/docs/html/libraries/base4.13.0.0/DataMonoid.html