base-4.18.2.1: Core data structures and operations

Data.Semigroup

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

Expand

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

Synopsis

# Documentation

class Semigroup a where Source #

The class of semigroups (types with an associative binary operation).

Instances should satisfy the following:

Associativity
x <> (y <> z) = (x <> y) <> z

You can alternatively define sconcat instead of (<>), in which case the laws are:

Unit
sconcat (pure x) = x
Multiplication
sconcat (join xss) = sconcat (fmap sconcat xss)

Since: base-4.9.0.0

Minimal complete definition

Methods

(<>) :: a -> a -> a infixr 6 Source #

An associative operation.

#### Examples

Expand
>>> [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

Expand

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 Expand >>> stimes 4 [1] [1,1,1,1]  >>> stimes 5 (putStr "hi!") hi!hi!hi!hi!hi!  >>> stimes 3 (Right ":)") Right ":)"  #### Instances Instances details  Source # Since: base-4.17.0.0 Instance detailsDefined in Data.Array.Byte Methodsstimes :: Integral b => b -> ByteArray -> ByteArray Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: All -> All -> All Source #stimes :: Integral b => b -> All -> All Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Any -> Any -> Any Source #stimes :: Integral b => b -> Any -> Any Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: Void -> Void -> Void Source #stimes :: Integral b => b -> Void -> Void Source # Source # Since: base-4.10.0.0 Instance detailsDefined in GHC.Event.Internal.Types Methodsstimes :: Integral b => b -> Event -> Event Source # Source # Since: base-4.10.0.0 Instance detailsDefined in GHC.Event.Internal.Types Methodsstimes :: Integral b => b -> Lifetime -> Lifetime Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsstimes :: Integral b => b -> Ordering -> Ordering Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: () -> () -> () Source #sconcat :: NonEmpty () -> () Source #stimes :: Integral b => b -> () -> () Source # Bits a => Semigroup (And a) Source # Since: base-4.16 Instance detailsDefined in Data.Bits Methods(<>) :: And a -> And a -> And a Source #sconcat :: NonEmpty (And a) -> And a Source #stimes :: Integral b => b -> And a -> And a Source # FiniteBits a => Semigroup (Iff a) Source # This constraint is arguably too strong. However, as some types (such as Natural) have undefined complement, this is the only safe choice.Since: base-4.16 Instance detailsDefined in Data.Bits Methods(<>) :: Iff a -> Iff a -> Iff a Source #sconcat :: NonEmpty (Iff a) -> Iff a Source #stimes :: Integral b => b -> Iff a -> Iff a Source # Bits a => Semigroup (Ior a) Source # Since: base-4.16 Instance detailsDefined in Data.Bits Methods(<>) :: Ior a -> Ior a -> Ior a Source #sconcat :: NonEmpty (Ior a) -> Ior a Source #stimes :: Integral b => b -> Ior a -> Ior a Source # Bits a => Semigroup (Xor a) Source # Since: base-4.16 Instance detailsDefined in Data.Bits Methods(<>) :: Xor a -> Xor a -> Xor a Source #sconcat :: NonEmpty (Xor a) -> Xor a Source #stimes :: Integral b => b -> Xor a -> Xor a Source # Source # (<>) on comparisons combines results with (<>) @Ordering. Without newtypes this equals liftA2 (liftA2 (<>)).(<>) :: Comparison a -> Comparison a -> Comparison a Comparison cmp <> Comparison cmp' = Comparison a a' -> cmp a a' <> cmp a a'  Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Comparison a -> Comparison a -> Comparison a Source #stimes :: Integral b => b -> Comparison a -> Comparison a Source # Source # (<>) on equivalences uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (liftA2 (&&)).(<>) :: Equivalence a -> Equivalence a -> Equivalence a Equivalence equiv <> Equivalence equiv' = Equivalence a b -> equiv a b && equiv' a b  Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Equivalence a -> Equivalence a -> Equivalence a Source #stimes :: Integral b => b -> Equivalence a -> Equivalence a Source # Source # (<>) on predicates uses logical conjunction (&&) on the results. Without newtypes this equals liftA2 (&&).(<>) :: Predicate a -> Predicate a -> Predicate a Predicate pred <> Predicate pred' = Predicate a -> pred a && pred' a  Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Predicate a -> Predicate a -> Predicate a Source #stimes :: Integral b => b -> Predicate a -> Predicate a Source # Semigroup a => Semigroup (Identity a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Identity Methods(<>) :: Identity a -> Identity a -> Identity a Source #stimes :: Integral b => b -> Identity a -> Identity a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: First a -> First a -> First a Source #sconcat :: NonEmpty (First a) -> First a Source #stimes :: Integral b => b -> First a -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: Last a -> Last a -> Last a Source #sconcat :: NonEmpty (Last a) -> Last a Source #stimes :: Integral b => b -> Last a -> Last a Source # Semigroup a => Semigroup (Down a) Source # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methods(<>) :: Down a -> Down a -> Down a Source #sconcat :: NonEmpty (Down a) -> Down a Source #stimes :: Integral b => b -> Down a -> Down a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: First a -> First a -> First a Source #sconcat :: NonEmpty (First a) -> First a Source #stimes :: Integral b => b -> First a -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Last a -> Last a -> Last a Source #sconcat :: NonEmpty (Last a) -> Last a Source #stimes :: Integral b => b -> Last a -> Last a Source # Ord a => Semigroup (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Max a -> Max a -> Max a Source #sconcat :: NonEmpty (Max a) -> Max a Source #stimes :: Integral b => b -> Max a -> Max a Source # Ord a => Semigroup (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Min a -> Min a -> Min a Source #sconcat :: NonEmpty (Min a) -> Min a Source #stimes :: Integral b => b -> Min a -> Min a Source # Monoid m => Semigroup (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsstimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # Semigroup a => Semigroup (Dual a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Dual a -> Dual a -> Dual a Source #sconcat :: NonEmpty (Dual a) -> Dual a Source #stimes :: Integral b => b -> Dual a -> Dual a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Endo a -> Endo a -> Endo a Source #sconcat :: NonEmpty (Endo a) -> Endo a Source #stimes :: Integral b => b -> Endo a -> Endo a Source # Num a => Semigroup (Product a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Product a -> Product a -> Product a Source #sconcat :: NonEmpty (Product a) -> Product a Source #stimes :: Integral b => b -> Product a -> Product a Source # Num a => Semigroup (Sum a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Sum a -> Sum a -> Sum a Source #sconcat :: NonEmpty (Sum a) -> Sum a Source #stimes :: Integral b => b -> Sum a -> Sum a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a Source #stimes :: Integral b => b -> NonEmpty a -> NonEmpty a Source # Semigroup a => Semigroup (STM a) Source # Since: base-4.17.0.0 Instance detailsDefined in GHC.Conc.Sync Methods(<>) :: STM a -> STM a -> STM a Source #sconcat :: NonEmpty (STM a) -> STM a Source #stimes :: Integral b => b -> STM a -> STM a Source # (Generic a, Semigroup (Rep a ())) => Semigroup (Generically a) Source # Since: base-4.17.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: Generically a -> 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 Instance detailsDefined in GHC.Generics Methods(<>) :: Par1 p -> Par1 p -> Par1 p Source #sconcat :: NonEmpty (Par1 p) -> Par1 p Source #stimes :: Integral b => b -> Par1 p -> Par1 p Source # Semigroup a => Semigroup (IO a) Source # Since: base-4.10.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: IO a -> IO a -> IO a Source #sconcat :: NonEmpty (IO a) -> IO a Source #stimes :: Integral b => b -> IO a -> IO a Source # Semigroup a => Semigroup (Maybe a) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: Maybe a -> Maybe a -> Maybe a Source #sconcat :: NonEmpty (Maybe a) -> Maybe a Source #stimes :: Integral b => b -> Maybe a -> Maybe a Source # Semigroup a => Semigroup (a) Source # Since: base-4.15 Instance detailsDefined in GHC.Base Methods(<>) :: (a) -> (a) -> (a) Source #sconcat :: NonEmpty (a) -> (a) Source #stimes :: Integral b => b -> (a) -> (a) Source # Semigroup [a] Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: [a] -> [a] -> [a] Source #sconcat :: NonEmpty [a] -> [a] Source #stimes :: Integral b => b -> [a] -> [a] Source # Semigroup (Either a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Either Methods(<>) :: Either a b -> Either a b -> Either a b Source #sconcat :: NonEmpty (Either a b) -> Either a b Source #stimes :: Integral b0 => b0 -> Either a b -> Either a b Source # Semigroup a => Semigroup (Op a b) Source # (<>) @(Op a b) without newtypes is (<>) @(b->a) = liftA2 (<>). This lifts the Semigroup operation (<>) over the output of a.(<>) :: Op a b -> Op a b -> Op a b Op f <> Op g = Op a -> f a <> g a  Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Op a b -> Op a b -> Op a b Source #sconcat :: NonEmpty (Op a b) -> Op a b Source #stimes :: Integral b0 => b0 -> Op a b -> Op a b Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Proxy Methods(<>) :: Proxy s -> Proxy s -> Proxy s Source #sconcat :: NonEmpty (Proxy s) -> Proxy s Source #stimes :: Integral b => b -> Proxy s -> Proxy s Source # Semigroup (U1 p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: U1 p -> U1 p -> U1 p Source #sconcat :: NonEmpty (U1 p) -> U1 p Source #stimes :: Integral b => b -> U1 p -> U1 p Source # Semigroup (V1 p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: V1 p -> V1 p -> V1 p Source #sconcat :: NonEmpty (V1 p) -> V1 p Source #stimes :: Integral b => b -> V1 p -> V1 p Source # Semigroup a => Semigroup (ST s a) Source # Since: base-4.11.0.0 Instance detailsDefined in GHC.ST Methods(<>) :: ST s a -> ST s a -> ST s a Source #sconcat :: NonEmpty (ST s a) -> ST s a Source #stimes :: Integral b => b -> ST s a -> ST s a Source # (Semigroup a, Semigroup b) => Semigroup (a, b) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b) -> (a, b) -> (a, b) Source #sconcat :: NonEmpty (a, b) -> (a, b) Source #stimes :: Integral b0 => b0 -> (a, b) -> (a, b) Source # Semigroup b => Semigroup (a -> b) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a -> b) -> (a -> b) -> a -> b Source #sconcat :: NonEmpty (a -> b) -> a -> b Source #stimes :: Integral b0 => b0 -> (a -> b) -> a -> b Source # Semigroup a => Semigroup (Const a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(<>) :: Const a b -> Const a b -> Const a b Source #sconcat :: NonEmpty (Const a b) -> Const a b Source #stimes :: Integral b0 => b0 -> Const a b -> Const a b Source # (Applicative f, Semigroup a) => Semigroup (Ap f a) Source # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: Ap f a -> Ap f a -> Ap f a Source #sconcat :: NonEmpty (Ap f a) -> Ap f a Source #stimes :: Integral b => b -> Ap f a -> Ap f a Source # Alternative f => Semigroup (Alt f a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Alt f a -> Alt f a -> Alt f a Source #sconcat :: NonEmpty (Alt f a) -> Alt f a Source #stimes :: Integral b => b -> Alt f a -> Alt f a Source # Semigroup (f p) => Semigroup (Rec1 f p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p Source #sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p Source #stimes :: Integral b => b -> Rec1 f p -> Rec1 f p Source # (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) Source #sconcat :: NonEmpty (a, b, c) -> (a, b, c) Source #stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) Source # (Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a) Source # Since: base-4.16.0.0 Instance detailsDefined in Data.Functor.Product Methods(<>) :: Product f g a -> Product f g a -> Product f g a Source #sconcat :: NonEmpty (Product f g a) -> Product f g a Source #stimes :: Integral b => b -> Product f g a -> Product f g a Source # (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p Source #sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p Source #stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p Source # Semigroup c => Semigroup (K1 i c p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: K1 i c p -> K1 i c p -> K1 i c p Source #sconcat :: NonEmpty (K1 i c p) -> K1 i c p Source #stimes :: Integral b => b -> K1 i c p -> K1 i c p Source # (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) Source #sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) Source #stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) Source # Semigroup (f (g a)) => Semigroup (Compose f g a) Source # Since: base-4.16.0.0 Instance detailsDefined in Data.Functor.Compose Methods(<>) :: Compose f g a -> Compose f g a -> Compose f g a Source #sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source #stimes :: Integral b => b -> Compose f g a -> Compose f g a Source # Semigroup (f (g p)) => Semigroup ((f :.: g) p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p Source #sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p Source #stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p Source # Semigroup (f p) => Semigroup (M1 i c f p) Source # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: M1 i c f p -> M1 i c f p -> M1 i c f p Source #sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p Source #stimes :: Integral b => b -> M1 i c f p -> M1 i c f p Source # (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) Source # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b, c, d, e) -> (a, b, c, d, e) -> (a, b, c, d, e) Source #sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) Source #stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) Source # 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 Expand >>> mtimesDefault 0 "bark" []  >>> mtimesDefault 3 "meow" "meowmeowmeow"  # Semigroups newtype Min a Source # The Min Monoid and Semigroup always choose the smaller element as by the Ord instance and min of the contained type. #### Examples Expand >>> Min 42 <> Min 3 Min 3  >>> sconcat$ Min 1 :| [ Min n | n <- [2 .. 100]]
Min {getMin = 1}


Constructors

 Min FieldsgetMin :: a

#### Instances

Instances details
 Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Min a) -> Min a Source # Source # Since: base-4.9.0.0 Instance detailsDefined 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 #toList :: Min a -> [a] Source #null :: Min a -> Bool Source #length :: Min a -> Int Source #elem :: Eq a => a -> Min a -> Bool Source #maximum :: Ord a => Min a -> a Source #minimum :: Ord a => Min a -> a Source #sum :: Num a => Min a -> a Source #product :: Num a => Min a -> a Source # Source # Since: base-4.18.0.0 Instance detailsDefined 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 #head :: Min a -> a Source #last :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) Source #sequenceA :: Applicative f => Min (f a) -> f (Min a) Source #mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) Source #sequence :: Monad m => Min (m a) -> m (Min a) Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Min a Source #(<*>) :: Min (a -> b) -> Min a -> Min b Source #liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c Source #(*>) :: Min a -> Min b -> Min b Source #(<*) :: Min a -> Min b -> Min a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Min a -> Min b Source #(<$) :: a -> Min b -> Min a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Min a -> (a -> Min b) -> Min b Source #(>>) :: Min a -> Min b -> Min b Source #return :: a -> Min a Source # Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Min :: k -> Type Source # Methodsfrom1 :: forall (a :: k). Min a -> Rep1 Min a Source #to1 :: forall (a :: k). Rep1 Min a -> Min a Source # Data a => Data (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 #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 # (Ord a, Bounded a) => Monoid (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmappend :: Min a -> Min a -> Min a Source #mconcat :: [Min a] -> Min a Source # Ord a => Semigroup (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Min a -> Min a -> Min a Source #sconcat :: NonEmpty (Min a) -> Min a Source #stimes :: Integral b => b -> Min a -> Min a Source # Bounded a => Bounded (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: Min a -> Min a Source #pred :: Min a -> Min a Source #toEnum :: Int -> Min a Source #fromEnum :: Min a -> Int Source #enumFrom :: Min a -> [Min a] Source #enumFromThen :: Min a -> Min a -> [Min a] Source #enumFromTo :: Min a -> Min a -> [Min a] Source #enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] Source # Generic (Min a) Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Min a) :: Type -> Type Source # Methodsfrom :: Min a -> Rep (Min a) x Source #to :: Rep (Min a) x -> Min a Source # Num a => Num (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(+) :: Min a -> Min a -> Min a Source #(-) :: Min a -> Min a -> Min a Source #(*) :: Min a -> Min a -> Min a Source #negate :: Min a -> Min a Source #abs :: Min a -> Min a Source #signum :: Min a -> Min a Source # Read a => Read (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Min a) Source # Show a => Show (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Min a -> ShowS Source #show :: Min a -> String Source #showList :: [Min a] -> ShowS Source # Eq a => Eq (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Min a -> Min a -> Bool Source #(/=) :: Min a -> Min a -> Bool Source # Ord a => Ord (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: Min a -> Min a -> Ordering Source #(<) :: Min a -> Min a -> Bool Source #(<=) :: Min a -> Min a -> Bool Source #(>) :: Min a -> Min a -> Bool Source #(>=) :: Min a -> Min a -> Bool Source #max :: Min a -> Min a -> Min a Source #min :: Min a -> Min a -> Min a Source # type Rep1 Min Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep1 Min = D1 ('MetaData "Min" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (Min a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep (Min a) = D1 ('MetaData "Min" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Min" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMin") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) newtype Max a Source # The Max Monoid and Semigroup always choose the bigger element as by the Ord instance and max of the contained type. #### Examples Expand >>> Max 42 <> Max 3 Max 42  >>> sconcat$ Max 1 :| [ Max n | n <- [2 .. 100]]
Max {getMax = 100}


Constructors

 Max FieldsgetMax :: a

#### Instances

Instances details
 Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Max a) -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined 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 #toList :: Max a -> [a] Source #null :: Max a -> Bool Source #length :: Max a -> Int Source #elem :: Eq a => a -> Max a -> Bool Source #maximum :: Ord a => Max a -> a Source #minimum :: Ord a => Max a -> a Source #sum :: Num a => Max a -> a Source #product :: Num a => Max a -> a Source # Source # Since: base-4.18.0.0 Instance detailsDefined 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 #head :: Max a -> a Source #last :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) Source #sequenceA :: Applicative f => Max (f a) -> f (Max a) Source #mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) Source #sequence :: Monad m => Max (m a) -> m (Max a) Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Max a Source #(<*>) :: Max (a -> b) -> Max a -> Max b Source #liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c Source #(*>) :: Max a -> Max b -> Max b Source #(<*) :: Max a -> Max b -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Max a -> Max b Source #(<$) :: a -> Max b -> Max a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Max a -> (a -> Max b) -> Max b Source #(>>) :: Max a -> Max b -> Max b Source #return :: a -> Max a Source # Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Max :: k -> Type Source # Methodsfrom1 :: forall (a :: k). Max a -> Rep1 Max a Source #to1 :: forall (a :: k). Rep1 Max a -> Max a Source # Data a => Data (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 #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 # (Ord a, Bounded a) => Monoid (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmappend :: Max a -> Max a -> Max a Source #mconcat :: [Max a] -> Max a Source # Ord a => Semigroup (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Max a -> Max a -> Max a Source #sconcat :: NonEmpty (Max a) -> Max a Source #stimes :: Integral b => b -> Max a -> Max a Source # Bounded a => Bounded (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: Max a -> Max a Source #pred :: Max a -> Max a Source #toEnum :: Int -> Max a Source #fromEnum :: Max a -> Int Source #enumFrom :: Max a -> [Max a] Source #enumFromThen :: Max a -> Max a -> [Max a] Source #enumFromTo :: Max a -> Max a -> [Max a] Source #enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] Source # Generic (Max a) Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Max a) :: Type -> Type Source # Methodsfrom :: Max a -> Rep (Max a) x Source #to :: Rep (Max a) x -> Max a Source # Num a => Num (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(+) :: Max a -> Max a -> Max a Source #(-) :: Max a -> Max a -> Max a Source #(*) :: Max a -> Max a -> Max a Source #negate :: Max a -> Max a Source #abs :: Max a -> Max a Source #signum :: Max a -> Max a Source # Read a => Read (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Max a) Source # Show a => Show (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Max a -> ShowS Source #show :: Max a -> String Source #showList :: [Max a] -> ShowS Source # Eq a => Eq (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Max a -> Max a -> Bool Source #(/=) :: Max a -> Max a -> Bool Source # Ord a => Ord (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: Max a -> Max a -> Ordering Source #(<) :: Max a -> Max a -> Bool Source #(<=) :: Max a -> Max a -> Bool Source #(>) :: Max a -> Max a -> Bool Source #(>=) :: Max a -> Max a -> Bool Source #max :: Max a -> Max a -> Max a Source #min :: Max a -> Max a -> Max a Source # type Rep1 Max Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep1 Max = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (Max a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep (Max a) = D1 ('MetaData "Max" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Max" 'PrefixI 'True) (S1 ('MetaSel ('Just "getMax") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) newtype First a Source # 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 Expand >>> First 0 <> First 10 First 0  >>> sconcat$ First 1 :| [ First n | n <- [2 ..] ]
First 1


Constructors

 First FieldsgetFirst :: a

#### Instances

Instances details
 Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> First a) -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined 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 #sum :: Num a => First a -> a Source #product :: Num a => First a -> a Source # Source # Since: base-4.18.0.0 Instance detailsDefined 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 #maximum :: Ord a => First a -> a Source #minimum :: Ord a => First a -> a Source #head :: First a -> a Source #last :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> First a -> f (First b) Source #sequenceA :: Applicative f => First (f a) -> f (First a) Source #mapM :: Monad m => (a -> m b) -> First a -> m (First b) Source #sequence :: Monad m => First (m a) -> m (First a) Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> First a Source #(<*>) :: First (a -> b) -> First a -> First b Source #liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #(*>) :: First a -> First b -> First b Source #(<*) :: First a -> First b -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> First a -> First b Source #(<$) :: a -> First b -> First a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: First a -> (a -> First b) -> First b Source #(>>) :: First a -> First b -> First b Source #return :: a -> First a Source # Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 First :: k -> Type Source # Methodsfrom1 :: forall (a :: k). First a -> Rep1 First a Source #to1 :: forall (a :: k). Rep1 First a -> First a Source # Data a => Data (First a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 #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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: First a -> First a -> First a Source #sconcat :: NonEmpty (First a) -> First a Source #stimes :: Integral b => b -> First a -> First a Source # Bounded a => Bounded (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: First a -> First a Source #pred :: First a -> 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 # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (First a) :: Type -> Type Source # Methodsfrom :: First a -> Rep (First a) x Source #to :: Rep (First a) x -> First a Source # Read a => Read (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Show a => Show (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> First a -> ShowS Source #show :: First a -> String Source #showList :: [First a] -> ShowS Source # Eq a => Eq (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: First a -> First a -> Bool Source #(/=) :: First a -> First a -> Bool Source # Ord a => Ord (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: First a -> First a -> Ordering Source #(<) :: First a -> First a -> Bool Source #(<=) :: First a -> First a -> Bool Source #(>) :: First a -> First a -> Bool Source #(>=) :: First a -> First a -> Bool Source #max :: First a -> First a -> First a Source #min :: First a -> First a -> First a Source # type Rep1 First Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep1 First = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (First a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep (First a) = D1 ('MetaData "First" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "First" 'PrefixI 'True) (S1 ('MetaSel ('Just "getFirst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) newtype Last a Source # 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 Expand >>> Last 0 <> Last 10 Last {getLast = 10}  >>> sconcat$ Last 1 :| [ Last n | n <- [2..]]
Last {getLast = * hangs forever *


Constructors

 Last FieldsgetLast :: a

#### Instances

Instances details
 Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Last a) -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined 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 #null :: Last a -> Bool Source #length :: Last a -> Int Source #elem :: Eq a => a -> Last a -> Bool Source #maximum :: Ord a => Last a -> a Source #minimum :: Ord a => Last a -> a Source #sum :: Num a => Last a -> a Source #product :: Num a => Last a -> a Source # Source # Since: base-4.18.0.0 Instance detailsDefined 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 #maximum :: Ord a => Last a -> a Source #minimum :: Ord a => Last a -> a Source #head :: Last a -> a Source #last :: 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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) Source #sequenceA :: Applicative f => Last (f a) -> f (Last a) Source #mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) Source #sequence :: Monad m => Last (m a) -> m (Last a) Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Last a Source #(<*>) :: Last (a -> b) -> Last a -> Last b Source #liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #(*>) :: Last a -> Last b -> Last b Source #(<*) :: Last a -> Last b -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Last a -> Last b Source #(<$) :: a -> Last b -> Last a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Last a -> (a -> Last b) -> Last b Source #(>>) :: Last a -> Last b -> Last b Source #return :: a -> Last a Source # Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Last :: k -> Type Source # Methodsfrom1 :: forall (a :: k). Last a -> Rep1 Last a Source #to1 :: forall (a :: k). Rep1 Last a -> Last a Source # Data a => Data (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 #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 # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Last a -> Last a -> Last a Source #sconcat :: NonEmpty (Last a) -> Last a Source #stimes :: Integral b => b -> Last a -> Last a Source # Bounded a => Bounded (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Last a) :: Type -> Type Source # Methodsfrom :: Last a -> Rep (Last a) x Source #to :: Rep (Last a) x -> Last a Source # Read a => Read (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Last a) Source # Show a => Show (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Last a -> ShowS Source #show :: Last a -> String Source #showList :: [Last a] -> ShowS Source # Eq a => Eq (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Last a -> Last a -> Bool Source #(/=) :: Last a -> Last a -> Bool Source # Ord a => Ord (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: Last a -> Last a -> Ordering Source #(<) :: Last a -> Last a -> Bool Source #(<=) :: Last a -> Last a -> Bool Source #(>) :: Last a -> Last a -> Bool Source #(>=) :: Last a -> Last a -> Bool Source #max :: Last a -> Last a -> Last a Source #min :: Last a -> Last a -> Last a Source # type Rep1 Last Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep1 Last = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (Last a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep (Last a) = D1 ('MetaData "Last" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Last" 'PrefixI 'True) (S1 ('MetaSel ('Just "getLast") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) 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 FieldsunwrapMonoid :: m #### Instances Instances details  Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 WrappedMonoid :: k -> Type Source # Methodsfrom1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a Source #to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a Source # Data m => Data (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> WrappedMonoid m -> c (WrappedMonoid m) Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) Source #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) Source #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) Source #gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m Source #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r Source #gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] Source #gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u Source #gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source #gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) Source # Monoid m => Monoid (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmconcat :: [WrappedMonoid m] -> WrappedMonoid m Source # Monoid m => Semigroup (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsstimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m Source # Bounded m => Bounded (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (WrappedMonoid a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsenumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] Source # Source # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (WrappedMonoid m) :: Type -> Type Source # Methodsfrom :: WrappedMonoid m -> Rep (WrappedMonoid m) x Source #to :: Rep (WrappedMonoid m) x -> WrappedMonoid m Source # Read m => Read (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Show m => Show (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowList :: [WrappedMonoid m] -> ShowS Source # Eq m => Eq (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Ord m => Ord (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep1 WrappedMonoid = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (WrappedMonoid m) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup type Rep (WrappedMonoid m) = D1 ('MetaData "WrappedMonoid" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "WrapMonoid" 'PrefixI 'True) (S1 ('MetaSel ('Just "unwrapMonoid") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 m))) # Re-exported monoids from Data.Monoid newtype Dual a Source # The dual of a Monoid, obtained by swapping the arguments of mappend. | The dual of a Monoid, obtained by swapping the arguments of (<>). Dual a <> Dual b == Dual (b <> a) #### Examples Expand >>> Dual "Hello" <> Dual "World" Dual {getDual = "WorldHello"}  >>> Dual (Dual "Hello") <> Dual (Dual "World") Dual {getDual = Dual {getDual = "HelloWorld"}}  Constructors  Dual FieldsgetDual :: a #### Instances Instances details  Source # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Fix Methodsmfix :: (a -> Dual a) -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Zip Methodsmzip :: Dual a -> Dual b -> Dual (a, b) Source #mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #munzip :: Dual (a, b) -> (Dual a, Dual b) Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Dual m -> m Source #foldMap :: Monoid m => (a -> m) -> Dual a -> m Source #foldMap' :: Monoid m => (a -> m) -> Dual a -> m Source #foldr :: (a -> b -> b) -> b -> Dual a -> b Source #foldr' :: (a -> b -> b) -> b -> Dual a -> b Source #foldl :: (b -> a -> b) -> b -> Dual a -> b Source #foldl' :: (b -> a -> b) -> b -> Dual a -> b Source #foldr1 :: (a -> a -> a) -> Dual a -> a Source #foldl1 :: (a -> a -> a) -> Dual a -> a Source #toList :: Dual a -> [a] Source #null :: Dual a -> Bool Source #length :: Dual a -> Int Source #elem :: Eq a => a -> Dual a -> Bool Source #maximum :: Ord a => Dual a -> a Source #minimum :: Ord a => Dual a -> a Source #sum :: Num a => Dual a -> a Source #product :: Num a => Dual a -> a Source # Source # Since: base-4.18.0.0 Instance detailsDefined 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 #maximum :: Ord a => Dual a -> a Source #minimum :: Ord a => Dual a -> a Source #head :: Dual a -> a Source #last :: 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 # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) Source #sequenceA :: Applicative f => Dual (f a) -> f (Dual a) Source #mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) Source #sequence :: Monad m => Dual (m a) -> m (Dual a) Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Dual a Source #(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source #liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #(*>) :: Dual a -> Dual b -> Dual b Source #(<*) :: Dual a -> Dual b -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b Source #(<$) :: a -> Dual b -> Dual a Source # Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Dual a -> (a -> Dual b) -> Dual b Source #(>>) :: Dual a -> Dual b -> Dual b Source #return :: a -> Dual a Source # Source # Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep1 Dual :: k -> Type Source # Methodsfrom1 :: forall (a :: k). Dual a -> Rep1 Dual a Source #to1 :: forall (a :: k). Rep1 Dual a -> Dual a Source # Data a => Data (Dual a) Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Dual a -> c (Dual a) Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) Source #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 # Monoid a => Monoid (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: Dual a -> Dual a -> Dual a Source #mconcat :: [Dual a] -> Dual a Source # Semigroup a => Semigroup (Dual a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Dual a -> Dual a -> Dual a Source #sconcat :: NonEmpty (Dual a) -> Dual a Source #stimes :: Integral b => b -> Dual a -> Dual a Source # Bounded a => Bounded (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Generic (Dual a) Source # Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Dual a) :: Type -> Type Source # Methodsfrom :: Dual a -> Rep (Dual a) x Source #to :: Rep (Dual a) x -> Dual a Source # Read a => Read (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsreadsPrec :: Int -> ReadS (Dual a) Source # Show a => Show (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Dual a -> ShowS Source #show :: Dual a -> String Source #showList :: [Dual a] -> ShowS Source # Eq a => Eq (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Dual a -> Dual a -> Bool Source #(/=) :: Dual a -> Dual a -> Bool Source # Ord a => Ord (Dual a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Dual a -> Dual a -> Ordering Source #(<) :: Dual a -> Dual a -> Bool Source #(<=) :: Dual a -> Dual a -> Bool Source #(>) :: Dual a -> Dual a -> Bool Source #(>=) :: Dual a -> Dual a -> Bool Source #max :: Dual a -> Dual a -> Dual a Source #min :: Dual a -> Dual a -> Dual a Source # type Rep1 Dual Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal type Rep1 Dual = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) type Rep (Dual a) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal type Rep (Dual a) = D1 ('MetaData "Dual" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Dual" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDual") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Endo a Source #

The monoid of endomorphisms under composition.

Endo f <> Endo g == Endo (f . g)

#### Examples

Expand
>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

>>> let computation = Endo (*3) <> Endo (+1)
>>> appEndo computation 1
6


Constructors

 Endo FieldsappEndo :: a -> a

#### Instances

Instances details
 Monoid (Endo a) Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: Endo a -> Endo a -> Endo a Source #mconcat :: [Endo a] -> Endo a Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Endo a -> Endo a -> Endo a Source #sconcat :: NonEmpty (Endo a) -> Endo a Source #stimes :: Integral b => b -> Endo a -> Endo a Source # Generic (Endo a) Source # Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Endo a) :: Type -> Type Source # Methodsfrom :: Endo a -> Rep (Endo a) x Source #to :: Rep (Endo a) x -> Endo a Source # type Rep (Endo a) Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal type Rep (Endo a) = D1 ('MetaData "Endo" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Endo" 'PrefixI 'True) (S1 ('MetaSel ('Just "appEndo") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a -> a))))

newtype All Source #

Boolean monoid under conjunction (&&).

All x <> All y = All (x && y)

#### Examples

Expand
>>> 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}


Constructors

 All FieldsgetAll :: Bool

#### Instances

Instances details
 Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> All -> c All Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All Source #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 # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: All -> All -> All Source #mconcat :: [All] -> All Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: All -> All -> All Source #stimes :: Integral b => b -> All -> All Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Source # Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep All :: Type -> Type Source # Methodsfrom :: All -> Rep All x Source #to :: Rep All x -> All Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowList :: [All] -> ShowS Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: All -> All -> Bool Source #(/=) :: All -> All -> Bool Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(<) :: All -> All -> Bool Source #(<=) :: All -> All -> Bool Source #(>) :: All -> All -> Bool Source #(>=) :: All -> All -> Bool Source #max :: All -> All -> All Source #min :: All -> All -> All Source # type Rep All Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal type Rep All = D1 ('MetaData "All" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "All" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAll") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Any Source #

Boolean monoid under disjunction (||).

Any x <> Any y = Any (x || y)

#### Examples

Expand
>>> 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}


Constructors

 Any FieldsgetAny :: Bool

#### Instances

Instances details
 Source # Since: base-4.8.0.0 Instance detailsDefined in Data.Data Methodsgfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Any -> c Any Source #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any Source #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 # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: Any -> Any -> Any Source #mconcat :: [Any] -> Any Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Any -> Any -> Any Source #stimes :: Integral b => b -> Any -> Any Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Source # Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep Any :: Type -> Type Source # Methodsfrom :: Any -> Rep Any x Source #to :: Rep Any x -> Any Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowList :: [Any] -> ShowS Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Any -> Any -> Bool Source #(/=) :: Any -> Any -> Bool Source # Source # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(<) :: Any -> Any -> Bool Source #(<=) :: Any -> Any -> Bool Source #(>) :: Any -> Any -> Bool Source #(>=) :: Any -> Any -> Bool Source #max :: Any -> Any -> Any Source #min :: Any -> Any -> Any Source # type Rep Any Source # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal type Rep Any = D1 ('MetaData "Any" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Any" 'PrefixI 'True) (S1 ('MetaSel ('Just "getAny") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Bool)))

newtype Sum a Source #

Sum a <> Sum b = Sum (a + b)

#### Examples

Expand
>>> Sum 1 <> Sum 2 <> mempty
Sum {getSum = 3}

>>> mconcat [ Sum n | n <- [3 .. 9]]
Sum {getSum = 42}


Constructors

 Sum FieldsgetSum :: a

#### Instances

Instances details

# 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

Expand
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.

Expand
>>> 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 data Arg a b Source # 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 Expand >>> 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 FieldsaThe argument used for comparisons in Eq and Ord.bThe "value" exposed via the Functor, Foldable etc. instances. #### Instances Instances details  Source # Since: base-4.10.0.0 Instance detailsDefined in Data.Semigroup Methodsbifold :: Monoid m => Arg m m -> m Source #bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m Source #bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c Source #bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c Source # Source # Instance detailsDefined in Data.Bifoldable1 Methodsbifold1 :: Semigroup m => Arg m m -> m Source #bifoldMap1 :: Semigroup m => (a -> m) -> (b -> m) -> Arg a b -> m Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsbimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d Source #first :: (a -> b) -> Arg a c -> Arg b c Source #second :: (b -> c) -> Arg a b -> Arg a c Source # Source # Since: base-4.10.0.0 Instance detailsDefined 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 # Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 (Arg a) :: k -> Type Source # Methodsfrom1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 Source #to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 Source # Foldable (Arg a) Source # Since: base-4.9.0.0 Instance detailsDefined 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 #sum :: Num a0 => Arg a a0 -> a0 Source #product :: Num a0 => Arg a a0 -> a0 Source # Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) Source #sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) Source #mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) Source #sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) Source # Functor (Arg a) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a0 -> b) -> Arg a a0 -> Arg a b Source #(<$) :: a0 -> Arg a b -> Arg a a0 Source # (Data a, Data b) => Data (Arg a b) Source # Since: base-4.9.0.0 Instance detailsDefined 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 # Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Arg a b) :: Type -> Type Source # Methodsfrom :: Arg a b -> Rep (Arg a b) x Source #to :: Rep (Arg a b) x -> Arg a b Source # (Read a, Read b) => Read (Arg a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Arg a b) Source #readList :: ReadS [Arg a b] Source #readPrec :: ReadPrec (Arg a b) Source # (Show a, Show b) => Show (Arg a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Arg a b -> ShowS Source #show :: Arg a b -> String Source #showList :: [Arg a b] -> ShowS Source # Eq a => Eq (Arg a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Arg a b -> Arg a b -> Bool Source #(/=) :: Arg a b -> Arg a b -> Bool Source # Ord a => Ord (Arg a b) Source # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: Arg a b -> Arg a b -> Ordering Source #(<) :: Arg a b -> Arg a b -> Bool Source #(<=) :: Arg a b -> Arg a b -> Bool Source #(>) :: Arg a b -> Arg a b -> Bool Source #(>=) :: Arg a b -> Arg a b -> Bool Source #max :: Arg a b -> Arg a b -> Arg a b Source #min :: Arg a b -> Arg a b -> Arg a b Source # type Rep1 (Arg a :: Type -> Type) Source # Since: base-4.9.0.0 Instance detailsDefined 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) Source # Since: base-4.9.0.0 Instance detailsDefined 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)))

type ArgMin a b = Min (Arg a b) Source #

#### Examples

Expand
>>> 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

Expand
>>> Max (Arg 0 ()) <> Max (Arg 1 ())
Max {getMax = Arg 1 ()}

>>> maximum [ Arg (length name) name | name <- ["violencia", "lea", "pixie"]]
Arg 9 "violencia"