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

License  BSDstyle (see the file libraries/base/LICENSE) 
Maintainer  libraries@haskell.org 
Stability  experimental 
Portability  portable 
Safe Haskell  Trustworthy 
Language  Haskell2010 
A class for monoids (types with an associative binary operation that has an identity) with various generalpurpose instances.
Synopsis
 class Semigroup a => Monoid a where
 (<>) :: Semigroup a => a > a > a
 newtype Dual a = Dual {
 getDual :: a
 newtype Endo a = Endo {
 appEndo :: a > a
 newtype All = All {}
 newtype Any = Any {}
 newtype Sum a = Sum {
 getSum :: a
 newtype Product a = Product {
 getProduct :: a
 newtype First a = First {}
 newtype Last a = Last {}
 newtype Alt f a = Alt {
 getAlt :: f a
Monoid
typeclass
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 laws:
x
<>
mempty
= xmempty
<>
x = xx
(<>
(y<>
z) = (x<>
y)<>
zSemigroup
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
mappend :: a > a > a Source #
An associative operation
NOTE: This method is redundant and has the default
implementation
since base4.11.0.0.mappend
= '(<>)'
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.
Instances
Monoid Ordering Source #  Since: 2.1 
Monoid () Source #  Since: 2.1 
Monoid Any Source #  Since: 2.1 
Monoid All Source #  Since: 2.1 
Monoid Lifetime Source # 
Since: 4.8.0.0 
Monoid Event Source #  Since: 4.3.1.0 
Monoid [a] Source #  Since: 2.1 
Semigroup a => Monoid (Maybe a) Source #  Lift a semigroup into Since 4.11.0: constraint on inner Since: 2.1 
Monoid a => Monoid (IO a) Source #  Since: 4.9.0.0 
Monoid a => Monoid (Down a) Source #  Since: 4.11.0.0 
Num a => Monoid (Product a) Source #  Since: 2.1 
Num a => Monoid (Sum a) Source #  Since: 2.1 
Monoid (Endo a) Source #  Since: 2.1 
Monoid a => Monoid (Dual a) Source #  Since: 2.1 
Monoid (Last a) Source #  Since: 2.1 
Monoid (First a) Source #  Since: 2.1 
Monoid a => Monoid (Identity a) Source #  
Semigroup a => Monoid (Option a) Source #  Since: 4.9.0.0 
Monoid m => Monoid (WrappedMonoid m) Source #  Since: 4.9.0.0 
mempty :: WrappedMonoid m Source # mappend :: WrappedMonoid m > WrappedMonoid m > WrappedMonoid m Source # mconcat :: [WrappedMonoid m] > WrappedMonoid m Source #  
(Ord a, Bounded a) => Monoid (Max a) Source #  Since: 4.9.0.0 
(Ord a, Bounded a) => Monoid (Min a) Source #  Since: 4.9.0.0 
Monoid b => Monoid (a > b) Source #  Since: 2.1 
(Monoid a, Monoid b) => Monoid (a, b) Source #  Since: 2.1 
Monoid a => Monoid (ST s a) Source #  Since: 4.11.0.0 
Monoid (Proxy s) Source #  Since: 4.7.0.0 
(Monoid a, Monoid b, Monoid c) => Monoid (a, b, c) Source #  Since: 2.1 
Alternative f => Monoid (Alt f a) Source #  Since: 4.8.0.0 
Monoid a => Monoid (Const a b) Source #  
(Monoid a, Monoid b, Monoid c, Monoid d) => Monoid (a, b, c, d) Source #  Since: 2.1 
(Monoid a, Monoid b, Monoid c, Monoid d, Monoid e) => Monoid (a, b, c, d, e) Source #  Since: 2.1 
The dual of a Monoid
, obtained by swapping the arguments of mappend
.
>>>
getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"
Instances
Monad Dual Source #  Since: 4.8.0.0 
Functor Dual Source #  Since: 4.8.0.0 
MonadFix Dual Source #  Since: 4.8.0.0 
Applicative Dual Source #  Since: 4.8.0.0 
Foldable Dual Source #  Since: 4.8.0.0 
fold :: Monoid m => Dual m > m Source # foldMap :: Monoid m => (a > m) > Dual a > m Source # foldr :: (a > b > b) > b > Dual a > b Source # foldr' :: (a > b > b) > b > Dual a > b Source # foldl :: (b > a > b) > b > Dual a > b Source # foldl' :: (b > a > b) > b > Dual a > b Source # foldr1 :: (a > a > a) > Dual a > a Source # foldl1 :: (a > a > a) > Dual a > a Source # toList :: Dual a > [a] Source # null :: Dual a > Bool Source # length :: Dual a > Int Source # elem :: Eq a => a > Dual a > Bool Source # maximum :: Ord a => Dual a > a Source # minimum :: Ord a => Dual a > a Source #  
Traversable Dual Source #  Since: 4.8.0.0 
MonadZip Dual Source #  Since: 4.8.0.0 
Bounded a => Bounded (Dual a) Source #  
Eq a => Eq (Dual a) Source #  
Data a => Data (Dual a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Dual a > c (Dual a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Dual a) Source # toConstr :: Dual a > Constr Source # dataTypeOf :: Dual a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Dual a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Dual a)) Source # gmapT :: (forall b. Data b => b > b) > Dual a > Dual a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Dual a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Dual a > r Source # gmapQ :: (forall d. Data d => d > u) > Dual a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Dual a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Dual a > m (Dual a) Source #  
Ord a => Ord (Dual a) Source #  
Read a => Read (Dual a) Source #  
Show a => Show (Dual a) Source #  
Generic (Dual a) Source #  
Semigroup a => Semigroup (Dual a) Source #  Since: 4.9.0.0 
Monoid a => Monoid (Dual a) Source #  Since: 2.1 
Generic1 Dual Source #  
type Rep (Dual a) Source #  
type Rep1 Dual Source #  
The monoid of endomorphisms under composition.
>>>
let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>>
appEndo computation "Haskell"
"Hello, Haskell!"
Bool
wrappers
Boolean monoid under conjunction (&&
).
>>>
getAll (All True <> mempty <> All False)
False
>>>
getAll (mconcat (map (\x > All (even x)) [2,4,6,7,8]))
False
Instances
Bounded All Source #  
Eq All Source #  
Data All Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > All > c All Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c All Source # toConstr :: All > Constr Source # dataTypeOf :: All > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c All) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c All) Source # gmapT :: (forall b. Data b => b > b) > All > All Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > All > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > All > r Source # gmapQ :: (forall d. Data d => d > u) > All > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > All > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > All > m All Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > All > m All Source #  
Ord All Source #  
Read All Source #  
Show All Source #  
Generic All Source #  
Semigroup All Source #  Since: 4.9.0.0 
Monoid All Source #  Since: 2.1 
type Rep All Source #  
Boolean monoid under disjunction (
).
>>>
getAny (Any True <> mempty <> Any False)
True
>>>
getAny (mconcat (map (\x > Any (even x)) [2,4,6,7,8]))
True
Instances
Bounded Any Source #  
Eq Any Source #  
Data Any Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Any > c Any Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c Any Source # toConstr :: Any > Constr Source # dataTypeOf :: Any > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c Any) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c Any) Source # gmapT :: (forall b. Data b => b > b) > Any > Any Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Any > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Any > r Source # gmapQ :: (forall d. Data d => d > u) > Any > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Any > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Any > m Any Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Any > m Any Source #  
Ord Any Source #  
Read Any Source #  
Show Any Source #  
Generic Any Source #  
Semigroup Any Source #  Since: 4.9.0.0 
Monoid Any Source #  Since: 2.1 
type Rep Any Source #  
Num
wrappers
Monoid under addition.
>>>
getSum (Sum 1 <> Sum 2 <> mempty)
3
Instances
Monad Sum Source #  Since: 4.8.0.0 
Functor Sum Source #  Since: 4.8.0.0 
MonadFix Sum Source #  Since: 4.8.0.0 
Applicative Sum Source #  Since: 4.8.0.0 
Foldable Sum Source #  Since: 4.8.0.0 
fold :: Monoid m => Sum m > m Source # foldMap :: Monoid m => (a > m) > Sum a > m Source # foldr :: (a > b > b) > b > Sum a > b Source # foldr' :: (a > b > b) > b > Sum a > b Source # foldl :: (b > a > b) > b > Sum a > b Source # foldl' :: (b > a > b) > b > Sum a > b Source # foldr1 :: (a > a > a) > Sum a > a Source # foldl1 :: (a > a > a) > Sum a > a Source # toList :: Sum a > [a] Source # null :: Sum a > Bool Source # length :: Sum a > Int Source # elem :: Eq a => a > Sum a > Bool Source # maximum :: Ord a => Sum a > a Source # minimum :: Ord a => Sum a > a Source #  
Traversable Sum Source #  Since: 4.8.0.0 
MonadZip Sum Source #  Since: 4.8.0.0 
Bounded a => Bounded (Sum a) Source #  
Eq a => Eq (Sum a) Source #  
Data a => Data (Sum a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Sum a > c (Sum a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Sum a) Source # toConstr :: Sum a > Constr Source # dataTypeOf :: Sum a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Sum a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Sum a)) Source # gmapT :: (forall b. Data b => b > b) > Sum a > Sum a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Sum a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Sum a > r Source # gmapQ :: (forall d. Data d => d > u) > Sum a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Sum a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Sum a > m (Sum a) Source #  
Num a => Num (Sum a) Source #  
Ord a => Ord (Sum a) Source #  
Read a => Read (Sum a) Source #  
Show a => Show (Sum a) Source #  
Generic (Sum a) Source #  
Num a => Semigroup (Sum a) Source #  Since: 4.9.0.0 
Num a => Monoid (Sum a) Source #  Since: 2.1 
Generic1 Sum Source #  
type Rep (Sum a) Source #  
type Rep1 Sum Source #  
Monoid under multiplication.
>>>
getProduct (Product 3 <> Product 4 <> mempty)
12
Product  

Instances
Monad Product Source #  Since: 4.8.0.0 
Functor Product Source #  Since: 4.8.0.0 
MonadFix Product Source #  Since: 4.8.0.0 
Applicative Product Source #  Since: 4.8.0.0 
Foldable Product Source #  Since: 4.8.0.0 
fold :: Monoid m => Product m > m Source # foldMap :: Monoid m => (a > m) > Product a > m Source # foldr :: (a > b > b) > b > Product a > b Source # foldr' :: (a > b > b) > b > Product a > b Source # foldl :: (b > a > b) > b > Product a > b Source # foldl' :: (b > a > b) > b > Product a > b Source # foldr1 :: (a > a > a) > Product a > a Source # foldl1 :: (a > a > a) > Product a > a Source # toList :: Product a > [a] Source # null :: Product a > Bool Source # length :: Product a > Int Source # elem :: Eq a => a > Product a > Bool Source # maximum :: Ord a => Product a > a Source # minimum :: Ord a => Product a > a Source #  
Traversable Product Source #  Since: 4.8.0.0 
MonadZip Product Source #  Since: 4.8.0.0 
Bounded a => Bounded (Product a) Source #  
Eq a => Eq (Product a) Source #  
Data a => Data (Product a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Product a > c (Product a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Product a) Source # toConstr :: Product a > Constr Source # dataTypeOf :: Product a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Product a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Product a)) Source # gmapT :: (forall b. Data b => b > b) > Product a > Product a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Product a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Product a > r Source # gmapQ :: (forall d. Data d => d > u) > Product a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Product a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Product a > m (Product a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Product a > m (Product a) Source #  
Num a => Num (Product a) Source #  
(+) :: Product a > Product a > Product a Source # () :: Product a > Product a > Product a Source # (*) :: Product a > Product a > Product a Source # negate :: Product a > Product a Source # abs :: Product a > Product a Source # signum :: Product a > Product a Source # fromInteger :: Integer > Product a Source #  
Ord a => Ord (Product a) Source #  
Read a => Read (Product a) Source #  
Show a => Show (Product a) Source #  
Generic (Product a) Source #  
Num a => Semigroup (Product a) Source #  Since: 4.9.0.0 
Num a => Monoid (Product a) Source #  Since: 2.1 
Generic1 Product Source #  
type Rep (Product a) Source #  
type Rep1 Product Source #  
Maybe
wrappers
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 Data.Map's interface can be implemented with
Data.Map.alter. Some of the rest can be implemented with a new
alterA
function and either First
or Last
:
alterA :: (Applicative f, Ord k) => (Maybe a > f (Maybe a)) > k > Map k a > f (Map k a) instance Monoid a => Applicative ((,) a)  from Control.Applicative
insertLookupWithKey :: Ord k => (k > v > v > v) > k > v > Map k v > (Maybe v, Map k v) insertLookupWithKey combine key value = Arrow.first getFirst . alterA 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.
is isomorphic to First
a
, but precedes it
historically.Alt
Maybe
a
>>>
getFirst (First (Just "hello") <> First Nothing <> First (Just "world"))
Just "hello"
Instances
Monad First Source #  
Functor First Source #  
MonadFix First Source #  Since: 4.8.0.0 
Applicative First Source #  
Foldable First Source #  Since: 4.8.0.0 
fold :: Monoid m => First m > m Source # foldMap :: Monoid m => (a > m) > First a > m Source # foldr :: (a > b > b) > b > First a > b Source # foldr' :: (a > b > b) > b > First a > b Source # foldl :: (b > a > b) > b > First a > b Source # foldl' :: (b > a > b) > b > First a > b Source # foldr1 :: (a > a > a) > First a > a Source # foldl1 :: (a > a > a) > First a > a Source # toList :: First a > [a] Source # null :: First a > Bool Source # length :: First a > Int Source # elem :: Eq a => a > First a > Bool Source # maximum :: Ord a => First a > a Source # minimum :: Ord a => First a > a Source #  
Traversable First Source #  Since: 4.8.0.0 
MonadZip First Source #  Since: 4.8.0.0 
Eq a => Eq (First a) Source #  
Data a => Data (First a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > First a > c (First a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (First a) Source # toConstr :: First a > Constr Source # dataTypeOf :: First a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (First a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (First a)) Source # gmapT :: (forall b. Data b => b > b) > First a > First a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > First a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > First a > r Source # gmapQ :: (forall d. Data d => d > u) > First a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > First a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > First a > m (First a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > First a > m (First a) Source #  
Ord a => Ord (First a) Source #  
Read a => Read (First a) Source #  
Show a => Show (First a) Source #  
Generic (First a) Source #  
Semigroup (First a) Source #  Since: 4.9.0.0 
Monoid (First a) Source #  Since: 2.1 
Generic1 First Source #  
type Rep (First a) Source #  
type Rep1 First Source #  
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
Monad Last Source #  
Functor Last Source #  
MonadFix Last Source #  Since: 4.8.0.0 
Applicative Last Source #  
Foldable Last Source #  Since: 4.8.0.0 
fold :: Monoid m => Last m > m Source # foldMap :: Monoid m => (a > m) > Last a > m Source # foldr :: (a > b > b) > b > Last a > b Source # foldr' :: (a > b > b) > b > Last a > b Source # foldl :: (b > a > b) > b > Last a > b Source # foldl' :: (b > a > b) > b > Last a > b Source # foldr1 :: (a > a > a) > Last a > a Source # foldl1 :: (a > a > a) > Last a > a Source # toList :: Last a > [a] Source # null :: Last a > Bool Source # length :: Last a > Int Source # elem :: Eq a => a > Last a > Bool Source # maximum :: Ord a => Last a > a Source # minimum :: Ord a => Last a > a Source #  
Traversable Last Source #  Since: 4.8.0.0 
MonadZip Last Source #  Since: 4.8.0.0 
Eq a => Eq (Last a) Source #  
Data a => Data (Last a) Source #  Since: 4.8.0.0 
gfoldl :: (forall d b. Data d => c (d > b) > d > c b) > (forall g. g > c g) > Last a > c (Last a) Source # gunfold :: (forall b r. Data b => c (b > r) > c r) > (forall r. r > c r) > Constr > c (Last a) Source # toConstr :: Last a > Constr Source # dataTypeOf :: Last a > DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) > Maybe (c (Last a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) > Maybe (c (Last a)) Source # gmapT :: (forall b. Data b => b > b) > Last a > Last a Source # gmapQl :: (r > r' > r) > r > (forall d. Data d => d > r') > Last a > r Source # gmapQr :: (r' > r > r) > r > (forall d. Data d => d > r') > Last a > r Source # gmapQ :: (forall d. Data d => d > u) > Last a > [u] Source # gmapQi :: Int > (forall d. Data d => d > u) > Last a > u Source # gmapM :: Monad m => (forall d. Data d => d > m d) > Last a > m (Last a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d > m d) > Last a > m (Last a) Source #  
Ord a => Ord (Last a) Source #  
Read a => Read (Last a) Source #  
Show a => Show (Last a) Source #  
Generic (Last a) Source #  
Semigroup (Last a) Source #  Since: 4.9.0.0 
Monoid (Last a) Source #  Since: 2.1 
Generic1 Last Source #  
type Rep (Last a) Source #  
type Rep1 Last Source #  
Alternative
wrapper
Monoid under <>
.
Since: 4.8.0.0
Instances
Generic1 (Alt f :: k > *) Source #  
Monad f => Monad (Alt f) Source #  
Functor f => Functor (Alt f) Source #  
MonadFix f => MonadFix (Alt f) Source #  Since: 4.8.0.0 
Applicative f => Applicative (Alt f) Source #  
MonadPlus f => MonadPlus (Alt f) Source #  
Alternative f => Alternative (Alt f) Source #  
MonadZip f => MonadZip (Alt f) Source #  Since: 4.8.0.0 
Enum (f a) => Enum (Alt f a) Source #  
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 #  
Eq (f a) => Eq (Alt f a) Source #  
(Data (f a), Data a, Typeable f) => Data (Alt f a) Source #  Since: 4.8.0.0 
gfoldl :: (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 :: (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) Source #  
Ord (f a) => Ord (Alt f a) Source #  
Read (f a) => Read (Alt f a) Source #  
Show (f a) => Show (Alt f a) Source #  
Generic (Alt f a) Source #  
Alternative f => Semigroup (Alt f a) Source #  Since: 4.9.0.0 
Alternative f => Monoid (Alt f a) Source #  Since: 4.8.0.0 
type Rep1 (Alt f :: k > *) Source #  
type Rep (Alt f a) Source #  