Data.Semigroup

A type a is a Semigroup if it provides an associative function (<>) that lets you combine any two values of type a into one. Where being associative means that the following must always hold:

(a <> b) <> c == a <> (b <> c)

Examples

The Min Semigroup instance for Int is defined to always pick the smaller number: >>> Min 1 <> Min 2 <> Min 3 <> Min 4 :: Min Int Min {getMin = 1}

If we need to combine multiple values we can use the sconcat function to do so. We need to ensure however that we have at least one value to operate on, since otherwise our result would be undefined. It is for this reason that sconcat uses Data.List.NonEmpty.NonEmpty - a list that can never be empty:

>>> (1 :| [])
1 :| []               -- equivalent to [1] but guaranteed to be non-empty.

>>> (1 :| [2, 3, 4])
1 :| [2,3,4]          -- equivalent to [1,2,3,4] but guaranteed to be non-empty.

Equipped with this guaranteed to be non-empty data structure, we can combine values using sconcat and a Semigroup of our choosing. We can try the Min and Max instances of Int which pick the smallest, or largest number respectively:

>>> sconcat (1 :| [2, 3, 4]) :: Min Int
Min {getMin = 1}
>>> sconcat (1 :| [2, 3, 4]) :: Max Int
Max {getMax = 4}

String concatenation is another example of a Semigroup instance:

>>> "foo" <> "bar"
"foobar"

A Semigroup is a generalization of a Monoid. Yet unlike the Semigroup, the Monoid requires the presence of a neutral element (mempty) in addition to the associative operator. The requirement for a neutral element prevents many types from being a full Monoid, like Data.List.NonEmpty.NonEmpty.

Note that the use of (<>) in this module conflicts with an operator with the same name that is being exported by Data.Monoid. However, this package re-exports (most of) the contents of Data.Monoid, so to use semigroups and monoids in the same package just

import Data.Semigroup

Since: base-4.9.0.0

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.

>>> [1,2,3] <> [4,5,6]
[1,2,3,4,5,6]

sconcat :: NonEmpty a -> a

Reduce a non-empty list with <>

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

>>> import Data.List.NonEmpty (NonEmpty (..))
>>> sconcat $ "Hello" :| [" ", "Haskell", "!"]
"Hello Haskell!"

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

Repeat a value n times.

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

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

>>> stimes 4 [1]
[1,1,1,1]

Instances

Semigroup ByteArray

Since: base-4.17.0.0

Defined in Data.Array.Byte

Methods

(<>) :: ByteArray -> ByteArray -> ByteArray

sconcat :: NonEmpty ByteArray -> ByteArray

stimes :: Integral b => b -> ByteArray -> ByteArray

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Semigroup Void

Since: base-4.9.0.0

Defined in Data.Void

Methods

(<>) :: Void -> Void -> Void

sconcat :: NonEmpty Void -> Void

stimes :: Integral b => b -> Void -> Void

Semigroup Event

Since: base-4.10.0.0

Defined in GHC.Event.Internal.Types

Methods

(<>) :: Event -> Event -> Event

sconcat :: NonEmpty Event -> Event

stimes :: Integral b => b -> Event -> Event

Semigroup Lifetime

Since: base-4.10.0.0

Defined in GHC.Event.Internal.Types

Methods

(<>) :: Lifetime -> Lifetime -> Lifetime

sconcat :: NonEmpty Lifetime -> Lifetime

stimes :: Integral b => b -> Lifetime -> Lifetime

Semigroup Ordering

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: Ordering -> Ordering -> Ordering

sconcat :: NonEmpty Ordering -> Ordering

stimes :: Integral b => b -> Ordering -> Ordering

Semigroup ()

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: () -> () -> ()

sconcat :: NonEmpty () -> ()

stimes :: Integral b => b -> () -> ()

Bits a => Semigroup (And a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: And a -> And a -> And a

sconcat :: NonEmpty (And a) -> And a

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

FiniteBits a => Semigroup (Iff a)

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

Defined in Data.Bits

Methods

(<>) :: Iff a -> Iff a -> Iff a

sconcat :: NonEmpty (Iff a) -> Iff a

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

Bits a => Semigroup (Ior a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Ior a -> Ior a -> Ior a

sconcat :: NonEmpty (Ior a) -> Ior a

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

Bits a => Semigroup (Xor a)

Since: base-4.16

Defined in Data.Bits

Methods

(<>) :: Xor a -> Xor a -> Xor a

sconcat :: NonEmpty (Xor a) -> Xor a

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

Semigroup (Comparison a)

(<>) 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'

Defined in Data.Functor.Contravariant

Methods

(<>) :: Comparison a -> Comparison a -> Comparison a

sconcat :: NonEmpty (Comparison a) -> Comparison a

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

Semigroup (Equivalence a)

(<>) 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

Defined in Data.Functor.Contravariant

Methods

(<>) :: Equivalence a -> Equivalence a -> Equivalence a

sconcat :: NonEmpty (Equivalence a) -> Equivalence a

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

Semigroup (Predicate a)

(<>) 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

Defined 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 a => Semigroup (Identity a)

Since: base-4.9.0.0

Defined 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 (First a)

Since: base-4.9.0.0

Defined 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 (Last a)

Since: base-4.9.0.0

Defined in Data.Monoid

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

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

Semigroup a => Semigroup (Down a)

Since: base-4.11.0.0

Defined in Data.Ord

Methods

(<>) :: Down a -> Down a -> Down a

sconcat :: NonEmpty (Down a) -> Down a

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

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

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

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

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

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined 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

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

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

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined 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

Semigroup (Endo a)

Since: base-4.9.0.0

Defined 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

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined 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

Defined 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

Semigroup a => Semigroup (STM a)

Since: base-4.17.0.0

Defined in GHC.Conc.Sync

Methods

(<>) :: STM a -> STM a -> STM a

sconcat :: NonEmpty (STM a) -> STM a

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

(Generic a, Semigroup (Rep a ())) => Semigroup (Generically a)

Since: base-4.17.0.0

Defined in GHC.Generics

Methods

(<>) :: Generically a -> Generically a -> Generically a

sconcat :: NonEmpty (Generically a) -> Generically a

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

Semigroup p => Semigroup (Par1 p)

Since: base-4.12.0.0

Defined in GHC.Generics

Methods

(<>) :: Par1 p -> Par1 p -> Par1 p

sconcat :: NonEmpty (Par1 p) -> Par1 p

stimes :: Integral b => b -> Par1 p -> Par1 p

Semigroup a => Semigroup (IO a)

Since: base-4.10.0.0

Defined 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 (NonEmpty a)

Since: base-4.9.0.0

Defined 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 (Maybe a)

Since: base-4.9.0.0

Defined 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 (a)

Since: base-4.15

Defined in GHC.Base

Methods

(<>) :: (a) -> (a) -> (a)

sconcat :: NonEmpty (a) -> (a)

stimes :: Integral b => b -> (a) -> (a)

Semigroup [a]

Since: base-4.9.0.0

Defined in GHC.Base

Methods

(<>) :: [a] -> [a] -> [a]

sconcat :: NonEmpty [a] -> [a]

stimes :: Integral b => b -> [a] -> [a]

Semigroup (Either a b)

Since: base-4.9.0.0

Defined 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 a => Semigroup (Op a b)

(<>) @(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

Defined 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 (Proxy s)

Since: base-4.9.0.0

Defined 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 (U1 p)

Since: base-4.12.0.0

Defined 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 (V1 p)

Since: base-4.12.0.0

Defined 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 a => Semigroup (ST s a)

Since: base-4.11.0.0

Defined 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

Semigroup b => Semigroup (a -> b)

Since: base-4.9.0.0

Defined 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 b) => Semigroup (a, b)

Since: base-4.9.0.0

Defined 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 (Const a b)

Since: base-4.9.0.0

Defined 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

(Applicative f, Semigroup a) => Semigroup (Ap f a)

Since: base-4.12.0.0

Defined 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

Alternative f => Semigroup (Alt f a)

Since: base-4.9.0.0

Defined 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

Semigroup (f p) => Semigroup (Rec1 f p)

Since: base-4.12.0.0

Defined 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

Defined 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)

(Semigroup (f a), Semigroup (g a)) => Semigroup (Product f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Product

Methods

(<>) :: Product f g a -> Product f g a -> Product f g a

sconcat :: NonEmpty (Product f g a) -> Product f g a

stimes :: Integral b => b -> Product f g a -> Product f g a

(Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p)

Since: base-4.12.0.0

Defined 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 c => Semigroup (K1 i c p)

Since: base-4.12.0.0

Defined 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 a, Semigroup b, Semigroup c, Semigroup d) => Semigroup (a, b, c, d)

Since: base-4.9.0.0

Defined 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 (g a)) => Semigroup (Compose f g a)

Since: base-4.16.0.0

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a

sconcat :: NonEmpty (Compose f g a) -> Compose f g a

stimes :: Integral b => b -> Compose f g a -> Compose f g a

Semigroup (f (g p)) => Semigroup ((f :.: g) p)

Since: base-4.12.0.0

Defined 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 (f p) => Semigroup (M1 i c f p)

Since: base-4.12.0.0

Defined 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 a, Semigroup b, Semigroup c, Semigroup d, Semigroup e) => Semigroup (a, b, c, d, e)

Since: base-4.9.0.0

Defined 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 \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

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 \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

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

Repeat a value n times.

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

In many cases, `stimes 0 a` for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a) instance Constraint2 a => Monoid (T a) @

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

Semigroups

newtype Min a

Constructors

Min

Fields

• getMin :: a

Instances

MonadFix Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mfix :: (a -> Min a) -> Min a

Foldable Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Min m -> m

foldMap :: Monoid m => (a -> m) -> Min a -> m

foldMap' :: Monoid m => (a -> m) -> Min a -> m

foldr :: (a -> b -> b) -> b -> Min a -> b

foldr' :: (a -> b -> b) -> b -> Min a -> b

foldl :: (b -> a -> b) -> b -> Min a -> b

foldl' :: (b -> a -> b) -> b -> Min a -> b

foldr1 :: (a -> a -> a) -> Min a -> a

foldl1 :: (a -> a -> a) -> Min a -> a

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

Traversable Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: 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)

Applicative Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: 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

Functor Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Min a -> Min b

(<$) :: a -> Min b -> Min a

Monad Min

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Min a -> (a -> Min b) -> Min b

(>>) :: Min a -> Min b -> Min b

return :: a -> Min a

Generic1 Min

Defined in Data.Semigroup

Associated Types

type Rep1 Min :: k -> Type

Methods

from1 :: forall (a :: k). Min a -> Rep1 Min a

to1 :: forall (a :: k). Rep1 Min a -> Min a

Data a => Data (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Min a -> c (Min a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Min a)

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)

(Ord a, Bounded a) => Monoid (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Min a

mappend :: Min a -> Min a -> Min a

mconcat :: [Min a] -> Min a

Ord a => Semigroup (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Min a -> Min a -> Min a

sconcat :: NonEmpty (Min a) -> Min a

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

Bounded a => Bounded (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: Min a

maxBound :: Min a

Enum a => Enum (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: 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]

Generic (Min a)

Defined in Data.Semigroup

Associated Types

type Rep (Min a) :: Type -> Type

Methods

from :: Min a -> Rep (Min a) x

to :: Rep (Min a) x -> Min a

Num a => Num (Min a)

Since: base-4.9.0.0

Defined 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

fromInteger :: Integer -> Min a

Read a => Read (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Min a)

readList :: ReadS [Min a]

readPrec :: ReadPrec (Min a)

readListPrec :: ReadPrec [Min a]

Show a => Show (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Min a -> ShowS

show :: Min a -> String

showList :: [Min a] -> ShowS

Eq a => Eq (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Min a -> Min a -> Bool

(/=) :: Min a -> Min a -> Bool

Ord a => Ord (Min a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: Min a -> Min a -> Ordering

(<) :: Min a -> Min a -> Bool

(<=) :: Min a -> Min a -> Bool

(>) :: Min a -> Min a -> Bool

(>=) :: Min a -> Min a -> Bool

max :: Min a -> Min a -> Min a

min :: Min a -> Min a -> Min a

type Rep1 Min

Since: base-4.9.0.0

Defined 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)

Since: base-4.9.0.0

Defined 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

Constructors

Max

Fields

• getMax :: a

Instances

MonadFix Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mfix :: (a -> Max a) -> Max a

Foldable Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Max m -> m

foldMap :: Monoid m => (a -> m) -> Max a -> m

foldMap' :: Monoid m => (a -> m) -> Max a -> m

foldr :: (a -> b -> b) -> b -> Max a -> b

foldr' :: (a -> b -> b) -> b -> Max a -> b

foldl :: (b -> a -> b) -> b -> Max a -> b

foldl' :: (b -> a -> b) -> b -> Max a -> b

foldr1 :: (a -> a -> a) -> Max a -> a

foldl1 :: (a -> a -> a) -> Max a -> a

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

Traversable Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: 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)

Applicative Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: 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

Functor Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Max a -> Max b

(<$) :: a -> Max b -> Max a

Monad Max

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Max a -> (a -> Max b) -> Max b

(>>) :: Max a -> Max b -> Max b

return :: a -> Max a

Generic1 Max

Defined in Data.Semigroup

Associated Types

type Rep1 Max :: k -> Type

Methods

from1 :: forall (a :: k). Max a -> Rep1 Max a

to1 :: forall (a :: k). Rep1 Max a -> Max a

Data a => Data (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Max a -> c (Max a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Max a)

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)

(Ord a, Bounded a) => Monoid (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: Max a

mappend :: Max a -> Max a -> Max a

mconcat :: [Max a] -> Max a

Ord a => Semigroup (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Max a -> Max a -> Max a

sconcat :: NonEmpty (Max a) -> Max a

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

Bounded a => Bounded (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: Max a

maxBound :: Max a

Enum a => Enum (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: 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]

Generic (Max a)

Defined in Data.Semigroup

Associated Types

type Rep (Max a) :: Type -> Type

Methods

from :: Max a -> Rep (Max a) x

to :: Rep (Max a) x -> Max a

Num a => Num (Max a)

Since: base-4.9.0.0

Defined 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

fromInteger :: Integer -> Max a

Read a => Read (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Max a)

readList :: ReadS [Max a]

readPrec :: ReadPrec (Max a)

readListPrec :: ReadPrec [Max a]

Show a => Show (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Max a -> ShowS

show :: Max a -> String

showList :: [Max a] -> ShowS

Eq a => Eq (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Max a -> Max a -> Bool

(/=) :: Max a -> Max a -> Bool

Ord a => Ord (Max a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: Max a -> Max a -> Ordering

(<) :: Max a -> Max a -> Bool

(<=) :: Max a -> Max a -> Bool

(>) :: Max a -> Max a -> Bool

(>=) :: Max a -> Max a -> Bool

max :: Max a -> Max a -> Max a

min :: Max a -> Max a -> Max a

type Rep1 Max

Since: base-4.9.0.0

Defined 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)

Since: base-4.9.0.0

Defined 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

Constructors

First

Fields

• getFirst :: a

Instances

MonadFix First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mfix :: (a -> First a) -> First a

Foldable First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => First m -> m

foldMap :: Monoid m => (a -> m) -> First a -> m

foldMap' :: Monoid m => (a -> m) -> First a -> m

foldr :: (a -> b -> b) -> b -> First a -> b

foldr' :: (a -> b -> b) -> b -> First a -> b

foldl :: (b -> a -> b) -> b -> First a -> b

foldl' :: (b -> a -> b) -> b -> First a -> b

foldr1 :: (a -> a -> a) -> First a -> a

foldl1 :: (a -> a -> a) -> First a -> a

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

Traversable First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: 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)

Applicative First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: 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

Functor First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> First a -> First b

(<$) :: a -> First b -> First a

Monad First

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: First a -> (a -> First b) -> First b

(>>) :: First a -> First b -> First b

return :: a -> First a

Generic1 First

Defined in Data.Semigroup

Associated Types

type Rep1 First :: k -> Type

Methods

from1 :: forall (a :: k). First a -> Rep1 First a

to1 :: forall (a :: k). Rep1 First a -> First a

Data a => Data (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> First a -> c (First a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (First a)

toConstr :: First a -> Constr

dataTypeOf :: First a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (First a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (First a))

gmapT :: (forall b. Data b => b -> b) -> First a -> First a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> First a -> r

gmapQ :: (forall d. Data d => d -> u) -> First a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> First a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> First a -> m (First a)

Semigroup (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: First a -> First a -> First a

sconcat :: NonEmpty (First a) -> First a

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

Bounded a => Bounded (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: First a

maxBound :: First a

Enum a => Enum (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: 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]

Generic (First a)

Defined in Data.Semigroup

Associated Types

type Rep (First a) :: Type -> Type

Methods

from :: First a -> Rep (First a) x

to :: Rep (First a) x -> First a

Read a => Read (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (First a)

readList :: ReadS [First a]

readPrec :: ReadPrec (First a)

readListPrec :: ReadPrec [First a]

Show a => Show (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> First a -> ShowS

show :: First a -> String

showList :: [First a] -> ShowS

Eq a => Eq (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: First a -> First a -> Bool

(/=) :: First a -> First a -> Bool

Ord a => Ord (First a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: First a -> First a -> Ordering

(<) :: First a -> First a -> Bool

(<=) :: First a -> First a -> Bool

(>) :: First a -> First a -> Bool

(>=) :: First a -> First a -> Bool

max :: First a -> First a -> First a

min :: First a -> First a -> First a

type Rep1 First

Since: base-4.9.0.0

Defined 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)

Since: base-4.9.0.0

Defined 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

Constructors

Last

Fields

• getLast :: a

Instances

MonadFix Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mfix :: (a -> Last a) -> Last a

Foldable Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Last m -> m

foldMap :: Monoid m => (a -> m) -> Last a -> m

foldMap' :: Monoid m => (a -> m) -> Last a -> m

foldr :: (a -> b -> b) -> b -> Last a -> b

foldr' :: (a -> b -> b) -> b -> Last a -> b

foldl :: (b -> a -> b) -> b -> Last a -> b

foldl' :: (b -> a -> b) -> b -> Last a -> b

foldr1 :: (a -> a -> a) -> Last a -> a

foldl1 :: (a -> a -> a) -> Last a -> a

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

Traversable Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: 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)

Applicative Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

pure :: 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

Functor Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a -> b) -> Last a -> Last b

(<$) :: a -> Last b -> Last a

Monad Last

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(>>=) :: Last a -> (a -> Last b) -> Last b

(>>) :: Last a -> Last b -> Last b

return :: a -> Last a

Generic1 Last

Defined in Data.Semigroup

Associated Types

type Rep1 Last :: k -> Type

Methods

from1 :: forall (a :: k). Last a -> Rep1 Last a

to1 :: forall (a :: k). Rep1 Last a -> Last a

Data a => Data (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Last a -> c (Last a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Last a)

toConstr :: Last a -> Constr

dataTypeOf :: Last a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Last a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Last a))

gmapT :: (forall b. Data b => b -> b) -> Last a -> Last a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Last a -> r

gmapQ :: (forall d. Data d => d -> u) -> Last a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Last a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Last a -> m (Last a)

Semigroup (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: Last a -> Last a -> Last a

sconcat :: NonEmpty (Last a) -> Last a

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

Bounded a => Bounded (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: Last a

maxBound :: Last a

Enum a => Enum (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: 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]

Generic (Last a)

Defined in Data.Semigroup

Associated Types

type Rep (Last a) :: Type -> Type

Methods

from :: Last a -> Rep (Last a) x

to :: Rep (Last a) x -> Last a

Read a => Read (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (Last a)

readList :: ReadS [Last a]

readPrec :: ReadPrec (Last a)

readListPrec :: ReadPrec [Last a]

Show a => Show (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Last a -> ShowS

show :: Last a -> String

showList :: [Last a] -> ShowS

Eq a => Eq (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Last a -> Last a -> Bool

(/=) :: Last a -> Last a -> Bool

Ord a => Ord (Last a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: Last a -> Last a -> Ordering

(<) :: Last a -> Last a -> Bool

(<=) :: Last a -> Last a -> Bool

(>) :: Last a -> Last a -> Bool

(>=) :: Last a -> Last a -> Bool

max :: Last a -> Last a -> Last a

min :: Last a -> Last a -> Last a

type Rep1 Last

Since: base-4.9.0.0

Defined 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)

Since: base-4.9.0.0

Defined 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

Provide a Semigroup for an arbitrary Monoid.

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

Constructors

WrapMonoid

Fields

• unwrapMonoid :: m

Instances

Generic1 WrappedMonoid

Defined in Data.Semigroup

Associated Types

type Rep1 WrappedMonoid :: k -> Type

Methods

from1 :: forall (a :: k). WrappedMonoid a -> Rep1 WrappedMonoid a

to1 :: forall (a :: k). Rep1 WrappedMonoid a -> WrappedMonoid a

Data m => Data (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> 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)

toConstr :: WrappedMonoid m -> Constr

dataTypeOf :: WrappedMonoid m -> DataType

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)

Monoid m => Monoid (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

mempty :: WrappedMonoid m

mappend :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

mconcat :: [WrappedMonoid m] -> WrappedMonoid m

Monoid m => Semigroup (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(<>) :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

sconcat :: NonEmpty (WrappedMonoid m) -> WrappedMonoid m

stimes :: Integral b => b -> WrappedMonoid m -> WrappedMonoid m

Bounded m => Bounded (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

minBound :: WrappedMonoid m

maxBound :: WrappedMonoid m

Enum a => Enum (WrappedMonoid a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

succ :: WrappedMonoid a -> WrappedMonoid a

pred :: WrappedMonoid a -> WrappedMonoid a

toEnum :: Int -> WrappedMonoid a

fromEnum :: WrappedMonoid a -> Int

enumFrom :: 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]

Generic (WrappedMonoid m)

Defined in Data.Semigroup

Associated Types

type Rep (WrappedMonoid m) :: Type -> Type

Methods

from :: WrappedMonoid m -> Rep (WrappedMonoid m) x

to :: Rep (WrappedMonoid m) x -> WrappedMonoid m

Read m => Read (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: Int -> ReadS (WrappedMonoid m)

readList :: ReadS [WrappedMonoid m]

readPrec :: ReadPrec (WrappedMonoid m)

readListPrec :: ReadPrec [WrappedMonoid m]

Show m => Show (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

showsPrec :: Int -> WrappedMonoid m -> ShowS

show :: WrappedMonoid m -> String

showList :: [WrappedMonoid m] -> ShowS

Eq m => Eq (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(/=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

Ord m => Ord (WrappedMonoid m)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: WrappedMonoid m -> WrappedMonoid m -> Ordering

(<) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(<=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>) :: WrappedMonoid m -> WrappedMonoid m -> Bool

(>=) :: WrappedMonoid m -> WrappedMonoid m -> Bool

max :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

min :: WrappedMonoid m -> WrappedMonoid m -> WrappedMonoid m

type Rep1 WrappedMonoid

Since: base-4.9.0.0

Defined 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)

Since: base-4.9.0.0

Defined 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

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

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

Constructors

Dual

Fields

• getDual :: a

Instances

MonadFix Dual

Since: base-4.8.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Dual a) -> Dual a

MonadZip Dual

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: 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)

Foldable Dual

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Dual m -> m

foldMap :: Monoid m => (a -> m) -> Dual a -> m

foldMap' :: Monoid m => (a -> m) -> Dual a -> m

foldr :: (a -> b -> b) -> b -> Dual a -> b

foldr' :: (a -> b -> b) -> b -> Dual a -> b

foldl :: (b -> a -> b) -> b -> Dual a -> b

foldl' :: (b -> a -> b) -> b -> Dual a -> b

foldr1 :: (a -> a -> a) -> Dual a -> a

foldl1 :: (a -> a -> a) -> Dual a -> a

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

Traversable Dual

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: 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)

Applicative Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: 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

Functor Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Dual a -> Dual b

(<$) :: a -> Dual b -> Dual a

Monad Dual

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Dual a -> (a -> Dual b) -> Dual b

(>>) :: Dual a -> Dual b -> Dual b

return :: a -> Dual a

Generic1 Dual

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Dual :: k -> Type

Methods

from1 :: forall (a :: k). Dual a -> Rep1 Dual a

to1 :: forall (a :: k). Rep1 Dual a -> Dual a

Data a => Data (Dual a)

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (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)

Monoid a => Monoid (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Dual a

mappend :: Dual a -> Dual a -> Dual a

mconcat :: [Dual a] -> Dual a

Semigroup a => Semigroup (Dual a)

Since: base-4.9.0.0

Defined 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

Bounded a => Bounded (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Dual a

maxBound :: Dual a

Generic (Dual a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Dual a) :: Type -> Type

Methods

from :: Dual a -> Rep (Dual a) x

to :: Rep (Dual a) x -> Dual a

Read a => Read (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Dual a)

readList :: ReadS [Dual a]

readPrec :: ReadPrec (Dual a)

readListPrec :: ReadPrec [Dual a]

Show a => Show (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

Eq a => Eq (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Dual a -> Dual a -> Bool

(/=) :: Dual a -> Dual a -> Bool

Ord a => Ord (Dual a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Dual a -> Dual a -> Ordering

(<) :: Dual a -> Dual a -> Bool

(<=) :: Dual a -> Dual a -> Bool

(>) :: Dual a -> Dual a -> Bool

(>=) :: Dual a -> Dual a -> Bool

max :: Dual a -> Dual a -> Dual a

min :: Dual a -> Dual a -> Dual a

type Rep1 Dual

Since: base-4.7.0.0

Defined 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)

Since: base-4.7.0.0

Defined 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

The monoid of endomorphisms under composition.

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

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Monoid (Endo a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Semigroup (Endo a)

Since: base-4.9.0.0

Defined 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

Generic (Endo a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: Type -> Type

Methods

from :: Endo a -> Rep (Endo a) x

to :: Rep (Endo a) x -> Endo a

type Rep (Endo a)

Since: base-4.7.0.0

Defined 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

Fields

• getAll :: Bool

Instances

Data All

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (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

toConstr :: All -> Constr

dataTypeOf :: All -> DataType

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

Monoid All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: All

mappend :: All -> All -> All

mconcat :: [All] -> All

Semigroup All

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: All -> All -> All

sconcat :: NonEmpty All -> All

stimes :: Integral b => b -> All -> All

Bounded All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: All

maxBound :: All

Generic All

Defined in Data.Semigroup.Internal

Associated Types

type Rep All :: Type -> Type

Methods

from :: All -> Rep All x

to :: Rep All x -> All

Read All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS All

readList :: ReadS [All]

readPrec :: ReadPrec All

readListPrec :: ReadPrec [All]

Show All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> All -> ShowS

show :: All -> String

showList :: [All] -> ShowS

Eq All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: All -> All -> Bool

(/=) :: All -> All -> Bool

Ord All

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: All -> All -> Ordering

(<) :: All -> All -> Bool

(<=) :: All -> All -> Bool

(>) :: All -> All -> Bool

(>=) :: All -> All -> Bool

max :: All -> All -> All

min :: All -> All -> All

type Rep All

Since: base-4.7.0.0

Defined 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

Fields

• getAny :: Bool

Instances

Data Any

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (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

toConstr :: Any -> Constr

dataTypeOf :: Any -> DataType

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

Monoid Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Any

mappend :: Any -> Any -> Any

mconcat :: [Any] -> Any

Semigroup Any

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Any -> Any -> Any

sconcat :: NonEmpty Any -> Any

stimes :: Integral b => b -> Any -> Any

Bounded Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Any

maxBound :: Any

Generic Any

Defined in Data.Semigroup.Internal

Associated Types

type Rep Any :: Type -> Type

Methods

from :: Any -> Rep Any x

to :: Rep Any x -> Any

Read Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS Any

readList :: ReadS [Any]

readPrec :: ReadPrec Any

readListPrec :: ReadPrec [Any]

Show Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Any -> ShowS

show :: Any -> String

showList :: [Any] -> ShowS

Eq Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Any -> Any -> Bool

(/=) :: Any -> Any -> Bool

Ord Any

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Any -> Any -> Ordering

(<) :: Any -> Any -> Bool

(<=) :: Any -> Any -> Bool

(>) :: Any -> Any -> Bool

(>=) :: Any -> Any -> Bool

max :: Any -> Any -> Any

min :: Any -> Any -> Any

type Rep Any

Since: base-4.7.0.0

Defined 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

Fields

• getSum :: a

Instances

MonadFix Sum

Since: base-4.8.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Sum a) -> Sum a

MonadZip Sum

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: 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)

Foldable Sum

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Sum m -> m

foldMap :: Monoid m => (a -> m) -> Sum a -> m

foldMap' :: Monoid m => (a -> m) -> Sum a -> m

foldr :: (a -> b -> b) -> b -> Sum a -> b

foldr' :: (a -> b -> b) -> b -> Sum a -> b

foldl :: (b -> a -> b) -> b -> Sum a -> b

foldl' :: (b -> a -> b) -> b -> Sum a -> b

foldr1 :: (a -> a -> a) -> Sum a -> a

foldl1 :: (a -> a -> a) -> Sum a -> a

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

Traversable Sum

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: 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)

Applicative Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: 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

Functor Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Sum a -> Sum b

(<$) :: a -> Sum b -> Sum a

Monad Sum

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Sum a -> (a -> Sum b) -> Sum b

(>>) :: Sum a -> Sum b -> Sum b

return :: a -> Sum a

Generic1 Sum

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Sum :: k -> Type

Methods

from1 :: forall (a :: k). Sum a -> Rep1 Sum a

to1 :: forall (a :: k). Rep1 Sum a -> Sum a

Data a => Data (Sum a)

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (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 => Monoid (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Num a => Semigroup (Sum a)

Since: base-4.9.0.0

Defined 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

Bounded a => Bounded (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Sum a

maxBound :: Sum a

Generic (Sum a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Sum a) :: Type -> Type

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Num a => Num (Sum a)

Since: base-4.7.0.0

Defined 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

fromInteger :: Integer -> Sum a

Read a => Read (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Sum a)

readList :: ReadS [Sum a]

readPrec :: ReadPrec (Sum a)

readListPrec :: ReadPrec [Sum a]

Show a => Show (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Eq a => Eq (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

Ord a => Ord (Sum a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Sum a -> Sum a -> Ordering

(<) :: Sum a -> Sum a -> Bool

(<=) :: Sum a -> Sum a -> Bool

(>) :: Sum a -> Sum a -> Bool

(>=) :: Sum a -> Sum a -> Bool

max :: Sum a -> Sum a -> Sum a

min :: Sum a -> Sum a -> Sum a

type Rep1 Sum

Since: base-4.7.0.0

Defined 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))

type Rep (Sum a)

Since: base-4.7.0.0

Defined 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)))

newtype Product a

Monoid under multiplication.

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

Constructors

Product

Fields

• getProduct :: a

Instances

MonadFix Product

Since: base-4.8.0.0

Defined in Control.Monad.Fix

Methods

mfix :: (a -> Product a) -> Product a

MonadZip Product

Since: base-4.8.0.0

Defined in Control.Monad.Zip

Methods

mzip :: 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)

Foldable Product

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Product m -> m

foldMap :: Monoid m => (a -> m) -> Product a -> m

foldMap' :: Monoid m => (a -> m) -> Product a -> m

foldr :: (a -> b -> b) -> b -> Product a -> b

foldr' :: (a -> b -> b) -> b -> Product a -> b

foldl :: (b -> a -> b) -> b -> Product a -> b

foldl' :: (b -> a -> b) -> b -> Product a -> b

foldr1 :: (a -> a -> a) -> Product a -> a

foldl1 :: (a -> a -> a) -> Product a -> a

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

Traversable Product

Since: base-4.8.0.0

Defined in Data.Traversable

Methods

traverse :: 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)

Applicative Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

pure :: 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

Functor Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

fmap :: (a -> b) -> Product a -> Product b

(<$) :: a -> Product b -> Product a

Monad Product

Since: base-4.8.0.0

Defined in Data.Semigroup.Internal

Methods

(>>=) :: Product a -> (a -> Product b) -> Product b

(>>) :: Product a -> Product b -> Product b

return :: a -> Product a

Generic1 Product

Defined in Data.Semigroup.Internal

Associated Types

type Rep1 Product :: k -> Type

Methods

from1 :: forall (a :: k). Product a -> Rep1 Product a

to1 :: forall (a :: k). Rep1 Product a -> Product a

Data a => Data (Product a)

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (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

dataTypeOf :: Product a -> DataType

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 => Monoid (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Num a => Semigroup (Product a)

Since: base-4.9.0.0

Defined 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

Bounded a => Bounded (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

minBound :: Product a

maxBound :: Product a

Generic (Product a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Product a) :: Type -> Type

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Num (Product a)

Since: base-4.7.0.0

Defined 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

fromInteger :: Integer -> Product a

Read a => Read (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

readsPrec :: Int -> ReadS (Product a)

readList :: ReadS [Product a]

readPrec :: ReadPrec (Product a)

readListPrec :: ReadPrec [Product a]

Show a => Show (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Eq a => Eq (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

(==) :: Product a -> Product a -> Bool

(/=) :: Product a -> Product a -> Bool

Ord a => Ord (Product a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

compare :: Product a -> Product a -> Ordering

(<) :: Product a -> Product a -> Bool

(<=) :: Product a -> Product a -> Bool

(>) :: Product a -> Product a -> Bool

(>=) :: Product a -> Product a -> Bool

max :: Product a -> Product a -> Product a

min :: Product a -> Product a -> Product a

type Rep1 Product

Since: base-4.7.0.0

Defined 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))

type Rep (Product a)

Since: base-4.7.0.0

Defined 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)))

Difference lists of a semigroup

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

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

Example:

>>> let hello = diff "Hello, "
>>> appEndo hello "World!"
"Hello, World!"
>>> appEndo (hello <> mempty) "World!"
"Hello, World!"
>>> appEndo (mempty <> hello) "World!"
"Hello, World!"
>>> let world = diff "World"
>>> let excl = diff "!"
>>> appEndo (hello <> (world <> excl)) mempty
"Hello, World!"
>>> appEndo ((hello <> world) <> excl) mempty
"Hello, World!"

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.

>>> minimum [ Arg (x * x) x | x <- [-10 .. 10] ]
Arg 0 0

Constructors

Arg

Fields

• a

  The argument used for comparisons in Eq and Ord.

• b

  The "value" exposed via the Functor, Foldable etc. instances.

Instances

Bifoldable Arg

Since: base-4.10.0.0

Defined in Data.Semigroup

Methods

bifold :: 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

Bifunctor Arg

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

bimap :: (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

Bitraversable Arg

Since: base-4.10.0.0

Defined in Data.Semigroup

Methods

bitraverse :: Applicative f => (a -> f c) -> (b -> f d) -> Arg a b -> f (Arg c d)

Generic1 (Arg a :: Type -> Type)

Defined in Data.Semigroup

Associated Types

type Rep1 (Arg a) :: k -> Type

Methods

from1 :: forall (a0 :: k). Arg a a0 -> Rep1 (Arg a) a0

to1 :: forall (a0 :: k). Rep1 (Arg a) a0 -> Arg a a0

Foldable (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fold :: Monoid m => Arg a m -> m

foldMap :: Monoid m => (a0 -> m) -> Arg a a0 -> m

foldMap' :: Monoid m => (a0 -> m) -> Arg a a0 -> m

foldr :: (a0 -> b -> b) -> b -> Arg a a0 -> b

foldr' :: (a0 -> b -> b) -> b -> Arg a a0 -> b

foldl :: (b -> a0 -> b) -> b -> Arg a a0 -> b

foldl' :: (b -> a0 -> b) -> b -> Arg a a0 -> b

foldr1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0

foldl1 :: (a0 -> a0 -> a0) -> Arg a a0 -> a0

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

Traversable (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

traverse :: 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)

Functor (Arg a)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

fmap :: (a0 -> b) -> Arg a a0 -> Arg a b

(<$) :: a0 -> Arg a b -> Arg a a0

(Data a, Data b) => Data (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Arg a b -> c (Arg a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Arg a b)

toConstr :: Arg a b -> Constr

dataTypeOf :: Arg a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Arg a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Arg a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Arg a b -> Arg a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Arg a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Arg a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Arg a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Arg a b -> m (Arg a b)

Generic (Arg a b)

Defined in Data.Semigroup

Associated Types

type Rep (Arg a b) :: Type -> Type

Methods

from :: Arg a b -> Rep (Arg a b) x

to :: Rep (Arg a b) x -> Arg a b

(Read a, Read b) => Read (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

readsPrec :: 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

Defined in Data.Semigroup

Methods

showsPrec :: Int -> Arg a b -> ShowS

show :: Arg a b -> String

showList :: [Arg a b] -> ShowS

Eq a => Eq (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

(==) :: Arg a b -> Arg a b -> Bool

(/=) :: Arg a b -> Arg a b -> Bool

Ord a => Ord (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

Methods

compare :: Arg a b -> Arg a b -> Ordering

(<) :: Arg a b -> Arg a b -> Bool

(<=) :: Arg a b -> Arg a b -> Bool

(>) :: Arg a b -> Arg a b -> Bool

(>=) :: Arg a b -> Arg a b -> Bool

max :: Arg a b -> Arg a b -> Arg a b

min :: Arg a b -> Arg a b -> Arg a b

type Rep1 (Arg a :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep1 (Arg a :: Type -> Type) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) Par1))

type Rep (Arg a b)

Since: base-4.9.0.0

Defined in Data.Semigroup

type Rep (Arg a b) = D1 ('MetaData "Arg" "Data.Semigroup" "base" 'False) (C1 ('MetaCons "Arg" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 b)))

type ArgMin a b = Min (Arg a b)

>>> Min (Arg 0 ()) <> Min (Arg 1 ())
Min {getMin = Arg 0 ()}

type ArgMax a b = Max (Arg a b)

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