base-4.13.0.0: Basic libraries

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 #

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

Instances should satisfy the following:

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

Since: base-4.9.0.0

Minimal complete definition

(<>)

Methods

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

An associative operation.

sconcat :: NonEmpty a -> a #

Reduce a non-empty list with <>

The default definition should be sufficient, but this can be overridden for efficiency.

stimes :: Integral b => b -> a -> a #

Repeat a value n times.

Given that this works on a Semigroup it is allowed to fail if you request 0 or fewer repetitions, and the default definition will do so.

By making this a member of the class, idempotent semigroups and monoids can upgrade this to execute in O(1) by picking stimes = stimesIdempotent or stimes = stimesIdempotentMonoid respectively.

#### Instances

Instances details
 # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methodsstimes :: Integral b => b -> Ordering -> Ordering # # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: () -> () -> () #sconcat :: NonEmpty () -> () #stimes :: Integral b => b -> () -> () # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Any -> Any -> Any #stimes :: Integral b => b -> Any -> Any # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: All -> All -> All #stimes :: Integral b => b -> All -> All # # Since: base-4.10.0.0 Instance detailsDefined in GHC.Event.Internal Methodsstimes :: Integral b => b -> Lifetime -> Lifetime # # Since: base-4.10.0.0 Instance detailsDefined in GHC.Event.Internal Methods(<>) :: Event -> Event -> Event #stimes :: Integral b => b -> Event -> Event # # Since: base-4.9.0.0 Instance detailsDefined in Data.Void Methods(<>) :: Void -> Void -> Void #stimes :: Integral b => b -> Void -> Void # Semigroup [a] # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: [a] -> [a] -> [a] #sconcat :: NonEmpty [a] -> [a] #stimes :: Integral b => b -> [a] -> [a] # Semigroup a => Semigroup (Maybe a) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: Maybe a -> Maybe a -> Maybe a #sconcat :: NonEmpty (Maybe a) -> Maybe a #stimes :: Integral b => b -> Maybe a -> Maybe a # Semigroup a => Semigroup (IO a) # Since: base-4.10.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: IO a -> IO a -> IO a #sconcat :: NonEmpty (IO a) -> IO a #stimes :: Integral b => b -> IO a -> IO a # Semigroup p => Semigroup (Par1 p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: Par1 p -> Par1 p -> Par1 p #sconcat :: NonEmpty (Par1 p) -> Par1 p #stimes :: Integral b => b -> Par1 p -> Par1 p # # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: NonEmpty a -> NonEmpty a -> NonEmpty a #sconcat :: NonEmpty (NonEmpty a) -> NonEmpty a #stimes :: Integral b => b -> NonEmpty a -> NonEmpty a # Semigroup a => Semigroup (Down a) # Since: base-4.11.0.0 Instance detailsDefined in Data.Ord Methods(<>) :: Down a -> Down a -> Down a #sconcat :: NonEmpty (Down a) -> Down a #stimes :: Integral b => b -> Down a -> Down a # Num a => Semigroup (Product a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Product a -> Product a -> Product a #sconcat :: NonEmpty (Product a) -> Product a #stimes :: Integral b => b -> Product a -> Product a # Num a => Semigroup (Sum a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Sum a -> Sum a -> Sum a #sconcat :: NonEmpty (Sum a) -> Sum a #stimes :: Integral b => b -> Sum a -> Sum a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Endo a -> Endo a -> Endo a #sconcat :: NonEmpty (Endo a) -> Endo a #stimes :: Integral b => b -> Endo a -> Endo a # Semigroup a => Semigroup (Dual a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Dual a -> Dual a -> Dual a #sconcat :: NonEmpty (Dual a) -> Dual a #stimes :: Integral b => b -> Dual a -> Dual a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: Last a -> Last a -> Last a #sconcat :: NonEmpty (Last a) -> Last a #stimes :: Integral b => b -> Last a -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: First a -> First a -> First a #sconcat :: NonEmpty (First a) -> First a #stimes :: Integral b => b -> First a -> First a # Semigroup a => Semigroup (Identity a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Identity Methods(<>) :: Identity a -> Identity a -> Identity a #sconcat :: NonEmpty (Identity a) -> Identity a #stimes :: Integral b => b -> Identity a -> Identity a # Semigroup a => Semigroup (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Option a -> Option a -> Option a #sconcat :: NonEmpty (Option a) -> Option a #stimes :: Integral b => b -> Option a -> Option a # Monoid m => Semigroup (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Last a -> Last a -> Last a #sconcat :: NonEmpty (Last a) -> Last a #stimes :: Integral b => b -> Last a -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: First a -> First a -> First a #sconcat :: NonEmpty (First a) -> First a #stimes :: Integral b => b -> First a -> First a # Ord a => Semigroup (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Max a -> Max a -> Max a #sconcat :: NonEmpty (Max a) -> Max a #stimes :: Integral b => b -> Max a -> Max a # Ord a => Semigroup (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Min a -> Min a -> Min a #sconcat :: NonEmpty (Min a) -> Min a #stimes :: Integral b => b -> Min a -> Min a # # Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Equivalence a -> Equivalence a -> Equivalence a #stimes :: Integral b => b -> Equivalence a -> Equivalence a # # Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Comparison a -> Comparison a -> Comparison a #sconcat :: NonEmpty (Comparison a) -> Comparison a #stimes :: Integral b => b -> Comparison a -> Comparison a # # Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Predicate a -> Predicate a -> Predicate a #sconcat :: NonEmpty (Predicate a) -> Predicate a #stimes :: Integral b => b -> Predicate a -> Predicate a # Semigroup b => Semigroup (a -> b) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a -> b) -> (a -> b) -> a -> b #sconcat :: NonEmpty (a -> b) -> a -> b #stimes :: Integral b0 => b0 -> (a -> b) -> a -> b # Semigroup (Either a b) # Since: base-4.9.0.0 Instance detailsDefined in Data.Either Methods(<>) :: Either a b -> Either a b -> Either a b #sconcat :: NonEmpty (Either a b) -> Either a b #stimes :: Integral b0 => b0 -> Either a b -> Either a b # Semigroup (V1 p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: V1 p -> V1 p -> V1 p #sconcat :: NonEmpty (V1 p) -> V1 p #stimes :: Integral b => b -> V1 p -> V1 p # Semigroup (U1 p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: U1 p -> U1 p -> U1 p #sconcat :: NonEmpty (U1 p) -> U1 p #stimes :: Integral b => b -> U1 p -> U1 p # (Semigroup a, Semigroup b) => Semigroup (a, b) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b) -> (a, b) -> (a, b) #sconcat :: NonEmpty (a, b) -> (a, b) #stimes :: Integral b0 => b0 -> (a, b) -> (a, b) # Semigroup a => Semigroup (ST s a) # Since: base-4.11.0.0 Instance detailsDefined in GHC.ST Methods(<>) :: ST s a -> ST s a -> ST s a #sconcat :: NonEmpty (ST s a) -> ST s a #stimes :: Integral b => b -> ST s a -> ST s a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Proxy Methods(<>) :: Proxy s -> Proxy s -> Proxy s #sconcat :: NonEmpty (Proxy s) -> Proxy s #stimes :: Integral b => b -> Proxy s -> Proxy s # Semigroup a => Semigroup (Op a b) # Instance detailsDefined in Data.Functor.Contravariant Methods(<>) :: Op a b -> Op a b -> Op a b #sconcat :: NonEmpty (Op a b) -> Op a b #stimes :: Integral b0 => b0 -> Op a b -> Op a b # Semigroup (f p) => Semigroup (Rec1 f p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: Rec1 f p -> Rec1 f p -> Rec1 f p #sconcat :: NonEmpty (Rec1 f p) -> Rec1 f p #stimes :: Integral b => b -> Rec1 f p -> Rec1 f p # (Semigroup a, Semigroup b, Semigroup c) => Semigroup (a, b, c) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b, c) -> (a, b, c) -> (a, b, c) #sconcat :: NonEmpty (a, b, c) -> (a, b, c) #stimes :: Integral b0 => b0 -> (a, b, c) -> (a, b, c) # Alternative f => Semigroup (Alt f a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Alt f a -> Alt f a -> Alt f a #sconcat :: NonEmpty (Alt f a) -> Alt f a #stimes :: Integral b => b -> Alt f a -> Alt f a # (Applicative f, Semigroup a) => Semigroup (Ap f a) # Since: base-4.12.0.0 Instance detailsDefined in Data.Monoid Methods(<>) :: Ap f a -> Ap f a -> Ap f a #sconcat :: NonEmpty (Ap f a) -> Ap f a #stimes :: Integral b => b -> Ap f a -> Ap f a # Semigroup a => Semigroup (Const a b) # Since: base-4.9.0.0 Instance detailsDefined in Data.Functor.Const Methods(<>) :: Const a b -> Const a b -> Const a b #sconcat :: NonEmpty (Const a b) -> Const a b #stimes :: Integral b0 => b0 -> Const a b -> Const a b # Semigroup c => Semigroup (K1 i c p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: K1 i c p -> K1 i c p -> K1 i c p #sconcat :: NonEmpty (K1 i c p) -> K1 i c p #stimes :: Integral b => b -> K1 i c p -> K1 i c p # (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p #sconcat :: NonEmpty ((f :*: g) p) -> (f :*: g) p #stimes :: Integral b => b -> (f :*: g) p -> (f :*: g) p # (Semigroup a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d) # Since: base-4.9.0.0 Instance detailsDefined in GHC.Base Methods(<>) :: (a, b, c, d) -> (a, b, c, d) -> (a, b, c, d) #sconcat :: NonEmpty (a, b, c, d) -> (a, b, c, d) #stimes :: Integral b0 => b0 -> (a, b, c, d) -> (a, b, c, d) # Semigroup (f p) => Semigroup (M1 i c f p) # 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 #sconcat :: NonEmpty (M1 i c f p) -> M1 i c f p #stimes :: Integral b => b -> M1 i c f p -> M1 i c f p # Semigroup (f (g p)) => Semigroup ((f :.: g) p) # Since: base-4.12.0.0 Instance detailsDefined in GHC.Generics Methods(<>) :: (f :.: g) p -> (f :.: g) p -> (f :.: g) p #sconcat :: NonEmpty ((f :.: g) p) -> (f :.: g) p #stimes :: Integral b => b -> (f :.: g) p -> (f :.: g) p # (Semigroup a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e) # 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) #sconcat :: NonEmpty (a, b, c, d, e) -> (a, b, c, d, e) #stimes :: Integral b0 => b0 -> (a, b, c, d, e) -> (a, b, c, d, e) #

stimesMonoid :: (Integral b, Monoid a) => b -> a -> a #

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 #

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in O(1) rather than O(log n).

stimesIdempotentMonoid :: (Integral b, Monoid a) => b -> a -> a #

This is a valid definition of stimes for an idempotent Monoid.

When mappend x x = x, this definition should be preferred, because it works in O(1) rather than O(log n)

mtimesDefault :: (Integral b, Monoid a) => b -> a -> a #

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

Implemented using stimes and mempty.

This is a suitable definition for an mtimes member of Monoid.

# Semigroups

newtype Min a #

Constructors

 Min FieldsgetMin :: a

#### Instances

Instances details
 # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Min a -> (a -> Min b) -> Min b #(>>) :: Min a -> Min b -> Min b #return :: a -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Min a -> Min b #(<$) :: a -> Min b -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Min a) -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Min a #(<*>) :: Min (a -> b) -> Min a -> Min b #liftA2 :: (a -> b -> c) -> Min a -> Min b -> Min c #(*>) :: Min a -> Min b -> Min b #(<*) :: Min a -> Min b -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => Min m -> m #foldMap :: Monoid m => (a -> m) -> Min a -> m #foldMap' :: Monoid m => (a -> m) -> Min a -> m #foldr :: (a -> b -> b) -> b -> Min a -> b #foldr' :: (a -> b -> b) -> b -> Min a -> b #foldl :: (b -> a -> b) -> b -> Min a -> b #foldl' :: (b -> a -> b) -> b -> Min a -> b #foldr1 :: (a -> a -> a) -> Min a -> a #foldl1 :: (a -> a -> a) -> Min a -> a #toList :: Min a -> [a] #null :: Min a -> Bool #length :: Min a -> Int #elem :: Eq a => a -> Min a -> Bool #maximum :: Ord a => Min a -> a #minimum :: Ord a => Min a -> a #sum :: Num a => Min a -> a #product :: Num a => Min a -> a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Min a -> f (Min b) #sequenceA :: Applicative f => Min (f a) -> f (Min a) #mapM :: Monad m => (a -> m b) -> Min a -> m (Min b) #sequence :: Monad m => Min (m a) -> m (Min a) # Bounded a => Bounded (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsminBound :: Min a #maxBound :: Min a # Enum a => Enum (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: Min a -> Min a #pred :: Min a -> Min a #toEnum :: Int -> Min a #fromEnum :: Min a -> Int #enumFrom :: Min a -> [Min a] #enumFromThen :: Min a -> Min a -> [Min a] #enumFromTo :: Min a -> Min a -> [Min a] #enumFromThenTo :: Min a -> Min a -> Min a -> [Min a] # Eq a => Eq (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Min a -> Min a -> Bool Source #(/=) :: Min a -> Min a -> Bool Source # Data a => Data (Min a) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a) #toConstr :: Min a -> Constr #dataTypeOf :: Min a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Min a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Min a)) #gmapT :: (forall b. Data b => b -> b) -> Min a -> Min a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Min a -> r #gmapQ :: (forall d. Data d => d -> u) -> Min a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Min a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Min a -> m (Min a) # Num a => Num (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(+) :: Min a -> Min a -> Min a #(-) :: Min a -> Min a -> Min a #(*) :: Min a -> Min a -> Min a #negate :: Min a -> Min a #abs :: Min a -> Min a #signum :: Min a -> Min a # Ord a => Ord (Min a) # 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 # Read a => Read (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Min a) #readList :: ReadS [Min a] #readPrec :: ReadPrec (Min a) # Show a => Show (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Min a -> ShowS #show :: Min a -> String #showList :: [Min a] -> ShowS # Generic (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Min a) :: Type -> Type # Methodsfrom :: Min a -> Rep (Min a) x #to :: Rep (Min a) x -> Min a # Ord a => Semigroup (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Min a -> Min a -> Min a #sconcat :: NonEmpty (Min a) -> Min a #stimes :: Integral b => b -> Min a -> Min a # (Ord a, Bounded a) => Monoid (Min a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmempty :: Min a #mappend :: Min a -> Min a -> Min a #mconcat :: [Min a] -> Min a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Min :: k -> Type # Methodsfrom1 :: forall (a :: k). Min a -> Rep1 Min a #to1 :: forall (a :: k). Rep1 Min a -> Min a # type Rep (Min a) # 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))) type Rep1 Min # 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)) newtype Max a # Constructors  Max FieldsgetMax :: a #### Instances Instances details  # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Max a -> (a -> Max b) -> Max b #(>>) :: Max a -> Max b -> Max b #return :: a -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Max a -> Max b #(<$) :: a -> Max b -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Max a) -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Max a #(<*>) :: Max (a -> b) -> Max a -> Max b #liftA2 :: (a -> b -> c) -> Max a -> Max b -> Max c #(*>) :: Max a -> Max b -> Max b #(<*) :: Max a -> Max b -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => Max m -> m #foldMap :: Monoid m => (a -> m) -> Max a -> m #foldMap' :: Monoid m => (a -> m) -> Max a -> m #foldr :: (a -> b -> b) -> b -> Max a -> b #foldr' :: (a -> b -> b) -> b -> Max a -> b #foldl :: (b -> a -> b) -> b -> Max a -> b #foldl' :: (b -> a -> b) -> b -> Max a -> b #foldr1 :: (a -> a -> a) -> Max a -> a #foldl1 :: (a -> a -> a) -> Max a -> a #toList :: Max a -> [a] #null :: Max a -> Bool #length :: Max a -> Int #elem :: Eq a => a -> Max a -> Bool #maximum :: Ord a => Max a -> a #minimum :: Ord a => Max a -> a #sum :: Num a => Max a -> a #product :: Num a => Max a -> a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Max a -> f (Max b) #sequenceA :: Applicative f => Max (f a) -> f (Max a) #mapM :: Monad m => (a -> m b) -> Max a -> m (Max b) #sequence :: Monad m => Max (m a) -> m (Max a) # Bounded a => Bounded (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsminBound :: Max a #maxBound :: Max a # Enum a => Enum (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: Max a -> Max a #pred :: Max a -> Max a #toEnum :: Int -> Max a #fromEnum :: Max a -> Int #enumFrom :: Max a -> [Max a] #enumFromThen :: Max a -> Max a -> [Max a] #enumFromTo :: Max a -> Max a -> [Max a] #enumFromThenTo :: Max a -> Max a -> Max a -> [Max a] # Eq a => Eq (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Max a -> Max a -> Bool Source #(/=) :: Max a -> Max a -> Bool Source # Data a => Data (Max a) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a) #toConstr :: Max a -> Constr #dataTypeOf :: Max a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Max a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Max a)) #gmapT :: (forall b. Data b => b -> b) -> Max a -> Max a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Max a -> r #gmapQ :: (forall d. Data d => d -> u) -> Max a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Max a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Max a -> m (Max a) # Num a => Num (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(+) :: Max a -> Max a -> Max a #(-) :: Max a -> Max a -> Max a #(*) :: Max a -> Max a -> Max a #negate :: Max a -> Max a #abs :: Max a -> Max a #signum :: Max a -> Max a # Ord a => Ord (Max a) # 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 # Read a => Read (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Max a) #readList :: ReadS [Max a] #readPrec :: ReadPrec (Max a) # Show a => Show (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Max a -> ShowS #show :: Max a -> String #showList :: [Max a] -> ShowS # Generic (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Max a) :: Type -> Type # Methodsfrom :: Max a -> Rep (Max a) x #to :: Rep (Max a) x -> Max a # Ord a => Semigroup (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Max a -> Max a -> Max a #sconcat :: NonEmpty (Max a) -> Max a #stimes :: Integral b => b -> Max a -> Max a # (Ord a, Bounded a) => Monoid (Max a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmempty :: Max a #mappend :: Max a -> Max a -> Max a #mconcat :: [Max a] -> Max a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Max :: k -> Type # Methodsfrom1 :: forall (a :: k). Max a -> Rep1 Max a #to1 :: forall (a :: k). Rep1 Max a -> Max a # type Rep (Max a) # 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))) type Rep1 Max # 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))

newtype First a #

Use Option (First a) to get the behavior of First from Data.Monoid.

Constructors

 First FieldsgetFirst :: a

#### Instances

Instances details
 # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: First a -> (a -> First b) -> First b #(>>) :: First a -> First b -> First b #return :: a -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> First a -> First b #(<$) :: a -> First b -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> First a) -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> First a #(<*>) :: First (a -> b) -> First a -> First b #liftA2 :: (a -> b -> c) -> First a -> First b -> First c #(*>) :: First a -> First b -> First b #(<*) :: First a -> First b -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => First m -> m #foldMap :: Monoid m => (a -> m) -> First a -> m #foldMap' :: Monoid m => (a -> m) -> First a -> m #foldr :: (a -> b -> b) -> b -> First a -> b #foldr' :: (a -> b -> b) -> b -> First a -> b #foldl :: (b -> a -> b) -> b -> First a -> b #foldl' :: (b -> a -> b) -> b -> First a -> b #foldr1 :: (a -> a -> a) -> First a -> a #foldl1 :: (a -> a -> a) -> First a -> a #toList :: First a -> [a] #null :: First a -> Bool #length :: First a -> Int #elem :: Eq a => a -> First a -> Bool #maximum :: Ord a => First a -> a #minimum :: Ord a => First a -> a #sum :: Num a => First a -> a #product :: Num a => First a -> a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> First a -> f (First b) #sequenceA :: Applicative f => First (f a) -> f (First a) #mapM :: Monad m => (a -> m b) -> First a -> m (First b) #sequence :: Monad m => First (m a) -> m (First a) # Bounded a => Bounded (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: First a -> First a #pred :: First a -> First a #toEnum :: Int -> First a #fromEnum :: First a -> Int #enumFrom :: First a -> [First a] #enumFromThen :: First a -> First a -> [First a] #enumFromTo :: First a -> First a -> [First a] #enumFromThenTo :: First a -> First a -> First a -> [First a] # Eq a => Eq (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: First a -> First a -> Bool Source #(/=) :: First a -> First a -> Bool Source # Data a => Data (First a) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a) #toConstr :: First a -> Constr #dataTypeOf :: First a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a)) #gmapT :: (forall b. Data b => b -> b) -> First a -> First a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r #gmapQ :: (forall d. Data d => d -> u) -> First a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a) # Ord a => Ord (First a) # 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 # Read a => Read (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (First a) #readList :: ReadS [First a] # Show a => Show (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> First a -> ShowS #show :: First a -> String #showList :: [First a] -> ShowS # Generic (First a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (First a) :: Type -> Type # Methodsfrom :: First a -> Rep (First a) x #to :: Rep (First a) x -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: First a -> First a -> First a #sconcat :: NonEmpty (First a) -> First a #stimes :: Integral b => b -> First a -> First a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 First :: k -> Type # Methodsfrom1 :: forall (a :: k). First a -> Rep1 First a #to1 :: forall (a :: k). Rep1 First a -> First a # type Rep (First a) # 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))) type Rep1 First # 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)) newtype Last a # Use Option (Last a) to get the behavior of Last from Data.Monoid Constructors  Last FieldsgetLast :: a #### Instances Instances details  # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Last a -> (a -> Last b) -> Last b #(>>) :: Last a -> Last b -> Last b #return :: a -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Last a -> Last b #(<$) :: a -> Last b -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Last a) -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Last a #(<*>) :: Last (a -> b) -> Last a -> Last b #liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c #(*>) :: Last a -> Last b -> Last b #(<*) :: Last a -> Last b -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => Last m -> m #foldMap :: Monoid m => (a -> m) -> Last a -> m #foldMap' :: Monoid m => (a -> m) -> Last a -> m #foldr :: (a -> b -> b) -> b -> Last a -> b #foldr' :: (a -> b -> b) -> b -> Last a -> b #foldl :: (b -> a -> b) -> b -> Last a -> b #foldl' :: (b -> a -> b) -> b -> Last a -> b #foldr1 :: (a -> a -> a) -> Last a -> a #foldl1 :: (a -> a -> a) -> Last a -> a #toList :: Last a -> [a] #null :: Last a -> Bool #length :: Last a -> Int #elem :: Eq a => a -> Last a -> Bool #maximum :: Ord a => Last a -> a #minimum :: Ord a => Last a -> a #sum :: Num a => Last a -> a #product :: Num a => Last a -> a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Last a -> f (Last b) #sequenceA :: Applicative f => Last (f a) -> f (Last a) #mapM :: Monad m => (a -> m b) -> Last a -> m (Last b) #sequence :: Monad m => Last (m a) -> m (Last a) # Bounded a => Bounded (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodssucc :: Last a -> Last a #pred :: Last a -> Last a #toEnum :: Int -> Last a #fromEnum :: Last a -> Int #enumFrom :: Last a -> [Last a] #enumFromThen :: Last a -> Last a -> [Last a] #enumFromTo :: Last a -> Last a -> [Last a] #enumFromThenTo :: Last a -> Last a -> Last a -> [Last a] # Eq a => Eq (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Last a -> Last a -> Bool Source #(/=) :: Last a -> Last a -> Bool Source # Data a => Data (Last a) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a) #toConstr :: Last a -> Constr #dataTypeOf :: Last a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a)) #gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r #gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a) # Ord a => Ord (Last a) # 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 # Read a => Read (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Last a) #readList :: ReadS [Last a] # Show a => Show (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Last a -> ShowS #show :: Last a -> String #showList :: [Last a] -> ShowS # Generic (Last a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Last a) :: Type -> Type # Methodsfrom :: Last a -> Rep (Last a) x #to :: Rep (Last a) x -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Last a -> Last a -> Last a #sconcat :: NonEmpty (Last a) -> Last a #stimes :: Integral b => b -> Last a -> Last a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Last :: k -> Type # Methodsfrom1 :: forall (a :: k). Last a -> Rep1 Last a #to1 :: forall (a :: k). Rep1 Last a -> Last a # type Rep (Last a) # 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))) type Rep1 Last # 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))

newtype WrappedMonoid m #

Provide a Semigroup for an arbitrary Monoid.

NOTE: This is not needed anymore since Semigroup became a superclass of Monoid in base-4.11 and this newtype be deprecated at some point in the future.

Constructors

 WrapMonoid FieldsunwrapMonoid :: m

#### Instances

Instances details
 Bounded m => Bounded (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Enum a => Enum (WrappedMonoid a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsenumFrom :: WrappedMonoid a -> [WrappedMonoid a] #enumFromThen :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #enumFromTo :: WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] #enumFromThenTo :: WrappedMonoid a -> WrappedMonoid a -> WrappedMonoid a -> [WrappedMonoid a] # Eq m => Eq (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Data m => Data (WrappedMonoid m) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (WrappedMonoid m) #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (WrappedMonoid m)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (WrappedMonoid m)) #gmapT :: (forall b. Data b => b -> b) -> WrappedMonoid m -> WrappedMonoid m #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> WrappedMonoid m -> r #gmapQ :: (forall d. Data d => d -> u) -> WrappedMonoid m -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> WrappedMonoid m -> u #gmapM :: Monad m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #gmapMp :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) #gmapMo :: MonadPlus m0 => (forall d. Data d => d -> m0 d) -> WrappedMonoid m -> m0 (WrappedMonoid m) # Ord m => Ord (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source #(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool Source # Read m => Read (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods Show m => Show (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> WrappedMonoid m -> ShowS #show :: WrappedMonoid m -> String #showList :: [WrappedMonoid m] -> ShowS # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (WrappedMonoid m) :: Type -> Type # Methodsfrom :: WrappedMonoid m -> Rep (WrappedMonoid m) x #to :: Rep (WrappedMonoid m) x -> WrappedMonoid m # Monoid m => Semigroup (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m #stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m # Monoid m => Monoid (WrappedMonoid m) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmconcat :: [WrappedMonoid m] -> WrappedMonoid m # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 WrappedMonoid :: k -> Type # Methodsfrom1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a #to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a # type Rep (WrappedMonoid m) # 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))) # 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))

# Re-exported monoids from Data.Monoid

newtype Dual a #

The dual of a Monoid, obtained by swapping the arguments of mappend.

>>> getDual (mappend (Dual "Hello") (Dual "World"))
"WorldHello"


Constructors

 Dual FieldsgetDual :: a

#### Instances

Instances details
 # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Dual a -> (a -> Dual b) -> Dual b #(>>) :: Dual a -> Dual b -> Dual b #return :: a -> Dual a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Dual a -> Dual b #(<$) :: a -> Dual b -> Dual a # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Fix Methodsmfix :: (a -> Dual a) -> Dual a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Dual a #(<*>) :: Dual (a -> b) -> Dual a -> Dual b #liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #(*>) :: Dual a -> Dual b -> Dual b #(<*) :: Dual a -> Dual b -> Dual a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Dual m -> m #foldMap :: Monoid m => (a -> m) -> Dual a -> m #foldMap' :: Monoid m => (a -> m) -> Dual a -> m #foldr :: (a -> b -> b) -> b -> Dual a -> b #foldr' :: (a -> b -> b) -> b -> Dual a -> b #foldl :: (b -> a -> b) -> b -> Dual a -> b #foldl' :: (b -> a -> b) -> b -> Dual a -> b #foldr1 :: (a -> a -> a) -> Dual a -> a #foldl1 :: (a -> a -> a) -> Dual a -> a #toList :: Dual a -> [a] #null :: Dual a -> Bool #length :: Dual a -> Int #elem :: Eq a => a -> Dual a -> Bool #maximum :: Ord a => Dual a -> a #minimum :: Ord a => Dual a -> a #sum :: Num a => Dual a -> a #product :: Num a => Dual a -> a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b) #sequenceA :: Applicative f => Dual (f a) -> f (Dual a) #mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b) #sequence :: Monad m => Dual (m a) -> m (Dual a) # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Zip Methodsmzip :: Dual a -> Dual b -> Dual (a, b) #mzipWith :: (a -> b -> c) -> Dual a -> Dual b -> Dual c #munzip :: Dual (a, b) -> (Dual a, Dual b) # Bounded a => Bounded (Dual a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Eq a => Eq (Dual a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Dual a -> Dual a -> Bool Source #(/=) :: Dual a -> Dual a -> Bool Source # Data a => Data (Dual a) # 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) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Dual a) #toConstr :: Dual a -> Constr #dataTypeOf :: Dual a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Dual a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Dual a)) #gmapT :: (forall b. Data b => b -> b) -> Dual a -> Dual a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Dual a -> r #gmapQ :: (forall d. Data d => d -> u) -> Dual a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Dual a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Dual a -> m (Dual a) # Ord a => Ord (Dual a) # 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 # Read a => Read (Dual a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsreadsPrec :: Int -> ReadS (Dual a) #readList :: ReadS [Dual a] # Show a => Show (Dual a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Dual a -> ShowS #show :: Dual a -> String #showList :: [Dual a] -> ShowS # Generic (Dual a) # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Dual a) :: Type -> Type # Methodsfrom :: Dual a -> Rep (Dual a) x #to :: Rep (Dual a) x -> Dual a # Semigroup a => Semigroup (Dual a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Dual a -> Dual a -> Dual a #sconcat :: NonEmpty (Dual a) -> Dual a #stimes :: Integral b => b -> Dual a -> Dual a # Monoid a => Monoid (Dual a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmempty :: Dual a #mappend :: Dual a -> Dual a -> Dual a #mconcat :: [Dual a] -> Dual a # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep1 Dual :: k -> Type # Methodsfrom1 :: forall (a :: k). Dual a -> Rep1 Dual a #to1 :: forall (a :: k). Rep1 Dual a -> Dual a # type Rep (Dual a) # 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))) type Rep1 Dual # 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)) newtype Endo a # The monoid of endomorphisms under composition. >>> let computation = Endo ("Hello, " ++) <> Endo (++ "!") >>> appEndo computation "Haskell" "Hello, Haskell!"  Constructors  Endo FieldsappEndo :: a -> a #### Instances Instances details  Generic (Endo a) # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Endo a) :: Type -> Type # Methodsfrom :: Endo a -> Rep (Endo a) x #to :: Rep (Endo a) x -> Endo a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Endo a -> Endo a -> Endo a #sconcat :: NonEmpty (Endo a) -> Endo a #stimes :: Integral b => b -> Endo a -> Endo a # Monoid (Endo a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmempty :: Endo a #mappend :: Endo a -> Endo a -> Endo a #mconcat :: [Endo a] -> Endo a # type Rep (Endo a) # 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 # Boolean monoid under conjunction (&&). >>> getAll (All True <> mempty <> All False) False  >>> getAll (mconcat (map (\x -> All (even x)) [2,4,6,7,8])) False  Constructors  All FieldsgetAll :: Bool #### Instances Instances details  # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: All -> All -> Bool Source #(/=) :: All -> All -> Bool 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 #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c All #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c All) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c All) #gmapT :: (forall b. Data b => b -> b) -> All -> All #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> All -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> All -> r #gmapQ :: (forall d. Data d => d -> u) -> All -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> All -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> All -> m All #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> All -> m All # # 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 # # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> All -> ShowS #show :: All -> String #showList :: [All] -> ShowS # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep All :: Type -> Type # Methodsfrom :: All -> Rep All x #to :: Rep All x -> All # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: All -> All -> All #stimes :: Integral b => b -> All -> All # # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: All -> All -> All #mconcat :: [All] -> All # type Rep All # 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 # Boolean monoid under disjunction (||). >>> getAny (Any True <> mempty <> Any False) True  >>> getAny (mconcat (map (\x -> Any (even x)) [2,4,6,7,8])) True  Constructors  Any FieldsgetAny :: Bool #### Instances Instances details  # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Any -> Any -> Bool Source #(/=) :: Any -> Any -> Bool 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 #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c Any #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c Any) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c Any) #gmapT :: (forall b. Data b => b -> b) -> Any -> Any #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Any -> r #gmapQ :: (forall d. Data d => d -> u) -> Any -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Any -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Any -> m Any #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Any -> m Any # # 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 # # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Any -> ShowS #show :: Any -> String #showList :: [Any] -> ShowS # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep Any :: Type -> Type # Methodsfrom :: Any -> Rep Any x #to :: Rep Any x -> Any # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Any -> Any -> Any #stimes :: Integral b => b -> Any -> Any # # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: Any -> Any -> Any #mconcat :: [Any] -> Any # type Rep Any # 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 # Monoid under addition. >>> getSum (Sum 1 <> Sum 2 <> mempty) 3  Constructors  Sum FieldsgetSum :: a #### Instances Instances details  # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Sum a -> (a -> Sum b) -> Sum b #(>>) :: Sum a -> Sum b -> Sum b #return :: a -> Sum a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Sum a -> Sum b #(<$) :: a -> Sum b -> Sum a # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Fix Methodsmfix :: (a -> Sum a) -> Sum a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Sum a #(<*>) :: Sum (a -> b) -> Sum a -> Sum b #liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #(*>) :: Sum a -> Sum b -> Sum b #(<*) :: Sum a -> Sum b -> Sum a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Sum m -> m #foldMap :: Monoid m => (a -> m) -> Sum a -> m #foldMap' :: Monoid m => (a -> m) -> Sum a -> m #foldr :: (a -> b -> b) -> b -> Sum a -> b #foldr' :: (a -> b -> b) -> b -> Sum a -> b #foldl :: (b -> a -> b) -> b -> Sum a -> b #foldl' :: (b -> a -> b) -> b -> Sum a -> b #foldr1 :: (a -> a -> a) -> Sum a -> a #foldl1 :: (a -> a -> a) -> Sum a -> a #toList :: Sum a -> [a] #null :: Sum a -> Bool #length :: Sum a -> Int #elem :: Eq a => a -> Sum a -> Bool #maximum :: Ord a => Sum a -> a #minimum :: Ord a => Sum a -> a #sum :: Num a => Sum a -> a #product :: Num a => Sum a -> a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Sum a -> f (Sum b) #sequenceA :: Applicative f => Sum (f a) -> f (Sum a) #mapM :: Monad m => (a -> m b) -> Sum a -> m (Sum b) #sequence :: Monad m => Sum (m a) -> m (Sum a) # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Zip Methodsmzip :: Sum a -> Sum b -> Sum (a, b) #mzipWith :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #munzip :: Sum (a, b) -> (Sum a, Sum b) # Bounded a => Bounded (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsminBound :: Sum a #maxBound :: Sum a # Eq a => Eq (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Sum a -> Sum a -> Bool Source #(/=) :: Sum a -> Sum a -> Bool Source # Data a => Data (Sum a) # 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) -> Sum a -> c (Sum a) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Sum a) #toConstr :: Sum a -> Constr #dataTypeOf :: Sum a -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Sum a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Sum a)) #gmapT :: (forall b. Data b => b -> b) -> Sum a -> Sum a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Sum a -> r #gmapQ :: (forall d. Data d => d -> u) -> Sum a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Sum a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Sum a -> m (Sum a) # Num a => Num (Sum a) # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(+) :: Sum a -> Sum a -> Sum a #(-) :: Sum a -> Sum a -> Sum a #(*) :: Sum a -> Sum a -> Sum a #negate :: Sum a -> Sum a #abs :: Sum a -> Sum a #signum :: Sum a -> Sum a # Ord a => Ord (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Sum a -> Sum a -> Ordering Source #(<) :: Sum a -> Sum a -> Bool Source #(<=) :: Sum a -> Sum a -> Bool Source #(>) :: Sum a -> Sum a -> Bool Source #(>=) :: Sum a -> Sum a -> Bool Source #max :: Sum a -> Sum a -> Sum a Source #min :: Sum a -> Sum a -> Sum a Source # Read a => Read (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsreadsPrec :: Int -> ReadS (Sum a) #readList :: ReadS [Sum a] #readPrec :: ReadPrec (Sum a) # Show a => Show (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Sum a -> ShowS #show :: Sum a -> String #showList :: [Sum a] -> ShowS # Generic (Sum a) # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Sum a) :: Type -> Type # Methodsfrom :: Sum a -> Rep (Sum a) x #to :: Rep (Sum a) x -> Sum a # Num a => Semigroup (Sum a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Sum a -> Sum a -> Sum a #sconcat :: NonEmpty (Sum a) -> Sum a #stimes :: Integral b => b -> Sum a -> Sum a # Num a => Monoid (Sum a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmempty :: Sum a #mappend :: Sum a -> Sum a -> Sum a #mconcat :: [Sum a] -> Sum a # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep1 Sum :: k -> Type # Methodsfrom1 :: forall (a :: k). Sum a -> Rep1 Sum a #to1 :: forall (a :: k). Rep1 Sum a -> Sum a # type Rep (Sum a) # Instance detailsDefined in Data.Semigroup.Internal type Rep (Sum a) = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) type Rep1 Sum # Instance detailsDefined in Data.Semigroup.Internal type Rep1 Sum = D1 ('MetaData "Sum" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Sum" 'PrefixI 'True) (S1 ('MetaSel ('Just "getSum") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

newtype Product a #

Monoid under multiplication.

>>> getProduct (Product 3 <> Product 4 <> mempty)
12


Constructors

 Product FieldsgetProduct :: a

#### Instances

Instances details
 # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(>>=) :: Product a -> (a -> Product b) -> Product b #(>>) :: Product a -> Product b -> Product b #return :: a -> Product a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodsfmap :: (a -> b) -> Product a -> Product b #(<$) :: a -> Product b -> Product a # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Fix Methodsmfix :: (a -> Product a) -> Product a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Semigroup.Internal Methodspure :: a -> Product a #(<*>) :: Product (a -> b) -> Product a -> Product b #liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c #(*>) :: Product a -> Product b -> Product b #(<*) :: Product a -> Product b -> Product a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Foldable Methodsfold :: Monoid m => Product m -> m #foldMap :: Monoid m => (a -> m) -> Product a -> m #foldMap' :: Monoid m => (a -> m) -> Product a -> m #foldr :: (a -> b -> b) -> b -> Product a -> b #foldr' :: (a -> b -> b) -> b -> Product a -> b #foldl :: (b -> a -> b) -> b -> Product a -> b #foldl' :: (b -> a -> b) -> b -> Product a -> b #foldr1 :: (a -> a -> a) -> Product a -> a #foldl1 :: (a -> a -> a) -> Product a -> a #toList :: Product a -> [a] #null :: Product a -> Bool #length :: Product a -> Int #elem :: Eq a => a -> Product a -> Bool #maximum :: Ord a => Product a -> a #minimum :: Ord a => Product a -> a #sum :: Num a => Product a -> a #product :: Num a => Product a -> a # # Since: base-4.8.0.0 Instance detailsDefined in Data.Traversable Methodstraverse :: Applicative f => (a -> f b) -> Product a -> f (Product b) #sequenceA :: Applicative f => Product (f a) -> f (Product a) #mapM :: Monad m => (a -> m b) -> Product a -> m (Product b) #sequence :: Monad m => Product (m a) -> m (Product a) # # Since: base-4.8.0.0 Instance detailsDefined in Control.Monad.Zip Methodsmzip :: Product a -> Product b -> Product (a, b) #mzipWith :: (a -> b -> c) -> Product a -> Product b -> Product c #munzip :: Product (a, b) -> (Product a, Product b) # Bounded a => Bounded (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods Eq a => Eq (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methods(==) :: Product a -> Product a -> Bool Source #(/=) :: Product a -> Product a -> Bool Source # Data a => Data (Product a) # 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) -> Product a -> c (Product a) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Product a) #toConstr :: Product a -> Constr #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Product a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Product a)) #gmapT :: (forall b. Data b => b -> b) -> Product a -> Product a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Product a -> r #gmapQ :: (forall d. Data d => d -> u) -> Product a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Product a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Product a -> m (Product a) # Num a => Num (Product a) # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(+) :: Product a -> Product a -> Product a #(-) :: Product a -> Product a -> Product a #(*) :: Product a -> Product a -> Product a #negate :: Product a -> Product a #abs :: Product a -> Product a #signum :: Product a -> Product a # Ord a => Ord (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodscompare :: Product a -> Product a -> Ordering Source #(<) :: Product a -> Product a -> Bool Source #(<=) :: Product a -> Product a -> Bool Source #(>) :: Product a -> Product a -> Bool Source #(>=) :: Product a -> Product a -> Bool Source #max :: Product a -> Product a -> Product a Source #min :: Product a -> Product a -> Product a Source # Read a => Read (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsreadsPrec :: Int -> ReadS (Product a) # Show a => Show (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal MethodsshowsPrec :: Int -> Product a -> ShowS #show :: Product a -> String #showList :: [Product a] -> ShowS # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep (Product a) :: Type -> Type # Methodsfrom :: Product a -> Rep (Product a) x #to :: Rep (Product a) x -> Product a # Num a => Semigroup (Product a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup.Internal Methods(<>) :: Product a -> Product a -> Product a #sconcat :: NonEmpty (Product a) -> Product a #stimes :: Integral b => b -> Product a -> Product a # Num a => Monoid (Product a) # Since: base-2.1 Instance detailsDefined in Data.Semigroup.Internal Methodsmappend :: Product a -> Product a -> Product a #mconcat :: [Product a] -> Product a # # Since: base-4.7.0.0 Instance detailsDefined in Data.Semigroup.Internal Associated Typestype Rep1 Product :: k -> Type # Methodsfrom1 :: forall (a :: k). Product a -> Rep1 Product a #to1 :: forall (a :: k). Rep1 Product a -> Product a # type Rep (Product a) # Instance detailsDefined in Data.Semigroup.Internal type Rep (Product a) = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a))) type Rep1 Product # Instance detailsDefined in Data.Semigroup.Internal type Rep1 Product = D1 ('MetaData "Product" "Data.Semigroup.Internal" "base" 'True) (C1 ('MetaCons "Product" 'PrefixI 'True) (S1 ('MetaSel ('Just "getProduct") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1)) # A better monoid for Maybe newtype Option a # Option is effectively Maybe with a better instance of Monoid, built off of an underlying Semigroup instead of an underlying Monoid. Ideally, this type would not exist at all and we would just fix the Monoid instance of Maybe. In GHC 8.4 and higher, the Monoid instance for Maybe has been corrected to lift a Semigroup instance instead of a Monoid instance. Consequently, this type is no longer useful. It will be marked deprecated in GHC 8.8 and removed in GHC 8.10. Constructors  Option FieldsgetOption :: Maybe a #### Instances Instances details  # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(>>=) :: Option a -> (a -> Option b) -> Option b #(>>) :: Option a -> Option b -> Option b #return :: a -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a -> b) -> Option a -> Option b #(<$) :: a -> Option b -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmfix :: (a -> Option a) -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodspure :: a -> Option a #(<*>) :: Option (a -> b) -> Option a -> Option b #liftA2 :: (a -> b -> c) -> Option a -> Option b -> Option c #(*>) :: Option a -> Option b -> Option b #(<*) :: Option a -> Option b -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => Option m -> m #foldMap :: Monoid m => (a -> m) -> Option a -> m #foldMap' :: Monoid m => (a -> m) -> Option a -> m #foldr :: (a -> b -> b) -> b -> Option a -> b #foldr' :: (a -> b -> b) -> b -> Option a -> b #foldl :: (b -> a -> b) -> b -> Option a -> b #foldl' :: (b -> a -> b) -> b -> Option a -> b #foldr1 :: (a -> a -> a) -> Option a -> a #foldl1 :: (a -> a -> a) -> Option a -> a #toList :: Option a -> [a] #null :: Option a -> Bool #length :: Option a -> Int #elem :: Eq a => a -> Option a -> Bool #maximum :: Ord a => Option a -> a #minimum :: Ord a => Option a -> a #sum :: Num a => Option a -> a #product :: Num a => Option a -> a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a -> f b) -> Option a -> f (Option b) #sequenceA :: Applicative f => Option (f a) -> f (Option a) #mapM :: Monad m => (a -> m b) -> Option a -> m (Option b) #sequence :: Monad m => Option (m a) -> m (Option a) # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmzero :: Option a #mplus :: Option a -> Option a -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsempty :: Option a #(<|>) :: Option a -> Option a -> Option a #some :: Option a -> Option [a] #many :: Option a -> Option [a] # Eq a => Eq (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(==) :: Option a -> Option a -> Bool Source #(/=) :: Option a -> Option a -> Bool Source # Data a => Data (Option a) # 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) -> Option a -> c (Option a) #gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Option a) #toConstr :: Option a -> Constr #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Option a)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Option a)) #gmapT :: (forall b. Data b => b -> b) -> Option a -> Option a #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Option a -> r #gmapQ :: (forall d. Data d => d -> u) -> Option a -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Option a -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Option a -> m (Option a) # Ord a => Ord (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodscompare :: Option a -> Option a -> Ordering Source #(<) :: Option a -> Option a -> Bool Source #(<=) :: Option a -> Option a -> Bool Source #(>) :: Option a -> Option a -> Bool Source #(>=) :: Option a -> Option a -> Bool Source #max :: Option a -> Option a -> Option a Source #min :: Option a -> Option a -> Option a Source # Read a => Read (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Option a) #readList :: ReadS [Option a] # Show a => Show (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Option a -> ShowS #show :: Option a -> String #showList :: [Option a] -> ShowS # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Option a) :: Type -> Type # Methodsfrom :: Option a -> Rep (Option a) x #to :: Rep (Option a) x -> Option a # Semigroup a => Semigroup (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methods(<>) :: Option a -> Option a -> Option a #sconcat :: NonEmpty (Option a) -> Option a #stimes :: Integral b => b -> Option a -> Option a # Semigroup a => Monoid (Option a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsmappend :: Option a -> Option a -> Option a #mconcat :: [Option a] -> Option a # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 Option :: k -> Type # Methodsfrom1 :: forall (a :: k). Option a -> Rep1 Option a #to1 :: forall (a :: k). Rep1 Option a -> Option a # type Rep (Option a) # Instance detailsDefined in Data.Semigroup type Rep (Option a) = D1 ('MetaData "Option" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Option" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOption") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Maybe a)))) type Rep1 Option # Instance detailsDefined in Data.Semigroup type Rep1 Option = D1 ('MetaData "Option" "Data.Semigroup" "base" 'True) (C1 ('MetaCons "Option" 'PrefixI 'True) (S1 ('MetaSel ('Just "getOption") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec1 Maybe)))

option :: b -> (a -> b) -> Option a -> b #

Fold an Option case-wise, just like maybe.

# Difference lists of a semigroup

diff :: Semigroup m => m -> Endo m #

This lets you use a difference list of a Semigroup as a Monoid.

cycle1 :: Semigroup m => m -> m #

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

# ArgMin, ArgMax

data Arg a b #

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.

Constructors

 Arg a b

#### Instances

Instances details
 # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsbimap :: (a -> b) -> (c -> d) -> Arg a c -> Arg b d #first :: (a -> b) -> Arg a c -> Arg b c #second :: (b -> c) -> Arg a b -> Arg a c # # Since: base-4.10.0.0 Instance detailsDefined in Data.Semigroup Methodsbifold :: Monoid m => Arg m m -> m #bifoldMap :: Monoid m => (a -> m) -> (b -> m) -> Arg a b -> m #bifoldr :: (a -> c -> c) -> (b -> c -> c) -> c -> Arg a b -> c #bifoldl :: (c -> a -> c) -> (c -> b -> c) -> c -> Arg a b -> c # # 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) # Functor (Arg a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfmap :: (a0 -> b) -> Arg a a0 -> Arg a b #(<\$) :: a0 -> Arg a b -> Arg a a0 # Foldable (Arg a) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodsfold :: Monoid m => Arg a m -> m #foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m #foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m #foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b #foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b #foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b #foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b #foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0 #toList :: Arg a a0 -> [a0] #null :: Arg a a0 -> Bool #length :: Arg a a0 -> Int #elem :: Eq a0 => a0 -> Arg a a0 -> Bool #maximum :: Ord a0 => Arg a a0 -> a0 #minimum :: Ord a0 => Arg a a0 -> a0 #sum :: Num a0 => Arg a a0 -> a0 #product :: Num a0 => Arg a a0 -> a0 # # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Methodstraverse :: Applicative f => (a0 -> f b) -> Arg a a0 -> f (Arg a b) #sequenceA :: Applicative f => Arg a (f a0) -> f (Arg a a0) #mapM :: Monad m => (a0 -> m b) -> Arg a a0 -> m (Arg a b) #sequence :: Monad m => Arg a (m a0) -> m (Arg a a0) # Generic1 (Arg a :: Type -> Type) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep1 (Arg a) :: k -> Type # Methodsfrom1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0 #to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0 # Eq a => Eq (Arg a b) # 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 # (Data a, Data b) => Data (Arg a b) # 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) #gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b) #toConstr :: Arg a b -> Constr #dataTypeOf :: Arg a b -> DataType #dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b)) #dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b)) #gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b #gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r #gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r #gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u] #gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u #gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) #gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b) # Ord a => Ord (Arg a b) # 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 # (Read a, Read b) => Read (Arg a b) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsreadsPrec :: Int -> ReadS (Arg a b) #readList :: ReadS [Arg a b] #readPrec :: ReadPrec (Arg a b) #readListPrec :: ReadPrec [Arg a b] # (Show a, Show b) => Show (Arg a b) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup MethodsshowsPrec :: Int -> Arg a b -> ShowS #show :: Arg a b -> String #showList :: [Arg a b] -> ShowS # Generic (Arg a b) # Since: base-4.9.0.0 Instance detailsDefined in Data.Semigroup Associated Typestype Rep (Arg a b) :: Type -> Type # Methodsfrom :: Arg a b -> Rep (Arg a b) x #to :: Rep (Arg a b) x -> Arg a b # type Rep1 (Arg a :: Type -> Type) # 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) # 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) #

type ArgMax a b = Max (Arg a b) #