| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Data.Semigroup.Compat
Description
This backports the modern Data.Semigroup interface back to
base-4.9/GHC 8.0.
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
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: base-4.9.0.0
Methods
(<>) :: a -> a -> a infixr 6 #
An associative operation.
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
>>>import Data.List.NonEmpty (NonEmpty (..))>>>sconcat $ "Hello" :| [" ", "Haskell", "!"]"Hello Haskell!"
stimes :: Integral b => b -> a -> a #
Repeat a value n times.
Given that this works on a Semigroup it is allowed to fail if
you request 0 or fewer repetitions, and the default definition
will do so.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by
picking stimes = or stimesIdempotentstimes =
respectively.stimesIdempotentMonoid
>>>stimes 4 [1][1,1,1,1]
Instances
| Semigroup All | Since: base-4.9.0.0 |
| Semigroup Any | Since: base-4.9.0.0 |
| Semigroup Void | Since: base-4.9.0.0 |
| Semigroup Ordering | Since: base-4.9.0.0 |
| Semigroup () | Since: base-4.9.0.0 |
| Bits a => Semigroup (And a) | Since: base-4.16 |
| FiniteBits a => Semigroup (Iff a) | This constraint is arguably
too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Semigroup (Ior a) | Since: base-4.16 |
| Bits a => Semigroup (Xor a) | Since: base-4.16 |
| Semigroup (FromMaybe b) | |
| Semigroup a => Semigroup (JoinWith a) | |
| Semigroup (NonEmptyDList a) | |
| Semigroup (Comparison a) |
(<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a' |
Defined in Data.Functor.Contravariant Methods (<>) :: Comparison a -> Comparison a -> Comparison a # sconcat :: NonEmpty (Comparison a) -> Comparison a # stimes :: Integral b => b -> Comparison a -> Comparison a # | |
| Semigroup (Equivalence a) |
(<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv' a b |
Defined in Data.Functor.Contravariant Methods (<>) :: Equivalence a -> Equivalence a -> Equivalence a # sconcat :: NonEmpty (Equivalence a) -> Equivalence a # stimes :: Integral b => b -> Equivalence a -> Equivalence a # | |
| Semigroup (Predicate a) |
(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a |
| Semigroup a => Semigroup (Identity a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods (<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m # sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m # stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # | |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Semigroup (Endo a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Semigroup (NonEmpty a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (STM a) | Since: base-4.17.0.0 |
| Semigroup a => Semigroup (IO a) | Since: base-4.10.0.0 |
| Semigroup a => Semigroup (Maybe a) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (a) | Since: base-4.15 |
| Semigroup [a] | Since: base-4.9.0.0 |
| Semigroup (Either a b) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) |
(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a |
| Semigroup (Proxy s) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (ST s a) | Since: base-4.11.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) | Since: base-4.9.0.0 |
| Semigroup b => Semigroup (a -> b) | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) | Since: base-4.12.0.0 |
| Alternative f => Semigroup (Alt f a) | Since: base-4.9.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) | Since: base-4.9.0.0 |
| (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) | Since: base-4.16.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) | Since: base-4.9.0.0 |
| Semigroup (f (g a)) => Semigroup (Compose f g a) | Since: base-4.16.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) | Since: base-4.9.0.0 |
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 #
Repeat a value n times.
mtimesDefault n a = a <> a <> ... <> a -- using <> (n-1) times
In many cases, `stimes 0 a` for a Monoid 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.
Semigroups
Instances
| MonadFix Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Foldable Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Min m -> m # foldMap :: Monoid m => (a -> m) -> Min a -> m # foldMap' :: Monoid m => (a -> m) -> Min a -> m # foldr :: (a -> b -> b) -> b -> Min a -> b # foldr' :: (a -> b -> b) -> b -> Min a -> b # foldl :: (b -> a -> b) -> b -> Min a -> b # foldl' :: (b -> a -> b) -> b -> Min a -> b # foldr1 :: (a -> a -> a) -> Min a -> a # foldl1 :: (a -> a -> a) -> Min a -> a # elem :: Eq a => a -> Min a -> Bool # maximum :: Ord a => Min a -> a # | |
| Foldable1 Min | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Min m -> m # foldMap1 :: Semigroup m => (a -> m) -> Min a -> m # foldMap1' :: Semigroup m => (a -> m) -> Min a -> m # toNonEmpty :: Min a -> NonEmpty a # maximum :: Ord a => Min a -> a # minimum :: Ord a => Min a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Min a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Min a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Min a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Min a -> b # | |
| Traversable Min | Since: base-4.9.0.0 |
| Applicative Min | Since: base-4.9.0.0 |
| Functor Min | Since: base-4.9.0.0 |
| Monad Min | Since: base-4.9.0.0 |
| Generic1 Min | |
| Data a => Data (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) # dataTypeOf :: Min a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) # gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r # gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # | |
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Min a) | Since: base-4.9.0.0 |
| Enum a => Enum (Min a) | Since: base-4.9.0.0 |
| Generic (Min a) | |
| Num a => Num (Min a) | Since: base-4.9.0.0 |
| Read a => Read (Min a) | Since: base-4.9.0.0 |
| Show a => Show (Min a) | Since: base-4.9.0.0 |
| Eq a => Eq (Min a) | Since: base-4.9.0.0 |
| Ord a => Ord (Min a) | Since: base-4.9.0.0 |
| type Rep1 Min | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| type Rep (Min a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
Instances
| MonadFix Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Foldable Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Max m -> m # foldMap :: Monoid m => (a -> m) -> Max a -> m # foldMap' :: Monoid m => (a -> m) -> Max a -> m # foldr :: (a -> b -> b) -> b -> Max a -> b # foldr' :: (a -> b -> b) -> b -> Max a -> b # foldl :: (b -> a -> b) -> b -> Max a -> b # foldl' :: (b -> a -> b) -> b -> Max a -> b # foldr1 :: (a -> a -> a) -> Max a -> a # foldl1 :: (a -> a -> a) -> Max a -> a # elem :: Eq a => a -> Max a -> Bool # maximum :: Ord a => Max a -> a # | |
| Foldable1 Max | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Max m -> m # foldMap1 :: Semigroup m => (a -> m) -> Max a -> m # foldMap1' :: Semigroup m => (a -> m) -> Max a -> m # toNonEmpty :: Max a -> NonEmpty a # maximum :: Ord a => Max a -> a # minimum :: Ord a => Max a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Max a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Max a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Max a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Max a -> b # | |
| Traversable Max | Since: base-4.9.0.0 |
| Applicative Max | Since: base-4.9.0.0 |
| Functor Max | Since: base-4.9.0.0 |
| Monad Max | Since: base-4.9.0.0 |
| Generic1 Max | |
| Data a => Data (Max a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) # dataTypeOf :: Max a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) # gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r # gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # | |
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Max a) | Since: base-4.9.0.0 |
| Enum a => Enum (Max a) | Since: base-4.9.0.0 |
| Generic (Max a) | |
| Num a => Num (Max a) | Since: base-4.9.0.0 |
| Read a => Read (Max a) | Since: base-4.9.0.0 |
| Show a => Show (Max a) | Since: base-4.9.0.0 |
| Eq a => Eq (Max a) | Since: base-4.9.0.0 |
| Ord a => Ord (Max a) | Since: base-4.9.0.0 |
| type Rep1 Max | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| type Rep (Max a) | Since: base-4.9.0.0 |
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 non-Nothing,
thus Data.Monoid.First Nothing <> x = x.
Instances
| MonadFix First | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Foldable First | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => First m -> m # foldMap :: Monoid m => (a -> m) -> First a -> m # foldMap' :: Monoid m => (a -> m) -> First a -> m # foldr :: (a -> b -> b) -> b -> First a -> b # foldr' :: (a -> b -> b) -> b -> First a -> b # foldl :: (b -> a -> b) -> b -> First a -> b # foldl' :: (b -> a -> b) -> b -> First a -> b # foldr1 :: (a -> a -> a) -> First a -> a # foldl1 :: (a -> a -> a) -> First a -> a # elem :: Eq a => a -> First a -> Bool # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # | |
| Foldable1 First | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => First m -> m # foldMap1 :: Semigroup m => (a -> m) -> First a -> m # foldMap1' :: Semigroup m => (a -> m) -> First a -> m # toNonEmpty :: First a -> NonEmpty a # maximum :: Ord a => First a -> a # minimum :: Ord a => First a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> First a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> First a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> First a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> First a -> b # | |
| Traversable First | Since: base-4.9.0.0 |
| Applicative First | Since: base-4.9.0.0 |
| Functor First | Since: base-4.9.0.0 |
| Monad First | Since: base-4.9.0.0 |
| Generic1 First | |
| Data a => Data (First a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) # toConstr :: First a -> Constr # dataTypeOf :: First a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) # gmapT :: (forall b. Data b => b -> b) -> First a -> First a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r # gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # | |
| Semigroup (First a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (First a) | Since: base-4.9.0.0 |
| Enum a => Enum (First a) | Since: base-4.9.0.0 |
| Generic (First a) | |
| Read a => Read (First a) | Since: base-4.9.0.0 |
| Show a => Show (First a) | Since: base-4.9.0.0 |
| Eq a => Eq (First a) | Since: base-4.9.0.0 |
| Ord a => Ord (First a) | Since: base-4.9.0.0 |
| type Rep1 First | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| type Rep (First a) | Since: base-4.9.0.0 |
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 non-Nothing,
thus x <> Data.Monoid.Last Nothing = x.
Instances
| MonadFix Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Foldable Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Last m -> m # foldMap :: Monoid m => (a -> m) -> Last a -> m # foldMap' :: Monoid m => (a -> m) -> Last a -> m # foldr :: (a -> b -> b) -> b -> Last a -> b # foldr' :: (a -> b -> b) -> b -> Last a -> b # foldl :: (b -> a -> b) -> b -> Last a -> b # foldl' :: (b -> a -> b) -> b -> Last a -> b # foldr1 :: (a -> a -> a) -> Last a -> a # foldl1 :: (a -> a -> a) -> Last a -> a # elem :: Eq a => a -> Last a -> Bool # maximum :: Ord a => Last a -> a # | |
| Foldable1 Last | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Last m -> m # foldMap1 :: Semigroup m => (a -> m) -> Last a -> m # foldMap1' :: Semigroup m => (a -> m) -> Last a -> m # toNonEmpty :: Last a -> NonEmpty a # maximum :: Ord a => Last a -> a # minimum :: Ord a => Last a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Last a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Last a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Last a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Last a -> b # | |
| Traversable Last | Since: base-4.9.0.0 |
| Applicative Last | Since: base-4.9.0.0 |
| Functor Last | Since: base-4.9.0.0 |
| Monad Last | Since: base-4.9.0.0 |
| Generic1 Last | |
| Data a => Data (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) # toConstr :: Last a -> Constr # dataTypeOf :: Last a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) # gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r # gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # | |
| Semigroup (Last a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Last a) | Since: base-4.9.0.0 |
| Enum a => Enum (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| Generic (Last a) | |
| Read a => Read (Last a) | Since: base-4.9.0.0 |
| Show a => Show (Last a) | Since: base-4.9.0.0 |
| Eq a => Eq (Last a) | Since: base-4.9.0.0 |
| Ord a => Ord (Last a) | Since: base-4.9.0.0 |
| type Rep1 Last | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
| type Rep (Last a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup | |
newtype WrappedMonoid m #
Provide a Semigroup for an arbitrary Monoid.
NOTE: This is not needed anymore since Semigroup became a superclass of
Monoid in base-4.11 and this newtype be deprecated at some point in the future.
Constructors
| WrapMonoid | |
Fields
| |
Instances
Re-exported monoids from Data.Monoid
The dual of a Monoid, obtained by swapping the arguments of mappend.
>>>getDual (mappend (Dual "Hello") (Dual "World"))"WorldHello"
Instances
| Foldable Dual | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Dual m -> m # foldMap :: Monoid m => (a -> m) -> Dual a -> m # foldMap' :: Monoid m => (a -> m) -> Dual a -> m # foldr :: (a -> b -> b) -> b -> Dual a -> b # foldr' :: (a -> b -> b) -> b -> Dual a -> b # foldl :: (b -> a -> b) -> b -> Dual a -> b # foldl' :: (b -> a -> b) -> b -> Dual a -> b # foldr1 :: (a -> a -> a) -> Dual a -> a # foldl1 :: (a -> a -> a) -> Dual a -> a # elem :: Eq a => a -> Dual a -> Bool # maximum :: Ord a => Dual a -> a # | |
| Foldable1 Dual | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Dual m -> m # foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m # foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m # toNonEmpty :: Dual a -> NonEmpty a # maximum :: Ord a => Dual a -> a # minimum :: Ord a => Dual a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b # | |
| Traversable Dual | Since: base-4.8.0.0 |
| Applicative Dual | Since: base-4.8.0.0 |
| Functor Dual | Since: base-4.8.0.0 |
| Monad Dual | Since: base-4.8.0.0 |
| Generic1 Dual | |
| Monoid a => Monoid (Dual a) | Since: base-2.1 |
| Semigroup a => Semigroup (Dual a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Dual a) | Since: base-2.1 |
| Generic (Dual a) | |
| Read a => Read (Dual a) | Since: base-2.1 |
| Show a => Show (Dual a) | Since: base-2.1 |
| Eq a => Eq (Dual a) | Since: base-2.1 |
| Ord a => Ord (Dual a) | Since: base-2.1 |
| type Rep1 Dual | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep (Dual a) | Since: base-4.7.0.0 |
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
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: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Sum m -> m # foldMap :: Monoid m => (a -> m) -> Sum a -> m # foldMap' :: Monoid m => (a -> m) -> Sum a -> m # foldr :: (a -> b -> b) -> b -> Sum a -> b # foldr' :: (a -> b -> b) -> b -> Sum a -> b # foldl :: (b -> a -> b) -> b -> Sum a -> b # foldl' :: (b -> a -> b) -> b -> Sum a -> b # foldr1 :: (a -> a -> a) -> Sum a -> a # foldl1 :: (a -> a -> a) -> Sum a -> a # elem :: Eq a => a -> Sum a -> Bool # maximum :: Ord a => Sum a -> a # | |
| Foldable1 Sum | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Sum m -> m # foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m # foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m # toNonEmpty :: Sum a -> NonEmpty a # maximum :: Ord a => Sum a -> a # minimum :: Ord a => Sum a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b # | |
| Traversable Sum | Since: base-4.8.0.0 |
| Applicative Sum | Since: base-4.8.0.0 |
| Functor Sum | Since: base-4.8.0.0 |
| Monad Sum | Since: base-4.8.0.0 |
| Generic1 Sum | |
| Num a => Monoid (Sum a) | Since: base-2.1 |
| Num a => Semigroup (Sum a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Sum a) | Since: base-2.1 |
| Generic (Sum a) | |
| Num a => Num (Sum a) | Since: base-4.7.0.0 |
| Read a => Read (Sum a) | Since: base-2.1 |
| Show a => Show (Sum a) | Since: base-2.1 |
| Eq a => Eq (Sum a) | Since: base-2.1 |
| Ord a => Ord (Sum a) | Since: base-2.1 |
| type Rep1 Sum | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep (Sum a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
Monoid under multiplication.
>>>getProduct (Product 3 <> Product 4 <> mempty)12
Constructors
| Product | |
Fields
| |
Instances
| Foldable Product | Since: base-4.8.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => Product m -> m # foldMap :: Monoid m => (a -> m) -> Product a -> m # foldMap' :: Monoid m => (a -> m) -> Product a -> m # foldr :: (a -> b -> b) -> b -> Product a -> b # foldr' :: (a -> b -> b) -> b -> Product a -> b # foldl :: (b -> a -> b) -> b -> Product a -> b # foldl' :: (b -> a -> b) -> b -> Product a -> b # foldr1 :: (a -> a -> a) -> Product a -> a # foldl1 :: (a -> a -> a) -> Product a -> a # elem :: Eq a => a -> Product a -> Bool # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # | |
| Foldable1 Product | Since: base-4.18.0.0 |
Defined in Data.Foldable1 Methods fold1 :: Semigroup m => Product m -> m # foldMap1 :: Semigroup m => (a -> m) -> Product a -> m # foldMap1' :: Semigroup m => (a -> m) -> Product a -> m # toNonEmpty :: Product a -> NonEmpty a # maximum :: Ord a => Product a -> a # minimum :: Ord a => Product a -> a # foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b # foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b # foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b # foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b # | |
| Traversable Product | Since: base-4.8.0.0 |
| Applicative Product | Since: base-4.8.0.0 |
| Functor Product | Since: base-4.8.0.0 |
| Monad Product | Since: base-4.8.0.0 |
| Generic1 Product | |
| Num a => Monoid (Product a) | Since: base-2.1 |
| Num a => Semigroup (Product a) | Since: base-4.9.0.0 |
| Bounded a => Bounded (Product a) | Since: base-2.1 |
| Generic (Product a) | |
| Num a => Num (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| Read a => Read (Product a) | Since: base-2.1 |
| Show a => Show (Product a) | Since: base-2.1 |
| Eq a => Eq (Product a) | Since: base-2.1 |
| Ord a => Ord (Product a) | Since: base-2.1 |
| type Rep1 Product | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
| type Rep (Product a) | Since: base-4.7.0.0 |
Defined in Data.Semigroup.Internal | |
Difference lists of a semigroup
diff :: Semigroup m => m -> Endo m #
This lets you use a difference list of a Semigroup as a Monoid.
Example:
>>>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.
>>>minimum [ Arg (x * x) x | x <- [-10 .. 10] ]Arg 0 0
Constructors
| Arg | |
Instances
| Bifoldable Arg | Since: base-4.10.0.0 |
| Bifoldable1 Arg | |
Defined in Data.Bifoldable1 | |
| Bifunctor Arg | Since: base-4.9.0.0 |
| Bitraversable Arg | Since: base-4.10.0.0 |
Defined in Data.Semigroup Methods bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) # | |
| Generic1 (Arg a :: Type -> Type) | |
| Foldable (Arg a) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods fold :: Monoid m => Arg a m -> m # foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 # elem :: Eq a0 => a0 -> Arg a a0 -> Bool # maximum :: Ord a0 => Arg a a0 -> a0 # minimum :: Ord a0 => Arg a a0 -> a0 # | |
| Traversable (Arg a) | Since: base-4.9.0.0 |
| Functor (Arg a) | Since: base-4.9.0.0 |
| (Data a, Data b) => Data (Arg a b) | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) # toConstr :: Arg a b -> Constr # dataTypeOf :: Arg a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # | |
| Generic (Arg a b) | |
| (Read a, Read b) => Read (Arg a b) | Since: base-4.9.0.0 |
| (Show a, Show b) => Show (Arg a b) | Since: base-4.9.0.0 |
| Eq a => Eq (Arg a b) | Since: base-4.9.0.0 |
| Ord a => Ord (Arg a b) | Since: base-4.9.0.0 |
| type Rep1 (Arg a :: Type -> Type) | Since: base-4.9.0.0 |
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) | Since: base-4.9.0.0 |
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))) | |