Data.Semigroup
| Copyright | (C) 2011-2015 Edward Kmett |
|---|---|
| License | BSD-style (see the file LICENSE) |
| Maintainer | libraries@haskell.org |
| Stability | provisional |
| Portability | portable |
| Safe Haskell | Trustworthy |
| Language | Haskell2010 |
Description
A type a is a Semigroup if it provides an associative function (<>) that lets you combine any two values of type a into one. Where being associative means that the following must always hold:
(a <> b) <> c == a <> (b <> c)
Examples
The Min Semigroup instance for Int is defined to always pick the smaller number:
>>> Min 1 <> Min 2 <> Min 3 <> Min 4 :: Min Int
Min {getMin = 1}
If we need to combine multiple values we can use the sconcat function to do so. We need to ensure however that we have at least one value to operate on, since otherwise our result would be undefined. It is for this reason that sconcat uses Data.List.NonEmpty.NonEmpty - a list that can never be empty:
>>> (1 :| []) 1 :| []
- - equivalent to [1] but guaranteed to be non-empty.
>>> (1 :| [2, 3, 4]) 1 :| [2,3,4]
- - equivalent to [1,2,3,4] but guaranteed to be non-empty.
Equipped with this guaranteed to be non-empty data structure, we can combine values using sconcat and a Semigroup of our choosing. We can try the Min and Max instances of Int which pick the smallest, or largest number respectively:
>>> sconcat (1 :| [2, 3, 4]) :: Min Int
Min {getMin = 1}
>>> sconcat (1 :| [2, 3, 4]) :: Max Int
Max {getMax = 4}
String concatenation is another example of a Semigroup instance:
>>> "foo" <> "bar" "foobar"
A Semigroup is a generalization of a Monoid. Yet unlike the Semigroup, the Monoid requires the presence of a neutral element (mempty) in addition to the associative operator. The requirement for a neutral element prevents many types from being a full Monoid, like Data.List.NonEmpty.NonEmpty.
Note that the use of (<>) in this module conflicts with an operator with the same name that is being exported by Data.Monoid. However, this package re-exports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just
import Data.Semigroup
Since: base-4.9.0.0
class Semigroup a where Source
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 Source
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!
sconcat :: NonEmpty a -> a Source
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 Source
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 = stimesIdempotent or stimes =
stimesIdempotentMonoid respectively.
Examples
>>> stimes 4 [1] [1,1,1,1]
>>> stimes 5 (putStr "hi!") hi!hi!hi!hi!hi!
>>> stimes 3 (Right ":)") Right ":)"
Instances
| Semigroup ByteArray Source | Since: base-4.17.0.0 |
| Semigroup Void Source | Since: base-4.9.0.0 |
| Semigroup All Source | Since: base-4.9.0.0 |
| Semigroup Any Source | Since: base-4.9.0.0 |
| Semigroup Event Source | Since: base-4.10.0.0 |
| Semigroup EventLifetime Source | Since: base-4.11.0.0 |
| Semigroup Lifetime Source | Since: base-4.10.0.0 |
| Semigroup ExceptionContext Source | |
Defined in GHC.Internal.Exception.Context Methods(<>) :: ExceptionContext -> ExceptionContext -> ExceptionContext Source sconcat :: NonEmpty ExceptionContext -> ExceptionContext Source stimes :: Integral b => b -> ExceptionContext -> ExceptionContext Source | |
| Semigroup Ordering Source | Since: base-4.9.0.0 |
| Semigroup () Source | Since: base-4.9.0.0 |
| Semigroup (Comparison a) Source |
(<>) :: 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 Source sconcat :: NonEmpty (Comparison a) -> Comparison a Source stimes :: Integral b => b -> Comparison a -> Comparison a Source | |
| Semigroup (Equivalence a) Source |
(<>) :: 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 Source sconcat :: NonEmpty (Equivalence a) -> Equivalence a Source stimes :: Integral b => b -> Equivalence a -> Equivalence a Source | |
| Semigroup (Predicate a) Source |
(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a |
| Semigroup (First a) Source | Since: base-4.9.0.0 |
| Semigroup (Last a) Source | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) Source | Since: base-4.9.0.0 |
| Ord a => Semigroup (Min a) Source | Since: base-4.9.0.0 |
| Monoid m => Semigroup (WrappedMonoid m) Source | Since: base-4.9.0.0 |
Defined in Data.Semigroup Methods(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m Source sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m Source stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source | |
| Semigroup (NonEmpty a) Source | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (STM a) Source | Since: base-4.17.0.0 |
| Bits a => Semigroup (And a) Source | Since: base-4.16 |
| FiniteBits a => Semigroup (Iff a) Source |
This constraint is arguably too strong. However, as some types (such as Since: base-4.16 |
| Bits a => Semigroup (Ior a) Source | Since: base-4.16 |
| Bits a => Semigroup (Xor a) Source | Since: base-4.16 |
| Semigroup a => Semigroup (Identity a) Source | Since: base-4.9.0.0 |
| Ord a => Semigroup (Max a) Source | Since: base-4.11.0.0 |
| Ord a => Semigroup (Min a) Source | Since: base-4.11.0.0 |
| Semigroup (First a) Source | Since: base-4.9.0.0 |
| Semigroup (Last a) Source | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Down a) Source | Since: base-4.11.0.0 |
| Semigroup a => Semigroup (Dual a) Source | Since: base-4.9.0.0 |
| Semigroup (Endo a) Source | Since: base-4.9.0.0 |
| Num a => Semigroup (Product a) Source | Since: base-4.9.0.0 |
| Num a => Semigroup (Sum a) Source | Since: base-4.9.0.0 |
| (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source | Since: base-4.17.0.0 |
Defined in GHC.Internal.Generics Methods(<>) :: Generically a -> Generically a -> Generically a Source sconcat :: NonEmpty (Generically a) -> Generically a Source stimes :: Integral b => b -> Generically a -> Generically a Source | |
| Semigroup p => Semigroup (Par1 p) Source | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (Q a) Source | Since: ghc-internal-2.17.0.0 |
| Semigroup a => Semigroup (IO a) Source | Since: base-4.10.0.0 |
| Semigroup a => Semigroup (Maybe a) Source | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Solo a) Source | Since: base-4.15 |
| Semigroup [a] Source | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Op a b) Source |
(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a |
| Semigroup (Either a b) Source | Since: base-4.9.0.0 |
| Semigroup (Proxy s) Source | Since: base-4.9.0.0 |
| Semigroup (U1 p) Source | Since: base-4.12.0.0 |
| Semigroup (V1 p) Source | Since: base-4.12.0.0 |
| Semigroup a => Semigroup (ST s a) Source | Since: base-4.11.0.0 |
| (Semigroup a, Semigroup b) => Semigroup (a, b) Source | Since: base-4.9.0.0 |
| Semigroup b => Semigroup (a -> b) Source | Since: base-4.9.0.0 |
| Semigroup a => Semigroup (Const a b) Source | Since: base-4.9.0.0 |
| (Applicative f, Semigroup a) => Semigroup (Ap f a) Source | Since: base-4.12.0.0 |
| Alternative f => Semigroup (Alt f a) Source | Since: base-4.9.0.0 |
| Semigroup (f p) => Semigroup (Rec1 f p) Source | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source | Since: base-4.9.0.0 |
| (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source | Since: base-4.16.0.0 |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source | Since: base-4.12.0.0 |
| Semigroup c => Semigroup (K1 i c p) Source | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source | Since: base-4.9.0.0 |
| Semigroup (f (g a)) => Semigroup (Compose f g a) Source | Since: base-4.16.0.0 |
| Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source | Since: base-4.12.0.0 |
| Semigroup (f p) => Semigroup (M1 i c f p) Source | Since: base-4.12.0.0 |
| (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source | Since: base-4.9.0.0 |
stimesMonoid :: (Integral b, Monoid a) => b -> a -> a Source
This is a valid definition of stimes for a Monoid.
Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.
stimesIdempotent :: Integral b => b -> a -> a Source
This is a valid definition of stimes for an idempotent Semigroup.
When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).
stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a Source
This is a valid definition of stimes for an idempotent Monoid.
When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)
mtimesDefault :: (Integral b, Monoid a) => b -> a -> a Source
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.
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 3
Min {getMin = 3}
>>> sconcat $ Min 1 :| [ Min n | n <- [2 .. 100]]
Min {getMin = 1}
Instances
| Foldable1 Min Source | Since: base-4.18.0.0 |
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Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Min m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Min a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Min a -> m Source toNonEmpty :: Min a -> NonEmpty a Source maximum :: Ord a => Min a -> a Source minimum :: Ord a => Min a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Min a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Min a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Min a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Min a -> b Source | |||||
| Applicative Min Source | Since: base-4.9.0.0 |
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| Functor Min Source | Since: base-4.9.0.0 |
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| Monad Min Source | Since: base-4.9.0.0 |
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| MonadFix Min Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| Foldable Min Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsfold :: Monoid m => Min m -> m Source foldMap :: Monoid m => (a -> m) -> Min a -> m Source foldMap' :: Monoid m => (a -> m) -> Min a -> m Source foldr :: (a -> b -> b) -> b -> Min a -> b Source foldr' :: (a -> b -> b) -> b -> Min a -> b Source foldl :: (b -> a -> b) -> b -> Min a -> b Source foldl' :: (b -> a -> b) -> b -> Min a -> b Source foldr1 :: (a -> a -> a) -> Min a -> a Source foldl1 :: (a -> a -> a) -> Min a -> a Source elem :: Eq a => a -> Min a -> Bool Source maximum :: Ord a => Min a -> a Source minimum :: Ord a => Min a -> a Source | |||||
| Traversable Min Source | Since: base-4.9.0.0 |
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| Generic1 Min Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| (Ord a, Bounded a) => Monoid (Min a) Source | Since: base-4.9.0.0 |
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| Ord a => Semigroup (Min a) Source | Since: base-4.9.0.0 |
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| Data a => Data (Min a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) Source toConstr :: Min a -> Constr Source dataTypeOf :: Min a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) Source gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) Source | |||||
| Bounded a => Bounded (Min a) Source | Since: base-4.9.0.0 |
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| Enum a => Enum (Min a) Source | Since: base-4.9.0.0 |
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| Generic (Min a) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Num a => Num (Min a) Source | Since: base-4.9.0.0 |
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| Read a => Read (Min a) Source | Since: base-4.9.0.0 |
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| Show a => Show (Min a) Source | Since: base-4.9.0.0 |
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| Eq a => Eq (Min a) Source | Since: base-4.9.0.0 |
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| Ord a => Ord (Min a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| type Rep1 Min Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| type Rep (Min a) Source | Since: base-4.9.0.0 |
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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 3
Max {getMax = 42}
>>> sconcat $ Max 1 :| [ Max n | n <- [2 .. 100]]
Max {getMax = 100}
Instances
| Foldable1 Max Source | Since: base-4.18.0.0 |
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Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Max m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Max a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Max a -> m Source toNonEmpty :: Max a -> NonEmpty a Source maximum :: Ord a => Max a -> a Source minimum :: Ord a => Max a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Max a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Max a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Max a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Max a -> b Source | |||||
| Applicative Max Source | Since: base-4.9.0.0 |
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| Functor Max Source | Since: base-4.9.0.0 |
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| Monad Max Source | Since: base-4.9.0.0 |
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| MonadFix Max Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| Foldable Max Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsfold :: Monoid m => Max m -> m Source foldMap :: Monoid m => (a -> m) -> Max a -> m Source foldMap' :: Monoid m => (a -> m) -> Max a -> m Source foldr :: (a -> b -> b) -> b -> Max a -> b Source foldr' :: (a -> b -> b) -> b -> Max a -> b Source foldl :: (b -> a -> b) -> b -> Max a -> b Source foldl' :: (b -> a -> b) -> b -> Max a -> b Source foldr1 :: (a -> a -> a) -> Max a -> a Source foldl1 :: (a -> a -> a) -> Max a -> a Source elem :: Eq a => a -> Max a -> Bool Source maximum :: Ord a => Max a -> a Source minimum :: Ord a => Max a -> a Source | |||||
| Traversable Max Source | Since: base-4.9.0.0 |
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| Generic1 Max Source | |||||
Defined in Data.Semigroup Associated Types
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| (Ord a, Bounded a) => Monoid (Max a) Source | Since: base-4.9.0.0 |
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| Ord a => Semigroup (Max a) Source | Since: base-4.9.0.0 |
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| Data a => Data (Max a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a) Source gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) Source toConstr :: Max a -> Constr Source dataTypeOf :: Max a -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) Source gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r Source gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) Source | |||||
| Bounded a => Bounded (Max a) Source | Since: base-4.9.0.0 |
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| Enum a => Enum (Max a) Source | Since: base-4.9.0.0 |
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| Generic (Max a) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Num a => Num (Max a) Source | Since: base-4.9.0.0 |
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| Read a => Read (Max a) Source | Since: base-4.9.0.0 |
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| Show a => Show (Max a) Source | Since: base-4.9.0.0 |
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| Eq a => Eq (Max a) Source | Since: base-4.9.0.0 |
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| Ord a => Ord (Max a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| type Rep1 Max Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| type Rep (Max a) Source | Since: base-4.9.0.0 |
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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 10
First {getFirst = 0}
>>> sconcat $ First 1 :| [ First n | n <- [2 ..] ]
First {getFirst = 1}
Instances
| Foldable1 First Source | Since: base-4.18.0.0 |
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Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => First m -> m Source foldMap1 :: Semigroup m => (a -> m) -> First a -> m Source foldMap1' :: Semigroup m => (a -> m) -> First a -> m Source toNonEmpty :: First a -> NonEmpty a Source maximum :: Ord a => First a -> a Source minimum :: Ord a => First a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> First a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> First a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> First a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> First a -> b Source | |||||
| Applicative First Source | Since: base-4.9.0.0 |
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| Functor First Source | Since: base-4.9.0.0 |
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| Monad First Source | Since: base-4.9.0.0 |
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| MonadFix First Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup | |||||
| Foldable First Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup 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 Source | Since: base-4.9.0.0 |
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| Generic1 First Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Semigroup (First a) Source | Since: base-4.9.0.0 |
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| Data a => Data (First a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup 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 | |||||
| Bounded a => Bounded (First a) Source | Since: base-4.9.0.0 |
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| Enum a => Enum (First a) Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup Methodssucc :: First a -> First a Source pred :: First a -> First a Source toEnum :: Int -> First a Source fromEnum :: First a -> Int Source enumFrom :: First a -> [First a] Source enumFromThen :: First a -> First a -> [First a] Source enumFromTo :: First a -> First a -> [First a] Source enumFromThenTo :: First a -> First a -> First a -> [First a] Source | |||||
| Generic (First a) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Read a => Read (First a) Source | Since: base-4.9.0.0 |
||||
| Show a => Show (First a) Source | Since: base-4.9.0.0 |
||||
| Eq a => Eq (First a) Source | Since: base-4.9.0.0 |
||||
| Ord a => Ord (First a) Source | Since: base-4.9.0.0 |
||||
| type Rep1 First Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup | |||||
| type Rep (First a) Source | 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 10
Last {getLast = 10}
>>> sconcat $ Last 1 :| [ Last n | n <- [2..]] * Hangs forever *
Instances
| Foldable1 Last Source | Since: base-4.18.0.0 |
||||
Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Last m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Last a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Last a -> m Source toNonEmpty :: Last a -> NonEmpty a Source maximum :: Ord a => Last a -> a Source minimum :: Ord a => Last a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Last a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Last a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Last a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Last a -> b Source | |||||
| Applicative Last Source | Since: base-4.9.0.0 |
||||
| Functor Last Source | Since: base-4.9.0.0 |
||||
| Monad Last Source | Since: base-4.9.0.0 |
||||
| MonadFix Last Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup | |||||
| Foldable Last Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup 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 Source | Since: base-4.9.0.0 |
||||
| Generic1 Last Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Semigroup (Last a) Source | Since: base-4.9.0.0 |
||||
| Data a => Data (Last a) Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup 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 | |||||
| Bounded a => Bounded (Last a) Source | Since: base-4.9.0.0 |
||||
| Enum a => Enum (Last a) Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup Methodssucc :: Last a -> Last a Source pred :: Last a -> Last a Source toEnum :: Int -> Last a Source fromEnum :: Last a -> Int Source enumFrom :: Last a -> [Last a] Source enumFromThen :: Last a -> Last a -> [Last a] Source enumFromTo :: Last a -> Last a -> [Last a] Source enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] Source | |||||
| Generic (Last a) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Read a => Read (Last a) Source | Since: base-4.9.0.0 |
||||
| Show a => Show (Last a) Source | Since: base-4.9.0.0 |
||||
| Eq a => Eq (Last a) Source | Since: base-4.9.0.0 |
||||
| Ord a => Ord (Last a) Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup | |||||
| type Rep1 Last Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup | |||||
| type Rep (Last a) Source | Since: base-4.9.0.0 |
||||
Defined in Data.Semigroup | |||||
newtype WrappedMonoid m Source
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
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
| Foldable1 Dual Source | Since: base-4.18.0.0 |
||||
Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Dual m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Dual a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Dual a -> m Source toNonEmpty :: Dual a -> NonEmpty a Source maximum :: Ord a => Dual a -> a Source minimum :: Ord a => Dual a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Dual a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Dual a -> b Source | |||||
| Applicative Dual Source | Since: base-4.8.0.0 |
||||
| Functor Dual Source | Since: base-4.8.0.0 |
||||
| Monad Dual Source | Since: base-4.8.0.0 |
||||
| MonadFix Dual Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.Control.Monad.Fix | |||||
| MonadZip Dual Source | Since: ghc-internal-4.8.0.0 |
||||
| Foldable Dual Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 Source | Since: base-4.8.0.0 |
||||
| Generic1 Dual Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Monoid a => Monoid (Dual a) Source | Since: base-2.1 |
||||
| Semigroup a => Semigroup (Dual a) Source | Since: base-4.9.0.0 |
||||
| Data a => Data (Dual a) Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 | |||||
| Bounded a => Bounded (Dual a) Source | Since: base-2.1 |
||||
| Generic (Dual a) Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read a => Read (Dual a) Source | Since: base-2.1 |
||||
| Show a => Show (Dual a) Source | Since: base-2.1 |
||||
| Eq a => Eq (Dual a) Source | Since: base-2.1 |
||||
| Ord a => Ord (Dual a) Source | Since: base-2.1 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Dual Source | Since: base-4.7.0.0 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Dual a) Source | 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 1 6
Instances
| Monoid (Endo a) Source | Since: base-2.1 |
||||
| Semigroup (Endo a) Source | Since: base-4.9.0.0 |
||||
| Generic (Endo a) Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| type Rep (Endo a) Source | 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 <> mempty
All {getAll = True}
Instances
| Monoid All Source | Since: base-2.1 |
||||
| Semigroup All Source | Since: base-4.9.0.0 |
||||
| Data All Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 | |||||
| Bounded All Source | Since: base-2.1 |
||||
| Generic All Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read All Source | Since: base-2.1 |
||||
| Show All Source | Since: base-2.1 |
||||
| Eq All Source | Since: base-2.1 |
||||
| Ord All Source | Since: base-2.1 |
||||
| type Rep All Source | 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 False
Any {getAny = True}
>>> mconcat (map (\x -> Any (even x)) [2,4,6,7,8])
Any {getAny = True}
>>> Any False <> mempty
Any {getAny = False}
Instances
| Monoid Any Source | Since: base-2.1 |
||||
| Semigroup Any Source | Since: base-4.9.0.0 |
||||
| Data Any Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 | |||||
| Bounded Any Source | Since: base-2.1 |
||||
| Generic Any Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Read Any Source | Since: base-2.1 |
||||
| Show Any Source | Since: base-2.1 |
||||
| Eq Any Source | Since: base-2.1 |
||||
| Ord Any Source | Since: base-2.1 |
||||
| type Rep Any Source | 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 <> mempty
Sum {getSum = 3}
>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}
Instances
| Foldable1 Sum Source | Since: base-4.18.0.0 |
||||
Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Sum m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Sum a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Sum a -> m Source toNonEmpty :: Sum a -> NonEmpty a Source maximum :: Ord a => Sum a -> a Source minimum :: Ord a => Sum a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Sum a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Sum a -> b Source | |||||
| Applicative Sum Source | Since: base-4.8.0.0 |
||||
| Functor Sum Source | Since: base-4.8.0.0 |
||||
| Monad Sum Source | Since: base-4.8.0.0 |
||||
| MonadFix Sum Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.Control.Monad.Fix | |||||
| MonadZip Sum Source | Since: ghc-internal-4.8.0.0 |
||||
| Foldable Sum Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 Source | Since: base-4.8.0.0 |
||||
| Generic1 Sum Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Sum a) Source | Since: base-2.1 |
||||
| Num a => Semigroup (Sum a) Source | Since: base-4.9.0.0 |
||||
| Data a => Data (Sum a) Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 | |||||
| Bounded a => Bounded (Sum a) Source | Since: base-2.1 |
||||
| Generic (Sum a) Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Sum a) Source | Since: base-4.7.0.0 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Read a => Read (Sum a) Source | Since: base-2.1 |
||||
| Show a => Show (Sum a) Source | Since: base-2.1 |
||||
| Eq a => Eq (Sum a) Source | Since: base-2.1 |
||||
| Ord a => Ord (Sum a) Source | Since: base-2.1 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Sum Source | Since: base-4.7.0.0 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Sum a) Source | 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 <> mempty
Product {getProduct = 12}
>>> mconcat [ Product n | n <- [2 .. 10]]
Product {getProduct = 3628800}
Constructors
| Product | |
Fields
| |
Instances
| Foldable1 Product Source | Since: base-4.18.0.0 |
||||
Defined in Data.Foldable1 Methodsfold1 :: Semigroup m => Product m -> m Source foldMap1 :: Semigroup m => (a -> m) -> Product a -> m Source foldMap1' :: Semigroup m => (a -> m) -> Product a -> m Source toNonEmpty :: Product a -> NonEmpty a Source maximum :: Ord a => Product a -> a Source minimum :: Ord a => Product a -> a Source foldrMap1 :: (a -> b) -> (a -> b -> b) -> Product a -> b Source foldlMap1' :: (a -> b) -> (b -> a -> b) -> Product a -> b Source foldlMap1 :: (a -> b) -> (b -> a -> b) -> Product a -> b Source foldrMap1' :: (a -> b) -> (a -> b -> b) -> Product a -> b Source | |||||
| Applicative Product Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| Functor Product Source | Since: base-4.8.0.0 |
||||
| Monad Product Source | Since: base-4.8.0.0 |
||||
| MonadFix Product Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.Control.Monad.Fix | |||||
| MonadZip Product Source | Since: ghc-internal-4.8.0.0 |
||||
| Foldable Product Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.Data.Traversable | |||||
| Generic1 Product Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Monoid (Product a) Source | Since: base-2.1 |
||||
| Num a => Semigroup (Product a) Source | Since: base-4.9.0.0 |
||||
| Data a => Data (Product a) Source | Since: base-4.8.0.0 |
||||
Defined in GHC.Internal.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 | |||||
| Bounded a => Bounded (Product a) Source | Since: base-2.1 |
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| Generic (Product a) Source | |||||
Defined in GHC.Internal.Data.Semigroup.Internal Associated Types
| |||||
| Num a => Num (Product a) Source | Since: base-4.7.0.0 |
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Defined in GHC.Internal.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 | |||||
| Read a => Read (Product a) Source | Since: base-2.1 |
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| Show a => Show (Product a) Source | Since: base-2.1 |
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| Eq a => Eq (Product a) Source | Since: base-2.1 |
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| Ord a => Ord (Product a) Source | Since: base-2.1 |
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Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep1 Product Source | Since: base-4.7.0.0 |
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Defined in GHC.Internal.Data.Semigroup.Internal | |||||
| type Rep (Product a) Source | Since: base-4.7.0.0 |
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Defined in GHC.Internal.Data.Semigroup.Internal | |||||
Difference lists of a semigroup
diff :: Semigroup m => m -> Endo m Source
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!"
cycle1 :: Semigroup m => m -> m Source
A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.
Examples
>>> take 10 $ cycle1 [1, 2, 3] [1,2,3,1,2,3,1,2,3,1]
>>> cycle1 (Right 1) Right 1
>>> cycle1 (Left 1) * Hangs forever *
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. In the event of ties, the leftmost qualifying Arg is chosen; contrast with the behavior of minimum and maximum for many other types, where ties are broken by considering elements to the left in the structure to be less than elements to the right.
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 Source | Since: base-4.10.0.0 |
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| Bifoldable1 Arg Source | |||||
Defined in Data.Bifoldable1 | |||||
| Bifunctor Arg Source | Since: base-4.9.0.0 |
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| Bitraversable Arg Source | Since: base-4.10.0.0 |
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Defined in Data.Semigroup Methodsbitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d) Source | |||||
| Generic1 (Arg a :: Type -> Type) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| Functor (Arg a) Source | Since: base-4.9.0.0 |
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| Foldable (Arg a) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsfold :: Monoid m => Arg a m -> m Source foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m Source foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b Source foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b Source foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 Source toList :: Arg a a0 -> [a0] Source null :: Arg a a0 -> Bool Source length :: Arg a a0 -> Int Source elem :: Eq a0 => a0 -> Arg a a0 -> Bool Source maximum :: Ord a0 => Arg a a0 -> a0 Source minimum :: Ord a0 => Arg a a0 -> a0 Source | |||||
| Traversable (Arg a) Source | Since: base-4.9.0.0 |
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| (Data a, Data b) => Data (Arg a b) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup Methodsgfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b) Source gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) Source toConstr :: Arg a b -> Constr Source dataTypeOf :: Arg a b -> DataType Source dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) Source dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) Source gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b Source gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r Source gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] Source gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u Source gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) Source | |||||
| Generic (Arg a b) Source | |||||
Defined in Data.Semigroup Associated Types
| |||||
| (Read a, Read b) => Read (Arg a b) Source | Since: base-4.9.0.0 |
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| (Show a, Show b) => Show (Arg a b) Source | Since: base-4.9.0.0 |
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| Eq a => Eq (Arg a b) Source |
Note that >>> Arg 0 0 == Arg 0 1 True >>> let f (Arg _ x) = x in f (Arg 0 0) == f (Arg 0 1) False Since: base-4.9.0.0 |
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| Ord a => Ord (Arg a b) Source |
Note that Since: base-4.9.0.0 |
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| type Rep1 (Arg a :: Type -> Type) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-8e62" '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) Source | Since: base-4.9.0.0 |
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Defined in Data.Semigroup type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base-4.21.0.0-8e62" '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))) | |||||
type ArgMin a b = Min (Arg a b) Source
Examples
>>> Min (Arg 0 ()) <> Min (Arg 1 ())
Min {getMin = Arg 0 ()}
>>> minimum [ Arg (length name) name | name <- ["violencia", "lea", "pixie"]] Arg 3 "lea"
type ArgMax a b = Max (Arg a b) Source
Examples
>>> Max (Arg 0 ()) <> Max (Arg 1 ())
Max {getMax = Arg 1 ()}
>>> maximum [ Arg (length name) name | name <- ["violencia", "lea", "pixie"]] Arg 9 "violencia"
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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/Data-Semigroup.html