| 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.
Examples
>>>[1,2,3] <> [4,5,6][1,2,3,4,5,6]
>>>Just [1, 2, 3] <> Just [4, 5, 6]Just [1,2,3,4,5,6]
>>>putStr "Hello, " <> putStrLn "World!"Hello, World!
Reduce a non-empty list with <>
The default definition should be sufficient, but this can be overridden for efficiency.
Examples
For the following examples, we will assume that we have:
>>>import Data.List.NonEmpty (NonEmpty (..))
>>>sconcat $ "Hello" :| [" ", "Haskell", "!"]"Hello Haskell!"
>>>sconcat $ Just [1, 2, 3] :| [Nothing, Just [4, 5, 6]]Just [1,2,3,4,5,6]
>>>sconcat $ Left 1 :| [Right 2, Left 3, Right 4]Right 2
stimes :: Integral b => b -> a -> a #
Repeat a value n times.
The default definition will raise an exception for a multiplier that is <= 0.
This may be overridden with an implementation that is total. For monoids
it is preferred to use stimesMonoid.
By making this a member of the class, idempotent semigroups
and monoids can upgrade this to execute in \(\mathcal{O}(1)\) by
picking stimes = or stimesIdempotentstimes =
respectively.stimesIdempotentMonoid
Examples
>>>stimes 4 [1][1,1,1,1]
>>>stimes 5 (putStr "hi!")hi!hi!hi!hi!hi!
>>>stimes 3 (Right ":)")Right ":)"
Instances
| Semigroup ByteArray | Since: base-4.17.0.0 |
| Semigroup Void | @since base-4.9.0.0 |
| Semigroup All | @since base-4.9.0.0 |
| Semigroup Any | @since base-4.9.0.0 |
| Semigroup Ordering | @since base-4.9.0.0 |
| Semigroup () | @since base-4.9.0.0 |
| 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 (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 (NonEmpty a) | @since base-4.9.0.0 |
| Semigroup a => Semigroup (STM a) | @since base-4.17.0.0 |
| 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 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 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 |
| (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) | @since base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods (<>) :: Generically a -> Generically a -> Generically a # sconcat :: NonEmpty (Generically a) -> Generically a # stimes :: Integral b => b -> Generically a -> Generically a # | |
| Semigroup p => Semigroup (Par1 p) | @since base-4.12.0.0 |
| 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 (Solo a) | @since base-4.15 |
| Semigroup [a] | @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 (Either a b) | @since base-4.9.0.0 |
| Semigroup (Proxy s) | @since base-4.9.0.0 |
| Semigroup (U1 p) | @since base-4.12.0.0 |
| Semigroup (V1 p) | @since base-4.12.0.0 |
| 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 (f p) => Semigroup (Rec1 f p) | @since base-4.12.0.0 |
| (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 (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | @since base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) | @since base-4.12.0.0 |
| (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 (f (g p)) => Semigroup ((f :.: g) p) | @since base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) | @since base-4.12.0.0 |
| (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, for a stimes 0 aMonoid will produce mempty.
However, there are situations when it cannot do so. In particular,
the following situation is fairly common:
data T a = ... class Constraint1 a class Constraint1 a => Constraint2 a
instance Constraint1 a =>Semigroup(T a) instance Constraint2 a =>Monoid(T a)
Since Constraint1 is insufficient to implement mempty,
stimes for T a cannot do so.
When working with such a type, or when working polymorphically with
Semigroup instances, mtimesDefault should be used when the
multiplier might be zero. It is implemented using stimes when
the multiplier is nonzero and mempty when it is zero.
Examples
>>>mtimesDefault 0 "bark"[]
>>>mtimesDefault 3 "meow""meowmeowmeow"
Semigroups
The Min Monoid and Semigroup always choose the smaller element as
by the Ord instance and min of the contained type.
Examples
>>>Min 42 <> Min 3Min 3
>>>sconcat $ Min 1 :| [ Min n | n <- [2 .. 100]]Min {getMin = 1}
Instances
| 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 # | |||||
| Applicative Min | Since: base-4.9.0.0 | ||||
| Functor Min | Since: base-4.9.0.0 | ||||
| Monad Min | Since: base-4.9.0.0 | ||||
| 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 # | |||||
| Traversable Min | Since: base-4.9.0.0 | ||||
| Generic1 Min | |||||
Defined in Data.Semigroup Associated Types
| |||||
| (Ord a, Bounded a) => Monoid (Min a) | Since: base-4.9.0.0 | ||||
| Ord a => Semigroup (Min a) | Since: base-4.9.0.0 | ||||
| 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) # | |||||
| 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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| 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 | |||||
The Max Monoid and Semigroup always choose the bigger element as
by the Ord instance and max of the contained type.
Examples
>>>Max 42 <> Max 3Max 42
>>>sconcat $ Max 1 :| [ Max n | n <- [2 .. 100]]Max {getMax = 100}
Instances
| 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 # | |||||
| Applicative Max | Since: base-4.9.0.0 | ||||
| Functor Max | Since: base-4.9.0.0 | ||||
| Monad Max | Since: base-4.9.0.0 | ||||
| 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 # | |||||
| Traversable Max | Since: base-4.9.0.0 | ||||
| Generic1 Max | |||||
Defined in Data.Semigroup Associated Types
| |||||
| (Ord a, Bounded a) => Monoid (Max a) | Since: base-4.9.0.0 | ||||
| Ord a => Semigroup (Max a) | Since: base-4.9.0.0 | ||||
| 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) # | |||||
| 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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| 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.
Examples
>>>First 0 <> First 10First 0
>>>sconcat $ First 1 :| [ First n | n <- [2 ..] ]First 1
Instances
| 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 # | |||||
| Applicative First | Since: base-4.9.0.0 | ||||
| Functor First | Since: base-4.9.0.0 | ||||
| Monad First | Since: base-4.9.0.0 | ||||
| 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 # | |||||
| Traversable First | Since: base-4.9.0.0 | ||||
| Generic1 First | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Semigroup (First a) | Since: base-4.9.0.0 | ||||
| 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) # | |||||
| 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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| 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.
Examples
>>>Last 0 <> Last 10Last {getLast = 10}
>>>sconcat $ Last 1 :| [ Last n | n <- [2..]]Last {getLast = * hangs forever *
Instances
| 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 # | |||||
| Applicative Last | Since: base-4.9.0.0 | ||||
| Functor Last | Since: base-4.9.0.0 | ||||
| Monad Last | Since: base-4.9.0.0 | ||||
| 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 # | |||||
| Traversable Last | Since: base-4.9.0.0 | ||||
| Generic1 Last | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Semigroup (Last a) | Since: base-4.9.0.0 | ||||
| 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) # | |||||
| 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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| 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 (<>).
Dual a <> Dual b == Dual (b <> a)
Examples
>>>Dual "Hello" <> Dual "World"Dual {getDual = "WorldHello"}
>>>Dual (Dual "Hello") <> Dual (Dual "World")Dual {getDual = Dual {getDual = "HelloWorld"}}
Instances
| MonadZip Dual | Since: base-4.8.0.0 | ||||
| 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 # | |||||
| Applicative Dual | @since base-4.8.0.0 | ||||
| Functor Dual | @since base-4.8.0.0 | ||||
| Monad Dual | @since base-4.8.0.0 | ||||
| Foldable Dual | @since base-4.8.0.0 | ||||
Defined in GHC.Internal.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 # | |||||
| Traversable Dual | @since base-4.8.0.0 | ||||
| Generic1 Dual | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Monoid a => Monoid (Dual a) | @since base-2.01 | ||||
| Semigroup a => Semigroup (Dual a) | @since base-4.9.0.0 | ||||
| Bounded a => Bounded (Dual a) | @since base-2.01 | ||||
| Generic (Dual a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read a => Read (Dual a) | @since base-2.01 | ||||
| Show a => Show (Dual a) | @since base-2.01 | ||||
| Eq a => Eq (Dual a) | @since base-2.01 | ||||
| Ord a => Ord (Dual a) | @since base-2.01 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Dual | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Dual a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
The monoid of endomorphisms under composition.
Endo f <> Endo g == Endo (f . g)
Examples
>>>let computation = Endo ("Hello, " ++) <> Endo (++ "!")>>>appEndo computation "Haskell""Hello, Haskell!"
>>>let computation = Endo (*3) <> Endo (+1)>>>appEndo computation 16
Instances
| Monoid (Endo a) | @since base-2.01 | ||||
| Semigroup (Endo a) | @since base-4.9.0.0 | ||||
| Generic (Endo a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| type Rep (Endo a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Boolean monoid under conjunction (&&).
All x <> All y = All (x && y)
Examples
>>>All True <> mempty <> All False)All {getAll = False}
>>>mconcat (map (\x -> All (even x)) [2,4,6,7,8])All {getAll = False}
>>>All True <> memptyAll {getAll = True}
Instances
| Monoid All | @since base-2.01 | ||||
| Semigroup All | @since base-4.9.0.0 | ||||
| Bounded All | @since base-2.01 | ||||
| Generic All | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read All | @since base-2.01 | ||||
| Show All | @since base-2.01 | ||||
| Eq All | @since base-2.01 | ||||
| Ord All | @since base-2.01 | ||||
| type Rep All | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Boolean monoid under disjunction (||).
Any x <> Any y = Any (x || y)
Examples
>>>Any True <> mempty <> Any FalseAny {getAny = True}
>>>mconcat (map (\x -> Any (even x)) [2,4,6,7,8])Any {getAny = True}
>>>Any False <> memptyAny {getAny = False}
Instances
| Monoid Any | @since base-2.01 | ||||
| Semigroup Any | @since base-4.9.0.0 | ||||
| Bounded Any | @since base-2.01 | ||||
| Generic Any | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read Any | @since base-2.01 | ||||
| Show Any | @since base-2.01 | ||||
| Eq Any | @since base-2.01 | ||||
| Ord Any | @since base-2.01 | ||||
| type Rep Any | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Monoid under addition.
Sum a <> Sum b = Sum (a + b)
Examples
>>>Sum 1 <> Sum 2 <> memptySum {getSum = 3}
>>>mconcat [ Sum n | n <- [3 .. 9]]Sum {getSum = 42}
Instances
| MonadZip Sum | Since: base-4.8.0.0 | ||||
| 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 # | |||||
| Applicative Sum | @since base-4.8.0.0 | ||||
| Functor Sum | @since base-4.8.0.0 | ||||
| Monad Sum | @since base-4.8.0.0 | ||||
| Foldable Sum | @since base-4.8.0.0 | ||||
Defined in GHC.Internal.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 # | |||||
| Traversable Sum | @since base-4.8.0.0 | ||||
| Generic1 Sum | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Sum a) | @since base-2.01 | ||||
| Num a => Semigroup (Sum a) | @since base-4.9.0.0 | ||||
| Bounded a => Bounded (Sum a) | @since base-2.01 | ||||
| Generic (Sum a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Sum a) | @since base-4.7.0.0 | ||||
| Read a => Read (Sum a) | @since base-2.01 | ||||
| Show a => Show (Sum a) | @since base-2.01 | ||||
| Eq a => Eq (Sum a) | @since base-2.01 | ||||
| Ord a => Ord (Sum a) | @since base-2.01 | ||||
| type Rep1 Sum | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Sum a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Monoid under multiplication.
Product x <> Product y == Product (x * y)
Examples
>>>Product 3 <> Product 4 <> memptyProduct {getProduct = 12}
>>>mconcat [ Product n | n <- [2 .. 10]]Product {getProduct = 3628800}
Constructors
| Product | |
Fields
| |
Instances
| MonadZip Product | Since: base-4.8.0.0 | ||||
| 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 # | |||||
| Applicative Product | @since base-4.8.0.0 | ||||
| Functor Product | @since base-4.8.0.0 | ||||
| Monad Product | @since base-4.8.0.0 | ||||
| Foldable Product | @since base-4.8.0.0 | ||||
Defined in GHC.Internal.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 # | |||||
| Traversable Product | @since base-4.8.0.0 | ||||
| Generic1 Product | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Product a) | @since base-2.01 | ||||
| Num a => Semigroup (Product a) | @since base-4.9.0.0 | ||||
| Bounded a => Bounded (Product a) | @since base-2.01 | ||||
| Generic (Product a) | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Product a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Read a => Read (Product a) | @since base-2.01 | ||||
| Show a => Show (Product a) | @since base-2.01 | ||||
| Eq a => Eq (Product a) | @since base-2.01 | ||||
| Ord a => Ord (Product a) | @since base-2.01 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Product | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Product a) | @since base-4.7.0.0 | ||||
Defined in GHC.Internal.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.
Examples
let hello = diff "Hello, "
>>>appEndo hello "World!""Hello, World!"
>>>appEndo (hello <> mempty) "World!""Hello, World!"
>>>appEndo (mempty <> hello) "World!""Hello, World!"
let world = diff "World" let excl = diff "!"
>>>appEndo (hello <> (world <> excl)) mempty"Hello, World!"
>>>appEndo ((hello <> world) <> excl) mempty"Hello, World!"
ArgMin, ArgMax
Arg isn't itself a Semigroup in its own right, but it can be
placed inside Min and Max to compute an arg min or arg max.
Examples
>>>minimum [ Arg (x * x) x | x <- [-10 .. 10] ]Arg 0 0
>>>maximum [ Arg (-0.2*x^2 + 1.5*x + 1) x | x <- [-10 .. 10] ]Arg 3.8 4.0
>>>minimum [ Arg (-0.2*x^2 + 1.5*x + 1) x | x <- [-10 .. 10] ]Arg (-34.0) (-10.0)
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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Functor (Arg a) | Since: base-4.9.0.0 | ||||
| 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 | ||||
| (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) | |||||
Defined in Data.Semigroup Associated Types
| |||||
| (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))) | |||||